id	sid	tid	token	lemma	pos
ap-7652	1	1	acta	acta	PROPN
ap-7652	1	2	polytechnica	polytechnica	PROPN
ap-7652	1	3	https://doi.org/10.14311/ap.2022.62.0100	https://doi.org/10.14311/ap.2022.62.0100	PROPN
ap-7652	1	4	acta	acta	PROPN
ap-7652	1	5	polytechnica	polytechnica	PROPN
ap-7652	1	6	62(1):100–117	62(1):100–117	PROPN
ap-7652	1	7	,	,	PUNCT
ap-7652	1	8	2022	2022	NUM
ap-7652	1	9	©	©	ADP
ap-7652	1	10	2022	2022	NUM
ap-7652	1	11	the	the	DET
ap-7652	1	12	author(s	author(s	NOUN
ap-7652	1	13	)	)	PUNCT
ap-7652	1	14	.	.	PUNCT
ap-7652	2	1	licensed	license	VERB
ap-7652	2	2	under	under	ADP
ap-7652	2	3	a	a	DET
ap-7652	2	4	cc	cc	NOUN
ap-7652	2	5	-	-	PUNCT
ap-7652	2	6	by	by	ADP
ap-7652	2	7	4.0	4.0	NUM
ap-7652	2	8	licence	licence	NOUN
ap-7652	2	9	published	publish	VERB
ap-7652	2	10	by	by	ADP
ap-7652	2	11	the	the	DET
ap-7652	2	12	czech	czech	PROPN
ap-7652	2	13	technical	technical	PROPN
ap-7652	2	14	university	university	PROPN
ap-7652	2	15	in	in	ADP
ap-7652	2	16	prague	prague	NOUN
ap-7652	2	17	quantization	quantization	NOUN
ap-7652	2	18	of	of	ADP
ap-7652	2	19	rationally	rationally	ADV
ap-7652	2	20	deformed	deform	VERB
ap-7652	2	21	morse	morse	ADJ
ap-7652	2	22	potentials	potential	NOUN
ap-7652	2	23	by	by	ADP
ap-7652	2	24	wronskian	wronskian	ADJ
ap-7652	2	25	transforms	transform	NOUN
ap-7652	2	26	of	of	ADP
ap-7652	2	27	romanovski	romanovski	NOUN
ap-7652	2	28	-	-	PUNCT
ap-7652	2	29	bessel	bessel	NOUN
ap-7652	2	30	polynomials	polynomial	NOUN
ap-7652	2	31	gregory	gregory	PROPN
ap-7652	2	32	natanson	natanson	PROPN
ap-7652	2	33	ai	ai	PROPN
ap-7652	2	34	-	-	PUNCT
ap-7652	2	35	solutions	solution	NOUN
ap-7652	2	36	silver	silver	NOUN
ap-7652	2	37	spring	spring	NOUN
ap-7652	2	38	md	md	PROPN
ap-7652	2	39	20904	20904	NUM
ap-7652	2	40	,	,	PUNCT
ap-7652	2	41	u.s.a	u.s.a	PROPN
ap-7652	2	42	.	.	PROPN
ap-7652	2	43	correspondence	correspondence	NOUN
ap-7652	2	44	:	:	PUNCT
ap-7652	3	1	gregorynatanson@gmail.com	gregorynatanson@gmail.com	X
ap-7652	3	2	abstract	abstract	ADJ
ap-7652	3	3	.	.	PUNCT
ap-7652	4	1	the	the	DET
ap-7652	4	2	paper	paper	NOUN
ap-7652	4	3	advances	advance	NOUN
ap-7652	4	4	odake	odake	NOUN
ap-7652	4	5	and	and	CCONJ
ap-7652	4	6	sasaki	sasaki	PROPN
ap-7652	4	7	’s	’s	PART
ap-7652	4	8	idea	idea	NOUN
ap-7652	4	9	to	to	PART
ap-7652	4	10	re	re	VERB
ap-7652	4	11	-	-	VERB
ap-7652	4	12	write	write	VERB
ap-7652	4	13	eigenfunctions	eigenfunction	NOUN
ap-7652	4	14	of	of	ADP
ap-7652	4	15	rationally	rationally	ADV
ap-7652	4	16	deformed	deform	VERB
ap-7652	4	17	morse	morse	ADJ
ap-7652	4	18	potentials	potential	NOUN
ap-7652	4	19	in	in	ADP
ap-7652	4	20	terms	term	NOUN
ap-7652	4	21	of	of	ADP
ap-7652	4	22	wronskians	wronskian	NOUN
ap-7652	4	23	of	of	ADP
ap-7652	4	24	laguerre	laguerre	NOUN
ap-7652	4	25	polynomials	polynomial	NOUN
ap-7652	4	26	in	in	ADP
ap-7652	4	27	the	the	DET
ap-7652	4	28	reciprocal	reciprocal	ADJ
ap-7652	4	29	argument	argument	NOUN
ap-7652	4	30	.	.	PUNCT
ap-7652	5	1	it	it	PRON
ap-7652	5	2	is	be	AUX
ap-7652	5	3	shown	show	VERB
ap-7652	5	4	that	that	SCONJ
ap-7652	5	5	the	the	DET
ap-7652	5	6	constructed	construct	VERB
ap-7652	5	7	quasi	quasi	ADJ
ap-7652	5	8	-	-	ADJ
ap-7652	5	9	rational	rational	ADJ
ap-7652	5	10	seed	seed	NOUN
ap-7652	5	11	solutions	solution	NOUN
ap-7652	5	12	of	of	ADP
ap-7652	5	13	the	the	DET
ap-7652	5	14	schrödinger	schrödinger	ADJ
ap-7652	5	15	equation	equation	NOUN
ap-7652	5	16	with	with	ADP
ap-7652	5	17	the	the	DET
ap-7652	5	18	morse	morse	ADJ
ap-7652	5	19	potential	potential	NOUN
ap-7652	5	20	are	be	AUX
ap-7652	5	21	formed	form	VERB
ap-7652	5	22	by	by	ADP
ap-7652	5	23	generalized	generalized	ADJ
ap-7652	5	24	bessel	bessel	ADJ
ap-7652	5	25	polynomials	polynomial	NOUN
ap-7652	5	26	with	with	ADP
ap-7652	5	27	degree	degree	NOUN
ap-7652	5	28	-	-	PUNCT
ap-7652	5	29	independent	independent	ADJ
ap-7652	5	30	indexes	index	NOUN
ap-7652	5	31	.	.	PUNCT
ap-7652	6	1	as	as	ADP
ap-7652	6	2	a	a	DET
ap-7652	6	3	new	new	ADJ
ap-7652	6	4	achievement	achievement	NOUN
ap-7652	6	5	we	we	PRON
ap-7652	6	6	can	can	AUX
ap-7652	6	7	point	point	VERB
ap-7652	6	8	to	to	ADP
ap-7652	6	9	the	the	DET
ap-7652	6	10	construction	construction	NOUN
ap-7652	6	11	of	of	ADP
ap-7652	6	12	the	the	DET
ap-7652	6	13	darboux	darboux	ADJ
ap-7652	6	14	-	-	PUNCT
ap-7652	6	15	crum	crum	NOUN
ap-7652	6	16	net	net	NOUN
ap-7652	6	17	of	of	ADP
ap-7652	6	18	isospectral	isospectral	ADJ
ap-7652	6	19	rational	rational	ADJ
ap-7652	6	20	potentials	potential	NOUN
ap-7652	6	21	using	use	VERB
ap-7652	6	22	wronskians	wronskian	NOUN
ap-7652	6	23	of	of	ADP
ap-7652	6	24	generalized	generalized	ADJ
ap-7652	6	25	bessel	bessel	ADJ
ap-7652	6	26	polynomials	polynomial	NOUN
ap-7652	6	27	with	with	ADP
ap-7652	6	28	no	no	DET
ap-7652	6	29	positive	positive	ADJ
ap-7652	6	30	zeros	zero	NOUN
ap-7652	6	31	.	.	PUNCT
ap-7652	7	1	one	one	PRON
ap-7652	7	2	can	can	AUX
ap-7652	7	3	extend	extend	VERB
ap-7652	7	4	this	this	DET
ap-7652	7	5	isospectral	isospectral	ADJ
ap-7652	7	6	family	family	NOUN
ap-7652	7	7	of	of	ADP
ap-7652	7	8	solvable	solvable	ADJ
ap-7652	7	9	rational	rational	ADJ
ap-7652	7	10	potentials	potential	NOUN
ap-7652	7	11	by	by	ADP
ap-7652	7	12	including	include	VERB
ap-7652	7	13	‘	'	PUNCT
ap-7652	7	14	juxtaposed	juxtapose	VERB
ap-7652	7	15	’	'	PUNCT
ap-7652	7	16	pairs	pair	NOUN
ap-7652	7	17	of	of	ADP
ap-7652	7	18	romanovski	romanovski	NOUN
ap-7652	7	19	-	-	PUNCT
ap-7652	7	20	bessel	bessel	NOUN
ap-7652	7	21	polynomials	polynomial	NOUN
ap-7652	7	22	into	into	ADP
ap-7652	7	23	the	the	DET
ap-7652	7	24	aforementioned	aforementioned	ADJ
ap-7652	7	25	polynomial	polynomial	ADJ
ap-7652	7	26	wronskians	wronskian	NOUN
ap-7652	7	27	which	which	PRON
ap-7652	7	28	results	result	VERB
ap-7652	7	29	in	in	ADP
ap-7652	7	30	deleting	delete	VERB
ap-7652	7	31	the	the	DET
ap-7652	7	32	corresponding	correspond	VERB
ap-7652	7	33	pairs	pair	NOUN
ap-7652	7	34	of	of	ADP
ap-7652	7	35	bound	bind	VERB
ap-7652	7	36	energy	energy	NOUN
ap-7652	7	37	states	state	NOUN
ap-7652	7	38	.	.	PUNCT
ap-7652	8	1	keywords	keyword	NOUN
ap-7652	8	2	:	:	PUNCT
ap-7652	8	3	translationally	translationally	ADV
ap-7652	8	4	form	form	NOUN
ap-7652	8	5	-	-	PUNCT
ap-7652	8	6	invariant	invariant	ADJ
ap-7652	8	7	sturm	sturm	NOUN
ap-7652	8	8	-	-	PUNCT
ap-7652	8	9	liouville	liouville	NOUN
ap-7652	8	10	equation	equation	NOUN
ap-7652	8	11	,	,	PUNCT
ap-7652	8	12	generalized	generalized	ADJ
ap-7652	8	13	bessel	bessel	NOUN
ap-7652	8	14	polynomials	polynomial	NOUN
ap-7652	8	15	,	,	PUNCT
ap-7652	8	16	romanovski	romanovski	NOUN
ap-7652	8	17	-	-	PUNCT
ap-7652	8	18	bessel	bessel	NOUN
ap-7652	8	19	polynomials	polynomial	NOUN
ap-7652	8	20	,	,	PUNCT
ap-7652	8	21	rational	rational	ADJ
ap-7652	8	22	darboux	darboux	ADJ
ap-7652	8	23	-	-	PUNCT
ap-7652	8	24	crum	crum	NOUN
ap-7652	8	25	transformations	transformation	NOUN
ap-7652	8	26	,	,	PUNCT
ap-7652	8	27	polynomial	polynomial	ADJ
ap-7652	8	28	wronskians	wronskian	NOUN
ap-7652	8	29	.	.	PUNCT
ap-7652	9	1	1	1	X
ap-7652	9	2	.	.	X
ap-7652	9	3	introduction	introduction	NOUN
ap-7652	9	4	in	in	ADP
ap-7652	9	5	recent	recent	ADJ
ap-7652	9	6	publication	publication	NOUN
ap-7652	9	7	[	[	X
ap-7652	9	8	1	1	X
ap-7652	9	9	]	]	PUNCT
ap-7652	9	10	alhaidari	alhaidari	PROPN
ap-7652	9	11	pointed	point	VERB
ap-7652	9	12	to	to	ADP
ap-7652	9	13	a	a	DET
ap-7652	9	14	new	new	ADJ
ap-7652	9	15	form	form	NOUN
ap-7652	9	16	of	of	ADP
ap-7652	9	17	‘	'	PUNCT
ap-7652	9	18	quasi	quasi	ADJ
ap-7652	9	19	-	-	ADJ
ap-7652	9	20	rational	rational	ADJ
ap-7652	9	21	’	'	PUNCT
ap-7652	9	22	[	[	X
ap-7652	9	23	2	2	NUM
ap-7652	9	24	]	]	X
ap-7652	9	25	solutions	solution	NOUN
ap-7652	9	26	(	(	PUNCT
ap-7652	9	27	q	q	NOUN
ap-7652	9	28	-	-	NOUN
ap-7652	9	29	rss	rss	NOUN
ap-7652	9	30	)	)	PUNCT
ap-7652	9	31	of	of	ADP
ap-7652	9	32	the	the	DET
ap-7652	9	33	schrödinger	schrödinger	ADJ
ap-7652	9	34	equation	equation	NOUN
ap-7652	9	35	with	with	ADP
ap-7652	9	36	the	the	DET
ap-7652	9	37	morse	morse	ADJ
ap-7652	9	38	potential	potential	NOUN
ap-7652	9	39	in	in	ADP
ap-7652	9	40	terms	term	NOUN
ap-7652	9	41	of	of	ADP
ap-7652	9	42	generalized	generalized	ADJ
ap-7652	9	43	bessel	bessel	ADJ
ap-7652	9	44	polynomials	polynomial	NOUN
ap-7652	9	45	[	[	X
ap-7652	9	46	3–6	3–6	NUM
ap-7652	9	47	]	]	X
ap-7652	9	48	,	,	PUNCT
ap-7652	9	49	instead	instead	ADV
ap-7652	9	50	of	of	ADP
ap-7652	9	51	using	use	VERB
ap-7652	9	52	the	the	DET
ap-7652	9	53	conventional	conventional	ADJ
ap-7652	9	54	q	q	ADJ
ap-7652	9	55	-	-	PUNCT
ap-7652	9	56	rss	rss	NOUN
ap-7652	9	57	composed	compose	VERB
ap-7652	9	58	of	of	ADP
ap-7652	9	59	weighted	weight	VERB
ap-7652	9	60	laguerre	laguerre	NOUN
ap-7652	9	61	polynomials	polynomial	NOUN
ap-7652	10	1	[	[	X
ap-7652	10	2	7–11	7–11	NOUN
ap-7652	10	3	]	]	X
ap-7652	10	4	;	;	PUNCT
ap-7652	10	5	though	though	ADV
ap-7652	10	6	,	,	PUNCT
ap-7652	10	7	to	to	PART
ap-7652	10	8	be	be	AUX
ap-7652	10	9	more	more	ADV
ap-7652	10	10	accurate	accurate	ADJ
ap-7652	10	11	,	,	PUNCT
ap-7652	10	12	the	the	DET
ap-7652	10	13	possibility	possibility	NOUN
ap-7652	10	14	to	to	PART
ap-7652	10	15	quantize	quantize	VERB
ap-7652	10	16	the	the	DET
ap-7652	10	17	morse	morse	ADJ
ap-7652	10	18	potential	potential	NOUN
ap-7652	10	19	by	by	ADP
ap-7652	10	20	romanovski	romanovski	NOUN
ap-7652	10	21	-	-	PUNCT
ap-7652	10	22	bessel	bessel	NOUN
ap-7652	10	23	(	(	PUNCT
ap-7652	10	24	r	r	NOUN
ap-7652	10	25	-	-	PUNCT
ap-7652	10	26	bessel	bessel	ADJ
ap-7652	10	27	)	)	PUNCT
ap-7652	10	28	polynomials	polynomial	NOUN
ap-7652	10	29	[	[	X
ap-7652	10	30	12	12	NUM
ap-7652	10	31	,	,	PUNCT
ap-7652	10	32	13	13	NUM
ap-7652	10	33	]	]	PUNCT
ap-7652	10	34	has	have	AUX
ap-7652	10	35	been	be	AUX
ap-7652	10	36	already	already	ADV
ap-7652	10	37	recognized	recognize	VERB
ap-7652	10	38	by	by	ADP
ap-7652	10	39	quesne	quesne	NOUN
ap-7652	10	40	[	[	X
ap-7652	10	41	14	14	NUM
ap-7652	10	42	]	]	PUNCT
ap-7652	10	43	,	,	PUNCT
ap-7652	10	44	with	with	ADP
ap-7652	10	45	reference	reference	NOUN
ap-7652	10	46	to	to	ADP
ap-7652	10	47	cotfas	cotfas	NOUN
ap-7652	10	48	’	'	PUNCT
ap-7652	10	49	papers	paper	NOUN
ap-7652	10	50	[	[	X
ap-7652	10	51	15	15	NUM
ap-7652	10	52	,	,	PUNCT
ap-7652	10	53	16	16	NUM
ap-7652	10	54	]	]	PUNCT
ap-7652	10	55	(	(	PUNCT
ap-7652	10	56	see	see	VERB
ap-7652	10	57	also	also	ADV
ap-7652	10	58	[	[	X
ap-7652	10	59	17	17	NUM
ap-7652	10	60	]	]	NUM
ap-7652	10	61	)	)	PUNCT
ap-7652	10	62	.	.	PUNCT
ap-7652	11	1	it	it	PRON
ap-7652	11	2	should	should	AUX
ap-7652	11	3	be	be	AUX
ap-7652	11	4	also	also	ADV
ap-7652	11	5	emphasized	emphasize	VERB
ap-7652	11	6	that	that	SCONJ
ap-7652	11	7	odake	odake	NOUN
ap-7652	11	8	and	and	CCONJ
ap-7652	11	9	sasaki	sasaki	PROPN
ap-7652	11	10	in	in	ADP
ap-7652	11	11	their	their	PRON
ap-7652	11	12	in	in	ADP
ap-7652	11	13	-	-	PUNCT
ap-7652	11	14	depth	depth	NOUN
ap-7652	11	15	study	study	NOUN
ap-7652	11	16	[	[	X
ap-7652	11	17	18	18	NUM
ap-7652	11	18	,	,	PUNCT
ap-7652	11	19	19	19	NUM
ap-7652	11	20	]	]	PUNCT
ap-7652	11	21	on	on	ADP
ap-7652	11	22	rational	rational	ADJ
ap-7652	11	23	darboux	darboux	NOUN
ap-7652	11	24	-	-	PUNCT
ap-7652	11	25	crum	crum	NOUN
ap-7652	11	26	[	[	X
ap-7652	11	27	20	20	NUM
ap-7652	11	28	,	,	PUNCT
ap-7652	11	29	21	21	NUM
ap-7652	11	30	]	]	PUNCT
ap-7652	11	31	transforms	transform	VERB
ap-7652	11	32	(	(	PUNCT
ap-7652	11	33	rdct	rdct	PROPN
ap-7652	11	34	s	s	X
ap-7652	11	35	)	)	PUNCT
ap-7652	11	36	of	of	ADP
ap-7652	11	37	translationally	translationally	ADJ
ap-7652	11	38	shape	shape	NOUN
ap-7652	11	39	-	-	PUNCT
ap-7652	11	40	invariant	invariant	ADJ
ap-7652	11	41	(	(	PUNCT
ap-7652	11	42	tsi	tsi	PROPN
ap-7652	11	43	)	)	PUNCT
ap-7652	11	44	potentials	potential	NOUN
ap-7652	11	45	did	do	AUX
ap-7652	11	46	implicitly	implicitly	ADV
ap-7652	11	47	express	express	VERB
ap-7652	11	48	eigenfunctions	eigenfunction	NOUN
ap-7652	11	49	of	of	ADP
ap-7652	11	50	the	the	DET
ap-7652	11	51	morse	morse	ADJ
ap-7652	11	52	potential	potential	NOUN
ap-7652	11	53	in	in	ADP
ap-7652	11	54	terms	term	NOUN
ap-7652	11	55	of	of	ADP
ap-7652	11	56	r	r	NOUN
ap-7652	11	57	-	-	PUNCT
ap-7652	11	58	bessel	bessel	ADJ
ap-7652	11	59	polynomials	polynomial	NOUN
ap-7652	11	60	with	with	ADP
ap-7652	11	61	degree	degree	NOUN
ap-7652	11	62	-	-	PUNCT
ap-7652	11	63	independent	independent	ADJ
ap-7652	11	64	indexes	index	NOUN
ap-7652	11	65	as	as	ADP
ap-7652	11	66	a	a	DET
ap-7652	11	67	substitute	substitute	NOUN
ap-7652	11	68	for	for	ADP
ap-7652	11	69	commonly	commonly	ADV
ap-7652	11	70	used	use	VERB
ap-7652	11	71	classical	classical	ADJ
ap-7652	11	72	laguerre	laguerre	NOUN
ap-7652	11	73	polynomials	polynomial	NOUN
ap-7652	11	74	[	[	X
ap-7652	11	75	22	22	NUM
ap-7652	11	76	]	]	PUNCT
ap-7652	11	77	.	.	PUNCT
ap-7652	12	1	(	(	PUNCT
ap-7652	12	2	though	though	SCONJ
ap-7652	12	3	the	the	DET
ap-7652	12	4	bochner	bochner	NOUN
ap-7652	12	5	-	-	PUNCT
ap-7652	12	6	type	type	NOUN
ap-7652	12	7	differential	differential	ADJ
ap-7652	12	8	equation	equation	NOUN
ap-7652	12	9	for	for	ADP
ap-7652	12	10	generalized	generalized	ADJ
ap-7652	12	11	bessel	bessel	ADJ
ap-7652	12	12	polynomials	polynomial	NOUN
ap-7652	12	13	was	be	AUX
ap-7652	12	14	also	also	ADV
ap-7652	12	15	listed	list	VERB
ap-7652	12	16	in	in	ADP
ap-7652	12	17	table	table	NOUN
ap-7652	12	18	1	1	NUM
ap-7652	12	19	in	in	ADP
ap-7652	12	20	[	[	X
ap-7652	12	21	7	7	X
ap-7652	12	22	]	]	PUNCT
ap-7652	12	23	on	on	ADP
ap-7652	12	24	the	the	DET
ap-7652	12	25	line	line	NOUN
ap-7652	12	26	linked	link	VERB
ap-7652	12	27	to	to	ADP
ap-7652	12	28	the	the	DET
ap-7652	12	29	morse	morse	ADJ
ap-7652	12	30	potential	potential	NOUN
ap-7652	12	31	the	the	DET
ap-7652	12	32	authors	author	NOUN
ap-7652	12	33	used	use	VERB
ap-7652	12	34	the	the	DET
ap-7652	12	35	conventional	conventional	ADJ
ap-7652	12	36	representation	representation	NOUN
ap-7652	12	37	for	for	ADP
ap-7652	12	38	eigenfunctions	eigenfunction	NOUN
ap-7652	12	39	[	[	X
ap-7652	12	40	22	22	NUM
ap-7652	12	41	]	]	PUNCT
ap-7652	12	42	to	to	PART
ap-7652	12	43	construct	construct	VERB
ap-7652	12	44	rationally	rationally	ADV
ap-7652	12	45	deformed	deform	VERB
ap-7652	12	46	morse	morse	ADJ
ap-7652	12	47	potentials	potential	NOUN
ap-7652	12	48	.	.	PUNCT
ap-7652	12	49	)	)	PUNCT
ap-7652	13	1	the	the	DET
ap-7652	13	2	remarkable	remarkable	ADJ
ap-7652	13	3	feature	feature	NOUN
ap-7652	13	4	of	of	ADP
ap-7652	13	5	the	the	DET
ap-7652	13	6	new	new	ADJ
ap-7652	13	7	rational	rational	ADJ
ap-7652	13	8	realization	realization	NOUN
ap-7652	13	9	for	for	ADP
ap-7652	13	10	the	the	DET
ap-7652	13	11	morse	morse	ADJ
ap-7652	13	12	oscillator	oscillator	NOUN
ap-7652	13	13	is	be	AUX
ap-7652	13	14	that	that	SCONJ
ap-7652	13	15	the	the	DET
ap-7652	13	16	resultant	resultant	NOUN
ap-7652	13	17	rational	rational	ADJ
ap-7652	13	18	canonical	canonical	ADJ
ap-7652	13	19	sturm	sturm	NOUN
ap-7652	13	20	-	-	PUNCT
ap-7652	13	21	liouville	liouville	NOUN
ap-7652	13	22	equation	equation	NOUN
ap-7652	13	23	(	(	PUNCT
ap-7652	13	24	rcsle	rcsle	PROPN
ap-7652	13	25	)	)	PUNCT
ap-7652	13	26	can	can	AUX
ap-7652	13	27	be	be	AUX
ap-7652	13	28	converted	convert	VERB
ap-7652	13	29	by	by	ADP
ap-7652	13	30	an	an	DET
ap-7652	13	31	energy	energy	NOUN
ap-7652	13	32	-	-	PUNCT
ap-7652	13	33	independent	independent	ADJ
ap-7652	13	34	gauge	gauge	NOUN
ap-7652	13	35	transformation	transformation	NOUN
ap-7652	13	36	to	to	ADP
ap-7652	13	37	the	the	DET
ap-7652	13	38	bochner	bochner	NOUN
ap-7652	13	39	-	-	PUNCT
ap-7652	13	40	type	type	NOUN
ap-7652	13	41	eigenequation	eigenequation	NOUN
ap-7652	13	42	with	with	ADP
ap-7652	13	43	a	a	DET
ap-7652	13	44	linear	linear	ADJ
ap-7652	13	45	coefficient	coefficient	NOUN
ap-7652	13	46	function	function	NOUN
ap-7652	13	47	of	of	ADP
ap-7652	13	48	the	the	DET
ap-7652	13	49	first	first	ADJ
ap-7652	13	50	derivative	derivative	ADJ
ap-7652	13	51	independent	independent	NOUN
ap-7652	13	52	of	of	ADP
ap-7652	13	53	degrees	degree	NOUN
ap-7652	13	54	of	of	ADP
ap-7652	13	55	sought	seek	VERB
ap-7652	13	56	-	-	PUNCT
ap-7652	13	57	for	for	ADP
ap-7652	13	58	polynomial	polynomial	ADJ
ap-7652	13	59	solutions	solution	NOUN
ap-7652	13	60	.	.	PUNCT
ap-7652	14	1	using	use	VERB
ap-7652	14	2	terminology	terminology	NOUN
ap-7652	14	3	of	of	ADP
ap-7652	14	4	our	our	PRON
ap-7652	14	5	recent	recent	ADJ
ap-7652	14	6	study	study	NOUN
ap-7652	14	7	[	[	X
ap-7652	14	8	23	23	NUM
ap-7652	14	9	]	]	PUNCT
ap-7652	14	10	on	on	ADP
ap-7652	14	11	translationally	translationally	ADJ
ap-7652	14	12	form	form	NOUN
ap-7652	14	13	-	-	PUNCT
ap-7652	14	14	invariant	invariant	ADJ
ap-7652	14	15	(	(	PUNCT
ap-7652	14	16	tfi	tfi	NOUN
ap-7652	14	17	)	)	PUNCT
ap-7652	14	18	csles	csle	NOUN
ap-7652	14	19	this	this	PRON
ap-7652	14	20	implies	imply	VERB
ap-7652	14	21	that	that	SCONJ
ap-7652	14	22	the	the	DET
ap-7652	14	23	given	give	VERB
ap-7652	14	24	rcsle	rcsle	PROPN
ap-7652	14	25	belongs	belong	VERB
ap-7652	14	26	to	to	ADP
ap-7652	14	27	tfi	tfi	PROPN
ap-7652	14	28	group	group	NOUN
ap-7652	14	29	a	a	NOUN
ap-7652	15	1	and	and	CCONJ
ap-7652	15	2	we	we	PRON
ap-7652	15	3	should	should	AUX
ap-7652	15	4	give	give	VERB
ap-7652	15	5	full	full	ADJ
ap-7652	15	6	credit	credit	NOUN
ap-7652	15	7	to	to	PART
ap-7652	15	8	odake	odake	VERB
ap-7652	15	9	and	and	CCONJ
ap-7652	15	10	sasaki[18	sasaki[18	PROPN
ap-7652	15	11	,	,	PUNCT
ap-7652	15	12	19	19	NUM
ap-7652	15	13	]	]	PUNCT
ap-7652	15	14	who	who	PRON
ap-7652	15	15	initially	initially	ADV
ap-7652	15	16	came	come	VERB
ap-7652	15	17	up	up	ADP
ap-7652	15	18	with	with	ADP
ap-7652	15	19	this	this	DET
ap-7652	15	20	breakthrough	breakthrough	ADJ
ap-7652	15	21	idea	idea	NOUN
ap-7652	15	22	to	to	PART
ap-7652	15	23	treat	treat	VERB
ap-7652	15	24	the	the	DET
ap-7652	15	25	morse	morse	ADJ
ap-7652	15	26	oscillator	oscillator	NOUN
ap-7652	15	27	as	as	ADP
ap-7652	15	28	a	a	DET
ap-7652	15	29	rational	rational	ADJ
ap-7652	15	30	tsi	tsi	NOUN
ap-7652	15	31	potential	potential	NOUN
ap-7652	15	32	of	of	ADP
ap-7652	15	33	group	group	NOUN
ap-7652	15	34	a.	a.	NOUN
ap-7652	15	35	keeping	keeping	NOUN
ap-7652	15	36	in	in	ADP
ap-7652	15	37	mind	mind	NOUN
ap-7652	15	38	that	that	SCONJ
ap-7652	15	39	the	the	DET
ap-7652	15	40	tfi	tfi	NOUN
ap-7652	15	41	equation	equation	NOUN
ap-7652	15	42	under	under	ADP
ap-7652	15	43	consideration	consideration	NOUN
ap-7652	15	44	has	have	VERB
ap-7652	15	45	only	only	ADV
ap-7652	15	46	two	two	NUM
ap-7652	15	47	basic	basic	ADJ
ap-7652	15	48	solutions	solution	NOUN
ap-7652	15	49	the	the	DET
ap-7652	15	50	net	net	NOUN
ap-7652	15	51	of	of	ADP
ap-7652	15	52	its	its	PRON
ap-7652	15	53	rdct	rdct	ADJ
ap-7652	15	54	s	s	NOUN
ap-7652	15	55	is	be	AUX
ap-7652	15	56	uniquely	uniquely	ADV
ap-7652	15	57	specified	specify	VERB
ap-7652	15	58	by	by	ADP
ap-7652	15	59	a	a	DET
ap-7652	15	60	single	single	ADJ
ap-7652	15	61	series	series	NOUN
ap-7652	15	62	of	of	ADP
ap-7652	15	63	maya	maya	PROPN
ap-7652	15	64	diagrams	diagram	NOUN
ap-7652	15	65	[	[	X
ap-7652	15	66	24	24	NUM
ap-7652	15	67	]	]	PUNCT
ap-7652	15	68	and	and	CCONJ
ap-7652	15	69	therefore	therefore	ADV
ap-7652	15	70	any	any	DET
ap-7652	15	71	rationally	rationally	ADV
ap-7652	15	72	deformed	deform	VERB
ap-7652	15	73	morse	morse	ADJ
ap-7652	15	74	potential	potential	NOUN
ap-7652	15	75	can	can	AUX
ap-7652	15	76	be	be	AUX
ap-7652	15	77	re	re	VERB
ap-7652	15	78	-	-	VERB
ap-7652	15	79	expressed	express	VERB
ap-7652	15	80	in	in	ADP
ap-7652	15	81	terms	term	NOUN
ap-7652	15	82	the	the	DET
ap-7652	15	83	wronskian	wronskian	NOUN
ap-7652	15	84	of	of	ADP
ap-7652	15	85	generalized	generalized	ADJ
ap-7652	15	86	bessel	bessel	NOUN
ap-7652	15	87	polynomials	polynomial	NOUN
ap-7652	15	88	with	with	ADP
ap-7652	15	89	a	a	DET
ap-7652	15	90	common	common	ADJ
ap-7652	15	91	degree	degree	NOUN
ap-7652	15	92	-	-	PUNCT
ap-7652	15	93	independent	independent	ADJ
ap-7652	15	94	index	index	NOUN
ap-7652	15	95	,	,	PUNCT
ap-7652	15	96	as	as	SCONJ
ap-7652	15	97	it	it	PRON
ap-7652	15	98	has	have	AUX
ap-7652	15	99	been	be	AUX
ap-7652	15	100	done	do	VERB
ap-7652	15	101	in	in	ADP
ap-7652	15	102	[	[	X
ap-7652	15	103	19	19	NUM
ap-7652	15	104	]	]	PUNCT
ap-7652	15	105	though	though	SCONJ
ap-7652	15	106	in	in	ADP
ap-7652	15	107	slightly	slightly	ADV
ap-7652	15	108	different	different	ADJ
ap-7652	15	109	terms	term	NOUN
ap-7652	15	110	.	.	PUNCT
ap-7652	16	1	the	the	DET
ap-7652	16	2	novel	novel	ADJ
ap-7652	16	3	representation	representation	NOUN
ap-7652	16	4	of	of	ADP
ap-7652	16	5	seed	seed	NOUN
ap-7652	16	6	eigenfunctions	eigenfunction	NOUN
ap-7652	16	7	[	[	X
ap-7652	16	8	19	19	NUM
ap-7652	16	9	]	]	PUNCT
ap-7652	16	10	is	be	AUX
ap-7652	16	11	in	in	ADP
ap-7652	16	12	a	a	DET
ap-7652	16	13	sharp	sharp	ADJ
ap-7652	16	14	contrast	contrast	NOUN
ap-7652	16	15	with	with	ADP
ap-7652	16	16	their	their	PRON
ap-7652	16	17	conventional	conventional	ADJ
ap-7652	16	18	representation	representation	NOUN
ap-7652	16	19	in	in	ADP
ap-7652	16	20	terms	term	NOUN
ap-7652	16	21	of	of	ADP
ap-7652	16	22	classical	classical	ADJ
ap-7652	16	23	laguerre	laguerre	NOUN
ap-7652	16	24	polynomials	polynomial	NOUN
ap-7652	16	25	with	with	ADP
ap-7652	16	26	degree	degree	NOUN
ap-7652	16	27	-	-	PUNCT
ap-7652	16	28	dependent	dependent	ADJ
ap-7652	16	29	indexes	index	NOUN
ap-7652	16	30	[	[	X
ap-7652	16	31	10	10	NUM
ap-7652	16	32	,	,	PUNCT
ap-7652	16	33	11	11	NUM
ap-7652	16	34	]	]	PUNCT
ap-7652	16	35	.	.	PUNCT
ap-7652	17	1	the	the	DET
ap-7652	17	2	main	main	ADJ
ap-7652	17	3	purpose	purpose	NOUN
ap-7652	17	4	of	of	ADP
ap-7652	17	5	this	this	DET
ap-7652	17	6	work	work	NOUN
ap-7652	17	7	is	be	AUX
ap-7652	17	8	to	to	PART
ap-7652	17	9	present	present	VERB
ap-7652	17	10	new	new	ADJ
ap-7652	17	11	simplified	simplified	ADJ
ap-7652	17	12	expressions	expression	NOUN
ap-7652	17	13	for	for	ADP
ap-7652	17	14	eigenfunctions	eigenfunction	NOUN
ap-7652	17	15	of	of	ADP
ap-7652	17	16	the	the	DET
ap-7652	17	17	schrödinger	schrödinger	ADJ
ap-7652	17	18	equation	equation	NOUN
ap-7652	17	19	with	with	ADP
ap-7652	17	20	a	a	DET
ap-7652	17	21	rationally	rationally	ADV
ap-7652	17	22	deformed	deform	VERB
ap-7652	17	23	morse	morse	ADJ
ap-7652	17	24	potential	potential	NOUN
ap-7652	17	25	by	by	ADP
ap-7652	17	26	re	re	VERB
ap-7652	17	27	-	-	VERB
ap-7652	17	28	writing	write	VERB
ap-7652	17	29	them	they	PRON
ap-7652	17	30	in	in	ADP
ap-7652	17	31	terms	term	NOUN
ap-7652	17	32	of	of	ADP
ap-7652	17	33	finite	finite	ADJ
ap-7652	17	34	exceptional	exceptional	ADJ
ap-7652	17	35	orthogonal	orthogonal	ADJ
ap-7652	17	36	polynomial	polynomial	NOUN
ap-7652	17	37	(	(	PUNCT
ap-7652	17	38	eop	eop	PROPN
ap-7652	17	39	)	)	PUNCT
ap-7652	17	40	sequences	sequence	NOUN
ap-7652	17	41	formed	form	VERB
ap-7652	17	42	by	by	ADP
ap-7652	17	43	wronskian	wronskian	ADJ
ap-7652	17	44	transforms	transform	NOUN
ap-7652	17	45	of	of	ADP
ap-7652	17	46	r	r	NOUN
ap-7652	17	47	-	-	PUNCT
ap-7652	17	48	bessel	bessel	ADJ
ap-7652	17	49	polynomials	polynomial	NOUN
ap-7652	17	50	.	.	PUNCT
ap-7652	18	1	100	100	NUM
ap-7652	18	2	https://doi.org/10.14311/ap.2022.62.0100	https://doi.org/10.14311/ap.2022.62.0100	PROPN
ap-7652	18	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7652	18	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7652	18	5	vol	vol	NOUN
ap-7652	18	6	.	.	PROPN
ap-7652	19	1	62	62	NUM
ap-7652	19	2	no	no	INTJ
ap-7652	19	3	.	.	PUNCT
ap-7652	20	1	1/2022	1/2022	NUM
ap-7652	20	2	quantization	quantization	NOUN
ap-7652	20	3	of	of	ADP
ap-7652	20	4	rationally	rationally	ADV
ap-7652	20	5	deformed	deform	VERB
ap-7652	20	6	morse	morse	ADJ
ap-7652	20	7	potentials	potential	NOUN
ap-7652	20	8	.	.	PUNCT
ap-7652	20	9	.	.	PUNCT
ap-7652	20	10	.	.	PUNCT
ap-7652	21	1	2	2	X
ap-7652	21	2	.	.	X
ap-7652	21	3	tfi	tfi	PROPN
ap-7652	21	4	sturm	sturm	PROPN
ap-7652	21	5	-	-	PUNCT
ap-7652	21	6	liouville	liouville	NOUN
ap-7652	21	7	equations	equation	NOUN
ap-7652	21	8	2.1	2.1	NUM
ap-7652	21	9	.	.	PUNCT
ap-7652	21	10	liouville	liouville	NOUN
ap-7652	21	11	-	-	PUNCT
ap-7652	21	12	darboux	darboux	VERB
ap-7652	21	13	transformations	transformation	NOUN
ap-7652	21	14	let	let	VERB
ap-7652	21	15	ϕτ	ϕτ	ADP
ap-7652	22	1	[	[	X
ap-7652	22	2	ξ;q	ξ;q	X
ap-7652	22	3	]	]	PUNCT
ap-7652	22	4	be	be	VERB
ap-7652	22	5	a	a	DET
ap-7652	22	6	solution	solution	NOUN
ap-7652	22	7	of	of	ADP
ap-7652	22	8	the	the	DET
ap-7652	22	9	generic	generic	ADJ
ap-7652	22	10	csle	csle	NOUN
ap-7652	22	11	{	{	PUNCT
ap-7652	22	12	d2	d2	PROPN
ap-7652	22	13	dξ2	dξ2	NOUN
ap-7652	22	14	+	+	CCONJ
ap-7652	22	15	i0[ξ;q	i0[ξ;q	PROPN
ap-7652	22	16	]	]	X
ap-7652	22	17	+	+	CCONJ
ap-7652	22	18	ετ	ετ	X
ap-7652	22	19	(	(	PUNCT
ap-7652	22	20	q)ρ[ξ	q)ρ[ξ	NOUN
ap-7652	22	21	]	]	PUNCT
ap-7652	22	22	}	}	PUNCT
ap-7652	22	23	ϕτ	ϕτ	ADP
ap-7652	23	1	[	[	X
ap-7652	23	2	ξ;q	ξ;q	X
ap-7652	23	3	]	]	X
ap-7652	23	4	=	=	SYM
ap-7652	23	5	0	0	PUNCT
ap-7652	23	6	(	(	PUNCT
ap-7652	23	7	1	1	NUM
ap-7652	23	8	)	)	PUNCT
ap-7652	23	9	at	at	ADP
ap-7652	23	10	an	an	DET
ap-7652	23	11	energy	energy	NOUN
ap-7652	23	12	ετ	ετ	NOUN
ap-7652	23	13	(	(	PUNCT
ap-7652	23	14	q	q	NOUN
ap-7652	23	15	)	)	PUNCT
ap-7652	23	16	,	,	PUNCT
ap-7652	23	17	where	where	SCONJ
ap-7652	23	18	the	the	DET
ap-7652	23	19	index	index	NOUN
ap-7652	23	20	τ	τ	PROPN
ap-7652	23	21	specifies	specify	VERB
ap-7652	23	22	the	the	DET
ap-7652	23	23	factorization	factorization	NOUN
ap-7652	23	24	function	function	NOUN
ap-7652	23	25	(	(	PUNCT
ap-7652	23	26	ff	ff	NOUN
ap-7652	23	27	)	)	PUNCT
ap-7652	23	28	in	in	ADP
ap-7652	23	29	question	question	NOUN
ap-7652	23	30	.	.	PUNCT
ap-7652	24	1	in	in	ADP
ap-7652	24	2	the	the	DET
ap-7652	24	3	problems	problem	NOUN
ap-7652	24	4	of	of	ADP
ap-7652	24	5	our	our	PRON
ap-7652	24	6	current	current	ADJ
ap-7652	24	7	interest	interest	NOUN
ap-7652	24	8	i0[ξ;q	i0[ξ;q	X
ap-7652	24	9	]	]	X
ap-7652	24	10	is	be	AUX
ap-7652	24	11	a	a	DET
ap-7652	24	12	rational	rational	ADJ
ap-7652	24	13	function	function	NOUN
ap-7652	24	14	of	of	ADP
ap-7652	24	15	ξ	ξ	PROPN
ap-7652	24	16	termed	term	VERB
ap-7652	24	17	‘	'	PUNCT
ap-7652	24	18	reference	reference	NOUN
ap-7652	24	19	polynomial	polynomial	ADJ
ap-7652	24	20	fraction	fraction	NOUN
ap-7652	24	21	’	'	PUNCT
ap-7652	24	22	(	(	PUNCT
ap-7652	24	23	refpf	refpf	NOUN
ap-7652	24	24	)	)	PUNCT
ap-7652	24	25	.	.	PUNCT
ap-7652	25	1	we	we	PRON
ap-7652	25	2	prefer	prefer	VERB
ap-7652	25	3	to	to	PART
ap-7652	25	4	keep	keep	VERB
ap-7652	25	5	this	this	DET
ap-7652	25	6	notation	notation	NOUN
ap-7652	25	7	in	in	ADP
ap-7652	25	8	the	the	DET
ap-7652	25	9	general	general	ADJ
ap-7652	25	10	case	case	NOUN
ap-7652	25	11	when	when	SCONJ
ap-7652	25	12	i0[ξ;q	i0[ξ;q	PROPN
ap-7652	25	13	]	]	X
ap-7652	25	14	is	be	AUX
ap-7652	25	15	an	an	DET
ap-7652	25	16	arbitrarily	arbitrarily	ADV
ap-7652	25	17	chosen	choose	VERB
ap-7652	25	18	real	real	ADJ
ap-7652	25	19	function	function	NOUN
ap-7652	25	20	of	of	ADP
ap-7652	25	21	ξ	ξ	PROPN
ap-7652	25	22	also	also	ADV
ap-7652	25	23	dependent	dependent	ADJ
ap-7652	25	24	on	on	ADP
ap-7652	25	25	some	some	DET
ap-7652	25	26	parameters	parameter	NOUN
ap-7652	25	27	q.	q.	ADV
ap-7652	25	28	we	we	PRON
ap-7652	25	29	will	will	AUX
ap-7652	25	30	replace	replace	VERB
ap-7652	25	31	q	q	NOUN
ap-7652	25	32	by	by	ADP
ap-7652	25	33	⇀	⇀	PROPN
ap-7652	25	34	a	a	DET
ap-7652	25	35	,	,	PUNCT
ap-7652	25	36	b	b	NOUN
ap-7652	25	37	after	after	ADP
ap-7652	25	38	restricting	restrict	VERB
ap-7652	25	39	the	the	DET
ap-7652	25	40	analysis	analysis	NOUN
ap-7652	25	41	solely	solely	ADV
ap-7652	25	42	to	to	ADP
ap-7652	25	43	tfi	tfi	NOUN
ap-7652	25	44	csles	csle	NOUN
ap-7652	25	45	.	.	PUNCT
ap-7652	26	1	in	in	ADP
ap-7652	26	2	[	[	X
ap-7652	26	3	23	23	NUM
ap-7652	26	4	]	]	PUNCT
ap-7652	26	5	we	we	PRON
ap-7652	26	6	identified	identify	VERB
ap-7652	26	7	four	four	NUM
ap-7652	26	8	families	family	NOUN
ap-7652	26	9	of	of	ADP
ap-7652	26	10	refpfs	refpf	NOUN
ap-7652	26	11	associated	associate	VERB
ap-7652	26	12	with	with	ADP
ap-7652	26	13	rational	rational	ADJ
ap-7652	26	14	tsi	tsi	PROPN
ap-7652	26	15	potentials	potential	NOUN
ap-7652	26	16	termed	term	VERB
ap-7652	26	17	‘	'	PUNCT
ap-7652	26	18	jacobi	jacobi	PROPN
ap-7652	26	19	’	'	PUNCT
ap-7652	26	20	,	,	PUNCT
ap-7652	26	21	‘	'	PUNCT
ap-7652	26	22	laguerre	laguerre	NOUN
ap-7652	26	23	’	'	PUNCT
ap-7652	26	24	,	,	PUNCT
ap-7652	26	25	‘	'	PUNCT
ap-7652	26	26	routh	routh	PROPN
ap-7652	26	27	’	'	PUNCT
ap-7652	26	28	and	and	CCONJ
ap-7652	26	29	‘	'	PUNCT
ap-7652	26	30	bessel	bessel	NOUN
ap-7652	26	31	’	'	PUNCT
ap-7652	26	32	(	(	PUNCT
ap-7652	26	33	or	or	CCONJ
ap-7652	26	34	j	j	PROPN
ap-7652	26	35	ref	ref	NOUN
ap-7652	26	36	,	,	PUNCT
ap-7652	26	37	l	l	PROPN
ap-7652	26	38	ref	ref	NOUN
ap-7652	26	39	,	,	PUNCT
ap-7652	26	40	rref	rref	VERB
ap-7652	26	41	,	,	PUNCT
ap-7652	26	42	and	and	CCONJ
ap-7652	26	43	bref	bref	NOUN
ap-7652	26	44	for	for	ADP
ap-7652	26	45	briefness	briefness	NOUN
ap-7652	26	46	)	)	PUNCT
ap-7652	26	47	so	so	CCONJ
ap-7652	26	48	the	the	DET
ap-7652	26	49	corresponding	corresponding	ADJ
ap-7652	26	50	q	q	NOUN
ap-7652	26	51	-	-	PUNCT
ap-7652	26	52	rss	rss	NOUN
ap-7652	26	53	are	be	AUX
ap-7652	26	54	composed	compose	VERB
ap-7652	26	55	of	of	ADP
ap-7652	26	56	polynomials	polynomial	NOUN
ap-7652	26	57	(	(	PUNCT
ap-7652	26	58	with	with	ADP
ap-7652	26	59	degree	degree	NOUN
ap-7652	26	60	-	-	PUNCT
ap-7652	26	61	dependent	dependent	ADJ
ap-7652	26	62	indexes	index	NOUN
ap-7652	26	63	in	in	ADP
ap-7652	26	64	general	general	ADJ
ap-7652	26	65	)	)	PUNCT
ap-7652	26	66	from	from	ADP
ap-7652	26	67	one	one	NUM
ap-7652	26	68	of	of	ADP
ap-7652	26	69	four	four	NUM
ap-7652	26	70	conventional	conventional	ADJ
ap-7652	26	71	differential	differential	ADJ
ap-7652	26	72	polynomial	polynomial	ADJ
ap-7652	26	73	systems	system	NOUN
ap-7652	26	74	(	(	PUNCT
ap-7652	26	75	dpss	dpss	PROPN
ap-7652	26	76	)	)	PUNCT
ap-7652	27	1	[	[	X
ap-7652	27	2	25	25	NUM
ap-7652	27	3	,	,	PUNCT
ap-7652	27	4	26	26	NUM
ap-7652	27	5	]	]	PUNCT
ap-7652	27	6	.	.	PUNCT
ap-7652	28	1	the	the	DET
ap-7652	28	2	density	density	NOUN
ap-7652	28	3	function	function	NOUN
ap-7652	28	4	ρ[ξ	ρ[ξ	NOUN
ap-7652	28	5	]	]	PUNCT
ap-7652	28	6	plays	play	VERB
ap-7652	28	7	a	a	DET
ap-7652	28	8	crucial	crucial	ADJ
ap-7652	28	9	role	role	NOUN
ap-7652	28	10	in	in	ADP
ap-7652	28	11	our	our	PRON
ap-7652	28	12	analysis	analysis	NOUN
ap-7652	28	13	because	because	SCONJ
ap-7652	28	14	,	,	PUNCT
ap-7652	28	15	as	as	SCONJ
ap-7652	28	16	indicated	indicate	VERB
ap-7652	28	17	by	by	ADP
ap-7652	28	18	eq	eq	PROPN
ap-7652	28	19	.	.	PUNCT
ap-7652	29	1	(	(	PUNCT
ap-7652	29	2	4	4	NUM
ap-7652	29	3	)	)	PUNCT
ap-7652	29	4	below	below	ADV
ap-7652	29	5	,	,	PUNCT
ap-7652	29	6	it	it	PRON
ap-7652	29	7	determines	determine	VERB
ap-7652	29	8	the	the	DET
ap-7652	29	9	change	change	NOUN
ap-7652	29	10	of	of	ADP
ap-7652	29	11	variable	variable	ADJ
ap-7652	29	12	converting	convert	VERB
ap-7652	29	13	csle	csle	NOUN
ap-7652	29	14	(	(	PUNCT
ap-7652	29	15	1	1	X
ap-7652	29	16	)	)	PUNCT
ap-7652	29	17	to	to	ADP
ap-7652	29	18	the	the	DET
ap-7652	29	19	schrödinger	schrödinger	ADJ
ap-7652	29	20	equation	equation	NOUN
ap-7652	29	21	[	[	X
ap-7652	29	22	27	27	NUM
ap-7652	29	23	,	,	PUNCT
ap-7652	29	24	28	28	NUM
ap-7652	29	25	]	]	PUNCT
ap-7652	29	26	.	.	PUNCT
ap-7652	30	1	it	it	PRON
ap-7652	30	2	was	be	AUX
ap-7652	30	3	rudjak	rudjak	ADJ
ap-7652	30	4	and	and	CCONJ
ap-7652	30	5	zakhariev	zakhariev	X
ap-7652	31	1	[	[	X
ap-7652	31	2	29	29	NUM
ap-7652	31	3	]	]	PUNCT
ap-7652	31	4	who	who	PRON
ap-7652	31	5	extended	extend	VERB
ap-7652	31	6	the	the	DET
ap-7652	31	7	intertwining	intertwine	VERB
ap-7652	31	8	technique	technique	NOUN
ap-7652	31	9	[	[	X
ap-7652	31	10	30	30	NUM
ap-7652	31	11	]	]	PUNCT
ap-7652	31	12	from	from	ADP
ap-7652	31	13	the	the	DET
ap-7652	31	14	schrödinger	schrödinger	ADJ
ap-7652	31	15	equation	equation	NOUN
ap-7652	31	16	to	to	ADP
ap-7652	31	17	the	the	DET
ap-7652	31	18	csle	csle	NOUN
ap-7652	31	19	.	.	PUNCT
ap-7652	32	1	here	here	ADV
ap-7652	32	2	we	we	PRON
ap-7652	32	3	however	however	ADV
ap-7652	32	4	use	use	VERB
ap-7652	32	5	a	a	DET
ap-7652	32	6	slightly	slightly	ADV
ap-7652	32	7	different	different	ADJ
ap-7652	32	8	definition	definition	NOUN
ap-7652	32	9	of	of	ADP
ap-7652	32	10	the	the	DET
ap-7652	32	11	socalled	socalled	ADJ
ap-7652	32	12	[	[	X
ap-7652	32	13	31	31	NUM
ap-7652	32	14	,	,	PUNCT
ap-7652	32	15	32	32	NUM
ap-7652	32	16	]	]	PUNCT
ap-7652	32	17	‘	'	PUNCT
ap-7652	32	18	generalized	generalized	ADJ
ap-7652	32	19	’	'	PUNCT
ap-7652	32	20	darboux	darboux	VERB
ap-7652	32	21	transformations	transformation	NOUN
ap-7652	32	22	introducing	introduce	VERB
ap-7652	32	23	them	they	PRON
ap-7652	32	24	via	via	ADP
ap-7652	32	25	the	the	DET
ap-7652	32	26	requirement	requirement	NOUN
ap-7652	32	27	that	that	SCONJ
ap-7652	32	28	the	the	DET
ap-7652	32	29	function	function	NOUN
ap-7652	32	30	∗ϕτ	∗ϕτ	PROPN
ap-7652	33	1	[	[	X
ap-7652	33	2	ξ;q	ξ;q	X
ap-7652	33	3	]	]	X
ap-7652	33	4	∝	∝	X
ap-7652	33	5	ρ−1/2[ξ]/ϕτ	ρ−1/2[ξ]/ϕτ	PROPN
ap-7652	34	1	[	[	X
ap-7652	34	2	ξ;q	ξ;q	NUM
ap-7652	34	3	]	]	X
ap-7652	34	4	(	(	PUNCT
ap-7652	34	5	2	2	X
ap-7652	34	6	)	)	PUNCT
ap-7652	34	7	is	be	AUX
ap-7652	34	8	a	a	DET
ap-7652	34	9	solution	solution	NOUN
ap-7652	34	10	of	of	ADP
ap-7652	34	11	the	the	DET
ap-7652	34	12	transformed	transform	VERB
ap-7652	34	13	csle	csle	NOUN
ap-7652	34	14	at	at	ADP
ap-7652	34	15	the	the	DET
ap-7652	34	16	same	same	ADJ
ap-7652	34	17	energy	energy	NOUN
ap-7652	34	18	ετ	ετ	NOUN
ap-7652	34	19	(	(	PUNCT
ap-7652	34	20	q	q	NOUN
ap-7652	34	21	)	)	PUNCT
ap-7652	34	22	,	,	PUNCT
ap-7652	34	23	i.e.	i.e.	X
ap-7652	34	24	,	,	PUNCT
ap-7652	34	25	{	{	PUNCT
ap-7652	34	26	d2	d2	NOUN
ap-7652	34	27	dξ2	dξ2	NOUN
ap-7652	34	28	+	+	CCONJ
ap-7652	34	29	i0[ξ;q	i0[ξ;q	PROPN
ap-7652	34	30	|	|	ADV
ap-7652	34	31	τ	τ	X
ap-7652	34	32	]	]	PUNCT
ap-7652	35	1	+	+	CCONJ
ap-7652	35	2	ετ	ετ	X
ap-7652	35	3	(	(	PUNCT
ap-7652	35	4	q)ρ[ξ	q)ρ[ξ	NOUN
ap-7652	35	5	]	]	PUNCT
ap-7652	35	6	}	}	PUNCT
ap-7652	35	7	∗ϕτ	∗ϕτ	PROPN
ap-7652	36	1	[	[	X
ap-7652	36	2	ξ;q	ξ;q	X
ap-7652	36	3	]	]	X
ap-7652	36	4	=	=	SYM
ap-7652	36	5	0	0	X
ap-7652	36	6	.	.	PUNCT
ap-7652	37	1	(	(	PUNCT
ap-7652	37	2	3	3	X
ap-7652	37	3	)	)	PUNCT
ap-7652	37	4	rudjak	rudjak	ADV
ap-7652	37	5	and	and	CCONJ
ap-7652	37	6	zakhariev	zakhariev	X
ap-7652	37	7	’s	’s	PART
ap-7652	37	8	reciprocal	reciprocal	ADJ
ap-7652	37	9	formula	formula	NOUN
ap-7652	37	10	(	(	PUNCT
ap-7652	37	11	2	2	X
ap-7652	37	12	)	)	PUNCT
ap-7652	37	13	thus	thus	ADV
ap-7652	37	14	plays	play	VERB
ap-7652	37	15	a	a	DET
ap-7652	37	16	crucial	crucial	ADJ
ap-7652	37	17	role	role	NOUN
ap-7652	37	18	in	in	ADP
ap-7652	37	19	our	our	PRON
ap-7652	37	20	approach	approach	NOUN
ap-7652	37	21	to	to	ADP
ap-7652	37	22	the	the	DET
ap-7652	37	23	theory	theory	NOUN
ap-7652	37	24	of	of	ADP
ap-7652	37	25	tfi	tfi	NOUN
ap-7652	37	26	csles	csle	NOUN
ap-7652	37	27	.	.	PUNCT
ap-7652	38	1	since	since	SCONJ
ap-7652	38	2	various	various	ADJ
ap-7652	38	3	authors	author	NOUN
ap-7652	38	4	give	give	VERB
ap-7652	38	5	the	the	DET
ap-7652	38	6	term	term	NOUN
ap-7652	38	7	‘	'	PUNCT
ap-7652	38	8	generalized	generalized	ADJ
ap-7652	38	9	darboux	darboux	VERB
ap-7652	38	10	transformation	transformation	NOUN
ap-7652	38	11	’	'	PUNCT
ap-7652	38	12	completely	completely	ADV
ap-7652	38	13	different	different	ADJ
ap-7652	38	14	meanings	meaning	NOUN
ap-7652	38	15	it	it	PRON
ap-7652	38	16	seems	seem	VERB
ap-7652	38	17	preferable	preferable	ADJ
ap-7652	38	18	to	to	PART
ap-7652	38	19	refer	refer	VERB
ap-7652	38	20	to	to	ADP
ap-7652	38	21	these	these	DET
ap-7652	38	22	operations	operation	NOUN
ap-7652	38	23	as	as	ADP
ap-7652	38	24	‘	'	PUNCT
ap-7652	38	25	liouville	liouville	NOUN
ap-7652	38	26	-	-	PUNCT
ap-7652	38	27	darboux	darboux	NOUN
ap-7652	38	28	’	'	PUNCT
ap-7652	38	29	transformations	transformation	NOUN
ap-7652	38	30	keeping	keep	VERB
ap-7652	38	31	in	in	ADP
ap-7652	38	32	mind	mind	NOUN
ap-7652	38	33	that	that	SCONJ
ap-7652	38	34	they	they	PRON
ap-7652	38	35	can	can	AUX
ap-7652	38	36	be	be	AUX
ap-7652	38	37	performed	perform	VERB
ap-7652	38	38	in	in	ADP
ap-7652	38	39	three	three	NUM
ap-7652	38	40	sequential	sequential	ADJ
ap-7652	38	41	steps	step	NOUN
ap-7652	38	42	:	:	PUNCT
ap-7652	38	43	(	(	PUNCT
ap-7652	38	44	1	1	NUM
ap-7652	38	45	.	.	PUNCT
ap-7652	38	46	)	)	PUNCT
ap-7652	39	1	the	the	DET
ap-7652	39	2	liouville	liouville	NOUN
ap-7652	39	3	transformation	transformation	NOUN
ap-7652	39	4	ξ(x	ξ(x	NOUN
ap-7652	39	5	):	):	PUNCT
ap-7652	39	6	ξ′(x	ξ′(x	SYM
ap-7652	39	7	)	)	PUNCT
ap-7652	39	8	=	=	SYM
ap-7652	39	9	ρ−1/2[ξ(x	ρ−1/2[ξ(x	NUM
ap-7652	39	10	)	)	PUNCT
ap-7652	39	11	]	]	PUNCT
ap-7652	39	12	(	(	PUNCT
ap-7652	39	13	4	4	NUM
ap-7652	39	14	)	)	PUNCT
ap-7652	39	15	from	from	ADP
ap-7652	39	16	the	the	DET
ap-7652	39	17	csle	csle	NOUN
ap-7652	39	18	{	{	PUNCT
ap-7652	39	19	d2	d2	PROPN
ap-7652	39	20	dξ2	dξ2	NOUN
ap-7652	39	21	+	+	CCONJ
ap-7652	39	22	i0[ξ;q	i0[ξ;q	PROPN
ap-7652	39	23	]	]	X
ap-7652	39	24	+	+	CCONJ
ap-7652	39	25	ερ[ξ	ερ[ξ	NOUN
ap-7652	39	26	]	]	PUNCT
ap-7652	39	27	}	}	PUNCT
ap-7652	39	28	φ[ξ;q	φ[ξ;q	NOUN
ap-7652	39	29	;	;	PUNCT
ap-7652	39	30	ε	ε	X
ap-7652	39	31	]	]	X
ap-7652	39	32	=	=	SYM
ap-7652	39	33	0	0	NUM
ap-7652	39	34	(	(	PUNCT
ap-7652	39	35	5	5	NUM
ap-7652	39	36	)	)	PUNCT
ap-7652	39	37	to	to	ADP
ap-7652	39	38	the	the	DET
ap-7652	39	39	stationary	stationary	ADJ
ap-7652	39	40	1d	1d	NUM
ap-7652	39	41	schrödinger	schrödinger	ADJ
ap-7652	39	42	equation	equation	NOUN
ap-7652	39	43	with	with	ADP
ap-7652	39	44	the	the	DET
ap-7652	39	45	potential	potential	NOUN
ap-7652	39	46	[	[	X
ap-7652	39	47	27	27	NUM
ap-7652	39	48	,	,	PUNCT
ap-7652	39	49	28	28	NUM
ap-7652	39	50	]	]	SYM
ap-7652	39	51	v	v	ADP
ap-7652	40	1	[	[	X
ap-7652	40	2	ξ(x);q	ξ(x);q	X
ap-7652	40	3	]	]	X
ap-7652	40	4	=	=	PUNCT
ap-7652	40	5	−ρ−1[ξ(x)]i0[ξ(x);q	−ρ−1[ξ(x)]i0[ξ(x);q	X
ap-7652	40	6	]	]	X
ap-7652	40	7	−	−	PROPN
ap-7652	40	8	1/2	1/2	NUM
ap-7652	40	9	{	{	PUNCT
ap-7652	40	10	ξ	ξ	PROPN
ap-7652	40	11	,	,	PUNCT
ap-7652	40	12	x	x	SYM
ap-7652	40	13	}	}	PUNCT
ap-7652	40	14	(	(	PUNCT
ap-7652	40	15	6	6	NUM
ap-7652	40	16	)	)	PUNCT
ap-7652	40	17	where	where	SCONJ
ap-7652	40	18	{	{	PUNCT
ap-7652	40	19	ξ	ξ	X
ap-7652	40	20	,	,	PUNCT
ap-7652	40	21	x	x	PRON
ap-7652	40	22	}	}	PUNCT
ap-7652	40	23	stands	stand	VERB
ap-7652	40	24	for	for	ADP
ap-7652	40	25	the	the	DET
ap-7652	40	26	‘	'	PUNCT
ap-7652	40	27	schwarzian	schwarzian	ADJ
ap-7652	40	28	derivative	derivative	NOUN
ap-7652	40	29	’	'	PUNCT
ap-7652	40	30	;	;	PUNCT
ap-7652	40	31	(	(	PUNCT
ap-7652	40	32	2	2	NUM
ap-7652	40	33	.	.	PUNCT
ap-7652	40	34	)	)	PUNCT
ap-7652	41	1	the	the	DET
ap-7652	41	2	darboux	darboux	ADJ
ap-7652	41	3	deformation	deformation	NOUN
ap-7652	41	4	of	of	ADP
ap-7652	41	5	liouville	liouville	NOUN
ap-7652	41	6	potential	potential	NOUN
ap-7652	41	7	(	(	PUNCT
ap-7652	41	8	6	6	NUM
ap-7652	41	9	)	)	PUNCT
ap-7652	41	10	using	use	VERB
ap-7652	41	11	the	the	DET
ap-7652	41	12	ff	ff	NOUN
ap-7652	41	13	ψτ	ψτ	PROPN
ap-7652	41	14	(	(	PUNCT
ap-7652	41	15	x;q	x;q	NUM
ap-7652	41	16	)	)	PUNCT
ap-7652	42	1	=	=	SYM
ap-7652	42	2	ρ1/4[ξ(x)]ϕτ	ρ1/4[ξ(x)]ϕτ	NOUN
ap-7652	43	1	[	[	X
ap-7652	43	2	ξ(x);q	ξ(x);q	NOUN
ap-7652	43	3	]	]	X
ap-7652	43	4	;	;	PUNCT
ap-7652	43	5	(	(	PUNCT
ap-7652	43	6	7	7	X
ap-7652	43	7	)	)	PUNCT
ap-7652	43	8	(	(	PUNCT
ap-7652	43	9	3	3	NUM
ap-7652	43	10	.	.	PUNCT
ap-7652	43	11	)	)	PUNCT
ap-7652	43	12	reverse	reverse	VERB
ap-7652	43	13	liouville	liouville	NOUN
ap-7652	43	14	transformation	transformation	NOUN
ap-7652	43	15	from	from	ADP
ap-7652	43	16	the	the	DET
ap-7652	43	17	schrödinger	schrödinger	ADJ
ap-7652	43	18	equation	equation	NOUN
ap-7652	43	19	to	to	ADP
ap-7652	43	20	the	the	DET
ap-7652	43	21	new	new	ADJ
ap-7652	43	22	csle	csle	PROPN
ap-7652	43	23	{	{	PUNCT
ap-7652	43	24	d2	d2	NOUN
ap-7652	43	25	dξ2	dξ2	NOUN
ap-7652	43	26	+	+	CCONJ
ap-7652	43	27	i0[ξ;q	i0[ξ;q	PROPN
ap-7652	43	28	|	|	ADV
ap-7652	43	29	τ	τ	X
ap-7652	43	30	]	]	PUNCT
ap-7652	44	1	+	+	CCONJ
ap-7652	44	2	ερ[ξ	ερ[ξ	NOUN
ap-7652	44	3	]	]	PUNCT
ap-7652	44	4	}	}	PUNCT
ap-7652	44	5	φ[ξ;q	φ[ξ;q	PROPN
ap-7652	44	6	;	;	PUNCT
ap-7652	44	7	ε	ε	PROPN
ap-7652	44	8	|	|	ADV
ap-7652	44	9	τ	τ	X
ap-7652	44	10	]	]	PUNCT
ap-7652	44	11	=	=	PUNCT
ap-7652	45	1	0	0	X
ap-7652	45	2	.	.	PUNCT
ap-7652	46	1	(	(	PUNCT
ap-7652	46	2	8)	8)	NUM
ap-7652	46	3	obviously	obviously	ADV
ap-7652	46	4	any	any	DET
ap-7652	46	5	tfi	tfi	NOUN
ap-7652	46	6	theorem	theorem	NOUN
ap-7652	46	7	proven	prove	VERB
ap-7652	46	8	for	for	ADP
ap-7652	46	9	liouville	liouville	NOUN
ap-7652	46	10	-	-	PUNCT
ap-7652	46	11	darboux	darboux	VERB
ap-7652	46	12	transformations	transformation	NOUN
ap-7652	46	13	of	of	ADP
ap-7652	46	14	csle	csle	NOUN
ap-7652	46	15	(	(	PUNCT
ap-7652	46	16	5	5	X
ap-7652	46	17	)	)	PUNCT
ap-7652	46	18	can	can	AUX
ap-7652	46	19	be	be	AUX
ap-7652	46	20	directly	directly	ADV
ap-7652	46	21	applied	apply	VERB
ap-7652	46	22	to	to	ADP
ap-7652	46	23	the	the	DET
ap-7652	46	24	resultant	resultant	NOUN
ap-7652	46	25	liouville	liouville	NOUN
ap-7652	46	26	potential	potential	NOUN
ap-7652	46	27	thus	thus	ADV
ap-7652	46	28	linking	link	VERB
ap-7652	46	29	the	the	DET
ap-7652	46	30	new	new	ADJ
ap-7652	46	31	technique	technique	NOUN
ap-7652	46	32	to	to	ADP
ap-7652	46	33	the	the	DET
ap-7652	46	34	conventional	conventional	ADJ
ap-7652	46	35	darboux	darboux	VERB
ap-7652	46	36	-	-	PUNCT
ap-7652	46	37	crum	crum	NOUN
ap-7652	46	38	theory	theory	NOUN
ap-7652	46	39	of	of	ADP
ap-7652	46	40	tsi	tsi	PROPN
ap-7652	46	41	potentials	potential	VERB
ap-7652	46	42	[	[	X
ap-7652	46	43	11	11	NUM
ap-7652	46	44	,	,	PUNCT
ap-7652	46	45	19	19	NUM
ap-7652	46	46	,	,	PUNCT
ap-7652	46	47	33	33	NUM
ap-7652	46	48	]	]	PUNCT
ap-7652	46	49	.	.	PUNCT
ap-7652	47	1	101	101	NUM
ap-7652	47	2	gregory	gregory	PROPN
ap-7652	47	3	natanson	natanson	PROPN
ap-7652	47	4	acta	acta	PROPN
ap-7652	47	5	polytechnica	polytechnica	PROPN
ap-7652	47	6	2.2	2.2	NUM
ap-7652	47	7	.	.	PUNCT
ap-7652	48	1	translational	translational	ADJ
ap-7652	48	2	from	from	ADP
ap-7652	48	3	-	-	PUNCT
ap-7652	48	4	invariance	invariance	NOUN
ap-7652	48	5	of	of	ADP
ap-7652	48	6	sturm	sturm	NOUN
ap-7652	48	7	-	-	PUNCT
ap-7652	48	8	liouville	liouville	NOUN
ap-7652	48	9	equation	equation	NOUN
ap-7652	48	10	we	we	PRON
ap-7652	48	11	call	call	VERB
ap-7652	48	12	a	a	DET
ap-7652	48	13	csle	csle	NOUN
ap-7652	48	14	‘	'	PUNCT
ap-7652	48	15	translationally	translationally	ADV
ap-7652	48	16	form	form	NOUN
ap-7652	48	17	-	-	PUNCT
ap-7652	48	18	invariant	invariant	ADJ
ap-7652	48	19	’	'	PUNCT
ap-7652	48	20	if	if	SCONJ
ap-7652	48	21	it	it	PRON
ap-7652	48	22	has	have	VERB
ap-7652	48	23	two	two	NUM
ap-7652	48	24	‘	'	PUNCT
ap-7652	48	25	basic	basic	ADJ
ap-7652	48	26	’	'	PUNCT
ap-7652	48	27	solutions	solution	NOUN
ap-7652	48	28	ϕ+,0[ξ	ϕ+,0[ξ	NOUN
ap-7652	48	29	,	,	PUNCT
ap-7652	48	30	⇀	⇀	PROPN
ap-7652	48	31	a	a	PRON
ap-7652	48	32	,	,	PUNCT
ap-7652	48	33	b	b	NOUN
ap-7652	48	34	]	]	PUNCT
ap-7652	48	35	and	and	CCONJ
ap-7652	48	36	ϕ−,0[ξ	ϕ−,0[ξ	NOUN
ap-7652	48	37	,	,	PUNCT
ap-7652	48	38	⇀	⇀	PROPN
ap-7652	48	39	a	a	DET
ap-7652	48	40	,	,	PUNCT
ap-7652	48	41	b	b	NOUN
ap-7652	48	42	]	]	X
ap-7652	48	43	{	{	PUNCT
ap-7652	48	44	d2	d2	PROPN
ap-7652	48	45	dξ2	dξ2	NOUN
ap-7652	48	46	+	+	X
ap-7652	48	47	i0[ξ	i0[ξ	NOUN
ap-7652	48	48	;	;	PUNCT
ap-7652	49	1	⇀	⇀	NUM
ap-7652	49	2	a	a	DET
ap-7652	49	3	,	,	PUNCT
ap-7652	49	4	b	b	AUX
ap-7652	49	5	]	]	X
ap-7652	49	6	+	+	CCONJ
ap-7652	49	7	ε±,0	ε±,0	X
ap-7652	49	8	(	(	PUNCT
ap-7652	49	9	⇀	⇀	PROPN
ap-7652	49	10	a	a	PRON
ap-7652	49	11	,	,	PUNCT
ap-7652	49	12	b)ρ[ξ	b)ρ[ξ	NOUN
ap-7652	49	13	]	]	PUNCT
ap-7652	49	14	}	}	PUNCT
ap-7652	49	15	ϕ±,0[ξ	ϕ±,0[ξ	PROPN
ap-7652	49	16	;	;	PUNCT
ap-7652	49	17	⇀	⇀	NUM
ap-7652	49	18	a	a	DET
ap-7652	49	19	,	,	PUNCT
ap-7652	49	20	b	b	X
ap-7652	49	21	]	]	X
ap-7652	49	22	=	=	SYM
ap-7652	49	23	0	0	NUM
ap-7652	49	24	(	(	PUNCT
ap-7652	49	25	9	9	NUM
ap-7652	49	26	)	)	PUNCT
ap-7652	49	27	related	relate	VERB
ap-7652	49	28	via	via	ADP
ap-7652	49	29	the	the	DET
ap-7652	49	30	following	following	ADJ
ap-7652	49	31	reciprocal	reciprocal	ADJ
ap-7652	49	32	formulas	formula	NOUN
ap-7652	49	33	:	:	PUNCT
ap-7652	49	34	ϕ±,0[ξ	ϕ±,0[ξ	NOUN
ap-7652	49	35	;	;	PUNCT
ap-7652	49	36	⇀	⇀	PROPN
ap-7652	49	37	a	a	DET
ap-7652	49	38	±	±	NUM
ap-7652	49	39	⇀	⇀	NUM
ap-7652	49	40	1	1	NUM
ap-7652	49	41	,	,	PUNCT
ap-7652	49	42	b	b	X
ap-7652	49	43	]	]	X
ap-7652	49	44	=	=	SYM
ap-7652	49	45	ρ−1/2[ξ]/ϕ±,0[ξ	ρ−1/2[ξ]/ϕ±,0[ξ	PROPN
ap-7652	49	46	;	;	PUNCT
ap-7652	49	47	⇀	⇀	NUM
ap-7652	49	48	a	a	DET
ap-7652	49	49	,	,	PUNCT
ap-7652	49	50	b	b	NOUN
ap-7652	49	51	]	]	X
ap-7652	49	52	.	.	PUNCT
ap-7652	50	1	(	(	PUNCT
ap-7652	50	2	10	10	NUM
ap-7652	50	3	)	)	PUNCT
ap-7652	50	4	it	it	PRON
ap-7652	50	5	has	have	AUX
ap-7652	50	6	been	be	AUX
ap-7652	50	7	proven	prove	VERB
ap-7652	50	8	[	[	X
ap-7652	50	9	23	23	NUM
ap-7652	50	10	]	]	PUNCT
ap-7652	50	11	that	that	DET
ap-7652	50	12	i0[ξ	i0[ξ	NOUN
ap-7652	50	13	;	;	PUNCT
ap-7652	50	14	⇀	⇀	NUM
ap-7652	50	15	a	a	DET
ap-7652	50	16	,	,	PUNCT
ap-7652	50	17	b	b	PROPN
ap-7652	50	18	|	|	ADJ
ap-7652	50	19	±	±	NUM
ap-7652	50	20	,	,	PUNCT
ap-7652	50	21	0	0	NUM
ap-7652	50	22	]	]	PUNCT
ap-7652	50	23	=	=	SYM
ap-7652	50	24	i0[ξ	i0[ξ	PROPN
ap-7652	50	25	;	;	PUNCT
ap-7652	50	26	⇀	⇀	PROPN
ap-7652	50	27	a	a	DET
ap-7652	50	28	±	±	NUM
ap-7652	50	29	⇀	⇀	NUM
ap-7652	50	30	1	1	NUM
ap-7652	50	31	,	,	PUNCT
ap-7652	50	32	b	b	NOUN
ap-7652	50	33	]	]	X
ap-7652	50	34	+	+	NUM
ap-7652	50	35	e±1	e±1	NOUN
ap-7652	50	36	(	(	PUNCT
ap-7652	50	37	⇀	⇀	PROPN
ap-7652	50	38	a	a	PRON
ap-7652	50	39	,	,	PUNCT
ap-7652	50	40	b)ρ[ξ	b)ρ[ξ	PROPN
ap-7652	50	41	]	]	PUNCT
ap-7652	50	42	,	,	PUNCT
ap-7652	50	43	(	(	PUNCT
ap-7652	50	44	11	11	NUM
ap-7652	50	45	)	)	PUNCT
ap-7652	51	1	where	where	SCONJ
ap-7652	51	2	e±1	e±1	NOUN
ap-7652	51	3	(	(	PUNCT
ap-7652	51	4	⇀	⇀	PROPN
ap-7652	51	5	a	a	PRON
ap-7652	51	6	,	,	PUNCT
ap-7652	51	7	b	b	NOUN
ap-7652	51	8	)	)	PUNCT
ap-7652	51	9	≡	≡	PROPN
ap-7652	51	10	ε∓,0	ε∓,0	PROPN
ap-7652	51	11	(	(	PUNCT
ap-7652	51	12	⇀	⇀	PROPN
ap-7652	51	13	a	a	DET
ap-7652	51	14	±	±	NUM
ap-7652	51	15	⇀	⇀	NUM
ap-7652	51	16	1	1	NUM
ap-7652	51	17	,	,	PUNCT
ap-7652	51	18	b	b	NOUN
ap-7652	51	19	)	)	PUNCT
ap-7652	51	20	−	−	PROPN
ap-7652	52	1	ε±,0	ε±,0	PROPN
ap-7652	52	2	(	(	PUNCT
ap-7652	52	3	⇀	⇀	PROPN
ap-7652	52	4	a	a	DET
ap-7652	52	5	,	,	PUNCT
ap-7652	52	6	b	b	NOUN
ap-7652	52	7	)	)	PUNCT
ap-7652	52	8	.	.	PUNCT
ap-7652	53	1	(	(	PUNCT
ap-7652	53	2	12	12	NUM
ap-7652	53	3	)	)	PUNCT
ap-7652	53	4	the	the	DET
ap-7652	53	5	liouville	liouville	NOUN
ap-7652	53	6	transformations	transformation	NOUN
ap-7652	53	7	of	of	ADP
ap-7652	53	8	the	the	DET
ap-7652	53	9	csles	csle	NOUN
ap-7652	53	10	with	with	ADP
ap-7652	53	11	zero	zero	NUM
ap-7652	53	12	-	-	PUNCT
ap-7652	53	13	energy	energy	NOUN
ap-7652	53	14	free	free	ADJ
ap-7652	53	15	terms	term	NOUN
ap-7652	53	16	i0[ξ	i0[ξ	NOUN
ap-7652	53	17	;	;	PUNCT
ap-7652	53	18	a	a	DET
ap-7652	53	19	,	,	PUNCT
ap-7652	53	20	b	b	NOUN
ap-7652	53	21	]	]	X
ap-7652	53	22	and	and	CCONJ
ap-7652	53	23	i0[ξ	i0[ξ	NOUN
ap-7652	53	24	;	;	PUNCT
ap-7652	53	25	a	a	DET
ap-7652	53	26	,	,	PUNCT
ap-7652	53	27	b	b	PROPN
ap-7652	53	28	|	|	ADJ
ap-7652	53	29	±	±	NUM
ap-7652	53	30	,	,	PUNCT
ap-7652	53	31	0	0	NUM
ap-7652	53	32	]	]	PUNCT
ap-7652	53	33	then	then	ADV
ap-7652	53	34	brings	bring	VERB
ap-7652	53	35	us	we	PRON
ap-7652	53	36	to	to	ADP
ap-7652	53	37	gendenshtein	gendenshtein	VERB
ap-7652	53	38	’s	’s	PART
ap-7652	53	39	conventional	conventional	ADJ
ap-7652	53	40	definition	definition	NOUN
ap-7652	53	41	of	of	ADP
ap-7652	53	42	a	a	DET
ap-7652	53	43	tsi	tsi	PROPN
ap-7652	53	44	potential	potential	NOUN
ap-7652	53	45	[	[	X
ap-7652	53	46	34	34	NUM
ap-7652	53	47	]	]	SYM
ap-7652	53	48	v	v	ADP
ap-7652	53	49	[	[	X
ap-7652	53	50	ξ	ξ	X
ap-7652	53	51	;	;	PUNCT
ap-7652	53	52	⇀	⇀	NUM
ap-7652	53	53	a	a	PRON
ap-7652	53	54	,	,	PUNCT
ap-7652	53	55	b	b	PROPN
ap-7652	54	1	|	|	ADV
ap-7652	54	2	+	+	ADJ
ap-7652	54	3	,	,	PUNCT
ap-7652	54	4	0	0	NUM
ap-7652	55	1	]	]	PUNCT
ap-7652	55	2	=	=	SYM
ap-7652	55	3	v	v	PART
ap-7652	55	4	[	[	X
ap-7652	55	5	ξ	ξ	X
ap-7652	55	6	;	;	PUNCT
ap-7652	55	7	⇀	⇀	NUM
ap-7652	55	8	a	a	PRON
ap-7652	56	1	+	+	NOUN
ap-7652	56	2	⇀	⇀	NUM
ap-7652	56	3	1	1	NUM
ap-7652	56	4	,	,	PUNCT
ap-7652	56	5	b	b	NOUN
ap-7652	56	6	]	]	X
ap-7652	56	7	−	−	X
ap-7652	57	1	e+1	e+1	NUM
ap-7652	57	2	(	(	PUNCT
ap-7652	57	3	⇀	⇀	X
ap-7652	57	4	a	a	DET
ap-7652	57	5	,	,	PUNCT
ap-7652	57	6	b	b	NOUN
ap-7652	57	7	)	)	PUNCT
ap-7652	57	8	(	(	PUNCT
ap-7652	57	9	13	13	NUM
ap-7652	57	10	)	)	PUNCT
ap-7652	57	11	or	or	CCONJ
ap-7652	57	12	v	v	ADP
ap-7652	57	13	[	[	X
ap-7652	57	14	ξ	ξ	X
ap-7652	57	15	;	;	PUNCT
ap-7652	57	16	⇀	⇀	NUM
ap-7652	57	17	a	a	PRON
ap-7652	57	18	,	,	PUNCT
ap-7652	57	19	b	b	PROPN
ap-7652	57	20	|	|	ADV
ap-7652	57	21	−	−	NOUN
ap-7652	57	22	,	,	PUNCT
ap-7652	57	23	0	0	NUM
ap-7652	57	24	]	]	PUNCT
ap-7652	57	25	=	=	SYM
ap-7652	57	26	v	v	PART
ap-7652	57	27	[	[	X
ap-7652	57	28	ξ	ξ	X
ap-7652	57	29	;	;	PUNCT
ap-7652	57	30	⇀	⇀	NUM
ap-7652	58	1	a	a	DET
ap-7652	58	2	−	−	NOUN
ap-7652	58	3	⇀	⇀	NUM
ap-7652	58	4	1	1	NUM
ap-7652	58	5	,	,	PUNCT
ap-7652	58	6	b	b	NOUN
ap-7652	58	7	]	]	X
ap-7652	58	8	−	−	PROPN
ap-7652	58	9	e−1	e−1	PROPN
ap-7652	58	10	(	(	PUNCT
ap-7652	58	11	⇀	⇀	PROPN
ap-7652	58	12	a	a	DET
ap-7652	58	13	,	,	PUNCT
ap-7652	58	14	b	b	NOUN
ap-7652	58	15	)	)	PUNCT
ap-7652	58	16	(	(	PUNCT
ap-7652	58	17	14	14	NUM
ap-7652	58	18	)	)	PUNCT
ap-7652	58	19	depending	depend	VERB
ap-7652	58	20	on	on	ADP
ap-7652	58	21	which	which	PRON
ap-7652	58	22	basic	basic	ADJ
ap-7652	58	23	solution	solution	NOUN
ap-7652	58	24	ϕ+,0[ξ	ϕ+,0[ξ	NOUN
ap-7652	58	25	;	;	PUNCT
ap-7652	58	26	⇀	⇀	PROPN
ap-7652	58	27	a	a	DET
ap-7652	58	28	,	,	PUNCT
ap-7652	58	29	b	b	NOUN
ap-7652	58	30	]	]	PUNCT
ap-7652	58	31	or	or	CCONJ
ap-7652	58	32	ϕ−,0[ξ	ϕ−,0[ξ	INTJ
ap-7652	58	33	;	;	PUNCT
ap-7652	58	34	⇀	⇀	NUM
ap-7652	58	35	a	a	DET
ap-7652	58	36	,	,	PUNCT
ap-7652	58	37	b	b	AUX
ap-7652	58	38	]	]	PUNCT
ap-7652	58	39	represents	represent	VERB
ap-7652	58	40	the	the	DET
ap-7652	58	41	lowest	low	ADJ
ap-7652	58	42	energy	energy	NOUN
ap-7652	58	43	eigenfunction	eigenfunction	NOUN
ap-7652	58	44	.	.	PUNCT
ap-7652	59	1	note	note	VERB
ap-7652	59	2	that	that	SCONJ
ap-7652	59	3	the	the	DET
ap-7652	59	4	russian	russian	ADJ
ap-7652	59	5	word	word	NOUN
ap-7652	59	6	‘	'	PUNCT
ap-7652	59	7	форма	форма	NOUN
ap-7652	59	8	’	'	PUNCT
ap-7652	59	9	used	use	VERB
ap-7652	59	10	by	by	ADP
ap-7652	59	11	gendenshtein	gendenshtein	NOUN
ap-7652	59	12	[	[	X
ap-7652	59	13	34	34	NUM
ap-7652	59	14	]	]	PUNCT
ap-7652	59	15	has	have	VERB
ap-7652	59	16	two	two	NUM
ap-7652	59	17	meanings	meaning	NOUN
ap-7652	59	18	‘	'	PUNCT
ap-7652	59	19	form	form	NOUN
ap-7652	59	20	’	'	PUNCT
ap-7652	59	21	and	and	CCONJ
ap-7652	59	22	‘	'	PUNCT
ap-7652	59	23	shape	shape	NOUN
ap-7652	59	24	’	'	PUNCT
ap-7652	59	25	.	.	PUNCT
ap-7652	60	1	the	the	DET
ap-7652	60	2	term	term	NOUN
ap-7652	60	3	‘	'	PUNCT
ap-7652	60	4	form	form	NOUN
ap-7652	60	5	invariant	invariant	ADJ
ap-7652	60	6	’	'	PUNCT
ap-7652	60	7	with	with	ADP
ap-7652	60	8	reference	reference	NOUN
ap-7652	60	9	to	to	ADP
ap-7652	60	10	csles	csle	NOUN
ap-7652	60	11	was	be	AUX
ap-7652	60	12	adopted	adopt	VERB
ap-7652	60	13	by	by	ADP
ap-7652	60	14	us	we	PRON
ap-7652	60	15	from	from	ADP
ap-7652	60	16	the	the	DET
ap-7652	60	17	english	english	ADJ
ap-7652	60	18	translation	translation	NOUN
ap-7652	60	19	of	of	ADP
ap-7652	60	20	gendenshtein	gendenshtein	PROPN
ap-7652	60	21	’s	’s	PART
ap-7652	60	22	joint	joint	ADJ
ap-7652	60	23	paper	paper	NOUN
ap-7652	60	24	with	with	ADP
ap-7652	60	25	kreve	kreve	PROPN
ap-7652	60	26	[	[	X
ap-7652	60	27	35	35	NUM
ap-7652	60	28	]	]	PUNCT
ap-7652	60	29	while	while	SCONJ
ap-7652	60	30	the	the	DET
ap-7652	60	31	commonly	commonly	ADV
ap-7652	60	32	accepted	accept	VERB
ap-7652	60	33	term	term	NOUN
ap-7652	60	34	‘	'	PUNCT
ap-7652	60	35	shape	shape	NOUN
ap-7652	60	36	-	-	PUNCT
ap-7652	60	37	invariance	invariance	NOUN
ap-7652	60	38	’	'	PUNCT
ap-7652	60	39	is	be	AUX
ap-7652	60	40	preserved	preserve	VERB
ap-7652	60	41	for	for	ADP
ap-7652	60	42	the	the	DET
ap-7652	60	43	corresponding	corresponding	ADJ
ap-7652	60	44	liouville	liouville	NOUN
ap-7652	60	45	potentials	potential	NOUN
ap-7652	60	46	.	.	PUNCT
ap-7652	61	1	the	the	DET
ap-7652	61	2	shift	shift	NOUN
ap-7652	61	3	of	of	ADP
ap-7652	61	4	the	the	DET
ap-7652	61	5	translational	translational	ADJ
ap-7652	61	6	parameters	parameter	NOUN
ap-7652	61	7	⇀	⇀	X
ap-7652	61	8	a	a	PRON
ap-7652	61	9	by	by	ADP
ap-7652	61	10	1	1	NUM
ap-7652	61	11	thus	thus	ADV
ap-7652	61	12	retains	retain	VERB
ap-7652	61	13	the	the	DET
ap-7652	61	14	analytical	analytical	ADJ
ap-7652	61	15	form	form	NOUN
ap-7652	61	16	of	of	ADP
ap-7652	61	17	the	the	DET
ap-7652	61	18	tfi	tfi	NOUN
ap-7652	61	19	csle	csle	NOUN
ap-7652	61	20	while	while	SCONJ
ap-7652	61	21	preserving	preserve	VERB
ap-7652	61	22	the	the	DET
ap-7652	61	23	‘	'	PUNCT
ap-7652	61	24	shape	shape	NOUN
ap-7652	61	25	’	'	PUNCT
ap-7652	61	26	of	of	ADP
ap-7652	61	27	its	its	PRON
ap-7652	61	28	liouville	liouville	NOUN
ap-7652	61	29	potential	potential	NOUN
ap-7652	61	30	.	.	PUNCT
ap-7652	62	1	it	it	PRON
ap-7652	62	2	is	be	AUX
ap-7652	62	3	true	true	ADJ
ap-7652	62	4	that	that	SCONJ
ap-7652	62	5	the	the	DET
ap-7652	62	6	liouville	liouville	NOUN
ap-7652	62	7	transformation	transformation	NOUN
ap-7652	62	8	of	of	ADP
ap-7652	62	9	the	the	DET
ap-7652	62	10	tfi	tfi	PROPN
ap-7652	62	11	csle	csle	PROPN
ap-7652	62	12	results	result	VERB
ap-7652	62	13	in	in	ADP
ap-7652	62	14	a	a	DET
ap-7652	62	15	’	'	PUNCT
ap-7652	62	16	translationally	translationally	ADV
ap-7652	62	17	shape	shape	NOUN
ap-7652	62	18	-	-	PUNCT
ap-7652	62	19	invariant	invariant	ADJ
ap-7652	62	20	(	(	PUNCT
ap-7652	62	21	tsi	tsi	NOUN
ap-7652	62	22	)	)	PUNCT
ap-7652	62	23	potential	potential	NOUN
ap-7652	62	24	.	.	PUNCT
ap-7652	63	1	however	however	ADV
ap-7652	63	2	the	the	DET
ap-7652	63	3	class	class	NOUN
ap-7652	63	4	of	of	ADP
ap-7652	63	5	tfi	tfi	X
ap-7652	63	6	sles	sle	NOUN
ap-7652	63	7	is	be	AUX
ap-7652	63	8	defined	define	VERB
ap-7652	63	9	via	via	ADP
ap-7652	63	10	(	(	PUNCT
ap-7652	63	11	10	10	NUM
ap-7652	63	12	)	)	PUNCT
ap-7652	63	13	with	with	ADP
ap-7652	63	14	no	no	DET
ap-7652	63	15	reference	reference	NOUN
ap-7652	63	16	to	to	ADP
ap-7652	63	17	the	the	DET
ap-7652	63	18	associated	associated	ADJ
ap-7652	63	19	schrödinger	schrödinger	ADJ
ap-7652	63	20	equation	equation	NOUN
ap-7652	63	21	.	.	PUNCT
ap-7652	64	1	2.3	2.3	NUM
ap-7652	64	2	.	.	PUNCT
ap-7652	64	3	equivalence	equivalence	NOUN
ap-7652	64	4	theorem	theorem	VERB
ap-7652	64	5	for	for	ADP
ap-7652	64	6	darboux	darboux	ADJ
ap-7652	64	7	-	-	PUNCT
ap-7652	64	8	crum	crum	NOUN
ap-7652	64	9	transforms	transform	NOUN
ap-7652	64	10	of	of	ADP
ap-7652	64	11	a	a	DET
ap-7652	64	12	tfi	tfi	NOUN
ap-7652	64	13	csle	csle	NOUN
ap-7652	64	14	with	with	ADP
ap-7652	64	15	two	two	NUM
ap-7652	64	16	basic	basic	ADJ
ap-7652	64	17	solutions	solution	NOUN
ap-7652	64	18	it	it	PRON
ap-7652	64	19	has	have	AUX
ap-7652	64	20	been	be	AUX
ap-7652	64	21	proven	prove	VERB
ap-7652	64	22	[	[	X
ap-7652	64	23	23	23	NUM
ap-7652	64	24	]	]	PUNCT
ap-7652	64	25	that	that	SCONJ
ap-7652	64	26	any	any	DET
ap-7652	64	27	tfi	tfi	NOUN
ap-7652	64	28	csle	csle	NOUN
ap-7652	64	29	has	have	AUX
ap-7652	64	30	at	at	ADV
ap-7652	64	31	least	least	ADV
ap-7652	64	32	two	two	NUM
ap-7652	64	33	infinite	infinite	ADJ
ap-7652	64	34	sets	set	NOUN
ap-7652	64	35	of	of	ADP
ap-7652	64	36	solutions	solution	NOUN
ap-7652	64	37	ϕ±,m+1[ξ	ϕ±,m+1[ξ	NUM
ap-7652	64	38	;	;	PUNCT
ap-7652	64	39	⇀	⇀	NUM
ap-7652	65	1	a	a	DET
ap-7652	65	2	,	,	PUNCT
ap-7652	65	3	b	b	X
ap-7652	65	4	]	]	X
ap-7652	65	5	=	=	PUNCT
ap-7652	65	6	ρ−1/2[ξ]w	ρ−1/2[ξ]w	PROPN
ap-7652	65	7	[	[	X
ap-7652	65	8	ξ	ξ	X
ap-7652	65	9	;	;	PUNCT
ap-7652	65	10	⇀	⇀	NUM
ap-7652	65	11	a	a	DET
ap-7652	65	12	±	±	NUM
ap-7652	65	13	⇀	⇀	NUM
ap-7652	65	14	1	1	NUM
ap-7652	65	15	,	,	PUNCT
ap-7652	65	16	b	b	PROPN
ap-7652	66	1	|	|	ADV
ap-7652	66	2	∓	∓	PROPN
ap-7652	66	3	,	,	PUNCT
ap-7652	66	4	0	0	NUM
ap-7652	66	5	;	;	PUNCT
ap-7652	66	6	±,m]/ϕ±,0[ξ	±,m]/ϕ±,0[ξ	ADP
ap-7652	66	7	;	;	PUNCT
ap-7652	67	1	⇀	⇀	NUM
ap-7652	67	2	a	a	DET
ap-7652	67	3	±	±	NUM
ap-7652	67	4	⇀	⇀	NUM
ap-7652	67	5	1	1	NUM
ap-7652	67	6	,	,	PUNCT
ap-7652	67	7	b	b	NOUN
ap-7652	67	8	]	]	X
ap-7652	67	9	,	,	PUNCT
ap-7652	67	10	(	(	PUNCT
ap-7652	67	11	15	15	NUM
ap-7652	67	12	)	)	PUNCT
ap-7652	67	13	where	where	SCONJ
ap-7652	67	14	w	w	ADP
ap-7652	67	15	[	[	X
ap-7652	67	16	ξ	ξ	X
ap-7652	67	17	;	;	PUNCT
ap-7652	67	18	⇀	⇀	NUM
ap-7652	67	19	a	a	DET
ap-7652	67	20	,	,	PUNCT
ap-7652	67	21	b	b	PROPN
ap-7652	67	22	|	|	NOUN
ap-7652	67	23	±,m	±,m	NOUN
ap-7652	67	24	;	;	PUNCT
ap-7652	67	25	∓,m′	∓,m′	PROPN
ap-7652	67	26	]	]	PUNCT
ap-7652	68	1	≡	≡	PROPN
ap-7652	68	2	w	w	PROPN
ap-7652	68	3	{	{	PUNCT
ap-7652	68	4	ϕ±,m[ξ	ϕ±,m[ξ	ADV
ap-7652	68	5	;	;	PUNCT
ap-7652	68	6	⇀	⇀	NUM
ap-7652	68	7	a	a	PRON
ap-7652	68	8	,	,	PUNCT
ap-7652	68	9	b]ϕ∓,m′	b]ϕ∓,m′	NOUN
ap-7652	68	10	[	[	X
ap-7652	68	11	ξ	ξ	X
ap-7652	68	12	;	;	PUNCT
ap-7652	68	13	⇀	⇀	NUM
ap-7652	68	14	a	a	DET
ap-7652	68	15	,	,	PUNCT
ap-7652	68	16	b	b	NOUN
ap-7652	68	17	]	]	PUNCT
ap-7652	68	18	}	}	PUNCT
ap-7652	68	19	.	.	PUNCT
ap-7652	69	1	(	(	PUNCT
ap-7652	69	2	16	16	NUM
ap-7652	69	3	)	)	PUNCT
ap-7652	69	4	the	the	DET
ap-7652	69	5	cited	cite	VERB
ap-7652	69	6	‘	'	PUNCT
ap-7652	69	7	raising	raise	VERB
ap-7652	69	8	’	'	PUNCT
ap-7652	69	9	recurrence	recurrence	NOUN
ap-7652	69	10	relations	relation	NOUN
ap-7652	69	11	can	can	AUX
ap-7652	69	12	be	be	AUX
ap-7652	69	13	conveniently	conveniently	ADV
ap-7652	69	14	re	re	VERB
ap-7652	69	15	-	-	VERB
ap-7652	69	16	written	write	VERB
ap-7652	69	17	as	as	ADP
ap-7652	69	18	f±,m+1[ξ	f±,m+1[ξ	PRON
ap-7652	69	19	;	;	PUNCT
ap-7652	69	20	⇀	⇀	NUM
ap-7652	69	21	a	a	DET
ap-7652	69	22	±	±	NUM
ap-7652	69	23	⇀	⇀	NOUN
ap-7652	69	24	1	1	NUM
ap-7652	69	25	;	;	PUNCT
ap-7652	70	1	b	b	X
ap-7652	70	2	]	]	X
ap-7652	70	3	=	=	PUNCT
ap-7652	70	4	ḟ±,m[ξ	ḟ±,m[ξ	PROPN
ap-7652	70	5	;	;	PUNCT
ap-7652	70	6	⇀	⇀	NUM
ap-7652	70	7	a	a	DET
ap-7652	70	8	,	,	PUNCT
ap-7652	70	9	b	b	NOUN
ap-7652	70	10	]	]	X
ap-7652	70	11	,	,	PUNCT
ap-7652	70	12	(	(	PUNCT
ap-7652	70	13	17	17	NUM
ap-7652	70	14	)	)	PUNCT
ap-7652	70	15	where	where	SCONJ
ap-7652	70	16	f±,m+1[ξ	f±,m+1[ξ	NUM
ap-7652	70	17	;	;	PUNCT
ap-7652	70	18	⇀	⇀	NUM
ap-7652	70	19	a	a	DET
ap-7652	70	20	,	,	PUNCT
ap-7652	70	21	b	b	X
ap-7652	70	22	]	]	X
ap-7652	70	23	≡	≡	PROPN
ap-7652	70	24	ϕ±,m[ξ	ϕ±,m[ξ	PROPN
ap-7652	70	25	;	;	PUNCT
ap-7652	70	26	⇀	⇀	PROPN
ap-7652	70	27	a	a	PRON
ap-7652	70	28	,	,	PUNCT
ap-7652	70	29	b]/ϕ∓,0[ξ	b]/ϕ∓,0[ξ	PROPN
ap-7652	70	30	;	;	PUNCT
ap-7652	70	31	⇀	⇀	NUM
ap-7652	70	32	a	a	DET
ap-7652	70	33	,	,	PUNCT
ap-7652	70	34	b	b	AUX
ap-7652	70	35	]	]	X
ap-7652	70	36	(	(	PUNCT
ap-7652	70	37	18	18	NUM
ap-7652	70	38	)	)	PUNCT
ap-7652	70	39	and	and	CCONJ
ap-7652	70	40	dot	dot	NOUN
ap-7652	70	41	denotes	denote	NOUN
ap-7652	70	42	the	the	DET
ap-7652	70	43	first	first	ADJ
ap-7652	70	44	derivative	derivative	NOUN
ap-7652	70	45	with	with	ADP
ap-7652	70	46	respect	respect	NOUN
ap-7652	70	47	to	to	ADP
ap-7652	70	48	ξ	ξ	PROPN
ap-7652	70	49	.	.	PUNCT
ap-7652	71	1	the	the	DET
ap-7652	71	2	solutions	solution	NOUN
ap-7652	71	3	ϕ±,m[ξ	ϕ±,m[ξ	ADV
ap-7652	71	4	;	;	PUNCT
ap-7652	71	5	⇀	⇀	NUM
ap-7652	71	6	a	a	DET
ap-7652	71	7	,	,	PUNCT
ap-7652	71	8	b	b	AUX
ap-7652	71	9	]	]	PUNCT
ap-7652	71	10	also	also	ADV
ap-7652	71	11	obey	obey	VERB
ap-7652	71	12	the	the	DET
ap-7652	71	13	´	´	NOUN
ap-7652	71	14	lovering	lovering	ADJ
ap-7652	71	15	´	´	NOUN
ap-7652	71	16	recurrence	recurrence	NOUN
ap-7652	71	17	relations	relation	NOUN
ap-7652	71	18	:	:	PUNCT
ap-7652	71	19	ϕ±,m[ξ	ϕ±,m[ξ	ADV
ap-7652	71	20	;	;	PUNCT
ap-7652	71	21	⇀	⇀	NUM
ap-7652	71	22	a	a	DET
ap-7652	71	23	,	,	PUNCT
ap-7652	71	24	b	b	NOUN
ap-7652	71	25	]	]	X
ap-7652	71	26	≡	≡	PROPN
ap-7652	71	27	ρ−1/2[ξ]w[ξ	ρ−1/2[ξ]w[ξ	NUM
ap-7652	71	28	;	;	PUNCT
ap-7652	71	29	a	a	DET
ap-7652	71	30	,	,	PUNCT
ap-7652	71	31	b	b	PROPN
ap-7652	71	32	|	|	NOUN
ap-7652	71	33	±	±	NUM
ap-7652	71	34	...	...	PUNCT
ap-7652	71	35	0,m]/ϕ±,0[ξ	0,m]/ϕ±,0[ξ	NUM
ap-7652	71	36	;	;	PUNCT
ap-7652	71	37	⇀	⇀	NUM
ap-7652	71	38	a	a	DET
ap-7652	71	39	,	,	PUNCT
ap-7652	71	40	b	b	X
ap-7652	71	41	]	]	X
ap-7652	71	42	=	=	PUNCT
ap-7652	71	43	=	=	SYM
ap-7652	72	1	−e±,m−1	−e±,m−1	PROPN
ap-7652	72	2	(	(	PUNCT
ap-7652	72	3	⇀	⇀	DET
ap-7652	72	4	a	a	DET
ap-7652	72	5	±	±	NUM
ap-7652	72	6	⇀	⇀	NUM
ap-7652	72	7	1	1	NUM
ap-7652	72	8	,	,	PUNCT
ap-7652	72	9	b)ϕ±,m−1[ξ	b)ϕ±,m−1[ξ	NOUN
ap-7652	72	10	;	;	PUNCT
ap-7652	72	11	⇀	⇀	PROPN
ap-7652	72	12	a	a	DET
ap-7652	72	13	±	±	NUM
ap-7652	73	1	⇀	⇀	NOUN
ap-7652	73	2	1	1	NUM
ap-7652	73	3	;	;	PUNCT
ap-7652	73	4	⇀	⇀	PROPN
ap-7652	73	5	b	b	X
ap-7652	73	6	]	]	X
ap-7652	73	7	for	for	ADP
ap-7652	73	8	m	m	PROPN
ap-7652	73	9	≥	≥	NOUN
ap-7652	73	10	1	1	NUM
ap-7652	73	11	,	,	PUNCT
ap-7652	73	12	(	(	PUNCT
ap-7652	73	13	19	19	NUM
ap-7652	73	14	)	)	PUNCT
ap-7652	74	1	where	where	SCONJ
ap-7652	74	2	e±,m	e±,m	PROPN
ap-7652	74	3	(	(	PUNCT
ap-7652	74	4	⇀	⇀	PROPN
ap-7652	74	5	a	a	DET
ap-7652	74	6	,	,	PUNCT
ap-7652	74	7	b	b	NOUN
ap-7652	74	8	)	)	PUNCT
ap-7652	74	9	≡	≡	PROPN
ap-7652	74	10	ε±,m	ε±,m	PROPN
ap-7652	74	11	(	(	PUNCT
ap-7652	74	12	⇀	⇀	PROPN
ap-7652	74	13	a	a	DET
ap-7652	74	14	,	,	PUNCT
ap-7652	74	15	b	b	NOUN
ap-7652	74	16	)	)	PUNCT
ap-7652	74	17	−	−	PROPN
ap-7652	74	18	ε∓,0	ε∓,0	PROPN
ap-7652	74	19	(	(	PUNCT
ap-7652	74	20	⇀	⇀	PROPN
ap-7652	74	21	a	a	DET
ap-7652	74	22	,	,	PUNCT
ap-7652	74	23	b	b	NOUN
ap-7652	74	24	)	)	PUNCT
ap-7652	74	25	.	.	PUNCT
ap-7652	75	1	(	(	PUNCT
ap-7652	75	2	20	20	NUM
ap-7652	75	3	)	)	PUNCT
ap-7652	75	4	solutions	solution	NOUN
ap-7652	75	5	from	from	ADP
ap-7652	75	6	both	both	DET
ap-7652	75	7	infinite	infinite	ADJ
ap-7652	75	8	sets	set	NOUN
ap-7652	75	9	can	can	AUX
ap-7652	75	10	be	be	AUX
ap-7652	75	11	then	then	ADV
ap-7652	75	12	used	use	VERB
ap-7652	75	13	as	as	ADP
ap-7652	75	14	seed	seed	NOUN
ap-7652	75	15	functions	function	NOUN
ap-7652	75	16	for	for	ADP
ap-7652	75	17	darboux	darboux	ADJ
ap-7652	75	18	-	-	PUNCT
ap-7652	75	19	crum	crum	NOUN
ap-7652	75	20	transformations	transformation	NOUN
ap-7652	75	21	(	(	PUNCT
ap-7652	75	22	dcts	dct	NOUN
ap-7652	75	23	)	)	PUNCT
ap-7652	75	24	of	of	ADP
ap-7652	75	25	the	the	DET
ap-7652	75	26	given	give	VERB
ap-7652	75	27	tfi	tfi	NOUN
ap-7652	75	28	csle	csle	NOUN
ap-7652	75	29	which	which	PRON
ap-7652	75	30	results	result	VERB
ap-7652	75	31	in	in	ADP
ap-7652	75	32	an	an	DET
ap-7652	75	33	infinite	infinite	ADJ
ap-7652	75	34	net	net	NOUN
ap-7652	75	35	of	of	ADP
ap-7652	75	36	solvable	solvable	ADJ
ap-7652	75	37	sles	sle	NOUN
ap-7652	75	38	specified	specify	VERB
ap-7652	75	39	by	by	ADP
ap-7652	75	40	a	a	DET
ap-7652	75	41	single	single	ADJ
ap-7652	75	42	series	series	NOUN
ap-7652	75	43	of	of	ADP
ap-7652	75	44	maya	maya	PROPN
ap-7652	75	45	102	102	NUM
ap-7652	75	46	vol	vol	NOUN
ap-7652	75	47	.	.	PUNCT
ap-7652	76	1	62	62	NUM
ap-7652	76	2	no	no	INTJ
ap-7652	76	3	.	.	PUNCT
ap-7652	77	1	1/2022	1/2022	NUM
ap-7652	77	2	quantization	quantization	NOUN
ap-7652	77	3	of	of	ADP
ap-7652	77	4	rationally	rationally	ADV
ap-7652	77	5	deformed	deform	VERB
ap-7652	77	6	morse	morse	ADJ
ap-7652	77	7	potentials	potential	NOUN
ap-7652	77	8	.	.	PUNCT
ap-7652	77	9	.	.	PUNCT
ap-7652	77	10	.	.	PUNCT
ap-7652	78	1	diagrams	diagram	NOUN
ap-7652	79	1	[	[	X
ap-7652	79	2	24	24	NUM
ap-7652	79	3	]	]	PUNCT
ap-7652	79	4	.	.	PUNCT
ap-7652	80	1	following	follow	VERB
ap-7652	80	2	the	the	DET
ap-7652	80	3	arguments	argument	NOUN
ap-7652	80	4	presented	present	VERB
ap-7652	80	5	in	in	ADP
ap-7652	80	6	[	[	X
ap-7652	80	7	33	33	NUM
ap-7652	80	8	]	]	PUNCT
ap-7652	80	9	for	for	ADP
ap-7652	80	10	rationally	rationally	ADV
ap-7652	80	11	deformed	deform	VERB
ap-7652	80	12	tsi	tsi	PROPN
ap-7652	80	13	potentials	potential	VERB
ap-7652	80	14	we	we	PRON
ap-7652	80	15	[	[	X
ap-7652	80	16	23	23	NUM
ap-7652	80	17	]	]	PUNCT
ap-7652	80	18	proved	prove	VERB
ap-7652	80	19	that	that	SCONJ
ap-7652	80	20	any	any	DET
ap-7652	80	21	csle	csle	NOUN
ap-7652	80	22	in	in	ADP
ap-7652	80	23	this	this	DET
ap-7652	80	24	net	net	NOUN
ap-7652	80	25	can	can	AUX
ap-7652	80	26	obtained	obtain	VERB
ap-7652	80	27	using	use	VERB
ap-7652	80	28	only	only	ADJ
ap-7652	80	29	seed	seed	NOUN
ap-7652	80	30	solutions	solution	NOUN
ap-7652	80	31	of	of	ADP
ap-7652	80	32	the	the	DET
ap-7652	80	33	same	same	ADJ
ap-7652	80	34	type	type	NOUN
ap-7652	80	35	.	.	PUNCT
ap-7652	81	1	let	let	VERB
ap-7652	81	2	us	we	PRON
ap-7652	81	3	parametrize	parametrize	VERB
ap-7652	81	4	a	a	DET
ap-7652	81	5	set	set	NOUN
ap-7652	81	6	of	of	ADP
ap-7652	81	7	seed	seed	NOUN
ap-7652	81	8	functions	function	NOUN
ap-7652	81	9	of	of	ADP
ap-7652	81	10	the	the	DET
ap-7652	81	11	same	same	ADJ
ap-7652	81	12	type	type	NOUN
ap-7652	81	13	,	,	PUNCT
ap-7652	81	14	m(∆1→l	m(∆1→l	PROPN
ap-7652	81	15	)	)	PUNCT
ap-7652	81	16	=	=	SYM
ap-7652	81	17	m1	m1	NOUN
ap-7652	81	18	,	,	PUNCT
ap-7652	81	19	.	.	PUNCT
ap-7652	81	20	.	.	PUNCT
ap-7652	82	1	.	.	PUNCT
ap-7652	83	1	,	,	PUNCT
ap-7652	83	2	m|δ1→l|	m|δ1→l|	PROPN
ap-7652	83	3	,	,	PUNCT
ap-7652	83	4	(	(	PUNCT
ap-7652	83	5	21	21	NUM
ap-7652	83	6	)	)	PUNCT
ap-7652	83	7	by	by	ADP
ap-7652	83	8	two	two	NUM
ap-7652	83	9	partitions	partition	NOUN
ap-7652	83	10	of	of	ADP
ap-7652	83	11	an	an	DET
ap-7652	83	12	equal	equal	ADJ
ap-7652	83	13	size	size	NOUN
ap-7652	83	14	l	l	NOUN
ap-7652	83	15	:	:	PUNCT
ap-7652	83	16	∆1→l	∆1→l	PROPN
ap-7652	83	17	≡	≡	PROPN
ap-7652	83	18	δ1→l	δ1→l	PROPN
ap-7652	83	19	;	;	PUNCT
ap-7652	83	20	δ′1→l	δ′1→l	PROPN
ap-7652	83	21	(	(	PUNCT
ap-7652	83	22	22	22	NUM
ap-7652	83	23	)	)	PUNCT
ap-7652	83	24	such	such	ADJ
ap-7652	83	25	that	that	SCONJ
ap-7652	83	26	mk	mk	NOUN
ap-7652	83	27	=	=	PUNCT
ap-7652	83	28	δ′	δ′	PROPN
ap-7652	83	29	1	1	NUM
ap-7652	84	1	+	+	CCONJ
ap-7652	84	2	k	k	PROPN
ap-7652	84	3	−	−	NOUN
ap-7652	84	4	1	1	NUM
ap-7652	84	5	for	for	ADP
ap-7652	84	6	1	1	NUM
ap-7652	84	7	<	<	X
ap-7652	84	8	k	k	PROPN
ap-7652	84	9	≤	≤	PROPN
ap-7652	84	10	δ1	δ1	NOUN
ap-7652	84	11	,	,	PUNCT
ap-7652	84	12	(	(	PUNCT
ap-7652	84	13	23	23	NUM
ap-7652	84	14	)	)	PUNCT
ap-7652	84	15	m|δ1→l−1|+1	m|δ1→l−1|+1	PROPN
ap-7652	84	16	=	=	SYM
ap-7652	84	17	m|δ1→l−1|	m|δ1→l−1|	PROPN
ap-7652	84	18	+	+	CCONJ
ap-7652	84	19	δ′	δ′	PROPN
ap-7652	84	20	l	l	NOUN
ap-7652	85	1	+	+	CCONJ
ap-7652	85	2	1	1	NUM
ap-7652	85	3	=	=	SYM
ap-7652	85	4	|	|	NOUN
ap-7652	85	5	∆1→l−1	∆1→l−1	VERB
ap-7652	85	6	|	|	ADV
ap-7652	85	7	+	+	NOUN
ap-7652	85	8	δ′	δ′	NOUN
ap-7652	85	9	l	l	NOUN
ap-7652	86	1	+	+	CCONJ
ap-7652	86	2	1	1	NUM
ap-7652	86	3	for	for	ADP
ap-7652	86	4	1	1	NUM
ap-7652	86	5	<	<	X
ap-7652	86	6	l	l	NOUN
ap-7652	86	7	≤	≤	PROPN
ap-7652	86	8	l	l	NOUN
ap-7652	86	9	,	,	PUNCT
ap-7652	86	10	(	(	PUNCT
ap-7652	86	11	24	24	NUM
ap-7652	86	12	)	)	PUNCT
ap-7652	86	13	m|δ1→l−1|+k	m|δ1→l−1|+k	PROPN
ap-7652	86	14	=	=	SYM
ap-7652	86	15	m|δ1→l−1|+1	m|δ1→l−1|+1	PROPN
ap-7652	87	1	+	+	CCONJ
ap-7652	87	2	k	k	PROPN
ap-7652	88	1	−	−	PROPN
ap-7652	88	2	1	1	NUM
ap-7652	88	3	for	for	ADP
ap-7652	88	4	1	1	NUM
ap-7652	88	5	<	<	X
ap-7652	88	6	l	l	NOUN
ap-7652	88	7	≤	≤	PROPN
ap-7652	88	8	l	l	NOUN
ap-7652	88	9	,	,	PUNCT
ap-7652	88	10	1	1	NUM
ap-7652	88	11	<	<	X
ap-7652	88	12	k	k	PROPN
ap-7652	88	13	≤	≤	PROPN
ap-7652	88	14	δl	δl	X
ap-7652	88	15	,	,	PUNCT
ap-7652	88	16	(	(	PUNCT
ap-7652	88	17	25	25	NUM
ap-7652	88	18	)	)	PUNCT
ap-7652	88	19	one	one	NOUN
ap-7652	88	20	can	can	AUX
ap-7652	88	21	easily	easily	ADV
ap-7652	88	22	verify	verify	VERB
ap-7652	88	23	that	that	SCONJ
ap-7652	88	24	the	the	DET
ap-7652	88	25	largest	large	ADJ
ap-7652	88	26	element	element	NOUN
ap-7652	88	27	in	in	ADP
ap-7652	88	28	partition	partition	NOUN
ap-7652	88	29	(	(	PUNCT
ap-7652	88	30	21	21	NUM
ap-7652	88	31	)	)	PUNCT
ap-7652	88	32	coincides	coincide	VERB
ap-7652	88	33	with	with	ADP
ap-7652	88	34	the	the	DET
ap-7652	88	35	sum	sum	NOUN
ap-7652	88	36	of	of	ADP
ap-7652	88	37	the	the	DET
ap-7652	88	38	partition	partition	NOUN
ap-7652	88	39	lengths	length	NOUN
ap-7652	88	40	|	|	ADV
ap-7652	88	41	δ1→l	δ1→l	NOUN
ap-7652	89	1	|	|	ADV
ap-7652	89	2	and	and	CCONJ
ap-7652	89	3	|	|	ADV
ap-7652	89	4	δ′1→l	δ′1→l	PROPN
ap-7652	89	5	|	|	PROPN
ap-7652	89	6	,	,	PUNCT
ap-7652	89	7	i.e.	i.e.	X
ap-7652	89	8	,	,	PUNCT
ap-7652	89	9	m|δ1→l|	m|δ1→l|	PROPN
ap-7652	89	10	=|	=|	NOUN
ap-7652	89	11	∆1→l	∆1→l	NOUN
ap-7652	89	12	|≡|	|≡|	ADP
ap-7652	89	13	δ1→l	δ1→l	X
ap-7652	90	1	|	|	ADV
ap-7652	91	1	+	+	CCONJ
ap-7652	91	2	|	|	ADV
ap-7652	91	3	δ′1→l	δ′1→l	PROPN
ap-7652	91	4	|	|	ADV
ap-7652	91	5	.	.	PUNCT
ap-7652	92	1	(	(	PUNCT
ap-7652	92	2	26	26	NUM
ap-7652	92	3	)	)	PUNCT
ap-7652	92	4	it	it	PRON
ap-7652	92	5	has	have	AUX
ap-7652	92	6	been	be	AUX
ap-7652	92	7	proved	prove	VERB
ap-7652	92	8	in	in	ADP
ap-7652	92	9	[	[	X
ap-7652	92	10	23	23	NUM
ap-7652	92	11	]	]	PUNCT
ap-7652	92	12	that	that	SCONJ
ap-7652	92	13	use	use	NOUN
ap-7652	92	14	of	of	ADP
ap-7652	92	15	the	the	DET
ap-7652	92	16	conjugated	conjugated	ADJ
ap-7652	92	17	set	set	NOUN
ap-7652	92	18	of	of	ADP
ap-7652	92	19	seed	seed	NOUN
ap-7652	92	20	solutions	solution	NOUN
ap-7652	92	21	of	of	ADP
ap-7652	92	22	opposite	opposite	ADJ
ap-7652	92	23	type	type	NOUN
ap-7652	92	24	,	,	PUNCT
ap-7652	92	25	∆′	∆′	PROPN
ap-7652	92	26	l→1	l→1	PROPN
ap-7652	92	27	≡	≡	PROPN
ap-7652	92	28	δ′	δ′	PROPN
ap-7652	92	29	l→1	l→1	PROPN
ap-7652	92	30	;	;	PUNCT
ap-7652	92	31	δl→1	δl→1	PROPN
ap-7652	92	32	≡	≡	PROPN
ap-7652	92	33	δ′	δ′	PROPN
ap-7652	92	34	l	l	PROPN
ap-7652	92	35	,	,	PUNCT
ap-7652	92	36	δ	δ	PROPN
ap-7652	92	37	′	′	NUM
ap-7652	92	38	l−1	l−1	NOUN
ap-7652	92	39	,	,	PUNCT
ap-7652	92	40	.	.	PUNCT
ap-7652	92	41	.	.	PUNCT
ap-7652	93	1	.	.	PUNCT
ap-7652	94	1	,	,	PUNCT
ap-7652	94	2	δ	δ	PROPN
ap-7652	94	3	′	′	NOUN
ap-7652	94	4	1	1	NUM
ap-7652	94	5	;	;	PUNCT
ap-7652	94	6	δl	δl	X
ap-7652	94	7	,	,	PUNCT
ap-7652	94	8	δl−1	δl−1	PROPN
ap-7652	94	9	,	,	PUNCT
ap-7652	94	10	.	.	PUNCT
ap-7652	94	11	.	.	PUNCT
ap-7652	95	1	.	.	PUNCT
ap-7652	96	1	,	,	PUNCT
ap-7652	96	2	δ1	δ1	NOUN
ap-7652	96	3	,	,	PUNCT
ap-7652	96	4	(	(	PUNCT
ap-7652	96	5	27	27	NUM
ap-7652	96	6	)	)	PUNCT
ap-7652	96	7	results	result	NOUN
ap-7652	96	8	in	in	ADP
ap-7652	96	9	an	an	DET
ap-7652	96	10	equivalent	equivalent	ADJ
ap-7652	96	11	csle	csle	NOUN
ap-7652	97	1	so	so	SCONJ
ap-7652	97	2	the	the	DET
ap-7652	97	3	corresponding	corresponding	ADJ
ap-7652	97	4	liouville	liouville	NOUN
ap-7652	97	5	potential	potential	NOUN
ap-7652	97	6	v	v	ADP
ap-7652	97	7	[	[	X
ap-7652	97	8	ξ	ξ	X
ap-7652	97	9	;	;	PUNCT
ap-7652	97	10	⇀	⇀	NUM
ap-7652	97	11	a	a	DET
ap-7652	97	12	(	(	PUNCT
ap-7652	97	13	δ	δ	NOUN
ap-7652	97	14	)	)	PUNCT
ap-7652	97	15	,	,	PUNCT
ap-7652	98	1	b	b	X
ap-7652	98	2	|	|	ADV
ap-7652	98	3	∓,m(∆′	∓,m(∆′	NOUN
ap-7652	98	4	l→1	l→1	NOUN
ap-7652	98	5	)	)	PUNCT
ap-7652	98	6	]	]	PUNCT
ap-7652	98	7	computed	compute	VERB
ap-7652	98	8	at	at	ADP
ap-7652	98	9	shifted	shift	VERB
ap-7652	98	10	values	value	NOUN
ap-7652	98	11	of	of	ADP
ap-7652	98	12	the	the	DET
ap-7652	98	13	translational	translational	ADJ
ap-7652	98	14	parameters	parameter	NOUN
ap-7652	98	15	,	,	PUNCT
ap-7652	98	16	⇀	⇀	PROPN
ap-7652	98	17	a	a	PRON
ap-7652	98	18	(	(	PUNCT
ap-7652	98	19	δ	δ	NOUN
ap-7652	98	20	)	)	PUNCT
ap-7652	98	21	≡	≡	PROPN
ap-7652	99	1	⇀	⇀	PROPN
ap-7652	100	1	a	a	DET
ap-7652	100	2	+	+	NOUN
ap-7652	100	3	δ	δ	NOUN
ap-7652	100	4	⇀	⇀	NOUN
ap-7652	100	5	1	1	NUM
ap-7652	100	6	,	,	PUNCT
ap-7652	100	7	(	(	PUNCT
ap-7652	100	8	28	28	NUM
ap-7652	100	9	)	)	PUNCT
ap-7652	100	10	where	where	SCONJ
ap-7652	100	11	δ	δ	PROPN
ap-7652	100	12	is	be	AUX
ap-7652	100	13	a	a	DET
ap-7652	100	14	nonzero	nonzero	NOUN
ap-7652	100	15	integer	integer	NOUN
ap-7652	100	16	,	,	PUNCT
ap-7652	100	17	differs	differ	VERB
ap-7652	100	18	from	from	ADP
ap-7652	100	19	the	the	DET
ap-7652	100	20	liouville	liouville	NOUN
ap-7652	100	21	potential	potential	NOUN
ap-7652	100	22	v	v	ADP
ap-7652	100	23	[	[	X
ap-7652	100	24	ξ	ξ	X
ap-7652	100	25	;	;	PUNCT
ap-7652	100	26	⇀	⇀	NUM
ap-7652	100	27	a	a	PRON
ap-7652	100	28	,	,	PUNCT
ap-7652	100	29	b	b	PROPN
ap-7652	100	30	|	|	ADV
ap-7652	100	31	±,m(∆′1→l	±,m(∆′1→l	NOUN
ap-7652	100	32	)	)	PUNCT
ap-7652	100	33	]	]	PUNCT
ap-7652	100	34	only	only	ADV
ap-7652	100	35	by	by	ADP
ap-7652	100	36	a	a	DET
ap-7652	100	37	zero	zero	NUM
ap-7652	100	38	-	-	PUNCT
ap-7652	100	39	point	point	NOUN
ap-7652	100	40	energy	energy	NOUN
ap-7652	100	41	.	.	PUNCT
ap-7652	101	1	in	in	ADP
ap-7652	101	2	[	[	X
ap-7652	101	3	23	23	NUM
ap-7652	101	4	]	]	PUNCT
ap-7652	101	5	we	we	PRON
ap-7652	101	6	have	have	AUX
ap-7652	101	7	derived	derive	VERB
ap-7652	101	8	the	the	DET
ap-7652	101	9	following	follow	VERB
ap-7652	101	10	relation	relation	NOUN
ap-7652	101	11	between	between	ADP
ap-7652	101	12	the	the	DET
ap-7652	101	13	wronskians	wronskian	NOUN
ap-7652	101	14	of	of	ADP
ap-7652	101	15	two	two	NUM
ap-7652	101	16	equivalent	equivalent	ADJ
ap-7652	101	17	sets	set	NOUN
ap-7652	101	18	of	of	ADP
ap-7652	101	19	seed	seed	NOUN
ap-7652	101	20	solutions	solution	NOUN
ap-7652	101	21	of	of	ADP
ap-7652	101	22	the	the	DET
ap-7652	101	23	same	same	ADJ
ap-7652	101	24	type	type	NOUN
ap-7652	101	25	w[ξ	w[ξ	NOUN
ap-7652	101	26	;	;	PUNCT
ap-7652	102	1	⇀	⇀	NUM
ap-7652	102	2	a	a	PRON
ap-7652	102	3	,	,	PUNCT
ap-7652	102	4	b	b	NOUN
ap-7652	103	1	|	|	NOUN
ap-7652	103	2	+	+	CCONJ
ap-7652	103	3	...	...	PUNCT
ap-7652	103	4	m(∆1→l	m(∆1→l	PROPN
ap-7652	103	5	)	)	PUNCT
ap-7652	103	6	]	]	PUNCT
ap-7652	104	1	ρ1/4|δ1→l|(|δ1→l|−1)[ξ	ρ1/4|δ1→l|(|δ1→l|−1)[ξ	NUM
ap-7652	104	2	]	]	PUNCT
ap-7652	104	3	l∏	l∏	PROPN
ap-7652	105	1	l=1	l=1	X
ap-7652	106	1	χ−δl	χ−δl	ADJ
ap-7652	106	2	[	[	X
ap-7652	106	3	ξ	ξ	X
ap-7652	106	4	;	;	PUNCT
ap-7652	106	5	⇀	⇀	NUM
ap-7652	106	6	a	a	PRON
ap-7652	106	7	(	(	PUNCT
ap-7652	106	8	|∆′	|∆′	X
ap-7652	106	9	l→1|−δl	l→1|−δl	PROPN
ap-7652	106	10	)	)	PUNCT
ap-7652	106	11	,	,	PUNCT
ap-7652	106	12	b	b	X
ap-7652	106	13	]	]	X
ap-7652	106	14	∝	∝	PROPN
ap-7652	106	15	w[ξ	w[ξ	NOUN
ap-7652	106	16	;	;	PUNCT
ap-7652	106	17	⇀	⇀	NUM
ap-7652	106	18	a	a	PRON
ap-7652	106	19	(	(	PUNCT
ap-7652	106	20	|∆′	|∆′	X
ap-7652	106	21	l→1|	l→1|	NOUN
ap-7652	106	22	)	)	PUNCT
ap-7652	106	23	,	,	PUNCT
ap-7652	106	24	b	b	X
ap-7652	106	25	|	|	ADV
ap-7652	106	26	−	−	PROPN
ap-7652	106	27	...	...	PUNCT
ap-7652	106	28	m(∆′	m(∆′	NOUN
ap-7652	106	29	l→1	l→1	NOUN
ap-7652	106	30	)	)	PUNCT
ap-7652	106	31	]	]	PUNCT
ap-7652	107	1	ρ1/4|δ′	ρ1/4|δ′	NUM
ap-7652	107	2	l→1|(|δ′	l→1|(|δ′	NOUN
ap-7652	107	3	l→1|−1)[ξ	l→1|−1)[ξ	PROPN
ap-7652	107	4	]	]	PUNCT
ap-7652	108	1	l∏	l∏	NOUN
ap-7652	109	1	l=1	l=1	PROPN
ap-7652	109	2	χδl	χδl	VERB
ap-7652	109	3	[	[	X
ap-7652	109	4	ξ	ξ	X
ap-7652	109	5	;	;	PUNCT
ap-7652	109	6	⇀	⇀	NUM
ap-7652	110	1	a	a	DET
ap-7652	110	2	(	(	PUNCT
ap-7652	110	3	|∆′	|∆′	X
ap-7652	110	4	l−1→1|+δ′	l−1→1|+δ′	NUM
ap-7652	110	5	l	l	NOUN
ap-7652	110	6	)	)	PUNCT
ap-7652	110	7	,	,	PUNCT
ap-7652	110	8	b	b	X
ap-7652	110	9	]	]	X
ap-7652	110	10	,	,	PUNCT
ap-7652	110	11	(	(	PUNCT
ap-7652	110	12	29	29	NUM
ap-7652	110	13	)	)	PUNCT
ap-7652	110	14	where	where	SCONJ
ap-7652	110	15	χ∓|n	χ∓|n	PROPN
ap-7652	110	16	|[ξ	|[ξ	NOUN
ap-7652	110	17	;	;	PUNCT
ap-7652	110	18	⇀	⇀	NUM
ap-7652	110	19	a	a	PRON
ap-7652	110	20	,	,	PUNCT
ap-7652	110	21	b	b	NOUN
ap-7652	110	22	]	]	X
ap-7652	110	23	≡	≡	PROPN
ap-7652	110	24	|n	|n	NOUN
ap-7652	110	25	|−1∏	|−1∏	ADP
ap-7652	110	26	k=0	k=0	PROPN
ap-7652	110	27	ϕ±,0[ξ	ϕ±,0[ξ	PROPN
ap-7652	110	28	;	;	PUNCT
ap-7652	111	1	⇀	⇀	NUM
ap-7652	111	2	a	a	PRON
ap-7652	111	3	(	(	PUNCT
ap-7652	111	4	±k	±k	NOUN
ap-7652	111	5	)	)	PUNCT
ap-7652	111	6	,	,	PUNCT
ap-7652	111	7	b	b	X
ap-7652	111	8	]	]	X
ap-7652	111	9	.	.	PUNCT
ap-7652	112	1	(	(	PUNCT
ap-7652	112	2	30	30	NUM
ap-7652	112	3	)	)	PUNCT
ap-7652	112	4	for	for	ADP
ap-7652	112	5	any	any	DET
ap-7652	112	6	csle	csle	NOUN
ap-7652	112	7	from	from	ADP
ap-7652	112	8	group	group	PROPN
ap-7652	112	9	a	a	DET
ap-7652	112	10	the	the	DET
ap-7652	112	11	derived	derive	VERB
ap-7652	112	12	relation	relation	NOUN
ap-7652	112	13	turns	turn	VERB
ap-7652	112	14	into	into	ADP
ap-7652	112	15	the	the	DET
ap-7652	112	16	equivalence	equivalence	NOUN
ap-7652	112	17	relations	relation	NOUN
ap-7652	112	18	between	between	ADP
ap-7652	112	19	the	the	DET
ap-7652	112	20	wronskians	wronskian	NOUN
ap-7652	112	21	of	of	ADP
ap-7652	112	22	the	the	DET
ap-7652	112	23	corresponding	corresponding	ADJ
ap-7652	112	24	seed	seed	NOUN
ap-7652	112	25	polynomials	polynomial	NOUN
ap-7652	112	26	discovered	discover	VERB
ap-7652	112	27	in	in	ADP
ap-7652	112	28	the	the	DET
ap-7652	112	29	breakthrough	breakthrough	NOUN
ap-7652	112	30	paper	paper	NOUN
ap-7652	112	31	by	by	ADP
ap-7652	112	32	odake	odake	NOUN
ap-7652	112	33	and	and	CCONJ
ap-7652	112	34	sasaki	sasaki	PROPN
ap-7652	112	35	[	[	X
ap-7652	112	36	19	19	NUM
ap-7652	112	37	]	]	PUNCT
ap-7652	112	38	.	.	PUNCT
ap-7652	113	1	we	we	PRON
ap-7652	113	2	illuminate	illuminate	VERB
ap-7652	113	3	these	these	DET
ap-7652	113	4	relations	relation	NOUN
ap-7652	113	5	in	in	ADP
ap-7652	113	6	more	more	ADJ
ap-7652	113	7	details	detail	NOUN
ap-7652	113	8	in	in	ADP
ap-7652	113	9	subsection	subsection	NOUN
ap-7652	113	10	3.4	3.4	NUM
ap-7652	113	11	below	below	ADP
ap-7652	113	12	using	use	VERB
ap-7652	113	13	wronskians	wronskian	NOUN
ap-7652	113	14	of	of	ADP
ap-7652	113	15	generalized	generalized	ADJ
ap-7652	113	16	bessel	bessel	ADJ
ap-7652	113	17	polynomials	polynomial	NOUN
ap-7652	113	18	as	as	ADP
ap-7652	113	19	an	an	DET
ap-7652	113	20	example	example	NOUN
ap-7652	113	21	.	.	PUNCT
ap-7652	114	1	if	if	SCONJ
ap-7652	114	2	the	the	DET
ap-7652	114	3	given	give	VERB
ap-7652	114	4	rational	rational	ADJ
ap-7652	114	5	tsi	tsi	PROPN
ap-7652	114	6	potential	potential	NOUN
ap-7652	114	7	has	have	VERB
ap-7652	114	8	only	only	ADV
ap-7652	114	9	a	a	DET
ap-7652	114	10	finite	finite	ADJ
ap-7652	114	11	number	number	NOUN
ap-7652	114	12	of	of	ADP
ap-7652	114	13	eigenfunctions	eigenfunction	NOUN
ap-7652	114	14	then	then	ADV
ap-7652	114	15	the	the	DET
ap-7652	114	16	set	set	NOUN
ap-7652	114	17	of	of	ADP
ap-7652	114	18	seed	seed	NOUN
ap-7652	114	19	functions	function	NOUN
ap-7652	114	20	+	+	PROPN
ap-7652	114	21	,	,	PUNCT
ap-7652	114	22	m	m	VERB
ap-7652	114	23	or	or	CCONJ
ap-7652	114	24	−,m	−,m	PRON
ap-7652	114	25	which	which	PRON
ap-7652	114	26	starts	start	VERB
ap-7652	114	27	from	from	ADP
ap-7652	114	28	these	these	DET
ap-7652	114	29	eigenfunctions	eigenfunction	NOUN
ap-7652	114	30	(	(	PUNCT
ap-7652	114	31	−,m	−,m	VERB
ap-7652	114	32	in	in	ADP
ap-7652	114	33	case	case	NOUN
ap-7652	114	34	of	of	ADP
ap-7652	114	35	our	our	PRON
ap-7652	114	36	current	current	ADJ
ap-7652	114	37	interest	interest	NOUN
ap-7652	114	38	)	)	PUNCT
ap-7652	114	39	also	also	ADV
ap-7652	114	40	contains	contain	VERB
ap-7652	114	41	infinitely	infinitely	ADV
ap-7652	114	42	many	many	ADJ
ap-7652	114	43	q	q	ADJ
ap-7652	114	44	-	-	ADJ
ap-7652	114	45	rss	rss	NOUN
ap-7652	114	46	vanishing	vanishing	NOUN
ap-7652	114	47	at	at	ADP
ap-7652	114	48	only	only	ADV
ap-7652	114	49	one	one	NUM
ap-7652	114	50	quantization	quantization	NOUN
ap-7652	114	51	end	end	NOUN
ap-7652	114	52	(	(	PUNCT
ap-7652	114	53	virtual	virtual	ADJ
ap-7652	114	54	state	state	NOUN
ap-7652	114	55	wavefunctions	wavefunction	NOUN
ap-7652	114	56	in	in	ADP
ap-7652	114	57	odake	odake	NOUN
ap-7652	114	58	and	and	CCONJ
ap-7652	114	59	sasaki	sasaki	PROPN
ap-7652	114	60	’s	’s	PART
ap-7652	114	61	terms	term	NOUN
ap-7652	114	62	[	[	X
ap-7652	114	63	18	18	NUM
ap-7652	114	64	,	,	PUNCT
ap-7652	114	65	19	19	NUM
ap-7652	114	66	]	]	PUNCT
ap-7652	114	67	)	)	PUNCT
ap-7652	114	68	,	,	PUNCT
ap-7652	114	69	with	with	ADP
ap-7652	114	70	the	the	DET
ap-7652	114	71	gendenshtein	gendenshtein	NOUN
ap-7652	114	72	(	(	PUNCT
ap-7652	114	73	scarf	scarf	PROPN
ap-7652	114	74	ii	ii	NOUN
ap-7652	114	75	)	)	PUNCT
ap-7652	114	76	potential	potential	NOUN
ap-7652	114	77	[	[	X
ap-7652	114	78	34	34	NUM
ap-7652	114	79	]	]	PUNCT
ap-7652	114	80	as	as	ADP
ap-7652	114	81	the	the	DET
ap-7652	114	82	sole	sole	ADJ
ap-7652	114	83	exception	exception	NOUN
ap-7652	114	84	(	(	PUNCT
ap-7652	114	85	including	include	VERB
ap-7652	114	86	its	its	PRON
ap-7652	114	87	symmetric	symmetric	ADJ
ap-7652	114	88	limit	limit	NOUN
ap-7652	114	89	represented	represent	VERB
ap-7652	114	90	by	by	ADP
ap-7652	114	91	the	the	DET
ap-7652	114	92	sech	sech	NOUN
ap-7652	114	93	-	-	PUNCT
ap-7652	114	94	squared	square	VERB
ap-7652	114	95	potential	potential	NOUN
ap-7652	114	96	well	well	NOUN
ap-7652	114	97	)	)	PUNCT
ap-7652	114	98	.	.	PUNCT
ap-7652	115	1	the	the	DET
ap-7652	115	2	dcts	dct	NOUN
ap-7652	115	3	using	use	VERB
ap-7652	115	4	nodeless	nodeless	ADJ
ap-7652	115	5	q	q	NOUN
ap-7652	115	6	-	-	NOUN
ap-7652	115	7	rss	rss	NOUN
ap-7652	115	8	of	of	ADP
ap-7652	115	9	the	the	DET
ap-7652	115	10	selected	select	VERB
ap-7652	115	11	type	type	NOUN
ap-7652	115	12	results	result	NOUN
ap-7652	115	13	in	in	ADP
ap-7652	115	14	a	a	DET
ap-7652	115	15	net	net	NOUN
ap-7652	115	16	of	of	ADP
ap-7652	115	17	isospectral	isospectral	ADJ
ap-7652	115	18	potentials	potential	NOUN
ap-7652	115	19	.	.	PUNCT
ap-7652	116	1	therefore	therefore	ADV
ap-7652	116	2	,	,	PUNCT
ap-7652	116	3	except	except	SCONJ
ap-7652	116	4	for	for	ADP
ap-7652	116	5	the	the	DET
ap-7652	116	6	gendenshtein	gendenshtein	ADJ
ap-7652	116	7	potential	potential	NOUN
ap-7652	116	8	,	,	PUNCT
ap-7652	116	9	we	we	PRON
ap-7652	116	10	do	do	AUX
ap-7652	116	11	n’t	not	PART
ap-7652	116	12	need	need	VERB
ap-7652	116	13	to	to	PART
ap-7652	116	14	include	include	VERB
ap-7652	116	15	‘	'	PUNCT
ap-7652	116	16	state	state	NOUN
ap-7652	116	17	-	-	PUNCT
ap-7652	116	18	inserting	insert	VERB
ap-7652	116	19	‘	'	PUNCT
ap-7652	116	20	solutions	solution	NOUN
ap-7652	116	21	(	(	PUNCT
ap-7652	116	22	’	'	PUNCT
ap-7652	116	23	pseudo	pseudo	NOUN
ap-7652	116	24	-	-	ADJ
ap-7652	116	25	virtual	virtual	ADJ
ap-7652	116	26	state	state	NOUN
ap-7652	116	27	wave	wave	NOUN
ap-7652	116	28	functions	function	NOUN
ap-7652	116	29	’	'	PUNCT
ap-7652	116	30	in	in	ADP
ap-7652	116	31	odake	odake	NOUN
ap-7652	116	32	and	and	CCONJ
ap-7652	116	33	sasaki	sasaki	PROPN
ap-7652	116	34	’s	’s	PART
ap-7652	116	35	terms	term	NOUN
ap-7652	116	36	)	)	PUNCT
ap-7652	116	37	into	into	ADP
ap-7652	116	38	the	the	DET
ap-7652	116	39	given	give	VERB
ap-7652	116	40	set	set	NOUN
ap-7652	116	41	of	of	ADP
ap-7652	116	42	seed	seed	NOUN
ap-7652	116	43	functions	function	NOUN
ap-7652	116	44	–	–	PUNCT
ap-7652	116	45	a	a	DET
ap-7652	116	46	remarkable	remarkable	ADJ
ap-7652	116	47	corollary	corollary	NOUN
ap-7652	116	48	of	of	ADP
ap-7652	116	49	the	the	DET
ap-7652	116	50	‘	'	PUNCT
ap-7652	116	51	extended	extended	ADJ
ap-7652	116	52	’	'	PUNCT
ap-7652	116	53	krein	krein	NOUN
ap-7652	116	54	-	-	PUNCT
ap-7652	116	55	adler	adler	PROPN
ap-7652	116	56	theorem	theorem	VERB
ap-7652	116	57	[	[	PUNCT
ap-7652	116	58	11	11	NUM
ap-7652	116	59	]	]	PUNCT
ap-7652	116	60	.	.	PUNCT
ap-7652	117	1	if	if	SCONJ
ap-7652	117	2	the	the	DET
ap-7652	117	3	given	give	VERB
ap-7652	117	4	partition	partition	NOUN
ap-7652	117	5	∆1→l	∆1→l	PROPN
ap-7652	117	6	is	be	AUX
ap-7652	117	7	composed	compose	VERB
ap-7652	117	8	of	of	ADP
ap-7652	117	9	alternating	alternate	VERB
ap-7652	117	10	even	even	ADV
ap-7652	117	11	and	and	CCONJ
ap-7652	117	12	odd	odd	ADJ
ap-7652	117	13	integers	integer	NOUN
ap-7652	117	14	staring	stare	VERB
ap-7652	117	15	from	from	ADP
ap-7652	117	16	an	an	DET
ap-7652	117	17	even	even	ADV
ap-7652	117	18	integer	integer	NOUN
ap-7652	117	19	δ′	δ′	NOUN
ap-7652	117	20	1	1	NUM
ap-7652	117	21	then	then	ADV
ap-7652	117	22	all	all	DET
ap-7652	117	23	the	the	DET
ap-7652	117	24	integers	integer	NOUN
ap-7652	117	25	δ′	δ′	PROPN
ap-7652	117	26	l	l	NOUN
ap-7652	117	27	=	=	SYM
ap-7652	117	28	m|δ1→1|+1	m|δ1→1|+1	PROPN
ap-7652	117	29	−m|δ1→1|	−m|δ1→1|	PROPN
ap-7652	117	30	−	−	PROPN
ap-7652	117	31	1	1	NUM
ap-7652	117	32	>	>	X
ap-7652	117	33	0	0	NUM
ap-7652	118	1	for	for	ADP
ap-7652	118	2	any	any	DET
ap-7652	118	3	l	l	NOUN
ap-7652	118	4	<	<	X
ap-7652	118	5	l	l	X
ap-7652	118	6	(	(	PUNCT
ap-7652	118	7	31	31	NUM
ap-7652	118	8	)	)	PUNCT
ap-7652	118	9	103	103	NUM
ap-7652	118	10	gregory	gregory	PROPN
ap-7652	118	11	natanson	natanson	PROPN
ap-7652	118	12	acta	acta	PROPN
ap-7652	118	13	polytechnica	polytechnica	PROPN
ap-7652	118	14	must	must	AUX
ap-7652	118	15	be	be	AUX
ap-7652	118	16	also	also	ADV
ap-7652	118	17	even	even	ADV
ap-7652	118	18	which	which	PRON
ap-7652	118	19	implies	imply	VERB
ap-7652	118	20	that	that	SCONJ
ap-7652	118	21	the	the	DET
ap-7652	118	22	set	set	NOUN
ap-7652	118	23	of	of	ADP
ap-7652	118	24	seed	seed	NOUN
ap-7652	118	25	solutions	solution	NOUN
ap-7652	118	26	±,m(∆′	±,m(∆′	ADJ
ap-7652	118	27	l→1	l→1	NOUN
ap-7652	118	28	)	)	PUNCT
ap-7652	118	29	is	be	AUX
ap-7652	118	30	composed	compose	VERB
ap-7652	118	31	of	of	ADP
ap-7652	118	32	l	l	NOUN
ap-7652	118	33	segments	segment	NOUN
ap-7652	118	34	of	of	ADP
ap-7652	118	35	even	even	ADV
ap-7652	118	36	lengths	length	NOUN
ap-7652	118	37	[	[	X
ap-7652	118	38	11	11	NUM
ap-7652	118	39	,	,	PUNCT
ap-7652	118	40	19	19	NUM
ap-7652	118	41	]	]	PUNCT
ap-7652	118	42	or	or	CCONJ
ap-7652	118	43	in	in	ADP
ap-7652	118	44	other	other	ADJ
ap-7652	118	45	words	word	NOUN
ap-7652	118	46	is	be	AUX
ap-7652	118	47	formed	form	VERB
ap-7652	118	48	by	by	ADP
ap-7652	118	49	‘	'	PUNCT
ap-7652	118	50	juxtaposed	juxtapose	VERB
ap-7652	118	51	’	'	PUNCT
ap-7652	119	1	[	[	X
ap-7652	119	2	36–38	36–38	NUM
ap-7652	119	3	]	]	X
ap-7652	119	4	pairs	pair	NOUN
ap-7652	119	5	of	of	ADP
ap-7652	119	6	seed	seed	NOUN
ap-7652	119	7	solutions	solution	NOUN
ap-7652	119	8	±,m′,±,m′	±,m′,±,m′	NOUN
ap-7652	119	9	+	+	CCONJ
ap-7652	119	10	1	1	X
ap-7652	119	11	.	.	X
ap-7652	120	1	similarly	similarly	ADV
ap-7652	120	2	if	if	SCONJ
ap-7652	120	3	the	the	DET
ap-7652	120	4	set	set	NOUN
ap-7652	120	5	of	of	ADP
ap-7652	120	6	seed	seed	NOUN
ap-7652	120	7	solutions	solution	NOUN
ap-7652	120	8	,	,	PUNCT
ap-7652	120	9	±,m(∆′)l→1	±,m(∆′)l→1	PROPN
ap-7652	120	10	is	be	AUX
ap-7652	120	11	formed	form	VERB
ap-7652	120	12	by	by	ADP
ap-7652	120	13	‘	'	PUNCT
ap-7652	120	14	juxtaposed	juxtapose	VERB
ap-7652	120	15	’	'	PUNCT
ap-7652	120	16	pairs	pair	NOUN
ap-7652	120	17	of	of	ADP
ap-7652	120	18	seed	seed	NOUN
ap-7652	120	19	solutions	solution	NOUN
ap-7652	120	20	±,m,±,m+1	±,m,±,m+1	PRON
ap-7652	120	21	then	then	ADV
ap-7652	120	22	the	the	DET
ap-7652	120	23	conjugated	conjugated	ADJ
ap-7652	120	24	set	set	NOUN
ap-7652	120	25	is	be	AUX
ap-7652	120	26	formed	form	VERB
ap-7652	120	27	by	by	ADP
ap-7652	120	28	seed	seed	NOUN
ap-7652	120	29	solutions	solution	NOUN
ap-7652	120	30	∓,m′	∓,m′	PROPN
ap-7652	120	31	with	with	ADP
ap-7652	120	32	only	only	ADV
ap-7652	120	33	even	even	ADV
ap-7652	120	34	gap	gap	NOUN
ap-7652	120	35	lengths	length	NOUN
ap-7652	120	36	,	,	PUNCT
ap-7652	120	37	again	again	ADV
ap-7652	120	38	starting	start	VERB
ap-7652	120	39	from	from	ADP
ap-7652	120	40	an	an	DET
ap-7652	120	41	even	even	ADJ
ap-7652	120	42	number	number	NOUN
ap-7652	120	43	.	.	PUNCT
ap-7652	121	1	we	we	PRON
ap-7652	121	2	refer	refer	VERB
ap-7652	121	3	the	the	DET
ap-7652	121	4	reader	reader	NOUN
ap-7652	121	5	to	to	PART
ap-7652	121	6	subsection	subsection	VERB
ap-7652	121	7	3.4	3.4	NUM
ap-7652	121	8	below	below	ADP
ap-7652	121	9	for	for	ADP
ap-7652	121	10	a	a	DET
ap-7652	121	11	scrupulous	scrupulous	ADJ
ap-7652	121	12	analysis	analysis	NOUN
ap-7652	121	13	of	of	ADP
ap-7652	121	14	this	this	DET
ap-7652	121	15	issue	issue	NOUN
ap-7652	121	16	in	in	ADP
ap-7652	121	17	connection	connection	NOUN
ap-7652	121	18	with	with	ADP
ap-7652	121	19	juxtaposed	juxtaposed	ADJ
ap-7652	121	20	pairs	pair	NOUN
ap-7652	121	21	of	of	ADP
ap-7652	121	22	eigenfunctions	eigenfunction	NOUN
ap-7652	121	23	of	of	ADP
ap-7652	121	24	the	the	DET
ap-7652	121	25	schrödinger	schrödinger	ADJ
ap-7652	121	26	equation	equation	NOUN
ap-7652	121	27	with	with	ADP
ap-7652	121	28	the	the	DET
ap-7652	121	29	morse	morse	ADJ
ap-7652	121	30	potential	potential	NOUN
ap-7652	121	31	in	in	ADP
ap-7652	121	32	the	the	DET
ap-7652	121	33	bref	bref	PROPN
ap-7652	121	34	representation	representation	NOUN
ap-7652	121	35	[	[	X
ap-7652	121	36	19	19	NUM
ap-7652	121	37	]	]	PUNCT
ap-7652	121	38	.	.	PUNCT
ap-7652	122	1	3	3	X
ap-7652	122	2	.	.	X
ap-7652	122	3	quantization	quantization	NOUN
ap-7652	122	4	of	of	ADP
ap-7652	122	5	rationally	rationally	ADV
ap-7652	122	6	deformed	deform	VERB
ap-7652	122	7	morse	morse	ADJ
ap-7652	122	8	potentials	potential	NOUN
ap-7652	122	9	by	by	ADP
ap-7652	122	10	wronskian	wronskian	ADJ
ap-7652	122	11	transforms	transform	NOUN
ap-7652	122	12	of	of	ADP
ap-7652	122	13	r	r	NOUN
ap-7652	122	14	-	-	PUNCT
ap-7652	122	15	bessel	bessel	ADJ
ap-7652	122	16	polynomials	polynomial	NOUN
ap-7652	122	17	3.1	3.1	NUM
ap-7652	122	18	.	.	PUNCT
ap-7652	123	1	schrödinger	schrödinger	ADJ
ap-7652	123	2	equation	equation	NOUN
ap-7652	123	3	with	with	ADP
ap-7652	123	4	morse	morse	ADJ
ap-7652	123	5	potential	potential	NOUN
ap-7652	123	6	in	in	ADP
ap-7652	123	7	bessel	bessel	ADJ
ap-7652	123	8	form	form	NOUN
ap-7652	123	9	in	in	ADP
ap-7652	123	10	this	this	DET
ap-7652	123	11	paper	paper	NOUN
ap-7652	123	12	we	we	PRON
ap-7652	123	13	focus	focus	VERB
ap-7652	123	14	solely	solely	ADV
ap-7652	123	15	on	on	ADP
ap-7652	123	16	the	the	DET
ap-7652	123	17	tfi	tfi	PROPN
ap-7652	123	18	csle	csle	PROPN
ap-7652	123	19	{	{	PUNCT
ap-7652	123	20	d2	d2	PROPN
ap-7652	123	21	dy2	dy2	PROPN
ap-7652	123	22	+	+	CCONJ
ap-7652	123	23	i0[y	i0[y	PROPN
ap-7652	123	24	;	;	PUNCT
ap-7652	123	25	a	a	DET
ap-7652	123	26	]	]	X
ap-7652	123	27	+	+	NUM
ap-7652	123	28	ε∞ρ⋄[y	ε∞ρ⋄[y	NUM
ap-7652	123	29	]	]	PUNCT
ap-7652	123	30	}	}	PUNCT
ap-7652	123	31	∞	∞	PROPN
ap-7652	123	32	φ[y	φ[y	NOUN
ap-7652	123	33	;	;	PUNCT
ap-7652	123	34	a	a	PRON
ap-7652	123	35	;	;	PUNCT
ap-7652	123	36	ε	ε	X
ap-7652	123	37	]	]	X
ap-7652	123	38	=	=	SYM
ap-7652	123	39	0	0	NUM
ap-7652	123	40	(	(	PUNCT
ap-7652	123	41	32	32	NUM
ap-7652	123	42	)	)	PUNCT
ap-7652	123	43	with	with	ADP
ap-7652	123	44	the	the	DET
ap-7652	123	45	refpf	refpf	NOUN
ap-7652	123	46	i0[y	i0[y	VERB
ap-7652	123	47	;	;	PUNCT
ap-7652	123	48	a	a	PRON
ap-7652	123	49	]	]	X
ap-7652	123	50	=	=	SYM
ap-7652	123	51	2ay−3	2ay−3	NOUN
ap-7652	123	52	−	−	PROPN
ap-7652	123	53	y−4	y−4	PROPN
ap-7652	124	1	+	+	CCONJ
ap-7652	124	2	1/4y−2	1/4y−2	NUM
ap-7652	124	3	(	(	PUNCT
ap-7652	124	4	33	33	NUM
ap-7652	124	5	)	)	PUNCT
ap-7652	124	6	and	and	CCONJ
ap-7652	124	7	the	the	DET
ap-7652	124	8	density	density	NOUN
ap-7652	124	9	function	function	NOUN
ap-7652	124	10	∞ρ⋄[y	∞ρ⋄[y	PROPN
ap-7652	124	11	]	]	X
ap-7652	124	12	≡	≡	PROPN
ap-7652	124	13	∞σ	∞σ	PART
ap-7652	124	14	−1[y	−1[y	PROPN
ap-7652	124	15	]	]	X
ap-7652	124	16	=	=	SYM
ap-7652	124	17	y−2	y−2	PROPN
ap-7652	124	18	(	(	PUNCT
ap-7652	124	19	34	34	NUM
ap-7652	124	20	)	)	PUNCT
ap-7652	124	21	one	one	NOUN
ap-7652	124	22	can	can	AUX
ap-7652	124	23	directly	directly	ADV
ap-7652	124	24	verify	verify	VERB
ap-7652	124	25	that	that	DET
ap-7652	124	26	csle	csle	NOUN
ap-7652	124	27	(	(	PUNCT
ap-7652	124	28	32	32	NUM
ap-7652	124	29	)	)	PUNCT
ap-7652	124	30	has	have	VERB
ap-7652	124	31	a	a	DET
ap-7652	124	32	pair	pair	NOUN
ap-7652	124	33	of	of	ADP
ap-7652	124	34	’	'	PUNCT
ap-7652	124	35	basic	basic	ADJ
ap-7652	124	36	’	'	PUNCT
ap-7652	124	37	solutions	solution	NOUN
ap-7652	124	38	∞ϕ±,0(y	∞ϕ±,0(y	PROPN
ap-7652	124	39	;	;	PUNCT
ap-7652	125	1	a	a	X
ap-7652	125	2	)	)	PUNCT
ap-7652	125	3	=	=	SYM
ap-7652	125	4	y1±ae±1	y1±ae±1	PROPN
ap-7652	125	5	/	/	SYM
ap-7652	125	6	y	y	PROPN
ap-7652	125	7	(	(	PUNCT
ap-7652	125	8	y	y	PROPN
ap-7652	125	9	>	>	X
ap-7652	125	10	0	0	NUM
ap-7652	125	11	)	)	PUNCT
ap-7652	125	12	(	(	PUNCT
ap-7652	125	13	35	35	NUM
ap-7652	125	14	)	)	PUNCT
ap-7652	125	15	at	at	ADP
ap-7652	125	16	the	the	DET
ap-7652	125	17	energies	energy	NOUN
ap-7652	125	18	∞ε±,0(a	∞ε±,0(a	PROPN
ap-7652	125	19	)	)	PUNCT
ap-7652	125	20	=	=	SYM
ap-7652	126	1	−(a±	−(a±	ADJ
ap-7652	126	2	1/2)2	1/2)2	NUM
ap-7652	126	3	.	.	PUNCT
ap-7652	127	1	(	(	PUNCT
ap-7652	127	2	36	36	NUM
ap-7652	127	3	)	)	PUNCT
ap-7652	127	4	examination	examination	NOUN
ap-7652	127	5	of	of	ADP
ap-7652	127	6	solutions	solution	NOUN
ap-7652	127	7	(	(	PUNCT
ap-7652	127	8	35	35	NUM
ap-7652	127	9	)	)	PUNCT
ap-7652	127	10	shows	show	VERB
ap-7652	127	11	that	that	SCONJ
ap-7652	127	12	they	they	PRON
ap-7652	127	13	obey	obey	VERB
ap-7652	127	14	the	the	DET
ap-7652	127	15	following	follow	VERB
ap-7652	127	16	symmetry	symmetry	NOUN
ap-7652	127	17	relations	relation	NOUN
ap-7652	127	18	∞ϕ±,0[y	∞ϕ±,0[y	PROPN
ap-7652	127	19	;	;	PUNCT
ap-7652	127	20	a+	a+	X
ap-7652	127	21	k	k	X
ap-7652	128	1	]	]	X
ap-7652	128	2	=	=	PUNCT
ap-7652	128	3	y±k	y±k	PROPN
ap-7652	128	4	∞ϕ±,0[y	∞ϕ±,0[y	ADP
ap-7652	128	5	;	;	PUNCT
ap-7652	128	6	a	a	X
ap-7652	128	7	]	]	X
ap-7652	128	8	(	(	PUNCT
ap-7652	128	9	37	37	NUM
ap-7652	128	10	)	)	PUNCT
ap-7652	128	11	for	for	ADP
ap-7652	128	12	any	any	DET
ap-7652	128	13	integer	integer	NOUN
ap-7652	128	14	k	k	PROPN
ap-7652	128	15	and	and	CCONJ
ap-7652	128	16	∞ϕ+,0(y	∞ϕ+,0(y	PROPN
ap-7652	128	17	;	;	PUNCT
ap-7652	128	18	a)∞ϕ−,0(y	a)∞ϕ−,0(y	X
ap-7652	128	19	;	;	PUNCT
ap-7652	128	20	a	a	X
ap-7652	128	21	)	)	PUNCT
ap-7652	128	22	=	=	SYM
ap-7652	128	23	y2	y2	INTJ
ap-7652	128	24	(	(	PUNCT
ap-7652	128	25	38	38	NUM
ap-7652	128	26	)	)	PUNCT
ap-7652	128	27	whereas	whereas	SCONJ
ap-7652	128	28	the	the	DET
ap-7652	128	29	function	function	NOUN
ap-7652	128	30	f±,0[ξ	f±,0[ξ	NOUN
ap-7652	128	31	;	;	PUNCT
ap-7652	128	32	⇀	⇀	NUM
ap-7652	128	33	a	a	DET
ap-7652	128	34	,	,	PUNCT
ap-7652	128	35	b	b	NOUN
ap-7652	128	36	]	]	X
ap-7652	128	37	≡	≡	PROPN
ap-7652	128	38	ϕ∓,0[ξ	ϕ∓,0[ξ	PROPN
ap-7652	128	39	;	;	PUNCT
ap-7652	128	40	⇀	⇀	NUM
ap-7652	128	41	a	a	PRON
ap-7652	128	42	,	,	PUNCT
ap-7652	128	43	b]/ϕ±,0[ξ	b]/ϕ±,0[ξ	NOUN
ap-7652	128	44	;	;	PUNCT
ap-7652	128	45	⇀	⇀	NUM
ap-7652	128	46	a	a	DET
ap-7652	128	47	,	,	PUNCT
ap-7652	128	48	b	b	NOUN
ap-7652	128	49	]	]	X
ap-7652	128	50	(	(	PUNCT
ap-7652	128	51	39	39	NUM
ap-7652	128	52	)	)	PUNCT
ap-7652	128	53	takes	take	VERB
ap-7652	128	54	form	form	NOUN
ap-7652	128	55	∞f±,0[ξ	∞f±,0[ξ	ADP
ap-7652	128	56	;	;	PUNCT
ap-7652	128	57	a	a	PRON
ap-7652	128	58	]	]	PUNCT
ap-7652	128	59	≡	≡	PROPN
ap-7652	128	60	y∓2ae∓2	y∓2ae∓2	PROPN
ap-7652	128	61	/	/	PUNCT
ap-7652	129	1	y.	y.	NOUN
ap-7652	129	2	(	(	PUNCT
ap-7652	129	3	40	40	NUM
ap-7652	129	4	)	)	PUNCT
ap-7652	129	5	we	we	PRON
ap-7652	129	6	thus	thus	ADV
ap-7652	129	7	proved	prove	VERB
ap-7652	129	8	that	that	SCONJ
ap-7652	129	9	the	the	DET
ap-7652	129	10	pair	pair	NOUN
ap-7652	129	11	of	of	ADP
ap-7652	129	12	basic	basic	ADJ
ap-7652	129	13	solutions	solution	NOUN
ap-7652	129	14	in	in	ADP
ap-7652	129	15	question	question	NOUN
ap-7652	129	16	satisfy	satisfy	VERB
ap-7652	129	17	the	the	DET
ap-7652	129	18	tfi	tfi	NOUN
ap-7652	129	19	condition	condition	NOUN
ap-7652	130	1	[	[	X
ap-7652	130	2	23	23	NUM
ap-7652	130	3	]	]	PUNCT
ap-7652	130	4	∞ϕ∓,0[y	∞ϕ∓,0[y	ADP
ap-7652	130	5	;	;	PUNCT
ap-7652	130	6	a±	a±	PROPN
ap-7652	130	7	1	1	NUM
ap-7652	130	8	]	]	X
ap-7652	130	9	=	=	SYM
ap-7652	130	10	∞ρ	∞ρ	X
ap-7652	130	11	−1/2	−1/2	VERB
ap-7652	130	12	⋄	⋄	PROPN
ap-7652	131	1	[	[	X
ap-7652	131	2	y]/∞ϕ±,0(y	y]/∞ϕ±,0(y	X
ap-7652	131	3	;	;	PUNCT
ap-7652	131	4	a	a	PRON
ap-7652	131	5	)	)	PUNCT
ap-7652	131	6	.	.	PUNCT
ap-7652	132	1	(	(	PUNCT
ap-7652	132	2	41	41	NUM
ap-7652	132	3	)	)	PUNCT
ap-7652	132	4	one	one	NOUN
ap-7652	132	5	can	can	AUX
ap-7652	132	6	directly	directly	ADV
ap-7652	132	7	verify	verify	VERB
ap-7652	132	8	that	that	SCONJ
ap-7652	132	9	∞ε∓,0(a±	∞ε∓,0(a±	ADJ
ap-7652	132	10	1	1	NUM
ap-7652	132	11	)	)	PUNCT
ap-7652	132	12	=	=	SYM
ap-7652	132	13	∞ε±,0(a	∞ε±,0(a	PROPN
ap-7652	132	14	)	)	PUNCT
ap-7652	132	15	(	(	PUNCT
ap-7652	132	16	42	42	NUM
ap-7652	132	17	)	)	PUNCT
ap-7652	132	18	and	and	CCONJ
ap-7652	132	19	thereby	thereby	ADV
ap-7652	132	20	∞e±1(a	∞e±1(a	ADP
ap-7652	132	21	)	)	PUNCT
ap-7652	132	22	≡	≡	PROPN
ap-7652	132	23	∞ε∓,0(a±	∞ε∓,0(a±	ADJ
ap-7652	133	1	1	1	NUM
ap-7652	133	2	)	)	PUNCT
ap-7652	133	3	−	−	PROPN
ap-7652	133	4	∞ε±,0(a	∞ε±,0(a	PROPN
ap-7652	133	5	)	)	PUNCT
ap-7652	133	6	=	=	SYM
ap-7652	133	7	0	0	PUNCT
ap-7652	133	8	(	(	PUNCT
ap-7652	133	9	43	43	NUM
ap-7652	133	10	)	)	PUNCT
ap-7652	133	11	so	so	SCONJ
ap-7652	133	12	the	the	DET
ap-7652	133	13	symmetry	symmetry	NOUN
ap-7652	133	14	condition	condition	NOUN
ap-7652	133	15	[	[	X
ap-7652	133	16	23	23	NUM
ap-7652	133	17	]	]	X
ap-7652	133	18	e∓1(a±	e∓1(a±	PROPN
ap-7652	133	19	1	1	NUM
ap-7652	133	20	)	)	PUNCT
ap-7652	133	21	=	=	SYM
ap-7652	133	22	−e±1(a	−e±1(a	PROPN
ap-7652	133	23	)	)	PUNCT
ap-7652	133	24	.	.	PUNCT
ap-7652	134	1	(	(	PUNCT
ap-7652	134	2	44	44	NUM
ap-7652	134	3	)	)	PUNCT
ap-7652	134	4	trivially	trivially	ADV
ap-7652	134	5	holds	hold	VERB
ap-7652	134	6	.	.	PUNCT
ap-7652	135	1	the	the	DET
ap-7652	135	2	gauge	gauge	NOUN
ap-7652	135	3	transformations	transformation	VERB
ap-7652	135	4	∞φ[y	∞φ[y	PROPN
ap-7652	135	5	;	;	PUNCT
ap-7652	135	6	a	a	PRON
ap-7652	135	7	;	;	PUNCT
ap-7652	135	8	ε	ε	X
ap-7652	135	9	]	]	X
ap-7652	135	10	=	=	SYM
ap-7652	135	11	εϕ±[y	εϕ±[y	NOUN
ap-7652	135	12	;	;	PUNCT
ap-7652	135	13	a]∞f±[y	a]∞f±[y	NOUN
ap-7652	135	14	;	;	PUNCT
ap-7652	135	15	a	a	PRON
ap-7652	135	16	;	;	PUNCT
ap-7652	135	17	ε	ε	PROPN
ap-7652	135	18	]	]	X
ap-7652	135	19	(	(	PUNCT
ap-7652	135	20	45	45	NUM
ap-7652	135	21	)	)	PUNCT
ap-7652	135	22	convert	convert	NOUN
ap-7652	135	23	csle	csle	NOUN
ap-7652	135	24	(	(	PUNCT
ap-7652	135	25	32	32	NUM
ap-7652	135	26	)	)	PUNCT
ap-7652	135	27	to	to	ADP
ap-7652	135	28	a	a	DET
ap-7652	135	29	pair	pair	NOUN
ap-7652	135	30	of	of	ADP
ap-7652	135	31	bochner	bochner	NOUN
ap-7652	135	32	-	-	PUNCT
ap-7652	135	33	type	type	NOUN
ap-7652	135	34	eigenequations	eigenequation	NOUN
ap-7652	135	35	{	{	PUNCT
ap-7652	135	36	y2	y2	NOUN
ap-7652	135	37	d	d	PROPN
ap-7652	135	38	2	2	NUM
ap-7652	135	39	dy2	dy2	NOUN
ap-7652	135	40	+	+	CCONJ
ap-7652	136	1	∞τ±[y	∞τ±[y	PROPN
ap-7652	136	2	;	;	PUNCT
ap-7652	136	3	a	a	DET
ap-7652	136	4	]	]	X
ap-7652	136	5	d	d	X
ap-7652	136	6	dy	dy	NOUN
ap-7652	136	7	+	+	PROPN
ap-7652	137	1	[	[	X
ap-7652	137	2	ε−∞	ε−∞	X
ap-7652	137	3	ε±,0(a	ε±,0(a	PROPN
ap-7652	137	4	)	)	PUNCT
ap-7652	137	5	]	]	PUNCT
ap-7652	137	6	}	}	PUNCT
ap-7652	137	7	∞f±[y	∞f±[y	PROPN
ap-7652	137	8	;	;	PUNCT
ap-7652	137	9	a	a	PRON
ap-7652	137	10	;	;	PUNCT
ap-7652	137	11	ε	ε	X
ap-7652	137	12	]	]	X
ap-7652	137	13	=	=	SYM
ap-7652	137	14	0	0	NUM
ap-7652	137	15	,	,	PUNCT
ap-7652	137	16	(	(	PUNCT
ap-7652	137	17	46	46	NUM
ap-7652	137	18	)	)	PUNCT
ap-7652	137	19	with	with	ADP
ap-7652	137	20	∞τ	∞τ	PRON
ap-7652	137	21	±[y	±[y	NOUN
ap-7652	137	22	;	;	PUNCT
ap-7652	137	23	a	a	PRON
ap-7652	137	24	]	]	X
ap-7652	137	25	=	=	SYM
ap-7652	137	26	2(1	2(1	NUM
ap-7652	137	27	±	±	NOUN
ap-7652	137	28	a)y	a)y	X
ap-7652	137	29	∓	∓	NOUN
ap-7652	137	30	2	2	X
ap-7652	137	31	.	.	PUNCT
ap-7652	137	32	(	(	PUNCT
ap-7652	137	33	47	47	NUM
ap-7652	137	34	)	)	PUNCT
ap-7652	137	35	104	104	NUM
ap-7652	137	36	vol	vol	NOUN
ap-7652	137	37	.	.	PUNCT
ap-7652	138	1	62	62	NUM
ap-7652	138	2	no	no	INTJ
ap-7652	138	3	.	.	PUNCT
ap-7652	139	1	1/2022	1/2022	NUM
ap-7652	139	2	quantization	quantization	NOUN
ap-7652	139	3	of	of	ADP
ap-7652	139	4	rationally	rationally	ADV
ap-7652	139	5	deformed	deform	VERB
ap-7652	139	6	morse	morse	ADJ
ap-7652	139	7	potentials	potential	NOUN
ap-7652	139	8	.	.	PUNCT
ap-7652	139	9	.	.	PUNCT
ap-7652	140	1	.	.	PUNCT
ap-7652	141	1	we	we	PRON
ap-7652	141	2	define	define	VERB
ap-7652	141	3	generalized	generalized	ADJ
ap-7652	141	4	bessel	bessel	ADJ
ap-7652	141	5	polynomials	polynomial	NOUN
ap-7652	141	6	as	as	ADP
ap-7652	141	7	y	y	PROPN
ap-7652	141	8	(	(	PUNCT
ap-7652	141	9	α	α	NOUN
ap-7652	141	10	,	,	PUNCT
ap-7652	141	11	β	β	NOUN
ap-7652	141	12	)	)	PUNCT
ap-7652	141	13	n	n	PROPN
ap-7652	141	14	(	(	PUNCT
ap-7652	141	15	y	y	NOUN
ap-7652	141	16	)	)	PUNCT
ap-7652	141	17	≡	≡	PROPN
ap-7652	141	18	y	y	PROPN
ap-7652	141	19	(	(	PUNCT
ap-7652	141	20	α	α	NOUN
ap-7652	141	21	)	)	PUNCT
ap-7652	141	22	n	n	PROPN
ap-7652	141	23	(	(	PUNCT
ap-7652	141	24	y	y	NOUN
ap-7652	141	25	/	/	SYM
ap-7652	141	26	β	β	NOUN
ap-7652	141	27	)	)	PUNCT
ap-7652	141	28	,	,	PUNCT
ap-7652	141	29	(	(	PUNCT
ap-7652	141	30	48	48	NUM
ap-7652	141	31	)	)	PUNCT
ap-7652	141	32	where	where	SCONJ
ap-7652	141	33	the	the	DET
ap-7652	141	34	polynomial	polynomial	ADJ
ap-7652	141	35	y	y	PROPN
ap-7652	141	36	(	(	PUNCT
ap-7652	141	37	α	α	NOUN
ap-7652	141	38	)	)	PUNCT
ap-7652	141	39	n	n	PROPN
ap-7652	141	40	(	(	PUNCT
ap-7652	141	41	x	x	X
ap-7652	141	42	)	)	PUNCT
ap-7652	141	43	is	be	AUX
ap-7652	141	44	given	give	VERB
ap-7652	141	45	by	by	ADP
ap-7652	141	46	(	(	PUNCT
ap-7652	141	47	2	2	NUM
ap-7652	141	48	)	)	PUNCT
ap-7652	141	49	in	in	ADP
ap-7652	141	50	[	[	X
ap-7652	141	51	4	4	NUM
ap-7652	141	52	]	]	PUNCT
ap-7652	141	53	and	and	CCONJ
ap-7652	141	54	thereby	thereby	ADV
ap-7652	141	55	coincides	coincide	VERB
ap-7652	141	56	with	with	ADP
ap-7652	141	57	polynomial	polynomial	ADJ
ap-7652	141	58	(	(	PUNCT
ap-7652	141	59	9.13.1	9.13.1	NUM
ap-7652	141	60	)	)	PUNCT
ap-7652	141	61	in	in	ADP
ap-7652	141	62	[	[	X
ap-7652	141	63	6	6	NUM
ap-7652	141	64	]	]	X
ap-7652	141	65	y	y	PROPN
ap-7652	141	66	(	(	PUNCT
ap-7652	141	67	α	α	NOUN
ap-7652	141	68	)	)	PUNCT
ap-7652	141	69	n	n	PROPN
ap-7652	141	70	(	(	PUNCT
ap-7652	141	71	x	x	X
ap-7652	141	72	)	)	PUNCT
ap-7652	141	73	≡	≡	PROPN
ap-7652	141	74	yn(x;α	yn(x;α	PROPN
ap-7652	141	75	)	)	PUNCT
ap-7652	141	76	.	.	PUNCT
ap-7652	142	1	(	(	PUNCT
ap-7652	142	2	49	49	X
ap-7652	142	3	)	)	PUNCT
ap-7652	142	4	note	note	NOUN
ap-7652	142	5	that	that	SCONJ
ap-7652	142	6	chihara	chihara	PROPN
ap-7652	142	7	’s	’s	PART
ap-7652	142	8	relation	relation	NOUN
ap-7652	142	9	(	(	PUNCT
ap-7652	142	10	4.3	4.3	NUM
ap-7652	142	11	)	)	PUNCT
ap-7652	142	12	in	in	ADP
ap-7652	142	13	[	[	X
ap-7652	142	14	5	5	NUM
ap-7652	142	15	]	]	PUNCT
ap-7652	142	16	is	be	AUX
ap-7652	142	17	apparently	apparently	ADV
ap-7652	142	18	based	base	VERB
ap-7652	142	19	on	on	ADP
ap-7652	142	20	brafman	brafman	PROPN
ap-7652	142	21	’s	’s	PART
ap-7652	142	22	definition	definition	NOUN
ap-7652	143	1	[	[	X
ap-7652	143	2	39	39	NUM
ap-7652	143	3	]	]	PUNCT
ap-7652	143	4	for	for	ADP
ap-7652	143	5	the	the	DET
ap-7652	143	6	polynomial	polynomial	PROPN
ap-7652	143	7	yn(x;α	yn(x;α	PROPN
ap-7652	143	8	,	,	PUNCT
ap-7652	143	9	β	β	X
ap-7652	143	10	)	)	PUNCT
ap-7652	143	11	such	such	ADJ
ap-7652	143	12	that	that	SCONJ
ap-7652	143	13	yn(x;α	yn(x;α	PROPN
ap-7652	143	14	+	+	CCONJ
ap-7652	143	15	2	2	NUM
ap-7652	143	16	,	,	PUNCT
ap-7652	143	17	2	2	NUM
ap-7652	143	18	)	)	PUNCT
ap-7652	143	19	=	=	NOUN
ap-7652	143	20	yn(x;α	yn(x;α	PROPN
ap-7652	143	21	)	)	PUNCT
ap-7652	143	22	.	.	PUNCT
ap-7652	144	1	adding	add	VERB
ap-7652	144	2	the	the	DET
ap-7652	144	3	second	second	ADJ
ap-7652	144	4	index	index	NOUN
ap-7652	144	5	to	to	ADP
ap-7652	144	6	the	the	DET
ap-7652	144	7	conventional	conventional	ADJ
ap-7652	144	8	notation	notation	NOUN
ap-7652	144	9	[	[	X
ap-7652	144	10	4	4	NUM
ap-7652	144	11	,	,	PUNCT
ap-7652	144	12	5	5	NUM
ap-7652	144	13	]	]	PUNCT
ap-7652	144	14	allows	allow	VERB
ap-7652	144	15	us	we	PRON
ap-7652	144	16	to	to	PART
ap-7652	144	17	avoid	avoid	VERB
ap-7652	144	18	uncertainties	uncertainty	NOUN
ap-7652	144	19	in	in	ADP
ap-7652	144	20	the	the	DET
ap-7652	144	21	definition	definition	NOUN
ap-7652	144	22	of	of	ADP
ap-7652	144	23	the	the	DET
ap-7652	144	24	variable	variable	NOUN
ap-7652	144	25	used	use	VERB
ap-7652	144	26	to	to	PART
ap-7652	144	27	differentiate	differentiate	VERB
ap-7652	144	28	a	a	DET
ap-7652	144	29	polynomial	polynomial	NOUN
ap-7652	144	30	in	in	ADP
ap-7652	144	31	the	the	DET
ap-7652	144	32	reflected	reflect	VERB
ap-7652	144	33	argument	argument	NOUN
ap-7652	144	34	,	,	PUNCT
ap-7652	144	35	keeping	keep	VERB
ap-7652	144	36	in	in	ADP
ap-7652	144	37	mind	mind	NOUN
ap-7652	144	38	that	that	SCONJ
ap-7652	144	39	y	y	PROPN
ap-7652	144	40	(	(	PUNCT
ap-7652	144	41	α	α	NOUN
ap-7652	144	42	)	)	PUNCT
ap-7652	144	43	n	n	PROPN
ap-7652	144	44	(	(	PUNCT
ap-7652	144	45	−y	−y	NOUN
ap-7652	144	46	)	)	PUNCT
ap-7652	144	47	≡	≡	PROPN
ap-7652	144	48	y	y	PROPN
ap-7652	144	49	(	(	PUNCT
ap-7652	144	50	α,−2	α,−2	NUM
ap-7652	144	51	)	)	PUNCT
ap-7652	144	52	n	n	CCONJ
ap-7652	144	53	(	(	PUNCT
ap-7652	144	54	y	y	NOUN
ap-7652	144	55	)	)	PUNCT
ap-7652	144	56	.	.	PUNCT
ap-7652	145	1	(	(	PUNCT
ap-7652	145	2	50	50	NUM
ap-7652	145	3	)	)	PUNCT
ap-7652	145	4	eq	eq	NOUN
ap-7652	145	5	.	.	PUNCT
ap-7652	146	1	(	(	PUNCT
ap-7652	146	2	37	37	NUM
ap-7652	146	3	)	)	PUNCT
ap-7652	146	4	for	for	ADP
ap-7652	146	5	the	the	DET
ap-7652	146	6	bessel	bessel	NOUN
ap-7652	146	7	dps	dps	NOUN
ap-7652	146	8	in	in	ADP
ap-7652	146	9	[	[	X
ap-7652	146	10	40	40	NUM
ap-7652	146	11	]	]	PUNCT
ap-7652	146	12	thus	thus	ADV
ap-7652	146	13	corresponds	correspond	VERB
ap-7652	146	14	to	to	ADP
ap-7652	146	15	the	the	DET
ap-7652	146	16	polynomials	polynomial	NOUN
ap-7652	146	17	y	y	PROPN
ap-7652	146	18	(	(	PUNCT
ap-7652	146	19	α−2,β	α−2,β	PROPN
ap-7652	146	20	)	)	PUNCT
ap-7652	147	1	n	n	CCONJ
ap-7652	147	2	(	(	PUNCT
ap-7652	147	3	y	y	NOUN
ap-7652	147	4	)	)	PUNCT
ap-7652	147	5	in	in	ADP
ap-7652	147	6	our	our	PRON
ap-7652	147	7	terms	term	NOUN
ap-7652	147	8	.	.	PUNCT
ap-7652	148	1	(	(	PUNCT
ap-7652	148	2	we	we	PRON
ap-7652	148	3	prefer	prefer	VERB
ap-7652	148	4	to	to	PART
ap-7652	148	5	preserve	preserve	VERB
ap-7652	148	6	symbol	symbol	NOUN
ap-7652	148	7	‘	'	PUNCT
ap-7652	148	8	b	b	NOUN
ap-7652	148	9	’	'	PUNCT
ap-7652	148	10	for	for	ADP
ap-7652	148	11	their	their	PRON
ap-7652	148	12	orthogonal	orthogonal	ADJ
ap-7652	148	13	subset	subset	NOUN
ap-7652	148	14	composed	compose	VERB
ap-7652	148	15	of	of	ADP
ap-7652	148	16	r	r	NOUN
ap-7652	148	17	-	-	PUNCT
ap-7652	148	18	bessel	bessel	ADJ
ap-7652	148	19	polynomials	polynomial	NOUN
ap-7652	148	20	[	[	X
ap-7652	148	21	12	12	NUM
ap-7652	148	22	,	,	PUNCT
ap-7652	148	23	13	13	NUM
ap-7652	148	24	]	]	PUNCT
ap-7652	148	25	.	.	PUNCT
ap-7652	148	26	)	)	PUNCT
ap-7652	149	1	it	it	PRON
ap-7652	149	2	is	be	AUX
ap-7652	149	3	also	also	ADV
ap-7652	149	4	worth	worth	ADJ
ap-7652	149	5	mentioning	mention	VERB
ap-7652	149	6	that	that	DET
ap-7652	149	7	alhaidari	alhaidari	PROPN
ap-7652	150	1	[	[	X
ap-7652	150	2	1	1	NUM
ap-7652	150	3	]	]	PUNCT
ap-7652	150	4	introduced	introduce	VERB
ap-7652	150	5	a	a	DET
ap-7652	150	6	slightly	slightly	ADV
ap-7652	150	7	modified	modify	VERB
ap-7652	150	8	notation	notation	NOUN
ap-7652	150	9	for	for	ADP
ap-7652	150	10	generalized	generalized	ADJ
ap-7652	150	11	bessel	bessel	ADJ
ap-7652	150	12	polynomials	polynomial	NOUN
ap-7652	150	13	:	:	PUNCT
ap-7652	150	14	ja	ja	PROPN
ap-7652	150	15	n(1/2y	n(1/2y	PROPN
ap-7652	150	16	)	)	PUNCT
ap-7652	150	17	≡	≡	PROPN
ap-7652	150	18	y	y	PROPN
ap-7652	150	19	(	(	PUNCT
ap-7652	150	20	2a	2a	NUM
ap-7652	150	21	)	)	PUNCT
ap-7652	150	22	n	n	CCONJ
ap-7652	150	23	(	(	PUNCT
ap-7652	150	24	y	y	NOUN
ap-7652	150	25	)	)	PUNCT
ap-7652	150	26	=	=	SYM
ap-7652	150	27	(	(	PUNCT
ap-7652	150	28	2n+	2n+	NUM
ap-7652	150	29	2a)n(y/2)n	2a)n(y/2)n	VERB
ap-7652	150	30	1f1(−n	1f1(−n	NUM
ap-7652	150	31	;	;	PUNCT
ap-7652	150	32	−2a−	−2a−	NUM
ap-7652	150	33	n	n	CCONJ
ap-7652	150	34	;	;	PUNCT
ap-7652	150	35	2	2	X
ap-7652	150	36	/	/	SYM
ap-7652	150	37	y	y	NOUN
ap-7652	150	38	)	)	PUNCT
ap-7652	150	39	,	,	PUNCT
ap-7652	150	40	(	(	PUNCT
ap-7652	150	41	51	51	NUM
ap-7652	150	42	)	)	PUNCT
ap-7652	150	43	with	with	ADP
ap-7652	150	44	the	the	DET
ap-7652	150	45	pochhammer	pochhammer	NOUN
ap-7652	150	46	symbol	symbol	NOUN
ap-7652	150	47	(	(	PUNCT
ap-7652	150	48	a)n	a)n	NOUN
ap-7652	150	49	standing	standing	NOUN
ap-7652	150	50	for	for	ADP
ap-7652	150	51	the	the	DET
ap-7652	150	52	falling	fall	VERB
ap-7652	150	53	factorial	factorial	NOUN
ap-7652	150	54	.	.	PUNCT
ap-7652	151	1	and	and	CCONJ
ap-7652	151	2	indeed	indeed	ADV
ap-7652	151	3	it	it	PRON
ap-7652	151	4	would	would	AUX
ap-7652	151	5	be	be	AUX
ap-7652	151	6	possibly	possibly	ADV
ap-7652	151	7	more	more	ADV
ap-7652	151	8	convenient	convenient	ADJ
ap-7652	151	9	to	to	PART
ap-7652	151	10	use	use	VERB
ap-7652	151	11	the	the	DET
ap-7652	151	12	parameter	parameter	NOUN
ap-7652	151	13	a	a	PRON
ap-7652	151	14	as	as	ADP
ap-7652	151	15	the	the	DET
ap-7652	151	16	polynomial	polynomial	ADJ
ap-7652	151	17	index	index	NOUN
ap-7652	151	18	keeping	keeping	NOUN
ap-7652	151	19	in	in	ADP
ap-7652	151	20	mind	mind	NOUN
ap-7652	151	21	that	that	SCONJ
ap-7652	151	22	the	the	DET
ap-7652	151	23	forward	forward	ADJ
ap-7652	151	24	and	and	CCONJ
ap-7652	151	25	backward	backward	ADJ
ap-7652	151	26	shift	shift	NOUN
ap-7652	151	27	relations	relation	NOUN
ap-7652	151	28	change	change	VERB
ap-7652	151	29	the	the	DET
ap-7652	151	30	polynomial	polynomial	ADJ
ap-7652	151	31	index	index	NOUN
ap-7652	151	32	by	by	ADP
ap-7652	151	33	1	1	NUM
ap-7652	151	34	.	.	PUNCT
ap-7652	152	1	however	however	SCONJ
ap-7652	152	2	we	we	PRON
ap-7652	152	3	prefer	prefer	VERB
ap-7652	152	4	to	to	PART
ap-7652	152	5	stick	stick	VERB
ap-7652	152	6	to	to	ADP
ap-7652	152	7	the	the	DET
ap-7652	152	8	more	more	ADV
ap-7652	152	9	conventional	conventional	ADJ
ap-7652	152	10	notation	notation	NOUN
ap-7652	152	11	.	.	PUNCT
ap-7652	153	1	the	the	DET
ap-7652	153	2	basic	basic	ADJ
ap-7652	153	3	solution	solution	NOUN
ap-7652	153	4	∞ϕ±,0[y	∞ϕ±,0[y	ADP
ap-7652	153	5	;	;	PUNCT
ap-7652	153	6	a	a	PRON
ap-7652	153	7	]	]	X
ap-7652	153	8	is	be	AUX
ap-7652	153	9	thus	thus	ADV
ap-7652	153	10	nothing	nothing	PRON
ap-7652	153	11	but	but	SCONJ
ap-7652	153	12	a	a	DET
ap-7652	153	13	constant	constant	ADJ
ap-7652	153	14	solution	solution	NOUN
ap-7652	153	15	of	of	ADP
ap-7652	153	16	eigenequation	eigenequation	NOUN
ap-7652	153	17	(	(	PUNCT
ap-7652	153	18	46	46	NUM
ap-7652	153	19	)	)	PUNCT
ap-7652	153	20	converted	convert	VERB
ap-7652	153	21	back	back	ADV
ap-7652	153	22	by	by	ADP
ap-7652	153	23	gauge	gauge	ADJ
ap-7652	153	24	transformation	transformation	NOUN
ap-7652	153	25	(	(	PUNCT
ap-7652	153	26	45	45	NUM
ap-7652	153	27	)	)	PUNCT
ap-7652	153	28	.	.	PUNCT
ap-7652	154	1	similarly	similarly	ADV
ap-7652	154	2	the	the	DET
ap-7652	154	3	reverse	reverse	ADJ
ap-7652	154	4	gauge	gauge	NOUN
ap-7652	154	5	transformation	transformation	NOUN
ap-7652	154	6	of	of	ADP
ap-7652	154	7	each	each	PRON
ap-7652	154	8	of	of	ADP
ap-7652	154	9	the	the	DET
ap-7652	154	10	dpss	dpss	NOUN
ap-7652	154	11	composed	compose	VERB
ap-7652	154	12	of	of	ADP
ap-7652	154	13	polynomials	polynomial	NOUN
ap-7652	154	14	y	y	PROPN
ap-7652	154	15	(	(	PUNCT
ap-7652	154	16	±2a,∓2	±2a,∓2	PROPN
ap-7652	154	17	)	)	PUNCT
ap-7652	154	18	m	m	PROPN
ap-7652	154	19	(	(	PUNCT
ap-7652	154	20	y	y	NOUN
ap-7652	154	21	)	)	PUNCT
ap-7652	154	22	results	result	NOUN
ap-7652	154	23	in	in	ADP
ap-7652	154	24	pairs	pair	NOUN
ap-7652	154	25	of	of	ADP
ap-7652	154	26	infinite	infinite	ADJ
ap-7652	154	27	sequences	sequence	NOUN
ap-7652	154	28	of	of	ADP
ap-7652	154	29	q	q	NOUN
ap-7652	154	30	-	-	PUNCT
ap-7652	154	31	rss	rss	NOUN
ap-7652	154	32	of	of	ADP
ap-7652	154	33	csle	csle	PROPN
ap-7652	154	34	(	(	PUNCT
ap-7652	154	35	32	32	NUM
ap-7652	154	36	):	):	PUNCT
ap-7652	154	37	∞ϕ±,m[y	∞ϕ±,m[y	PROPN
ap-7652	154	38	;	;	PUNCT
ap-7652	154	39	a	a	DET
ap-7652	154	40	]	]	X
ap-7652	154	41	=	=	SYM
ap-7652	154	42	∞c±,m(a)∞ϕ±,0[y	∞c±,m(a)∞ϕ±,0[y	PROPN
ap-7652	154	43	;	;	PUNCT
ap-7652	154	44	a]y	a]y	NOUN
ap-7652	154	45	(	(	PUNCT
ap-7652	154	46	±2a,∓2	±2a,∓2	PROPN
ap-7652	154	47	)	)	PUNCT
ap-7652	154	48	m	m	PROPN
ap-7652	154	49	(	(	PUNCT
ap-7652	154	50	y	y	NOUN
ap-7652	154	51	)	)	PUNCT
ap-7652	154	52	.	.	PUNCT
ap-7652	155	1	(	(	PUNCT
ap-7652	155	2	52	52	NUM
ap-7652	155	3	)	)	PUNCT
ap-7652	155	4	the	the	DET
ap-7652	155	5	multiplier	multipli	ADJ
ap-7652	155	6	lc±,m	lc±,m	NOUN
ap-7652	155	7	will	will	AUX
ap-7652	155	8	be	be	AUX
ap-7652	155	9	chosen	choose	VERB
ap-7652	155	10	below	below	ADP
ap-7652	155	11	in	in	ADP
ap-7652	155	12	such	such	DET
ap-7652	155	13	a	a	DET
ap-7652	155	14	way	way	NOUN
ap-7652	155	15	that	that	PRON
ap-7652	155	16	q	q	X
ap-7652	155	17	-	-	PUNCT
ap-7652	155	18	rss	rss	NOUN
ap-7652	155	19	(	(	PUNCT
ap-7652	155	20	52	52	NUM
ap-7652	155	21	)	)	PUNCT
ap-7652	155	22	satisfy	satisfy	NOUN
ap-7652	155	23	recurrence	recurrence	NOUN
ap-7652	155	24	relations	relation	NOUN
ap-7652	155	25	(	(	PUNCT
ap-7652	155	26	15	15	NUM
ap-7652	155	27	)	)	PUNCT
ap-7652	155	28	.	.	PUNCT
ap-7652	156	1	the	the	DET
ap-7652	156	2	crucial	crucial	ADJ
ap-7652	156	3	advantage	advantage	NOUN
ap-7652	156	4	of	of	ADP
ap-7652	156	5	expressing	express	VERB
ap-7652	156	6	q	q	NOUN
ap-7652	156	7	-	-	NOUN
ap-7652	156	8	rss	rss	NOUN
ap-7652	156	9	in	in	ADP
ap-7652	156	10	terms	term	NOUN
ap-7652	156	11	of	of	ADP
ap-7652	156	12	generalized	generalized	ADJ
ap-7652	156	13	bessel	bessel	ADJ
ap-7652	156	14	polynomials	polynomial	NOUN
ap-7652	156	15	,	,	PUNCT
ap-7652	156	16	instead	instead	ADV
ap-7652	156	17	of	of	ADP
ap-7652	156	18	laguerre	laguerre	NOUN
ap-7652	156	19	polynomials	polynomial	NOUN
ap-7652	157	1	[	[	X
ap-7652	157	2	7–11	7–11	NOUN
ap-7652	157	3	]	]	PUNCT
ap-7652	157	4	,	,	PUNCT
ap-7652	157	5	is	be	AUX
ap-7652	157	6	that	that	SCONJ
ap-7652	157	7	the	the	DET
ap-7652	157	8	weight	weight	NOUN
ap-7652	157	9	function	function	NOUN
ap-7652	157	10	∞ϕ±,0[y	∞ϕ±,0[y	PART
ap-7652	157	11	;	;	PUNCT
ap-7652	157	12	a	a	PRON
ap-7652	157	13	]	]	X
ap-7652	157	14	in	in	ADP
ap-7652	157	15	the	the	DET
ap-7652	157	16	right	right	ADJ
ap-7652	157	17	-	-	PUNCT
ap-7652	157	18	hand	hand	NOUN
ap-7652	157	19	side	side	NOUN
ap-7652	157	20	of	of	ADP
ap-7652	157	21	(	(	PUNCT
ap-7652	157	22	52	52	NUM
ap-7652	157	23	)	)	PUNCT
ap-7652	157	24	does	do	AUX
ap-7652	157	25	not	not	PART
ap-7652	157	26	depend	depend	VERB
ap-7652	157	27	on	on	ADP
ap-7652	157	28	the	the	DET
ap-7652	157	29	polynomial	polynomial	ADJ
ap-7652	157	30	degree	degree	NOUN
ap-7652	157	31	–	–	PUNCT
ap-7652	157	32	the	the	DET
ap-7652	157	33	direct	direct	ADJ
ap-7652	157	34	consequence	consequence	NOUN
ap-7652	157	35	of	of	ADP
ap-7652	157	36	the	the	DET
ap-7652	157	37	fact	fact	NOUN
ap-7652	157	38	that	that	SCONJ
ap-7652	157	39	the	the	DET
ap-7652	157	40	given	give	VERB
ap-7652	157	41	tfi	tfi	NOUN
ap-7652	157	42	csle	csle	PROPN
ap-7652	157	43	belongs	belong	VERB
ap-7652	157	44	to	to	AUX
ap-7652	157	45	group	group	PROPN
ap-7652	157	46	a	a	PRON
ap-7652	158	1	[	[	X
ap-7652	158	2	18	18	NUM
ap-7652	158	3	,	,	PUNCT
ap-7652	158	4	19	19	NUM
ap-7652	158	5	,	,	PUNCT
ap-7652	158	6	23	23	NUM
ap-7652	158	7	]	]	PUNCT
ap-7652	158	8	,	,	PUNCT
ap-7652	158	9	in	in	ADP
ap-7652	158	10	contrast	contrast	NOUN
ap-7652	158	11	with	with	ADP
ap-7652	158	12	the	the	DET
ap-7652	158	13	conventional	conventional	ADJ
ap-7652	158	14	representation	representation	NOUN
ap-7652	158	15	of	of	ADP
ap-7652	158	16	eigenfunctions	eigenfunction	NOUN
ap-7652	158	17	of	of	ADP
ap-7652	158	18	the	the	DET
ap-7652	158	19	schrödinger	schrödinger	ADJ
ap-7652	158	20	equation	equation	NOUN
ap-7652	158	21	with	with	ADP
ap-7652	158	22	the	the	DET
ap-7652	158	23	morse	morse	ADJ
ap-7652	158	24	potential	potential	NOUN
ap-7652	158	25	in	in	ADP
ap-7652	158	26	terms	term	NOUN
ap-7652	158	27	of	of	ADP
ap-7652	158	28	classical	classical	ADJ
ap-7652	158	29	laguerre	laguerre	NOUN
ap-7652	158	30	polynomials	polynomial	NOUN
ap-7652	158	31	[	[	X
ap-7652	158	32	22	22	NUM
ap-7652	158	33	]	]	PUNCT
ap-7652	158	34	.	.	PUNCT
ap-7652	159	1	according	accord	VERB
ap-7652	159	2	to	to	ADP
ap-7652	159	3	the	the	DET
ap-7652	159	4	general	general	ADJ
ap-7652	159	5	theory	theory	NOUN
ap-7652	159	6	of	of	ADP
ap-7652	159	7	bochner	bochner	NOUN
ap-7652	159	8	-	-	PUNCT
ap-7652	159	9	type	type	NOUN
ap-7652	159	10	eigenequations	eigenequation	NOUN
ap-7652	159	11	[	[	X
ap-7652	159	12	41	41	NUM
ap-7652	159	13	]	]	PUNCT
ap-7652	159	14	differential	differential	ADJ
ap-7652	159	15	equation	equation	NOUN
ap-7652	159	16	(	(	PUNCT
ap-7652	159	17	46	46	NUM
ap-7652	159	18	)	)	PUNCT
ap-7652	159	19	has	have	VERB
ap-7652	159	20	a	a	DET
ap-7652	159	21	polynomial	polynomial	ADJ
ap-7652	159	22	solution	solution	NOUN
ap-7652	159	23	of	of	ADP
ap-7652	159	24	degree	degree	NOUN
ap-7652	159	25	m	m	NOUN
ap-7652	159	26	at	at	ADP
ap-7652	159	27	ε	ε	PROPN
ap-7652	159	28	=	=	SYM
ap-7652	159	29	∞ε±,m(a	∞ε±,m(a	PROPN
ap-7652	159	30	)	)	PUNCT
ap-7652	159	31	=	=	SYM
ap-7652	159	32	∞ε±,0(a	∞ε±,0(a	PROPN
ap-7652	159	33	)	)	PUNCT
ap-7652	159	34	−m[2(1	−m[2(1	NOUN
ap-7652	159	35	±	±	PROPN
ap-7652	159	36	a	a	NOUN
ap-7652	159	37	)	)	PUNCT
ap-7652	160	1	+	+	ADP
ap-7652	160	2	m−	m−	PROPN
ap-7652	160	3	1	1	NUM
ap-7652	160	4	]	]	PUNCT
ap-7652	160	5	,	,	PUNCT
ap-7652	160	6	(	(	PUNCT
ap-7652	160	7	53	53	NUM
ap-7652	160	8	)	)	PUNCT
ap-7652	160	9	which	which	PRON
ap-7652	160	10	,	,	PUNCT
ap-7652	160	11	coupled	couple	VERB
ap-7652	160	12	with	with	ADP
ap-7652	160	13	(	(	PUNCT
ap-7652	160	14	36	36	NUM
ap-7652	160	15	)	)	PUNCT
ap-7652	160	16	,	,	PUNCT
ap-7652	160	17	gives	give	VERB
ap-7652	160	18	∞ε±,m(a	∞ε±,m(a	NOUN
ap-7652	160	19	)	)	PUNCT
ap-7652	161	1	=	=	SYM
ap-7652	161	2	−(m+	−(m+	NUM
ap-7652	161	3	1/2	1/2	NUM
ap-7652	161	4	±	±	NUM
ap-7652	161	5	a)2	a)2	PROPN
ap-7652	161	6	.	.	PUNCT
ap-7652	162	1	(	(	PUNCT
ap-7652	162	2	54	54	NUM
ap-7652	162	3	)	)	PUNCT
ap-7652	162	4	this	this	PRON
ap-7652	162	5	brings	bring	VERB
ap-7652	162	6	us	we	PRON
ap-7652	162	7	to	to	ADP
ap-7652	162	8	the	the	DET
ap-7652	162	9	simplified	simplified	ADJ
ap-7652	162	10	version	version	NOUN
ap-7652	162	11	of	of	ADP
ap-7652	162	12	the	the	DET
ap-7652	162	13	raising	raise	VERB
ap-7652	162	14	ladder	ladder	NOUN
ap-7652	162	15	relations	relation	NOUN
ap-7652	162	16	[	[	X
ap-7652	162	17	23	23	NUM
ap-7652	162	18	]	]	PUNCT
ap-7652	162	19	for	for	ADP
ap-7652	162	20	the	the	DET
ap-7652	162	21	energies	energy	NOUN
ap-7652	162	22	of	of	ADP
ap-7652	162	23	q	q	NOUN
ap-7652	162	24	-	-	ADJ
ap-7652	162	25	rss	rss	NOUN
ap-7652	162	26	(	(	PUNCT
ap-7652	162	27	15	15	NUM
ap-7652	162	28	):	):	PUNCT
ap-7652	162	29	∞ε±,m+1(a	∞ε±,m+1(a	X
ap-7652	162	30	)	)	PUNCT
ap-7652	162	31	=	=	SYM
ap-7652	162	32	∞ε±,m(a±	∞ε±,m(a±	PROPN
ap-7652	162	33	1	1	NUM
ap-7652	162	34	)	)	PUNCT
ap-7652	162	35	(	(	PUNCT
ap-7652	162	36	55	55	NUM
ap-7652	162	37	)	)	PUNCT
ap-7652	162	38	with	with	ADP
ap-7652	162	39	e±1(a	e±1(a	PROPN
ap-7652	162	40	)	)	PUNCT
ap-7652	162	41	≡	≡	PROPN
ap-7652	162	42	0	0	NUM
ap-7652	162	43	.	.	PUNCT
ap-7652	163	1	to	to	PART
ap-7652	163	2	be	be	AUX
ap-7652	163	3	historically	historically	ADV
ap-7652	163	4	accurate	accurate	ADJ
ap-7652	163	5	,	,	PUNCT
ap-7652	163	6	it	it	PRON
ap-7652	163	7	is	be	AUX
ap-7652	163	8	worth	worth	ADJ
ap-7652	163	9	mentioning	mention	VERB
ap-7652	163	10	that	that	DET
ap-7652	163	11	cotfas	cotfas	NOUN
ap-7652	163	12	’	'	PUNCT
ap-7652	163	13	eq	eq	NOUN
ap-7652	163	14	.	.	PUNCT
ap-7652	164	1	(	(	PUNCT
ap-7652	164	2	10	10	NUM
ap-7652	164	3	)	)	PUNCT
ap-7652	164	4	in	in	ADP
ap-7652	164	5	[	[	X
ap-7652	164	6	16	16	NUM
ap-7652	164	7	]	]	PUNCT
ap-7652	164	8	with	with	ADP
ap-7652	164	9	the	the	DET
ap-7652	164	10	leading	lead	VERB
ap-7652	164	11	coefficient	coefficient	NOUN
ap-7652	164	12	σ(s	σ(s	NOUN
ap-7652	164	13	)	)	PUNCT
ap-7652	164	14	=	=	SYM
ap-7652	164	15	s2	s2	PROPN
ap-7652	164	16	does	do	AUX
ap-7652	164	17	list	list	VERB
ap-7652	164	18	al	al	PROPN
ap-7652	164	19	-	-	PUNCT
ap-7652	164	20	salam	salam	PROPN
ap-7652	164	21	’s	’s	PART
ap-7652	165	1	[	[	X
ap-7652	165	2	4	4	NUM
ap-7652	165	3	]	]	PUNCT
ap-7652	165	4	formula	formula	NOUN
ap-7652	165	5	y	y	PROPN
ap-7652	165	6	(	(	PUNCT
ap-7652	165	7	α	α	NOUN
ap-7652	165	8	)	)	PUNCT
ap-7652	165	9	n	n	PROPN
ap-7652	165	10	(	(	PUNCT
ap-7652	165	11	y	y	NOUN
ap-7652	165	12	)	)	PUNCT
ap-7652	165	13	=	=	SYM
ap-7652	165	14	n	n	X
ap-7652	165	15	!	!	PUNCT
ap-7652	166	1	(	(	PUNCT
ap-7652	166	2	−y/2)nl(−α−2n−1	−y/2)nl(−α−2n−1	NUM
ap-7652	166	3	)	)	PUNCT
ap-7652	166	4	n	n	CCONJ
ap-7652	166	5	(	(	PUNCT
ap-7652	166	6	2	2	NUM
ap-7652	166	7	/	/	SYM
ap-7652	166	8	y	y	NOUN
ap-7652	166	9	)	)	PUNCT
ap-7652	166	10	(	(	PUNCT
ap-7652	166	11	56	56	NUM
ap-7652	166	12	)	)	PUNCT
ap-7652	166	13	for	for	ADP
ap-7652	166	14	the	the	DET
ap-7652	166	15	generalized	generalize	VERB
ap-7652	166	16	bessel	bessel	ADJ
ap-7652	166	17	polynomials	polynomial	NOUN
ap-7652	166	18	in	in	ADP
ap-7652	166	19	terms	term	NOUN
ap-7652	166	20	of	of	ADP
ap-7652	166	21	laguerre	laguerre	NOUN
ap-7652	166	22	polynomials	polynomial	NOUN
ap-7652	166	23	in	in	ADP
ap-7652	166	24	the	the	DET
ap-7652	166	25	reciprocal	reciprocal	ADJ
ap-7652	166	26	argument	argument	NOUN
ap-7652	166	27	2	2	NUM
ap-7652	166	28	/	/	SYM
ap-7652	166	29	y	y	PROPN
ap-7652	166	30	(	(	PUNCT
ap-7652	166	31	though	though	SCONJ
ap-7652	166	32	without	without	ADP
ap-7652	166	33	mentioning	mention	VERB
ap-7652	166	34	the	the	DET
ap-7652	166	35	former	former	ADJ
ap-7652	166	36	polynomials	polynomial	NOUN
ap-7652	166	37	by	by	ADP
ap-7652	166	38	name	name	NOUN
ap-7652	166	39	)	)	PUNCT
ap-7652	166	40	.	.	PUNCT
ap-7652	167	1	actually	actually	ADV
ap-7652	167	2	cotfas	cotfas	NOUN
ap-7652	167	3	discusses	discuss	VERB
ap-7652	167	4	only	only	ADV
ap-7652	167	5	eigenfunctions	eigenfunction	NOUN
ap-7652	167	6	of	of	ADP
ap-7652	167	7	the	the	DET
ap-7652	167	8	corresponding	corresponding	ADJ
ap-7652	167	9	sturm	sturm	PROPN
ap-7652	167	10	-	-	PUNCT
ap-7652	167	11	liouville	liouville	NOUN
ap-7652	167	12	problem	problem	NOUN
ap-7652	167	13	so	so	SCONJ
ap-7652	167	14	the	the	DET
ap-7652	167	15	cited	cite	VERB
ap-7652	167	16	formula	formula	NOUN
ap-7652	167	17	specifies	specifie	NOUN
ap-7652	167	18	r	r	NOUN
ap-7652	167	19	-	-	PUNCT
ap-7652	167	20	bessel	bessel	ADJ
ap-7652	167	21	polynomials	polynomial	NOUN
ap-7652	167	22	expressed	express	VERB
ap-7652	167	23	in	in	ADP
ap-7652	167	24	terms	term	NOUN
ap-7652	167	25	of	of	ADP
ap-7652	167	26	classical	classical	ADJ
ap-7652	167	27	laguerre	laguerre	NOUN
ap-7652	167	28	polynomials	polynomial	NOUN
ap-7652	167	29	in	in	ADP
ap-7652	167	30	2	2	NUM
ap-7652	167	31	/	/	SYM
ap-7652	167	32	y	y	NOUN
ap-7652	167	33	:	:	PUNCT
ap-7652	167	34	b(a	b(a	NOUN
ap-7652	167	35	)	)	PUNCT
ap-7652	167	36	n	n	CCONJ
ap-7652	167	37	(	(	PUNCT
ap-7652	167	38	y	y	NOUN
ap-7652	167	39	)	)	PUNCT
ap-7652	167	40	≡	≡	PROPN
ap-7652	167	41	y	y	PROPN
ap-7652	167	42	(	(	PUNCT
ap-7652	167	43	−2a−1	−2a−1	PROPN
ap-7652	167	44	)	)	PUNCT
ap-7652	167	45	n	n	CCONJ
ap-7652	167	46	(	(	PUNCT
ap-7652	167	47	y	y	NOUN
ap-7652	167	48	)	)	PUNCT
ap-7652	167	49	=	=	SYM
ap-7652	167	50	n	n	X
ap-7652	167	51	!	!	PUNCT
ap-7652	167	52	(	(	PUNCT
ap-7652	167	53	−y/2)nl(2a−2n	−y/2)nl(2a−2n	PROPN
ap-7652	167	54	)	)	PUNCT
ap-7652	167	55	n	n	CCONJ
ap-7652	167	56	(	(	PUNCT
ap-7652	167	57	2	2	NUM
ap-7652	167	58	/	/	SYM
ap-7652	167	59	y	y	NOUN
ap-7652	167	60	)	)	PUNCT
ap-7652	167	61	for	for	ADP
ap-7652	167	62	n	n	X
ap-7652	167	63	<	<	X
ap-7652	167	64	a	a	PRON
ap-7652	167	65	,	,	PUNCT
ap-7652	167	66	(	(	PUNCT
ap-7652	167	67	57	57	NUM
ap-7652	167	68	)	)	PUNCT
ap-7652	167	69	with	with	ADP
ap-7652	167	70	cotfas	cotfas	NOUN
ap-7652	167	71	’	'	PUNCT
ap-7652	167	72	parameter	parameter	NOUN
ap-7652	167	73	α	α	PROPN
ap-7652	167	74	standing	stand	VERB
ap-7652	167	75	for	for	ADP
ap-7652	167	76	1	1	NUM
ap-7652	167	77	−	−	PROPN
ap-7652	167	78	2a	2a	NUM
ap-7652	167	79	here	here	ADV
ap-7652	167	80	.	.	PUNCT
ap-7652	168	1	the	the	DET
ap-7652	168	2	remarkable	remarkable	ADJ
ap-7652	168	3	feature	feature	NOUN
ap-7652	168	4	of	of	ADP
ap-7652	168	5	this	this	DET
ap-7652	168	6	finite	finite	ADJ
ap-7652	168	7	subsequence	subsequence	NOUN
ap-7652	168	8	of	of	ADP
ap-7652	168	9	generalized	generalized	ADJ
ap-7652	168	10	bessel	bessel	ADJ
ap-7652	168	11	polynomials	polynomial	NOUN
ap-7652	168	12	is	be	AUX
ap-7652	168	13	that	that	SCONJ
ap-7652	168	14	the	the	DET
ap-7652	168	15	polynomials	polynomial	NOUN
ap-7652	168	16	in	in	ADP
ap-7652	168	17	question	question	NOUN
ap-7652	168	18	are	be	AUX
ap-7652	168	19	orthogonal	orthogonal	ADJ
ap-7652	168	20	on	on	ADP
ap-7652	168	21	the	the	DET
ap-7652	168	22	positive	positive	ADJ
ap-7652	168	23	semi	semi	ADJ
ap-7652	168	24	-	-	ADJ
ap-7652	168	25	axis	axis	ADJ
ap-7652	168	26	as	as	SCONJ
ap-7652	168	27	prescribed	prescribe	VERB
ap-7652	168	28	by	by	ADP
ap-7652	168	29	orthonormality	orthonormality	NOUN
ap-7652	168	30	relations	relation	NOUN
ap-7652	168	31	(	(	PUNCT
ap-7652	168	32	9.13.2	9.13.2	NUM
ap-7652	168	33	)	)	PUNCT
ap-7652	168	34	in	in	ADP
ap-7652	168	35	[	[	PUNCT
ap-7652	168	36	6]:∫	6]:∫	NUM
ap-7652	168	37	∞	∞	NOUN
ap-7652	168	38	0	0	NUM
ap-7652	168	39	∞ρ⋄[y]∞ϕ2	∞ρ⋄[y]∞ϕ2	PROPN
ap-7652	169	1	−,0[y;a+	−,0[y;a+	PROPN
ap-7652	169	2	1/2]b(a	1/2]b(a	NUM
ap-7652	169	3	)	)	PUNCT
ap-7652	169	4	n	n	PROPN
ap-7652	169	5	(	(	PUNCT
ap-7652	169	6	y)b(a	y)b(a	ADJ
ap-7652	169	7	)	)	PUNCT
ap-7652	169	8	˜	˜	PROPN
ap-7652	169	9	n	n	CCONJ
ap-7652	169	10	(	(	PUNCT
ap-7652	169	11	y)dy	y)dy	PROPN
ap-7652	169	12	≡	≡	PROPN
ap-7652	170	1	∫	∫	PROPN
ap-7652	171	1	∞	∞	PROPN
ap-7652	171	2	0	0	NUM
ap-7652	171	3	y−2a−1e−2	y−2a−1e−2	NOUN
ap-7652	171	4	/	/	SYM
ap-7652	171	5	yb(a	yb(a	NOUN
ap-7652	171	6	)	)	PUNCT
ap-7652	171	7	n	n	CCONJ
ap-7652	171	8	(	(	PUNCT
ap-7652	171	9	y)b(a	y)b(a	ADJ
ap-7652	171	10	)	)	PUNCT
ap-7652	171	11	˜	˜	PROPN
ap-7652	171	12	n	n	CCONJ
ap-7652	171	13	(	(	PUNCT
ap-7652	171	14	y)dy	y)dy	PROPN
ap-7652	171	15	=	=	SYM
ap-7652	171	16	n	n	CCONJ
ap-7652	171	17	!	!	NOUN
ap-7652	171	18	γ(2a+	γ(2a+	VERB
ap-7652	171	19	1	1	NUM
ap-7652	171	20	−	−	NOUN
ap-7652	171	21	n	n	CCONJ
ap-7652	171	22	)	)	PUNCT
ap-7652	172	1	2a−	2a−	PROPN
ap-7652	173	1	2n−	2n−	NUM
ap-7652	173	2	1	1	NUM
ap-7652	173	3	δn	δn	NOUN
ap-7652	173	4	˜	˜	PROPN
ap-7652	173	5	n.	n.	NOUN
ap-7652	173	6	(	(	PUNCT
ap-7652	173	7	58	58	NUM
ap-7652	173	8	)	)	PUNCT
ap-7652	173	9	105	105	NUM
ap-7652	173	10	gregory	gregory	PROPN
ap-7652	173	11	natanson	natanson	PROPN
ap-7652	173	12	acta	acta	PROPN
ap-7652	173	13	polytechnica	polytechnica	PROPN
ap-7652	173	14	making	make	VERB
ap-7652	173	15	use	use	NOUN
ap-7652	173	16	of	of	ADP
ap-7652	173	17	(	(	PUNCT
ap-7652	173	18	39	39	NUM
ap-7652	173	19	)	)	PUNCT
ap-7652	173	20	we	we	PRON
ap-7652	173	21	can	can	AUX
ap-7652	173	22	represent	represent	VERB
ap-7652	173	23	backward	backward	ADJ
ap-7652	173	24	shift	shift	NOUN
ap-7652	173	25	relation	relation	NOUN
ap-7652	173	26	(	(	PUNCT
ap-7652	173	27	9.13.8	9.13.8	NUM
ap-7652	173	28	)	)	PUNCT
ap-7652	173	29	in	in	ADP
ap-7652	173	30	[	[	X
ap-7652	173	31	6	6	NUM
ap-7652	173	32	]	]	PUNCT
ap-7652	173	33	as	as	ADP
ap-7652	173	34	d	d	PROPN
ap-7652	173	35	dy	dy	X
ap-7652	173	36	î	î	PROPN
ap-7652	173	37	∞f+,0	∞f+,0	NOUN
ap-7652	173	38	[	[	PUNCT
ap-7652	173	39	ξ	ξ	X
ap-7652	173	40	;	;	PUNCT
ap-7652	173	41	a	a	PRON
ap-7652	173	42	]	]	X
ap-7652	173	43	y	y	PROPN
ap-7652	173	44	(	(	PUNCT
ap-7652	173	45	−2a,2	−2a,2	NOUN
ap-7652	173	46	)	)	PUNCT
ap-7652	173	47	m	m	VERB
ap-7652	173	48	(	(	PUNCT
ap-7652	173	49	y	y	NOUN
ap-7652	173	50	)	)	PUNCT
ap-7652	173	51	ó	ó	NOUN
ap-7652	173	52	=	=	SYM
ap-7652	173	53	2∞f+,0[ξ	2∞f+,0[ξ	NUM
ap-7652	173	54	;	;	PUNCT
ap-7652	173	55	a+	a+	X
ap-7652	173	56	1]y	1]y	NUM
ap-7652	173	57	(	(	PUNCT
ap-7652	173	58	−2a−2,2	−2a−2,2	PROPN
ap-7652	173	59	)	)	PUNCT
ap-7652	174	1	m+1	m+1	PROPN
ap-7652	174	2	(	(	PUNCT
ap-7652	174	3	y	y	NOUN
ap-7652	174	4	)	)	PUNCT
ap-7652	174	5	(	(	PUNCT
ap-7652	174	6	59	59	NUM
ap-7652	174	7	)	)	PUNCT
ap-7652	174	8	so	so	SCONJ
ap-7652	174	9	the	the	DET
ap-7652	174	10	functions	function	NOUN
ap-7652	174	11	∞f+,m[ξ	∞f+,m[ξ	NOUN
ap-7652	174	12	;	;	PUNCT
ap-7652	174	13	a	a	PRON
ap-7652	174	14	]	]	X
ap-7652	174	15	=	=	SYM
ap-7652	174	16	∞c−,m(a)∞f∞,0[ξ	∞c−,m(a)∞f∞,0[ξ	PROPN
ap-7652	174	17	;	;	PUNCT
ap-7652	174	18	a]y	a]y	NOUN
ap-7652	174	19	(	(	PUNCT
ap-7652	174	20	−2a	−2a	PROPN
ap-7652	174	21	)	)	PUNCT
ap-7652	174	22	m	m	PROPN
ap-7652	174	23	(	(	PUNCT
ap-7652	174	24	y	y	NOUN
ap-7652	174	25	)	)	PUNCT
ap-7652	174	26	(	(	PUNCT
ap-7652	174	27	60	60	NUM
ap-7652	174	28	)	)	PUNCT
ap-7652	174	29	satisfy	satisfy	NOUN
ap-7652	174	30	raising	raise	VERB
ap-7652	174	31	relation	relation	NOUN
ap-7652	174	32	(	(	PUNCT
ap-7652	174	33	17	17	NUM
ap-7652	174	34	)	)	PUNCT
ap-7652	174	35	provided	provide	VERB
ap-7652	174	36	we	we	PRON
ap-7652	174	37	choose	choose	VERB
ap-7652	174	38	∞c−,m+1(a	∞c−,m+1(a	NUM
ap-7652	174	39	)	)	PUNCT
ap-7652	174	40	=	=	PUNCT
ap-7652	175	1	2∞c−,m(a−	2∞c−,m(a−	NUM
ap-7652	175	2	1	1	NUM
ap-7652	175	3	)	)	PUNCT
ap-7652	175	4	≡	≡	PROPN
ap-7652	175	5	2m+1	2m+1	PROPN
ap-7652	175	6	(	(	PUNCT
ap-7652	175	7	61	61	NUM
ap-7652	175	8	)	)	PUNCT
ap-7652	175	9	keeping	keep	VERB
ap-7652	175	10	in	in	ADP
ap-7652	175	11	mind	mind	NOUN
ap-7652	175	12	that	that	SCONJ
ap-7652	175	13	∞c−,0(a	∞c−,0(a	PROPN
ap-7652	175	14	)	)	PUNCT
ap-7652	175	15	≡	≡	PROPN
ap-7652	175	16	1	1	NUM
ap-7652	175	17	.	.	PUNCT
ap-7652	176	1	substituting	substitute	VERB
ap-7652	176	2	(	(	PUNCT
ap-7652	176	3	54	54	NUM
ap-7652	176	4	)	)	PUNCT
ap-7652	176	5	into	into	ADP
ap-7652	176	6	(	(	PUNCT
ap-7652	176	7	20	20	NUM
ap-7652	176	8	)	)	PUNCT
ap-7652	176	9	gives	give	VERB
ap-7652	176	10	∞e−,m−1(a−	∞e−,m−1(a−	ADV
ap-7652	176	11	1	1	NUM
ap-7652	176	12	)	)	PUNCT
ap-7652	176	13	=	=	PUNCT
ap-7652	176	14	−m(m+	−m(m+	ADP
ap-7652	176	15	1	1	NUM
ap-7652	176	16	−	−	NOUN
ap-7652	176	17	2a	2a	NUM
ap-7652	176	18	)	)	PUNCT
ap-7652	176	19	(	(	PUNCT
ap-7652	176	20	62	62	NUM
ap-7652	176	21	)	)	PUNCT
ap-7652	176	22	so	so	ADV
ap-7652	176	23	recurrence	recurrence	NOUN
ap-7652	176	24	relation	relation	NOUN
ap-7652	176	25	(	(	PUNCT
ap-7652	176	26	19	19	NUM
ap-7652	176	27	)	)	PUNCT
ap-7652	176	28	can	can	AUX
ap-7652	176	29	be	be	AUX
ap-7652	176	30	re	re	VERB
ap-7652	176	31	-	-	VERB
ap-7652	176	32	written	write	VERB
ap-7652	176	33	as	as	ADP
ap-7652	176	34	2myẏ	2myẏ	NUM
ap-7652	176	35	(	(	PUNCT
ap-7652	176	36	−2a,2	−2a,2	NUM
ap-7652	176	37	)	)	PUNCT
ap-7652	176	38	m	m	VERB
ap-7652	176	39	(	(	PUNCT
ap-7652	176	40	y	y	NOUN
ap-7652	176	41	)	)	PUNCT
ap-7652	177	1	=	=	PUNCT
ap-7652	177	2	m(m+	m(m+	VERB
ap-7652	177	3	1	1	NUM
ap-7652	177	4	−	−	NOUN
ap-7652	177	5	2a)∞ϕ−,m−1[y	2a)∞ϕ−,m−1[y	NUM
ap-7652	177	6	;	;	PUNCT
ap-7652	177	7	a−	a−	PROPN
ap-7652	177	8	1]/∞ϕ−,0[y	1]/∞ϕ−,0[y	NUM
ap-7652	177	9	;	;	PUNCT
ap-7652	177	10	a	a	PRON
ap-7652	177	11	]	]	X
ap-7652	177	12	.	.	PUNCT
ap-7652	178	1	(	(	PUNCT
ap-7652	178	2	63	63	NUM
ap-7652	178	3	)	)	PUNCT
ap-7652	178	4	combining	combine	VERB
ap-7652	178	5	(	(	PUNCT
ap-7652	178	6	52	52	NUM
ap-7652	178	7	)	)	PUNCT
ap-7652	178	8	,	,	PUNCT
ap-7652	178	9	(	(	PUNCT
ap-7652	178	10	61	61	NUM
ap-7652	178	11	)	)	PUNCT
ap-7652	178	12	,	,	PUNCT
ap-7652	178	13	and	and	CCONJ
ap-7652	178	14	(	(	PUNCT
ap-7652	178	15	37	37	NUM
ap-7652	178	16	)	)	PUNCT
ap-7652	178	17	with	with	ADP
ap-7652	178	18	k	k	PROPN
ap-7652	178	19	=	=	SYM
ap-7652	178	20	1	1	NUM
ap-7652	178	21	brings	bring	VERB
ap-7652	178	22	us	we	PRON
ap-7652	178	23	to	to	ADP
ap-7652	178	24	’	'	PUNCT
ap-7652	178	25	forward	forward	ADV
ap-7652	178	26	shift	shift	NOUN
ap-7652	178	27	operator	operator	NOUN
ap-7652	178	28	’	'	PUNCT
ap-7652	178	29	(	(	PUNCT
ap-7652	178	30	9.13.6	9.13.6	NUM
ap-7652	178	31	)	)	PUNCT
ap-7652	178	32	in	in	ADP
ap-7652	178	33	(	(	PUNCT
ap-7652	178	34	6	6	X
ap-7652	178	35	)	)	PUNCT
ap-7652	178	36	ẏ	ẏ	NOUN
ap-7652	178	37	(	(	PUNCT
ap-7652	178	38	−2a,2	−2a,2	NOUN
ap-7652	178	39	)	)	PUNCT
ap-7652	178	40	m	m	VERB
ap-7652	178	41	(	(	PUNCT
ap-7652	178	42	y	y	NOUN
ap-7652	178	43	)	)	PUNCT
ap-7652	179	1	=	=	SYM
ap-7652	179	2	0.5m(m+	0.5m(m+	NOUN
ap-7652	179	3	1	1	NUM
ap-7652	180	1	−	−	PROPN
ap-7652	180	2	2a)y	2a)y	NUM
ap-7652	180	3	(	(	PUNCT
ap-7652	180	4	2−2a,2	2−2a,2	NUM
ap-7652	180	5	)	)	PUNCT
ap-7652	180	6	m−1	m−1	PROPN
ap-7652	180	7	(	(	PUNCT
ap-7652	180	8	y	y	NOUN
ap-7652	180	9	)	)	PUNCT
ap-7652	180	10	.	.	PUNCT
ap-7652	181	1	(	(	PUNCT
ap-7652	181	2	64	64	NUM
ap-7652	181	3	)	)	PUNCT
ap-7652	181	4	to	to	PART
ap-7652	181	5	formulate	formulate	VERB
ap-7652	181	6	the	the	DET
ap-7652	181	7	sturm	sturm	NOUN
ap-7652	181	8	-	-	PUNCT
ap-7652	181	9	liouville	liouville	NOUN
ap-7652	181	10	problem	problem	NOUN
ap-7652	181	11	of	of	ADP
ap-7652	181	12	our	our	PRON
ap-7652	181	13	interest	interest	NOUN
ap-7652	181	14	it	it	PRON
ap-7652	181	15	is	be	AUX
ap-7652	181	16	worthy	worthy	ADJ
ap-7652	181	17	to	to	PART
ap-7652	181	18	convert	convert	VERB
ap-7652	181	19	csle	csle	NOUN
ap-7652	181	20	(	(	PUNCT
ap-7652	181	21	32	32	NUM
ap-7652	181	22	)	)	PUNCT
ap-7652	181	23	to	to	ADP
ap-7652	181	24	its	its	PRON
ap-7652	181	25	‘	'	PUNCT
ap-7652	181	26	prime	prime	ADJ
ap-7652	181	27	’	'	PUNCT
ap-7652	181	28	[	[	X
ap-7652	181	29	42	42	NUM
ap-7652	181	30	]	]	SYM
ap-7652	181	31	form	form	NOUN
ap-7652	181	32	at	at	ADP
ap-7652	181	33	∞	∞	PROPN
ap-7652	181	34	using	use	VERB
ap-7652	181	35	the	the	DET
ap-7652	181	36	gauge	gauge	ADJ
ap-7652	181	37	transformation	transformation	NOUN
ap-7652	181	38	∞	∞	PROPN
ap-7652	181	39	̸ψ	̸ψ	NOUN
ap-7652	182	1	[	[	X
ap-7652	182	2	y	y	X
ap-7652	182	3	;	;	PUNCT
ap-7652	182	4	a	a	PRON
ap-7652	182	5	;	;	PUNCT
ap-7652	182	6	ε	ε	X
ap-7652	182	7	]	]	X
ap-7652	182	8	=	=	PUNCT
ap-7652	182	9	y−1/2	y−1/2	PROPN
ap-7652	182	10	∞φ[y	∞φ[y	PROPN
ap-7652	182	11	;	;	PUNCT
ap-7652	182	12	a	a	PRON
ap-7652	182	13	;	;	PUNCT
ap-7652	182	14	ε	ε	PROPN
ap-7652	182	15	]	]	X
ap-7652	182	16	(	(	PUNCT
ap-7652	182	17	65	65	NUM
ap-7652	182	18	)	)	PUNCT
ap-7652	182	19	and	and	CCONJ
ap-7652	182	20	then	then	ADV
ap-7652	182	21	to	to	PART
ap-7652	182	22	solve	solve	VERB
ap-7652	182	23	the	the	DET
ap-7652	182	24	resultant	resultant	NOUN
ap-7652	182	25	rsle	rsle	NOUN
ap-7652	182	26	{	{	PUNCT
ap-7652	182	27	d	d	PROPN
ap-7652	182	28	dy	dy	NOUN
ap-7652	182	29	y	y	PROPN
ap-7652	182	30	d	d	PROPN
ap-7652	182	31	dy	dy	NOUN
ap-7652	183	1	−	−	NOUN
ap-7652	183	2	y−3	y−3	PROPN
ap-7652	183	3	+	+	CCONJ
ap-7652	183	4	2ay−2	2ay−2	NUM
ap-7652	183	5	+	+	CCONJ
ap-7652	183	6	εy−1	εy−1	ADJ
ap-7652	183	7	}	}	PUNCT
ap-7652	183	8	∞	∞	PROPN
ap-7652	183	9	̸ψ	̸ψ	VERB
ap-7652	183	10	[	[	X
ap-7652	183	11	y	y	X
ap-7652	183	12	;	;	PUNCT
ap-7652	183	13	a	a	DET
ap-7652	183	14	;	;	PUNCT
ap-7652	183	15	ε	ε	X
ap-7652	183	16	]	]	X
ap-7652	183	17	=	=	SYM
ap-7652	183	18	0	0	NUM
ap-7652	183	19	(	(	PUNCT
ap-7652	183	20	66	66	NUM
ap-7652	183	21	)	)	PUNCT
ap-7652	183	22	under	under	ADP
ap-7652	183	23	the	the	DET
ap-7652	183	24	dirichlet	dirichlet	PROPN
ap-7652	183	25	boundary	boundary	ADJ
ap-7652	183	26	conditions	condition	NOUN
ap-7652	183	27	(	(	PUNCT
ap-7652	183	28	dbcs	dbc	NOUN
ap-7652	183	29	):	):	PUNCT
ap-7652	183	30	lim	lim	PROPN
ap-7652	183	31	y→0	y→0	PROPN
ap-7652	184	1	∞	∞	PROPN
ap-7652	184	2	̸ψ	̸ψ	VERB
ap-7652	184	3	[	[	X
ap-7652	184	4	y	y	X
ap-7652	184	5	;	;	PUNCT
ap-7652	184	6	a	a	PRON
ap-7652	184	7	;	;	PUNCT
ap-7652	184	8	εn	εn	X
ap-7652	184	9	]	]	X
ap-7652	184	10	=	=	SYM
ap-7652	184	11	lim	lim	PROPN
ap-7652	184	12	y→∞	y→∞	NUM
ap-7652	184	13	∞	∞	PROPN
ap-7652	184	14	̸ψ	̸ψ	VERB
ap-7652	184	15	[	[	X
ap-7652	184	16	y	y	X
ap-7652	184	17	;	;	PUNCT
ap-7652	184	18	a	a	PRON
ap-7652	184	19	;	;	PUNCT
ap-7652	184	20	εn	εn	X
ap-7652	184	21	]	]	PUNCT
ap-7652	184	22	=	=	SYM
ap-7652	184	23	0	0	X
ap-7652	184	24	.	.	PUNCT
ap-7652	185	1	(	(	PUNCT
ap-7652	185	2	67	67	NUM
ap-7652	185	3	)	)	PUNCT
ap-7652	185	4	the	the	DET
ap-7652	185	5	main	main	ADJ
ap-7652	185	6	advantage	advantage	NOUN
ap-7652	185	7	of	of	ADP
ap-7652	185	8	converting	convert	VERB
ap-7652	185	9	csle	csle	NOUN
ap-7652	185	10	(	(	PUNCT
ap-7652	185	11	32	32	NUM
ap-7652	185	12	)	)	PUNCT
ap-7652	185	13	to	to	ADP
ap-7652	185	14	its	its	PRON
ap-7652	185	15	prime	prime	ADJ
ap-7652	185	16	form	form	NOUN
ap-7652	185	17	with	with	ADP
ap-7652	185	18	respect	respect	NOUN
ap-7652	185	19	to	to	ADP
ap-7652	185	20	the	the	DET
ap-7652	185	21	regular	regular	ADJ
ap-7652	185	22	singular	singular	ADJ
ap-7652	185	23	point	point	NOUN
ap-7652	185	24	at	at	ADP
ap-7652	185	25	infinity	infinity	NOUN
ap-7652	185	26	comes	come	VERB
ap-7652	185	27	from	from	ADP
ap-7652	185	28	our	our	PRON
ap-7652	185	29	observation	observation	NOUN
ap-7652	185	30	[	[	X
ap-7652	185	31	42	42	NUM
ap-7652	185	32	]	]	PUNCT
ap-7652	185	33	that	that	SCONJ
ap-7652	185	34	the	the	DET
ap-7652	185	35	characteristic	characteristic	ADJ
ap-7652	185	36	exponents	exponent	NOUN
ap-7652	185	37	for	for	ADP
ap-7652	185	38	this	this	DET
ap-7652	185	39	singular	singular	ADJ
ap-7652	185	40	end	end	NOUN
ap-7652	185	41	have	have	VERB
ap-7652	185	42	opposite	opposite	ADJ
ap-7652	185	43	signs	sign	NOUN
ap-7652	185	44	and	and	CCONJ
ap-7652	185	45	therefore	therefore	ADV
ap-7652	185	46	the	the	DET
ap-7652	185	47	corresponding	corresponding	ADJ
ap-7652	185	48	principal	principal	ADJ
ap-7652	185	49	frobenius	frobenius	NOUN
ap-7652	185	50	solution	solution	NOUN
ap-7652	185	51	is	be	AUX
ap-7652	185	52	unambiguously	unambiguously	ADV
ap-7652	185	53	selected	select	VERB
ap-7652	185	54	by	by	ADP
ap-7652	185	55	the	the	DET
ap-7652	185	56	dbc	dbc	PROPN
ap-7652	185	57	.	.	PUNCT
ap-7652	186	1	prime	prime	PROPN
ap-7652	186	2	rsle	rsle	PROPN
ap-7652	186	3	(	(	PUNCT
ap-7652	186	4	66	66	NUM
ap-7652	186	5	)	)	PUNCT
ap-7652	186	6	can	can	AUX
ap-7652	186	7	be	be	AUX
ap-7652	186	8	also	also	ADV
ap-7652	186	9	re	re	VERB
ap-7652	186	10	-	-	VERB
ap-7652	186	11	written	write	VERB
ap-7652	186	12	in	in	ADP
ap-7652	186	13	the	the	DET
ap-7652	186	14	form	form	NOUN
ap-7652	186	15	of	of	ADP
ap-7652	186	16	the	the	DET
ap-7652	186	17	‘	'	PUNCT
ap-7652	186	18	algebraic	algebraic	ADJ
ap-7652	186	19	’	'	PUNCT
ap-7652	186	20	[	[	X
ap-7652	186	21	42	42	NUM
ap-7652	186	22	]	]	X
ap-7652	186	23	schrödinger	schrödinger	ADJ
ap-7652	186	24	equation	equation	NOUN
ap-7652	186	25	{	{	PUNCT
ap-7652	186	26	y	y	NOUN
ap-7652	186	27	d	d	PROPN
ap-7652	186	28	dy	dy	NOUN
ap-7652	186	29	y	y	PROPN
ap-7652	186	30	d	d	PROPN
ap-7652	186	31	dy	dy	NOUN
ap-7652	187	1	−	−	PROPN
ap-7652	187	2	y−2	y−2	PROPN
ap-7652	187	3	+	+	CCONJ
ap-7652	187	4	2ay−1	2ay−1	PROPN
ap-7652	187	5	+	+	CCONJ
ap-7652	187	6	ε	ε	PROPN
ap-7652	187	7	}	}	PUNCT
ap-7652	187	8	∞	∞	PROPN
ap-7652	187	9	̸ψ	̸ψ	VERB
ap-7652	187	10	[	[	X
ap-7652	187	11	y	y	X
ap-7652	187	12	;	;	PUNCT
ap-7652	187	13	a	a	DET
ap-7652	187	14	;	;	PUNCT
ap-7652	187	15	ε	ε	X
ap-7652	187	16	]	]	X
ap-7652	187	17	=	=	SYM
ap-7652	187	18	0	0	X
ap-7652	187	19	.	.	PUNCT
ap-7652	188	1	(	(	PUNCT
ap-7652	188	2	68	68	NUM
ap-7652	188	3	)	)	PUNCT
ap-7652	188	4	(	(	PUNCT
ap-7652	188	5	as	as	SCONJ
ap-7652	188	6	discussed	discuss	VERB
ap-7652	188	7	in	in	ADP
ap-7652	188	8	the	the	DET
ap-7652	188	9	following	follow	VERB
ap-7652	188	10	subsections	subsection	NOUN
ap-7652	188	11	this	this	PRON
ap-7652	188	12	is	be	AUX
ap-7652	188	13	the	the	DET
ap-7652	188	14	common	common	ADJ
ap-7652	188	15	remarkable	remarkable	ADJ
ap-7652	188	16	feature	feature	NOUN
ap-7652	188	17	of	of	ADP
ap-7652	188	18	rcsles	rcsle	NOUN
ap-7652	188	19	with	with	ADP
ap-7652	188	20	density	density	NOUN
ap-7652	188	21	function	function	NOUN
ap-7652	188	22	(	(	PUNCT
ap-7652	188	23	34	34	NUM
ap-7652	188	24	)	)	PUNCT
ap-7652	188	25	assuming	assume	VERB
ap-7652	188	26	that	that	SCONJ
ap-7652	188	27	the	the	DET
ap-7652	188	28	singular	singular	ADJ
ap-7652	188	29	point	point	NOUN
ap-7652	188	30	at	at	ADP
ap-7652	188	31	infinity	infinity	NOUN
ap-7652	188	32	is	be	AUX
ap-7652	188	33	regular	regular	ADJ
ap-7652	188	34	.	.	PUNCT
ap-7652	188	35	)	)	PUNCT
ap-7652	189	1	reformulating	reformulate	VERB
ap-7652	189	2	the	the	DET
ap-7652	189	3	given	give	VERB
ap-7652	189	4	spectral	spectral	ADJ
ap-7652	189	5	problem	problem	NOUN
ap-7652	189	6	in	in	ADP
ap-7652	189	7	such	such	DET
ap-7652	189	8	a	a	DET
ap-7652	189	9	way	way	NOUN
ap-7652	189	10	allows	allow	VERB
ap-7652	189	11	us	we	PRON
ap-7652	189	12	to	to	PART
ap-7652	189	13	take	take	VERB
ap-7652	189	14	advantage	advantage	NOUN
ap-7652	189	15	of	of	ADP
ap-7652	189	16	powerful	powerful	ADJ
ap-7652	189	17	theorems	theorem	NOUN
ap-7652	189	18	proven	prove	VERB
ap-7652	189	19	in	in	ADP
ap-7652	189	20	[	[	X
ap-7652	189	21	43	43	NUM
ap-7652	189	22	]	]	PUNCT
ap-7652	189	23	for	for	SCONJ
ap-7652	189	24	zeros	zero	NOUN
ap-7652	189	25	of	of	ADP
ap-7652	189	26	principal	principal	ADJ
ap-7652	189	27	solutions	solution	NOUN
ap-7652	189	28	of	of	ADP
ap-7652	189	29	sles	sle	NOUN
ap-7652	189	30	solved	solve	VERB
ap-7652	189	31	under	under	ADP
ap-7652	189	32	the	the	DET
ap-7652	189	33	dbcs	dbc	NOUN
ap-7652	189	34	at	at	ADP
ap-7652	189	35	singular	singular	NOUN
ap-7652	189	36	ends	end	VERB
ap-7652	189	37	.	.	PUNCT
ap-7652	190	1	the	the	DET
ap-7652	190	2	eigenfunctions	eigenfunction	NOUN
ap-7652	190	3	of	of	ADP
ap-7652	190	4	rsle	rsle	NOUN
ap-7652	190	5	(	(	PUNCT
ap-7652	190	6	66	66	NUM
ap-7652	190	7	)	)	PUNCT
ap-7652	190	8	thus	thus	ADV
ap-7652	190	9	take	take	VERB
ap-7652	190	10	form	form	NOUN
ap-7652	190	11	∞	∞	NOUN
ap-7652	190	12	̸ψ−,n	̸ψ−,n	ADJ
ap-7652	191	1	[	[	X
ap-7652	191	2	y	y	X
ap-7652	191	3	;	;	PUNCT
ap-7652	191	4	a	a	X
ap-7652	191	5	]	]	X
ap-7652	191	6	=	=	PUNCT
ap-7652	191	7	y−1/2	y−1/2	PROPN
ap-7652	191	8	∞ϕ−,n[y	∞ϕ−,n[y	PROPN
ap-7652	191	9	;	;	PUNCT
ap-7652	191	10	a	a	PRON
ap-7652	191	11	]	]	X
ap-7652	191	12	=	=	SYM
ap-7652	191	13	2ny1/2−ae−1	2ny1/2−ae−1	NUM
ap-7652	191	14	/	/	SYM
ap-7652	191	15	yb(a−1/2	yb(a−1/2	NOUN
ap-7652	191	16	)	)	PUNCT
ap-7652	192	1	n	n	CCONJ
ap-7652	192	2	(	(	PUNCT
ap-7652	192	3	y	y	NOUN
ap-7652	192	4	)	)	PUNCT
ap-7652	192	5	for	for	ADP
ap-7652	192	6	n	n	NOUN
ap-7652	192	7	=	=	SYM
ap-7652	192	8	0	0	NUM
ap-7652	192	9	,	,	PUNCT
ap-7652	192	10	.	.	PUNCT
ap-7652	192	11	.	.	PUNCT
ap-7652	193	1	.	.	PUNCT
ap-7652	194	1	,	,	PUNCT
ap-7652	195	1	n(a	n(a	NUM
ap-7652	195	2	)	)	PUNCT
ap-7652	195	3	.	.	PUNCT
ap-7652	196	1	(	(	PUNCT
ap-7652	196	2	69	69	NUM
ap-7652	196	3	)	)	PUNCT
ap-7652	196	4	one	one	NOUN
ap-7652	196	5	can	can	AUX
ap-7652	196	6	then	then	ADV
ap-7652	196	7	directly	directly	ADV
ap-7652	196	8	verify	verify	VERB
ap-7652	196	9	that	that	SCONJ
ap-7652	196	10	each	each	DET
ap-7652	196	11	eigenfunction	eigenfunction	NOUN
ap-7652	196	12	obeys	obey	VERB
ap-7652	196	13	the	the	DET
ap-7652	196	14	dbc	dbc	NOUN
ap-7652	196	15	at	at	ADP
ap-7652	196	16	both	both	DET
ap-7652	196	17	singular	singular	PROPN
ap-7652	196	18	ends	end	VERB
ap-7652	196	19	.	.	PUNCT
ap-7652	197	1	since	since	SCONJ
ap-7652	197	2	r	r	NOUN
ap-7652	197	3	-	-	PUNCT
ap-7652	197	4	bessel	bessel	ADJ
ap-7652	197	5	polynomials	polynomial	NOUN
ap-7652	197	6	(	(	PUNCT
ap-7652	197	7	57	57	NUM
ap-7652	197	8	)	)	PUNCT
ap-7652	197	9	form	form	VERB
ap-7652	197	10	an	an	DET
ap-7652	197	11	orthogonal	orthogonal	ADJ
ap-7652	197	12	sequence	sequence	NOUN
ap-7652	197	13	the	the	DET
ap-7652	197	14	eigenfunction	eigenfunction	NOUN
ap-7652	197	15	∞	∞	NOUN
ap-7652	197	16	̸ψ−,n	̸ψ−,n	X
ap-7652	198	1	[	[	X
ap-7652	198	2	y	y	X
ap-7652	198	3	;	;	PUNCT
ap-7652	198	4	a	a	PRON
ap-7652	198	5	]	]	X
ap-7652	198	6	must	must	AUX
ap-7652	198	7	have	have	VERB
ap-7652	198	8	exactly	exactly	ADV
ap-7652	198	9	n	n	PRON
ap-7652	198	10	nodes	node	NOUN
ap-7652	198	11	and	and	CCONJ
ap-7652	198	12	therefore	therefore	ADV
ap-7652	198	13	[	[	X
ap-7652	198	14	43	43	NUM
ap-7652	198	15	]	]	PUNCT
ap-7652	198	16	the	the	DET
ap-7652	198	17	sequence	sequence	NOUN
ap-7652	198	18	of	of	ADP
ap-7652	198	19	eigenfunctions	eigenfunction	NOUN
ap-7652	198	20	(	(	PUNCT
ap-7652	198	21	69	69	NUM
ap-7652	198	22	)	)	PUNCT
ap-7652	198	23	corresponds	correspond	VERB
ap-7652	198	24	to	to	ADP
ap-7652	198	25	⌈a⌉	⌈a⌉	NOUN
ap-7652	198	26	=	=	SYM
ap-7652	198	27	n(a	n(a	PROPN
ap-7652	198	28	)	)	PUNCT
ap-7652	199	1	+	+	CCONJ
ap-7652	199	2	1	1	NUM
ap-7652	199	3	lowest	low	ADJ
ap-7652	199	4	eigenvalues	eigenvalue	NOUN
ap-7652	199	5	of	of	ADP
ap-7652	199	6	rsle	rsle	NOUN
ap-7652	199	7	(	(	PUNCT
ap-7652	199	8	66	66	NUM
ap-7652	199	9	)	)	PUNCT
ap-7652	199	10	with	with	ADP
ap-7652	199	11	n(a	n(a	NOUN
ap-7652	199	12	)	)	PUNCT
ap-7652	199	13	=	=	PUNCT
ap-7652	199	14	⌊a−	⌊a−	X
ap-7652	199	15	1/2⌋	1/2⌋	NUM
ap-7652	199	16	≡	≡	PROPN
ap-7652	199	17	⌊a⌋.	⌊a⌋.	PROPN
ap-7652	199	18	(	(	PUNCT
ap-7652	199	19	70	70	NUM
ap-7652	199	20	)	)	PUNCT
ap-7652	199	21	note	note	NOUN
ap-7652	199	22	also	also	ADV
ap-7652	199	23	that	that	SCONJ
ap-7652	199	24	eigenfunctions	eigenfunction	NOUN
ap-7652	199	25	(	(	PUNCT
ap-7652	199	26	69	69	NUM
ap-7652	199	27	)	)	PUNCT
ap-7652	199	28	are	be	AUX
ap-7652	199	29	orthogonal	orthogonal	ADJ
ap-7652	199	30	with	with	ADP
ap-7652	199	31	the	the	DET
ap-7652	199	32	weight	weight	NOUN
ap-7652	199	33	y−1	y−1	PROPN
ap-7652	199	34	and	and	CCONJ
ap-7652	199	35	that	that	SCONJ
ap-7652	199	36	any	any	DET
ap-7652	199	37	solution	solution	NOUN
ap-7652	199	38	normalizable	normalizable	ADJ
ap-7652	199	39	with	with	ADP
ap-7652	199	40	this	this	DET
ap-7652	199	41	weight	weight	NOUN
ap-7652	199	42	must	must	AUX
ap-7652	199	43	vanish	vanish	VERB
ap-7652	199	44	at	at	ADP
ap-7652	199	45	infinity	infinity	NOUN
ap-7652	199	46	.	.	PUNCT
ap-7652	200	1	106	106	NUM
ap-7652	200	2	vol	vol	NOUN
ap-7652	200	3	.	.	PUNCT
ap-7652	201	1	62	62	NUM
ap-7652	201	2	no	no	INTJ
ap-7652	201	3	.	.	PUNCT
ap-7652	202	1	1/2022	1/2022	NUM
ap-7652	202	2	quantization	quantization	NOUN
ap-7652	202	3	of	of	ADP
ap-7652	202	4	rationally	rationally	ADV
ap-7652	202	5	deformed	deform	VERB
ap-7652	202	6	morse	morse	ADJ
ap-7652	202	7	potentials	potential	NOUN
ap-7652	202	8	.	.	PUNCT
ap-7652	202	9	.	.	PUNCT
ap-7652	202	10	.	.	PUNCT
ap-7652	203	1	the	the	DET
ap-7652	203	2	presented	present	VERB
ap-7652	203	3	argumentation	argumentation	NOUN
ap-7652	203	4	does	do	AUX
ap-7652	203	5	not	not	PART
ap-7652	203	6	exclude	exclude	VERB
ap-7652	203	7	existence	existence	NOUN
ap-7652	203	8	of	of	ADP
ap-7652	203	9	eigenfunctions	eigenfunction	NOUN
ap-7652	203	10	with	with	ADP
ap-7652	203	11	the	the	DET
ap-7652	203	12	number	number	NOUN
ap-7652	203	13	of	of	ADP
ap-7652	203	14	nodes	node	NOUN
ap-7652	203	15	larger	large	ADJ
ap-7652	203	16	than	than	ADP
ap-7652	203	17	n(a	n(a	NOUN
ap-7652	203	18	)	)	PUNCT
ap-7652	203	19	−	−	PROPN
ap-7652	204	1	1	1	X
ap-7652	204	2	.	.	PUNCT
ap-7652	204	3	to	to	PART
ap-7652	204	4	confirm	confirm	VERB
ap-7652	204	5	that	that	SCONJ
ap-7652	204	6	the	the	DET
ap-7652	204	7	problem	problem	NOUN
ap-7652	204	8	in	in	ADP
ap-7652	204	9	question	question	NOUN
ap-7652	204	10	is	be	AUX
ap-7652	204	11	indeed	indeed	ADV
ap-7652	204	12	exactly	exactly	ADV
ap-7652	204	13	solvable	solvable	ADJ
ap-7652	204	14	one	one	PRON
ap-7652	204	15	can	can	AUX
ap-7652	204	16	simply	simply	ADV
ap-7652	204	17	take	take	VERB
ap-7652	204	18	advantage	advantage	NOUN
ap-7652	204	19	of	of	ADP
ap-7652	204	20	the	the	DET
ap-7652	204	21	conventional	conventional	ADJ
ap-7652	204	22	analysis	analysis	NOUN
ap-7652	204	23	of	of	ADP
ap-7652	204	24	the	the	DET
ap-7652	204	25	schrödinger	schrödinger	ADJ
ap-7652	204	26	equation	equation	NOUN
ap-7652	204	27	with	with	ADP
ap-7652	204	28	the	the	DET
ap-7652	204	29	morse	morse	ADJ
ap-7652	204	30	potential	potential	NOUN
ap-7652	205	1	[	[	X
ap-7652	205	2	22	22	NUM
ap-7652	205	3	]	]	PUNCT
ap-7652	205	4	in	in	ADP
ap-7652	205	5	the	the	DET
ap-7652	205	6	l	l	NOUN
ap-7652	205	7	ref	ref	NOUN
ap-7652	205	8	representation	representation	NOUN
ap-7652	205	9	.	.	PUNCT
ap-7652	206	1	the	the	DET
ap-7652	206	2	reader	reader	NOUN
ap-7652	206	3	can	can	AUX
ap-7652	206	4	argue	argue	VERB
ap-7652	206	5	that	that	SCONJ
ap-7652	206	6	the	the	DET
ap-7652	206	7	problem	problem	NOUN
ap-7652	206	8	must	must	AUX
ap-7652	206	9	be	be	AUX
ap-7652	206	10	exactly	exactly	ADV
ap-7652	206	11	solvable	solvable	ADJ
ap-7652	206	12	since	since	SCONJ
ap-7652	206	13	the	the	DET
ap-7652	206	14	morse	morse	ADJ
ap-7652	206	15	potential	potential	NOUN
ap-7652	206	16	is	be	AUX
ap-7652	206	17	tsi	tsi	PROPN
ap-7652	206	18	.	.	PUNCT
ap-7652	207	1	however	however	ADV
ap-7652	207	2	the	the	DET
ap-7652	207	3	author	author	NOUN
ap-7652	207	4	[	[	X
ap-7652	207	5	44	44	NUM
ap-7652	207	6	]	]	PUNCT
ap-7652	207	7	has	have	VERB
ap-7652	207	8	an	an	DET
ap-7652	207	9	issue	issue	NOUN
ap-7652	207	10	with	with	ADP
ap-7652	207	11	this	this	DET
ap-7652	207	12	assertion	assertion	NOUN
ap-7652	207	13	.	.	PUNCT
ap-7652	208	1	though	though	SCONJ
ap-7652	208	2	the	the	DET
ap-7652	208	3	gendenshtein	gendenshtein	NOUN
ap-7652	208	4	’s	’s	PART
ap-7652	208	5	claim	claim	NOUN
ap-7652	208	6	[	[	X
ap-7652	208	7	34	34	NUM
ap-7652	208	8	]	]	PUNCT
ap-7652	208	9	concerning	concern	VERB
ap-7652	208	10	the	the	DET
ap-7652	208	11	exact	exact	ADJ
ap-7652	208	12	solvability	solvability	NOUN
ap-7652	208	13	of	of	ADP
ap-7652	208	14	shape	shape	NOUN
ap-7652	208	15	-	-	PUNCT
ap-7652	208	16	invariant	invariant	ADJ
ap-7652	208	17	potentials	potential	NOUN
ap-7652	208	18	is	be	AUX
ap-7652	208	19	most	most	ADV
ap-7652	208	20	likely	likely	ADJ
ap-7652	208	21	correct	correct	ADJ
ap-7652	208	22	it	it	PRON
ap-7652	208	23	has	have	AUX
ap-7652	208	24	been	be	AUX
ap-7652	208	25	never	never	ADV
ap-7652	208	26	accurately	accurately	ADV
ap-7652	208	27	proven	prove	VERB
ap-7652	208	28	to	to	ADP
ap-7652	208	29	our	our	PRON
ap-7652	208	30	knowledge	knowledge	NOUN
ap-7652	208	31	.	.	PUNCT
ap-7652	209	1	the	the	DET
ap-7652	209	2	catch	catch	NOUN
ap-7652	209	3	is	be	AUX
ap-7652	209	4	that	that	DET
ap-7652	209	5	gendenshtein	gendenshtein	NOUN
ap-7652	209	6	’s	’s	PART
ap-7652	209	7	arguments	argument	NOUN
ap-7652	209	8	decreasing	decrease	VERB
ap-7652	209	9	the	the	DET
ap-7652	209	10	translational	translational	ADJ
ap-7652	209	11	parameter	parameter	NOUN
ap-7652	209	12	a	a	DET
ap-7652	209	13	one	one	NUM
ap-7652	209	14	by	by	ADP
ap-7652	209	15	one	one	NUM
ap-7652	209	16	bring	bring	VERB
ap-7652	209	17	us	we	PRON
ap-7652	209	18	to	to	ADP
ap-7652	209	19	the	the	DET
ap-7652	209	20	sturm	sturm	NOUN
ap-7652	209	21	-	-	PUNCT
ap-7652	209	22	liouville	liouville	NOUN
ap-7652	209	23	problem	problem	NOUN
ap-7652	209	24	with	with	ADP
ap-7652	209	25	|	|	ADV
ap-7652	209	26	a	a	DET
ap-7652	209	27	|	|	NOUN
ap-7652	209	28	<	<	X
ap-7652	209	29	1/2	1/2	NUM
ap-7652	209	30	and	and	CCONJ
ap-7652	209	31	then	then	ADV
ap-7652	209	32	we	we	PRON
ap-7652	209	33	still	still	ADV
ap-7652	209	34	need	need	VERB
ap-7652	209	35	to	to	PART
ap-7652	209	36	prove	prove	VERB
ap-7652	209	37	that	that	SCONJ
ap-7652	209	38	the	the	DET
ap-7652	209	39	resultant	resultant	NOUN
ap-7652	209	40	sle	sle	NOUN
ap-7652	209	41	has	have	VERB
ap-7652	209	42	no	no	DET
ap-7652	209	43	discrete	discrete	ADJ
ap-7652	209	44	energy	energy	NOUN
ap-7652	209	45	spectrum	spectrum	NOUN
ap-7652	209	46	.	.	PUNCT
ap-7652	210	1	the	the	DET
ap-7652	210	2	change	change	NOUN
ap-7652	210	3	of	of	ADP
ap-7652	210	4	variable	variable	NOUN
ap-7652	210	5	y(x	y(x	NOUN
ap-7652	210	6	)	)	PUNCT
ap-7652	210	7	=	=	PUNCT
ap-7652	211	1	ex	ex	X
ap-7652	211	2	converts	convert	VERB
ap-7652	211	3	bref	bref	PROPN
ap-7652	211	4	csle	csle	PROPN
ap-7652	211	5	(	(	PUNCT
ap-7652	211	6	32	32	NUM
ap-7652	211	7	)	)	PUNCT
ap-7652	211	8	into	into	ADP
ap-7652	211	9	the	the	DET
ap-7652	211	10	schrödinger	schrödinger	ADJ
ap-7652	211	11	equation	equation	NOUN
ap-7652	211	12	with	with	ADP
ap-7652	211	13	the	the	DET
ap-7652	211	14	morse	morse	ADJ
ap-7652	211	15	potential	potential	NOUN
ap-7652	211	16	∞v	∞v	NUM
ap-7652	212	1	[	[	X
ap-7652	212	2	y(x	y(x	NOUN
ap-7652	212	3	)	)	PUNCT
ap-7652	212	4	;	;	PUNCT
ap-7652	212	5	a	a	DET
ap-7652	212	6	]	]	X
ap-7652	212	7	,	,	PUNCT
ap-7652	212	8	where	where	SCONJ
ap-7652	212	9	∞v	∞v	ADP
ap-7652	213	1	[	[	X
ap-7652	213	2	y	y	X
ap-7652	213	3	;	;	PUNCT
ap-7652	213	4	a	a	X
ap-7652	213	5	]	]	X
ap-7652	213	6	=	=	SYM
ap-7652	213	7	−y2i0[y	−y2i0[y	PROPN
ap-7652	213	8	;	;	PUNCT
ap-7652	213	9	a	a	PRON
ap-7652	213	10	]	]	X
ap-7652	213	11	+	+	NUM
ap-7652	213	12	1/4	1/4	NUM
ap-7652	213	13	(	(	PUNCT
ap-7652	213	14	71	71	NUM
ap-7652	213	15	)	)	PUNCT
ap-7652	213	16	=	=	SYM
ap-7652	213	17	−2ay−1	−2ay−1	PROPN
ap-7652	213	18	+	+	NUM
ap-7652	213	19	y−2	y−2	PROPN
ap-7652	213	20	.	.	PUNCT
ap-7652	214	1	(	(	PUNCT
ap-7652	214	2	72	72	X
ap-7652	214	3	)	)	PUNCT
ap-7652	214	4	comparing	compare	VERB
ap-7652	214	5	(	(	PUNCT
ap-7652	214	6	72	72	NUM
ap-7652	214	7	)	)	PUNCT
ap-7652	214	8	with	with	ADP
ap-7652	214	9	(	(	PUNCT
ap-7652	214	10	1	1	X
ap-7652	214	11	)	)	PUNCT
ap-7652	214	12	in	in	ADP
ap-7652	214	13	[	[	X
ap-7652	214	14	10	10	NUM
ap-7652	214	15	]	]	PUNCT
ap-7652	214	16	shows	show	VERB
ap-7652	214	17	that	that	SCONJ
ap-7652	214	18	∞v	∞v	ADP
ap-7652	215	1	[	[	X
ap-7652	215	2	y(x);a+	y(x);a+	ADJ
ap-7652	215	3	1/2	1/2	NUM
ap-7652	215	4	]	]	PUNCT
ap-7652	215	5	=	=	SYM
ap-7652	215	6	va,1(x	va,1(x	NOUN
ap-7652	215	7	)	)	PUNCT
ap-7652	215	8	in	in	ADP
ap-7652	215	9	quesne	quesne	NOUN
ap-7652	215	10	’s	’s	PART
ap-7652	215	11	notation	notation	NOUN
ap-7652	215	12	.	.	PUNCT
ap-7652	216	1	according	accord	VERB
ap-7652	216	2	to	to	ADP
ap-7652	216	3	the	the	DET
ap-7652	216	4	general	general	ADJ
ap-7652	216	5	theorem	theorem	NOUN
ap-7652	216	6	presented	present	VERB
ap-7652	216	7	in	in	ADP
ap-7652	216	8	[	[	X
ap-7652	216	9	43	43	NUM
ap-7652	216	10	]	]	PUNCT
ap-7652	216	11	for	for	ADP
ap-7652	216	12	singular	singular	ADJ
ap-7652	216	13	sles	sle	NOUN
ap-7652	216	14	solved	solve	VERB
ap-7652	216	15	under	under	ADP
ap-7652	216	16	the	the	DET
ap-7652	216	17	dbcs	dbc	NOUN
ap-7652	216	18	any	any	DET
ap-7652	216	19	principal	principal	ADJ
ap-7652	216	20	solution	solution	NOUN
ap-7652	216	21	∞	∞	PROPN
ap-7652	216	22	̸ψ−,m	̸ψ−,m	X
ap-7652	217	1	[	[	X
ap-7652	217	2	y	y	X
ap-7652	217	3	;	;	PUNCT
ap-7652	217	4	a	a	PRON
ap-7652	217	5	]	]	X
ap-7652	217	6	near	near	ADP
ap-7652	217	7	the	the	DET
ap-7652	217	8	singular	singular	PROPN
ap-7652	217	9	end	end	NOUN
ap-7652	217	10	point	point	NOUN
ap-7652	217	11	y	y	PROPN
ap-7652	217	12	=	=	SYM
ap-7652	217	13	0	0	PROPN
ap-7652	217	14	has	have	VERB
ap-7652	217	15	nodes	node	NOUN
ap-7652	217	16	at	at	ADP
ap-7652	217	17	the	the	DET
ap-7652	217	18	positive	positive	ADJ
ap-7652	217	19	semi	semi	ADJ
ap-7652	217	20	-	-	ADJ
ap-7652	217	21	axis	axis	ADJ
ap-7652	217	22	iff	iff	NOUN
ap-7652	217	23	it	it	PRON
ap-7652	217	24	lies	lie	VERB
ap-7652	217	25	above	above	ADP
ap-7652	217	26	the	the	DET
ap-7652	217	27	ground	ground	NOUN
ap-7652	217	28	energy	energy	NOUN
ap-7652	217	29	level	level	NOUN
ap-7652	217	30	.	.	PUNCT
ap-7652	218	1	examination	examination	NOUN
ap-7652	218	2	of	of	ADP
ap-7652	218	3	the	the	DET
ap-7652	218	4	inequality	inequality	NOUN
ap-7652	218	5	∞ε−,m(a	∞ε−,m(a	PROPN
ap-7652	218	6	)	)	PUNCT
ap-7652	218	7	<	<	X
ap-7652	218	8	∞ε−,0(a	∞ε−,0(a	PROPN
ap-7652	218	9	)	)	PUNCT
ap-7652	218	10	(	(	PUNCT
ap-7652	218	11	73	73	NUM
ap-7652	218	12	)	)	PUNCT
ap-7652	218	13	thus	thus	ADV
ap-7652	218	14	shows	show	VERB
ap-7652	218	15	that	that	SCONJ
ap-7652	218	16	the	the	DET
ap-7652	218	17	q	q	NOUN
ap-7652	218	18	-	-	PUNCT
ap-7652	218	19	rs	rs	NOUN
ap-7652	218	20	∞	∞	NUM
ap-7652	218	21	̸ψ−,m	̸ψ−,m	NOUN
ap-7652	218	22	[	[	X
ap-7652	218	23	y	y	X
ap-7652	218	24	;	;	PUNCT
ap-7652	218	25	a	a	X
ap-7652	218	26	]	]	X
ap-7652	218	27	with	with	ADP
ap-7652	218	28	m	m	PROPN
ap-7652	218	29	̸=	̸=	PROPN
ap-7652	218	30	0	0	NUM
ap-7652	218	31	preserves	preserve	VERB
ap-7652	218	32	its	its	PRON
ap-7652	218	33	sign	sign	NOUN
ap-7652	218	34	on	on	ADP
ap-7652	218	35	the	the	DET
ap-7652	218	36	positive	positive	ADJ
ap-7652	218	37	semi	semi	ADJ
ap-7652	218	38	-	-	ADJ
ap-7652	218	39	axis	axis	ADJ
ap-7652	218	40	iff	iff	PROPN
ap-7652	218	41	m	m	VERB
ap-7652	218	42	>	>	X
ap-7652	219	1	2a−	2a−	NUM
ap-7652	219	2	1	1	NUM
ap-7652	219	3	=	=	SYM
ap-7652	219	4	2a	2a	NUM
ap-7652	219	5	(	(	PUNCT
ap-7652	219	6	74	74	NUM
ap-7652	219	7	)	)	PUNCT
ap-7652	219	8	(	(	PUNCT
ap-7652	219	9	cf.(12	cf.(12	NOUN
ap-7652	219	10	)	)	PUNCT
ap-7652	219	11	in	in	ADP
ap-7652	219	12	[	[	X
ap-7652	219	13	10	10	NUM
ap-7652	219	14	]	]	NUM
ap-7652	219	15	)	)	PUNCT
ap-7652	219	16	.	.	PUNCT
ap-7652	220	1	it	it	PRON
ap-7652	220	2	will	will	AUX
ap-7652	220	3	be	be	AUX
ap-7652	220	4	proven	prove	VERB
ap-7652	220	5	in	in	ADP
ap-7652	220	6	next	next	ADJ
ap-7652	220	7	subsection	subsection	NOUN
ap-7652	220	8	that	that	SCONJ
ap-7652	220	9	one	one	PRON
ap-7652	220	10	can	can	AUX
ap-7652	220	11	use	use	VERB
ap-7652	220	12	any	any	DET
ap-7652	220	13	combination	combination	NOUN
ap-7652	220	14	of	of	ADP
ap-7652	220	15	admissible	admissible	ADJ
ap-7652	220	16	q	q	ADJ
ap-7652	220	17	-	-	NOUN
ap-7652	220	18	rss	rss	ADJ
ap-7652	220	19	∞	∞	PROPN
ap-7652	220	20	̸ψ−,m	̸ψ−,m	NOUN
ap-7652	221	1	[	[	X
ap-7652	221	2	y	y	X
ap-7652	221	3	;	;	PUNCT
ap-7652	221	4	a	a	PRON
ap-7652	221	5	]	]	X
ap-7652	221	6	as	as	SCONJ
ap-7652	221	7	seed	seed	NOUN
ap-7652	221	8	functions	function	NOUN
ap-7652	221	9	to	to	PART
ap-7652	221	10	construct	construct	VERB
ap-7652	221	11	an	an	DET
ap-7652	221	12	exactly	exactly	ADV
ap-7652	221	13	solvable	solvable	ADJ
ap-7652	221	14	rdct	rdct	ADJ
ap-7652	221	15	of	of	ADP
ap-7652	221	16	the	the	DET
ap-7652	221	17	bref	bref	PROPN
ap-7652	221	18	csle	csle	PROPN
ap-7652	221	19	.	.	PUNCT
ap-7652	222	1	according	accord	VERB
ap-7652	222	2	to	to	ADP
ap-7652	222	3	(	(	PUNCT
ap-7652	222	4	9.13.1	9.13.1	NUM
ap-7652	222	5	)	)	PUNCT
ap-7652	222	6	in	in	ADP
ap-7652	222	7	[	[	X
ap-7652	222	8	6	6	NUM
ap-7652	222	9	]	]	X
ap-7652	222	10	y	y	PROPN
ap-7652	222	11	(	(	PUNCT
ap-7652	222	12	−2a,+2	−2a,+2	NOUN
ap-7652	222	13	)	)	PUNCT
ap-7652	222	14	m	m	PROPN
ap-7652	222	15	(	(	PUNCT
ap-7652	222	16	y	y	NOUN
ap-7652	222	17	)	)	PUNCT
ap-7652	222	18	=	=	SYM
ap-7652	222	19	2−m(2m−	2−m(2m−	PROPN
ap-7652	222	20	2a)mŷ	2a)mŷ	NUM
ap-7652	222	21	(	(	PUNCT
ap-7652	222	22	−2a,+2	−2a,+2	NOUN
ap-7652	222	23	)	)	PUNCT
ap-7652	222	24	m	m	PROPN
ap-7652	222	25	(	(	PUNCT
ap-7652	222	26	y	y	NOUN
ap-7652	222	27	)	)	PUNCT
ap-7652	222	28	(	(	PUNCT
ap-7652	222	29	75	75	NUM
ap-7652	222	30	)	)	PUNCT
ap-7652	222	31	where	where	SCONJ
ap-7652	222	32	,	,	PUNCT
ap-7652	222	33	in	in	ADP
ap-7652	222	34	following	follow	VERB
ap-7652	222	35	[	[	X
ap-7652	222	36	5	5	NUM
ap-7652	222	37	]	]	PUNCT
ap-7652	222	38	,	,	PUNCT
ap-7652	222	39	we	we	PRON
ap-7652	222	40	use	use	VERB
ap-7652	222	41	hut	hut	NOUN
ap-7652	222	42	to	to	PART
ap-7652	222	43	indicate	indicate	VERB
ap-7652	222	44	that	that	SCONJ
ap-7652	222	45	the	the	DET
ap-7652	222	46	polynomial	polynomial	NOUN
ap-7652	222	47	in	in	ADP
ap-7652	222	48	question	question	NOUN
ap-7652	222	49	is	be	AUX
ap-7652	222	50	written	write	VERB
ap-7652	222	51	in	in	ADP
ap-7652	222	52	its	its	PRON
ap-7652	222	53	monic	monic	ADJ
ap-7652	222	54	form	form	NOUN
ap-7652	222	55	.	.	PUNCT
ap-7652	223	1	it	it	PRON
ap-7652	223	2	is	be	AUX
ap-7652	223	3	essential	essential	ADJ
ap-7652	223	4	that	that	SCONJ
ap-7652	223	5	the	the	DET
ap-7652	223	6	multiplier	multipli	ADJ
ap-7652	223	7	(	(	PUNCT
ap-7652	223	8	2m−	2m−	PROPN
ap-7652	223	9	2a)m	2a)m	NOUN
ap-7652	223	10	=	=	SYM
ap-7652	223	11	m−1∏	m−1∏	PROPN
ap-7652	223	12	l=0	l=0	PROPN
ap-7652	223	13	(	(	PUNCT
ap-7652	223	14	2m−	2m−	PROPN
ap-7652	223	15	2a−	2a−	NUM
ap-7652	223	16	l	l	NOUN
ap-7652	223	17	)	)	PUNCT
ap-7652	223	18	=	=	SYM
ap-7652	223	19	m∏	m∏	PROPN
ap-7652	223	20	l′=1	l′=1	PROPN
ap-7652	223	21	(	(	PUNCT
ap-7652	223	22	m−	m−	PROPN
ap-7652	223	23	2a+	2a+	NUM
ap-7652	223	24	l′	l′	NOUN
ap-7652	223	25	)	)	PUNCT
ap-7652	223	26	(	(	PUNCT
ap-7652	223	27	76	76	NUM
ap-7652	223	28	)	)	PUNCT
ap-7652	223	29	necessarily	necessarily	ADV
ap-7652	223	30	differs	differ	VERB
ap-7652	223	31	from	from	ADP
ap-7652	223	32	0	0	NUM
ap-7652	223	33	if	if	SCONJ
ap-7652	223	34	either	either	PRON
ap-7652	223	35	2m−	2m−	PROPN
ap-7652	223	36	2a	2a	NUM
ap-7652	223	37	<	<	X
ap-7652	223	38	−1	−1	NOUN
ap-7652	223	39	(	(	PUNCT
ap-7652	223	40	r	r	NOUN
ap-7652	223	41	-	-	PUNCT
ap-7652	223	42	bessel	bessel	ADJ
ap-7652	223	43	polynomials	polynomial	NOUN
ap-7652	223	44	)	)	PUNCT
ap-7652	223	45	or	or	CCONJ
ap-7652	223	46	m	m	PROPN
ap-7652	223	47	=	=	VERB
ap-7652	223	48	m	m	VERB
ap-7652	223	49	>	>	X
ap-7652	223	50	2a−	2a−	NUM
ap-7652	223	51	1	1	NUM
ap-7652	223	52	(	(	PUNCT
ap-7652	223	53	generalized	generalized	ADJ
ap-7652	223	54	bessel	bessel	NOUN
ap-7652	223	55	polynomials	polynomial	NOUN
ap-7652	223	56	with	with	ADP
ap-7652	223	57	no	no	DET
ap-7652	223	58	positive	positive	ADJ
ap-7652	223	59	zeros	zero	NOUN
ap-7652	223	60	)	)	PUNCT
ap-7652	223	61	so	so	SCONJ
ap-7652	223	62	the	the	DET
ap-7652	223	63	polynomial	polynomial	ADJ
ap-7652	223	64	degree	degree	NOUN
ap-7652	223	65	is	be	AUX
ap-7652	223	66	equal	equal	ADJ
ap-7652	223	67	to	to	ADP
ap-7652	223	68	m	m	PROPN
ap-7652	223	69	in	in	ADP
ap-7652	223	70	both	both	DET
ap-7652	223	71	cases	case	NOUN
ap-7652	223	72	of	of	ADP
ap-7652	223	73	our	our	PRON
ap-7652	223	74	primary	primary	ADJ
ap-7652	223	75	interest	interest	NOUN
ap-7652	223	76	.	.	PUNCT
ap-7652	224	1	3.2	3.2	NUM
ap-7652	224	2	.	.	PUNCT
ap-7652	224	3	rdct	rdct	PROPN
ap-7652	224	4	s	s	PROPN
ap-7652	224	5	of	of	ADP
ap-7652	224	6	principal	principal	ADJ
ap-7652	224	7	solutions	solution	NOUN
ap-7652	224	8	near	near	ADP
ap-7652	224	9	singular	singular	PROPN
ap-7652	224	10	end	end	NOUN
ap-7652	224	11	points	point	NOUN
ap-7652	224	12	using	use	VERB
ap-7652	224	13	an	an	DET
ap-7652	224	14	arbitrary	arbitrary	ADJ
ap-7652	224	15	set	set	NOUN
ap-7652	224	16	mp	mp	NOUN
ap-7652	224	17	=	=	SYM
ap-7652	224	18	m1	m1	PROPN
ap-7652	224	19	,	,	PUNCT
ap-7652	224	20	.	.	PUNCT
ap-7652	224	21	.	.	PUNCT
ap-7652	225	1	.	.	PUNCT
ap-7652	226	1	,	,	PUNCT
ap-7652	226	2	mp	mp	PROPN
ap-7652	226	3	of	of	ADP
ap-7652	226	4	seed	seed	NOUN
ap-7652	226	5	functions	function	NOUN
ap-7652	226	6	∞ϕ±,mk	∞ϕ±,mk	PROPN
ap-7652	227	1	[	[	X
ap-7652	227	2	y	y	X
ap-7652	227	3	;	;	PUNCT
ap-7652	227	4	a	a	X
ap-7652	227	5	]	]	X
ap-7652	227	6	of	of	ADP
ap-7652	227	7	the	the	DET
ap-7652	227	8	same	same	ADJ
ap-7652	227	9	type	type	NOUN
ap-7652	227	10	(	(	PUNCT
ap-7652	227	11	0	0	NUM
ap-7652	227	12	<	<	X
ap-7652	227	13	mk	mk	X
ap-7652	227	14	<	<	X
ap-7652	227	15	mk+1	mk+1	X
ap-7652	227	16	for	for	ADP
ap-7652	227	17	k	k	PROPN
ap-7652	227	18	=	=	SYM
ap-7652	227	19	1	1	NUM
ap-7652	227	20	,	,	PUNCT
ap-7652	227	21	.	.	PUNCT
ap-7652	227	22	.	.	PUNCT
ap-7652	227	23	.	.	PUNCT
ap-7652	228	1	,	,	PUNCT
ap-7652	228	2	p−	p−	NOUN
ap-7652	228	3	1	1	X
ap-7652	228	4	)	)	PUNCT
ap-7652	228	5	we	we	PRON
ap-7652	228	6	can	can	AUX
ap-7652	228	7	represent	represent	VERB
ap-7652	228	8	the	the	DET
ap-7652	228	9	corresponding	correspond	VERB
ap-7652	228	10	rdct	rdct	PROPN
ap-7652	228	11	of	of	ADP
ap-7652	228	12	bref	bref	PROPN
ap-7652	228	13	csle	csle	PROPN
ap-7652	228	14	(	(	PUNCT
ap-7652	228	15	32	32	NUM
ap-7652	228	16	)	)	PUNCT
ap-7652	228	17	as	as	ADP
ap-7652	228	18	{	{	PUNCT
ap-7652	228	19	d2	d2	PROPN
ap-7652	228	20	dy2	dy2	PROPN
ap-7652	228	21	+	+	CCONJ
ap-7652	228	22	∞i	∞i	NUM
ap-7652	228	23	0[y	0[y	NUM
ap-7652	228	24	;	;	PUNCT
ap-7652	228	25	a	a	DET
ap-7652	228	26	|	|	NOUN
ap-7652	228	27	±	±	NUM
ap-7652	228	28	...	...	PUNCT
ap-7652	228	29	mp	mp	X
ap-7652	228	30	]	]	X
ap-7652	228	31	+	+	CCONJ
ap-7652	228	32	εy−2	εy−2	NOUN
ap-7652	228	33	}	}	PUNCT
ap-7652	228	34	∞φ[y	∞φ[y	PROPN
ap-7652	228	35	;	;	PUNCT
ap-7652	228	36	a	a	PRON
ap-7652	228	37	;	;	PUNCT
ap-7652	228	38	ε	ε	PROPN
ap-7652	228	39	|	|	ADV
ap-7652	228	40	±	±	NUM
ap-7652	228	41	...	...	PUNCT
ap-7652	228	42	mp	mp	X
ap-7652	228	43	]	]	X
ap-7652	228	44	=	=	SYM
ap-7652	228	45	0	0	NUM
ap-7652	228	46	,	,	PUNCT
ap-7652	228	47	(	(	PUNCT
ap-7652	228	48	77	77	NUM
ap-7652	228	49	)	)	PUNCT
ap-7652	228	50	where	where	SCONJ
ap-7652	228	51	∞i	∞i	NUM
ap-7652	228	52	0[y	0[y	NUM
ap-7652	228	53	;	;	PUNCT
ap-7652	228	54	a	a	DET
ap-7652	228	55	|	|	NOUN
ap-7652	228	56	...	...	PUNCT
ap-7652	228	57	mp	mp	NOUN
ap-7652	228	58	]	]	X
ap-7652	228	59	=	=	SYM
ap-7652	228	60	∞i	∞i	NUM
ap-7652	229	1	0[y	0[y	PRON
ap-7652	229	2	;	;	PUNCT
ap-7652	229	3	a	a	PRON
ap-7652	229	4	]	]	X
ap-7652	229	5	+	+	NUM
ap-7652	229	6	2	2	NUM
ap-7652	229	7	y	y	NOUN
ap-7652	229	8	d	d	PROPN
ap-7652	229	9	dy	dy	X
ap-7652	229	10	(	(	PUNCT
ap-7652	229	11	y	y	PROPN
ap-7652	229	12	ld∞w[y	ld∞w[y	PROPN
ap-7652	229	13	;	;	PUNCT
ap-7652	229	14	a	a	DET
ap-7652	229	15	|	|	NOUN
ap-7652	229	16	±	±	NUM
ap-7652	229	17	...	...	PUNCT
ap-7652	229	18	mp	mp	PROPN
ap-7652	229	19	]	]	X
ap-7652	229	20	)	)	PUNCT
ap-7652	229	21	(	(	PUNCT
ap-7652	229	22	78	78	NUM
ap-7652	229	23	)	)	PUNCT
ap-7652	229	24	with	with	ADP
ap-7652	229	25	∞w[y	∞w[y	NOUN
ap-7652	229	26	;	;	PUNCT
ap-7652	229	27	a	a	DET
ap-7652	229	28	|	|	NOUN
ap-7652	229	29	±	±	NUM
ap-7652	229	30	...	...	PUNCT
ap-7652	230	1	m1	m1	NOUN
ap-7652	230	2	]	]	PUNCT
ap-7652	231	1	≡	≡	PROPN
ap-7652	231	2	∞ϕ±,m1	∞ϕ±,m1	VERB
ap-7652	232	1	[	[	X
ap-7652	232	2	y	y	X
ap-7652	232	3	;	;	PUNCT
ap-7652	232	4	a	a	PRON
ap-7652	232	5	]	]	X
ap-7652	232	6	,	,	PUNCT
ap-7652	232	7	(	(	PUNCT
ap-7652	232	8	79	79	NUM
ap-7652	232	9	)	)	PUNCT
ap-7652	232	10	∞w[y	∞w[y	NOUN
ap-7652	232	11	;	;	PUNCT
ap-7652	232	12	a	a	DET
ap-7652	232	13	|	|	NOUN
ap-7652	232	14	±	±	NUM
ap-7652	232	15	...	...	PUNCT
ap-7652	232	16	mp	mp	PROPN
ap-7652	232	17	]	]	X
ap-7652	232	18	≡	≡	PROPN
ap-7652	232	19	w	w	PROPN
ap-7652	232	20	{	{	PUNCT
ap-7652	232	21	∞ϕ±,m1	∞ϕ±,m1	VERB
ap-7652	232	22	[	[	X
ap-7652	232	23	y	y	X
ap-7652	232	24	;	;	PUNCT
ap-7652	232	25	a	a	DET
ap-7652	232	26	]	]	X
ap-7652	232	27	,	,	PUNCT
ap-7652	232	28	.	.	PUNCT
ap-7652	232	29	.	.	PUNCT
ap-7652	232	30	.	.	PUNCT
ap-7652	233	1	,	,	PUNCT
ap-7652	233	2	∞ϕ±,mp	∞ϕ±,mp	PROPN
ap-7652	233	3	[	[	X
ap-7652	233	4	y	y	X
ap-7652	233	5	;	;	PUNCT
ap-7652	233	6	a	a	X
ap-7652	233	7	]	]	X
ap-7652	233	8	}	}	PUNCT
ap-7652	233	9	for	for	ADP
ap-7652	233	10	p	p	PROPN
ap-7652	233	11	>	>	X
ap-7652	233	12	1	1	NUM
ap-7652	233	13	,	,	PUNCT
ap-7652	233	14	(	(	PUNCT
ap-7652	233	15	80	80	NUM
ap-7652	233	16	)	)	PUNCT
ap-7652	233	17	and	and	CCONJ
ap-7652	233	18	the	the	DET
ap-7652	233	19	symbolic	symbolic	ADJ
ap-7652	233	20	expression	expression	NOUN
ap-7652	233	21	ld	ld	NOUN
ap-7652	233	22	standing	stand	VERB
ap-7652	233	23	for	for	ADP
ap-7652	233	24	the	the	DET
ap-7652	233	25	logarithmic	logarithmic	ADJ
ap-7652	233	26	derivative	derivative	NOUN
ap-7652	233	27	.	.	PUNCT
ap-7652	234	1	when	when	SCONJ
ap-7652	234	2	deriving	derive	VERB
ap-7652	234	3	(	(	PUNCT
ap-7652	234	4	78	78	NUM
ap-7652	234	5	)	)	PUNCT
ap-7652	234	6	we	we	PRON
ap-7652	234	7	also	also	ADV
ap-7652	234	8	took	take	VERB
ap-7652	234	9	into	into	ADP
ap-7652	234	10	account	account	NOUN
ap-7652	234	11	that	that	SCONJ
ap-7652	234	12	the	the	DET
ap-7652	234	13	so	so	ADV
ap-7652	234	14	-	-	PUNCT
ap-7652	234	15	called	call	VERB
ap-7652	234	16	[	[	X
ap-7652	234	17	42	42	NUM
ap-7652	234	18	]	]	PUNCT
ap-7652	234	19	‘	'	PUNCT
ap-7652	234	20	universal	universal	ADJ
ap-7652	234	21	correction	correction	NOUN
ap-7652	234	22	’	'	PUNCT
ap-7652	234	23	∆i	∆i	PROPN
ap-7652	234	24	{	{	PUNCT
ap-7652	234	25	ρ(y	ρ(y	NOUN
ap-7652	234	26	)	)	PUNCT
ap-7652	234	27	}	}	PUNCT
ap-7652	234	28	≡	≡	PROPN
ap-7652	234	29	0.5	0.5	NUM
ap-7652	234	30	»	»	NOUN
ap-7652	234	31	ρ(y	ρ(y	NOUN
ap-7652	234	32	)	)	PUNCT
ap-7652	234	33	d	d	NOUN
ap-7652	234	34	dy	dy	NOUN
ap-7652	234	35	ld	ld	PROPN
ap-7652	234	36	ρ(y)√	ρ(y)√	NOUN
ap-7652	234	37	ρ(y	ρ(y	NOUN
ap-7652	234	38	)	)	PUNCT
ap-7652	234	39	(	(	PUNCT
ap-7652	234	40	81	81	NUM
ap-7652	234	41	)	)	PUNCT
ap-7652	234	42	107	107	NUM
ap-7652	234	43	gregory	gregory	PROPN
ap-7652	234	44	natanson	natanson	PROPN
ap-7652	234	45	acta	acta	PROPN
ap-7652	234	46	polytechnica	polytechnica	PROPN
ap-7652	234	47	in	in	ADP
ap-7652	234	48	schulze	schulze	NOUN
ap-7652	234	49	-	-	PUNCT
ap-7652	234	50	halberg	halberg	PROPN
ap-7652	234	51	’s	’s	PART
ap-7652	234	52	[	[	X
ap-7652	234	53	45	45	NUM
ap-7652	234	54	]	]	PUNCT
ap-7652	234	55	generic	generic	ADJ
ap-7652	234	56	formula	formula	NOUN
ap-7652	234	57	for	for	ADP
ap-7652	234	58	zero	zero	NUM
ap-7652	234	59	-	-	PUNCT
ap-7652	234	60	energy	energy	NOUN
ap-7652	234	61	free	free	ADJ
ap-7652	234	62	term	term	NOUN
ap-7652	234	63	of	of	ADP
ap-7652	234	64	the	the	DET
ap-7652	234	65	transformed	transform	VERB
ap-7652	234	66	csle	csle	NOUN
ap-7652	234	67	vanishes	vanish	VERB
ap-7652	234	68	in	in	ADP
ap-7652	234	69	the	the	DET
ap-7652	234	70	case	case	NOUN
ap-7652	234	71	of	of	ADP
ap-7652	234	72	our	our	PRON
ap-7652	234	73	current	current	ADJ
ap-7652	234	74	interest	interest	NOUN
ap-7652	234	75	:	:	PUNCT
ap-7652	234	76	ρ(y	ρ(y	NOUN
ap-7652	234	77	)	)	PUNCT
ap-7652	235	1	=	=	SYM
ap-7652	235	2	y−2	y−2	PROPN
ap-7652	235	3	.	.	PUNCT
ap-7652	236	1	the	the	DET
ap-7652	236	2	common	common	ADJ
ap-7652	236	3	remarkable	remarkable	ADJ
ap-7652	236	4	feature	feature	NOUN
ap-7652	236	5	of	of	ADP
ap-7652	236	6	wronskians	wronskian	NOUN
ap-7652	236	7	(	(	PUNCT
ap-7652	236	8	80	80	NUM
ap-7652	236	9	)	)	PUNCT
ap-7652	236	10	for	for	ADP
ap-7652	236	11	tfi	tfi	NOUN
ap-7652	236	12	csles	csle	NOUN
ap-7652	236	13	from	from	ADP
ap-7652	236	14	group	group	PROPN
ap-7652	236	15	a	a	PROPN
ap-7652	236	16	(	(	PUNCT
ap-7652	236	17	originally	originally	ADV
ap-7652	236	18	noticed	notice	VERB
ap-7652	236	19	by	by	ADP
ap-7652	236	20	odake	odake	NOUN
ap-7652	236	21	and	and	CCONJ
ap-7652	236	22	sasaki	sasaki	PROPN
ap-7652	236	23	[	[	X
ap-7652	236	24	19	19	NUM
ap-7652	236	25	]	]	PUNCT
ap-7652	236	26	in	in	ADP
ap-7652	236	27	their	their	PRON
ap-7652	236	28	scrupulous	scrupulous	ADJ
ap-7652	236	29	study	study	NOUN
ap-7652	236	30	on	on	ADP
ap-7652	236	31	rdct	rdct	PROPN
ap-7652	236	32	s	s	PROPN
ap-7652	236	33	of	of	ADP
ap-7652	236	34	the	the	DET
ap-7652	236	35	corresponding	correspond	VERB
ap-7652	236	36	tsi	tsi	PROPN
ap-7652	236	37	potentials	potential	NOUN
ap-7652	236	38	)	)	PUNCT
ap-7652	236	39	is	be	AUX
ap-7652	236	40	that	that	SCONJ
ap-7652	236	41	each	each	PRON
ap-7652	236	42	can	can	AUX
ap-7652	236	43	be	be	AUX
ap-7652	236	44	represented	represent	VERB
ap-7652	236	45	as	as	ADP
ap-7652	236	46	the	the	DET
ap-7652	236	47	weighted	weighted	ADJ
ap-7652	236	48	polynomial	polynomial	ADJ
ap-7652	236	49	wronskian	wronskian	NOUN
ap-7652	236	50	∞w[y	∞w[y	NOUN
ap-7652	236	51	;	;	PUNCT
ap-7652	236	52	a	a	DET
ap-7652	236	53	|	|	NOUN
ap-7652	236	54	±	±	NUM
ap-7652	236	55	...	...	PUNCT
ap-7652	236	56	mp	mp	X
ap-7652	236	57	]	]	X
ap-7652	236	58	=	=	X
ap-7652	236	59	∞ϕ	∞ϕ	NOUN
ap-7652	236	60	p	p	PROPN
ap-7652	236	61	±,0[y	±,0[y	PROPN
ap-7652	236	62	;	;	PUNCT
ap-7652	236	63	a]∞wnmp	a]∞wnmp	PROPN
ap-7652	237	1	[	[	X
ap-7652	237	2	y	y	X
ap-7652	237	3	;	;	PUNCT
ap-7652	237	4	a	a	DET
ap-7652	237	5	|	|	NOUN
ap-7652	237	6	±	±	NUM
ap-7652	237	7	...	...	PUNCT
ap-7652	237	8	mp	mp	PROPN
ap-7652	237	9	]	]	X
ap-7652	237	10	,	,	PUNCT
ap-7652	237	11	(	(	PUNCT
ap-7652	237	12	82	82	NUM
ap-7652	237	13	)	)	PUNCT
ap-7652	237	14	where	where	SCONJ
ap-7652	237	15	the	the	DET
ap-7652	237	16	wronskian	wronskian	PROPN
ap-7652	237	17	∞wnmp	∞wnmp	PROPN
ap-7652	238	1	[	[	X
ap-7652	238	2	y	y	X
ap-7652	238	3	;	;	PUNCT
ap-7652	238	4	a	a	DET
ap-7652	238	5	|	|	NOUN
ap-7652	238	6	±	±	NUM
ap-7652	238	7	...	...	PUNCT
ap-7652	238	8	mp	mp	PROPN
ap-7652	238	9	]	]	X
ap-7652	238	10	≡	≡	PROPN
ap-7652	238	11	w	w	PROPN
ap-7652	238	12	{	{	PUNCT
ap-7652	238	13	y	y	PROPN
ap-7652	238	14	(	(	PUNCT
ap-7652	238	15	±2a,∓2	±2a,∓2	PROPN
ap-7652	238	16	)	)	PUNCT
ap-7652	238	17	m1	m1	NOUN
ap-7652	238	18	(	(	PUNCT
ap-7652	238	19	y	y	NOUN
ap-7652	238	20	)	)	PUNCT
ap-7652	238	21	,	,	PUNCT
ap-7652	238	22	.	.	PUNCT
ap-7652	238	23	.	.	PUNCT
ap-7652	238	24	.	.	PUNCT
ap-7652	239	1	,	,	PUNCT
ap-7652	239	2	y	y	PROPN
ap-7652	239	3	(	(	PUNCT
ap-7652	239	4	±2a,∓2	±2a,∓2	PROPN
ap-7652	239	5	)	)	PUNCT
ap-7652	239	6	mp	mp	NOUN
ap-7652	239	7	(	(	PUNCT
ap-7652	239	8	y	y	NOUN
ap-7652	239	9	)	)	PUNCT
ap-7652	239	10	}	}	PUNCT
ap-7652	239	11	(	(	PUNCT
ap-7652	239	12	83	83	NUM
ap-7652	239	13	)	)	PUNCT
ap-7652	239	14	is	be	AUX
ap-7652	239	15	a	a	DET
ap-7652	239	16	polynomial	polynomial	NOUN
ap-7652	239	17	of	of	ADP
ap-7652	239	18	degree	degree	NOUN
ap-7652	239	19	nmp	nmp	NOUN
ap-7652	239	20	=|	=|	X
ap-7652	239	21	mp	mp	PROPN
ap-7652	240	1	|	|	ADV
ap-7652	240	2	−0.5p(p−	−0.5p(p−	NUM
ap-7652	240	3	1	1	NUM
ap-7652	240	4	)	)	PUNCT
ap-7652	240	5	(	(	PUNCT
ap-7652	240	6	84	84	NUM
ap-7652	240	7	)	)	PUNCT
ap-7652	240	8	(	(	PUNCT
ap-7652	240	9	see	see	VERB
ap-7652	240	10	(	(	PUNCT
ap-7652	240	11	61	61	NUM
ap-7652	240	12	)	)	PUNCT
ap-7652	240	13	in	in	ADP
ap-7652	240	14	[	[	X
ap-7652	240	15	19	19	NUM
ap-7652	240	16	]	]	PUNCT
ap-7652	240	17	)	)	PUNCT
ap-7652	240	18	.	.	PUNCT
ap-7652	241	1	when	when	SCONJ
ap-7652	241	2	it	it	PRON
ap-7652	241	3	seems	seem	VERB
ap-7652	241	4	appropriate	appropriate	ADJ
ap-7652	241	5	we	we	PRON
ap-7652	241	6	will	will	AUX
ap-7652	241	7	drop	drop	VERB
ap-7652	241	8	the	the	DET
ap-7652	241	9	index	index	NOUN
ap-7652	241	10	specifying	specify	VERB
ap-7652	241	11	the	the	DET
ap-7652	241	12	degree	degree	NOUN
ap-7652	241	13	of	of	ADP
ap-7652	241	14	polynomial	polynomial	ADJ
ap-7652	241	15	wronskians	wronskian	NOUN
ap-7652	241	16	in	in	ADP
ap-7652	241	17	question	question	NOUN
ap-7652	241	18	.	.	PUNCT
ap-7652	242	1	substituting	substitute	VERB
ap-7652	242	2	(	(	PUNCT
ap-7652	242	3	82	82	NUM
ap-7652	242	4	)	)	PUNCT
ap-7652	242	5	into	into	ADP
ap-7652	242	6	(	(	PUNCT
ap-7652	242	7	78	78	NUM
ap-7652	242	8	)	)	PUNCT
ap-7652	242	9	,	,	PUNCT
ap-7652	242	10	coupled	couple	VERB
ap-7652	242	11	with	with	ADP
ap-7652	242	12	(	(	PUNCT
ap-7652	242	13	33	33	NUM
ap-7652	242	14	)	)	PUNCT
ap-7652	242	15	and	and	CCONJ
ap-7652	242	16	(	(	PUNCT
ap-7652	242	17	35	35	NUM
ap-7652	242	18	)	)	PUNCT
ap-7652	242	19	,	,	PUNCT
ap-7652	242	20	one	one	PRON
ap-7652	242	21	finds	find	VERB
ap-7652	242	22	∞i	∞i	NUM
ap-7652	242	23	0	0	NUM
ap-7652	243	1	[	[	PUNCT
ap-7652	243	2	y	y	NOUN
ap-7652	243	3	;	;	PUNCT
ap-7652	243	4	a	a	DET
ap-7652	243	5	|	|	NOUN
ap-7652	243	6	±	±	NUM
ap-7652	243	7	...	...	PUNCT
ap-7652	243	8	mp	mp	X
ap-7652	243	9	]	]	X
ap-7652	243	10	=	=	SYM
ap-7652	243	11	2(a±	2(a±	NUM
ap-7652	243	12	p)y−3	p)y−3	NOUN
ap-7652	243	13	−	−	PROPN
ap-7652	243	14	y−4	y−4	PROPN
ap-7652	244	1	+	+	CCONJ
ap-7652	244	2	1/4y−2	1/4y−2	NUM
ap-7652	244	3	+	+	CCONJ
ap-7652	244	4	2	2	NUM
ap-7652	244	5	y	y	NOUN
ap-7652	244	6	d	d	NOUN
ap-7652	244	7	dy	dy	X
ap-7652	244	8	å	å	PROPN
ap-7652	244	9	y	y	PROPN
ap-7652	244	10	ld∞w[y	ld∞w[y	PROPN
ap-7652	244	11	;	;	PUNCT
ap-7652	244	12	a	a	DET
ap-7652	244	13	|	|	NOUN
ap-7652	244	14	±	±	NUM
ap-7652	244	15	...	...	PUNCT
ap-7652	245	1	mp	mp	X
ap-7652	245	2	]	]	X
ap-7652	245	3	ã	ã	X
ap-7652	245	4	.	.	PUNCT
ap-7652	246	1	(	(	PUNCT
ap-7652	246	2	85	85	NUM
ap-7652	246	3	)	)	PUNCT
ap-7652	246	4	each	each	DET
ap-7652	246	5	rcsle	rcsle	NOUN
ap-7652	246	6	under	under	ADP
ap-7652	246	7	consideration	consideration	NOUN
ap-7652	246	8	can	can	AUX
ap-7652	246	9	be	be	AUX
ap-7652	246	10	alternatively	alternatively	ADV
ap-7652	246	11	obtained	obtain	VERB
ap-7652	246	12	via	via	ADP
ap-7652	246	13	sequential	sequential	ADJ
ap-7652	246	14	rdts	rdts	NOUN
ap-7652	246	15	with	with	ADP
ap-7652	246	16	the	the	DET
ap-7652	246	17	ffs	ff	NOUN
ap-7652	246	18	∞φ±,m	∞φ±,m	NUM
ap-7652	247	1	˜	˜	PROPN
ap-7652	247	2	p	p	PROPN
ap-7652	248	1	[	[	X
ap-7652	248	2	y	y	X
ap-7652	248	3	;	;	PUNCT
ap-7652	248	4	a	a	DET
ap-7652	248	5	|	|	NOUN
ap-7652	248	6	±	±	NUM
ap-7652	248	7	...	...	PUNCT
ap-7652	249	1	m	m	VERB
ap-7652	249	2	˜	˜	PROPN
ap-7652	249	3	p−1	p−1	PROPN
ap-7652	249	4	]	]	X
ap-7652	249	5	=	=	PUNCT
ap-7652	250	1	yp−1	yp−1	PROPN
ap-7652	250	2	∞w[y	∞w[y	PROPN
ap-7652	250	3	;	;	PUNCT
ap-7652	250	4	a	a	DET
ap-7652	250	5	|	|	NOUN
ap-7652	250	6	±	±	NUM
ap-7652	250	7	...	...	PUNCT
ap-7652	251	1	m	m	VERB
ap-7652	252	1	˜	˜	PROPN
ap-7652	252	2	p	p	X
ap-7652	252	3	]	]	X
ap-7652	252	4	∞w[y	∞w[y	NOUN
ap-7652	252	5	;	;	PUNCT
ap-7652	252	6	a	a	DET
ap-7652	252	7	|	|	NOUN
ap-7652	252	8	±	±	NUM
ap-7652	252	9	...	...	PUNCT
ap-7652	253	1	m	m	VERB
ap-7652	253	2	˜	˜	PROPN
ap-7652	253	3	p−1	p−1	PROPN
ap-7652	253	4	]	]	X
ap-7652	253	5	(	(	PUNCT
ap-7652	253	6	˜	˜	PROPN
ap-7652	253	7	p	p	NOUN
ap-7652	253	8	=	=	PROPN
ap-7652	253	9	1	1	NUM
ap-7652	253	10	,	,	PUNCT
ap-7652	253	11	.	.	PUNCT
ap-7652	253	12	.	.	PUNCT
ap-7652	253	13	.	.	PUNCT
ap-7652	254	1	,	,	PUNCT
ap-7652	254	2	p	p	X
ap-7652	254	3	)	)	PUNCT
ap-7652	254	4	(	(	PUNCT
ap-7652	254	5	86	86	NUM
ap-7652	254	6	)	)	PUNCT
ap-7652	255	1	so	so	ADV
ap-7652	255	2	refpfs	refpf	NOUN
ap-7652	255	3	(	(	PUNCT
ap-7652	255	4	85	85	NUM
ap-7652	255	5	)	)	PUNCT
ap-7652	255	6	can	can	AUX
ap-7652	255	7	be	be	AUX
ap-7652	255	8	determined	determine	VERB
ap-7652	255	9	via	via	ADP
ap-7652	255	10	the	the	DET
ap-7652	255	11	following	follow	VERB
ap-7652	255	12	sequence	sequence	NOUN
ap-7652	255	13	of	of	ADP
ap-7652	255	14	recurrence	recurrence	NOUN
ap-7652	255	15	relations	relation	NOUN
ap-7652	255	16	∞i	∞i	NUM
ap-7652	255	17	0[y	0[y	NUM
ap-7652	255	18	;	;	PUNCT
ap-7652	255	19	a	a	DET
ap-7652	255	20	|	|	NOUN
ap-7652	255	21	±	±	NUM
ap-7652	255	22	...	...	PUNCT
ap-7652	256	1	mp	mp	X
ap-7652	256	2	]	]	X
ap-7652	256	3	=	=	SYM
ap-7652	256	4	∞i	∞i	NUM
ap-7652	256	5	0[y	0[y	NUM
ap-7652	256	6	;	;	PUNCT
ap-7652	256	7	a	a	DET
ap-7652	256	8	|	|	NOUN
ap-7652	256	9	±	±	NUM
ap-7652	256	10	...	...	PUNCT
ap-7652	256	11	mp−1	mp−1	X
ap-7652	256	12	]	]	PUNCT
ap-7652	257	1	+	+	CCONJ
ap-7652	257	2	2	2	NUM
ap-7652	257	3	y	y	NOUN
ap-7652	257	4	d	d	NOUN
ap-7652	257	5	dy	dy	X
ap-7652	257	6	å	å	PROPN
ap-7652	257	7	y	y	NOUN
ap-7652	257	8	ld∞φ±,mp	ld∞φ±,mp	PUNCT
ap-7652	257	9	[	[	X
ap-7652	257	10	y	y	X
ap-7652	257	11	;	;	PUNCT
ap-7652	257	12	a	a	DET
ap-7652	257	13	|	|	NOUN
ap-7652	257	14	±	±	NUM
ap-7652	257	15	...	...	PUNCT
ap-7652	257	16	mp−1	mp−1	X
ap-7652	257	17	]	]	X
ap-7652	257	18	ã	ã	X
ap-7652	257	19	(	(	PUNCT
ap-7652	257	20	87	87	NUM
ap-7652	257	21	)	)	PUNCT
ap-7652	257	22	(	(	PUNCT
ap-7652	257	23	a	a	DET
ap-7652	257	24	natural	natural	ADJ
ap-7652	257	25	extension	extension	NOUN
ap-7652	257	26	of	of	ADP
ap-7652	257	27	the	the	DET
ap-7652	257	28	renown	renown	ADJ
ap-7652	257	29	crum	crum	PROPN
ap-7652	257	30	formulas	formula	NOUN
ap-7652	257	31	[	[	X
ap-7652	257	32	21	21	NUM
ap-7652	257	33	]	]	PUNCT
ap-7652	257	34	to	to	ADP
ap-7652	257	35	the	the	DET
ap-7652	257	36	csles	csle	NOUN
ap-7652	257	37	)	)	PUNCT
ap-7652	257	38	.	.	PUNCT
ap-7652	258	1	for	for	ADP
ap-7652	258	2	an	an	DET
ap-7652	258	3	arbitrary	arbitrary	ADJ
ap-7652	258	4	choice	choice	NOUN
ap-7652	258	5	of	of	ADP
ap-7652	258	6	the	the	DET
ap-7652	258	7	partition	partition	NOUN
ap-7652	258	8	mp	mp	PROPN
ap-7652	258	9	refpf	refpf	NOUN
ap-7652	258	10	(	(	PUNCT
ap-7652	258	11	85	85	NUM
ap-7652	258	12	)	)	PUNCT
ap-7652	258	13	generally	generally	ADV
ap-7652	258	14	has	have	VERB
ap-7652	258	15	poles	pole	NOUN
ap-7652	258	16	on	on	ADP
ap-7652	258	17	the	the	DET
ap-7652	258	18	positive	positive	ADJ
ap-7652	258	19	semi	semi	ADJ
ap-7652	258	20	-	-	ADJ
ap-7652	258	21	axis	axis	ADJ
ap-7652	258	22	and	and	CCONJ
ap-7652	258	23	therefore	therefore	ADV
ap-7652	258	24	rcsle	rcsle	PROPN
ap-7652	258	25	(	(	PUNCT
ap-7652	258	26	77	77	NUM
ap-7652	258	27	)	)	PUNCT
ap-7652	258	28	can	can	AUX
ap-7652	258	29	not	not	PART
ap-7652	258	30	be	be	AUX
ap-7652	258	31	quantized	quantize	VERB
ap-7652	258	32	analytically	analytically	ADV
ap-7652	258	33	.	.	PUNCT
ap-7652	259	1	so	so	ADV
ap-7652	259	2	let	let	VERB
ap-7652	259	3	us	we	PRON
ap-7652	259	4	choose	choose	VERB
ap-7652	259	5	a	a	DET
ap-7652	259	6	set	set	ADJ
ap-7652	259	7	m±	m±	NOUN
ap-7652	259	8	p	p	NOUN
ap-7652	259	9	=	=	NOUN
ap-7652	259	10	m±	m±	PROPN
ap-7652	259	11	1	1	NUM
ap-7652	259	12	,	,	PUNCT
ap-7652	259	13	.	.	PUNCT
ap-7652	259	14	.	.	PUNCT
ap-7652	260	1	.	.	PUNCT
ap-7652	261	1	,	,	PUNCT
ap-7652	261	2	m±	m±	PROPN
ap-7652	261	3	p	p	PROPN
ap-7652	261	4	of	of	ADP
ap-7652	261	5	seed	seed	NOUN
ap-7652	261	6	solutions	solution	NOUN
ap-7652	261	7	of	of	ADP
ap-7652	261	8	the	the	DET
ap-7652	261	9	sane	sane	ADJ
ap-7652	261	10	type	type	NOUN
ap-7652	261	11	,	,	PUNCT
ap-7652	261	12	∞ϕ±,mk	∞ϕ±,mk	PROPN
ap-7652	262	1	[	[	X
ap-7652	262	2	y	y	X
ap-7652	262	3	;	;	PUNCT
ap-7652	262	4	a	a	X
ap-7652	262	5	]	]	X
ap-7652	262	6	(	(	PUNCT
ap-7652	262	7	0	0	PUNCT
ap-7652	262	8	<	<	X
ap-7652	262	9	mk	mk	X
ap-7652	262	10	=	=	PROPN
ap-7652	262	11	m±	m±	PROPN
ap-7652	262	12	k	k	X
ap-7652	262	13	<	<	X
ap-7652	262	14	mk+1	mk+1	X
ap-7652	262	15	=	=	PUNCT
ap-7652	262	16	m±	m±	NOUN
ap-7652	262	17	k+1	k+1	X
ap-7652	262	18	for	for	ADP
ap-7652	262	19	k	k	PROPN
ap-7652	262	20	=	=	SYM
ap-7652	262	21	1	1	NUM
ap-7652	262	22	,	,	PUNCT
ap-7652	262	23	.	.	PUNCT
ap-7652	262	24	.	.	PUNCT
ap-7652	262	25	.	.	PUNCT
ap-7652	263	1	,	,	PUNCT
ap-7652	263	2	p−	p−	NOUN
ap-7652	263	3	1	1	NUM
ap-7652	263	4	)	)	PUNCT
ap-7652	263	5	,	,	PUNCT
ap-7652	263	6	in	in	ADP
ap-7652	263	7	such	such	DET
ap-7652	263	8	a	a	DET
ap-7652	263	9	way	way	NOUN
ap-7652	263	10	that	that	PRON
ap-7652	263	11	the	the	DET
ap-7652	263	12	seed	seed	NOUN
ap-7652	263	13	function	function	NOUN
ap-7652	263	14	∞ϕ±,m1	∞ϕ±,m1	VERB
ap-7652	264	1	[	[	X
ap-7652	264	2	y	y	X
ap-7652	264	3	;	;	PUNCT
ap-7652	264	4	a	a	X
ap-7652	264	5	]	]	X
ap-7652	264	6	and	and	CCONJ
ap-7652	264	7	all	all	DET
ap-7652	264	8	wronskians	wronskian	NOUN
ap-7652	264	9	∞w[y	∞w[y	NOUN
ap-7652	264	10	;	;	PUNCT
ap-7652	264	11	a	a	DET
ap-7652	264	12	|	|	NOUN
ap-7652	264	13	±	±	NUM
ap-7652	264	14	...	...	PUNCT
ap-7652	264	15	m±	m±	PROPN
ap-7652	264	16	p	p	X
ap-7652	264	17	]	]	PUNCT
ap-7652	264	18	for	for	ADP
ap-7652	264	19	˜	˜	PROPN
ap-7652	264	20	p	p	PROPN
ap-7652	264	21	=	=	PROPN
ap-7652	264	22	2	2	NUM
ap-7652	264	23	,	,	PUNCT
ap-7652	264	24	.	.	PUNCT
ap-7652	264	25	.	.	PUNCT
ap-7652	264	26	.	.	PUNCT
ap-7652	265	1	,	,	PUNCT
ap-7652	265	2	p	p	PRON
ap-7652	265	3	preserve	preserve	VERB
ap-7652	265	4	their	their	PRON
ap-7652	265	5	sign	sign	NOUN
ap-7652	265	6	on	on	ADP
ap-7652	265	7	the	the	DET
ap-7652	265	8	positive	positive	ADJ
ap-7652	265	9	semi	semi	ADJ
ap-7652	265	10	-	-	ADJ
ap-7652	265	11	axis	axis	ADJ
ap-7652	265	12	.	.	PUNCT
ap-7652	266	1	in	in	ADP
ap-7652	266	2	particular	particular	ADJ
ap-7652	266	3	odake	odake	NOUN
ap-7652	266	4	and	and	CCONJ
ap-7652	266	5	sasaki	sasaki	PROPN
ap-7652	266	6	[	[	X
ap-7652	266	7	19	19	NUM
ap-7652	266	8	]	]	PUNCT
ap-7652	266	9	and	and	CCONJ
ap-7652	266	10	nearly	nearly	ADV
ap-7652	266	11	the	the	DET
ap-7652	266	12	same	same	ADJ
ap-7652	266	13	time	time	NOUN
ap-7652	266	14	gomez	gomez	NOUN
ap-7652	266	15	-	-	PUNCT
ap-7652	266	16	ullate	ullate	NOUN
ap-7652	266	17	et	et	PROPN
ap-7652	266	18	al	al	PROPN
ap-7652	267	1	[	[	X
ap-7652	267	2	11	11	NUM
ap-7652	267	3	]	]	PUNCT
ap-7652	267	4	constructed	construct	VERB
ap-7652	267	5	the	the	DET
ap-7652	267	6	subnet	subnet	NOUN
ap-7652	267	7	of	of	ADP
ap-7652	267	8	rationally	rationally	ADV
ap-7652	267	9	deformed	deform	VERB
ap-7652	267	10	morse	morse	NOUN
ap-7652	267	11	potentials	potential	VERB
ap-7652	267	12	∞v	∞v	NUM
ap-7652	268	1	[	[	X
ap-7652	268	2	y	y	X
ap-7652	268	3	;	;	PUNCT
ap-7652	268	4	a	a	DET
ap-7652	268	5	|	|	NOUN
ap-7652	268	6	+	+	CCONJ
ap-7652	268	7	...	...	PUNCT
ap-7652	268	8	m+	m+	NUM
ap-7652	269	1	p	p	X
ap-7652	269	2	]	]	X
ap-7652	269	3	=	=	PUNCT
ap-7652	269	4	∞v	∞v	NUM
ap-7652	270	1	[	[	X
ap-7652	270	2	y	y	X
ap-7652	270	3	;	;	PUNCT
ap-7652	270	4	a	a	X
ap-7652	270	5	]	]	X
ap-7652	270	6	+	+	CCONJ
ap-7652	270	7	y2	y2	INTJ
ap-7652	270	8	{	{	PUNCT
ap-7652	270	9	∞i	∞i	NUM
ap-7652	270	10	0[y	0[y	NUM
ap-7652	270	11	;	;	PUNCT
ap-7652	270	12	a	a	PRON
ap-7652	270	13	]	]	X
ap-7652	270	14	−	−	NOUN
ap-7652	270	15	∞i	∞i	NUM
ap-7652	271	1	0[y	0[y	NUM
ap-7652	271	2	;	;	PUNCT
ap-7652	272	1	a	a	DET
ap-7652	272	2	|	|	NOUN
ap-7652	272	3	+	+	CCONJ
ap-7652	272	4	...	...	PUNCT
ap-7652	272	5	m+	m+	NUM
ap-7652	272	6	p	p	X
ap-7652	272	7	]	]	PUNCT
ap-7652	272	8	}	}	PUNCT
ap-7652	272	9	(	(	PUNCT
ap-7652	272	10	88	88	NUM
ap-7652	272	11	)	)	PUNCT
ap-7652	272	12	using	use	VERB
ap-7652	272	13	seed	seed	NOUN
ap-7652	272	14	solutions	solution	NOUN
ap-7652	272	15	infinite	infinite	ADJ
ap-7652	272	16	at	at	ADP
ap-7652	272	17	both	both	DET
ap-7652	272	18	quantization	quantization	NOUN
ap-7652	272	19	ends	end	VERB
ap-7652	272	20	.	.	PUNCT
ap-7652	273	1	in	in	ADP
ap-7652	273	2	next	next	ADJ
ap-7652	273	3	subsection	subsection	NOUN
ap-7652	273	4	we	we	PRON
ap-7652	273	5	will	will	AUX
ap-7652	273	6	introduce	introduce	VERB
ap-7652	273	7	another	another	DET
ap-7652	273	8	subnet	subnet	NOUN
ap-7652	273	9	of	of	ADP
ap-7652	273	10	rationally	rationally	ADV
ap-7652	273	11	deformed	deform	VERB
ap-7652	273	12	morse	morse	NOUN
ap-7652	273	13	potentials	potential	VERB
ap-7652	273	14	∞v	∞v	NUM
ap-7652	274	1	[	[	X
ap-7652	274	2	y	y	X
ap-7652	274	3	;	;	PUNCT
ap-7652	274	4	a	a	DET
ap-7652	274	5	|	|	NOUN
ap-7652	274	6	−	−	NOUN
ap-7652	274	7	...	...	PUNCT
ap-7652	275	1	m	m	VERB
ap-7652	275	2	_	_	NOUN
ap-7652	276	1	p	p	X
ap-7652	276	2	]	]	X
ap-7652	276	3	=	=	PUNCT
ap-7652	276	4	∞v	∞v	NUM
ap-7652	277	1	[	[	X
ap-7652	277	2	y	y	X
ap-7652	277	3	;	;	PUNCT
ap-7652	277	4	a	a	X
ap-7652	277	5	]	]	X
ap-7652	277	6	+	+	CCONJ
ap-7652	277	7	y2	y2	INTJ
ap-7652	277	8	{	{	PUNCT
ap-7652	277	9	∞i	∞i	NUM
ap-7652	277	10	0[y	0[y	NUM
ap-7652	277	11	;	;	PUNCT
ap-7652	277	12	a	a	PRON
ap-7652	277	13	]	]	X
ap-7652	277	14	−	−	NOUN
ap-7652	277	15	∞i	∞i	NUM
ap-7652	278	1	0[y	0[y	NUM
ap-7652	278	2	;	;	PUNCT
ap-7652	278	3	a	a	DET
ap-7652	278	4	|	|	NOUN
ap-7652	278	5	−	−	NOUN
ap-7652	278	6	...	...	PUNCT
ap-7652	279	1	m	m	VERB
ap-7652	279	2	_	_	NOUN
ap-7652	280	1	p	p	X
ap-7652	280	2	]	]	X
ap-7652	280	3	}	}	PUNCT
ap-7652	280	4	(	(	PUNCT
ap-7652	280	5	89	89	NUM
ap-7652	280	6	)	)	PUNCT
ap-7652	280	7	constructed	construct	VERB
ap-7652	280	8	by	by	ADP
ap-7652	280	9	means	mean	NOUN
ap-7652	280	10	of	of	ADP
ap-7652	280	11	ffs	ffs	NOUN
ap-7652	280	12	vanishing	vanish	VERB
ap-7652	280	13	at	at	ADP
ap-7652	280	14	the	the	DET
ap-7652	280	15	origin	origin	NOUN
ap-7652	280	16	.	.	PUNCT
ap-7652	281	1	the	the	DET
ap-7652	281	2	subnet	subnet	NOUN
ap-7652	281	3	starts	start	VERB
ap-7652	281	4	from	from	ADP
ap-7652	281	5	the	the	DET
ap-7652	281	6	potential	potential	NOUN
ap-7652	281	7	∞v	∞v	NUM
ap-7652	282	1	[	[	X
ap-7652	282	2	y	y	X
ap-7652	282	3	;	;	PUNCT
ap-7652	282	4	a	a	DET
ap-7652	282	5	|	|	NOUN
ap-7652	282	6	−	−	NOUN
ap-7652	282	7	...	...	PUNCT
ap-7652	282	8	m	m	VERB
ap-7652	282	9	]	]	X
ap-7652	282	10	with	with	ADP
ap-7652	282	11	a	a	DET
ap-7652	282	12	positive	positive	ADJ
ap-7652	282	13	integer	integer	NOUN
ap-7652	282	14	m	m	VERB
ap-7652	282	15	>	>	X
ap-7652	282	16	2a−	2a−	NUM
ap-7652	282	17	1	1	NUM
ap-7652	282	18	–	–	PUNCT
ap-7652	282	19	potential	potential	ADJ
ap-7652	282	20	function	function	NOUN
ap-7652	282	21	(	(	PUNCT
ap-7652	282	22	16	16	NUM
ap-7652	282	23	)	)	PUNCT
ap-7652	282	24	in	in	ADP
ap-7652	282	25	[	[	X
ap-7652	282	26	10	10	NUM
ap-7652	282	27	]	]	PUNCT
ap-7652	282	28	with	with	ADP
ap-7652	282	29	a	a	DET
ap-7652	282	30	=	=	SYM
ap-7652	282	31	a−	a−	PROPN
ap-7652	282	32	1/2	1/2	NUM
ap-7652	282	33	,	,	PUNCT
ap-7652	282	34	b	b	NOUN
ap-7652	282	35	=	=	SYM
ap-7652	282	36	1	1	X
ap-7652	282	37	.	.	X
ap-7652	283	1	substituting	substitute	VERB
ap-7652	283	2	(	(	PUNCT
ap-7652	283	3	82	82	NUM
ap-7652	283	4	)	)	PUNCT
ap-7652	283	5	into	into	ADP
ap-7652	283	6	(	(	PUNCT
ap-7652	283	7	86	86	NUM
ap-7652	283	8	)	)	PUNCT
ap-7652	283	9	and	and	CCONJ
ap-7652	283	10	also	also	ADV
ap-7652	283	11	making	make	VERB
ap-7652	283	12	use	use	NOUN
ap-7652	283	13	of	of	ADP
ap-7652	283	14	(	(	PUNCT
ap-7652	283	15	37	37	NUM
ap-7652	283	16	)	)	PUNCT
ap-7652	283	17	with	with	ADP
ap-7652	283	18	k	k	PROPN
ap-7652	283	19	=	=	SYM
ap-7652	283	20	p	p	PROPN
ap-7652	283	21	,	,	PUNCT
ap-7652	283	22	shows	show	VERB
ap-7652	283	23	that	that	SCONJ
ap-7652	283	24	rcsle	rcsle	PROPN
ap-7652	283	25	(	(	PUNCT
ap-7652	283	26	77	77	NUM
ap-7652	283	27	)	)	PUNCT
ap-7652	283	28	has	have	VERB
ap-7652	283	29	an	an	DET
ap-7652	283	30	infinite	infinite	ADJ
ap-7652	283	31	set	set	NOUN
ap-7652	283	32	of	of	ADP
ap-7652	283	33	q	q	ADJ
ap-7652	283	34	-	-	PUNCT
ap-7652	283	35	rss	rss	NOUN
ap-7652	283	36	∞φ±,m[y	∞φ±,m[y	PROPN
ap-7652	283	37	;	;	PUNCT
ap-7652	283	38	a	a	DET
ap-7652	283	39	|	|	NOUN
ap-7652	283	40	±	±	NUM
ap-7652	283	41	...	...	PUNCT
ap-7652	283	42	mp	mp	X
ap-7652	283	43	]	]	X
ap-7652	283	44	=	=	SYM
ap-7652	283	45	∞ϕ±,0[y	∞ϕ±,0[y	PROPN
ap-7652	283	46	;	;	PUNCT
ap-7652	283	47	a±	a±	PROPN
ap-7652	283	48	p	p	X
ap-7652	283	49	]	]	X
ap-7652	283	50	∞w[y	∞w[y	NOUN
ap-7652	283	51	;	;	PUNCT
ap-7652	283	52	a	a	DET
ap-7652	283	53	|	|	NOUN
ap-7652	283	54	±	±	NUM
ap-7652	283	55	...	...	PUNCT
ap-7652	283	56	mp	mp	PROPN
ap-7652	283	57	,	,	PUNCT
ap-7652	283	58	m	m	PROPN
ap-7652	283	59	]	]	X
ap-7652	283	60	∞w[y	∞w[y	NOUN
ap-7652	283	61	;	;	PUNCT
ap-7652	283	62	a	a	DET
ap-7652	283	63	|	|	NOUN
ap-7652	283	64	±	±	NUM
ap-7652	283	65	...	...	PUNCT
ap-7652	283	66	mp	mp	NOUN
ap-7652	283	67	]	]	PUNCT
ap-7652	283	68	.	.	PUNCT
ap-7652	284	1	(	(	PUNCT
ap-7652	284	2	90	90	NUM
ap-7652	284	3	)	)	PUNCT
ap-7652	284	4	apparently	apparently	ADV
ap-7652	284	5	q	q	ADJ
ap-7652	284	6	-	-	PUNCT
ap-7652	284	7	rs	rs	ADJ
ap-7652	284	8	(	(	PUNCT
ap-7652	284	9	90	90	NUM
ap-7652	284	10	)	)	PUNCT
ap-7652	284	11	with	with	ADP
ap-7652	284	12	the	the	DET
ap-7652	284	13	label	label	NOUN
ap-7652	284	14	‘	'	PUNCT
ap-7652	284	15	−	−	NOUN
ap-7652	284	16	’	'	PUNCT
ap-7652	284	17	represents	represent	VERB
ap-7652	284	18	the	the	DET
ap-7652	284	19	principal	principal	ADJ
ap-7652	284	20	solution	solution	NOUN
ap-7652	284	21	approaching	approach	VERB
ap-7652	284	22	0	0	NUM
ap-7652	284	23	as	as	ADP
ap-7652	284	24	yδ−(mp)e−1	yδ−(mp)e−1	PROPN
ap-7652	284	25	/	/	SYM
ap-7652	284	26	y	y	PROPN
ap-7652	284	27	in	in	ADP
ap-7652	284	28	the	the	DET
ap-7652	284	29	limit	limit	NOUN
ap-7652	284	30	y	y	PROPN
ap-7652	284	31	→	→	SYM
ap-7652	284	32	+0	+0	PROPN
ap-7652	284	33	.	.	PROPN
ap-7652	285	1	on	on	ADP
ap-7652	285	2	other	other	ADJ
ap-7652	285	3	hand	hand	NOUN
ap-7652	285	4	q	q	NOUN
ap-7652	285	5	-	-	PUNCT
ap-7652	285	6	rs	rs	ADJ
ap-7652	285	7	(	(	PUNCT
ap-7652	285	8	90	90	NUM
ap-7652	285	9	)	)	PUNCT
ap-7652	285	10	labelled	label	VERB
ap-7652	285	11	by	by	ADP
ap-7652	285	12	‘	'	PUNCT
ap-7652	285	13	+	+	NOUN
ap-7652	285	14	’	'	PUNCT
ap-7652	285	15	infinitely	infinitely	ADV
ap-7652	285	16	grows	grow	VERB
ap-7652	285	17	as	as	ADP
ap-7652	285	18	yδ+(mp)e1	yδ+(mp)e1	PROPN
ap-7652	285	19	/	/	SYM
ap-7652	285	20	y	y	PROPN
ap-7652	285	21	in	in	ADP
ap-7652	285	22	this	this	DET
ap-7652	285	23	limit	limit	NOUN
ap-7652	285	24	.	.	PUNCT
ap-7652	286	1	in	in	ADP
ap-7652	286	2	both	both	DET
ap-7652	286	3	cases	case	NOUN
ap-7652	286	4	ld∞φ±,m[y	ld∞φ±,m[y	PROPN
ap-7652	286	5	;	;	PUNCT
ap-7652	286	6	a	a	DET
ap-7652	286	7	|	|	NOUN
ap-7652	286	8	±	±	NUM
ap-7652	286	9	...	...	PUNCT
ap-7652	286	10	mp	mp	X
ap-7652	286	11	]	]	X
ap-7652	286	12	≈	≈	PROPN
ap-7652	286	13	∓y−2	∓y−2	PROPN
ap-7652	286	14	(	(	PUNCT
ap-7652	286	15	91	91	NUM
ap-7652	286	16	)	)	PUNCT
ap-7652	286	17	108	108	NUM
ap-7652	286	18	vol	vol	NOUN
ap-7652	286	19	.	.	PUNCT
ap-7652	287	1	62	62	NUM
ap-7652	287	2	no	no	INTJ
ap-7652	287	3	.	.	PUNCT
ap-7652	288	1	1/2022	1/2022	NUM
ap-7652	288	2	quantization	quantization	NOUN
ap-7652	288	3	of	of	ADP
ap-7652	288	4	rationally	rationally	ADV
ap-7652	288	5	deformed	deform	VERB
ap-7652	288	6	morse	morse	ADJ
ap-7652	288	7	potentials	potential	NOUN
ap-7652	288	8	.	.	PUNCT
ap-7652	288	9	.	.	PUNCT
ap-7652	289	1	.	.	PUNCT
ap-7652	290	1	and	and	CCONJ
ap-7652	290	2	consequently	consequently	ADV
ap-7652	290	3	ld	ld	PROPN
ap-7652	290	4	∗φ±,m[y	∗φ±,m[y	PROPN
ap-7652	290	5	;	;	PUNCT
ap-7652	290	6	a	a	DET
ap-7652	290	7	|	|	NOUN
ap-7652	290	8	±	±	NUM
ap-7652	290	9	...	...	PUNCT
ap-7652	290	10	mp	mp	PROPN
ap-7652	290	11	]	]	X
ap-7652	290	12	≡	≡	PROPN
ap-7652	290	13	ld	ld	PROPN
ap-7652	290	14	y	y	PROPN
ap-7652	290	15	−	−	PROPN
ap-7652	290	16	ld∞φ±,m[y	ld∞φ±,m[y	PROPN
ap-7652	290	17	;	;	PUNCT
ap-7652	290	18	a	a	DET
ap-7652	290	19	|	|	NOUN
ap-7652	290	20	±	±	NUM
ap-7652	290	21	...	...	PUNCT
ap-7652	290	22	mp	mp	X
ap-7652	290	23	]	]	X
ap-7652	290	24	≈	≈	PROPN
ap-7652	290	25	±y−2	±y−2	NUM
ap-7652	290	26	(	(	PUNCT
ap-7652	290	27	92	92	NUM
ap-7652	290	28	)	)	PUNCT
ap-7652	290	29	for	for	ADP
ap-7652	290	30	0	0	NUM
ap-7652	290	31	<	<	X
ap-7652	290	32	y	y	X
ap-7652	290	33	<	<	X
ap-7652	290	34	<	<	X
ap-7652	290	35	1	1	NUM
ap-7652	290	36	,	,	PUNCT
ap-7652	290	37	where	where	SCONJ
ap-7652	290	38	we	we	PRON
ap-7652	290	39	dropped	drop	VERB
ap-7652	290	40	subscript	subscript	NOUN
ap-7652	290	41	∞	∞	PROPN
ap-7652	290	42	in	in	ADP
ap-7652	290	43	the	the	DET
ap-7652	290	44	notation	notation	NOUN
ap-7652	290	45	of	of	ADP
ap-7652	290	46	the	the	DET
ap-7652	290	47	ff	ff	NOUN
ap-7652	290	48	for	for	ADP
ap-7652	290	49	the	the	DET
ap-7652	290	50	reverse	reverse	ADJ
ap-7652	290	51	rdt	rdt	PROPN
ap-7652	290	52	:	:	PUNCT
ap-7652	290	53	∗φ±,m[y	∗φ±,m[y	PROPN
ap-7652	290	54	;	;	PUNCT
ap-7652	290	55	a	a	DET
ap-7652	290	56	|	|	NOUN
ap-7652	290	57	±	±	NUM
ap-7652	290	58	...	...	PUNCT
ap-7652	290	59	mp	mp	PROPN
ap-7652	290	60	]	]	X
ap-7652	290	61	≡	≡	PROPN
ap-7652	290	62	y/∞φ±,m[y	y/∞φ±,m[y	PROPN
ap-7652	290	63	;	;	PUNCT
ap-7652	290	64	a	a	DET
ap-7652	290	65	|	|	NOUN
ap-7652	290	66	±	±	NUM
ap-7652	290	67	...	...	PUNCT
ap-7652	290	68	mp	mp	NOUN
ap-7652	290	69	]	]	PUNCT
ap-7652	290	70	.	.	PUNCT
ap-7652	291	1	(	(	PUNCT
ap-7652	291	2	93	93	NUM
ap-7652	291	3	)	)	PUNCT
ap-7652	291	4	note	note	VERB
ap-7652	291	5	that	that	SCONJ
ap-7652	291	6	the	the	DET
ap-7652	291	7	last	last	ADJ
ap-7652	291	8	summand	summand	NOUN
ap-7652	291	9	in	in	ADP
ap-7652	291	10	sum	sum	NOUN
ap-7652	291	11	(	(	PUNCT
ap-7652	291	12	85	85	NUM
ap-7652	291	13	)	)	PUNCT
ap-7652	291	14	has	have	VERB
ap-7652	291	15	a	a	DET
ap-7652	291	16	simple	simple	ADJ
ap-7652	291	17	pole	pole	NOUN
ap-7652	291	18	at	at	ADP
ap-7652	291	19	y	y	PROPN
ap-7652	291	20	=	=	PUNCT
ap-7652	291	21	0	0	NUM
ap-7652	292	1	so	so	ADV
ap-7652	292	2	an	an	DET
ap-7652	292	3	arbitrary	arbitrary	ADJ
ap-7652	292	4	principal	principal	ADJ
ap-7652	292	5	solution	solution	NOUN
ap-7652	292	6	of	of	ADP
ap-7652	292	7	rcsle	rcsle	PROPN
ap-7652	292	8	(	(	PUNCT
ap-7652	292	9	77	77	NUM
ap-7652	292	10	)	)	PUNCT
ap-7652	292	11	near	near	ADP
ap-7652	292	12	its	its	PRON
ap-7652	292	13	irregular	irregular	ADJ
ap-7652	292	14	singular	singular	ADJ
ap-7652	292	15	point	point	NOUN
ap-7652	292	16	at	at	ADP
ap-7652	292	17	y	y	PROPN
ap-7652	292	18	=	=	SYM
ap-7652	292	19	0	0	NUM
ap-7652	292	20	can	can	AUX
ap-7652	292	21	be	be	AUX
ap-7652	292	22	approximated	approximate	VERB
ap-7652	292	23	as	as	ADP
ap-7652	292	24	∞φ0[y	∞φ0[y	PROPN
ap-7652	292	25	;	;	PUNCT
ap-7652	292	26	a	a	PRON
ap-7652	292	27	;	;	PUNCT
ap-7652	292	28	ε	ε	PROPN
ap-7652	292	29	|	|	ADV
ap-7652	292	30	±	±	NUM
ap-7652	292	31	...	...	PUNCT
ap-7652	292	32	mp	mp	PROPN
ap-7652	292	33	]	]	X
ap-7652	292	34	∝	∝	PROPN
ap-7652	292	35	y∆±(a;mp)e−1	y∆±(a;mp)e−1	PROPN
ap-7652	292	36	/	/	SYM
ap-7652	292	37	y	y	PROPN
ap-7652	292	38	for	for	ADP
ap-7652	292	39	y	y	PROPN
ap-7652	292	40	<	<	X
ap-7652	292	41	<	<	X
ap-7652	292	42	1	1	NUM
ap-7652	292	43	,	,	PUNCT
ap-7652	292	44	(	(	PUNCT
ap-7652	292	45	94	94	NUM
ap-7652	292	46	)	)	PUNCT
ap-7652	292	47	where	where	SCONJ
ap-7652	292	48	∆±(a;mp	∆±(a;mp	NOUN
ap-7652	292	49	)	)	PUNCT
ap-7652	292	50	stands	stand	VERB
ap-7652	292	51	for	for	ADP
ap-7652	292	52	a	a	DET
ap-7652	292	53	finite	finite	ADJ
ap-7652	292	54	power	power	NOUN
ap-7652	292	55	exponent	exponent	NOUN
ap-7652	292	56	which	which	DET
ap-7652	292	57	particular	particular	ADJ
ap-7652	292	58	value	value	NOUN
ap-7652	292	59	is	be	AUX
ap-7652	292	60	non	non	ADJ
ap-7652	292	61	-	-	ADJ
ap-7652	292	62	essential	essential	ADJ
ap-7652	292	63	for	for	ADP
ap-7652	292	64	our	our	PRON
ap-7652	292	65	discussion	discussion	NOUN
ap-7652	292	66	.	.	PUNCT
ap-7652	293	1	examination	examination	NOUN
ap-7652	293	2	of	of	ADP
ap-7652	293	3	the	the	DET
ap-7652	293	4	quasi	quasi	ADJ
ap-7652	293	5	-	-	ADJ
ap-7652	293	6	rational	rational	ADJ
ap-7652	293	7	function	function	NOUN
ap-7652	293	8	∞φ0[y	∞φ0[y	ADV
ap-7652	293	9	;	;	PUNCT
ap-7652	293	10	a	a	PRON
ap-7652	293	11	;	;	PUNCT
ap-7652	293	12	ε	ε	PROPN
ap-7652	293	13	|	|	ADV
ap-7652	293	14	±	±	NUM
ap-7652	293	15	...	...	PUNCT
ap-7652	294	1	mp+1	mp+1	X
ap-7652	294	2	]	]	X
ap-7652	295	1	=	=	PUNCT
ap-7652	295	2	y	y	PROPN
ap-7652	295	3	w	w	PROPN
ap-7652	295	4	{	{	PUNCT
ap-7652	295	5	∞φ±,mp+1	∞φ±,mp+1	PROPN
ap-7652	296	1	[	[	X
ap-7652	296	2	y	y	X
ap-7652	296	3	;	;	PUNCT
ap-7652	296	4	a	a	DET
ap-7652	296	5	|	|	NOUN
ap-7652	296	6	±	±	NUM
ap-7652	296	7	...	...	PUNCT
ap-7652	296	8	mp	mp	PROPN
ap-7652	296	9	]	]	PUNCT
ap-7652	296	10	,	,	PUNCT
ap-7652	296	11	∞φ0[y	∞φ0[y	PROPN
ap-7652	296	12	;	;	PUNCT
ap-7652	296	13	a	a	PRON
ap-7652	296	14	;	;	PUNCT
ap-7652	296	15	ε	ε	PROPN
ap-7652	296	16	|	|	ADV
ap-7652	296	17	±	±	NUM
ap-7652	296	18	...	...	PUNCT
ap-7652	296	19	mp	mp	PROPN
ap-7652	296	20	]	]	PUNCT
ap-7652	296	21	}	}	PUNCT
ap-7652	296	22	∞φ±,mp+1	∞φ±,mp+1	NOUN
ap-7652	297	1	[	[	X
ap-7652	297	2	y	y	X
ap-7652	297	3	;	;	PUNCT
ap-7652	297	4	a	a	DET
ap-7652	297	5	|	|	NOUN
ap-7652	297	6	±	±	NUM
ap-7652	297	7	...	...	PUNCT
ap-7652	297	8	mp	mp	X
ap-7652	297	9	]	]	X
ap-7652	297	10	=	=	PUNCT
ap-7652	297	11	y	y	PROPN
ap-7652	297	12	∞φ̇0[y	∞φ̇0[y	PROPN
ap-7652	297	13	;	;	PUNCT
ap-7652	297	14	a	a	PRON
ap-7652	297	15	;	;	PUNCT
ap-7652	297	16	ε	ε	PROPN
ap-7652	297	17	|	|	ADV
ap-7652	297	18	±	±	NUM
ap-7652	297	19	...	...	PUNCT
ap-7652	297	20	mp	mp	PROPN
ap-7652	297	21	]	]	X
ap-7652	297	22	−	−	PROPN
ap-7652	297	23	y	y	PROPN
ap-7652	297	24	ld∞φ±,mp+1	ld∞φ±,mp+1	PUNCT
ap-7652	298	1	[	[	X
ap-7652	298	2	y	y	X
ap-7652	298	3	;	;	PUNCT
ap-7652	298	4	a	a	PRON
ap-7652	298	5	;	;	PUNCT
ap-7652	298	6	|	|	ADV
ap-7652	298	7	...	...	PUNCT
ap-7652	298	8	mp	mp	NOUN
ap-7652	298	9	]	]	X
ap-7652	298	10	∞φ0[y	∞φ0[y	PROPN
ap-7652	298	11	;	;	PUNCT
ap-7652	298	12	a	a	PRON
ap-7652	298	13	;	;	PUNCT
ap-7652	298	14	ε	ε	PROPN
ap-7652	298	15	|	|	ADV
ap-7652	298	16	±	±	NUM
ap-7652	298	17	...	...	PUNCT
ap-7652	298	18	mp	mp	PROPN
ap-7652	298	19	]	]	X
ap-7652	298	20	(	(	PUNCT
ap-7652	298	21	95	95	NUM
ap-7652	298	22	)	)	PUNCT
ap-7652	298	23	representing	represent	VERB
ap-7652	298	24	the	the	DET
ap-7652	298	25	rdt	rdt	NOUN
ap-7652	298	26	of	of	ADP
ap-7652	298	27	the	the	DET
ap-7652	298	28	principal	principal	ADJ
ap-7652	298	29	solution	solution	NOUN
ap-7652	298	30	of	of	ADP
ap-7652	298	31	rcsle	rcsle	PROPN
ap-7652	298	32	(	(	PUNCT
ap-7652	298	33	77	77	NUM
ap-7652	298	34	)	)	PUNCT
ap-7652	298	35	near	near	ADP
ap-7652	298	36	its	its	PRON
ap-7652	298	37	irregular	irregular	ADJ
ap-7652	298	38	singular	singular	ADJ
ap-7652	298	39	point	point	NOUN
ap-7652	298	40	at	at	ADP
ap-7652	298	41	y	y	PROPN
ap-7652	298	42	=	=	SYM
ap-7652	298	43	0	0	NUM
ap-7652	298	44	confirms	confirm	VERB
ap-7652	298	45	that	that	SCONJ
ap-7652	298	46	it	it	PRON
ap-7652	298	47	is	be	AUX
ap-7652	298	48	a	a	DET
ap-7652	298	49	principal	principal	ADJ
ap-7652	298	50	solution	solution	NOUN
ap-7652	298	51	of	of	ADP
ap-7652	298	52	the	the	DET
ap-7652	298	53	transformed	transform	VERB
ap-7652	298	54	rcsle	rcsle	NOUN
ap-7652	298	55	near	near	ADP
ap-7652	298	56	the	the	DET
ap-7652	298	57	singular	singular	ADJ
ap-7652	298	58	point	point	NOUN
ap-7652	298	59	in	in	ADP
ap-7652	298	60	question	question	NOUN
ap-7652	298	61	.	.	PUNCT
ap-7652	299	1	vice	vice	NOUN
ap-7652	299	2	versa	versa	ADV
ap-7652	299	3	the	the	DET
ap-7652	299	4	quasi	quasi	ADJ
ap-7652	299	5	-	-	ADJ
ap-7652	299	6	rational	rational	ADJ
ap-7652	299	7	function	function	NOUN
ap-7652	299	8	y	y	PROPN
ap-7652	299	9	w	w	PROPN
ap-7652	299	10	{	{	PUNCT
ap-7652	299	11	∗φ±,mp	∗φ±,mp	PROPN
ap-7652	299	12	[	[	X
ap-7652	299	13	y	y	X
ap-7652	299	14	;	;	PUNCT
ap-7652	299	15	a	a	DET
ap-7652	299	16	|	|	NOUN
ap-7652	299	17	±	±	NUM
ap-7652	299	18	...	...	PUNCT
ap-7652	299	19	mp	mp	PROPN
ap-7652	299	20	]	]	PUNCT
ap-7652	299	21	,	,	PUNCT
ap-7652	299	22	∞φ0[y	∞φ0[y	PROPN
ap-7652	299	23	;	;	PUNCT
ap-7652	299	24	a	a	PRON
ap-7652	299	25	;	;	PUNCT
ap-7652	299	26	ε	ε	PROPN
ap-7652	299	27	|	|	ADV
ap-7652	299	28	±	±	NUM
ap-7652	299	29	...	...	PUNCT
ap-7652	299	30	mp+1	mp+1	X
ap-7652	299	31	]	]	PUNCT
ap-7652	299	32	}	}	PUNCT
ap-7652	299	33	∗φ±,mp+1	∗φ±,mp+1	PUNCT
ap-7652	300	1	[	[	X
ap-7652	300	2	y	y	X
ap-7652	300	3	;	;	PUNCT
ap-7652	300	4	a	a	DET
ap-7652	300	5	|	|	NOUN
ap-7652	300	6	±	±	NUM
ap-7652	300	7	...	...	PUNCT
ap-7652	300	8	mp	mp	X
ap-7652	300	9	]	]	X
ap-7652	300	10	=	=	PUNCT
ap-7652	300	11	y	y	PROPN
ap-7652	300	12	∞φ̇0[y	∞φ̇0[y	PROPN
ap-7652	300	13	;	;	PUNCT
ap-7652	300	14	a	a	PRON
ap-7652	300	15	;	;	PUNCT
ap-7652	300	16	ε	ε	PROPN
ap-7652	300	17	|	|	ADV
ap-7652	300	18	±	±	NUM
ap-7652	300	19	...	...	PUNCT
ap-7652	300	20	mp+1	mp+1	X
ap-7652	300	21	]	]	PUNCT
ap-7652	300	22	−	−	PROPN
ap-7652	301	1	y	y	INTJ
ap-7652	301	2	ld∗φ±,mp+1	ld∗φ±,mp+1	PROPN
ap-7652	302	1	[	[	X
ap-7652	302	2	y	y	X
ap-7652	302	3	;	;	PUNCT
ap-7652	302	4	a	a	DET
ap-7652	302	5	|	|	NOUN
ap-7652	302	6	±	±	NUM
ap-7652	302	7	...	...	PUNCT
ap-7652	302	8	mp+1	mp+1	X
ap-7652	302	9	]	]	X
ap-7652	302	10	∞φ0[y	∞φ0[y	ADV
ap-7652	302	11	;	;	PUNCT
ap-7652	302	12	a	a	PRON
ap-7652	302	13	;	;	PUNCT
ap-7652	302	14	ε	ε	PROPN
ap-7652	302	15	|	|	ADV
ap-7652	302	16	±	±	NUM
ap-7652	302	17	...	...	PUNCT
ap-7652	303	1	mp+1	mp+1	X
ap-7652	303	2	]	]	X
ap-7652	303	3	(	(	PUNCT
ap-7652	303	4	96	96	NUM
ap-7652	303	5	)	)	PUNCT
ap-7652	303	6	representing	represent	VERB
ap-7652	303	7	the	the	DET
ap-7652	303	8	reverse	reverse	ADJ
ap-7652	303	9	rdt	rdt	PROPN
ap-7652	303	10	of	of	ADP
ap-7652	303	11	the	the	DET
ap-7652	303	12	principal	principal	ADJ
ap-7652	303	13	solution	solution	NOUN
ap-7652	303	14	(	(	PUNCT
ap-7652	303	15	95	95	NUM
ap-7652	303	16	)	)	PUNCT
ap-7652	303	17	is	be	AUX
ap-7652	303	18	the	the	DET
ap-7652	303	19	principal	principal	ADJ
ap-7652	303	20	solution	solution	NOUN
ap-7652	303	21	of	of	ADP
ap-7652	303	22	rcsle	rcsle	PROPN
ap-7652	303	23	(	(	PUNCT
ap-7652	303	24	77	77	NUM
ap-7652	303	25	)	)	PUNCT
ap-7652	303	26	near	near	ADP
ap-7652	303	27	its	its	PRON
ap-7652	303	28	irregular	irregular	ADJ
ap-7652	303	29	singular	singular	ADJ
ap-7652	303	30	point	point	NOUN
ap-7652	303	31	at	at	ADP
ap-7652	303	32	y	y	PROPN
ap-7652	303	33	=	=	SYM
ap-7652	303	34	0	0	PROPN
ap-7652	303	35	.	.	PUNCT
ap-7652	304	1	to	to	PART
ap-7652	304	2	study	study	VERB
ap-7652	304	3	a	a	DET
ap-7652	304	4	behavior	behavior	NOUN
ap-7652	304	5	of	of	ADP
ap-7652	304	6	frobenius	frobenius	ADJ
ap-7652	304	7	solutions	solution	NOUN
ap-7652	304	8	near	near	ADP
ap-7652	304	9	a	a	DET
ap-7652	304	10	regular	regular	ADJ
ap-7652	304	11	singular	singular	ADJ
ap-7652	304	12	point	point	NOUN
ap-7652	304	13	of	of	ADP
ap-7652	304	14	rcsle	rcsle	PROPN
ap-7652	304	15	(	(	PUNCT
ap-7652	304	16	77	77	NUM
ap-7652	304	17	)	)	PUNCT
ap-7652	304	18	at	at	ADP
ap-7652	304	19	infinity	infinity	NOUN
ap-7652	304	20	it	it	PRON
ap-7652	304	21	is	be	AUX
ap-7652	304	22	convenient	convenient	ADJ
ap-7652	304	23	to	to	PART
ap-7652	304	24	convert	convert	VERB
ap-7652	304	25	this	this	DET
ap-7652	304	26	equation	equation	NOUN
ap-7652	304	27	to	to	ADP
ap-7652	304	28	its	its	PRON
ap-7652	304	29	‘	'	PUNCT
ap-7652	304	30	prime	prime	ADJ
ap-7652	304	31	’	'	PUNCT
ap-7652	304	32	form	form	NOUN
ap-7652	304	33	[	[	X
ap-7652	304	34	42	42	NUM
ap-7652	304	35	]	]	PUNCT
ap-7652	304	36	using	use	VERB
ap-7652	304	37	the	the	DET
ap-7652	304	38	gauge	gauge	ADJ
ap-7652	304	39	transformation	transformation	NOUN
ap-7652	304	40	∞	∞	PROPN
ap-7652	304	41	̸ψ	̸ψ	NOUN
ap-7652	304	42	[	[	X
ap-7652	304	43	y	y	X
ap-7652	304	44	;	;	PUNCT
ap-7652	304	45	a	a	PRON
ap-7652	304	46	;	;	PUNCT
ap-7652	304	47	ε±	ε±	PROPN
ap-7652	304	48	...	...	PUNCT
ap-7652	304	49	mp	mp	PROPN
ap-7652	304	50	]	]	X
ap-7652	304	51	=	=	PUNCT
ap-7652	304	52	y−1/2	y−1/2	PROPN
ap-7652	304	53	∞φ[y	∞φ[y	PROPN
ap-7652	304	54	;	;	PUNCT
ap-7652	304	55	a	a	PRON
ap-7652	304	56	;	;	PUNCT
ap-7652	304	57	ε	ε	PROPN
ap-7652	304	58	|	|	ADV
ap-7652	304	59	...	...	PUNCT
ap-7652	304	60	mp	mp	PROPN
ap-7652	304	61	]	]	X
ap-7652	304	62	(	(	PUNCT
ap-7652	304	63	97	97	NUM
ap-7652	304	64	)	)	PUNCT
ap-7652	304	65	which	which	PRON
ap-7652	304	66	gives	give	VERB
ap-7652	304	67	{	{	PUNCT
ap-7652	304	68	d	d	PROPN
ap-7652	304	69	dy	dy	NOUN
ap-7652	304	70	y	y	PROPN
ap-7652	304	71	d	d	PROPN
ap-7652	304	72	dy	dy	NOUN
ap-7652	305	1	−	−	NOUN
ap-7652	305	2	y−3	y−3	PROPN
ap-7652	305	3	+	+	CCONJ
ap-7652	305	4	2(a±	2(a±	NUM
ap-7652	305	5	1)y−2	1)y−2	NUM
ap-7652	305	6	+	+	SYM
ap-7652	305	7	2	2	NUM
ap-7652	305	8	d	d	NOUN
ap-7652	305	9	dy	dy	X
ap-7652	305	10	(	(	PUNCT
ap-7652	305	11	y	y	PROPN
ap-7652	305	12	ld∞w[y	ld∞w[y	PROPN
ap-7652	305	13	;	;	PUNCT
ap-7652	305	14	a	a	DET
ap-7652	305	15	|	|	NOUN
ap-7652	305	16	±	±	NUM
ap-7652	305	17	...	...	PUNCT
ap-7652	305	18	mp	mp	PROPN
ap-7652	305	19	]	]	PUNCT
ap-7652	305	20	)	)	PUNCT
ap-7652	306	1	+	+	CCONJ
ap-7652	306	2	εy−1	εy−1	ADJ
ap-7652	306	3	}	}	PUNCT
ap-7652	306	4	∞	∞	PROPN
ap-7652	306	5	̸ψ	̸ψ	VERB
ap-7652	306	6	[	[	X
ap-7652	306	7	y	y	X
ap-7652	306	8	;	;	PUNCT
ap-7652	306	9	a	a	PRON
ap-7652	306	10	;	;	PUNCT
ap-7652	306	11	ε	ε	PROPN
ap-7652	306	12	|	|	ADV
ap-7652	306	13	±	±	NUM
ap-7652	306	14	...	...	PUNCT
ap-7652	306	15	mp	mp	X
ap-7652	306	16	]	]	X
ap-7652	306	17	=	=	SYM
ap-7652	306	18	0	0	PUNCT
ap-7652	306	19	(	(	PUNCT
ap-7652	306	20	98	98	NUM
ap-7652	306	21	)	)	PUNCT
ap-7652	306	22	as	as	SCONJ
ap-7652	306	23	explained	explain	VERB
ap-7652	306	24	above	above	ADP
ap-7652	306	25	the	the	DET
ap-7652	306	26	main	main	ADJ
ap-7652	306	27	advantage	advantage	NOUN
ap-7652	306	28	of	of	ADP
ap-7652	306	29	this	this	DET
ap-7652	306	30	representation	representation	NOUN
ap-7652	306	31	comes	come	VERB
ap-7652	306	32	from	from	ADP
ap-7652	306	33	the	the	DET
ap-7652	306	34	fact	fact	NOUN
ap-7652	306	35	that	that	SCONJ
ap-7652	306	36	the	the	DET
ap-7652	306	37	characteristic	characteristic	ADJ
ap-7652	306	38	exponents	exponent	NOUN
ap-7652	306	39	of	of	ADP
ap-7652	306	40	two	two	NUM
ap-7652	306	41	frobenius	frobenius	ADJ
ap-7652	306	42	solutions	solution	NOUN
ap-7652	306	43	of	of	ADP
ap-7652	306	44	rsle	rsle	NOUN
ap-7652	306	45	(	(	PUNCT
ap-7652	306	46	98	98	NUM
ap-7652	306	47	)	)	PUNCT
ap-7652	306	48	near	near	ADP
ap-7652	306	49	this	this	DET
ap-7652	306	50	singular	singular	ADJ
ap-7652	306	51	end	end	NOUN
ap-7652	306	52	have	have	AUX
ap-7652	306	53	opposite	opposite	ADJ
ap-7652	306	54	signs	sign	NOUN
ap-7652	306	55	,	,	PUNCT
ap-7652	306	56	with	with	ADP
ap-7652	306	57	the	the	DET
ap-7652	306	58	principal	principal	ADJ
ap-7652	306	59	frobenius	frobenius	NOUN
ap-7652	306	60	solution	solution	NOUN
ap-7652	306	61	decaying	decay	VERB
ap-7652	306	62	as	as	ADP
ap-7652	306	63	y−	y−	NOUN
ap-7652	306	64	√	√	ADP
ap-7652	306	65	−ε	−ε	PROPN
ap-7652	306	66	when	when	SCONJ
ap-7652	306	67	y	y	PROPN
ap-7652	306	68	→	→	SYM
ap-7652	306	69	∞.	∞.	PROPN
ap-7652	306	70	again	again	ADV
ap-7652	306	71	rsle	rsle	VERB
ap-7652	306	72	(	(	PUNCT
ap-7652	306	73	98	98	NUM
ap-7652	306	74	)	)	PUNCT
ap-7652	306	75	is	be	AUX
ap-7652	306	76	nothing	nothing	PRON
ap-7652	306	77	but	but	SCONJ
ap-7652	306	78	the	the	DET
ap-7652	306	79	‘	'	PUNCT
ap-7652	306	80	algebraic	algebraic	ADJ
ap-7652	306	81	’	'	PUNCT
ap-7652	306	82	[	[	X
ap-7652	306	83	42	42	NUM
ap-7652	306	84	]	]	SYM
ap-7652	306	85	form	form	NOUN
ap-7652	306	86	of	of	ADP
ap-7652	306	87	the	the	DET
ap-7652	306	88	schrödinger	schrödinger	ADJ
ap-7652	306	89	equation	equation	NOUN
ap-7652	306	90	with	with	ADP
ap-7652	306	91	the	the	DET
ap-7652	306	92	rationally	rationally	ADV
ap-7652	306	93	deformed	deform	VERB
ap-7652	306	94	morse	morse	ADJ
ap-7652	306	95	potentials	potential	NOUN
ap-7652	306	96	(	(	PUNCT
ap-7652	306	97	88	88	NUM
ap-7652	306	98	)	)	PUNCT
ap-7652	306	99	or	or	CCONJ
ap-7652	306	100	(	(	PUNCT
ap-7652	306	101	89	89	NUM
ap-7652	306	102	)	)	PUNCT
ap-7652	306	103	accordingly	accordingly	ADV
ap-7652	306	104	–	–	PUNCT
ap-7652	306	105	the	the	DET
ap-7652	306	106	common	common	ADJ
ap-7652	306	107	feature	feature	NOUN
ap-7652	306	108	of	of	ADP
ap-7652	306	109	rcsles	rcsle	NOUN
ap-7652	306	110	with	with	ADP
ap-7652	306	111	density	density	NOUN
ap-7652	306	112	function	function	NOUN
ap-7652	306	113	(	(	PUNCT
ap-7652	306	114	34	34	NUM
ap-7652	306	115	)	)	PUNCT
ap-7652	306	116	as	as	ADV
ap-7652	306	117	far	far	ADV
ap-7652	306	118	as	as	SCONJ
ap-7652	306	119	the	the	DET
ap-7652	306	120	given	give	VERB
ap-7652	306	121	sle	sle	PROPN
ap-7652	306	122	has	have	VERB
ap-7652	306	123	a	a	DET
ap-7652	306	124	regular	regular	ADJ
ap-7652	306	125	singular	singular	ADJ
ap-7652	306	126	point	point	NOUN
ap-7652	306	127	at	at	ADP
ap-7652	306	128	infinity	infinity	NOUN
ap-7652	306	129	.	.	PUNCT
ap-7652	307	1	apparently	apparently	ADV
ap-7652	307	2	∞	∞	NUM
ap-7652	307	3	̸ψ	̸ψ	NOUN
ap-7652	307	4	[	[	X
ap-7652	307	5	y	y	X
ap-7652	307	6	;	;	PUNCT
ap-7652	307	7	a	a	PRON
ap-7652	307	8	;	;	PUNCT
ap-7652	307	9	ε	ε	PROPN
ap-7652	307	10	|	|	ADV
ap-7652	307	11	±	±	NUM
ap-7652	307	12	...	...	PUNCT
ap-7652	307	13	mp+1	mp+1	X
ap-7652	307	14	]	]	X
ap-7652	307	15	≡	≡	PROPN
ap-7652	307	16	y−1/2	y−1/2	PROPN
ap-7652	307	17	∞φ[y	∞φ[y	PROPN
ap-7652	307	18	;	;	PUNCT
ap-7652	307	19	a	a	PRON
ap-7652	307	20	;	;	PUNCT
ap-7652	307	21	ε	ε	PROPN
ap-7652	307	22	|	|	ADV
ap-7652	307	23	±	±	NUM
ap-7652	307	24	...	...	PUNCT
ap-7652	308	1	mp+1	mp+1	X
ap-7652	308	2	]	]	X
ap-7652	309	1	=	=	PUNCT
ap-7652	309	2	y	y	PROPN
ap-7652	309	3	w	w	PROPN
ap-7652	309	4	{	{	PUNCT
ap-7652	309	5	∞	∞	PROPN
ap-7652	309	6	̸ψ	̸ψ	NOUN
ap-7652	309	7	[	[	X
ap-7652	309	8	y	y	X
ap-7652	309	9	;	;	PUNCT
ap-7652	309	10	a	a	PRON
ap-7652	309	11	;	;	PUNCT
ap-7652	309	12	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	309	13	)	)	PUNCT
ap-7652	310	1	|	|	ADV
ap-7652	310	2	±	±	NUM
ap-7652	310	3	...	...	PUNCT
ap-7652	310	4	mp	mp	PROPN
ap-7652	310	5	]	]	X
ap-7652	310	6	,	,	PUNCT
ap-7652	310	7	∞	∞	PROPN
ap-7652	310	8	̸ψ	̸ψ	VERB
ap-7652	310	9	[	[	X
ap-7652	310	10	y	y	X
ap-7652	310	11	;	;	PUNCT
ap-7652	310	12	a	a	PRON
ap-7652	310	13	;	;	PUNCT
ap-7652	310	14	ε	ε	PROPN
ap-7652	310	15	|	|	ADV
ap-7652	310	16	±	±	NUM
ap-7652	310	17	...	...	PUNCT
ap-7652	310	18	mp	mp	PROPN
ap-7652	310	19	]	]	X
ap-7652	310	20	}	}	PUNCT
ap-7652	310	21	∞	∞	PROPN
ap-7652	310	22	̸ψ	̸ψ	VERB
ap-7652	310	23	[	[	X
ap-7652	310	24	y	y	X
ap-7652	310	25	;	;	PUNCT
ap-7652	310	26	a	a	PRON
ap-7652	310	27	;	;	PUNCT
ap-7652	310	28	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	310	29	)	)	PUNCT
ap-7652	311	1	|	|	ADV
ap-7652	311	2	±	±	NUM
ap-7652	311	3	...	...	PUNCT
ap-7652	311	4	mp	mp	PROPN
ap-7652	311	5	]	]	X
ap-7652	311	6	(	(	PUNCT
ap-7652	311	7	99	99	NUM
ap-7652	311	8	)	)	PUNCT
ap-7652	311	9	here	here	ADV
ap-7652	311	10	we	we	PRON
ap-7652	311	11	are	be	AUX
ap-7652	311	12	only	only	ADV
ap-7652	311	13	interested	interested	ADJ
ap-7652	311	14	in	in	ADP
ap-7652	311	15	cases	case	NOUN
ap-7652	311	16	when	when	SCONJ
ap-7652	311	17	the	the	DET
ap-7652	311	18	ff	ff	NOUN
ap-7652	311	19	appearing	appear	VERB
ap-7652	311	20	in	in	ADP
ap-7652	311	21	the	the	DET
ap-7652	311	22	denominator	denominator	NOUN
ap-7652	311	23	of	of	ADP
ap-7652	311	24	pf	pf	PROPN
ap-7652	311	25	(	(	PUNCT
ap-7652	311	26	99	99	NUM
ap-7652	311	27	)	)	PUNCT
ap-7652	311	28	is	be	AUX
ap-7652	311	29	the	the	DET
ap-7652	311	30	non	non	ADJ
ap-7652	311	31	-	-	ADJ
ap-7652	311	32	principal	principal	ADJ
ap-7652	311	33	frobenius	frobenius	NOUN
ap-7652	311	34	solution	solution	NOUN
ap-7652	311	35	of	of	ADP
ap-7652	311	36	rsle	rsle	NOUN
ap-7652	311	37	(	(	PUNCT
ap-7652	311	38	98	98	NUM
ap-7652	311	39	)	)	PUNCT
ap-7652	311	40	near	near	ADP
ap-7652	311	41	the	the	DET
ap-7652	311	42	singular	singular	ADJ
ap-7652	311	43	point	point	NOUN
ap-7652	311	44	at	at	ADP
ap-7652	311	45	infinity	infinity	NOUN
ap-7652	311	46	so	so	SCONJ
ap-7652	311	47	∞	∞	NUM
ap-7652	311	48	̸ψ	̸ψ	NOUN
ap-7652	311	49	[	[	X
ap-7652	311	50	y	y	X
ap-7652	311	51	;	;	PUNCT
ap-7652	311	52	a	a	PRON
ap-7652	311	53	;	;	PUNCT
ap-7652	311	54	ε	ε	PROPN
ap-7652	311	55	|	|	ADV
ap-7652	311	56	±	±	NUM
ap-7652	311	57	...	...	PUNCT
ap-7652	311	58	mp+1	mp+1	X
ap-7652	311	59	]	]	X
ap-7652	312	1	≈	≈	PROPN
ap-7652	312	2	−	−	PROPN
ap-7652	312	3	[	[	PUNCT
ap-7652	312	4	√	√	NUM
ap-7652	312	5	−ε+	−ε+	INTJ
ap-7652	312	6	»	»	PUNCT
ap-7652	312	7	−ε±,mp+1(a)]y−	−ε±,mp+1(a)]y−	NOUN
ap-7652	313	1	√	√	ADP
ap-7652	313	2	−ε	−ε	PROPN
ap-7652	313	3	for	for	ADP
ap-7652	313	4	y	y	PROPN
ap-7652	313	5	>	>	PUNCT
ap-7652	313	6	>	>	X
ap-7652	313	7	1	1	NUM
ap-7652	313	8	(	(	PUNCT
ap-7652	313	9	100	100	NUM
ap-7652	313	10	)	)	PUNCT
ap-7652	313	11	109	109	NUM
ap-7652	313	12	gregory	gregory	PROPN
ap-7652	313	13	natanson	natanson	PROPN
ap-7652	313	14	acta	acta	PROPN
ap-7652	313	15	polytechnica	polytechnica	PROPN
ap-7652	313	16	if	if	SCONJ
ap-7652	313	17	∞	∞	PROPN
ap-7652	313	18	̸ψ	̸ψ	VERB
ap-7652	313	19	[	[	X
ap-7652	313	20	y	y	X
ap-7652	313	21	;	;	PUNCT
ap-7652	313	22	a	a	PRON
ap-7652	313	23	;	;	PUNCT
ap-7652	313	24	ε	ε	PROPN
ap-7652	313	25	|	|	ADV
ap-7652	313	26	±	±	NUM
ap-7652	313	27	...	...	PUNCT
ap-7652	313	28	mp	mp	PROPN
ap-7652	313	29	]	]	X
ap-7652	313	30	is	be	AUX
ap-7652	313	31	an	an	DET
ap-7652	313	32	arbitrary	arbitrary	ADJ
ap-7652	313	33	principal	principal	ADJ
ap-7652	313	34	frobenius	frobenius	NOUN
ap-7652	313	35	solution	solution	NOUN
ap-7652	313	36	of	of	ADP
ap-7652	313	37	this	this	DET
ap-7652	313	38	rsle	rsle	NOUN
ap-7652	313	39	near	near	ADP
ap-7652	313	40	the	the	DET
ap-7652	313	41	singular	singular	NOUN
ap-7652	313	42	end	end	VERB
ap-7652	313	43	in	in	ADP
ap-7652	313	44	question	question	NOUN
ap-7652	313	45	.	.	PUNCT
ap-7652	314	1	we	we	PRON
ap-7652	314	2	thus	thus	ADV
ap-7652	314	3	proved	prove	VERB
ap-7652	314	4	that	that	SCONJ
ap-7652	314	5	the	the	DET
ap-7652	314	6	rdt	rdt	NOUN
ap-7652	314	7	of	of	ADP
ap-7652	314	8	any	any	DET
ap-7652	314	9	principal	principal	ADJ
ap-7652	314	10	frobenius	frobenius	NOUN
ap-7652	314	11	solution	solution	NOUN
ap-7652	314	12	for	for	ADP
ap-7652	314	13	each	each	PRON
ap-7652	314	14	of	of	ADP
ap-7652	314	15	the	the	DET
ap-7652	314	16	singular	singular	PROPN
ap-7652	314	17	end	end	NOUN
ap-7652	314	18	points	point	NOUN
ap-7652	314	19	is	be	AUX
ap-7652	314	20	itself	itself	PRON
ap-7652	314	21	the	the	DET
ap-7652	314	22	principal	principal	ADJ
ap-7652	314	23	frobenius	frobenius	NOUN
ap-7652	314	24	solution	solution	NOUN
ap-7652	314	25	of	of	ADP
ap-7652	314	26	the	the	DET
ap-7652	314	27	transformed	transform	VERB
ap-7652	314	28	rsle	rsle	NOUN
ap-7652	314	29	near	near	ADP
ap-7652	314	30	the	the	DET
ap-7652	314	31	singular	singular	ADJ
ap-7652	314	32	point	point	NOUN
ap-7652	314	33	in	in	ADP
ap-7652	314	34	question	question	NOUN
ap-7652	314	35	.	.	PUNCT
ap-7652	315	1	suppose	suppose	VERB
ap-7652	315	2	that	that	SCONJ
ap-7652	315	3	rsle	rsle	NOUN
ap-7652	315	4	(	(	PUNCT
ap-7652	315	5	98	98	NUM
ap-7652	315	6	)	)	PUNCT
ap-7652	315	7	with	with	ADP
ap-7652	315	8	mp	mp	PROPN
ap-7652	315	9	replaced	replace	VERB
ap-7652	315	10	for	for	ADP
ap-7652	315	11	m±	m±	PROPN
ap-7652	315	12	p+1	p+1	PROPN
ap-7652	315	13	has	have	VERB
ap-7652	315	14	an	an	DET
ap-7652	315	15	additional	additional	ADJ
ap-7652	315	16	eigenfunction	eigenfunction	NOUN
ap-7652	315	17	∞	∞	NOUN
ap-7652	315	18	̸ψ	̸ψ	NOUN
ap-7652	316	1	[	[	X
ap-7652	316	2	y	y	X
ap-7652	316	3	;	;	PUNCT
ap-7652	316	4	a	a	PRON
ap-7652	316	5	;	;	PUNCT
ap-7652	316	6	ε∗(a	ε∗(a	PROPN
ap-7652	316	7	)	)	PUNCT
ap-7652	317	1	|	|	ADV
ap-7652	317	2	±	±	NUM
ap-7652	317	3	...	...	PUNCT
ap-7652	317	4	m±	m±	PROPN
ap-7652	317	5	p+1	p+1	X
ap-7652	317	6	]	]	X
ap-7652	317	7	at	at	ADP
ap-7652	317	8	the	the	DET
ap-7652	317	9	energy	energy	NOUN
ap-7652	317	10	ε∗(a	ε∗(a	PROPN
ap-7652	317	11	)	)	PUNCT
ap-7652	317	12	<	<	X
ap-7652	317	13	0	0	X
ap-7652	317	14	.	.	PUNCT
ap-7652	317	15	applying	apply	VERB
ap-7652	317	16	the	the	DET
ap-7652	317	17	reverse	reverse	NOUN
ap-7652	317	18	rdt	rdt	PROPN
ap-7652	317	19	with	with	ADP
ap-7652	317	20	the	the	DET
ap-7652	317	21	ff	ff	PROPN
ap-7652	317	22	y1/2/∞φ[y	y1/2/∞φ[y	PROPN
ap-7652	317	23	;	;	PUNCT
ap-7652	317	24	a	a	PRON
ap-7652	317	25	;	;	PUNCT
ap-7652	317	26	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	317	27	)	)	PUNCT
ap-7652	318	1	|	|	ADV
ap-7652	318	2	±	±	NUM
ap-7652	318	3	...	...	PUNCT
ap-7652	318	4	m±	m±	PROPN
ap-7652	318	5	p	p	X
ap-7652	318	6	]	]	X
ap-7652	318	7	=	=	PUNCT
ap-7652	319	1	∞	∞	NUM
ap-7652	319	2	̸ψ−1	̸ψ−1	NOUN
ap-7652	320	1	[	[	X
ap-7652	320	2	y	y	X
ap-7652	320	3	;	;	PUNCT
ap-7652	320	4	a	a	PRON
ap-7652	320	5	;	;	PUNCT
ap-7652	320	6	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	320	7	)	)	PUNCT
ap-7652	321	1	|	|	ADV
ap-7652	321	2	±	±	NUM
ap-7652	321	3	...	...	PUNCT
ap-7652	321	4	m±	m±	PROPN
ap-7652	321	5	p	p	X
ap-7652	321	6	]	]	X
ap-7652	321	7	(	(	PUNCT
ap-7652	321	8	101	101	NUM
ap-7652	321	9	)	)	PUNCT
ap-7652	321	10	to	to	ADP
ap-7652	321	11	the	the	DET
ap-7652	321	12	new	new	ADJ
ap-7652	321	13	eigenfunction	eigenfunction	NOUN
ap-7652	321	14	we	we	PRON
ap-7652	321	15	would	would	AUX
ap-7652	321	16	come	come	VERB
ap-7652	321	17	to	to	ADP
ap-7652	321	18	the	the	DET
ap-7652	321	19	solution	solution	NOUN
ap-7652	321	20	which	which	PRON
ap-7652	321	21	obeys	obey	VERB
ap-7652	321	22	the	the	DET
ap-7652	321	23	dbc	dbc	NOUN
ap-7652	321	24	at	at	ADP
ap-7652	321	25	infinity	infinity	NOUN
ap-7652	321	26	:	:	PUNCT
ap-7652	321	27	w	w	X
ap-7652	321	28	{	{	PUNCT
ap-7652	321	29	∞	∞	NUM
ap-7652	321	30	̸ψ−1	̸ψ−1	PROPN
ap-7652	322	1	[	[	X
ap-7652	322	2	y	y	X
ap-7652	322	3	;	;	PUNCT
ap-7652	322	4	a	a	PRON
ap-7652	322	5	;	;	PUNCT
ap-7652	322	6	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	322	7	)	)	PUNCT
ap-7652	323	1	|	|	ADV
ap-7652	323	2	±	±	NUM
ap-7652	323	3	...	...	PUNCT
ap-7652	323	4	m±	m±	PROPN
ap-7652	323	5	p	p	X
ap-7652	323	6	]	]	X
ap-7652	323	7	,	,	PUNCT
ap-7652	323	8	∞	∞	PROPN
ap-7652	323	9	̸ψ	̸ψ	VERB
ap-7652	323	10	[	[	X
ap-7652	323	11	y	y	X
ap-7652	323	12	;	;	PUNCT
ap-7652	323	13	a	a	PRON
ap-7652	323	14	;	;	PUNCT
ap-7652	323	15	ε∗(a	ε∗(a	PROPN
ap-7652	323	16	)	)	PUNCT
ap-7652	324	1	|	|	ADV
ap-7652	324	2	±	±	NUM
ap-7652	324	3	...	...	PUNCT
ap-7652	324	4	m±	m±	PROPN
ap-7652	324	5	p+1	p+1	NOUN
ap-7652	324	6	]	]	X
ap-7652	324	7	}	}	PUNCT
ap-7652	324	8	∞	∞	NUM
ap-7652	324	9	̸ψ−1	̸ψ−1	NOUN
ap-7652	325	1	[	[	X
ap-7652	325	2	y	y	X
ap-7652	325	3	;	;	PUNCT
ap-7652	325	4	a	a	PRON
ap-7652	325	5	;	;	PUNCT
ap-7652	325	6	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	325	7	)	)	PUNCT
ap-7652	326	1	|	|	ADV
ap-7652	326	2	±	±	NUM
ap-7652	326	3	...	...	PUNCT
ap-7652	327	1	m±	m±	PROPN
ap-7652	327	2	p	p	X
ap-7652	327	3	]	]	X
ap-7652	328	1	≈	≈	PROPN
ap-7652	328	2	[	[	PUNCT
ap-7652	328	3	»	»	X
ap-7652	328	4	−ε±,mp+1(a	−ε±,mp+1(a	NUM
ap-7652	328	5	)	)	PUNCT
ap-7652	329	1	−	−	NOUN
ap-7652	329	2	»	»	X
ap-7652	330	1	−ε∗(a)]y−	−ε∗(a)]y−	NOUN
ap-7652	330	2	√	√	NUM
ap-7652	330	3	−ε±,mp+1	−ε±,mp+1	PROPN
ap-7652	330	4	(	(	PUNCT
ap-7652	330	5	a	a	NOUN
ap-7652	330	6	)	)	PUNCT
ap-7652	330	7	for	for	ADP
ap-7652	330	8	y	y	PROPN
ap-7652	330	9	>	>	PUNCT
ap-7652	330	10	>	>	X
ap-7652	330	11	1	1	NUM
ap-7652	330	12	(	(	PUNCT
ap-7652	330	13	102	102	NUM
ap-7652	330	14	)	)	PUNCT
ap-7652	330	15	assuming	assume	VERB
ap-7652	330	16	that	that	SCONJ
ap-7652	330	17	ε∗(a	ε∗(a	PROPN
ap-7652	330	18	)	)	PUNCT
ap-7652	330	19	̸=	̸=	PROPN
ap-7652	330	20	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	330	21	)	)	PUNCT
ap-7652	330	22	.	.	PUNCT
ap-7652	331	1	on	on	ADP
ap-7652	331	2	other	other	ADJ
ap-7652	331	3	hand	hand	NOUN
ap-7652	331	4	,	,	PUNCT
ap-7652	331	5	the	the	DET
ap-7652	331	6	quasi	quasi	ADJ
ap-7652	331	7	-	-	ADJ
ap-7652	331	8	rational	rational	ADJ
ap-7652	331	9	function	function	NOUN
ap-7652	331	10	on	on	ADP
ap-7652	331	11	the	the	DET
ap-7652	331	12	left	left	NOUN
ap-7652	331	13	is	be	AUX
ap-7652	331	14	related	relate	VERB
ap-7652	331	15	to	to	ADP
ap-7652	331	16	principal	principal	ADJ
ap-7652	331	17	solution	solution	NOUN
ap-7652	331	18	(	(	PUNCT
ap-7652	331	19	96	96	NUM
ap-7652	331	20	)	)	PUNCT
ap-7652	331	21	via	via	ADP
ap-7652	331	22	gauge	gauge	ADJ
ap-7652	331	23	transformation	transformation	NOUN
ap-7652	331	24	(	(	PUNCT
ap-7652	331	25	97	97	NUM
ap-7652	331	26	)	)	PUNCT
ap-7652	331	27	with	with	ADP
ap-7652	331	28	ε	ε	PROPN
ap-7652	331	29	=	=	SYM
ap-7652	331	30	ε∗(a	ε∗(a	PROPN
ap-7652	331	31	)	)	PUNCT
ap-7652	331	32	and	and	CCONJ
ap-7652	331	33	therefore	therefore	ADV
ap-7652	331	34	the	the	DET
ap-7652	331	35	solution	solution	NOUN
ap-7652	331	36	in	in	ADP
ap-7652	331	37	question	question	NOUN
ap-7652	331	38	would	would	AUX
ap-7652	331	39	obey	obey	VERB
ap-7652	331	40	both	both	DET
ap-7652	331	41	dbcs	dbc	NOUN
ap-7652	331	42	which	which	PRON
ap-7652	331	43	contradicts	contradict	VERB
ap-7652	331	44	the	the	DET
ap-7652	331	45	assumption	assumption	NOUN
ap-7652	331	46	that	that	SCONJ
ap-7652	331	47	ε∗(a	ε∗(a	PROPN
ap-7652	331	48	)	)	PUNCT
ap-7652	331	49	is	be	AUX
ap-7652	331	50	a	a	DET
ap-7652	331	51	new	new	ADJ
ap-7652	331	52	eigenvalue	eigenvalue	NOUN
ap-7652	331	53	.	.	PUNCT
ap-7652	332	1	the	the	DET
ap-7652	332	2	only	only	ADJ
ap-7652	332	3	exception	exception	NOUN
ap-7652	332	4	corresponds	correspond	VERB
ap-7652	332	5	to	to	ADP
ap-7652	332	6	the	the	DET
ap-7652	332	7	case	case	NOUN
ap-7652	332	8	ε∗(a	ε∗(a	PROPN
ap-7652	332	9	)	)	PUNCT
ap-7652	332	10	=	=	SYM
ap-7652	332	11	ε±,mp+1(a	ε±,mp+1(a	NOUN
ap-7652	332	12	)	)	PUNCT
ap-7652	332	13	,	,	PUNCT
ap-7652	332	14	when	when	SCONJ
ap-7652	332	15	the	the	DET
ap-7652	332	16	rdt	rdt	PROPN
ap-7652	332	17	with	with	ADP
ap-7652	332	18	ff	ff	PROPN
ap-7652	332	19	(	(	PUNCT
ap-7652	332	20	100	100	NUM
ap-7652	332	21	)	)	PUNCT
ap-7652	332	22	insert	insert	VERB
ap-7652	332	23	the	the	DET
ap-7652	332	24	new	new	ADJ
ap-7652	332	25	bound	bind	VERB
ap-7652	332	26	energy	energy	NOUN
ap-7652	332	27	state	state	NOUN
ap-7652	332	28	below	below	ADP
ap-7652	332	29	the	the	DET
ap-7652	332	30	ground	ground	NOUN
ap-7652	332	31	energy	energy	NOUN
ap-7652	332	32	level	level	NOUN
ap-7652	332	33	of	of	ADP
ap-7652	332	34	rationally	rationally	ADV
ap-7652	332	35	deformed	deform	VERB
ap-7652	332	36	morse	morse	ADJ
ap-7652	332	37	potential	potential	NOUN
ap-7652	332	38	(	(	PUNCT
ap-7652	332	39	88	88	NUM
ap-7652	332	40	)	)	PUNCT
ap-7652	332	41	or	or	CCONJ
ap-7652	332	42	(	(	PUNCT
ap-7652	332	43	89	89	NUM
ap-7652	332	44	)	)	PUNCT
ap-7652	332	45	accordingly	accordingly	ADV
ap-7652	332	46	.	.	PUNCT
ap-7652	333	1	3.3	3.3	NUM
ap-7652	333	2	.	.	PUNCT
ap-7652	334	1	isospectral	isospectral	ADJ
ap-7652	334	2	family	family	NOUN
ap-7652	334	3	of	of	ADP
ap-7652	334	4	rationally	rationally	ADV
ap-7652	334	5	deformed	deform	VERB
ap-7652	334	6	morse	morse	NOUN
ap-7652	334	7	potentials	potential	NOUN
ap-7652	334	8	with	with	ADP
ap-7652	334	9	a	a	DET
ap-7652	334	10	regular	regular	ADJ
ap-7652	334	11	spectrum	spectrum	NOUN
ap-7652	334	12	let	let	VERB
ap-7652	334	13	us	we	PRON
ap-7652	334	14	prove	prove	VERB
ap-7652	334	15	that	that	SCONJ
ap-7652	334	16	any	any	DET
ap-7652	334	17	set	set	NOUN
ap-7652	334	18	m	m	NOUN
ap-7652	334	19	_	_	NOUN
ap-7652	334	20	p	p	NOUN
ap-7652	334	21	of	of	ADP
ap-7652	334	22	seed	seed	NOUN
ap-7652	334	23	solutions	solution	NOUN
ap-7652	334	24	ϕ−,mk	ϕ−,mk	NOUN
ap-7652	335	1	[	[	X
ap-7652	335	2	y	y	X
ap-7652	335	3	;	;	PUNCT
ap-7652	335	4	a	a	X
ap-7652	335	5	]	]	X
ap-7652	335	6	(	(	PUNCT
ap-7652	335	7	0	0	X
ap-7652	335	8	<	<	X
ap-7652	335	9	m1	m1	PROPN
ap-7652	335	10	<	<	X
ap-7652	335	11	mk	mk	X
ap-7652	335	12	<	<	X
ap-7652	335	13	mk+1	mk+1	NOUN
ap-7652	335	14	≤	≤	NOUN
ap-7652	335	15	p	p	X
ap-7652	335	16	)	)	PUNCT
ap-7652	335	17	is	be	AUX
ap-7652	335	18	admissible	admissible	ADJ
ap-7652	335	19	if	if	SCONJ
ap-7652	335	20	the	the	DET
ap-7652	335	21	generalized	generalized	ADJ
ap-7652	335	22	bessel	bessel	ADJ
ap-7652	335	23	polynomial	polynomial	ADJ
ap-7652	335	24	y	y	PROPN
ap-7652	335	25	(	(	PUNCT
ap-7652	335	26	−2a	−2a	PROPN
ap-7652	335	27	)	)	PUNCT
ap-7652	335	28	mk	mk	NOUN
ap-7652	335	29	(	(	PUNCT
ap-7652	335	30	y	y	NOUN
ap-7652	335	31	)	)	PUNCT
ap-7652	335	32	does	do	AUX
ap-7652	335	33	not	not	PART
ap-7652	335	34	have	have	VERB
ap-7652	335	35	positive	positive	ADJ
ap-7652	335	36	zeros	zero	NOUN
ap-7652	335	37	so	so	SCONJ
ap-7652	335	38	each	each	DET
ap-7652	335	39	seed	seed	NOUN
ap-7652	335	40	function	function	NOUN
ap-7652	335	41	∞ϕ−,mk	∞ϕ−,mk	NOUN
ap-7652	335	42	[	[	X
ap-7652	335	43	y	y	X
ap-7652	335	44	;	;	PUNCT
ap-7652	335	45	a	a	PRON
ap-7652	335	46	]	]	PUNCT
ap-7652	335	47	preserves	preserve	VERB
ap-7652	335	48	its	its	PRON
ap-7652	335	49	sign	sign	NOUN
ap-7652	335	50	on	on	ADP
ap-7652	335	51	the	the	DET
ap-7652	335	52	positive	positive	ADJ
ap-7652	335	53	semi	semi	ADJ
ap-7652	335	54	-	-	ADJ
ap-7652	335	55	axis	axis	ADJ
ap-7652	335	56	.	.	PUNCT
ap-7652	336	1	according	accord	VERB
ap-7652	336	2	to	to	ADP
ap-7652	336	3	(	(	PUNCT
ap-7652	336	4	73	73	NUM
ap-7652	336	5	)	)	PUNCT
ap-7652	336	6	,	,	PUNCT
ap-7652	336	7	this	this	PRON
ap-7652	336	8	is	be	AUX
ap-7652	336	9	possible	possible	ADJ
ap-7652	336	10	if	if	SCONJ
ap-7652	336	11	m	m	VERB
ap-7652	336	12	>	>	X
ap-7652	336	13	2a−	2a−	NUM
ap-7652	336	14	1	1	NUM
ap-7652	336	15	for	for	ADP
ap-7652	336	16	any	any	DET
ap-7652	336	17	m	m	NOUN
ap-7652	336	18	∈	∈	NOUN
ap-7652	336	19	m	m	NOUN
ap-7652	336	20	_	_	NOUN
ap-7652	336	21	p	p	X
ap-7652	336	22	.	.	PUNCT
ap-7652	337	1	in	in	ADP
ap-7652	337	2	other	other	ADJ
ap-7652	337	3	words	word	NOUN
ap-7652	337	4	we	we	PRON
ap-7652	337	5	have	have	VERB
ap-7652	337	6	to	to	PART
ap-7652	337	7	prove	prove	VERB
ap-7652	337	8	that	that	SCONJ
ap-7652	337	9	polynomial	polynomial	ADJ
ap-7652	337	10	wronskian	wronskian	NOUN
ap-7652	337	11	(	(	PUNCT
ap-7652	337	12	83	83	NUM
ap-7652	337	13	)	)	PUNCT
ap-7652	337	14	does	do	AUX
ap-7652	337	15	not	not	PART
ap-7652	337	16	have	have	VERB
ap-7652	337	17	positive	positive	ADJ
ap-7652	337	18	zeros	zero	NOUN
ap-7652	337	19	if	if	SCONJ
ap-7652	337	20	this	this	PRON
ap-7652	337	21	is	be	AUX
ap-7652	337	22	true	true	ADJ
ap-7652	337	23	for	for	ADP
ap-7652	337	24	each	each	DET
ap-7652	337	25	polynomial	polynomial	ADJ
ap-7652	337	26	y	y	PROPN
ap-7652	337	27	(	(	PUNCT
ap-7652	337	28	−2a	−2a	PROPN
ap-7652	337	29	)	)	PUNCT
ap-7652	337	30	mk	mk	NOUN
ap-7652	337	31	(	(	PUNCT
ap-7652	337	32	y	y	NOUN
ap-7652	337	33	)	)	PUNCT
ap-7652	337	34	.	.	PUNCT
ap-7652	338	1	this	this	DET
ap-7652	338	2	assertion	assertion	NOUN
ap-7652	338	3	is	be	AUX
ap-7652	338	4	obviously	obviously	ADV
ap-7652	338	5	trivial	trivial	ADJ
ap-7652	338	6	for	for	ADP
ap-7652	338	7	˜	˜	PROPN
ap-7652	338	8	p	p	NOUN
ap-7652	338	9	=	=	NOUN
ap-7652	338	10	1	1	X
ap-7652	338	11	.	.	PUNCT
ap-7652	339	1	it	it	PRON
ap-7652	339	2	also	also	ADV
ap-7652	339	3	directly	directly	ADV
ap-7652	339	4	follows	follow	VERB
ap-7652	339	5	from	from	ADP
ap-7652	339	6	the	the	DET
ap-7652	339	7	arguments	argument	NOUN
ap-7652	339	8	presented	present	VERB
ap-7652	339	9	in	in	ADP
ap-7652	339	10	previous	previous	ADJ
ap-7652	339	11	subsection	subsection	NOUN
ap-7652	339	12	that	that	SCONJ
ap-7652	339	13	the	the	DET
ap-7652	339	14	rdt	rdt	PROPN
ap-7652	339	15	of	of	ADP
ap-7652	339	16	bref	bref	PROPN
ap-7652	339	17	csle	csle	PROPN
ap-7652	339	18	(	(	PUNCT
ap-7652	339	19	32	32	NUM
ap-7652	339	20	)	)	PUNCT
ap-7652	339	21	with	with	ADP
ap-7652	339	22	the	the	DET
ap-7652	339	23	ff	ff	NOUN
ap-7652	339	24	ϕ−,m1	ϕ−,m1	PROPN
ap-7652	340	1	[	[	X
ap-7652	340	2	y	y	X
ap-7652	340	3	;	;	PUNCT
ap-7652	340	4	a	a	PRON
ap-7652	340	5	]	]	PUNCT
ap-7652	340	6	preserves	preserve	VERB
ap-7652	340	7	the	the	DET
ap-7652	340	8	discrete	discrete	ADJ
ap-7652	340	9	energy	energy	NOUN
ap-7652	340	10	spectrum	spectrum	NOUN
ap-7652	340	11	so	so	SCONJ
ap-7652	340	12	the	the	DET
ap-7652	340	13	prime	prime	ADJ
ap-7652	340	14	rsle	rsle	NOUN
ap-7652	340	15	{	{	PUNCT
ap-7652	340	16	d	d	PROPN
ap-7652	340	17	dy	dy	NOUN
ap-7652	340	18	y	y	PROPN
ap-7652	340	19	d	d	PROPN
ap-7652	340	20	dy	dy	NOUN
ap-7652	340	21	+	+	CCONJ
ap-7652	340	22	y∞i	y∞i	VERB
ap-7652	340	23	0[y	0[y	NUM
ap-7652	340	24	;	;	PUNCT
ap-7652	340	25	a	a	DET
ap-7652	340	26	|	|	NOUN
ap-7652	340	27	−	−	NOUN
ap-7652	340	28	...	...	PUNCT
ap-7652	340	29	m1	m1	NOUN
ap-7652	340	30	]	]	PUNCT
ap-7652	341	1	+	+	CCONJ
ap-7652	341	2	(	(	PUNCT
ap-7652	341	3	ε+	ε+	NOUN
ap-7652	341	4	1/2)y−1	1/2)y−1	NUM
ap-7652	341	5	}	}	PUNCT
ap-7652	341	6	∞	∞	PROPN
ap-7652	341	7	̸ψ	̸ψ	NOUN
ap-7652	341	8	[	[	X
ap-7652	341	9	y	y	X
ap-7652	341	10	;	;	PUNCT
ap-7652	341	11	a	a	PRON
ap-7652	341	12	;	;	PUNCT
ap-7652	341	13	ε	ε	PROPN
ap-7652	341	14	|	|	ADV
ap-7652	341	15	−	−	PROPN
ap-7652	341	16	...	...	PUNCT
ap-7652	341	17	m1	m1	NOUN
ap-7652	341	18	]	]	X
ap-7652	341	19	=	=	SYM
ap-7652	341	20	0	0	NUM
ap-7652	341	21	(	(	PUNCT
ap-7652	341	22	103	103	NUM
ap-7652	341	23	)	)	PUNCT
ap-7652	341	24	solved	solve	VERB
ap-7652	341	25	under	under	ADP
ap-7652	341	26	the	the	DET
ap-7652	341	27	dbcs	dbcs	ADJ
ap-7652	341	28	lim	lim	PROPN
ap-7652	341	29	y→0	y→0	PROPN
ap-7652	342	1	∞	∞	PROPN
ap-7652	342	2	̸ψ	̸ψ	VERB
ap-7652	342	3	[	[	X
ap-7652	342	4	y	y	X
ap-7652	342	5	;	;	PUNCT
ap-7652	342	6	a	a	PRON
ap-7652	342	7	;	;	PUNCT
ap-7652	342	8	εn(a	εn(a	NOUN
ap-7652	342	9	)	)	PUNCT
ap-7652	342	10	|	|	ADV
ap-7652	342	11	−	−	NOUN
ap-7652	342	12	...	...	PUNCT
ap-7652	342	13	m1	m1	NOUN
ap-7652	342	14	]	]	PUNCT
ap-7652	343	1	=	=	SYM
ap-7652	343	2	lim	lim	PROPN
ap-7652	343	3	y→∞	y→∞	NUM
ap-7652	343	4	∞	∞	PROPN
ap-7652	343	5	̸ψ	̸ψ	VERB
ap-7652	344	1	[	[	X
ap-7652	344	2	y	y	X
ap-7652	344	3	;	;	PUNCT
ap-7652	344	4	a	a	PRON
ap-7652	344	5	;	;	PUNCT
ap-7652	344	6	εn(a	εn(a	NOUN
ap-7652	344	7	)	)	PUNCT
ap-7652	344	8	|	|	ADV
ap-7652	344	9	−	−	NOUN
ap-7652	344	10	...	...	PUNCT
ap-7652	344	11	m1	m1	NOUN
ap-7652	344	12	]	]	X
ap-7652	345	1	=	=	SYM
ap-7652	345	2	0	0	PUNCT
ap-7652	345	3	(	(	PUNCT
ap-7652	345	4	104	104	NUM
ap-7652	345	5	)	)	PUNCT
ap-7652	345	6	has	have	VERB
ap-7652	345	7	exactly	exactly	ADV
ap-7652	345	8	n(a	n(a	NOUN
ap-7652	345	9	)	)	PUNCT
ap-7652	345	10	eigenfunctions	eigenfunction	NOUN
ap-7652	345	11	∞	∞	PROPN
ap-7652	345	12	̸ψ	̸ψ	NOUN
ap-7652	346	1	[	[	X
ap-7652	346	2	y	y	X
ap-7652	346	3	;	;	PUNCT
ap-7652	346	4	a	a	PRON
ap-7652	346	5	;	;	PUNCT
ap-7652	346	6	εn(a	εn(a	NOUN
ap-7652	346	7	)	)	PUNCT
ap-7652	346	8	|	|	ADV
ap-7652	346	9	−	−	NOUN
ap-7652	346	10	...	...	PUNCT
ap-7652	347	1	m1	m1	NOUN
ap-7652	347	2	]	]	PUNCT
ap-7652	347	3	≡	≡	PROPN
ap-7652	347	4	∞	∞	X
ap-7652	347	5	̸ψ−,n	̸ψ−,n	X
ap-7652	348	1	[	[	X
ap-7652	348	2	y	y	X
ap-7652	348	3	;	;	PUNCT
ap-7652	348	4	a	a	DET
ap-7652	348	5	|	|	NOUN
ap-7652	348	6	−	−	NOUN
ap-7652	348	7	...	...	PUNCT
ap-7652	348	8	m1	m1	NOUN
ap-7652	348	9	]	]	X
ap-7652	349	1	=	=	PUNCT
ap-7652	349	2	y−1/2	y−1/2	PROPN
ap-7652	349	3	∞φ−,n[y	∞φ−,n[y	PROPN
ap-7652	349	4	;	;	PUNCT
ap-7652	349	5	a	a	DET
ap-7652	349	6	|	|	NOUN
ap-7652	349	7	−	−	NOUN
ap-7652	349	8	...	...	PUNCT
ap-7652	349	9	m1	m1	NOUN
ap-7652	349	10	]	]	PUNCT
ap-7652	349	11	(	(	PUNCT
ap-7652	349	12	105	105	NUM
ap-7652	349	13	)	)	PUNCT
ap-7652	349	14	at	at	ADP
ap-7652	349	15	the	the	DET
ap-7652	349	16	energies	energy	NOUN
ap-7652	349	17	∞ε−,n(a	∞ε−,n(a	ADV
ap-7652	349	18	)	)	PUNCT
ap-7652	349	19	with	with	ADP
ap-7652	349	20	n	n	NUM
ap-7652	349	21	varying	vary	VERB
ap-7652	349	22	from	from	ADP
ap-7652	349	23	0	0	NUM
ap-7652	349	24	to	to	ADP
ap-7652	349	25	n(a	n(a	NOUN
ap-7652	349	26	)	)	PUNCT
ap-7652	350	1	−	−	PROPN
ap-7652	351	1	1	1	X
ap-7652	351	2	.	.	PUNCT
ap-7652	351	3	making	make	VERB
ap-7652	351	4	use	use	NOUN
ap-7652	351	5	of	of	ADP
ap-7652	351	6	(	(	PUNCT
ap-7652	351	7	90	90	NUM
ap-7652	351	8	)	)	PUNCT
ap-7652	351	9	with	with	ADP
ap-7652	351	10	p	p	NOUN
ap-7652	351	11	=	=	SYM
ap-7652	351	12	1	1	NUM
ap-7652	351	13	and	and	CCONJ
ap-7652	351	14	m	m	PROPN
ap-7652	351	15	=	=	SYM
ap-7652	351	16	n	n	CCONJ
ap-7652	351	17	,	,	PUNCT
ap-7652	351	18	they	they	PRON
ap-7652	351	19	can	can	AUX
ap-7652	351	20	be	be	AUX
ap-7652	351	21	also	also	ADV
ap-7652	351	22	re	re	VERB
ap-7652	351	23	-	-	VERB
ap-7652	351	24	written	write	VERB
ap-7652	351	25	in	in	ADP
ap-7652	351	26	the	the	DET
ap-7652	351	27	quasi	quasi	ADJ
ap-7652	351	28	-	-	ADJ
ap-7652	351	29	rational	rational	ADJ
ap-7652	351	30	form	form	NOUN
ap-7652	351	31	∞	∞	NOUN
ap-7652	351	32	̸ψ−,n	̸ψ−,n	X
ap-7652	352	1	[	[	X
ap-7652	352	2	y	y	X
ap-7652	352	3	;	;	PUNCT
ap-7652	352	4	a	a	DET
ap-7652	352	5	|	|	NOUN
ap-7652	352	6	−	−	NOUN
ap-7652	352	7	...	...	PUNCT
ap-7652	352	8	m1	m1	NOUN
ap-7652	352	9	]	]	PUNCT
ap-7652	353	1	=	=	SYM
ap-7652	353	2	∞	∞	NUM
ap-7652	353	3	̸ψ−,0	̸ψ−,0	PROPN
ap-7652	353	4	[	[	X
ap-7652	353	5	y	y	NOUN
ap-7652	353	6	;	;	PUNCT
ap-7652	353	7	a−	a−	PROPN
ap-7652	353	8	1	1	NUM
ap-7652	353	9	]	]	SYM
ap-7652	353	10	∞w[y	∞w[y	NOUN
ap-7652	353	11	;	;	PUNCT
ap-7652	353	12	a	a	DET
ap-7652	353	13	|	|	NOUN
ap-7652	353	14	−	−	NOUN
ap-7652	353	15	...	...	PUNCT
ap-7652	354	1	m1	m1	NOUN
ap-7652	354	2	,	,	PUNCT
ap-7652	354	3	n	n	CCONJ
ap-7652	354	4	]	]	X
ap-7652	354	5	y	y	PROPN
ap-7652	354	6	(	(	PUNCT
ap-7652	354	7	−2a	−2a	PROPN
ap-7652	354	8	)	)	PUNCT
ap-7652	354	9	m1	m1	NOUN
ap-7652	354	10	(	(	PUNCT
ap-7652	354	11	y	y	NOUN
ap-7652	354	12	)	)	PUNCT
ap-7652	354	13	(	(	PUNCT
ap-7652	354	14	106	106	X
ap-7652	354	15	)	)	PUNCT
ap-7652	354	16	keeping	keep	VERB
ap-7652	354	17	in	in	ADP
ap-7652	354	18	mind	mind	NOUN
ap-7652	354	19	that	that	SCONJ
ap-7652	354	20	the	the	DET
ap-7652	354	21	pf	pf	NOUN
ap-7652	354	22	in	in	ADP
ap-7652	354	23	the	the	DET
ap-7652	354	24	right	right	ADJ
ap-7652	354	25	-	-	PUNCT
ap-7652	354	26	hand	hand	NOUN
ap-7652	354	27	side	side	NOUN
ap-7652	354	28	of	of	ADP
ap-7652	354	29	the	the	DET
ap-7652	354	30	latter	latter	ADJ
ap-7652	354	31	expression	expression	NOUN
ap-7652	354	32	is	be	AUX
ap-7652	354	33	proportional	proportional	ADJ
ap-7652	354	34	to	to	ADP
ap-7652	354	35	yn−1	yn−1	PROPN
ap-7652	354	36	for	for	ADP
ap-7652	354	37	y	y	PROPN
ap-7652	354	38	>	>	PUNCT
ap-7652	354	39	>	>	X
ap-7652	354	40	1	1	NUM
ap-7652	354	41	one	one	NOUN
ap-7652	354	42	can	can	AUX
ap-7652	354	43	immediately	immediately	ADV
ap-7652	354	44	confirm	confirm	VERB
ap-7652	354	45	that	that	SCONJ
ap-7652	354	46	eigenfunctions	eigenfunction	NOUN
ap-7652	354	47	(	(	PUNCT
ap-7652	354	48	105	105	NUM
ap-7652	354	49	)	)	PUNCT
ap-7652	354	50	vanish	vanish	VERB
ap-7652	354	51	in	in	ADP
ap-7652	354	52	the	the	DET
ap-7652	354	53	limit	limit	NOUN
ap-7652	354	54	y	y	PROPN
ap-7652	354	55	→	→	SYM
ap-7652	354	56	∞	∞	PROPN
ap-7652	354	57	for	for	ADP
ap-7652	354	58	any	any	DET
ap-7652	354	59	n	n	NOUN
ap-7652	354	60	<	<	X
ap-7652	354	61	a−	a−	PROPN
ap-7652	354	62	1/2	1/2	NUM
ap-7652	354	63	.	.	PUNCT
ap-7652	355	1	let	let	VERB
ap-7652	355	2	us	we	PRON
ap-7652	355	3	now	now	ADV
ap-7652	355	4	use	use	VERB
ap-7652	355	5	the	the	DET
ap-7652	355	6	mathematical	mathematical	ADJ
ap-7652	355	7	induction	induction	NOUN
ap-7652	355	8	to	to	PART
ap-7652	355	9	prove	prove	VERB
ap-7652	355	10	that	that	SCONJ
ap-7652	355	11	the	the	DET
ap-7652	355	12	polynomial	polynomial	ADJ
ap-7652	355	13	∞w[y	∞w[y	NOUN
ap-7652	355	14	;	;	PUNCT
ap-7652	355	15	a	a	DET
ap-7652	355	16	|	|	NOUN
ap-7652	355	17	−	−	NOUN
ap-7652	355	18	...	...	PUNCT
ap-7652	356	1	m	m	PUNCT
ap-7652	356	2	_	_	NOUN
ap-7652	357	1	˜	˜	PROPN
ap-7652	357	2	p+1	p+1	X
ap-7652	357	3	]	]	X
ap-7652	357	4	does	do	AUX
ap-7652	357	5	not	not	PART
ap-7652	357	6	have	have	VERB
ap-7652	357	7	positive	positive	ADJ
ap-7652	357	8	zeros	zero	NOUN
ap-7652	357	9	if	if	SCONJ
ap-7652	357	10	this	this	DET
ap-7652	357	11	assertion	assertion	NOUN
ap-7652	357	12	holds	hold	VERB
ap-7652	357	13	for	for	ADP
ap-7652	357	14	the	the	DET
ap-7652	357	15	polynomial	polynomial	ADJ
ap-7652	357	16	∞w[y	∞w[y	NOUN
ap-7652	357	17	;	;	PUNCT
ap-7652	357	18	a	a	DET
ap-7652	357	19	|	|	NOUN
ap-7652	357	20	−	−	NOUN
ap-7652	357	21	...	...	PUNCT
ap-7652	358	1	m	m	PUNCT
ap-7652	358	2	_	_	NOUN
ap-7652	359	1	˜	˜	PROPN
ap-7652	359	2	p	p	X
ap-7652	359	3	]	]	X
ap-7652	359	4	.	.	PUNCT
ap-7652	360	1	again	again	ADV
ap-7652	360	2	it	it	PRON
ap-7652	360	3	is	be	AUX
ap-7652	360	4	suitable	suitable	ADJ
ap-7652	360	5	to	to	PART
ap-7652	360	6	convert	convert	VERB
ap-7652	360	7	rcsle	rcsle	NOUN
ap-7652	360	8	(	(	PUNCT
ap-7652	360	9	77	77	NUM
ap-7652	360	10	)	)	PUNCT
ap-7652	360	11	to	to	ADP
ap-7652	360	12	its	its	PRON
ap-7652	360	13	prime	prime	ADJ
ap-7652	360	14	form	form	NOUN
ap-7652	360	15	{	{	PUNCT
ap-7652	360	16	d	d	X
ap-7652	360	17	dy	dy	NOUN
ap-7652	360	18	y	y	PROPN
ap-7652	360	19	d	d	PROPN
ap-7652	360	20	dy	dy	NOUN
ap-7652	360	21	+	+	CCONJ
ap-7652	360	22	y∞i	y∞i	VERB
ap-7652	360	23	0[y	0[y	NUM
ap-7652	360	24	;	;	PUNCT
ap-7652	360	25	a	a	DET
ap-7652	360	26	|	|	NOUN
ap-7652	360	27	−	−	NOUN
ap-7652	361	1	...	...	PUNCT
ap-7652	362	1	m	m	PUNCT
ap-7652	362	2	_	_	NOUN
ap-7652	363	1	˜	˜	PROPN
ap-7652	363	2	p	p	X
ap-7652	363	3	]	]	X
ap-7652	363	4	+	+	CCONJ
ap-7652	363	5	(	(	PUNCT
ap-7652	363	6	ε+	ε+	NOUN
ap-7652	363	7	1/2)y−1	1/2)y−1	NUM
ap-7652	363	8	}	}	PUNCT
ap-7652	363	9	∞	∞	PROPN
ap-7652	363	10	̸ψ	̸ψ	NOUN
ap-7652	364	1	[	[	X
ap-7652	364	2	y	y	X
ap-7652	364	3	;	;	PUNCT
ap-7652	364	4	a	a	PRON
ap-7652	364	5	;	;	PUNCT
ap-7652	364	6	ε	ε	PROPN
ap-7652	364	7	|	|	ADV
ap-7652	364	8	−	−	PROPN
ap-7652	364	9	...	...	PUNCT
ap-7652	365	1	m	m	VERB
ap-7652	365	2	_	_	NOUN
ap-7652	366	1	˜	˜	PROPN
ap-7652	366	2	p	p	X
ap-7652	366	3	]	]	X
ap-7652	366	4	=	=	SYM
ap-7652	366	5	0	0	SYM
ap-7652	366	6	(	(	PUNCT
ap-7652	366	7	107	107	NUM
ap-7652	366	8	)	)	PUNCT
ap-7652	366	9	110	110	NUM
ap-7652	366	10	vol	vol	NOUN
ap-7652	366	11	.	.	PUNCT
ap-7652	367	1	62	62	NUM
ap-7652	367	2	no	no	INTJ
ap-7652	367	3	.	.	PUNCT
ap-7652	368	1	1/2022	1/2022	NUM
ap-7652	368	2	quantization	quantization	NOUN
ap-7652	368	3	of	of	ADP
ap-7652	368	4	rationally	rationally	ADV
ap-7652	368	5	deformed	deform	VERB
ap-7652	368	6	morse	morse	ADJ
ap-7652	368	7	potentials	potential	NOUN
ap-7652	368	8	.	.	PUNCT
ap-7652	368	9	.	.	PUNCT
ap-7652	369	1	.	.	PUNCT
ap-7652	370	1	solved	solve	VERB
ap-7652	370	2	under	under	ADP
ap-7652	370	3	the	the	DET
ap-7652	370	4	dbcs	dbcs	ADJ
ap-7652	370	5	lim	lim	PROPN
ap-7652	370	6	y→0	y→0	PROPN
ap-7652	371	1	∞	∞	PROPN
ap-7652	371	2	̸ψ	̸ψ	VERB
ap-7652	371	3	[	[	X
ap-7652	371	4	y	y	X
ap-7652	371	5	;	;	PUNCT
ap-7652	371	6	a	a	PRON
ap-7652	371	7	;	;	PUNCT
ap-7652	371	8	εn(a	εn(a	NOUN
ap-7652	371	9	)	)	PUNCT
ap-7652	371	10	|	|	ADV
ap-7652	371	11	−	−	NOUN
ap-7652	371	12	...	...	PUNCT
ap-7652	372	1	m	m	VERB
ap-7652	372	2	_	_	NOUN
ap-7652	373	1	˜	˜	PROPN
ap-7652	373	2	p	p	X
ap-7652	373	3	]	]	X
ap-7652	373	4	=	=	SYM
ap-7652	373	5	lim	lim	PROPN
ap-7652	373	6	y→∞	y→∞	NUM
ap-7652	373	7	∞	∞	PROPN
ap-7652	373	8	̸ψ	̸ψ	VERB
ap-7652	373	9	[	[	X
ap-7652	373	10	y	y	X
ap-7652	373	11	;	;	PUNCT
ap-7652	373	12	a	a	PRON
ap-7652	373	13	;	;	PUNCT
ap-7652	373	14	εn(a	εn(a	NOUN
ap-7652	373	15	)	)	PUNCT
ap-7652	373	16	|	|	ADV
ap-7652	373	17	−	−	NOUN
ap-7652	373	18	...	...	PUNCT
ap-7652	374	1	m	m	VERB
ap-7652	374	2	_	_	NOUN
ap-7652	375	1	˜	˜	PROPN
ap-7652	375	2	p	p	X
ap-7652	375	3	]	]	X
ap-7652	375	4	=	=	PUNCT
ap-7652	375	5	0	0	X
ap-7652	375	6	.	.	PUNCT
ap-7652	376	1	(	(	PUNCT
ap-7652	376	2	108	108	NUM
ap-7652	376	3	)	)	PUNCT
ap-7652	376	4	making	make	VERB
ap-7652	376	5	use	use	NOUN
ap-7652	376	6	of	of	ADP
ap-7652	376	7	(	(	PUNCT
ap-7652	376	8	90	90	NUM
ap-7652	376	9	)	)	PUNCT
ap-7652	376	10	with	with	ADP
ap-7652	376	11	p	p	PROPN
ap-7652	376	12	=	=	PUNCT
ap-7652	376	13	˜	˜	PROPN
ap-7652	376	14	p	p	NOUN
ap-7652	376	15	we	we	PRON
ap-7652	376	16	can	can	AUX
ap-7652	376	17	again	again	ADV
ap-7652	376	18	re	re	VERB
ap-7652	376	19	-	-	VERB
ap-7652	376	20	write	write	VERB
ap-7652	376	21	the	the	DET
ap-7652	376	22	eigenfunctions	eigenfunction	NOUN
ap-7652	376	23	∞	∞	NOUN
ap-7652	376	24	̸ψ−,n	̸ψ−,n	X
ap-7652	377	1	[	[	X
ap-7652	377	2	y	y	X
ap-7652	377	3	;	;	PUNCT
ap-7652	377	4	a	a	DET
ap-7652	377	5	|	|	NOUN
ap-7652	377	6	−	−	NOUN
ap-7652	377	7	...	...	PUNCT
ap-7652	378	1	m	m	PUNCT
ap-7652	378	2	_	_	NOUN
ap-7652	379	1	˜	˜	PROPN
ap-7652	379	2	p	p	X
ap-7652	379	3	]	]	PUNCT
ap-7652	379	4	≡	≡	PROPN
ap-7652	379	5	∞	∞	PROPN
ap-7652	379	6	̸ψ	̸ψ	VERB
ap-7652	380	1	[	[	X
ap-7652	380	2	y	y	X
ap-7652	380	3	;	;	PUNCT
ap-7652	380	4	a	a	PRON
ap-7652	380	5	;	;	PUNCT
ap-7652	380	6	εn(a	εn(a	NOUN
ap-7652	380	7	)	)	PUNCT
ap-7652	380	8	|	|	ADV
ap-7652	380	9	−	−	NOUN
ap-7652	380	10	...	...	PUNCT
ap-7652	381	1	m	m	VERB
ap-7652	381	2	_	_	NOUN
ap-7652	382	1	˜	˜	PROPN
ap-7652	382	2	p	p	X
ap-7652	382	3	]	]	X
ap-7652	382	4	=	=	SYM
ap-7652	382	5	y−1/2	y−1/2	PROPN
ap-7652	382	6	∞φ−,n[y	∞φ−,n[y	PROPN
ap-7652	382	7	;	;	PUNCT
ap-7652	382	8	a	a	DET
ap-7652	382	9	|	|	NOUN
ap-7652	382	10	−	−	NOUN
ap-7652	382	11	...	...	PUNCT
ap-7652	383	1	m	m	PUNCT
ap-7652	383	2	_	_	NOUN
ap-7652	384	1	˜	˜	PROPN
ap-7652	384	2	p	p	X
ap-7652	384	3	]	]	X
ap-7652	384	4	(	(	PUNCT
ap-7652	384	5	109	109	NUM
ap-7652	384	6	)	)	PUNCT
ap-7652	384	7	in	in	ADP
ap-7652	384	8	the	the	DET
ap-7652	384	9	quasi	quasi	ADJ
ap-7652	384	10	-	-	ADJ
ap-7652	384	11	rational	rational	ADJ
ap-7652	384	12	form	form	NOUN
ap-7652	384	13	∞	∞	PROPN
ap-7652	384	14	̸ψ	̸ψ	NOUN
ap-7652	384	15	[	[	X
ap-7652	384	16	y	y	X
ap-7652	384	17	;	;	PUNCT
ap-7652	384	18	a	a	DET
ap-7652	384	19	|	|	NOUN
ap-7652	384	20	−	−	NOUN
ap-7652	384	21	...	...	PUNCT
ap-7652	385	1	m	m	PUNCT
ap-7652	385	2	_	_	NOUN
ap-7652	386	1	˜	˜	PROPN
ap-7652	386	2	p	p	X
ap-7652	386	3	]	]	X
ap-7652	386	4	=	=	PUNCT
ap-7652	386	5	∞	∞	NUM
ap-7652	386	6	̸ψ−,0	̸ψ−,0	PROPN
ap-7652	387	1	[	[	X
ap-7652	387	2	y	y	NOUN
ap-7652	387	3	;	;	PUNCT
ap-7652	387	4	a−	a−	PROPN
ap-7652	387	5	˜	˜	PROPN
ap-7652	388	1	p	p	X
ap-7652	388	2	]	]	X
ap-7652	388	3	∞w[y	∞w[y	NOUN
ap-7652	388	4	;	;	PUNCT
ap-7652	388	5	a	a	DET
ap-7652	388	6	|	|	NOUN
ap-7652	388	7	−	−	NOUN
ap-7652	388	8	...	...	PUNCT
ap-7652	389	1	m	m	PUNCT
ap-7652	389	2	_	_	NOUN
ap-7652	390	1	˜	˜	PROPN
ap-7652	390	2	p+1	p+1	X
ap-7652	390	3	]	]	X
ap-7652	390	4	∞w[y	∞w[y	NOUN
ap-7652	390	5	;	;	PUNCT
ap-7652	390	6	a	a	DET
ap-7652	390	7	|	|	NOUN
ap-7652	390	8	−	−	NOUN
ap-7652	390	9	...	...	PUNCT
ap-7652	391	1	m	m	PUNCT
ap-7652	391	2	_	_	NOUN
ap-7652	392	1	˜	˜	PROPN
ap-7652	392	2	p	p	X
ap-7652	392	3	]	]	X
ap-7652	392	4	(	(	PUNCT
ap-7652	392	5	110	110	NUM
ap-7652	392	6	)	)	PUNCT
ap-7652	392	7	examination	examination	NOUN
ap-7652	392	8	of	of	ADP
ap-7652	392	9	q	q	NOUN
ap-7652	392	10	-	-	PUNCT
ap-7652	392	11	rs	rs	ADJ
ap-7652	392	12	(	(	PUNCT
ap-7652	392	13	110	110	NUM
ap-7652	392	14	)	)	PUNCT
ap-7652	392	15	reveals	reveal	VERB
ap-7652	392	16	that	that	SCONJ
ap-7652	392	17	it	it	PRON
ap-7652	392	18	vanishes	vanish	VERB
ap-7652	392	19	at	at	ADP
ap-7652	392	20	the	the	DET
ap-7652	392	21	origin	origin	NOUN
ap-7652	392	22	and	and	CCONJ
ap-7652	392	23	therefore	therefore	ADV
ap-7652	392	24	represents	represent	VERB
ap-7652	392	25	a	a	DET
ap-7652	392	26	principal	principal	ADJ
ap-7652	392	27	solution	solution	NOUN
ap-7652	392	28	of	of	ADP
ap-7652	392	29	prime	prime	ADJ
ap-7652	392	30	sle	sle	NOUN
ap-7652	392	31	(	(	PUNCT
ap-7652	392	32	103	103	NUM
ap-7652	392	33	)	)	PUNCT
ap-7652	392	34	near	near	ADP
ap-7652	392	35	its	its	PRON
ap-7652	392	36	irregular	irregular	ADJ
ap-7652	392	37	singular	singular	ADJ
ap-7652	392	38	point	point	NOUN
ap-7652	392	39	.	.	PUNCT
ap-7652	393	1	since	since	SCONJ
ap-7652	393	2	this	this	DET
ap-7652	393	3	solution	solution	NOUN
ap-7652	393	4	lies	lie	VERB
ap-7652	393	5	below	below	ADP
ap-7652	393	6	the	the	DET
ap-7652	393	7	lowest	low	ADJ
ap-7652	393	8	eigenvalue	eigenvalue	NOUN
ap-7652	393	9	it	it	PRON
ap-7652	393	10	must	must	AUX
ap-7652	393	11	be	be	AUX
ap-7652	393	12	nodeless	nodeless	ADJ
ap-7652	393	13	[	[	X
ap-7652	393	14	43	43	NUM
ap-7652	393	15	]	]	PUNCT
ap-7652	393	16	and	and	CCONJ
ap-7652	393	17	therefore	therefore	ADV
ap-7652	393	18	no	no	DET
ap-7652	393	19	wronskian	wronskian	NOUN
ap-7652	393	20	∞w[y	∞w[y	NOUN
ap-7652	393	21	;	;	PUNCT
ap-7652	393	22	a	a	DET
ap-7652	393	23	|	|	NOUN
ap-7652	393	24	−	−	NOUN
ap-7652	393	25	...	...	PUNCT
ap-7652	394	1	m	m	VERB
ap-7652	395	1	_	_	NOUN
ap-7652	396	1	p	p	X
ap-7652	396	2	]	]	PUNCT
ap-7652	396	3	has	have	VERB
ap-7652	396	4	positive	positive	ADJ
ap-7652	396	5	zeros	zero	NOUN
ap-7652	396	6	.	.	PUNCT
ap-7652	397	1	all	all	DET
ap-7652	397	2	the	the	DET
ap-7652	397	3	q	q	ADJ
ap-7652	397	4	-	-	PUNCT
ap-7652	397	5	rss	rss	NOUN
ap-7652	397	6	∞	∞	PROPN
ap-7652	397	7	̸ψ−,n	̸ψ−,n	NOUN
ap-7652	397	8	[	[	X
ap-7652	397	9	y	y	X
ap-7652	397	10	;	;	PUNCT
ap-7652	397	11	a	a	DET
ap-7652	397	12	|	|	NOUN
ap-7652	397	13	−	−	NOUN
ap-7652	397	14	...	...	PUNCT
ap-7652	398	1	m	m	VERB
ap-7652	398	2	_	_	NOUN
ap-7652	399	1	p	p	X
ap-7652	399	2	]	]	X
ap-7652	399	3	=	=	SYM
ap-7652	399	4	∞	∞	NUM
ap-7652	399	5	̸ψ−,0	̸ψ−,0	PROPN
ap-7652	400	1	[	[	X
ap-7652	400	2	y	y	NOUN
ap-7652	400	3	;	;	PUNCT
ap-7652	400	4	a−	a−	PROPN
ap-7652	400	5	p	p	X
ap-7652	400	6	]	]	X
ap-7652	400	7	∞w[y	∞w[y	NOUN
ap-7652	400	8	;	;	PUNCT
ap-7652	400	9	a	a	DET
ap-7652	400	10	|	|	NOUN
ap-7652	400	11	−	−	NOUN
ap-7652	400	12	...	...	PUNCT
ap-7652	401	1	m	m	VERB
ap-7652	402	1	_	_	NOUN
ap-7652	402	2	p	p	X
ap-7652	402	3	,	,	PUNCT
ap-7652	402	4	n	n	CCONJ
ap-7652	402	5	]	]	PUNCT
ap-7652	402	6	∞w[y	∞w[y	NOUN
ap-7652	402	7	;	;	PUNCT
ap-7652	402	8	a	a	DET
ap-7652	402	9	|	|	NOUN
ap-7652	402	10	−	−	NOUN
ap-7652	402	11	...	...	PUNCT
ap-7652	403	1	m	m	VERB
ap-7652	403	2	_	_	NOUN
ap-7652	404	1	p	p	X
ap-7652	404	2	]	]	X
ap-7652	404	3	(	(	PUNCT
ap-7652	404	4	111	111	NUM
ap-7652	404	5	)	)	PUNCT
ap-7652	404	6	vanish	vanish	VERB
ap-7652	404	7	at	at	ADP
ap-7652	404	8	infinity	infinity	NOUN
ap-7652	404	9	for	for	ADP
ap-7652	404	10	n	n	X
ap-7652	404	11	<	<	X
ap-7652	404	12	n(a	n(a	PROPN
ap-7652	404	13	)	)	PUNCT
ap-7652	404	14	=	=	PUNCT
ap-7652	404	15	⌊a⌋	⌊a⌋	PUNCT
ap-7652	404	16	since	since	SCONJ
ap-7652	404	17	the	the	DET
ap-7652	404	18	power	power	NOUN
ap-7652	404	19	exponent	exponent	NOUN
ap-7652	404	20	of	of	ADP
ap-7652	404	21	the	the	DET
ap-7652	404	22	pf	pf	NOUN
ap-7652	404	23	in	in	ADP
ap-7652	404	24	the	the	DET
ap-7652	404	25	right	right	ADJ
ap-7652	404	26	-	-	PUNCT
ap-7652	404	27	hand	hand	NOUN
ap-7652	404	28	side	side	NOUN
ap-7652	404	29	of	of	ADP
ap-7652	404	30	(	(	PUNCT
ap-7652	404	31	111	111	NUM
ap-7652	404	32	)	)	PUNCT
ap-7652	404	33	is	be	AUX
ap-7652	404	34	equal	equal	ADJ
ap-7652	404	35	to	to	ADP
ap-7652	404	36	n−	n−	PROPN
ap-7652	404	37	p	p	NOUN
ap-7652	404	38	in	in	ADP
ap-7652	404	39	the	the	DET
ap-7652	404	40	limit	limit	NOUN
ap-7652	404	41	y	y	PROPN
ap-7652	404	42	→	→	SYM
ap-7652	404	43	∞.	∞.	PROPN
ap-7652	404	44	this	this	PRON
ap-7652	404	45	confirms	confirm	VERB
ap-7652	404	46	that	that	SCONJ
ap-7652	404	47	the	the	DET
ap-7652	404	48	direchlet	direchlet	NOUN
ap-7652	404	49	problem	problem	NOUN
ap-7652	404	50	for	for	ADP
ap-7652	404	51	sle	sle	PROPN
ap-7652	404	52	(	(	PUNCT
ap-7652	404	53	103	103	NUM
ap-7652	404	54	)	)	PUNCT
ap-7652	404	55	has	have	VERB
ap-7652	404	56	exactly	exactly	ADV
ap-7652	404	57	n(a	n(a	NOUN
ap-7652	404	58	)	)	PUNCT
ap-7652	404	59	eigenfunctions	eigenfunction	NOUN
ap-7652	404	60	defined	define	VERB
ap-7652	404	61	via	via	ADP
ap-7652	404	62	(	(	PUNCT
ap-7652	404	63	111	111	NUM
ap-7652	404	64	)	)	PUNCT
ap-7652	404	65	with	with	ADP
ap-7652	404	66	n	n	X
ap-7652	404	67	<	<	X
ap-7652	404	68	n(a	n(a	NOUN
ap-7652	404	69	)	)	PUNCT
ap-7652	404	70	.	.	PUNCT
ap-7652	405	1	since	since	SCONJ
ap-7652	405	2	these	these	DET
ap-7652	405	3	eigenfunctions	eigenfunction	NOUN
ap-7652	405	4	must	must	AUX
ap-7652	405	5	be	be	AUX
ap-7652	405	6	orthogonal	orthogonal	ADJ
ap-7652	405	7	[	[	X
ap-7652	405	8	43	43	NUM
ap-7652	405	9	]	]	PUNCT
ap-7652	405	10	with	with	ADP
ap-7652	405	11	the	the	DET
ap-7652	405	12	weight	weight	NOUN
ap-7652	405	13	y−1	y−1	PROPN
ap-7652	405	14	the	the	DET
ap-7652	405	15	polynomial	polynomial	ADJ
ap-7652	405	16	wronskians	wronskian	NOUN
ap-7652	405	17	∞w[y	∞w[y	NOUN
ap-7652	405	18	;	;	PUNCT
ap-7652	405	19	a	a	DET
ap-7652	405	20	|	|	NOUN
ap-7652	405	21	−	−	NOUN
ap-7652	405	22	...	...	PUNCT
ap-7652	406	1	m	m	VERB
ap-7652	406	2	_	_	NOUN
ap-7652	406	3	p	p	X
ap-7652	406	4	,	,	PUNCT
ap-7652	406	5	n	n	CCONJ
ap-7652	406	6	]	]	PUNCT
ap-7652	406	7	with	with	ADP
ap-7652	406	8	n	n	NUM
ap-7652	406	9	varying	vary	VERB
ap-7652	406	10	from	from	ADP
ap-7652	406	11	0	0	NUM
ap-7652	406	12	to	to	ADP
ap-7652	406	13	n(a	n(a	NOUN
ap-7652	406	14	)	)	PUNCT
ap-7652	407	1	−	−	NOUN
ap-7652	407	2	1	1	NUM
ap-7652	407	3	are	be	AUX
ap-7652	407	4	orthogonal	orthogonal	ADJ
ap-7652	407	5	with	with	ADP
ap-7652	407	6	the	the	DET
ap-7652	407	7	positive	positive	ADJ
ap-7652	407	8	weight	weight	NOUN
ap-7652	407	9	∞w	∞w	NOUN
ap-7652	408	1	[	[	X
ap-7652	408	2	y	y	X
ap-7652	408	3	;	;	PUNCT
ap-7652	408	4	a	a	DET
ap-7652	408	5	|	|	NOUN
ap-7652	408	6	−	−	NOUN
ap-7652	408	7	...	...	PUNCT
ap-7652	409	1	m	m	VERB
ap-7652	409	2	_	_	NOUN
ap-7652	410	1	p	p	X
ap-7652	410	2	]	]	X
ap-7652	411	1	=	=	SYM
ap-7652	411	2	∞	∞	NUM
ap-7652	411	3	̸ψ2	̸ψ2	NOUN
ap-7652	411	4	−,0	−,0	PROPN
ap-7652	412	1	[	[	X
ap-7652	412	2	y	y	X
ap-7652	412	3	;	;	PUNCT
ap-7652	412	4	a−	a−	PROPN
ap-7652	412	5	p	p	X
ap-7652	412	6	]	]	X
ap-7652	412	7	y	y	PROPN
ap-7652	412	8	∞w2[y	∞w2[y	PROPN
ap-7652	412	9	;	;	PUNCT
ap-7652	412	10	a	a	DET
ap-7652	412	11	|	|	NOUN
ap-7652	412	12	−	−	NOUN
ap-7652	412	13	...	...	PUNCT
ap-7652	413	1	m	m	VERB
ap-7652	413	2	_	_	NOUN
ap-7652	413	3	p	p	X
ap-7652	413	4	]	]	PUNCT
ap-7652	413	5	.	.	PUNCT
ap-7652	414	1	(	(	PUNCT
ap-7652	414	2	112	112	NUM
ap-7652	414	3	)	)	PUNCT
ap-7652	414	4	if	if	SCONJ
ap-7652	414	5	the	the	DET
ap-7652	414	6	morse	morse	ADJ
ap-7652	414	7	potential	potential	NOUN
ap-7652	414	8	has	have	VERB
ap-7652	414	9	at	at	ADV
ap-7652	414	10	least	least	ADJ
ap-7652	414	11	2	2	NUM
ap-7652	414	12	energy	energy	NOUN
ap-7652	414	13	levels	level	NOUN
ap-7652	414	14	the	the	DET
ap-7652	414	15	sequence	sequence	NOUN
ap-7652	414	16	starts	start	VERB
ap-7652	414	17	from	from	ADP
ap-7652	414	18	a	a	DET
ap-7652	414	19	polynomial	polynomial	NOUN
ap-7652	414	20	of	of	ADP
ap-7652	414	21	degree	degree	NOUN
ap-7652	414	22	|	|	ADV
ap-7652	414	23	m	m	NOUN
ap-7652	414	24	_	_	NOUN
ap-7652	414	25	p	p	NOUN
ap-7652	415	1	|	|	ADJ
ap-7652	415	2	−0.5	−0.5	X
ap-7652	415	3	p(p+	p(p+	NOUN
ap-7652	415	4	1	1	NUM
ap-7652	415	5	)	)	PUNCT
ap-7652	415	6	≥	≥	NOUN
ap-7652	415	7	2p	2p	NUM
ap-7652	415	8	.	.	PUNCT
ap-7652	416	1	(	(	PUNCT
ap-7652	416	2	113	113	NUM
ap-7652	416	3	)	)	PUNCT
ap-7652	416	4	keeping	keep	VERB
ap-7652	416	5	in	in	ADP
ap-7652	416	6	mind	mind	NOUN
ap-7652	416	7	|	|	ADV
ap-7652	416	8	m	m	NOUN
ap-7652	416	9	_	_	NOUN
ap-7652	416	10	p	p	X
ap-7652	417	1	|	|	NOUN
ap-7652	417	2	>	>	X
ap-7652	417	3	(	(	PUNCT
ap-7652	417	4	2a−	2a−	PROPN
ap-7652	417	5	1)p+	1)p+	NUM
ap-7652	417	6	0.5p(p+	0.5p(p+	NOUN
ap-7652	417	7	1	1	NUM
ap-7652	417	8	)	)	PUNCT
ap-7652	417	9	>	>	X
ap-7652	418	1	2p+	2p+	NUM
ap-7652	418	2	0.5p(p+	0.5p(p+	NUM
ap-7652	418	3	1	1	NUM
ap-7652	418	4	)	)	PUNCT
ap-7652	418	5	(	(	PUNCT
ap-7652	418	6	114	114	NUM
ap-7652	418	7	)	)	PUNCT
ap-7652	418	8	in	in	ADP
ap-7652	418	9	this	this	DET
ap-7652	418	10	case	case	NOUN
ap-7652	418	11	.	.	PUNCT
ap-7652	419	1	the	the	DET
ap-7652	419	2	finite	finite	PROPN
ap-7652	419	3	eop	eop	PROPN
ap-7652	419	4	sequence	sequence	NOUN
ap-7652	419	5	in	in	ADP
ap-7652	419	6	question	question	NOUN
ap-7652	419	7	thus	thus	ADV
ap-7652	419	8	starts	start	VERB
ap-7652	419	9	from	from	ADP
ap-7652	419	10	a	a	DET
ap-7652	419	11	polynomial	polynomial	NOUN
ap-7652	419	12	of	of	ADP
ap-7652	419	13	at	at	ADV
ap-7652	419	14	least	least	ADJ
ap-7652	419	15	second	second	ADJ
ap-7652	419	16	degree	degree	NOUN
ap-7652	419	17	and	and	CCONJ
ap-7652	419	18	therefore	therefore	ADV
ap-7652	419	19	[	[	X
ap-7652	419	20	46	46	NUM
ap-7652	419	21	]	]	PUNCT
ap-7652	419	22	does	do	AUX
ap-7652	419	23	not	not	PART
ap-7652	419	24	obey	obey	VERB
ap-7652	419	25	the	the	DET
ap-7652	419	26	bochner	bochner	NOUN
ap-7652	419	27	theorem	theorem	NOUN
ap-7652	419	28	[	[	PUNCT
ap-7652	419	29	47	47	NUM
ap-7652	419	30	]	]	PUNCT
ap-7652	419	31	.	.	PUNCT
ap-7652	420	1	re	re	VERB
ap-7652	420	2	-	-	VERB
ap-7652	420	3	writing	write	VERB
ap-7652	420	4	(	(	PUNCT
ap-7652	420	5	85	85	NUM
ap-7652	420	6	)	)	PUNCT
ap-7652	420	7	with	with	ADP
ap-7652	420	8	mp	mp	PROPN
ap-7652	420	9	=	=	PUNCT
ap-7652	420	10	m	m	NOUN
ap-7652	420	11	_	_	NOUN
ap-7652	420	12	p	p	NOUN
ap-7652	420	13	as	as	ADP
ap-7652	420	14	∞i	∞i	NUM
ap-7652	420	15	0[y	0[y	NUM
ap-7652	420	16	;	;	PUNCT
ap-7652	420	17	a	a	DET
ap-7652	420	18	|	|	NOUN
ap-7652	420	19	−	−	NOUN
ap-7652	420	20	...	...	PUNCT
ap-7652	421	1	m	m	VERB
ap-7652	421	2	_	_	NOUN
ap-7652	422	1	p	p	X
ap-7652	422	2	]	]	X
ap-7652	422	3	=	=	SYM
ap-7652	422	4	∞i	∞i	NUM
ap-7652	422	5	0[y	0[y	NUM
ap-7652	422	6	;	;	PUNCT
ap-7652	422	7	a−	a−	PROPN
ap-7652	422	8	p	p	X
ap-7652	422	9	]	]	X
ap-7652	422	10	+	+	CCONJ
ap-7652	422	11	2	2	NUM
ap-7652	422	12	y	y	NOUN
ap-7652	422	13	d	d	NOUN
ap-7652	422	14	dy	dy	X
ap-7652	422	15	å	å	PROPN
ap-7652	422	16	y	y	PROPN
ap-7652	422	17	ld∞w[y	ld∞w[y	PROPN
ap-7652	422	18	;	;	PUNCT
ap-7652	422	19	a	a	DET
ap-7652	422	20	|	|	NOUN
ap-7652	422	21	−	−	NOUN
ap-7652	422	22	...	...	PUNCT
ap-7652	423	1	m	m	VERB
ap-7652	423	2	_	_	NOUN
ap-7652	424	1	p	p	X
ap-7652	424	2	]	]	X
ap-7652	424	3	ã	ã	X
ap-7652	424	4	(	(	PUNCT
ap-7652	424	5	115	115	NUM
ap-7652	424	6	)	)	PUNCT
ap-7652	424	7	we	we	PRON
ap-7652	424	8	can	can	AUX
ap-7652	424	9	then	then	ADV
ap-7652	424	10	explicitly	explicitly	ADV
ap-7652	424	11	express	express	VERB
ap-7652	424	12	corresponding	corresponding	ADJ
ap-7652	424	13	liouville	liouville	NOUN
ap-7652	424	14	potential	potential	NOUN
ap-7652	424	15	(	(	PUNCT
ap-7652	424	16	89	89	NUM
ap-7652	424	17	)	)	PUNCT
ap-7652	424	18	in	in	ADP
ap-7652	424	19	terms	term	NOUN
ap-7652	424	20	of	of	ADP
ap-7652	424	21	the	the	DET
ap-7652	424	22	admissible	admissible	ADJ
ap-7652	424	23	wronskian	wronskian	NOUN
ap-7652	424	24	∞w[y	∞w[y	NOUN
ap-7652	424	25	;	;	PUNCT
ap-7652	424	26	a	a	DET
ap-7652	424	27	|	|	NOUN
ap-7652	424	28	−	−	NOUN
ap-7652	424	29	...	...	PUNCT
ap-7652	425	1	m	m	VERB
ap-7652	425	2	_	_	NOUN
ap-7652	426	1	p	p	X
ap-7652	426	2	]	]	PUNCT
ap-7652	426	3	as	as	SCONJ
ap-7652	426	4	follows	follow	VERB
ap-7652	426	5	∞v	∞v	PUNCT
ap-7652	427	1	[	[	X
ap-7652	427	2	y	y	X
ap-7652	427	3	;	;	PUNCT
ap-7652	427	4	a	a	DET
ap-7652	427	5	|	|	NOUN
ap-7652	427	6	−	−	NOUN
ap-7652	427	7	...	...	PUNCT
ap-7652	428	1	m	m	PUNCT
ap-7652	428	2	_	_	NOUN
ap-7652	429	1	˜	˜	PROPN
ap-7652	429	2	p	p	X
ap-7652	429	3	]	]	X
ap-7652	429	4	=	=	PUNCT
ap-7652	429	5	∞v	∞v	NUM
ap-7652	430	1	[	[	X
ap-7652	430	2	y	y	X
ap-7652	430	3	;	;	PUNCT
ap-7652	430	4	a−	a−	PROPN
ap-7652	430	5	p	p	X
ap-7652	430	6	]	]	X
ap-7652	430	7	−	−	PROPN
ap-7652	430	8	2y	2y	PROPN
ap-7652	430	9	d	d	NOUN
ap-7652	430	10	dy	dy	NOUN
ap-7652	430	11	å	å	PROPN
ap-7652	430	12	y	y	PROPN
ap-7652	430	13	ld∞w[y	ld∞w[y	PROPN
ap-7652	430	14	;	;	PUNCT
ap-7652	430	15	a	a	DET
ap-7652	430	16	|	|	NOUN
ap-7652	430	17	−	−	NOUN
ap-7652	430	18	...	...	PUNCT
ap-7652	431	1	m	m	VERB
ap-7652	431	2	_	_	NOUN
ap-7652	432	1	p	p	X
ap-7652	432	2	]	]	X
ap-7652	432	3	ã	ã	X
ap-7652	432	4	(	(	PUNCT
ap-7652	432	5	116	116	NUM
ap-7652	432	6	)	)	PUNCT
ap-7652	432	7	as	as	SCONJ
ap-7652	432	8	mentioned	mention	VERB
ap-7652	432	9	in	in	ADP
ap-7652	432	10	previous	previous	ADJ
ap-7652	432	11	subsection	subsection	NOUN
ap-7652	432	12	this	this	DET
ap-7652	432	13	net	net	NOUN
ap-7652	432	14	of	of	ADP
ap-7652	432	15	isospectral	isospectral	ADJ
ap-7652	432	16	rational	rational	ADJ
ap-7652	432	17	potentials	potential	NOUN
ap-7652	432	18	starts	start	VERB
ap-7652	432	19	from	from	ADP
ap-7652	432	20	potential	potential	ADJ
ap-7652	432	21	function	function	NOUN
ap-7652	432	22	(	(	PUNCT
ap-7652	432	23	16	16	NUM
ap-7652	432	24	)	)	PUNCT
ap-7652	432	25	in	in	ADP
ap-7652	432	26	[	[	X
ap-7652	432	27	10	10	NUM
ap-7652	432	28	]	]	PUNCT
ap-7652	432	29	with	with	ADP
ap-7652	432	30	a	a	DET
ap-7652	432	31	=	=	SYM
ap-7652	432	32	a−	a−	PROPN
ap-7652	432	33	1/2	1/2	NUM
ap-7652	432	34	,	,	PUNCT
ap-7652	432	35	b	b	NOUN
ap-7652	432	36	=	=	SYM
ap-7652	432	37	1	1	NUM
ap-7652	432	38	,	,	PUNCT
ap-7652	432	39	after	after	SCONJ
ap-7652	432	40	the	the	DET
ap-7652	432	41	latter	latter	ADJ
ap-7652	432	42	is	be	AUX
ap-7652	432	43	expressed	express	VERB
ap-7652	432	44	in	in	ADP
ap-7652	432	45	terms	term	NOUN
ap-7652	432	46	of	of	ADP
ap-7652	432	47	the	the	DET
ap-7652	432	48	variable	variable	ADJ
ap-7652	432	49	y	y	PROPN
ap-7652	432	50	=	=	SYM
ap-7652	432	51	ex	ex	X
ap-7652	432	52	.	.	PROPN
ap-7652	432	53	111	111	NUM
ap-7652	432	54	gregory	gregory	PROPN
ap-7652	432	55	natanson	natanson	PROPN
ap-7652	432	56	acta	acta	PROPN
ap-7652	432	57	polytechnica	polytechnica	PROPN
ap-7652	432	58	3.4	3.4	NUM
ap-7652	432	59	.	.	PUNCT
ap-7652	433	1	subnet	subnet	NOUN
ap-7652	433	2	of	of	ADP
ap-7652	433	3	rationally	rationally	ADV
ap-7652	433	4	deformed	deform	VERB
ap-7652	433	5	morse	morse	ADJ
ap-7652	433	6	potentials	potential	NOUN
ap-7652	433	7	quantized	quantize	VERB
ap-7652	433	8	via	via	ADP
ap-7652	433	9	wronskians	wronskian	NOUN
ap-7652	433	10	of	of	ADP
ap-7652	433	11	r	r	NOUN
ap-7652	433	12	-	-	PUNCT
ap-7652	433	13	bessel	bessel	NOUN
ap-7652	433	14	polynomials	polynomial	VERB
ap-7652	433	15	another	another	DET
ap-7652	433	16	family	family	NOUN
ap-7652	433	17	of	of	ADP
ap-7652	433	18	solvable	solvable	ADJ
ap-7652	433	19	rdct	rdct	PROPN
ap-7652	433	20	s	s	PROPN
ap-7652	433	21	of	of	ADP
ap-7652	433	22	csle	csle	PROPN
ap-7652	433	23	(	(	PUNCT
ap-7652	433	24	32	32	NUM
ap-7652	433	25	)	)	PUNCT
ap-7652	433	26	can	can	AUX
ap-7652	433	27	be	be	AUX
ap-7652	433	28	constructed	construct	VERB
ap-7652	433	29	using	use	VERB
ap-7652	433	30	juxtaposed	juxtapose	VERB
ap-7652	433	31	pairs	pair	NOUN
ap-7652	433	32	of	of	ADP
ap-7652	433	33	eigenfunctions	eigenfunction	NOUN
ap-7652	433	34	∞ϕ−,nk	∞ϕ−,nk	PROPN
ap-7652	433	35	[	[	PROPN
ap-7652	433	36	y	y	PROPN
ap-7652	433	37	;	;	PUNCT
ap-7652	433	38	a	a	DET
ap-7652	433	39	]	]	X
ap-7652	433	40	,	,	PUNCT
ap-7652	433	41	∞ϕ−,nk+1[y	∞ϕ−,nk+1[y	PROPN
ap-7652	433	42	;	;	PUNCT
ap-7652	433	43	a	a	X
ap-7652	433	44	]	]	X
ap-7652	433	45	(	(	PUNCT
ap-7652	433	46	0	0	NUM
ap-7652	433	47	<	<	X
ap-7652	433	48	nk	nk	PROPN
ap-7652	433	49	<	<	X
ap-7652	433	50	nk+1	nk+1	NUM
ap-7652	433	51	−	−	PROPN
ap-7652	433	52	1	1	NUM
ap-7652	433	53	<	<	X
ap-7652	433	54	n(a	n(a	NOUN
ap-7652	433	55	)	)	PUNCT
ap-7652	433	56	for	for	ADP
ap-7652	433	57	k	k	PROPN
ap-7652	433	58	=	=	SYM
ap-7652	433	59	1	1	NUM
ap-7652	433	60	,	,	PUNCT
ap-7652	433	61	.	.	PUNCT
ap-7652	433	62	.	.	PUNCT
ap-7652	433	63	.	.	PUNCT
ap-7652	434	1	,	,	PUNCT
ap-7652	434	2	j	j	PROPN
ap-7652	434	3	)	)	PUNCT
ap-7652	434	4	.	.	PUNCT
ap-7652	435	1	the	the	DET
ap-7652	435	2	simplest	simple	ADJ
ap-7652	435	3	double	double	ADJ
ap-7652	435	4	-	-	PUNCT
ap-7652	435	5	step	step	NOUN
ap-7652	435	6	representative	representative	NOUN
ap-7652	435	7	of	of	ADP
ap-7652	435	8	this	this	DET
ap-7652	435	9	finite	finite	ADJ
ap-7652	435	10	family	family	NOUN
ap-7652	435	11	of	of	ADP
ap-7652	435	12	rationally	rationally	ADV
ap-7652	435	13	deformed	deform	VERB
ap-7652	435	14	morse	morse	ADJ
ap-7652	435	15	potentials	potential	NOUN
ap-7652	435	16	with	with	ADP
ap-7652	435	17	n1	n1	PROPN
ap-7652	435	18	=	=	SYM
ap-7652	435	19	1	1	NUM
ap-7652	435	20	,	,	PUNCT
ap-7652	435	21	j	j	PROPN
ap-7652	435	22	=	=	SYM
ap-7652	435	23	2	2	NUM
ap-7652	435	24	was	be	AUX
ap-7652	435	25	constructed	construct	VERB
ap-7652	435	26	by	by	ADP
ap-7652	435	27	bagrov	bagrov	NOUN
ap-7652	435	28	and	and	CCONJ
ap-7652	435	29	samsonov	samsonov	NOUN
ap-7652	435	30	[	[	X
ap-7652	435	31	38	38	NUM
ap-7652	435	32	,	,	PUNCT
ap-7652	435	33	48	48	NUM
ap-7652	435	34	]	]	PUNCT
ap-7652	435	35	in	in	ADP
ap-7652	435	36	the	the	DET
ap-7652	435	37	late	late	ADJ
ap-7652	435	38	nineties	ninety	NOUN
ap-7652	435	39	based	base	VERB
ap-7652	435	40	on	on	ADP
ap-7652	435	41	the	the	DET
ap-7652	435	42	conventional	conventional	ADJ
ap-7652	435	43	l	l	NOUN
ap-7652	435	44	ref	ref	NOUN
ap-7652	435	45	representation	representation	NOUN
ap-7652	435	46	of	of	ADP
ap-7652	435	47	the	the	DET
ap-7652	435	48	schrödinger	schrödinger	ADJ
ap-7652	435	49	equation	equation	NOUN
ap-7652	435	50	with	with	ADP
ap-7652	435	51	the	the	DET
ap-7652	435	52	morse	morse	ADJ
ap-7652	435	53	potential	potential	NOUN
ap-7652	435	54	.	.	PUNCT
ap-7652	436	1	the	the	DET
ap-7652	436	2	extensions	extension	NOUN
ap-7652	436	3	of	of	ADP
ap-7652	436	4	their	their	PRON
ap-7652	436	5	works	work	NOUN
ap-7652	436	6	to	to	ADP
ap-7652	436	7	an	an	DET
ap-7652	436	8	arbitrary	arbitrary	ADJ
ap-7652	436	9	number	number	NOUN
ap-7652	436	10	of	of	ADP
ap-7652	436	11	juxtaposed	juxtapose	VERB
ap-7652	436	12	pairs	pair	NOUN
ap-7652	436	13	of	of	ADP
ap-7652	436	14	eigenfunctions	eigenfunction	NOUN
ap-7652	436	15	in	in	ADP
ap-7652	436	16	both	both	DET
ap-7652	436	17	l	l	NOUN
ap-7652	436	18	ref	ref	NOUN
ap-7652	436	19	and	and	CCONJ
ap-7652	436	20	bref	bref	PROPN
ap-7652	436	21	representations	representation	NOUN
ap-7652	436	22	were	be	AUX
ap-7652	436	23	performed	perform	VERB
ap-7652	436	24	more	more	ADV
ap-7652	436	25	recently	recently	ADV
ap-7652	436	26	in	in	ADP
ap-7652	436	27	[	[	X
ap-7652	436	28	11	11	NUM
ap-7652	436	29	]	]	PUNCT
ap-7652	436	30	and	and	CCONJ
ap-7652	436	31	[	[	X
ap-7652	436	32	19	19	NUM
ap-7652	436	33	]	]	PUNCT
ap-7652	436	34	accordingly	accordingly	ADV
ap-7652	436	35	.	.	PUNCT
ap-7652	437	1	for	for	ADP
ap-7652	437	2	any	any	DET
ap-7652	437	3	tfi	tfi	NOUN
ap-7652	437	4	rcsle	rcsle	NOUN
ap-7652	437	5	from	from	ADP
ap-7652	437	6	group	group	PROPN
ap-7652	437	7	a	a	DET
ap-7652	437	8	one	one	NOUN
ap-7652	437	9	can	can	AUX
ap-7652	437	10	by	by	AUX
ap-7652	437	11	-	-	PUNCT
ap-7652	437	12	pass	pass	VERB
ap-7652	437	13	an	an	DET
ap-7652	437	14	analysis	analysis	NOUN
ap-7652	437	15	of	of	ADP
ap-7652	437	16	the	the	DET
ap-7652	437	17	pre	pre	NOUN
ap-7652	437	18	-	-	NOUN
ap-7652	437	19	requisites	requisite	NOUN
ap-7652	437	20	for	for	ADP
ap-7652	437	21	the	the	DET
ap-7652	437	22	krein	krein	PROPN
ap-7652	437	23	-	-	PUNCT
ap-7652	437	24	adler	adler	PROPN
ap-7652	437	25	theorem	theorem	VERB
ap-7652	437	26	[	[	X
ap-7652	437	27	49	49	NUM
ap-7652	437	28	,	,	PUNCT
ap-7652	437	29	50	50	NUM
ap-7652	437	30	]	]	PUNCT
ap-7652	437	31	by	by	ADP
ap-7652	437	32	taking	take	VERB
ap-7652	437	33	advantage	advantage	NOUN
ap-7652	437	34	of	of	ADP
ap-7652	437	35	the	the	DET
ap-7652	437	36	fact	fact	NOUN
ap-7652	437	37	that	that	SCONJ
ap-7652	437	38	the	the	DET
ap-7652	437	39	wronskians	wronskian	NOUN
ap-7652	437	40	of	of	ADP
ap-7652	437	41	eigenfunctions	eigenfunction	NOUN
ap-7652	437	42	are	be	AUX
ap-7652	437	43	composed	compose	VERB
ap-7652	437	44	of	of	ADP
ap-7652	437	45	weighted	weight	VERB
ap-7652	437	46	orthogonal	orthogonal	ADJ
ap-7652	437	47	polynomials	polynomial	NOUN
ap-7652	437	48	with	with	ADP
ap-7652	437	49	the	the	DET
ap-7652	437	50	common	common	ADJ
ap-7652	437	51	degree	degree	NOUN
ap-7652	437	52	-	-	PUNCT
ap-7652	437	53	independent	independent	ADJ
ap-7652	437	54	weight	weight	NOUN
ap-7652	437	55	and	and	CCONJ
ap-7652	437	56	therefore	therefore	ADV
ap-7652	437	57	the	the	DET
ap-7652	437	58	numbers	number	NOUN
ap-7652	437	59	of	of	ADP
ap-7652	437	60	their	their	PRON
ap-7652	437	61	positive	positive	ADJ
ap-7652	437	62	zeros	zero	NOUN
ap-7652	437	63	are	be	AUX
ap-7652	437	64	controlled	control	VERB
ap-7652	437	65	by	by	ADP
ap-7652	437	66	the	the	DET
ap-7652	437	67	general	general	ADJ
ap-7652	437	68	conjectures	conjecture	VERB
ap-7652	437	69	proven	prove	VERB
ap-7652	437	70	in	in	ADP
ap-7652	437	71	[	[	X
ap-7652	437	72	51	51	NUM
ap-7652	437	73	]	]	PUNCT
ap-7652	437	74	for	for	ADP
ap-7652	437	75	wronskians	wronskian	NOUN
ap-7652	437	76	of	of	ADP
ap-7652	437	77	positive	positive	ADJ
ap-7652	437	78	definite	definite	ADJ
ap-7652	437	79	orthogonal	orthogonal	ADJ
ap-7652	437	80	polynomials	polynomial	NOUN
ap-7652	437	81	.	.	PUNCT
ap-7652	438	1	in	in	ADP
ap-7652	438	2	particular	particular	ADJ
ap-7652	438	3	we	we	PRON
ap-7652	438	4	conclude	conclude	VERB
ap-7652	438	5	that	that	SCONJ
ap-7652	438	6	any	any	DET
ap-7652	438	7	wronskian	wronskian	NOUN
ap-7652	438	8	formed	form	VERB
ap-7652	438	9	by	by	ADP
ap-7652	438	10	juxtaposed	juxtapose	VERB
ap-7652	438	11	pairs	pair	NOUN
ap-7652	438	12	of	of	ADP
ap-7652	438	13	r	r	NOUN
ap-7652	438	14	-	-	PUNCT
ap-7652	438	15	bessel	bessel	ADJ
ap-7652	438	16	polynomials	polynomial	NOUN
ap-7652	438	17	of	of	ADP
ap-7652	438	18	non	non	ADJ
ap-7652	438	19	-	-	ADJ
ap-7652	438	20	zero	zero	ADJ
ap-7652	438	21	degrees	degree	NOUN
ap-7652	438	22	may	may	AUX
ap-7652	438	23	not	not	PART
ap-7652	438	24	have	have	VERB
ap-7652	438	25	positive	positive	ADJ
ap-7652	438	26	zeros	zero	NOUN
ap-7652	438	27	.	.	PUNCT
ap-7652	439	1	let	let	AUX
ap-7652	439	2	n2j	n2j	ADV
ap-7652	439	3	be	be	AUX
ap-7652	439	4	a	a	DET
ap-7652	439	5	set	set	NOUN
ap-7652	439	6	of	of	ADP
ap-7652	439	7	r	r	NOUN
ap-7652	439	8	-	-	PUNCT
ap-7652	439	9	bessel	bessel	ADJ
ap-7652	439	10	polynomials	polynomial	NOUN
ap-7652	439	11	of	of	ADP
ap-7652	439	12	degrees	degree	NOUN
ap-7652	439	13	n2j	n2j	ADV
ap-7652	440	1	=	=	PUNCT
ap-7652	440	2	m(∆′	m(∆′	NOUN
ap-7652	440	3	l→1	l→1	NOUN
ap-7652	440	4	)	)	PUNCT
ap-7652	441	1	=	=	SYM
ap-7652	441	2	n1	n1	NOUN
ap-7652	441	3	:	:	PUNCT
ap-7652	441	4	n1	n1	PROPN
ap-7652	441	5	+	+	CCONJ
ap-7652	441	6	2j1	2j1	NUM
ap-7652	441	7	−	−	NOUN
ap-7652	441	8	1	1	NUM
ap-7652	441	9	,	,	PUNCT
ap-7652	441	10	n2j1	n2j1	PUNCT
ap-7652	441	11	+	+	NOUN
ap-7652	441	12	1	1	NUM
ap-7652	441	13	:	:	PUNCT
ap-7652	441	14	n2j1	n2j1	PROPN
ap-7652	441	15	+	+	NOUN
ap-7652	441	16	1	1	NUM
ap-7652	441	17	+	+	NUM
ap-7652	441	18	2j2	2j2	NUM
ap-7652	441	19	−	−	NUM
ap-7652	441	20	1	1	NUM
ap-7652	441	21	,	,	PUNCT
ap-7652	441	22	.	.	PUNCT
ap-7652	441	23	.	.	PUNCT
ap-7652	441	24	.	.	PUNCT
ap-7652	442	1	,	,	PUNCT
ap-7652	442	2	n2j−2jl+1	n2j−2jl+1	PROPN
ap-7652	442	3	:	:	PUNCT
ap-7652	443	1	n2j(n1	n2j(n1	PROPN
ap-7652	443	2	>	>	X
ap-7652	443	3	0	0	PROPN
ap-7652	443	4	,	,	PUNCT
ap-7652	443	5	n2j	n2j	ADV
ap-7652	443	6	<	<	X
ap-7652	443	7	n	n	CCONJ
ap-7652	443	8	)	)	PUNCT
ap-7652	443	9	(	(	PUNCT
ap-7652	443	10	117	117	NUM
ap-7652	443	11	)	)	PUNCT
ap-7652	443	12	with	with	ADP
ap-7652	443	13	even	even	ADV
ap-7652	443	14	δ′	δ′	NOUN
ap-7652	443	15	l	l	NOUN
ap-7652	443	16	=	=	X
ap-7652	443	17	2jl	2jl	NOUN
ap-7652	443	18	(	(	PUNCT
ap-7652	443	19	l	l	NOUN
ap-7652	443	20	=	=	SYM
ap-7652	443	21	1	1	NUM
ap-7652	443	22	,	,	PUNCT
ap-7652	443	23	.	.	PUNCT
ap-7652	443	24	.	.	PUNCT
ap-7652	443	25	.	.	PUNCT
ap-7652	444	1	,	,	PUNCT
ap-7652	444	2	l	l	NOUN
ap-7652	444	3	)	)	PUNCT
ap-7652	444	4	.	.	PUNCT
ap-7652	445	1	(	(	PUNCT
ap-7652	445	2	118	118	NUM
ap-7652	445	3	)	)	PUNCT
ap-7652	445	4	examination	examination	NOUN
ap-7652	445	5	of	of	ADP
ap-7652	445	6	the	the	DET
ap-7652	445	7	q	q	ADJ
ap-7652	445	8	-	-	PUNCT
ap-7652	445	9	rs	rs	NOUN
ap-7652	445	10	functions	function	NOUN
ap-7652	445	11	∞	∞	NOUN
ap-7652	445	12	̸ψ−,n	̸ψ−,n	ADJ
ap-7652	446	1	[	[	X
ap-7652	446	2	y	y	X
ap-7652	446	3	;	;	PUNCT
ap-7652	446	4	a	a	DET
ap-7652	446	5	|	|	NOUN
ap-7652	446	6	−	−	NOUN
ap-7652	446	7	...	...	PUNCT
ap-7652	446	8	n2j	n2j	PROPN
ap-7652	446	9	]	]	X
ap-7652	446	10	=	=	PUNCT
ap-7652	446	11	y−1/2	y−1/2	PROPN
ap-7652	446	12	∞φ−,n[y	∞φ−,n[y	PROPN
ap-7652	446	13	;	;	PUNCT
ap-7652	446	14	a	a	DET
ap-7652	446	15	|	|	NOUN
ap-7652	446	16	−	−	NOUN
ap-7652	446	17	...	...	PUNCT
ap-7652	447	1	n2j	n2j	PROPN
ap-7652	447	2	]	]	PUNCT
ap-7652	448	1	=	=	PUNCT
ap-7652	448	2	∞	∞	NUM
ap-7652	448	3	̸ψ−,0	̸ψ−,0	PROPN
ap-7652	449	1	[	[	X
ap-7652	449	2	y	y	NOUN
ap-7652	449	3	;	;	PUNCT
ap-7652	449	4	a−	a−	X
ap-7652	449	5	2j	2j	X
ap-7652	449	6	]	]	PUNCT
ap-7652	450	1	∞w[y	∞w[y	NOUN
ap-7652	450	2	;	;	PUNCT
ap-7652	450	3	a	a	DET
ap-7652	450	4	|	|	NOUN
ap-7652	450	5	−	−	NOUN
ap-7652	450	6	...	...	PUNCT
ap-7652	451	1	n2j	n2j	INTJ
ap-7652	451	2	,	,	PUNCT
ap-7652	451	3	n	n	CCONJ
ap-7652	451	4	]	]	PUNCT
ap-7652	451	5	∞w[y	∞w[y	NOUN
ap-7652	451	6	;	;	PUNCT
ap-7652	451	7	a	a	DET
ap-7652	451	8	|	|	NOUN
ap-7652	451	9	−	−	NOUN
ap-7652	451	10	...	...	PUNCT
ap-7652	452	1	n2j	n2j	PROPN
ap-7652	452	2	]	]	X
ap-7652	452	3	(	(	PUNCT
ap-7652	452	4	n	n	X
ap-7652	452	5	/∈	/∈	PUNCT
ap-7652	452	6	n2j	n2j	PROPN
ap-7652	452	7	)	)	PUNCT
ap-7652	452	8	(	(	PUNCT
ap-7652	452	9	119	119	NUM
ap-7652	452	10	)	)	PUNCT
ap-7652	452	11	shows	show	VERB
ap-7652	452	12	that	that	SCONJ
ap-7652	452	13	they	they	PRON
ap-7652	452	14	all	all	PRON
ap-7652	452	15	represent	represent	VERB
ap-7652	452	16	principal	principal	ADJ
ap-7652	452	17	solutions	solution	NOUN
ap-7652	452	18	near	near	ADP
ap-7652	452	19	the	the	DET
ap-7652	452	20	irregular	irregular	ADJ
ap-7652	452	21	singular	singular	ADJ
ap-7652	452	22	point	point	NOUN
ap-7652	452	23	of	of	ADP
ap-7652	452	24	the	the	DET
ap-7652	452	25	prime	prime	ADJ
ap-7652	452	26	rsle	rsle	NOUN
ap-7652	453	1	{	{	PUNCT
ap-7652	453	2	d	d	PROPN
ap-7652	453	3	dy	dy	NOUN
ap-7652	453	4	y	y	PROPN
ap-7652	453	5	d	d	PROPN
ap-7652	453	6	dy	dy	NOUN
ap-7652	453	7	+	+	CCONJ
ap-7652	453	8	y∞i	y∞i	VERB
ap-7652	453	9	0[y	0[y	NUM
ap-7652	453	10	;	;	PUNCT
ap-7652	453	11	a	a	DET
ap-7652	453	12	|	|	NOUN
ap-7652	453	13	−	−	NOUN
ap-7652	453	14	...	...	PUNCT
ap-7652	454	1	n2j	n2j	PROPN
ap-7652	454	2	]	]	X
ap-7652	455	1	+	+	CCONJ
ap-7652	455	2	(	(	PUNCT
ap-7652	455	3	ε+	ε+	NOUN
ap-7652	455	4	1/2)y−1	1/2)y−1	NUM
ap-7652	455	5	}	}	PUNCT
ap-7652	455	6	∞	∞	PROPN
ap-7652	455	7	̸ψ	̸ψ	NOUN
ap-7652	455	8	[	[	X
ap-7652	455	9	y	y	X
ap-7652	455	10	;	;	PUNCT
ap-7652	455	11	a	a	PRON
ap-7652	455	12	;	;	PUNCT
ap-7652	455	13	ε	ε	PROPN
ap-7652	455	14	|	|	ADV
ap-7652	455	15	−	−	PROPN
ap-7652	455	16	...	...	PUNCT
ap-7652	455	17	n2j	n2j	PROPN
ap-7652	455	18	]	]	X
ap-7652	456	1	=	=	SYM
ap-7652	456	2	0	0	PUNCT
ap-7652	456	3	(	(	PUNCT
ap-7652	456	4	120	120	NUM
ap-7652	456	5	)	)	PUNCT
ap-7652	456	6	assuming	assume	VERB
ap-7652	456	7	again	again	ADV
ap-7652	456	8	that	that	SCONJ
ap-7652	456	9	the	the	DET
ap-7652	456	10	latter	latter	ADJ
ap-7652	456	11	equation	equation	NOUN
ap-7652	456	12	is	be	AUX
ap-7652	456	13	solved	solve	VERB
ap-7652	456	14	under	under	ADP
ap-7652	456	15	dbcs	dbc	NOUN
ap-7652	456	16	lim	lim	PROPN
ap-7652	456	17	y→0	y→0	PROPN
ap-7652	457	1	∞	∞	PROPN
ap-7652	457	2	̸ψ	̸ψ	VERB
ap-7652	457	3	[	[	X
ap-7652	457	4	y	y	X
ap-7652	457	5	;	;	PUNCT
ap-7652	457	6	a	a	PRON
ap-7652	457	7	;	;	PUNCT
ap-7652	457	8	εn	εn	ADP
ap-7652	457	9	|	|	ADV
ap-7652	457	10	−	−	PROPN
ap-7652	457	11	...	...	PUNCT
ap-7652	457	12	n2j	n2j	PROPN
ap-7652	457	13	]	]	X
ap-7652	458	1	=	=	SYM
ap-7652	458	2	lim	lim	PROPN
ap-7652	458	3	y→∞	y→∞	NUM
ap-7652	458	4	∞	∞	PROPN
ap-7652	458	5	̸ψ	̸ψ	VERB
ap-7652	459	1	[	[	X
ap-7652	459	2	y	y	X
ap-7652	459	3	;	;	PUNCT
ap-7652	459	4	a	a	PRON
ap-7652	459	5	;	;	PUNCT
ap-7652	459	6	εn	εn	ADP
ap-7652	459	7	|	|	ADV
ap-7652	459	8	−	−	PROPN
ap-7652	459	9	...	...	PUNCT
ap-7652	459	10	n2j	n2j	PROPN
ap-7652	459	11	]	]	PUNCT
ap-7652	459	12	=	=	PUNCT
ap-7652	460	1	0	0	X
ap-7652	460	2	.	.	PUNCT
ap-7652	461	1	(	(	PUNCT
ap-7652	461	2	121	121	NUM
ap-7652	461	3	)	)	PUNCT
ap-7652	461	4	note	note	NOUN
ap-7652	461	5	that	that	SCONJ
ap-7652	461	6	the	the	DET
ap-7652	461	7	pf	pf	NOUN
ap-7652	461	8	in	in	ADP
ap-7652	461	9	the	the	DET
ap-7652	461	10	right	right	ADJ
ap-7652	461	11	-	-	PUNCT
ap-7652	461	12	hand	hand	NOUN
ap-7652	461	13	side	side	NOUN
ap-7652	461	14	of	of	ADP
ap-7652	461	15	(	(	PUNCT
ap-7652	461	16	119	119	NUM
ap-7652	461	17	)	)	PUNCT
ap-7652	461	18	is	be	AUX
ap-7652	461	19	proportional	proportional	ADJ
ap-7652	461	20	to	to	ADP
ap-7652	461	21	yn−2j	yn−2j	PROPN
ap-7652	461	22	for	for	ADP
ap-7652	461	23	y	y	PROPN
ap-7652	461	24	>	>	PUNCT
ap-7652	461	25	>	>	X
ap-7652	462	1	1	1	NUM
ap-7652	463	1	so	so	ADV
ap-7652	463	2	each	each	DET
ap-7652	463	3	solution	solution	NOUN
ap-7652	463	4	with	with	ADP
ap-7652	463	5	n	n	PROPN
ap-7652	463	6	/∈	/∈	PUNCT
ap-7652	464	1	n2j	n2j	PROPN
ap-7652	464	2	<	<	X
ap-7652	464	3	n(a	n(a	NOUN
ap-7652	464	4	)	)	PUNCT
ap-7652	465	1	represents	represent	VERB
ap-7652	465	2	an	an	DET
ap-7652	465	3	eigenfunction	eigenfunction	NOUN
ap-7652	465	4	of	of	ADP
ap-7652	465	5	rsle	rsle	NOUN
ap-7652	465	6	(	(	PUNCT
ap-7652	465	7	120	120	NUM
ap-7652	465	8	)	)	PUNCT
ap-7652	465	9	.	.	PUNCT
ap-7652	466	1	again	again	ADV
ap-7652	466	2	these	these	DET
ap-7652	466	3	eigenfunctions	eigenfunction	NOUN
ap-7652	466	4	must	must	AUX
ap-7652	466	5	be	be	AUX
ap-7652	466	6	orthogonal	orthogonal	ADJ
ap-7652	466	7	with	with	ADP
ap-7652	466	8	the	the	DET
ap-7652	466	9	weight	weight	NOUN
ap-7652	466	10	y−1	y−1	PROPN
ap-7652	466	11	and	and	CCONJ
ap-7652	466	12	therefore	therefore	ADV
ap-7652	466	13	n(a	n(a	NOUN
ap-7652	466	14	)	)	PUNCT
ap-7652	467	1	−	−	NUM
ap-7652	467	2	2j	2j	NOUN
ap-7652	467	3	wronskians	wronskian	NOUN
ap-7652	467	4	∞w[y	∞w[y	NOUN
ap-7652	467	5	;	;	PUNCT
ap-7652	467	6	a	a	DET
ap-7652	467	7	|	|	NOUN
ap-7652	467	8	−	−	NOUN
ap-7652	467	9	...	...	PUNCT
ap-7652	468	1	n2j	n2j	INTJ
ap-7652	468	2	,	,	PUNCT
ap-7652	468	3	n	n	CCONJ
ap-7652	468	4	]	]	PUNCT
ap-7652	468	5	with	with	ADP
ap-7652	468	6	n	n	PROPN
ap-7652	468	7	/∈	/∈	PUNCT
ap-7652	469	1	n2j	n2j	PROPN
ap-7652	469	2	<	<	X
ap-7652	469	3	n(a	n(a	PROPN
ap-7652	469	4	)	)	PUNCT
ap-7652	470	1	form	form	VERB
ap-7652	470	2	a	a	DET
ap-7652	470	3	polynomial	polynomial	ADJ
ap-7652	470	4	set	set	NOUN
ap-7652	470	5	orthogonal	orthogonal	NOUN
ap-7652	470	6	with	with	ADP
ap-7652	470	7	the	the	DET
ap-7652	470	8	positive	positive	ADJ
ap-7652	470	9	weight	weight	NOUN
ap-7652	470	10	∞w	∞w	NOUN
ap-7652	471	1	[	[	X
ap-7652	471	2	y	y	X
ap-7652	471	3	;	;	PUNCT
ap-7652	471	4	a	a	DET
ap-7652	471	5	|	|	NOUN
ap-7652	471	6	−	−	NOUN
ap-7652	471	7	...	...	PUNCT
ap-7652	471	8	n2j	n2j	PROPN
ap-7652	471	9	]	]	PUNCT
ap-7652	472	1	=	=	PUNCT
ap-7652	472	2	∞	∞	NUM
ap-7652	472	3	̸ψ2	̸ψ2	NOUN
ap-7652	472	4	−,0	−,0	PROPN
ap-7652	473	1	[	[	X
ap-7652	473	2	y	y	X
ap-7652	473	3	;	;	PUNCT
ap-7652	473	4	a−	a−	X
ap-7652	473	5	2j	2j	X
ap-7652	473	6	]	]	PUNCT
ap-7652	474	1	y∞w2[y	y∞w2[y	PROPN
ap-7652	474	2	;	;	PUNCT
ap-7652	474	3	a	a	DET
ap-7652	474	4	|	|	NOUN
ap-7652	474	5	−	−	NOUN
ap-7652	474	6	...	...	PUNCT
ap-7652	474	7	n2j	n2j	PROPN
ap-7652	474	8	]	]	X
ap-7652	474	9	(	(	PUNCT
ap-7652	474	10	122	122	NUM
ap-7652	474	11	)	)	PUNCT
ap-7652	474	12	if	if	SCONJ
ap-7652	474	13	sequence	sequence	NOUN
ap-7652	474	14	(	(	PUNCT
ap-7652	474	15	117	117	NUM
ap-7652	474	16	)	)	PUNCT
ap-7652	474	17	starts	start	VERB
ap-7652	474	18	from	from	ADP
ap-7652	474	19	n1	n1	NOUN
ap-7652	474	20	=	=	SYM
ap-7652	474	21	1	1	NUM
ap-7652	474	22	then	then	ADV
ap-7652	474	23	the	the	DET
ap-7652	474	24	finite	finite	PROPN
ap-7652	474	25	eop	eop	PROPN
ap-7652	474	26	sequence	sequence	NOUN
ap-7652	474	27	in	in	ADP
ap-7652	474	28	question	question	NOUN
ap-7652	474	29	lacks	lack	VERB
ap-7652	474	30	the	the	DET
ap-7652	474	31	first	first	ADJ
ap-7652	474	32	-	-	PUNCT
ap-7652	474	33	degree	degree	NOUN
ap-7652	474	34	polynomial	polynomial	NOUN
ap-7652	474	35	.	.	PUNCT
ap-7652	475	1	otherwise	otherwise	ADV
ap-7652	475	2	it	it	PRON
ap-7652	475	3	always	always	ADV
ap-7652	475	4	starts	start	VERB
ap-7652	475	5	from	from	ADP
ap-7652	475	6	a	a	DET
ap-7652	475	7	polynomial	polynomial	NOUN
ap-7652	475	8	of	of	ADP
ap-7652	475	9	non	non	ADJ
ap-7652	475	10	-	-	ADJ
ap-7652	475	11	zero	zero	NUM
ap-7652	475	12	degree	degree	NOUN
ap-7652	476	1	|	|	INTJ
ap-7652	476	2	n2j	n2j	INTJ
ap-7652	477	1	|	|	ADV
ap-7652	477	2	−j(2j	−j(2j	NOUN
ap-7652	477	3	+	+	NOUN
ap-7652	477	4	1	1	NUM
ap-7652	477	5	)	)	PUNCT
ap-7652	477	6	>	>	PUNCT
ap-7652	478	1	(	(	PUNCT
ap-7652	478	2	n1	n1	PROPN
ap-7652	478	3	−	−	PROPN
ap-7652	478	4	1)(δ′	1)(δ′	NUM
ap-7652	478	5	1	1	NUM
ap-7652	478	6	−	−	NUM
ap-7652	478	7	1	1	NUM
ap-7652	478	8	)	)	PUNCT
ap-7652	478	9	≥	≥	NOUN
ap-7652	478	10	1	1	NUM
ap-7652	478	11	.	.	PUNCT
ap-7652	478	12	(	(	PUNCT
ap-7652	478	13	123	123	NUM
ap-7652	478	14	)	)	PUNCT
ap-7652	478	15	in	in	ADP
ap-7652	478	16	both	both	DET
ap-7652	478	17	cases	case	NOUN
ap-7652	478	18	the	the	DET
ap-7652	478	19	pre	pre	NOUN
ap-7652	478	20	-	-	NOUN
ap-7652	478	21	requisites	requisite	NOUN
ap-7652	478	22	of	of	ADP
ap-7652	478	23	the	the	DET
ap-7652	478	24	bochner	bochner	NOUN
ap-7652	478	25	theorem	theorem	NOUN
ap-7652	478	26	are	be	AUX
ap-7652	478	27	invalid	invalid	ADJ
ap-7652	478	28	as	as	SCONJ
ap-7652	478	29	expected	expect	VERB
ap-7652	478	30	[	[	X
ap-7652	478	31	46	46	NUM
ap-7652	478	32	]	]	PUNCT
ap-7652	478	33	.	.	PUNCT
ap-7652	479	1	the	the	DET
ap-7652	479	2	liouville	liouville	NOUN
ap-7652	479	3	potentials	potential	VERB
ap-7652	479	4	in	in	ADP
ap-7652	479	5	question	question	NOUN
ap-7652	479	6	can	can	AUX
ap-7652	479	7	be	be	AUX
ap-7652	479	8	thus	thus	ADV
ap-7652	479	9	expressed	express	VERB
ap-7652	479	10	in	in	ADP
ap-7652	479	11	terms	term	NOUN
ap-7652	479	12	of	of	ADP
ap-7652	479	13	the	the	DET
ap-7652	479	14	admissible	admissible	ADJ
ap-7652	479	15	wronskians	wronskian	NOUN
ap-7652	479	16	∞w[y	∞w[y	NOUN
ap-7652	479	17	;	;	PUNCT
ap-7652	479	18	a	a	DET
ap-7652	479	19	|	|	NOUN
ap-7652	479	20	−	−	NOUN
ap-7652	479	21	...	...	PUNCT
ap-7652	480	1	n2j	n2j	PROPN
ap-7652	480	2	]	]	X
ap-7652	480	3	as	as	SCONJ
ap-7652	480	4	follows	follow	VERB
ap-7652	480	5	∞v	∞v	PUNCT
ap-7652	481	1	[	[	X
ap-7652	481	2	y	y	X
ap-7652	481	3	;	;	PUNCT
ap-7652	481	4	a	a	DET
ap-7652	481	5	|	|	NOUN
ap-7652	481	6	−	−	NOUN
ap-7652	481	7	...	...	PUNCT
ap-7652	481	8	n2j	n2j	PROPN
ap-7652	481	9	]	]	X
ap-7652	481	10	=	=	PUNCT
ap-7652	481	11	∞v	∞v	NUM
ap-7652	482	1	[	[	X
ap-7652	482	2	y	y	X
ap-7652	482	3	;	;	PUNCT
ap-7652	482	4	a−	a−	X
ap-7652	482	5	2j	2j	X
ap-7652	482	6	]	]	PUNCT
ap-7652	483	1	−	−	PROPN
ap-7652	483	2	2y	2y	PROPN
ap-7652	484	1	d	d	NOUN
ap-7652	484	2	dy	dy	X
ap-7652	484	3	(	(	PUNCT
ap-7652	484	4	y	y	PROPN
ap-7652	484	5	ld∞w[y	ld∞w[y	PROPN
ap-7652	484	6	;	;	PUNCT
ap-7652	484	7	a	a	DET
ap-7652	484	8	|	|	NOUN
ap-7652	484	9	−	−	NOUN
ap-7652	484	10	...	...	PUNCT
ap-7652	484	11	n2j	n2j	PROPN
ap-7652	484	12	]	]	X
ap-7652	484	13	)	)	PUNCT
ap-7652	484	14	.	.	PUNCT
ap-7652	485	1	(	(	PUNCT
ap-7652	485	2	124	124	NUM
ap-7652	485	3	)	)	PUNCT
ap-7652	485	4	we	we	PRON
ap-7652	485	5	refer	refer	VERB
ap-7652	485	6	the	the	DET
ap-7652	485	7	reader	reader	NOUN
ap-7652	485	8	to	to	PART
ap-7652	485	9	conjectures	conjecture	VERB
ap-7652	485	10	in	in	ADP
ap-7652	485	11	[	[	X
ap-7652	485	12	51	51	NUM
ap-7652	485	13	]	]	PUNCT
ap-7652	485	14	to	to	PART
ap-7652	485	15	verify	verify	VERB
ap-7652	485	16	that	that	SCONJ
ap-7652	485	17	the	the	DET
ap-7652	485	18	number	number	NOUN
ap-7652	485	19	of	of	ADP
ap-7652	485	20	zeros	zero	NOUN
ap-7652	485	21	of	of	ADP
ap-7652	485	22	each	each	DET
ap-7652	485	23	wronskian	wronskian	NOUN
ap-7652	485	24	in	in	ADP
ap-7652	485	25	the	the	DET
ap-7652	485	26	constructed	construct	VERB
ap-7652	485	27	orthogonal	orthogonal	ADJ
ap-7652	485	28	polynomial	polynomial	ADJ
ap-7652	485	29	set	set	NOUN
ap-7652	485	30	changes	change	NOUN
ap-7652	485	31	exactly	exactly	ADV
ap-7652	485	32	by	by	ADP
ap-7652	485	33	1	1	NUM
ap-7652	485	34	even	even	ADV
ap-7652	485	35	if	if	SCONJ
ap-7652	485	36	a	a	DET
ap-7652	485	37	jump	jump	NOUN
ap-7652	485	38	in	in	ADP
ap-7652	485	39	the	the	DET
ap-7652	485	40	polynomial	polynomial	ADJ
ap-7652	485	41	degree	degree	NOUN
ap-7652	485	42	is	be	AUX
ap-7652	485	43	larger	large	ADJ
ap-7652	485	44	than	than	ADP
ap-7652	485	45	1	1	NUM
ap-7652	485	46	.	.	PUNCT
ap-7652	486	1	however	however	ADV
ap-7652	486	2	112	112	NUM
ap-7652	486	3	vol	vol	NOUN
ap-7652	486	4	.	.	PUNCT
ap-7652	487	1	62	62	NUM
ap-7652	487	2	no	no	INTJ
ap-7652	487	3	.	.	PUNCT
ap-7652	488	1	1/2022	1/2022	NUM
ap-7652	488	2	quantization	quantization	NOUN
ap-7652	488	3	of	of	ADP
ap-7652	488	4	rationally	rationally	ADV
ap-7652	488	5	deformed	deform	VERB
ap-7652	488	6	morse	morse	ADJ
ap-7652	488	7	potentials	potential	NOUN
ap-7652	488	8	.	.	PUNCT
ap-7652	488	9	.	.	PUNCT
ap-7652	488	10	.	.	PUNCT
ap-7652	489	1	even	even	ADV
ap-7652	489	2	if	if	SCONJ
ap-7652	489	3	we	we	PRON
ap-7652	489	4	take	take	VERB
ap-7652	489	5	advantage	advantage	NOUN
ap-7652	489	6	of	of	ADP
ap-7652	489	7	these	these	DET
ap-7652	489	8	elegant	elegant	ADJ
ap-7652	489	9	results	result	NOUN
ap-7652	489	10	we	we	PRON
ap-7652	489	11	still	still	ADV
ap-7652	489	12	need	need	VERB
ap-7652	489	13	to	to	PART
ap-7652	489	14	prove	prove	VERB
ap-7652	489	15	that	that	SCONJ
ap-7652	489	16	there	there	PRON
ap-7652	489	17	are	be	VERB
ap-7652	489	18	no	no	DET
ap-7652	489	19	additional	additional	ADJ
ap-7652	489	20	eigenfunctions	eigenfunction	NOUN
ap-7652	489	21	with	with	ADP
ap-7652	489	22	a	a	DET
ap-7652	489	23	number	number	NOUN
ap-7652	489	24	of	of	ADP
ap-7652	489	25	nodes	node	NOUN
ap-7652	489	26	larger	large	ADJ
ap-7652	489	27	than	than	ADP
ap-7652	489	28	n(a	n(a	NOUN
ap-7652	489	29	)	)	PUNCT
ap-7652	489	30	−	−	NOUN
ap-7652	490	1	2j	2j	NOUN
ap-7652	490	2	−	−	NOUN
ap-7652	490	3	1	1	NUM
ap-7652	490	4	.	.	PUNCT
ap-7652	491	1	in	in	ADP
ap-7652	491	2	contrast	contrast	NOUN
ap-7652	491	3	with	with	ADP
ap-7652	491	4	the	the	DET
ap-7652	491	5	analysis	analysis	NOUN
ap-7652	491	6	presented	present	VERB
ap-7652	491	7	in	in	ADP
ap-7652	491	8	the	the	DET
ap-7652	491	9	previous	previous	ADJ
ap-7652	491	10	section	section	NOUN
ap-7652	491	11	,	,	PUNCT
ap-7652	491	12	this	this	DET
ap-7652	491	13	proof	proof	NOUN
ap-7652	491	14	is	be	AUX
ap-7652	491	15	complicated	complicate	VERB
ap-7652	491	16	by	by	ADP
ap-7652	491	17	the	the	DET
ap-7652	491	18	fact	fact	NOUN
ap-7652	491	19	that	that	SCONJ
ap-7652	491	20	the	the	DET
ap-7652	491	21	rdt	rdt	PROPN
ap-7652	491	22	at	at	ADP
ap-7652	491	23	each	each	DET
ap-7652	491	24	odd	odd	ADJ
ap-7652	491	25	step	step	NOUN
ap-7652	491	26	results	result	NOUN
ap-7652	491	27	in	in	ADP
ap-7652	491	28	a	a	DET
ap-7652	491	29	non	non	ADJ
ap-7652	491	30	-	-	ADJ
ap-7652	491	31	solvable	solvable	ADJ
ap-7652	491	32	rsle	rsle	NOUN
ap-7652	491	33	with	with	ADP
ap-7652	491	34	singularities	singularity	NOUN
ap-7652	491	35	on	on	ADP
ap-7652	491	36	the	the	DET
ap-7652	491	37	positive	positive	ADJ
ap-7652	491	38	semi	semi	ADJ
ap-7652	491	39	-	-	ADJ
ap-7652	491	40	axis	axis	ADJ
ap-7652	491	41	.	.	PUNCT
ap-7652	492	1	luckily	luckily	ADV
ap-7652	492	2	we	we	PRON
ap-7652	492	3	deal	deal	VERB
ap-7652	492	4	with	with	ADP
ap-7652	492	5	the	the	DET
ap-7652	492	6	tfi	tfi	NOUN
ap-7652	492	7	csle	csle	NOUN
ap-7652	492	8	so	so	SCONJ
ap-7652	492	9	its	its	PRON
ap-7652	492	10	rdct	rdct	ADJ
ap-7652	492	11	using	use	VERB
ap-7652	492	12	juxtaposed	juxtapose	VERB
ap-7652	492	13	pairs	pair	NOUN
ap-7652	492	14	of	of	ADP
ap-7652	492	15	eigenfunctions	eigenfunction	NOUN
ap-7652	492	16	can	can	AUX
ap-7652	492	17	be	be	AUX
ap-7652	492	18	alternatively	alternatively	ADV
ap-7652	492	19	obtained	obtain	VERB
ap-7652	492	20	via	via	ADP
ap-7652	492	21	sequential	sequential	ADJ
ap-7652	492	22	rdts	rdts	NOUN
ap-7652	492	23	with	with	ADP
ap-7652	492	24	seed	seed	NOUN
ap-7652	492	25	solutions	solution	NOUN
ap-7652	492	26	from	from	ADP
ap-7652	492	27	the	the	DET
ap-7652	492	28	second	second	ADJ
ap-7652	492	29	sequence	sequence	NOUN
ap-7652	493	1	+	+	PROPN
ap-7652	493	2	,	,	PUNCT
ap-7652	493	3	m	m	AUX
ap-7652	493	4	[	[	X
ap-7652	493	5	11	11	NUM
ap-7652	493	6	,	,	PUNCT
ap-7652	493	7	19	19	NUM
ap-7652	493	8	]	]	PUNCT
ap-7652	493	9	.	.	PUNCT
ap-7652	494	1	namely	namely	ADV
ap-7652	494	2	,	,	PUNCT
ap-7652	494	3	as	as	SCONJ
ap-7652	494	4	already	already	ADV
ap-7652	494	5	mentioned	mention	VERB
ap-7652	494	6	in	in	ADP
ap-7652	494	7	the	the	DET
ap-7652	494	8	end	end	NOUN
ap-7652	494	9	of	of	ADP
ap-7652	494	10	section	section	NOUN
ap-7652	494	11	2	2	NUM
ap-7652	494	12	the	the	DET
ap-7652	494	13	conjugated	conjugate	VERB
ap-7652	494	14	partition	partition	NOUN
ap-7652	494	15	m+	m+	NUM
ap-7652	494	16	|δ1→l|	|δ1→l|	NOUN
ap-7652	494	17	=	=	SYM
ap-7652	494	18	m(∆1→l	m(∆1→l	PROPN
ap-7652	494	19	)	)	PUNCT
ap-7652	494	20	(	(	PUNCT
ap-7652	494	21	125	125	NUM
ap-7652	494	22	)	)	PUNCT
ap-7652	494	23	is	be	AUX
ap-7652	494	24	formed	form	VERB
ap-7652	494	25	by	by	ADP
ap-7652	494	26	alternating	alternate	VERB
ap-7652	494	27	even	even	ADV
ap-7652	494	28	and	and	CCONJ
ap-7652	494	29	odd	odd	ADJ
ap-7652	494	30	integers	integer	NOUN
ap-7652	494	31	starting	start	VERB
ap-7652	494	32	from	from	ADP
ap-7652	494	33	an	an	DET
ap-7652	494	34	even	even	ADV
ap-7652	494	35	integer	integer	NOUN
ap-7652	494	36	δ′	δ′	NOUN
ap-7652	494	37	1	1	NUM
ap-7652	494	38	.	.	PUNCT
ap-7652	495	1	the	the	DET
ap-7652	495	2	reverse	reverse	NOUN
ap-7652	495	3	is	be	AUX
ap-7652	495	4	also	also	ADV
ap-7652	495	5	true	true	ADJ
ap-7652	495	6	:	:	PUNCT
ap-7652	495	7	if	if	SCONJ
ap-7652	495	8	the	the	DET
ap-7652	495	9	partition	partition	NOUN
ap-7652	495	10	m+	m+	NUM
ap-7652	495	11	p	p	NOUN
ap-7652	495	12	=	=	X
ap-7652	495	13	m(pδ1→lp	m(pδ1→lp	PROPN
ap-7652	495	14	;	;	PUNCT
ap-7652	495	15	pδ′	pδ′	PROPN
ap-7652	495	16	1→lp	1→lp	NUM
ap-7652	495	17	)	)	PUNCT
ap-7652	495	18	(	(	PUNCT
ap-7652	495	19	126	126	NUM
ap-7652	495	20	)	)	PUNCT
ap-7652	495	21	is	be	AUX
ap-7652	495	22	composed	compose	VERB
ap-7652	495	23	of	of	ADP
ap-7652	495	24	alternating	alternate	VERB
ap-7652	495	25	even	even	ADV
ap-7652	495	26	and	and	CCONJ
ap-7652	495	27	odd	odd	ADJ
ap-7652	495	28	integers	integer	NOUN
ap-7652	495	29	starting	start	VERB
ap-7652	495	30	from	from	ADP
ap-7652	495	31	an	an	DET
ap-7652	495	32	even	even	ADV
ap-7652	495	33	integer	integer	NOUN
ap-7652	495	34	δ′	δ′	NOUN
ap-7652	495	35	1	1	NUM
ap-7652	495	36	then	then	ADV
ap-7652	495	37	each	each	DET
ap-7652	495	38	segment	segment	NOUN
ap-7652	495	39	of	of	ADP
ap-7652	495	40	the	the	DET
ap-7652	495	41	conjugated	conjugated	ADJ
ap-7652	495	42	partition	partition	NOUN
ap-7652	495	43	pn2jp	pn2jp	PROPN
ap-7652	495	44	=	=	SYM
ap-7652	495	45	m(pδ	m(pδ	PROPN
ap-7652	495	46	′	′	NUM
ap-7652	496	1	lp→1	lp→1	ADJ
ap-7652	496	2	;	;	PUNCT
ap-7652	496	3	pδlp→1	pδlp→1	PROPN
ap-7652	496	4	)	)	PUNCT
ap-7652	496	5	(	(	PUNCT
ap-7652	496	6	127	127	NUM
ap-7652	496	7	)	)	PUNCT
ap-7652	496	8	must	must	AUX
ap-7652	496	9	have	have	VERB
ap-7652	496	10	an	an	DET
ap-7652	496	11	even	even	ADJ
ap-7652	496	12	length	length	NOUN
ap-7652	496	13	,	,	PUNCT
ap-7652	496	14	with	with	ADP
ap-7652	496	15	the	the	DET
ap-7652	496	16	largest	large	ADJ
ap-7652	496	17	element	element	NOUN
ap-7652	496	18	m+	m+	NOUN
ap-7652	496	19	|pδ′	|pδ′	NOUN
ap-7652	496	20	1→lp	1→lp	NUM
ap-7652	496	21	|	|	NOUN
ap-7652	496	22	=|	=|	NOUN
ap-7652	496	23	p∆1→lp	p∆1→lp	ADJ
ap-7652	496	24	|	|	ADV
ap-7652	496	25	−1	−1	NOUN
ap-7652	496	26	=	=	SYM
ap-7652	496	27	m|pδlp→1|	m|pδlp→1|	PART
ap-7652	496	28	∈	∈	PROPN
ap-7652	496	29	pn2jp	pn2jp	PROPN
ap-7652	496	30	,	,	PUNCT
ap-7652	496	31	(	(	PUNCT
ap-7652	496	32	128	128	NUM
ap-7652	496	33	)	)	PUNCT
ap-7652	496	34	where	where	SCONJ
ap-7652	496	35	p∆1→lp	p∆1→lp	ADJ
ap-7652	496	36	≡	≡	PROPN
ap-7652	496	37	pδ1→lp	pδ1→lp	PROPN
ap-7652	496	38	;	;	PUNCT
ap-7652	496	39	pδ′	pδ′	PROPN
ap-7652	496	40	1→lp	1→lp	NUM
ap-7652	496	41	.	.	PUNCT
ap-7652	497	1	making	make	VERB
ap-7652	497	2	use	use	NOUN
ap-7652	497	3	of	of	ADP
ap-7652	497	4	(	(	PUNCT
ap-7652	497	5	37	37	NUM
ap-7652	497	6	)	)	PUNCT
ap-7652	497	7	one	one	PRON
ap-7652	497	8	can	can	AUX
ap-7652	497	9	verify	verify	VERB
ap-7652	497	10	that	that	SCONJ
ap-7652	497	11	quasi	quasi	ADJ
ap-7652	497	12	-	-	ADJ
ap-7652	497	13	rational	rational	ADJ
ap-7652	497	14	functions	function	NOUN
ap-7652	497	15	(	(	PUNCT
ap-7652	497	16	30	30	NUM
ap-7652	497	17	)	)	PUNCT
ap-7652	497	18	can	can	AUX
ap-7652	497	19	be	be	AUX
ap-7652	497	20	decomposed	decompose	VERB
ap-7652	497	21	as	as	ADP
ap-7652	497	22	∞χ∓n	∞χ∓n	NOUN
ap-7652	498	1	[	[	X
ap-7652	498	2	y	y	X
ap-7652	498	3	;	;	PUNCT
ap-7652	498	4	a	a	X
ap-7652	498	5	]	]	X
ap-7652	498	6	=	=	PUNCT
ap-7652	498	7	y1/2n(n−1)∓nδ[ξ]∞ϕn	y1/2n(n−1)∓nδ[ξ]∞ϕn	PROPN
ap-7652	498	8	±,0[y	±,0[y	PROPN
ap-7652	498	9	;	;	PUNCT
ap-7652	498	10	a(δ	a(δ	NUM
ap-7652	498	11	)	)	PUNCT
ap-7652	498	12	]	]	PUNCT
ap-7652	498	13	(	(	PUNCT
ap-7652	498	14	129	129	NUM
ap-7652	498	15	)	)	PUNCT
ap-7652	498	16	and	and	CCONJ
ap-7652	498	17	therefore	therefore	ADV
ap-7652	498	18	the	the	DET
ap-7652	498	19	denominators	denominator	NOUN
ap-7652	498	20	of	of	ADP
ap-7652	498	21	the	the	DET
ap-7652	498	22	fractions	fraction	NOUN
ap-7652	498	23	in	in	ADP
ap-7652	498	24	equivalence	equivalence	NOUN
ap-7652	498	25	relations	relation	NOUN
ap-7652	498	26	(	(	PUNCT
ap-7652	498	27	29	29	NUM
ap-7652	498	28	)	)	PUNCT
ap-7652	498	29	take	take	VERB
ap-7652	498	30	form	form	NOUN
ap-7652	498	31	y−1/2|δl|(|δl|−1	y−1/2|δl|(|δl|−1	NOUN
ap-7652	498	32	)	)	PUNCT
ap-7652	498	33	l∏	l∏	PROPN
ap-7652	499	1	l=1	l=1	NOUN
ap-7652	500	1	∞χ−δl	∞χ−δl	NOUN
ap-7652	501	1	[	[	X
ap-7652	501	2	y	y	NOUN
ap-7652	501	3	;	;	PUNCT
ap-7652	501	4	a(|∆′	a(|∆′	X
ap-7652	501	5	l→1|−δ	l→1|−δ	ADV
ap-7652	501	6	)	)	PUNCT
ap-7652	501	7	]	]	PUNCT
ap-7652	502	1	=	=	PUNCT
ap-7652	502	2	yσl	yσl	NOUN
ap-7652	502	3	∞ϕ	∞ϕ	ADP
ap-7652	502	4	|δl|	|δl|	ADV
ap-7652	502	5	−,0	−,0	PROPN
ap-7652	503	1	[	[	X
ap-7652	503	2	y	y	X
ap-7652	503	3	;	;	PUNCT
ap-7652	503	4	a	a	X
ap-7652	503	5	]	]	X
ap-7652	503	6	(	(	PUNCT
ap-7652	503	7	130	130	NUM
ap-7652	503	8	)	)	PUNCT
ap-7652	503	9	y−1/2|δ′	y−1/2|δ′	NOUN
ap-7652	503	10	l|(|δ′	l|(|δ′	ADJ
ap-7652	503	11	l|−1	l|−1	PROPN
ap-7652	503	12	)	)	PUNCT
ap-7652	504	1	l∏	l∏	PROPN
ap-7652	505	1	l=1	l=1	NOUN
ap-7652	505	2	∞χ−δ′	∞χ−δ′	NOUN
ap-7652	506	1	l	l	NOUN
ap-7652	507	1	[	[	X
ap-7652	507	2	y	y	NOUN
ap-7652	507	3	;	;	PUNCT
ap-7652	507	4	a(|∆′	a(|∆′	ADJ
ap-7652	507	5	l→1|−δ′	l→1|−δ′	PROPN
ap-7652	507	6	)	)	PUNCT
ap-7652	507	7	]	]	PUNCT
ap-7652	508	1	=	=	PUNCT
ap-7652	508	2	yσl	yσl	ADJ
ap-7652	508	3	∞ϕ	∞ϕ	NUM
ap-7652	508	4	|δ′	|δ′	PROPN
ap-7652	508	5	l|	l|	ADJ
ap-7652	509	1	−,0	−,0	PROPN
ap-7652	509	2	[	[	X
ap-7652	509	3	y	y	NOUN
ap-7652	509	4	;	;	PUNCT
ap-7652	509	5	a(|∆1→l|	a(|∆1→l|	PROPN
ap-7652	509	6	)	)	PUNCT
ap-7652	509	7	]	]	PUNCT
ap-7652	509	8	(	(	PUNCT
ap-7652	509	9	131	131	NUM
ap-7652	509	10	)	)	PUNCT
ap-7652	509	11	accordingly	accordingly	ADV
ap-7652	509	12	,	,	PUNCT
ap-7652	509	13	where	where	SCONJ
ap-7652	509	14	|	|	ADV
ap-7652	509	15	∆1→l	∆1→l	PROPN
ap-7652	509	16	|=|	|=|	PROPN
ap-7652	509	17	∆′	∆′	PROPN
ap-7652	509	18	l→1	l→1	NOUN
ap-7652	509	19	|	|	ADV
ap-7652	509	20	and	and	CCONJ
ap-7652	509	21	σl	σl	ADP
ap-7652	509	22	=	=	NOUN
ap-7652	509	23	l∑	l∑	NUM
ap-7652	510	1	l=1	l=1	PROPN
ap-7652	510	2	δ′	δ′	NOUN
ap-7652	510	3	l(δl	l(δl	NOUN
ap-7652	510	4	+	+	CCONJ
ap-7652	510	5	l∑	l∑	NUM
ap-7652	510	6	˜	˜	PROPN
ap-7652	510	7	l	l	PROPN
ap-7652	511	1	=	=	PROPN
ap-7652	511	2	l+1	l+1	NOUN
ap-7652	511	3	δ	δ	NOUN
ap-7652	511	4	˜	˜	PROPN
ap-7652	511	5	l	l	PROPN
ap-7652	511	6	)	)	PUNCT
ap-7652	511	7	=	=	PUNCT
ap-7652	512	1	l∑	l∑	PUNCT
ap-7652	513	1	l=1	l=1	X
ap-7652	513	2	δl(δ′	δl(δ′	INTJ
ap-7652	514	1	l	l	PROPN
ap-7652	514	2	+	+	CCONJ
ap-7652	514	3	l−1∑	l−1∑	ADJ
ap-7652	514	4	˜	˜	PROPN
ap-7652	514	5	l=1	l=1	PROPN
ap-7652	514	6	δ′	δ′	PROPN
ap-7652	514	7	˜	˜	PROPN
ap-7652	514	8	l	l	PROPN
ap-7652	514	9	)	)	PUNCT
ap-7652	514	10	.	.	PUNCT
ap-7652	515	1	(	(	PUNCT
ap-7652	515	2	132	132	NUM
ap-7652	515	3	)	)	PUNCT
ap-7652	515	4	we	we	PRON
ap-7652	515	5	thus	thus	ADV
ap-7652	515	6	come	come	VERB
ap-7652	515	7	to	to	ADP
ap-7652	515	8	the	the	DET
ap-7652	515	9	following	follow	VERB
ap-7652	515	10	equivalence	equivalence	NOUN
ap-7652	515	11	theorem	theorem	VERB
ap-7652	515	12	for	for	ADP
ap-7652	515	13	the	the	DET
ap-7652	515	14	wronskians	wronskian	NOUN
ap-7652	515	15	of	of	ADP
ap-7652	515	16	generalized	generalized	ADJ
ap-7652	515	17	bessel	bessel	NOUN
ap-7652	515	18	polynomials	polynomial	NOUN
ap-7652	515	19	∞ŵ[y	∞ŵ[y	NOUN
ap-7652	515	20	;	;	PUNCT
ap-7652	516	1	a	a	DET
ap-7652	516	2	|	|	NOUN
ap-7652	516	3	+	+	CCONJ
ap-7652	516	4	...	...	PUNCT
ap-7652	516	5	m(∆1→l	m(∆1→l	PROPN
ap-7652	516	6	)	)	PUNCT
ap-7652	516	7	]	]	PUNCT
ap-7652	517	1	=	=	SYM
ap-7652	517	2	∞ŵ[y	∞ŵ[y	PROPN
ap-7652	517	3	;	;	PUNCT
ap-7652	517	4	a(|∆1→l|	a(|∆1→l|	PROPN
ap-7652	517	5	)	)	PUNCT
ap-7652	517	6	|	|	ADV
ap-7652	517	7	−	−	NOUN
ap-7652	517	8	...	...	PUNCT
ap-7652	518	1	m(∆′	m(∆′	NOUN
ap-7652	518	2	l→1	l→1	NOUN
ap-7652	518	3	)	)	PUNCT
ap-7652	518	4	]	]	PUNCT
ap-7652	518	5	.	.	PUNCT
ap-7652	519	1	(	(	PUNCT
ap-7652	519	2	133	133	NUM
ap-7652	519	3	)	)	PUNCT
ap-7652	519	4	note	note	VERB
ap-7652	519	5	that	that	SCONJ
ap-7652	519	6	decomposition	decomposition	NOUN
ap-7652	519	7	(	(	PUNCT
ap-7652	519	8	129	129	NUM
ap-7652	519	9	)	)	PUNCT
ap-7652	519	10	holds	hold	VERB
ap-7652	519	11	for	for	ADP
ap-7652	519	12	any	any	DET
ap-7652	519	13	tfi	tfi	NOUN
ap-7652	519	14	csle	csle	NOUN
ap-7652	519	15	of	of	ADP
ap-7652	519	16	group	group	PROPN
ap-7652	519	17	a	a	DET
ap-7652	519	18	provided	provide	VERB
ap-7652	519	19	that	that	SCONJ
ap-7652	519	20	we	we	PRON
ap-7652	519	21	replace	replace	VERB
ap-7652	519	22	y2	y2	PROPN
ap-7652	519	23	for	for	ADP
ap-7652	519	24	the	the	DET
ap-7652	519	25	leading	lead	VERB
ap-7652	519	26	coefficient	coefficient	NOUN
ap-7652	519	27	lσ[y	lσ[y	PROPN
ap-7652	519	28	]	]	PUNCT
ap-7652	519	29	of	of	ADP
ap-7652	519	30	the	the	DET
ap-7652	519	31	corresponding	corresponding	PROPN
ap-7652	519	32	counter	counter	NOUN
ap-7652	519	33	-	-	NOUN
ap-7652	519	34	parts	part	NOUN
ap-7652	519	35	of	of	ADP
ap-7652	519	36	differential	differential	ADJ
ap-7652	519	37	eigenequations	eigenequation	NOUN
ap-7652	519	38	(	(	PUNCT
ap-7652	519	39	46	46	NUM
ap-7652	519	40	)	)	PUNCT
ap-7652	519	41	.	.	PUNCT
ap-7652	520	1	this	this	PRON
ap-7652	520	2	brings	bring	VERB
ap-7652	520	3	us	we	PRON
ap-7652	520	4	to	to	ADP
ap-7652	520	5	the	the	DET
ap-7652	520	6	equivalence	equivalence	NOUN
ap-7652	520	7	relations	relation	NOUN
ap-7652	520	8	for	for	ADP
ap-7652	520	9	polynomial	polynomial	ADJ
ap-7652	520	10	wronskians	wronskian	NOUN
ap-7652	520	11	discovered	discover	VERB
ap-7652	520	12	by	by	ADP
ap-7652	520	13	odake	odake	NOUN
ap-7652	520	14	and	and	CCONJ
ap-7652	520	15	sasaki	sasaki	PROPN
ap-7652	520	16	[	[	X
ap-7652	520	17	19	19	NUM
ap-7652	520	18	]	]	PUNCT
ap-7652	520	19	in	in	ADP
ap-7652	520	20	their	their	PRON
ap-7652	520	21	pioneering	pioneer	VERB
ap-7652	520	22	analysis	analysis	NOUN
ap-7652	520	23	of	of	ADP
ap-7652	520	24	tsi	tsi	PROPN
ap-7652	520	25	potentials	potential	NOUN
ap-7652	520	26	from	from	ADP
ap-7652	520	27	group	group	NOUN
ap-7652	520	28	a.	a.	NOUN
ap-7652	520	29	if	if	SCONJ
ap-7652	520	30	a	a	DET
ap-7652	520	31	>	>	X
ap-7652	520	32	1/2	1/2	NUM
ap-7652	520	33	then	then	ADV
ap-7652	520	34	,	,	PUNCT
ap-7652	520	35	according	accord	VERB
ap-7652	520	36	to	to	ADP
ap-7652	520	37	(	(	PUNCT
ap-7652	520	38	128	128	NUM
ap-7652	520	39	)	)	PUNCT
ap-7652	520	40	,	,	PUNCT
ap-7652	520	41	the	the	DET
ap-7652	520	42	largest	large	ADJ
ap-7652	520	43	element	element	NOUN
ap-7652	520	44	of	of	ADP
ap-7652	520	45	the	the	DET
ap-7652	520	46	partition	partition	NOUN
ap-7652	520	47	pn2jp	pn2jp	PROPN
ap-7652	520	48	is	be	AUX
ap-7652	520	49	smaller	small	ADJ
ap-7652	520	50	than	than	ADP
ap-7652	520	51	a+	a+	PUNCT
ap-7652	520	52	|	|	ADV
ap-7652	520	53	p∆l→lp	p∆l→lp	ADJ
ap-7652	520	54	|	|	ADV
ap-7652	520	55	−1/2	−1/2	ADJ
ap-7652	521	1	and	and	CCONJ
ap-7652	521	2	therefore	therefore	ADV
ap-7652	521	3	the	the	DET
ap-7652	521	4	wronskian	wronskian	NOUN
ap-7652	521	5	in	in	ADP
ap-7652	521	6	the	the	DET
ap-7652	521	7	right	right	ADJ
ap-7652	521	8	-	-	PUNCT
ap-7652	521	9	hand	hand	NOUN
ap-7652	521	10	side	side	NOUN
ap-7652	521	11	of	of	ADP
ap-7652	521	12	(	(	PUNCT
ap-7652	521	13	133	133	NUM
ap-7652	521	14	)	)	PUNCT
ap-7652	521	15	with	with	ADP
ap-7652	521	16	∆′	∆′	PROPN
ap-7652	521	17	l→1	l→1	PROPN
ap-7652	521	18	replaced	replace	VERB
ap-7652	521	19	for	for	ADP
ap-7652	521	20	p∆′	p∆′	X
ap-7652	522	1	lp→1	lp→1	PROPN
ap-7652	522	2	is	be	AUX
ap-7652	522	3	formed	form	VERB
ap-7652	522	4	by	by	ADP
ap-7652	522	5	juxtaposed	juxtapose	VERB
ap-7652	522	6	pairs	pair	NOUN
ap-7652	522	7	of	of	ADP
ap-7652	522	8	r	r	NOUN
ap-7652	522	9	-	-	PUNCT
ap-7652	522	10	bessel	bessel	ADJ
ap-7652	522	11	polynomials	polynomial	NOUN
ap-7652	522	12	.	.	PUNCT
ap-7652	523	1	this	this	PRON
ap-7652	523	2	confirms	confirm	VERB
ap-7652	523	3	that	that	SCONJ
ap-7652	523	4	none	none	NOUN
ap-7652	523	5	of	of	ADP
ap-7652	523	6	the	the	DET
ap-7652	523	7	polynomial	polynomial	ADJ
ap-7652	523	8	wronskians	wronskian	NOUN
ap-7652	523	9	∞ŵ[y	∞ŵ[y	PROPN
ap-7652	523	10	;	;	PUNCT
ap-7652	523	11	a	a	DET
ap-7652	523	12	|	|	NOUN
ap-7652	523	13	+	+	CCONJ
ap-7652	523	14	...	...	PUNCT
ap-7652	523	15	m+	m+	NUM
ap-7652	523	16	p	p	X
ap-7652	523	17	]	]	PUNCT
ap-7652	523	18	has	have	VERB
ap-7652	523	19	zeros	zero	NOUN
ap-7652	523	20	on	on	ADP
ap-7652	523	21	the	the	DET
ap-7652	523	22	positive	positive	ADJ
ap-7652	523	23	semi	semi	ADJ
ap-7652	523	24	-	-	ADJ
ap-7652	523	25	axis	axis	ADJ
ap-7652	523	26	and	and	CCONJ
ap-7652	523	27	therefore	therefore	ADV
ap-7652	523	28	each	each	DET
ap-7652	523	29	partition	partition	NOUN
ap-7652	523	30	m+	m+	PRON
ap-7652	523	31	p	p	NOUN
ap-7652	523	32	specifies	specify	VERB
ap-7652	523	33	an	an	DET
ap-7652	523	34	admissible	admissible	ADJ
ap-7652	523	35	sequence	sequence	NOUN
ap-7652	523	36	of	of	ADP
ap-7652	523	37	seed	seed	NOUN
ap-7652	523	38	solutions	solution	NOUN
ap-7652	523	39	∞ϕ+,mk	∞ϕ+,mk	NOUN
ap-7652	524	1	[	[	X
ap-7652	524	2	y	y	X
ap-7652	524	3	;	;	PUNCT
ap-7652	524	4	a	a	X
ap-7652	524	5	]	]	X
ap-7652	524	6	(	(	PUNCT
ap-7652	524	7	mk	mk	PROPN
ap-7652	524	8	∈	∈	PROPN
ap-7652	524	9	m+	m+	NUM
ap-7652	524	10	p	p	NOUN
ap-7652	524	11	for	for	ADP
ap-7652	524	12	k	k	PROPN
ap-7652	524	13	=	=	SYM
ap-7652	524	14	1	1	NUM
ap-7652	524	15	,	,	PUNCT
ap-7652	524	16	.	.	PUNCT
ap-7652	524	17	.	.	PUNCT
ap-7652	524	18	.	.	PUNCT
ap-7652	525	1	,	,	PUNCT
ap-7652	525	2	p	p	X
ap-7652	525	3	)	)	PUNCT
ap-7652	525	4	.	.	PUNCT
ap-7652	526	1	based	base	VERB
ap-7652	526	2	on	on	ADP
ap-7652	526	3	the	the	DET
ap-7652	526	4	arguments	argument	NOUN
ap-7652	526	5	presented	present	VERB
ap-7652	526	6	in	in	ADP
ap-7652	526	7	subsection	subsection	NOUN
ap-7652	526	8	3.2	3.2	NUM
ap-7652	526	9	we	we	PRON
ap-7652	526	10	thus	thus	ADV
ap-7652	526	11	assert	assert	VERB
ap-7652	526	12	that	that	SCONJ
ap-7652	526	13	the	the	DET
ap-7652	526	14	rdts	rdts	NOUN
ap-7652	526	15	in	in	ADP
ap-7652	526	16	question	question	NOUN
ap-7652	526	17	may	may	AUX
ap-7652	526	18	insert	insert	VERB
ap-7652	526	19	only	only	ADV
ap-7652	526	20	one	one	NUM
ap-7652	526	21	bound	bind	VERB
ap-7652	526	22	energy	energy	NOUN
ap-7652	526	23	level	level	NOUN
ap-7652	526	24	at	at	ADP
ap-7652	526	25	the	the	DET
ap-7652	526	26	energy	energy	NOUN
ap-7652	526	27	∞ε+,mp+1(a	∞ε+,mp+1(a	NOUN
ap-7652	526	28	)	)	PUNCT
ap-7652	526	29	which	which	PRON
ap-7652	526	30	by	by	ADP
ap-7652	526	31	definition	definition	NOUN
ap-7652	526	32	lies	lie	VERB
ap-7652	526	33	below	below	ADP
ap-7652	526	34	the	the	DET
ap-7652	526	35	ground	ground	NOUN
ap-7652	526	36	energy	energy	NOUN
ap-7652	526	37	level	level	NOUN
ap-7652	526	38	∞ε+,mp	∞ε+,mp	PUNCT
ap-7652	527	1	(	(	PUNCT
ap-7652	527	2	a	a	NOUN
ap-7652	527	3	)	)	PUNCT
ap-7652	527	4	of	of	ADP
ap-7652	527	5	the	the	DET
ap-7652	527	6	liouville	liouville	NOUN
ap-7652	527	7	potential	potential	NOUN
ap-7652	527	8	∞v	∞v	NUM
ap-7652	528	1	[	[	X
ap-7652	528	2	a	a	DET
ap-7652	528	3	|	|	NOUN
ap-7652	528	4	m+	m+	NOUN
ap-7652	528	5	p	p	NOUN
ap-7652	528	6	]	]	X
ap-7652	528	7	.	.	PUNCT
ap-7652	529	1	on	on	ADP
ap-7652	529	2	other	other	ADJ
ap-7652	529	3	hand	hand	NOUN
ap-7652	529	4	all	all	DET
ap-7652	529	5	the	the	DET
ap-7652	529	6	existent	existent	ADJ
ap-7652	529	7	energy	energy	NOUN
ap-7652	529	8	levels	level	NOUN
ap-7652	529	9	remain	remain	VERB
ap-7652	529	10	unchanged	unchanged	ADJ
ap-7652	529	11	.	.	PUNCT
ap-7652	530	1	as	as	ADP
ap-7652	530	2	the	the	DET
ap-7652	530	3	simplest	simple	ADJ
ap-7652	530	4	example	example	NOUN
ap-7652	530	5	we	we	PRON
ap-7652	530	6	can	can	AUX
ap-7652	530	7	cite	cite	VERB
ap-7652	530	8	the	the	DET
ap-7652	530	9	partition	partition	NOUN
ap-7652	530	10	1	1	NUM
ap-7652	530	11	,	,	PUNCT
ap-7652	530	12	2	2	NUM
ap-7652	530	13	,	,	PUNCT
ap-7652	530	14	.	.	PUNCT
ap-7652	530	15	.	.	PUNCT
ap-7652	531	1	.	.	PUNCT
ap-7652	532	1	,	,	PUNCT
ap-7652	532	2	2j	2j	NOUN
ap-7652	532	3	=	=	SYM
ap-7652	532	4	m(2j	m(2j	NOUN
ap-7652	532	5	,	,	PUNCT
ap-7652	532	6	1	1	NUM
ap-7652	532	7	)	)	PUNCT
ap-7652	532	8	=	=	NOUN
ap-7652	532	9	m	m	PROPN
ap-7652	532	10	†(1	†(1	NOUN
ap-7652	532	11	,	,	PUNCT
ap-7652	532	12	2j	2j	NUM
ap-7652	532	13	)	)	PUNCT
ap-7652	532	14	for	for	ADP
ap-7652	532	15	2j	2j	NUM
ap-7652	532	16	≤	≤	X
ap-7652	532	17	⌊a⌋	⌊a⌋	X
ap-7652	532	18	(	(	PUNCT
ap-7652	532	19	134	134	NUM
ap-7652	532	20	)	)	SYM
ap-7652	532	21	113	113	NUM
ap-7652	532	22	gregory	gregory	PROPN
ap-7652	532	23	natanson	natanson	PROPN
ap-7652	532	24	acta	acta	PROPN
ap-7652	532	25	polytechnica	polytechnica	PROPN
ap-7652	532	26	as	as	ADP
ap-7652	532	27	a	a	DET
ap-7652	532	28	direct	direct	ADJ
ap-7652	532	29	consequence	consequence	NOUN
ap-7652	532	30	of	of	ADP
ap-7652	532	31	the	the	DET
ap-7652	532	32	equivalence	equivalence	NOUN
ap-7652	532	33	theorem	theorem	VERB
ap-7652	532	34	we	we	PRON
ap-7652	532	35	find	find	VERB
ap-7652	533	1	that	that	DET
ap-7652	533	2	ŷ	ŷ	NUM
ap-7652	533	3	(	(	PUNCT
ap-7652	533	4	2a−2j−1,−2	2a−2j−1,−2	NUM
ap-7652	533	5	)	)	PUNCT
ap-7652	533	6	2j	2j	NOUN
ap-7652	533	7	(	(	PUNCT
ap-7652	533	8	y	y	NOUN
ap-7652	533	9	)	)	PUNCT
ap-7652	533	10	=	=	SYM
ap-7652	533	11	∞ŵ[y	∞ŵ[y	PROPN
ap-7652	533	12	;	;	PUNCT
ap-7652	533	13	a	a	DET
ap-7652	533	14	|	|	NOUN
ap-7652	533	15	−	−	NOUN
ap-7652	533	16	...	...	PUNCT
ap-7652	533	17	1	1	NUM
ap-7652	533	18	:	:	PUNCT
ap-7652	533	19	2j	2j	NUM
ap-7652	533	20	]	]	PUNCT
ap-7652	533	21	(	(	PUNCT
ap-7652	533	22	2j	2j	NUM
ap-7652	533	23	≤	≤	NUM
ap-7652	533	24	⌊a⌋	⌊a⌋	VERB
ap-7652	533	25	)	)	PUNCT
ap-7652	533	26	,	,	PUNCT
ap-7652	533	27	(	(	PUNCT
ap-7652	533	28	135	135	NUM
ap-7652	533	29	)	)	PUNCT
ap-7652	533	30	where	where	SCONJ
ap-7652	533	31	the	the	DET
ap-7652	533	32	wronskian	wronskian	NOUN
ap-7652	533	33	on	on	ADP
ap-7652	533	34	the	the	DET
ap-7652	533	35	right	right	NOUN
ap-7652	533	36	is	be	AUX
ap-7652	533	37	formed	form	VERB
ap-7652	533	38	by	by	ADP
ap-7652	533	39	2j	2j	NUM
ap-7652	533	40	sequential	sequential	ADJ
ap-7652	533	41	r	r	NOUN
ap-7652	533	42	-	-	PUNCT
ap-7652	533	43	bessel	bessel	ADJ
ap-7652	533	44	polynomials	polynomial	NOUN
ap-7652	533	45	of	of	ADP
ap-7652	533	46	non	non	ADJ
ap-7652	533	47	-	-	ADJ
ap-7652	533	48	zero	zero	NUM
ap-7652	533	49	degrees	degree	NOUN
ap-7652	533	50	smaller	small	ADJ
ap-7652	533	51	than	than	ADP
ap-7652	533	52	a	a	PRON
ap-7652	533	53	and	and	CCONJ
ap-7652	533	54	therefore	therefore	ADV
ap-7652	533	55	may	may	AUX
ap-7652	533	56	not	not	PART
ap-7652	533	57	have	have	VERB
ap-7652	533	58	positive	positive	ADJ
ap-7652	533	59	zeros	zero	NOUN
ap-7652	533	60	for	for	ADP
ap-7652	533	61	a	a	DET
ap-7652	533	62	>	>	X
ap-7652	533	63	−1/2	−1/2	PROPN
ap-7652	533	64	[	[	X
ap-7652	533	65	51	51	NUM
ap-7652	533	66	]	]	PUNCT
ap-7652	533	67	.	.	PUNCT
ap-7652	534	1	as	as	SCONJ
ap-7652	534	2	initially	initially	ADV
ap-7652	534	3	proven	prove	VERB
ap-7652	534	4	in	in	ADP
ap-7652	534	5	[	[	X
ap-7652	534	6	7	7	NUM
ap-7652	534	7	]	]	PUNCT
ap-7652	534	8	and	and	CCONJ
ap-7652	534	9	then	then	ADV
ap-7652	534	10	illuminated	illuminate	VERB
ap-7652	534	11	in	in	ADP
ap-7652	534	12	more	more	ADJ
ap-7652	534	13	details	detail	NOUN
ap-7652	534	14	in	in	ADP
ap-7652	534	15	[	[	X
ap-7652	534	16	8	8	NUM
ap-7652	534	17	]	]	PUNCT
ap-7652	534	18	using	use	VERB
ap-7652	534	19	the	the	DET
ap-7652	534	20	so	so	ADV
ap-7652	534	21	-	-	PUNCT
ap-7652	534	22	called	call	VERB
ap-7652	534	23	‘	'	PUNCT
ap-7652	534	24	kienast	kienast	ADJ
ap-7652	534	25	-	-	PUNCT
ap-7652	534	26	lawton	lawton	NOUN
ap-7652	534	27	-	-	PUNCT
ap-7652	534	28	hahn	hahn	PROPN
ap-7652	534	29	’s	’s	PART
ap-7652	534	30	theorem	theorem	ADJ
ap-7652	534	31	’	'	PUNCT
ap-7652	534	32	[	[	X
ap-7652	534	33	52–54	52–54	NUM
ap-7652	534	34	]	]	X
ap-7652	534	35	the	the	DET
ap-7652	534	36	latter	latter	ADJ
ap-7652	534	37	assertion	assertion	NOUN
ap-7652	534	38	holds	hold	VERB
ap-7652	534	39	for	for	ADP
ap-7652	534	40	any	any	DET
ap-7652	534	41	positive	positive	ADJ
ap-7652	534	42	j	j	NOUN
ap-7652	534	43	despite	despite	SCONJ
ap-7652	534	44	the	the	DET
ap-7652	534	45	fact	fact	NOUN
ap-7652	534	46	that	that	SCONJ
ap-7652	534	47	the	the	DET
ap-7652	534	48	seed	seed	NOUN
ap-7652	534	49	functions	function	NOUN
ap-7652	534	50	∞	∞	NUM
ap-7652	534	51	̸ψ−,m	̸ψ−,m	X
ap-7652	535	1	[	[	X
ap-7652	535	2	y	y	X
ap-7652	535	3	;	;	PUNCT
ap-7652	535	4	a(2j+1	a(2j+1	NOUN
ap-7652	535	5	)	)	PUNCT
ap-7652	535	6	]	]	PUNCT
ap-7652	535	7	have	have	VERB
ap-7652	535	8	nodes	node	NOUN
ap-7652	535	9	on	on	ADP
ap-7652	535	10	the	the	DET
ap-7652	535	11	positive	positive	ADJ
ap-7652	535	12	semi	semi	NOUN
ap-7652	535	13	-	-	ADJ
ap-7652	535	14	axis	axis	ADJ
ap-7652	535	15	for	for	ADP
ap-7652	535	16	a(2j+1	a(2j+1	NOUN
ap-7652	535	17	)	)	PUNCT
ap-7652	535	18	+	+	NUM
ap-7652	535	19	1/2	1/2	NUM
ap-7652	535	20	<	<	X
ap-7652	535	21	m	m	X
ap-7652	535	22	<	<	X
ap-7652	535	23	2a	2a	NUM
ap-7652	535	24	.	.	PUNCT
ap-7652	536	1	(	(	PUNCT
ap-7652	536	2	136	136	NUM
ap-7652	536	3	)	)	PUNCT
ap-7652	536	4	indeed	indeed	ADV
ap-7652	536	5	,	,	PUNCT
ap-7652	536	6	representing	represent	VERB
ap-7652	536	7	(	(	PUNCT
ap-7652	536	8	56	56	NUM
ap-7652	536	9	)	)	PUNCT
ap-7652	536	10	as	as	ADP
ap-7652	536	11	y	y	PROPN
ap-7652	536	12	(	(	PUNCT
ap-7652	536	13	2a,−2	2a,−2	PROPN
ap-7652	536	14	)	)	PUNCT
ap-7652	536	15	m	m	PROPN
ap-7652	536	16	(	(	PUNCT
ap-7652	536	17	y	y	NOUN
ap-7652	536	18	)	)	PUNCT
ap-7652	536	19	≡	≡	PROPN
ap-7652	536	20	y	y	PROPN
ap-7652	536	21	(	(	PUNCT
ap-7652	536	22	2a	2a	NUM
ap-7652	536	23	)	)	PUNCT
ap-7652	536	24	m	m	PROPN
ap-7652	536	25	(	(	PUNCT
ap-7652	536	26	−y/2	−y/2	NOUN
ap-7652	536	27	)	)	PUNCT
ap-7652	536	28	=	=	PUNCT
ap-7652	537	1	m	m	NOUN
ap-7652	537	2	!	!	PUNCT
ap-7652	538	1	(	(	PUNCT
ap-7652	538	2	−y/2)ml(−2a−2m−1	−y/2)ml(−2a−2m−1	NOUN
ap-7652	538	3	)	)	PUNCT
ap-7652	538	4	m	m	VERB
ap-7652	539	1	(	(	PUNCT
ap-7652	539	2	−2	−2	PROPN
ap-7652	539	3	/	/	SYM
ap-7652	539	4	y	y	NOUN
ap-7652	539	5	)	)	PUNCT
ap-7652	539	6	(	(	PUNCT
ap-7652	539	7	137	137	NUM
ap-7652	539	8	)	)	PUNCT
ap-7652	539	9	shows	show	VERB
ap-7652	539	10	that	that	SCONJ
ap-7652	539	11	the	the	DET
ap-7652	539	12	absolute	absolute	ADJ
ap-7652	539	13	value	value	NOUN
ap-7652	539	14	of	of	ADP
ap-7652	539	15	the	the	DET
ap-7652	539	16	negative	negative	ADJ
ap-7652	539	17	m	m	ADJ
ap-7652	539	18	-	-	PUNCT
ap-7652	539	19	dependent	dependent	ADJ
ap-7652	539	20	laguerre	laguerre	NOUN
ap-7652	539	21	index	index	NOUN
ap-7652	539	22	αm	αm	NOUN
ap-7652	540	1	=	=	PUNCT
ap-7652	540	2	−2a−	−2a−	NOUN
ap-7652	541	1	2m−	2m−	NUM
ap-7652	541	2	1	1	NUM
ap-7652	541	3	<	<	X
ap-7652	541	4	0	0	NUM
ap-7652	541	5	(	(	PUNCT
ap-7652	541	6	138	138	NUM
ap-7652	541	7	)	)	PUNCT
ap-7652	541	8	is	be	AUX
ap-7652	541	9	larger	large	ADJ
ap-7652	541	10	than	than	ADP
ap-7652	541	11	the	the	DET
ap-7652	541	12	polynomial	polynomial	ADJ
ap-7652	541	13	degree	degree	NOUN
ap-7652	541	14	and	and	CCONJ
ap-7652	541	15	therefore	therefore	ADV
ap-7652	541	16	the	the	DET
ap-7652	541	17	polynomial	polynomial	NOUN
ap-7652	541	18	in	in	ADP
ap-7652	541	19	question	question	NOUN
ap-7652	541	20	may	may	AUX
ap-7652	541	21	not	not	PART
ap-7652	541	22	have	have	VERB
ap-7652	541	23	zeros	zero	NOUN
ap-7652	541	24	at	at	ADP
ap-7652	541	25	negative	negative	ADJ
ap-7652	541	26	values	value	NOUN
ap-7652	541	27	of	of	ADP
ap-7652	541	28	its	its	PRON
ap-7652	541	29	argument	argument	NOUN
ap-7652	541	30	.	.	PUNCT
ap-7652	542	1	3.5	3.5	NUM
ap-7652	542	2	.	.	PUNCT
ap-7652	542	3	isospectral	isospectral	ADJ
ap-7652	542	4	rational	rational	ADJ
ap-7652	542	5	extensions	extension	NOUN
ap-7652	542	6	of	of	ADP
ap-7652	542	7	krein	krein	NOUN
ap-7652	542	8	-	-	PUNCT
ap-7652	542	9	adler	adler	PROPN
ap-7652	542	10	susy	susy	PROPN
ap-7652	542	11	partners	partner	NOUN
ap-7652	542	12	of	of	ADP
ap-7652	542	13	morse	morse	ADJ
ap-7652	542	14	potential	potential	NOUN
ap-7652	542	15	since	since	SCONJ
ap-7652	542	16	any	any	DET
ap-7652	542	17	rdct	rdct	NOUN
ap-7652	542	18	of	of	ADP
ap-7652	542	19	the	the	DET
ap-7652	542	20	morse	morse	NOUN
ap-7652	542	21	potentials	potential	VERB
ap-7652	542	22	using	use	VERB
ap-7652	542	23	pairs	pair	NOUN
ap-7652	542	24	of	of	ADP
ap-7652	542	25	juxtaposed	juxtapose	VERB
ap-7652	542	26	eigenfunctions	eigenfunction	NOUN
ap-7652	542	27	n2j	n2j	ADV
ap-7652	542	28	keeps	keep	VERB
ap-7652	542	29	unchanged	unchanged	ADJ
ap-7652	542	30	the	the	DET
ap-7652	542	31	ground	ground	NOUN
ap-7652	542	32	-	-	PUNCT
ap-7652	542	33	energy	energy	NOUN
ap-7652	542	34	level	level	NOUN
ap-7652	542	35	a	a	DET
ap-7652	542	36	set	set	NOUN
ap-7652	542	37	of	of	ADP
ap-7652	542	38	seed	seed	NOUN
ap-7652	542	39	functions	function	NOUN
ap-7652	542	40	∞ϕ+,m[y	∞ϕ+,m[y	NOUN
ap-7652	542	41	;	;	PUNCT
ap-7652	542	42	a	a	PRON
ap-7652	542	43	]	]	X
ap-7652	542	44	is	be	AUX
ap-7652	542	45	admissible	admissible	ADJ
ap-7652	542	46	iff	iff	NOUN
ap-7652	542	47	all	all	DET
ap-7652	542	48	m	m	VERB
ap-7652	542	49	∈	∈	NOUN
ap-7652	542	50	n2j	n2j	PROPN
ap-7652	542	51	,	,	PUNCT
ap-7652	542	52	m	m	VERB
ap-7652	542	53	_	_	NOUN
ap-7652	542	54	p	p	X
ap-7652	542	55	,	,	PUNCT
ap-7652	542	56	where	where	SCONJ
ap-7652	542	57	m	m	VERB
ap-7652	542	58	_	_	NOUN
ap-7652	542	59	p	p	PRON
ap-7652	542	60	is	be	AUX
ap-7652	542	61	an	an	DET
ap-7652	542	62	admissible	admissible	ADJ
ap-7652	542	63	set	set	NOUN
ap-7652	542	64	of	of	ADP
ap-7652	542	65	seed	seed	NOUN
ap-7652	542	66	polynomials	polynomial	NOUN
ap-7652	542	67	specified	specify	VERB
ap-7652	542	68	in	in	ADP
ap-7652	542	69	subsection	subsection	NOUN
ap-7652	542	70	3.3	3.3	NUM
ap-7652	542	71	.	.	PUNCT
ap-7652	543	1	we	we	PRON
ap-7652	543	2	can	can	AUX
ap-7652	543	3	then	then	ADV
ap-7652	543	4	use	use	VERB
ap-7652	543	5	the	the	DET
ap-7652	543	6	same	same	ADJ
ap-7652	543	7	arguments	argument	NOUN
ap-7652	543	8	as	as	ADP
ap-7652	543	9	in	in	ADP
ap-7652	543	10	subsection	subsection	NOUN
ap-7652	543	11	3.3	3.3	NUM
ap-7652	543	12	to	to	PART
ap-7652	543	13	prove	prove	VERB
ap-7652	543	14	that	that	SCONJ
ap-7652	543	15	any	any	DET
ap-7652	543	16	liouville	liouville	NOUN
ap-7652	543	17	potential	potential	NOUN
ap-7652	543	18	∞v	∞v	NUM
ap-7652	544	1	[	[	X
ap-7652	544	2	y	y	X
ap-7652	544	3	;	;	PUNCT
ap-7652	544	4	a	a	DET
ap-7652	544	5	|	|	NOUN
ap-7652	544	6	−	−	NOUN
ap-7652	544	7	...	...	PUNCT
ap-7652	545	1	n2j	n2j	INTJ
ap-7652	545	2	,	,	PUNCT
ap-7652	545	3	m	m	VERB
ap-7652	545	4	_	_	NOUN
ap-7652	546	1	p	p	X
ap-7652	546	2	]	]	X
ap-7652	546	3	=	=	PUNCT
ap-7652	546	4	∞v	∞v	NUM
ap-7652	547	1	[	[	X
ap-7652	547	2	y	y	X
ap-7652	547	3	;	;	PUNCT
ap-7652	547	4	a−	a−	X
ap-7652	547	5	2j	2j	NOUN
ap-7652	547	6	−	−	PROPN
ap-7652	548	1	p	p	X
ap-7652	548	2	]	]	X
ap-7652	548	3	−	−	PROPN
ap-7652	548	4	2y	2y	PROPN
ap-7652	549	1	d	d	NOUN
ap-7652	549	2	dy	dy	NOUN
ap-7652	549	3	å	å	PROPN
ap-7652	549	4	y	y	PROPN
ap-7652	549	5	ld∞w[y	ld∞w[y	PROPN
ap-7652	549	6	;	;	PUNCT
ap-7652	549	7	a	a	DET
ap-7652	549	8	|	|	NOUN
ap-7652	549	9	−	−	NOUN
ap-7652	549	10	...	...	PUNCT
ap-7652	550	1	n2j	n2j	INTJ
ap-7652	550	2	,	,	PUNCT
ap-7652	550	3	m	m	VERB
ap-7652	550	4	_	_	NOUN
ap-7652	551	1	p	p	X
ap-7652	551	2	]	]	X
ap-7652	551	3	ã	ã	X
ap-7652	551	4	(	(	PUNCT
ap-7652	551	5	139	139	NUM
ap-7652	551	6	)	)	PUNCT
ap-7652	551	7	has	have	VERB
ap-7652	551	8	exactly	exactly	ADV
ap-7652	551	9	the	the	DET
ap-7652	551	10	same	same	ADJ
ap-7652	551	11	discrete	discrete	ADJ
ap-7652	551	12	energy	energy	NOUN
ap-7652	551	13	spectrum	spectrum	NOUN
ap-7652	551	14	as	as	ADP
ap-7652	551	15	rationally	rationally	ADV
ap-7652	551	16	deformed	deform	VERB
ap-7652	551	17	morse	morse	ADJ
ap-7652	551	18	potential	potential	NOUN
ap-7652	551	19	(	(	PUNCT
ap-7652	551	20	124	124	NUM
ap-7652	551	21	)	)	PUNCT
ap-7652	551	22	constructed	construct	VERB
ap-7652	551	23	by	by	ADP
ap-7652	551	24	means	mean	NOUN
ap-7652	551	25	of	of	ADP
ap-7652	551	26	juxtaposed	juxtapose	VERB
ap-7652	551	27	pairs	pair	NOUN
ap-7652	551	28	of	of	ADP
ap-7652	551	29	r	r	NOUN
ap-7652	551	30	-	-	PUNCT
ap-7652	551	31	bessel	bessel	ADJ
ap-7652	551	32	polynomials	polynomial	NOUN
ap-7652	551	33	of	of	ADP
ap-7652	551	34	non	non	ADJ
ap-7652	551	35	-	-	ADJ
ap-7652	551	36	zero	zero	NUM
ap-7652	551	37	degrees	degree	NOUN
ap-7652	551	38	.	.	PUNCT
ap-7652	552	1	its	its	PRON
ap-7652	552	2	eigenfunctions	eigenfunction	NOUN
ap-7652	552	3	expressed	express	VERB
ap-7652	552	4	in	in	ADP
ap-7652	552	5	terms	term	NOUN
ap-7652	552	6	of	of	ADP
ap-7652	552	7	the	the	DET
ap-7652	552	8	variable	variable	ADJ
ap-7652	552	9	y	y	NOUN
ap-7652	553	1	=	=	PUNCT
ap-7652	553	2	ex	ex	PROPN
ap-7652	553	3	can	can	AUX
ap-7652	553	4	be	be	AUX
ap-7652	553	5	represented	represent	VERB
ap-7652	553	6	as	as	ADP
ap-7652	553	7	∞	∞	PROPN
ap-7652	553	8	̸ψ−,n	̸ψ−,n	X
ap-7652	554	1	[	[	X
ap-7652	554	2	y	y	X
ap-7652	554	3	;	;	PUNCT
ap-7652	554	4	a	a	DET
ap-7652	554	5	|	|	NOUN
ap-7652	554	6	−	−	NOUN
ap-7652	554	7	...	...	PUNCT
ap-7652	555	1	n2j	n2j	INTJ
ap-7652	555	2	,	,	PUNCT
ap-7652	555	3	m	m	VERB
ap-7652	555	4	_	_	NOUN
ap-7652	556	1	p	p	X
ap-7652	556	2	]	]	X
ap-7652	556	3	=	=	SYM
ap-7652	556	4	∞	∞	NUM
ap-7652	556	5	̸ψ−,0	̸ψ−,0	PROPN
ap-7652	556	6	[	[	X
ap-7652	556	7	y	y	NOUN
ap-7652	556	8	;	;	PUNCT
ap-7652	556	9	a−	a−	X
ap-7652	556	10	2j	2j	NOUN
ap-7652	556	11	−	−	PROPN
ap-7652	556	12	p	p	X
ap-7652	556	13	]	]	X
ap-7652	556	14	∞w[y	∞w[y	NOUN
ap-7652	556	15	;	;	PUNCT
ap-7652	556	16	a	a	DET
ap-7652	556	17	|	|	NOUN
ap-7652	556	18	−	−	NOUN
ap-7652	556	19	...	...	PUNCT
ap-7652	557	1	n2j	n2j	INTJ
ap-7652	557	2	,	,	PUNCT
ap-7652	557	3	n	n	CCONJ
ap-7652	557	4	,	,	PUNCT
ap-7652	557	5	m	m	VERB
ap-7652	557	6	_	_	NOUN
ap-7652	558	1	p	p	X
ap-7652	558	2	]	]	X
ap-7652	558	3	∞w[y	∞w[y	NOUN
ap-7652	558	4	;	;	PUNCT
ap-7652	558	5	a	a	DET
ap-7652	558	6	|	|	NOUN
ap-7652	558	7	−	−	NOUN
ap-7652	558	8	...	...	PUNCT
ap-7652	559	1	n2j	n2j	INTJ
ap-7652	559	2	,	,	PUNCT
ap-7652	559	3	m	m	VERB
ap-7652	559	4	_	_	NOUN
ap-7652	560	1	p	p	X
ap-7652	560	2	]	]	PUNCT
ap-7652	560	3	for	for	ADP
ap-7652	560	4	n	n	PROPN
ap-7652	560	5	/∈	/∈	PUNCT
ap-7652	561	1	n2j	n2j	PROPN
ap-7652	561	2	<	<	X
ap-7652	561	3	n(a	n(a	PROPN
ap-7652	561	4	)	)	PUNCT
ap-7652	562	1	(	(	PUNCT
ap-7652	562	2	140	140	NUM
ap-7652	562	3	)	)	PUNCT
ap-7652	562	4	keeping	keep	VERB
ap-7652	562	5	in	in	ADP
ap-7652	562	6	mind	mind	NOUN
ap-7652	562	7	that	that	SCONJ
ap-7652	562	8	the	the	DET
ap-7652	562	9	corresponding	corresponding	ADJ
ap-7652	562	10	prime	prime	ADJ
ap-7652	562	11	rsle	rsle	NOUN
ap-7652	562	12	is	be	AUX
ap-7652	562	13	nothing	nothing	PRON
ap-7652	562	14	but	but	SCONJ
ap-7652	562	15	the	the	DET
ap-7652	562	16	schrödinger	schrödinger	ADJ
ap-7652	562	17	equation	equation	NOUN
ap-7652	562	18	re	re	VERB
ap-7652	562	19	-	-	VERB
ap-7652	562	20	written	write	VERB
ap-7652	562	21	in	in	ADP
ap-7652	562	22	its	its	PRON
ap-7652	562	23	algebraic	algebraic	ADJ
ap-7652	562	24	form	form	NOUN
ap-7652	562	25	.	.	PUNCT
ap-7652	563	1	4	4	X
ap-7652	563	2	.	.	X
ap-7652	563	3	conclusions	conclusion	NOUN
ap-7652	563	4	the	the	DET
ap-7652	563	5	presented	present	VERB
ap-7652	563	6	analysis	analysis	NOUN
ap-7652	563	7	illuminates	illuminate	VERB
ap-7652	563	8	the	the	DET
ap-7652	563	9	non	non	ADJ
ap-7652	563	10	-	-	ADJ
ap-7652	563	11	conventional	conventional	ADJ
ap-7652	563	12	approach	approach	NOUN
ap-7652	563	13	[	[	X
ap-7652	563	14	19	19	NUM
ap-7652	563	15	]	]	PUNCT
ap-7652	563	16	to	to	ADP
ap-7652	563	17	the	the	DET
ap-7652	563	18	family	family	NOUN
ap-7652	563	19	of	of	ADP
ap-7652	563	20	rationally	rationally	ADV
ap-7652	563	21	deformed	deform	VERB
ap-7652	563	22	morse	morse	NOUN
ap-7652	563	23	potentials	potential	NOUN
ap-7652	563	24	using	use	VERB
ap-7652	563	25	seed	seed	NOUN
ap-7652	563	26	solutions	solution	NOUN
ap-7652	563	27	expressed	express	VERB
ap-7652	563	28	in	in	ADP
ap-7652	563	29	terms	term	NOUN
ap-7652	563	30	of	of	ADP
ap-7652	563	31	wronskians	wronskian	NOUN
ap-7652	563	32	of	of	ADP
ap-7652	563	33	generalized	generalized	ADJ
ap-7652	563	34	bessel	bessel	ADJ
ap-7652	563	35	polynomials	polynomial	NOUN
ap-7652	563	36	in	in	ADP
ap-7652	563	37	the	the	DET
ap-7652	563	38	variable	variable	ADJ
ap-7652	563	39	y	y	PROPN
ap-7652	563	40	=	=	SYM
ap-7652	563	41	ex	ex	PROPN
ap-7652	563	42	.	.	NOUN
ap-7652	563	43	as	as	ADP
ap-7652	563	44	a	a	DET
ap-7652	563	45	new	new	ADJ
ap-7652	563	46	achievement	achievement	NOUN
ap-7652	563	47	compared	compare	VERB
ap-7652	563	48	with	with	ADP
ap-7652	563	49	odake	odake	NOUN
ap-7652	563	50	and	and	CCONJ
ap-7652	563	51	saski	saski	PROPN
ap-7652	563	52	’s	’s	PART
ap-7652	564	1	[	[	X
ap-7652	564	2	19	19	NUM
ap-7652	564	3	]	]	PUNCT
ap-7652	564	4	study	study	NOUN
ap-7652	564	5	on	on	ADP
ap-7652	564	6	rdct	rdct	PROPN
ap-7652	564	7	s	s	PROPN
ap-7652	564	8	of	of	ADP
ap-7652	564	9	the	the	DET
ap-7652	564	10	morse	morse	ADJ
ap-7652	564	11	potential	potential	NOUN
ap-7652	564	12	(	(	PUNCT
ap-7652	564	13	see	see	VERB
ap-7652	564	14	also	also	ADV
ap-7652	564	15	[	[	X
ap-7652	564	16	11	11	NUM
ap-7652	564	17	]	]	PUNCT
ap-7652	564	18	where	where	SCONJ
ap-7652	564	19	a	a	DET
ap-7652	564	20	similar	similar	ADJ
ap-7652	564	21	analysis	analysis	NOUN
ap-7652	564	22	was	be	AUX
ap-7652	564	23	performed	perform	VERB
ap-7652	564	24	within	within	ADP
ap-7652	564	25	the	the	DET
ap-7652	564	26	conventional	conventional	ADJ
ap-7652	564	27	l	l	NOUN
ap-7652	564	28	ref	ref	NOUN
ap-7652	564	29	framework	framework	NOUN
ap-7652	564	30	)	)	PUNCT
ap-7652	564	31	we	we	PRON
ap-7652	564	32	constructed	construct	VERB
ap-7652	564	33	a	a	DET
ap-7652	564	34	new	new	ADJ
ap-7652	564	35	rdc	rdc	NOUN
ap-7652	564	36	net	net	NOUN
ap-7652	564	37	of	of	ADP
ap-7652	564	38	isospectral	isospectral	ADJ
ap-7652	564	39	potentials	potential	NOUN
ap-7652	564	40	by	by	ADP
ap-7652	564	41	expressing	express	VERB
ap-7652	564	42	them	they	PRON
ap-7652	564	43	in	in	ADP
ap-7652	564	44	terms	term	NOUN
ap-7652	564	45	of	of	ADP
ap-7652	564	46	the	the	DET
ap-7652	564	47	logarithmic	logarithmic	ADJ
ap-7652	564	48	derivative	derivative	NOUN
ap-7652	564	49	of	of	ADP
ap-7652	564	50	wronskians	wronskian	NOUN
ap-7652	564	51	of	of	ADP
ap-7652	564	52	generalized	generalized	ADJ
ap-7652	564	53	bessel	bessel	ADJ
ap-7652	564	54	polynomials	polynomial	NOUN
ap-7652	564	55	with	with	ADP
ap-7652	564	56	no	no	DET
ap-7652	564	57	positive	positive	ADJ
ap-7652	564	58	zeros	zero	NOUN
ap-7652	564	59	.	.	PUNCT
ap-7652	565	1	the	the	DET
ap-7652	565	2	constructed	construct	VERB
ap-7652	565	3	isospectral	isospectral	ADJ
ap-7652	565	4	family	family	NOUN
ap-7652	565	5	of	of	ADP
ap-7652	565	6	rationally	rationally	ADV
ap-7652	565	7	deformed	deform	VERB
ap-7652	565	8	morse	morse	ADJ
ap-7652	565	9	potentials	potential	NOUN
ap-7652	565	10	represents	represent	VERB
ap-7652	565	11	a	a	DET
ap-7652	565	12	natural	natural	ADJ
ap-7652	565	13	extension	extension	NOUN
ap-7652	565	14	of	of	ADP
ap-7652	565	15	the	the	DET
ap-7652	565	16	isospectral	isospectral	ADJ
ap-7652	565	17	rdt	rdt	PROPN
ap-7652	565	18	s	s	PROPN
ap-7652	565	19	of	of	ADP
ap-7652	565	20	the	the	DET
ap-7652	565	21	morse	morse	ADJ
ap-7652	565	22	potential	potential	NOUN
ap-7652	565	23	discovered	discover	VERB
ap-7652	565	24	by	by	ADP
ap-7652	565	25	quesne	quesne	NOUN
ap-7652	565	26	[	[	X
ap-7652	565	27	10	10	NUM
ap-7652	565	28	]	]	PUNCT
ap-7652	565	29	.	.	PUNCT
ap-7652	566	1	an	an	DET
ap-7652	566	2	important	important	ADJ
ap-7652	566	3	element	element	NOUN
ap-7652	566	4	of	of	ADP
ap-7652	566	5	our	our	PRON
ap-7652	566	6	analysis	analysis	NOUN
ap-7652	566	7	often	often	ADV
ap-7652	566	8	overlooked	overlook	VERB
ap-7652	566	9	in	in	ADP
ap-7652	566	10	the	the	DET
ap-7652	566	11	literature	literature	NOUN
ap-7652	566	12	is	be	AUX
ap-7652	566	13	the	the	DET
ap-7652	566	14	proof	proof	NOUN
ap-7652	566	15	that	that	SCONJ
ap-7652	566	16	the	the	DET
ap-7652	566	17	sequential	sequential	ADJ
ap-7652	566	18	rdts	rdts	NOUN
ap-7652	566	19	in	in	ADP
ap-7652	566	20	question	question	NOUN
ap-7652	566	21	do	do	AUX
ap-7652	566	22	not	not	PART
ap-7652	566	23	insert	insert	VERB
ap-7652	566	24	new	new	ADJ
ap-7652	566	25	bound	bind	VERB
ap-7652	566	26	energy	energy	NOUN
ap-7652	566	27	states	state	NOUN
ap-7652	566	28	.	.	PUNCT
ap-7652	567	1	the	the	DET
ap-7652	567	2	widespread	widespread	ADJ
ap-7652	567	3	argumentation	argumentation	NOUN
ap-7652	567	4	in	in	ADP
ap-7652	567	5	support	support	NOUN
ap-7652	567	6	of	of	ADP
ap-7652	567	7	this	this	PRON
ap-7652	567	8	(	(	PUNCT
ap-7652	567	9	usually	usually	ADV
ap-7652	567	10	taken	take	VERB
ap-7652	567	11	-	-	PUNCT
ap-7652	567	12	for	for	SCONJ
ap-7652	567	13	-	-	PUNCT
ap-7652	567	14	granted	grant	VERB
ap-7652	567	15	)	)	PUNCT
ap-7652	567	16	presumption	presumption	NOUN
ap-7652	567	17	is	be	AUX
ap-7652	567	18	based	base	VERB
ap-7652	567	19	on	on	ADP
ap-7652	567	20	the	the	DET
ap-7652	567	21	speculation	speculation	NOUN
ap-7652	567	22	that	that	SCONJ
ap-7652	567	23	the	the	DET
ap-7652	567	24	theorems	theorem	NOUN
ap-7652	567	25	of	of	ADP
ap-7652	567	26	the	the	DET
ap-7652	567	27	regular	regular	ADJ
ap-7652	567	28	sturm	sturm	NOUN
ap-7652	567	29	-	-	PUNCT
ap-7652	567	30	liouville	liouville	NOUN
ap-7652	567	31	theory	theory	NOUN
ap-7652	567	32	[	[	X
ap-7652	567	33	55	55	NUM
ap-7652	567	34	]	]	PUNCT
ap-7652	567	35	are	be	AUX
ap-7652	567	36	automatically	automatically	ADV
ap-7652	567	37	applied	apply	VERB
ap-7652	567	38	to	to	ADP
ap-7652	567	39	singular	singular	ADJ
ap-7652	567	40	sles	sle	NOUN
ap-7652	567	41	.	.	PUNCT
ap-7652	568	1	we	we	PRON
ap-7652	568	2	can	can	AUX
ap-7652	568	3	refer	refer	VERB
ap-7652	568	4	the	the	DET
ap-7652	568	5	reader	reader	NOUN
ap-7652	568	6	to	to	ADP
ap-7652	568	7	the	the	DET
ap-7652	568	8	scrupolous	scrupolous	ADJ
ap-7652	568	9	analysis	analysis	NOUN
ap-7652	568	10	performed	perform	VERB
ap-7652	568	11	in	in	ADP
ap-7652	568	12	[	[	X
ap-7652	568	13	43	43	NUM
ap-7652	568	14	]	]	PUNCT
ap-7652	568	15	for	for	ADP
ap-7652	568	16	sles	sle	NOUN
ap-7652	568	17	solved	solve	VERB
ap-7652	568	18	under	under	ADP
ap-7652	568	19	the	the	DET
ap-7652	568	20	dbcs	dbc	NOUN
ap-7652	568	21	as	as	ADP
ap-7652	568	22	an	an	DET
ap-7652	568	23	illustration	illustration	NOUN
ap-7652	568	24	that	that	SCONJ
ap-7652	568	25	this	this	PRON
ap-7652	568	26	is	be	AUX
ap-7652	568	27	by	by	ADP
ap-7652	568	28	no	no	DET
ap-7652	568	29	means	means	NOUN
ap-7652	568	30	a	a	DET
ap-7652	568	31	trivial	trivial	ADJ
ap-7652	568	32	issue	issue	NOUN
ap-7652	568	33	.	.	PUNCT
ap-7652	569	1	to	to	PART
ap-7652	569	2	be	be	AUX
ap-7652	569	3	able	able	ADJ
ap-7652	569	4	to	to	PART
ap-7652	569	5	prove	prove	VERB
ap-7652	569	6	the	the	DET
ap-7652	569	7	aforementioned	aforementioned	ADJ
ap-7652	569	8	assertion	assertion	NOUN
ap-7652	569	9	we	we	PRON
ap-7652	569	10	converted	convert	VERB
ap-7652	569	11	the	the	DET
ap-7652	569	12	given	give	VERB
ap-7652	569	13	rcsle	rcsle	PROPN
ap-7652	569	14	to	to	ADP
ap-7652	569	15	its	its	PRON
ap-7652	569	16	prime	prime	ADJ
ap-7652	569	17	form	form	NOUN
ap-7652	569	18	such	such	ADJ
ap-7652	569	19	that	that	SCONJ
ap-7652	569	20	the	the	DET
ap-7652	569	21	characteristic	characteristic	ADJ
ap-7652	569	22	exponents	exponent	NOUN
ap-7652	569	23	of	of	ADP
ap-7652	569	24	frobenius	frobenius	ADJ
ap-7652	569	25	solutions	solution	NOUN
ap-7652	569	26	for	for	ADP
ap-7652	569	27	the	the	DET
ap-7652	569	28	regular	regular	ADJ
ap-7652	569	29	singular	singular	ADJ
ap-7652	569	30	point	point	NOUN
ap-7652	569	31	at	at	ADP
ap-7652	569	32	∞	∞	PROPN
ap-7652	569	33	have	have	VERB
ap-7652	569	34	opposite	opposite	ADJ
ap-7652	569	35	signs	sign	NOUN
ap-7652	569	36	and	and	CCONJ
ap-7652	569	37	therefore	therefore	ADV
ap-7652	569	38	the	the	DET
ap-7652	569	39	principal	principal	ADJ
ap-7652	569	40	frobenius	frobenius	NOUN
ap-7652	569	41	solution	solution	NOUN
ap-7652	569	42	near	near	ADP
ap-7652	569	43	this	this	DET
ap-7652	569	44	singular	singular	ADJ
ap-7652	569	45	end	end	NOUN
ap-7652	569	46	is	be	AUX
ap-7652	569	47	unambiguously	unambiguously	ADV
ap-7652	569	48	selected	select	VERB
ap-7652	569	49	by	by	ADP
ap-7652	569	50	the	the	DET
ap-7652	569	51	corresponding	corresponding	PROPN
ap-7652	569	52	dbc	dbc	PROPN
ap-7652	569	53	.	.	PUNCT
ap-7652	570	1	(	(	PUNCT
ap-7652	570	2	in	in	ADP
ap-7652	570	3	the	the	DET
ap-7652	570	4	particular	particular	ADJ
ap-7652	570	5	case	case	NOUN
ap-7652	570	6	under	under	ADP
ap-7652	570	7	consideration	consideration	NOUN
ap-7652	570	8	the	the	DET
ap-7652	570	9	prime	prime	ADJ
ap-7652	570	10	rsle	rsle	NOUN
ap-7652	570	11	accidently	accidently	ADV
ap-7652	570	12	coincides	coincide	VERB
ap-7652	570	13	with	with	ADP
ap-7652	570	14	the	the	DET
ap-7652	570	15	schrödinger	schrödinger	ADJ
ap-7652	570	16	equation	equation	NOUN
ap-7652	570	17	re	re	VERB
ap-7652	570	18	-	-	VERB
ap-7652	570	19	written	write	VERB
ap-7652	570	20	in	in	ADP
ap-7652	570	21	the	the	DET
ap-7652	570	22	‘	'	PUNCT
ap-7652	570	23	algebraic	algebraic	ADJ
ap-7652	570	24	’	'	PUNCT
ap-7652	570	25	[	[	X
ap-7652	570	26	42	42	NUM
ap-7652	570	27	]	]	X
ap-7652	570	28	form	form	NOUN
ap-7652	570	29	but	but	CCONJ
ap-7652	570	30	this	this	PRON
ap-7652	570	31	is	be	AUX
ap-7652	570	32	114	114	NUM
ap-7652	570	33	vol	vol	NOUN
ap-7652	570	34	.	.	PUNCT
ap-7652	571	1	62	62	NUM
ap-7652	571	2	no	no	INTJ
ap-7652	571	3	.	.	PUNCT
ap-7652	572	1	1/2022	1/2022	NUM
ap-7652	572	2	quantization	quantization	NOUN
ap-7652	572	3	of	of	ADP
ap-7652	572	4	rationally	rationally	ADV
ap-7652	572	5	deformed	deform	VERB
ap-7652	572	6	morse	morse	ADJ
ap-7652	572	7	potentials	potential	NOUN
ap-7652	572	8	.	.	PUNCT
ap-7652	572	9	.	.	PUNCT
ap-7652	572	10	.	.	PUNCT
ap-7652	573	1	not	not	PART
ap-7652	573	2	true	true	ADJ
ap-7652	573	3	in	in	ADP
ap-7652	573	4	general	general	ADJ
ap-7652	573	5	.	.	PUNCT
ap-7652	573	6	)	)	PUNCT
ap-7652	574	1	re	re	VERB
ap-7652	574	2	-	-	VERB
ap-7652	574	3	formulating	formulate	VERB
ap-7652	574	4	the	the	DET
ap-7652	574	5	given	give	VERB
ap-7652	574	6	spectral	spectral	ADJ
ap-7652	574	7	problem	problem	NOUN
ap-7652	574	8	in	in	ADP
ap-7652	574	9	such	such	DET
ap-7652	574	10	a	a	DET
ap-7652	574	11	very	very	ADV
ap-7652	574	12	specific	specific	ADJ
ap-7652	574	13	way	way	NOUN
ap-7652	574	14	allowed	allow	VERB
ap-7652	574	15	us	we	PRON
ap-7652	574	16	to	to	PART
ap-7652	574	17	take	take	VERB
ap-7652	574	18	advantage	advantage	NOUN
ap-7652	574	19	of	of	ADP
ap-7652	574	20	powerful	powerful	ADJ
ap-7652	574	21	theorems	theorem	NOUN
ap-7652	574	22	proven	prove	VERB
ap-7652	574	23	in	in	ADP
ap-7652	574	24	[	[	X
ap-7652	574	25	43	43	NUM
ap-7652	574	26	]	]	PUNCT
ap-7652	574	27	for	for	SCONJ
ap-7652	574	28	zeros	zero	NOUN
ap-7652	574	29	of	of	ADP
ap-7652	574	30	principal	principal	ADJ
ap-7652	574	31	solutions	solution	NOUN
ap-7652	574	32	of	of	ADP
ap-7652	574	33	sles	sle	NOUN
ap-7652	574	34	solved	solve	VERB
ap-7652	574	35	under	under	ADP
ap-7652	574	36	the	the	DET
ap-7652	574	37	dbcs	dbc	NOUN
ap-7652	574	38	at	at	ADP
ap-7652	574	39	singular	singular	NOUN
ap-7652	574	40	ends	end	VERB
ap-7652	574	41	.	.	PUNCT
ap-7652	575	1	we	we	PRON
ap-7652	575	2	[	[	X
ap-7652	575	3	42	42	NUM
ap-7652	575	4	]	]	PUNCT
ap-7652	575	5	also	also	ADV
ap-7652	575	6	used	use	VERB
ap-7652	575	7	this	this	DET
ap-7652	575	8	simplified	simplified	ADJ
ap-7652	575	9	version	version	NOUN
ap-7652	575	10	of	of	ADP
ap-7652	575	11	the	the	DET
ap-7652	575	12	conventional	conventional	ADJ
ap-7652	575	13	spectral	spectral	ADJ
ap-7652	575	14	theory	theory	NOUN
ap-7652	575	15	to	to	PART
ap-7652	575	16	prove	prove	VERB
ap-7652	575	17	that	that	SCONJ
ap-7652	575	18	any	any	DET
ap-7652	575	19	rdt	rdt	NOUN
ap-7652	575	20	of	of	ADP
ap-7652	575	21	a	a	DET
ap-7652	575	22	principal	principal	NOUN
ap-7652	575	23	(	(	PUNCT
ap-7652	575	24	non	non	ADJ
ap-7652	575	25	-	-	ADJ
ap-7652	575	26	principal	principal	ADJ
ap-7652	575	27	)	)	PUNCT
ap-7652	575	28	frobenius	frobenius	NOUN
ap-7652	575	29	solution	solution	NOUN
ap-7652	575	30	near	near	ADP
ap-7652	575	31	the	the	DET
ap-7652	575	32	regular	regular	ADJ
ap-7652	575	33	singular	singular	ADJ
ap-7652	575	34	point	point	NOUN
ap-7652	575	35	at	at	ADP
ap-7652	575	36	∞	∞	PROPN
ap-7652	575	37	is	be	AUX
ap-7652	575	38	itself	itself	PRON
ap-7652	575	39	a	a	DET
ap-7652	575	40	principal	principal	NOUN
ap-7652	575	41	(	(	PUNCT
ap-7652	575	42	non	non	ADJ
ap-7652	575	43	-	-	ADJ
ap-7652	575	44	principal	principal	ADJ
ap-7652	575	45	)	)	PUNCT
ap-7652	575	46	frobenius	frobenius	NOUN
ap-7652	575	47	solution	solution	NOUN
ap-7652	575	48	of	of	ADP
ap-7652	575	49	the	the	DET
ap-7652	575	50	transformed	transform	VERB
ap-7652	575	51	rsle	rsle	NOUN
ap-7652	575	52	.	.	PUNCT
ap-7652	576	1	this	this	DET
ap-7652	576	2	assertion	assertion	NOUN
ap-7652	576	3	plays	play	VERB
ap-7652	576	4	a	a	DET
ap-7652	576	5	crucial	crucial	ADJ
ap-7652	576	6	role	role	NOUN
ap-7652	576	7	in	in	ADP
ap-7652	576	8	our	our	PRON
ap-7652	576	9	proof	proof	NOUN
ap-7652	576	10	of	of	ADP
ap-7652	576	11	the	the	DET
ap-7652	576	12	exact	exact	ADJ
ap-7652	576	13	solvability	solvability	NOUN
ap-7652	576	14	of	of	ADP
ap-7652	576	15	the	the	DET
ap-7652	576	16	constructed	construct	VERB
ap-7652	576	17	dc	dc	PROPN
ap-7652	576	18	net	net	NOUN
ap-7652	576	19	of	of	ADP
ap-7652	576	20	isospectral	isospectral	ADJ
ap-7652	576	21	rational	rational	ADJ
ap-7652	576	22	potentials	potential	NOUN
ap-7652	576	23	.	.	PUNCT
ap-7652	577	1	it	it	PRON
ap-7652	577	2	is	be	AUX
ap-7652	577	3	commonly	commonly	ADV
ap-7652	577	4	presumed	presume	VERB
ap-7652	577	5	that	that	SCONJ
ap-7652	577	6	the	the	DET
ap-7652	577	7	krein	krein	PROPN
ap-7652	577	8	-	-	PUNCT
ap-7652	577	9	adler	adler	PROPN
ap-7652	577	10	theorem	theorem	VERB
ap-7652	577	11	[	[	X
ap-7652	577	12	49	49	NUM
ap-7652	577	13	,	,	PUNCT
ap-7652	577	14	50	50	NUM
ap-7652	577	15	]	]	PUNCT
ap-7652	577	16	is	be	AUX
ap-7652	577	17	applied	apply	VERB
ap-7652	577	18	to	to	ADP
ap-7652	577	19	an	an	DET
ap-7652	577	20	arbitrary	arbitrary	ADJ
ap-7652	577	21	potential	potential	NOUN
ap-7652	577	22	regardless	regardless	ADV
ap-7652	577	23	its	its	PRON
ap-7652	577	24	behavior	behavior	NOUN
ap-7652	577	25	near	near	ADP
ap-7652	577	26	the	the	DET
ap-7652	577	27	singular	singular	ADJ
ap-7652	577	28	end	end	NOUN
ap-7652	577	29	points	point	NOUN
ap-7652	577	30	.	.	PUNCT
ap-7652	578	1	in	in	ADP
ap-7652	578	2	[	[	X
ap-7652	578	3	42	42	NUM
ap-7652	578	4	]	]	PUNCT
ap-7652	578	5	we	we	PRON
ap-7652	578	6	examined	examine	VERB
ap-7652	578	7	this	this	DET
ap-7652	578	8	presumption	presumption	NOUN
ap-7652	578	9	more	more	ADV
ap-7652	578	10	carefully	carefully	ADV
ap-7652	578	11	for	for	SCONJ
ap-7652	578	12	the	the	DET
ap-7652	578	13	dirichlet	dirichlet	PROPN
ap-7652	578	14	problems	problem	NOUN
ap-7652	578	15	of	of	ADP
ap-7652	578	16	our	our	PRON
ap-7652	578	17	interest	interest	NOUN
ap-7652	578	18	again	again	ADV
ap-7652	578	19	taking	take	VERB
ap-7652	578	20	advantage	advantage	NOUN
ap-7652	578	21	of	of	ADP
ap-7652	578	22	the	the	DET
ap-7652	578	23	theorems	theorem	NOUN
ap-7652	578	24	proven	prove	VERB
ap-7652	578	25	in	in	ADP
ap-7652	578	26	[	[	X
ap-7652	578	27	43	43	NUM
ap-7652	578	28	]	]	PUNCT
ap-7652	578	29	for	for	ADP
ap-7652	578	30	zeros	zero	NOUN
ap-7652	578	31	of	of	ADP
ap-7652	578	32	juxtaposed	juxtapose	VERB
ap-7652	578	33	eigenfunctions	eigenfunction	NOUN
ap-7652	578	34	.	.	PUNCT
ap-7652	579	1	however	however	ADV
ap-7652	579	2	one	one	PRON
ap-7652	579	3	can	can	AUX
ap-7652	579	4	by	by	AUX
ap-7652	579	5	-	-	PUNCT
ap-7652	579	6	pass	pass	VERB
ap-7652	579	7	this	this	DET
ap-7652	579	8	analysis	analysis	NOUN
ap-7652	579	9	for	for	ADP
ap-7652	579	10	any	any	DET
ap-7652	579	11	tfi	tfi	NOUN
ap-7652	579	12	rsle	rsle	NOUN
ap-7652	579	13	from	from	ADP
ap-7652	579	14	group	group	PROPN
ap-7652	579	15	a	a	DET
ap-7652	579	16	keeping	keeping	NOUN
ap-7652	579	17	in	in	ADP
ap-7652	579	18	mind	mind	NOUN
ap-7652	579	19	that	that	SCONJ
ap-7652	579	20	the	the	DET
ap-7652	579	21	wronskians	wronskian	NOUN
ap-7652	579	22	in	in	ADP
ap-7652	579	23	questions	question	NOUN
ap-7652	579	24	are	be	AUX
ap-7652	579	25	formed	form	VERB
ap-7652	579	26	by	by	ADP
ap-7652	579	27	orthogonal	orthogonal	ADJ
ap-7652	579	28	polynomials	polynomial	NOUN
ap-7652	579	29	with	with	ADP
ap-7652	579	30	degree	degree	NOUN
ap-7652	579	31	-	-	PUNCT
ap-7652	579	32	independent	independent	ADJ
ap-7652	579	33	indexes	index	NOUN
ap-7652	579	34	and	and	CCONJ
ap-7652	579	35	therefore	therefore	ADV
ap-7652	579	36	the	the	DET
ap-7652	579	37	numbers	number	NOUN
ap-7652	579	38	of	of	ADP
ap-7652	579	39	their	their	PRON
ap-7652	579	40	positive	positive	ADJ
ap-7652	579	41	zeros	zero	NOUN
ap-7652	579	42	are	be	AUX
ap-7652	579	43	controlled	control	VERB
ap-7652	579	44	by	by	ADP
ap-7652	579	45	the	the	DET
ap-7652	579	46	general	general	ADJ
ap-7652	579	47	conjectures	conjecture	VERB
ap-7652	579	48	proven	prove	VERB
ap-7652	579	49	in	in	ADP
ap-7652	579	50	[	[	X
ap-7652	579	51	51	51	NUM
ap-7652	579	52	]	]	PUNCT
ap-7652	579	53	.	.	PUNCT
ap-7652	580	1	in	in	ADP
ap-7652	580	2	particular	particular	ADJ
ap-7652	580	3	this	this	PRON
ap-7652	580	4	implies	imply	VERB
ap-7652	580	5	that	that	SCONJ
ap-7652	580	6	any	any	DET
ap-7652	580	7	wronskian	wronskian	NOUN
ap-7652	580	8	formed	form	VERB
ap-7652	580	9	by	by	ADP
ap-7652	580	10	juxtaposed	juxtapose	VERB
ap-7652	580	11	pairs	pair	NOUN
ap-7652	580	12	of	of	ADP
ap-7652	580	13	r	r	NOUN
ap-7652	580	14	-	-	PUNCT
ap-7652	580	15	bessel	bessel	ADJ
ap-7652	580	16	polynomials	polynomial	NOUN
ap-7652	580	17	of	of	ADP
ap-7652	580	18	non	non	ADJ
ap-7652	580	19	-	-	ADJ
ap-7652	580	20	zero	zero	ADJ
ap-7652	580	21	degrees	degree	NOUN
ap-7652	580	22	may	may	AUX
ap-7652	580	23	not	not	PART
ap-7652	580	24	have	have	VERB
ap-7652	580	25	positive	positive	ADJ
ap-7652	580	26	zeros	zero	NOUN
ap-7652	580	27	.	.	PUNCT
ap-7652	581	1	acknowledgements	acknowledgement	NOUN
ap-7652	581	2	i	i	PRON
ap-7652	581	3	am	be	AUX
ap-7652	581	4	grateful	grateful	ADJ
ap-7652	581	5	to	to	ADP
ap-7652	581	6	a.	a.	PROPN
ap-7652	581	7	d.	d.	PROPN
ap-7652	581	8	alhaidari	alhaidari	PROPN
ap-7652	581	9	for	for	ADP
ap-7652	581	10	bringing	bring	VERB
ap-7652	581	11	my	my	PRON
ap-7652	581	12	attention	attention	NOUN
ap-7652	581	13	to	to	ADP
ap-7652	581	14	the	the	DET
ap-7652	581	15	alternative	alternative	ADJ
ap-7652	581	16	representation	representation	NOUN
ap-7652	581	17	of	of	ADP
ap-7652	581	18	eigenfunctions	eigenfunction	NOUN
ap-7652	581	19	of	of	ADP
ap-7652	581	20	the	the	DET
ap-7652	581	21	schrödinger	schrödinger	ADJ
ap-7652	581	22	equation	equation	NOUN
ap-7652	581	23	with	with	ADP
ap-7652	581	24	the	the	DET
ap-7652	581	25	morse	morse	ADJ
ap-7652	581	26	potential	potential	NOUN
ap-7652	581	27	in	in	ADP
ap-7652	581	28	terms	term	NOUN
ap-7652	581	29	of	of	ADP
ap-7652	581	30	r	r	NOUN
ap-7652	581	31	-	-	PUNCT
ap-7652	581	32	bessel	bessel	ADJ
ap-7652	581	33	polynomials	polynomial	NOUN
ap-7652	581	34	with	with	ADP
ap-7652	581	35	degree	degree	NOUN
ap-7652	581	36	-	-	PUNCT
ap-7652	581	37	independent	independent	ADJ
ap-7652	581	38	indexes	index	NOUN
ap-7652	581	39	.	.	PUNCT
ap-7652	582	1	this	this	DET
ap-7652	582	2	alteration	alteration	NOUN
ap-7652	582	3	helped	help	VERB
ap-7652	582	4	me	i	PRON
ap-7652	582	5	to	to	PART
ap-7652	582	6	fully	fully	ADV
ap-7652	582	7	comprehend	comprehend	VERB
ap-7652	582	8	odake	odake	NOUN
ap-7652	582	9	and	and	CCONJ
ap-7652	582	10	sasaki	sasaki	PROPN
ap-7652	582	11	’s	’s	PART
ap-7652	582	12	suggestion	suggestion	NOUN
ap-7652	582	13	to	to	PART
ap-7652	582	14	place	place	VERB
ap-7652	582	15	the	the	DET
ap-7652	582	16	morse	morse	ADJ
ap-7652	582	17	oscillator	oscillator	NOUN
ap-7652	582	18	into	into	ADP
ap-7652	582	19	group	group	NOUN
ap-7652	582	20	a	a	PRON
ap-7652	582	21	of	of	ADP
ap-7652	582	22	rational	rational	ADJ
ap-7652	582	23	tsi	tsi	PROPN
ap-7652	582	24	potentials	potential	VERB
ap-7652	582	25	.	.	PUNCT
ap-7652	583	1	references	reference	NOUN
ap-7652	583	2	[	[	X
ap-7652	583	3	1	1	NUM
ap-7652	583	4	]	]	PUNCT
ap-7652	583	5	a.	a.	NOUN
ap-7652	583	6	d.	d.	PROPN
ap-7652	583	7	alhaidari	alhaidari	PROPN
ap-7652	583	8	.	.	PUNCT
ap-7652	584	1	exponentially	exponentially	ADV
ap-7652	584	2	confining	confine	VERB
ap-7652	584	3	potential	potential	ADJ
ap-7652	584	4	well	well	ADV
ap-7652	584	5	.	.	PUNCT
ap-7652	585	1	theoretical	theoretical	ADJ
ap-7652	585	2	and	and	CCONJ
ap-7652	585	3	mathematical	mathematical	ADJ
ap-7652	585	4	physics	physics	NOUN
ap-7652	585	5	volume	volume	NOUN
ap-7652	585	6	206:84–96	206:84–96	PROPN
ap-7652	585	7	,	,	PUNCT
ap-7652	585	8	2021	2021	NUM
ap-7652	585	9	.	.	PUNCT
ap-7652	586	1	https://doi.org/10.1134/s0040577921010050	https://doi.org/10.1134/s0040577921010050	VERB
ap-7652	586	2	.	.	PUNCT
ap-7652	587	1	[	[	X
ap-7652	587	2	2	2	X
ap-7652	587	3	]	]	PUNCT
ap-7652	587	4	j.	j.	PROPN
ap-7652	587	5	gibbons	gibbons	PROPN
ap-7652	587	6	,	,	PUNCT
ap-7652	587	7	a.	a.	NOUN
ap-7652	587	8	p.	p.	PROPN
ap-7652	587	9	veselov	veselov	NOUN
ap-7652	587	10	.	.	PUNCT
ap-7652	588	1	on	on	ADP
ap-7652	588	2	the	the	DET
ap-7652	588	3	rational	rational	ADJ
ap-7652	588	4	monodromy	monodromy	NOUN
ap-7652	588	5	-	-	PUNCT
ap-7652	588	6	free	free	ADJ
ap-7652	588	7	potentials	potential	NOUN
ap-7652	588	8	with	with	ADP
ap-7652	588	9	sextic	sextic	ADJ
ap-7652	588	10	growth	growth	NOUN
ap-7652	588	11	.	.	PUNCT
ap-7652	589	1	journal	journal	NOUN
ap-7652	589	2	of	of	ADP
ap-7652	589	3	mathematical	mathematical	ADJ
ap-7652	589	4	physics	physics	PROPN
ap-7652	589	5	50(1):013513	50(1):013513	NUM
ap-7652	589	6	,	,	PUNCT
ap-7652	589	7	2009	2009	NUM
ap-7652	589	8	.	.	PUNCT
ap-7652	590	1	https://doi.org/10.1063/1.3001604	https://doi.org/10.1063/1.3001604	X
ap-7652	590	2	.	.	PUNCT
ap-7652	591	1	[	[	X
ap-7652	591	2	3	3	X
ap-7652	591	3	]	]	X
ap-7652	591	4	h.	h.	PROPN
ap-7652	591	5	l.	l.	PROPN
ap-7652	591	6	krall	krall	PROPN
ap-7652	591	7	,	,	PUNCT
ap-7652	591	8	o.	o.	PROPN
ap-7652	591	9	frink	frink	PROPN
ap-7652	591	10	.	.	PUNCT
ap-7652	592	1	a	a	DET
ap-7652	592	2	new	new	ADJ
ap-7652	592	3	class	class	NOUN
ap-7652	592	4	of	of	ADP
ap-7652	592	5	orthogonal	orthogonal	ADJ
ap-7652	592	6	polynomials	polynomial	NOUN
ap-7652	592	7	:	:	PUNCT
ap-7652	592	8	the	the	DET
ap-7652	592	9	bessel	bessel	NOUN
ap-7652	592	10	polynomials	polynomial	NOUN
ap-7652	592	11	.	.	PUNCT
ap-7652	593	1	transactions	transaction	NOUN
ap-7652	593	2	of	of	ADP
ap-7652	593	3	the	the	DET
ap-7652	593	4	american	american	PROPN
ap-7652	593	5	mathematical	mathematical	PROPN
ap-7652	593	6	society	society	PROPN
ap-7652	593	7	65:100–105	65:100–105	PROPN
ap-7652	593	8	,	,	PUNCT
ap-7652	593	9	1949	1949	NUM
ap-7652	593	10	.	.	PUNCT
ap-7652	594	1	https://doi.org/10.1090/s0002-9947-1949-0028473-1	https://doi.org/10.1090/s0002-9947-1949-0028473-1	PROPN
ap-7652	594	2	.	.	PUNCT
ap-7652	595	1	[	[	X
ap-7652	595	2	4	4	X
ap-7652	595	3	]	]	PUNCT
ap-7652	595	4	w.	w.	PROPN
ap-7652	595	5	a.	a.	PROPN
ap-7652	595	6	al	al	PROPN
ap-7652	595	7	-	-	PUNCT
ap-7652	595	8	salam	salam	PROPN
ap-7652	595	9	.	.	PUNCT
ap-7652	596	1	the	the	DET
ap-7652	596	2	bessel	bessel	ADJ
ap-7652	596	3	polynomials	polynomial	NOUN
ap-7652	596	4	.	.	PUNCT
ap-7652	597	1	duke	duke	PROPN
ap-7652	597	2	mathematical	mathematical	PROPN
ap-7652	597	3	journal	journal	PROPN
ap-7652	597	4	24(4):529–545	24(4):529–545	NUM
ap-7652	597	5	,	,	PUNCT
ap-7652	597	6	1957	1957	NUM
ap-7652	597	7	.	.	PUNCT
ap-7652	598	1	https://doi.org/10.1215/s0012-7094-57-02460-2	https://doi.org/10.1215/s0012-7094-57-02460-2	X
ap-7652	598	2	.	.	PUNCT
ap-7652	599	1	[	[	X
ap-7652	599	2	5	5	X
ap-7652	599	3	]	]	PUNCT
ap-7652	599	4	t.	t.	PROPN
ap-7652	599	5	s.	s.	PROPN
ap-7652	599	6	chihara	chihara	PROPN
ap-7652	599	7	.	.	PUNCT
ap-7652	600	1	an	an	DET
ap-7652	600	2	introduction	introduction	NOUN
ap-7652	600	3	to	to	ADP
ap-7652	600	4	orthogonal	orthogonal	ADJ
ap-7652	600	5	polynomials	polynomial	NOUN
ap-7652	600	6	.	.	PUNCT
ap-7652	601	1	gordon	gordon	PROPN
ap-7652	601	2	and	and	CCONJ
ap-7652	601	3	breach	breach	PROPN
ap-7652	601	4	,	,	PUNCT
ap-7652	601	5	new	new	PROPN
ap-7652	601	6	york	york	PROPN
ap-7652	601	7	,	,	PUNCT
ap-7652	601	8	1978	1978	NUM
ap-7652	601	9	.	.	PUNCT
ap-7652	602	1	[	[	X
ap-7652	602	2	6	6	NUM
ap-7652	602	3	]	]	PUNCT
ap-7652	602	4	r.	r.	PROPN
ap-7652	602	5	koekoek	koekoek	PROPN
ap-7652	602	6	,	,	PUNCT
ap-7652	602	7	p.	p.	NOUN
ap-7652	602	8	a.	a.	NOUN
ap-7652	602	9	lesky	lesky	PROPN
ap-7652	602	10	,	,	PUNCT
ap-7652	602	11	r.	r.	PROPN
ap-7652	602	12	f.	f.	PROPN
ap-7652	602	13	swarttouw	swarttouw	PROPN
ap-7652	602	14	.	.	PUNCT
ap-7652	603	1	hypergeometric	hypergeometric	ADJ
ap-7652	603	2	orthogonal	orthogonal	ADJ
ap-7652	603	3	polynomials	polynomial	NOUN
ap-7652	603	4	and	and	CCONJ
ap-7652	603	5	their	their	PRON
ap-7652	603	6	q	q	NOUN
ap-7652	603	7	-	-	PUNCT
ap-7652	603	8	analogues	analogue	NOUN
ap-7652	603	9	.	.	PUNCT
ap-7652	604	1	springer	springer	NOUN
ap-7652	604	2	,	,	PUNCT
ap-7652	604	3	heidelberg	heidelberg	PROPN
ap-7652	604	4	,	,	PUNCT
ap-7652	604	5	2010	2010	NUM
ap-7652	604	6	.	.	PUNCT
ap-7652	605	1	[	[	X
ap-7652	605	2	7	7	X
ap-7652	605	3	]	]	X
ap-7652	605	4	d.	d.	PROPN
ap-7652	605	5	gomez	gomez	PROPN
ap-7652	605	6	-	-	PUNCT
ap-7652	605	7	ullate	ullate	PROPN
ap-7652	605	8	,	,	PUNCT
ap-7652	605	9	n.	n.	PROPN
ap-7652	605	10	kamran	kamran	PROPN
ap-7652	605	11	,	,	PUNCT
ap-7652	605	12	r.	r.	PROPN
ap-7652	605	13	milson	milson	PROPN
ap-7652	605	14	.	.	PUNCT
ap-7652	606	1	the	the	DET
ap-7652	606	2	darboux	darboux	VERB
ap-7652	606	3	transformation	transformation	NOUN
ap-7652	606	4	and	and	CCONJ
ap-7652	606	5	algebraic	algebraic	ADJ
ap-7652	606	6	deformations	deformation	NOUN
ap-7652	606	7	of	of	ADP
ap-7652	606	8	shape	shape	NOUN
ap-7652	606	9	-	-	PUNCT
ap-7652	606	10	invariant	invariant	ADJ
ap-7652	606	11	potentials	potential	NOUN
ap-7652	606	12	.	.	PUNCT
ap-7652	607	1	journal	journal	PROPN
ap-7652	607	2	of	of	ADP
ap-7652	607	3	physics	physics	PROPN
ap-7652	607	4	a	a	PRON
ap-7652	607	5	:	:	PUNCT
ap-7652	607	6	mathematical	mathematical	ADJ
ap-7652	607	7	and	and	CCONJ
ap-7652	607	8	general	general	ADJ
ap-7652	607	9	37(5):1789–1804	37(5):1789–1804	NUM
ap-7652	607	10	,	,	PUNCT
ap-7652	607	11	2004	2004	NUM
ap-7652	607	12	.	.	PUNCT
ap-7652	608	1	https://doi.org/10.1088/0305-4470/37/5/022	https://doi.org/10.1088/0305-4470/37/5/022	PROPN
ap-7652	608	2	.	.	PUNCT
ap-7652	609	1	[	[	X
ap-7652	609	2	8	8	NUM
ap-7652	609	3	]	]	X
ap-7652	609	4	y.	y.	PROPN
ap-7652	609	5	grandati	grandati	PROPN
ap-7652	609	6	.	.	PUNCT
ap-7652	610	1	solvable	solvable	ADJ
ap-7652	610	2	rational	rational	ADJ
ap-7652	610	3	extensions	extension	NOUN
ap-7652	610	4	of	of	ADP
ap-7652	610	5	the	the	DET
ap-7652	610	6	morse	morse	NOUN
ap-7652	610	7	and	and	CCONJ
ap-7652	610	8	kepler	kepler	NOUN
ap-7652	610	9	-	-	PUNCT
ap-7652	610	10	coulomb	coulomb	NOUN
ap-7652	610	11	potentials	potential	NOUN
ap-7652	610	12	.	.	PUNCT
ap-7652	611	1	journal	journal	PROPN
ap-7652	611	2	of	of	ADP
ap-7652	611	3	mathematical	mathematical	ADJ
ap-7652	611	4	physics	physics	NOUN
ap-7652	611	5	52(10):103505	52(10):103505	NUM
ap-7652	611	6	,	,	PUNCT
ap-7652	611	7	2011	2011	NUM
ap-7652	611	8	.	.	PUNCT
ap-7652	612	1	https://doi.org/10.1063/1.3651222	https://doi.org/10.1063/1.3651222	NOUN
ap-7652	612	2	.	.	PUNCT
ap-7652	613	1	[	[	X
ap-7652	613	2	9	9	NUM
ap-7652	613	3	]	]	X
ap-7652	613	4	c.-l	c.-l	NOUN
ap-7652	613	5	.	.	PUNCT
ap-7652	614	1	ho	ho	PROPN
ap-7652	614	2	.	.	PROPN
ap-7652	614	3	prepotential	prepotential	ADJ
ap-7652	614	4	approach	approach	NOUN
ap-7652	614	5	to	to	ADP
ap-7652	614	6	solvable	solvable	ADJ
ap-7652	614	7	rational	rational	ADJ
ap-7652	614	8	potentials	potential	NOUN
ap-7652	614	9	and	and	CCONJ
ap-7652	614	10	exceptional	exceptional	ADJ
ap-7652	614	11	orthogonal	orthogonal	ADJ
ap-7652	614	12	polynomials	polynomial	NOUN
ap-7652	614	13	.	.	PUNCT
ap-7652	615	1	progress	progress	NOUN
ap-7652	615	2	of	of	ADP
ap-7652	615	3	theoretical	theoretical	ADJ
ap-7652	615	4	physics	physics	NOUN
ap-7652	615	5	126(2):185–201	126(2):185–201	NUM
ap-7652	615	6	,	,	PUNCT
ap-7652	615	7	2011	2011	NUM
ap-7652	615	8	.	.	PUNCT
ap-7652	616	1	https://doi.org/10.1143/ptp.126.185	https://doi.org/10.1143/ptp.126.185	PROPN
ap-7652	616	2	.	.	PUNCT
ap-7652	617	1	[	[	X
ap-7652	617	2	10	10	NUM
ap-7652	617	3	]	]	X
ap-7652	617	4	c.	c.	NOUN
ap-7652	617	5	quesne	quesne	NOUN
ap-7652	617	6	.	.	PUNCT
ap-7652	618	1	revisiting	revisit	VERB
ap-7652	618	2	(	(	PUNCT
ap-7652	618	3	quasi-)exactly	quasi-)exactly	ADV
ap-7652	618	4	solvable	solvable	ADJ
ap-7652	618	5	rational	rational	ADJ
ap-7652	618	6	extensions	extension	NOUN
ap-7652	618	7	of	of	ADP
ap-7652	618	8	the	the	DET
ap-7652	618	9	morse	morse	ADJ
ap-7652	618	10	potential	potential	NOUN
ap-7652	618	11	.	.	PUNCT
ap-7652	619	1	international	international	ADJ
ap-7652	619	2	journal	journal	NOUN
ap-7652	619	3	of	of	ADP
ap-7652	619	4	modern	modern	ADJ
ap-7652	619	5	physics	physic	NOUN
ap-7652	619	6	a	a	PRON
ap-7652	619	7	27(13):1250073	27(13):1250073	NUM
ap-7652	619	8	,	,	PUNCT
ap-7652	619	9	2012	2012	NUM
ap-7652	619	10	.	.	PUNCT
ap-7652	620	1	https://doi.org/10.1142/s0217751x1250073x	https://doi.org/10.1142/s0217751x1250073x	ADJ
ap-7652	620	2	.	.	PUNCT
ap-7652	621	1	[	[	X
ap-7652	621	2	11	11	NUM
ap-7652	621	3	]	]	X
ap-7652	621	4	d.	d.	PROPN
ap-7652	621	5	gomez	gomez	PROPN
ap-7652	621	6	-	-	PUNCT
ap-7652	621	7	ullate	ullate	PROPN
ap-7652	621	8	,	,	PUNCT
ap-7652	621	9	y.	y.	PROPN
ap-7652	621	10	grandati	grandati	PROPN
ap-7652	621	11	,	,	PUNCT
ap-7652	621	12	r.	r.	PROPN
ap-7652	621	13	milson	milson	PROPN
ap-7652	621	14	.	.	PUNCT
ap-7652	622	1	extended	extend	VERB
ap-7652	622	2	krein	krein	PROPN
ap-7652	622	3	-	-	PUNCT
ap-7652	622	4	adler	adler	PROPN
ap-7652	622	5	theorem	theorem	NOUN
ap-7652	622	6	for	for	ADP
ap-7652	622	7	the	the	DET
ap-7652	622	8	translationally	translationally	ADJ
ap-7652	622	9	shape	shape	NOUN
ap-7652	622	10	invariant	invariant	ADJ
ap-7652	622	11	potentials	potential	NOUN
ap-7652	622	12	.	.	PUNCT
ap-7652	623	1	journal	journal	PROPN
ap-7652	623	2	of	of	ADP
ap-7652	623	3	mathematical	mathematical	ADJ
ap-7652	623	4	physics	physics	NOUN
ap-7652	623	5	55(4):043510	55(4):043510	NUM
ap-7652	623	6	,	,	PUNCT
ap-7652	623	7	2014	2014	NUM
ap-7652	623	8	.	.	PUNCT
ap-7652	624	1	https://doi.org/10.1063/1.4871443	https://doi.org/10.1063/1.4871443	PROPN
ap-7652	624	2	.	.	PUNCT
ap-7652	625	1	[	[	X
ap-7652	625	2	12	12	NUM
ap-7652	625	3	]	]	PUNCT
ap-7652	625	4	v.	v.	PROPN
ap-7652	625	5	i.	i.	PROPN
ap-7652	625	6	romanovski	romanovski	PROPN
ap-7652	625	7	.	.	PUNCT
ap-7652	626	1	sur	sur	PROPN
ap-7652	626	2	quelques	quelques	PROPN
ap-7652	626	3	classes	class	NOUN
ap-7652	626	4	nouvelles	nouvelles	X
ap-7652	626	5	de	de	X
ap-7652	626	6	polynomes	polynome	NOUN
ap-7652	626	7	orthogonaux	orthogonaux	ADJ
ap-7652	626	8	.	.	PUNCT
ap-7652	627	1	comptes	compte	VERB
ap-7652	627	2	rendus	rendus	PROPN
ap-7652	627	3	de	de	PROPN
ap-7652	627	4	l’académie	l’académie	PROPN
ap-7652	627	5	des	des	PROPN
ap-7652	627	6	sciences	sciences	PROPN
ap-7652	627	7	188:1023–1025	188:1023–1025	NUM
ap-7652	627	8	,	,	PUNCT
ap-7652	627	9	1929	1929	NUM
ap-7652	627	10	.	.	PUNCT
ap-7652	628	1	[	[	X
ap-7652	628	2	13	13	NUM
ap-7652	628	3	]	]	PUNCT
ap-7652	628	4	p.	p.	NOUN
ap-7652	628	5	a.	a.	NOUN
ap-7652	628	6	lesky	lesky	PROPN
ap-7652	628	7	.	.	PUNCT
ap-7652	629	1	einordnung	einordnung	PROPN
ap-7652	629	2	der	der	PROPN
ap-7652	629	3	polynome	polynome	PROPN
ap-7652	629	4	von	von	PROPN
ap-7652	629	5	romanovski	romanovski	PROPN
ap-7652	629	6	-	-	PUNCT
ap-7652	629	7	bessel	bessel	NOUN
ap-7652	629	8	in	in	ADP
ap-7652	629	9	das	das	PROPN
ap-7652	629	10	askey	askey	PROPN
ap-7652	629	11	-	-	PUNCT
ap-7652	629	12	tableau	tableau	PROPN
ap-7652	629	13	.	.	PUNCT
ap-7652	630	1	zeitschrift	zeitschrift	PROPN
ap-7652	630	2	für	für	PROPN
ap-7652	630	3	angewandte	angewandte	PROPN
ap-7652	630	4	mathematik	mathematik	PROPN
ap-7652	630	5	und	und	PROPN
ap-7652	630	6	mechanik	mechanik	PROPN
ap-7652	630	7	78(9):646–648	78(9):646–648	PROPN
ap-7652	630	8	,	,	PUNCT
ap-7652	630	9	1998	1998	NUM
ap-7652	630	10	.	.	PUNCT
ap-7652	631	1	https://doi.org/10.1002/(sici)1521-4001(199809)78:9<646::aid-zamm646>3.0.co;2-w	https://doi.org/10.1002/(sici)1521-4001(199809)78:9<646::aid-zamm646>3.0.co;2-w	PROPN
ap-7652	631	2	.	.	PUNCT
ap-7652	632	1	[	[	X
ap-7652	632	2	14	14	NUM
ap-7652	632	3	]	]	X
ap-7652	632	4	c.	c.	NOUN
ap-7652	632	5	quesne	quesne	NOUN
ap-7652	632	6	.	.	PUNCT
ap-7652	633	1	extending	extend	VERB
ap-7652	633	2	romanovski	romanovski	NOUN
ap-7652	633	3	polynomials	polynomial	NOUN
ap-7652	633	4	in	in	ADP
ap-7652	633	5	quantum	quantum	ADJ
ap-7652	633	6	mechanics	mechanic	NOUN
ap-7652	633	7	.	.	PUNCT
ap-7652	634	1	journal	journal	PROPN
ap-7652	634	2	of	of	ADP
ap-7652	634	3	mathematical	mathematical	ADJ
ap-7652	634	4	physics	physics	PROPN
ap-7652	634	5	54(12):122103	54(12):122103	NUM
ap-7652	634	6	,	,	PUNCT
ap-7652	634	7	2013	2013	NUM
ap-7652	634	8	.	.	PUNCT
ap-7652	635	1	https://doi.org/10.1063/1.4835555	https://doi.org/10.1063/1.4835555	NOUN
ap-7652	635	2	.	.	PUNCT
ap-7652	636	1	[	[	X
ap-7652	636	2	15	15	NUM
ap-7652	636	3	]	]	X
ap-7652	636	4	n.	n.	NOUN
ap-7652	636	5	cotfas	cotfas	NOUN
ap-7652	636	6	.	.	PUNCT
ap-7652	637	1	systems	system	NOUN
ap-7652	637	2	of	of	ADP
ap-7652	637	3	orthogonal	orthogonal	ADJ
ap-7652	637	4	polynomials	polynomial	NOUN
ap-7652	637	5	defined	define	VERB
ap-7652	637	6	by	by	ADP
ap-7652	637	7	hypergeometric	hypergeometric	ADJ
ap-7652	637	8	type	type	NOUN
ap-7652	637	9	equations	equation	NOUN
ap-7652	637	10	with	with	ADP
ap-7652	637	11	application	application	NOUN
ap-7652	637	12	to	to	ADP
ap-7652	637	13	quantum	quantum	ADJ
ap-7652	637	14	mechanics	mechanic	NOUN
ap-7652	637	15	.	.	PUNCT
ap-7652	638	1	central	central	ADJ
ap-7652	638	2	european	european	PROPN
ap-7652	638	3	journal	journal	PROPN
ap-7652	638	4	of	of	ADP
ap-7652	638	5	physics	physics	PROPN
ap-7652	638	6	2(3):456–466	2(3):456–466	NUM
ap-7652	638	7	,	,	PUNCT
ap-7652	638	8	2004	2004	NUM
ap-7652	638	9	.	.	PUNCT
ap-7652	639	1	https://doi.org/10.2478/bf02476425	https://doi.org/10.2478/bf02476425	X
ap-7652	639	2	.	.	PUNCT
ap-7652	640	1	[	[	X
ap-7652	640	2	16	16	NUM
ap-7652	640	3	]	]	X
ap-7652	640	4	n.	n.	NOUN
ap-7652	640	5	cotfas	cotfas	NOUN
ap-7652	640	6	.	.	PUNCT
ap-7652	640	7	shape	shape	NOUN
ap-7652	640	8	-	-	PUNCT
ap-7652	640	9	invariant	invariant	ADJ
ap-7652	640	10	hypergeometric	hypergeometric	ADJ
ap-7652	640	11	type	type	NOUN
ap-7652	640	12	operators	operator	NOUN
ap-7652	640	13	with	with	ADP
ap-7652	640	14	application	application	NOUN
ap-7652	640	15	to	to	ADP
ap-7652	640	16	quantum	quantum	ADJ
ap-7652	640	17	mechanics	mechanic	NOUN
ap-7652	640	18	.	.	PUNCT
ap-7652	641	1	central	central	ADJ
ap-7652	641	2	european	european	PROPN
ap-7652	641	3	journal	journal	PROPN
ap-7652	641	4	of	of	ADP
ap-7652	641	5	physics	physics	PROPN
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ap-7652	641	7	,	,	PUNCT
ap-7652	641	8	2006	2006	NUM
ap-7652	641	9	.	.	PUNCT
ap-7652	642	1	https://doi.org/10.2478/s11534-006-0023-0	https://doi.org/10.2478/s11534-006-0023-0	NUM
ap-7652	642	2	.	.	PUNCT
ap-7652	643	1	[	[	X
ap-7652	643	2	17	17	NUM
ap-7652	643	3	]	]	PUNCT
ap-7652	643	4	m.	m.	NOUN
ap-7652	643	5	a.	a.	PROPN
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ap-7652	643	8	h.	h.	PROPN
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ap-7652	643	10	.	.	PUNCT
ap-7652	644	1	parasupersymmetry	parasupersymmetry	NOUN
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ap-7652	644	3	shape	shape	VERB
ap-7652	644	4	invariance	invariance	NOUN
ap-7652	644	5	in	in	ADP
ap-7652	644	6	differential	differential	ADJ
ap-7652	644	7	equations	equation	NOUN
ap-7652	644	8	of	of	ADP
ap-7652	644	9	mathematical	mathematical	ADJ
ap-7652	644	10	physics	physics	NOUN
ap-7652	644	11	and	and	CCONJ
ap-7652	644	12	quantum	quantum	NOUN
ap-7652	644	13	mechanics	mechanic	NOUN
ap-7652	644	14	.	.	PUNCT
ap-7652	645	1	annals	annal	NOUN
ap-7652	645	2	of	of	ADP
ap-7652	645	3	physics	physics	NOUN
ap-7652	645	4	262(2):260–276	262(2):260–276	PROPN
ap-7652	645	5	,	,	PUNCT
ap-7652	645	6	1998	1998	NUM
ap-7652	645	7	.	.	PUNCT
ap-7652	646	1	https://doi.org/10.1006/aphy.1997.5745	https://doi.org/10.1006/aphy.1997.5745	PROPN
ap-7652	646	2	.	.	PUNCT
ap-7652	647	1	115	115	NUM
ap-7652	648	1	https://doi.org/10.1134/s0040577921010050	https://doi.org/10.1134/s0040577921010050	NUM
ap-7652	648	2	https://doi.org/10.1063/1.3001604	https://doi.org/10.1063/1.3001604	PROPN
ap-7652	648	3	https://doi.org/10.1090/s0002-9947-1949-0028473-1	https://doi.org/10.1090/s0002-9947-1949-0028473-1	PROPN
ap-7652	648	4	https://doi.org/10.1215/s0012-7094-57-02460-2	https://doi.org/10.1215/s0012-7094-57-02460-2	PROPN
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ap-7652	648	12	https://doi.org/10.2478/bf02476425	https://doi.org/10.2478/bf02476425	NOUN
ap-7652	648	13	https://doi.org/10.2478/s11534-006-0023-0	https://doi.org/10.2478/s11534-006-0023-0	PROPN
ap-7652	649	1	https://doi.org/10.1006/aphy.1997.5745	https://doi.org/10.1006/aphy.1997.5745	PROPN
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ap-7652	649	4	acta	acta	PROPN
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ap-7652	649	6	[	[	X
ap-7652	649	7	18	18	NUM
ap-7652	649	8	]	]	X
ap-7652	649	9	s.	s.	PROPN
ap-7652	649	10	odake	odake	PROPN
ap-7652	649	11	,	,	PUNCT
ap-7652	649	12	r.	r.	PROPN
ap-7652	649	13	sasaki	sasaki	PROPN
ap-7652	649	14	.	.	PUNCT
ap-7652	650	1	extensions	extension	NOUN
ap-7652	650	2	of	of	ADP
ap-7652	650	3	solvable	solvable	ADJ
ap-7652	650	4	potentials	potential	NOUN
ap-7652	650	5	with	with	ADP
ap-7652	650	6	finitely	finitely	ADV
ap-7652	650	7	many	many	ADJ
ap-7652	650	8	discrete	discrete	ADJ
ap-7652	650	9	eigenstates	eigenstate	NOUN
ap-7652	650	10	.	.	PUNCT
ap-7652	651	1	journal	journal	PROPN
ap-7652	651	2	of	of	ADP
ap-7652	651	3	physics	physics	PROPN
ap-7652	651	4	a	a	PRON
ap-7652	651	5	:	:	PUNCT
ap-7652	651	6	mathematical	mathematical	ADJ
ap-7652	651	7	and	and	CCONJ
ap-7652	651	8	theoretical	theoretical	ADJ
ap-7652	651	9	46(23):235205	46(23):235205	NUM
ap-7652	651	10	,	,	PUNCT
ap-7652	651	11	2013	2013	NUM
ap-7652	651	12	.	.	PUNCT
ap-7652	652	1	https://doi.org/10.1088/1751-8113/46/23/235205	https://doi.org/10.1088/1751-8113/46/23/235205	PROPN
ap-7652	652	2	.	.	PUNCT
ap-7652	653	1	[	[	X
ap-7652	653	2	19	19	NUM
ap-7652	653	3	]	]	X
ap-7652	653	4	s.	s.	PROPN
ap-7652	653	5	odake	odake	PROPN
ap-7652	653	6	.	.	PUNCT
ap-7652	654	1	krein	krein	PROPN
ap-7652	654	2	–	–	PUNCT
ap-7652	654	3	adler	adler	NOUN
ap-7652	654	4	transformations	transformation	NOUN
ap-7652	654	5	for	for	ADP
ap-7652	654	6	shape	shape	NOUN
ap-7652	654	7	-	-	PUNCT
ap-7652	654	8	invariant	invariant	ADJ
ap-7652	654	9	potentials	potential	NOUN
ap-7652	654	10	and	and	CCONJ
ap-7652	654	11	pseudo	pseudo	NOUN
ap-7652	654	12	virtual	virtual	ADJ
ap-7652	654	13	states	state	NOUN
ap-7652	654	14	.	.	PUNCT
ap-7652	655	1	journal	journal	PROPN
ap-7652	655	2	of	of	ADP
ap-7652	655	3	physics	physics	PROPN
ap-7652	655	4	a	a	PRON
ap-7652	655	5	:	:	PUNCT
ap-7652	655	6	mathematical	mathematical	ADJ
ap-7652	655	7	and	and	CCONJ
ap-7652	655	8	theoretical	theoretical	ADJ
ap-7652	655	9	46(24):245201	46(24):245201	NUM
ap-7652	655	10	,	,	PUNCT
ap-7652	655	11	2013	2013	NUM
ap-7652	655	12	.	.	PUNCT
ap-7652	656	1	https://doi.org/10.1088/1751-8113/46/24/245201	https://doi.org/10.1088/1751-8113/46/24/245201	NOUN
ap-7652	656	2	.	.	PUNCT
ap-7652	657	1	[	[	X
ap-7652	657	2	20	20	NUM
ap-7652	657	3	]	]	X
ap-7652	657	4	g.	g.	PROPN
ap-7652	657	5	darboux	darboux	NOUN
ap-7652	657	6	.	.	PUNCT
ap-7652	658	1	leçons	leçons	PROPN
ap-7652	658	2	sur	sur	PROPN
ap-7652	658	3	la	la	PROPN
ap-7652	658	4	théorie	théorie	PROPN
ap-7652	658	5	générale	générale	PROPN
ap-7652	658	6	des	des	PROPN
ap-7652	658	7	surfaces	surfaces	PROPN
ap-7652	658	8	et	et	NOUN
ap-7652	658	9	les	les	PROPN
ap-7652	658	10	applications	application	NOUN
ap-7652	658	11	géométriques	géométrique	VERB
ap-7652	658	12	du	du	PROPN
ap-7652	658	13	calcul	calcul	PROPN
ap-7652	658	14	infinitésimal	infinitésimal	PROPN
ap-7652	658	15	.	.	PUNCT
ap-7652	659	1	gauthier	gauthier	PROPN
ap-7652	659	2	-	-	PUNCT
ap-7652	659	3	villars	villars	PROPN
ap-7652	659	4	,	,	PUNCT
ap-7652	659	5	paris	paris	PROPN
ap-7652	659	6	,	,	PUNCT
ap-7652	659	7	1915	1915	NUM
ap-7652	659	8	.	.	PUNCT
ap-7652	660	1	[	[	X
ap-7652	660	2	21	21	NUM
ap-7652	660	3	]	]	PUNCT
ap-7652	660	4	m.	m.	NOUN
ap-7652	660	5	m.	m.	PROPN
ap-7652	660	6	crum	crum	PROPN
ap-7652	660	7	.	.	PUNCT
ap-7652	661	1	associated	associated	PROPN
ap-7652	661	2	sturm	sturm	PROPN
ap-7652	661	3	-	-	PUNCT
ap-7652	661	4	liouville	liouville	NOUN
ap-7652	661	5	systems	system	NOUN
ap-7652	661	6	.	.	PUNCT
ap-7652	662	1	the	the	DET
ap-7652	662	2	quarterly	quarterly	ADJ
ap-7652	662	3	journal	journal	NOUN
ap-7652	662	4	of	of	ADP
ap-7652	662	5	mathematics	mathematics	PROPN
ap-7652	662	6	6(1):121–127	6(1):121–127	NUM
ap-7652	662	7	,	,	PUNCT
ap-7652	662	8	1955	1955	NUM
ap-7652	662	9	.	.	PUNCT
ap-7652	663	1	https://doi.org/10.1093/qmath/6.1.121	https://doi.org/10.1093/qmath/6.1.121	X
ap-7652	663	2	.	.	PUNCT
ap-7652	664	1	[	[	X
ap-7652	664	2	22	22	NUM
ap-7652	664	3	]	]	X
ap-7652	664	4	l.	l.	PROPN
ap-7652	664	5	d.	d.	PROPN
ap-7652	664	6	landau	landau	PROPN
ap-7652	664	7	,	,	PUNCT
ap-7652	664	8	e.	e.	PROPN
ap-7652	664	9	m.	m.	PROPN
ap-7652	664	10	lifshity	lifshity	PROPN
ap-7652	664	11	.	.	PUNCT
ap-7652	665	1	quantum	quantum	ADJ
ap-7652	665	2	mechanics	mechanic	NOUN
ap-7652	665	3	(	(	PUNCT
ap-7652	665	4	non	non	ADJ
ap-7652	665	5	-	-	ADJ
ap-7652	665	6	relativistic	relativistic	ADJ
ap-7652	665	7	theory	theory	NOUN
ap-7652	665	8	)	)	PUNCT
ap-7652	665	9	.	.	PUNCT
ap-7652	666	1	3rd	3rd	ADJ
ap-7652	666	2	ed	ed	NOUN
ap-7652	666	3	.	.	PUNCT
ap-7652	667	1	butterworth	butterworth	PROPN
ap-7652	667	2	-	-	PUNCT
ap-7652	667	3	heinemann	heinemann	PROPN
ap-7652	667	4	,	,	PUNCT
ap-7652	667	5	1977	1977	NUM
ap-7652	667	6	.	.	PUNCT
ap-7652	668	1	[	[	X
ap-7652	668	2	23	23	NUM
ap-7652	668	3	]	]	X
ap-7652	668	4	g.	g.	PROPN
ap-7652	668	5	natanson	natanson	PROPN
ap-7652	668	6	.	.	PROPN
ap-7652	669	1	equivalence	equivalence	NOUN
ap-7652	669	2	relations	relation	NOUN
ap-7652	669	3	for	for	ADP
ap-7652	669	4	darboux	darboux	ADJ
ap-7652	669	5	-	-	PUNCT
ap-7652	669	6	crum	crum	NOUN
ap-7652	669	7	transforms	transform	NOUN
ap-7652	669	8	of	of	ADP
ap-7652	669	9	translationally	translationally	ADJ
ap-7652	669	10	form	form	NOUN
ap-7652	669	11	-	-	PUNCT
ap-7652	669	12	invariant	invariant	ADJ
ap-7652	669	13	sturm	sturm	NOUN
ap-7652	669	14	-	-	PUNCT
ap-7652	669	15	liouville	liouville	NOUN
ap-7652	669	16	equations	equation	NOUN
ap-7652	669	17	,	,	PUNCT
ap-7652	669	18	2021	2021	NUM
ap-7652	669	19	.	.	PUNCT
ap-7652	670	1	https://www.researchgate.net/publication/353131294	https://www.researchgate.net/publication/353131294	NOUN
ap-7652	670	2	.	.	PUNCT
ap-7652	671	1	[	[	X
ap-7652	671	2	24	24	NUM
ap-7652	671	3	]	]	X
ap-7652	671	4	d.	d.	PROPN
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ap-7652	671	6	-	-	PUNCT
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ap-7652	671	8	,	,	PUNCT
ap-7652	671	9	y.	y.	PROPN
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ap-7652	671	11	,	,	PUNCT
ap-7652	671	12	r.	r.	PROPN
ap-7652	671	13	milson	milson	PROPN
ap-7652	671	14	.	.	PUNCT
ap-7652	672	1	durfee	durfee	PROPN
ap-7652	672	2	rectangles	rectangle	NOUN
ap-7652	672	3	and	and	CCONJ
ap-7652	672	4	pseudo	pseudo	NOUN
ap-7652	672	5	-	-	NOUN
ap-7652	672	6	wronskian	wronskian	ADJ
ap-7652	672	7	equivalences	equivalence	VERB
ap-7652	672	8	for	for	ADP
ap-7652	672	9	hermite	hermite	ADJ
ap-7652	672	10	polynomials	polynomial	NOUN
ap-7652	672	11	.	.	PUNCT
ap-7652	673	1	studies	study	NOUN
ap-7652	673	2	in	in	ADP
ap-7652	673	3	applied	applied	ADJ
ap-7652	673	4	mathematics	mathematic	NOUN
ap-7652	673	5	141(4):596–625	141(4):596–625	NUM
ap-7652	673	6	,	,	PUNCT
ap-7652	673	7	2018	2018	NUM
ap-7652	673	8	.	.	PUNCT
ap-7652	674	1	https://doi.org/10.1111/sapm.12225	https://doi.org/10.1111/sapm.12225	X
ap-7652	674	2	.	.	PUNCT
ap-7652	675	1	[	[	X
ap-7652	675	2	25	25	NUM
ap-7652	675	3	]	]	PUNCT
ap-7652	675	4	w.	w.	PROPN
ap-7652	675	5	n.	n.	PROPN
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ap-7652	675	7	,	,	PUNCT
ap-7652	675	8	l.	l.	PROPN
ap-7652	675	9	l.	l.	PROPN
ap-7652	675	10	littlejohn	littlejohn	PROPN
ap-7652	675	11	.	.	PUNCT
ap-7652	676	1	orthogonal	orthogonal	ADJ
ap-7652	676	2	polynomials	polynomial	NOUN
ap-7652	676	3	and	and	CCONJ
ap-7652	676	4	spectral	spectral	ADJ
ap-7652	676	5	theory	theory	NOUN
ap-7652	676	6	:	:	PUNCT
ap-7652	676	7	a	a	DET
ap-7652	676	8	survey	survey	NOUN
ap-7652	676	9	.	.	PUNCT
ap-7652	677	1	in	in	ADP
ap-7652	677	2	c.	c.	PROPN
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ap-7652	677	4	,	,	PUNCT
ap-7652	677	5	l.	l.	PROPN
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ap-7652	677	7	,	,	PUNCT
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ap-7652	677	9	ronveaux	ronveaux	NOUN
ap-7652	677	10	(	(	PUNCT
ap-7652	677	11	eds	ed	NOUN
ap-7652	677	12	.	.	PUNCT
ap-7652	677	13	)	)	PUNCT
ap-7652	677	14	,	,	PUNCT
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ap-7652	677	16	polynomials	polynomial	NOUN
ap-7652	677	17	and	and	CCONJ
ap-7652	677	18	their	their	PRON
ap-7652	677	19	applications	application	NOUN
ap-7652	677	20	,	,	PUNCT
ap-7652	677	21	vol	vol	NOUN
ap-7652	677	22	.	.	PROPN
ap-7652	677	23	9	9	NUM
ap-7652	677	24	,	,	PUNCT
ap-7652	677	25	pp	pp	ADJ
ap-7652	677	26	.	.	PUNCT
ap-7652	677	27	21–55	21–55	X
ap-7652	677	28	.	.	PUNCT
ap-7652	677	29	1991	1991	NUM
ap-7652	677	30	.	.	PUNCT
ap-7652	678	1	imacs	imacs	PROPN
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ap-7652	678	3	on	on	ADP
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ap-7652	678	8	.	.	PUNCT
ap-7652	679	1	[	[	X
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ap-7652	679	4	w.	w.	PROPN
ap-7652	679	5	n.	n.	PROPN
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ap-7652	679	7	,	,	PUNCT
ap-7652	679	8	k.	k.	PROPN
ap-7652	679	9	h.	h.	PROPN
ap-7652	679	10	kwon	kwon	PROPN
ap-7652	679	11	,	,	PUNCT
ap-7652	679	12	l.	l.	PROPN
ap-7652	679	13	l.	l.	PROPN
ap-7652	679	14	littlejohn	littlejohn	PROPN
ap-7652	679	15	,	,	PUNCT
ap-7652	679	16	r.	r.	PROPN
ap-7652	679	17	wellman	wellman	PROPN
ap-7652	679	18	.	.	PUNCT
ap-7652	680	1	orthogonal	orthogonal	ADJ
ap-7652	680	2	polynomial	polynomial	ADJ
ap-7652	680	3	solutions	solution	NOUN
ap-7652	680	4	of	of	ADP
ap-7652	680	5	linear	linear	ADJ
ap-7652	680	6	ordinary	ordinary	ADJ
ap-7652	680	7	differential	differential	ADJ
ap-7652	680	8	equations	equation	NOUN
ap-7652	680	9	.	.	PUNCT
ap-7652	681	1	journal	journal	NOUN
ap-7652	681	2	of	of	ADP
ap-7652	681	3	computational	computational	ADJ
ap-7652	681	4	and	and	CCONJ
ap-7652	681	5	applied	apply	VERB
ap-7652	681	6	mathematics	mathematic	NOUN
ap-7652	681	7	133(1	133(1	NUM
ap-7652	681	8	-	-	SYM
ap-7652	681	9	2):85–109	2):85–109	NUM
ap-7652	681	10	,	,	PUNCT
ap-7652	681	11	2001	2001	NUM
ap-7652	681	12	.	.	PUNCT
ap-7652	682	1	https://doi.org/10.1016/s0377-0427(00)00636-1	https://doi.org/10.1016/s0377-0427(00)00636-1	NOUN
ap-7652	682	2	.	.	PUNCT
ap-7652	683	1	[	[	X
ap-7652	683	2	27	27	NUM
ap-7652	683	3	]	]	PUNCT
ap-7652	683	4	a.	a.	PROPN
ap-7652	683	5	k.	k.	PROPN
ap-7652	683	6	bose	bose	PROPN
ap-7652	683	7	.	.	PUNCT
ap-7652	684	1	a	a	DET
ap-7652	684	2	class	class	NOUN
ap-7652	684	3	of	of	ADP
ap-7652	684	4	solvable	solvable	ADJ
ap-7652	684	5	potentials	potential	NOUN
ap-7652	684	6	.	.	PUNCT
ap-7652	685	1	nuovo	nuovo	PROPN
ap-7652	685	2	cimento	cimento	PROPN
ap-7652	685	3	32:679–688	32:679–688	NUM
ap-7652	685	4	,	,	PUNCT
ap-7652	685	5	1964	1964	NUM
ap-7652	685	6	.	.	PUNCT
ap-7652	686	1	https://doi.org/10.1007/bf02735890	https://doi.org/10.1007/bf02735890	VERB
ap-7652	686	2	.	.	PUNCT
ap-7652	687	1	[	[	X
ap-7652	687	2	28	28	NUM
ap-7652	687	3	]	]	X
ap-7652	687	4	g.	g.	PROPN
ap-7652	687	5	a.	a.	PROPN
ap-7652	687	6	natanzon	natanzon	PROPN
ap-7652	687	7	.	.	PUNCT
ap-7652	688	1	study	study	NOUN
ap-7652	688	2	of	of	ADP
ap-7652	688	3	the	the	DET
ap-7652	688	4	one	one	NUM
ap-7652	688	5	-	-	PUNCT
ap-7652	688	6	dimensional	dimensional	ADJ
ap-7652	688	7	schrödinger	schrödinger	ADJ
ap-7652	688	8	equation	equation	NOUN
ap-7652	688	9	generated	generate	VERB
ap-7652	688	10	from	from	ADP
ap-7652	688	11	the	the	DET
ap-7652	688	12	hypergeometric	hypergeometric	ADJ
ap-7652	688	13	equation	equation	NOUN
ap-7652	688	14	.	.	PUNCT
ap-7652	689	1	vestnik	vestnik	PROPN
ap-7652	689	2	leningradskogo	leningradskogo	PROPN
ap-7652	689	3	universiteta	universiteta	PROPN
ap-7652	689	4	10:22–28	10:22–28	PROPN
ap-7652	689	5	,	,	PUNCT
ap-7652	689	6	1971	1971	NUM
ap-7652	689	7	.	.	PUNCT
ap-7652	690	1	english	english	ADJ
ap-7652	690	2	translation	translation	NOUN
ap-7652	690	3	https://arxiv.org/ps_cache/physics/pdf/9907/9907032v1.pdf	https://arxiv.org/ps_cache/physics/pdf/9907/9907032v1.pdf	NOUN
ap-7652	690	4	.	.	PUNCT
ap-7652	691	1	[	[	X
ap-7652	691	2	29	29	NUM
ap-7652	691	3	]	]	X
ap-7652	691	4	b.	b.	PROPN
ap-7652	692	1	v.	v.	PROPN
ap-7652	692	2	rudyak	rudyak	PROPN
ap-7652	692	3	,	,	PUNCT
ap-7652	692	4	b.	b.	PROPN
ap-7652	692	5	n.	n.	PROPN
ap-7652	692	6	zakhariev	zakhariev	PROPN
ap-7652	692	7	.	.	PUNCT
ap-7652	693	1	new	new	ADJ
ap-7652	693	2	exactly	exactly	ADV
ap-7652	693	3	solvable	solvable	ADJ
ap-7652	693	4	models	model	NOUN
ap-7652	693	5	for	for	ADP
ap-7652	693	6	schrödinger	schrödinger	ADJ
ap-7652	693	7	equation	equation	NOUN
ap-7652	693	8	.	.	PUNCT
ap-7652	694	1	inverse	inverse	NOUN
ap-7652	694	2	problems	problem	NOUN
ap-7652	694	3	3(1):125–133	3(1):125–133	NUM
ap-7652	694	4	,	,	PUNCT
ap-7652	694	5	1987	1987	NUM
ap-7652	694	6	.	.	PUNCT
ap-7652	695	1	https://doi.org/10.1088/0266-5611/3/1/014	https://doi.org/10.1088/0266-5611/3/1/014	PROPN
ap-7652	695	2	.	.	PUNCT
ap-7652	696	1	[	[	X
ap-7652	696	2	30	30	NUM
ap-7652	696	3	]	]	X
ap-7652	696	4	l.	l.	PROPN
ap-7652	696	5	d.	d.	PROPN
ap-7652	696	6	fadeev	fadeev	PROPN
ap-7652	696	7	,	,	PUNCT
ap-7652	696	8	b.	b.	PROPN
ap-7652	696	9	seckler	seckler	NOUN
ap-7652	696	10	.	.	PUNCT
ap-7652	697	1	the	the	DET
ap-7652	697	2	inverse	inverse	ADJ
ap-7652	697	3	problem	problem	NOUN
ap-7652	697	4	in	in	ADP
ap-7652	697	5	the	the	DET
ap-7652	697	6	quantum	quantum	ADJ
ap-7652	697	7	theory	theory	NOUN
ap-7652	697	8	of	of	ADP
ap-7652	697	9	scattering	scatter	VERB
ap-7652	697	10	.	.	PUNCT
ap-7652	698	1	journal	journal	PROPN
ap-7652	698	2	of	of	ADP
ap-7652	698	3	mathematical	mathematical	ADJ
ap-7652	698	4	physics	physics	PROPN
ap-7652	698	5	4(1):72–104	4(1):72–104	PROPN
ap-7652	698	6	,	,	PUNCT
ap-7652	698	7	1963	1963	NUM
ap-7652	698	8	.	.	PUNCT
ap-7652	699	1	https://doi.org/10.1063/1.1703891	https://doi.org/10.1063/1.1703891	NOUN
ap-7652	699	2	.	.	PUNCT
ap-7652	700	1	[	[	X
ap-7652	700	2	31	31	NUM
ap-7652	700	3	]	]	PUNCT
ap-7652	700	4	w.	w.	PROPN
ap-7652	700	5	a.	a.	NOUN
ap-7652	700	6	schnizer	schnizer	PROPN
ap-7652	700	7	,	,	PUNCT
ap-7652	700	8	h.	h.	PROPN
ap-7652	700	9	leeb	leeb	PROPN
ap-7652	700	10	.	.	PUNCT
ap-7652	701	1	exactly	exactly	ADV
ap-7652	701	2	solvable	solvable	ADJ
ap-7652	701	3	models	model	NOUN
ap-7652	701	4	for	for	ADP
ap-7652	701	5	the	the	DET
ap-7652	701	6	schrödinger	schrödinger	ADJ
ap-7652	701	7	equation	equation	NOUN
ap-7652	701	8	from	from	ADP
ap-7652	701	9	generalized	generalized	ADJ
ap-7652	701	10	darboux	darboux	NOUN
ap-7652	701	11	transformations	transformation	NOUN
ap-7652	701	12	.	.	PUNCT
ap-7652	702	1	journal	journal	PROPN
ap-7652	702	2	of	of	ADP
ap-7652	702	3	physics	physics	PROPN
ap-7652	702	4	a	a	PRON
ap-7652	702	5	:	:	PUNCT
ap-7652	702	6	mathematical	mathematical	ADJ
ap-7652	702	7	and	and	CCONJ
ap-7652	702	8	general	general	ADJ
ap-7652	702	9	26(19):5145–5156	26(19):5145–5156	NUM
ap-7652	702	10	,	,	PUNCT
ap-7652	702	11	1993	1993	NUM
ap-7652	702	12	.	.	PUNCT
ap-7652	703	1	https://doi.org/10.1088/0305-4470/26/19/041	https://doi.org/10.1088/0305-4470/26/19/041	NOUN
ap-7652	703	2	.	.	PUNCT
ap-7652	704	1	[	[	X
ap-7652	704	2	32	32	NUM
ap-7652	704	3	]	]	PUNCT
ap-7652	704	4	w.	w.	PROPN
ap-7652	704	5	a.	a.	NOUN
ap-7652	704	6	schnizer	schnizer	PROPN
ap-7652	704	7	,	,	PUNCT
ap-7652	704	8	h.	h.	PROPN
ap-7652	704	9	leeb	leeb	PROPN
ap-7652	704	10	.	.	PUNCT
ap-7652	705	1	generalized	generalize	VERB
ap-7652	705	2	darboux	darboux	ADJ
ap-7652	705	3	transformations	transformation	NOUN
ap-7652	705	4	:	:	PUNCT
ap-7652	705	5	classification	classification	NOUN
ap-7652	705	6	of	of	ADP
ap-7652	705	7	inverse	inverse	NOUN
ap-7652	705	8	scattering	scatter	VERB
ap-7652	705	9	methods	method	NOUN
ap-7652	705	10	for	for	ADP
ap-7652	705	11	the	the	DET
ap-7652	705	12	radial	radial	ADJ
ap-7652	705	13	schrödinger	schrödinger	ADJ
ap-7652	705	14	equation	equation	NOUN
ap-7652	705	15	.	.	PUNCT
ap-7652	706	1	journal	journal	PROPN
ap-7652	706	2	of	of	ADP
ap-7652	706	3	physics	physics	PROPN
ap-7652	706	4	a	a	PRON
ap-7652	706	5	:	:	PUNCT
ap-7652	706	6	mathematical	mathematical	ADJ
ap-7652	706	7	and	and	CCONJ
ap-7652	706	8	general	general	ADJ
ap-7652	706	9	27(7):2605–2614	27(7):2605–2614	NUM
ap-7652	706	10	,	,	PUNCT
ap-7652	706	11	1994	1994	NUM
ap-7652	706	12	.	.	PUNCT
ap-7652	707	1	https://doi.org/10.1088/0305-4470/27/7/035	https://doi.org/10.1088/0305-4470/27/7/035	PROPN
ap-7652	707	2	.	.	PUNCT
ap-7652	708	1	[	[	X
ap-7652	708	2	33	33	NUM
ap-7652	708	3	]	]	X
ap-7652	708	4	d.	d.	PROPN
ap-7652	708	5	gómez	gómez	PROPN
ap-7652	708	6	-	-	PUNCT
ap-7652	708	7	ullate	ullate	NOUN
ap-7652	708	8	,	,	PUNCT
ap-7652	708	9	y.	y.	PROPN
ap-7652	708	10	grandati	grandati	PROPN
ap-7652	708	11	,	,	PUNCT
ap-7652	708	12	r.	r.	PROPN
ap-7652	708	13	milson	milson	PROPN
ap-7652	708	14	.	.	PUNCT
ap-7652	709	1	shape	shape	PROPN
ap-7652	709	2	invariance	invariance	NOUN
ap-7652	709	3	and	and	CCONJ
ap-7652	709	4	equivalence	equivalence	NOUN
ap-7652	709	5	relations	relation	NOUN
ap-7652	709	6	for	for	ADP
ap-7652	709	7	pseudo	pseudo	NOUN
ap-7652	709	8	-	-	NOUN
ap-7652	709	9	wronskians	wronskian	NOUN
ap-7652	709	10	of	of	ADP
ap-7652	709	11	laguerre	laguerre	NOUN
ap-7652	709	12	and	and	CCONJ
ap-7652	709	13	jacobi	jacobi	PROPN
ap-7652	709	14	polynomials	polynomial	NOUN
ap-7652	709	15	.	.	PUNCT
ap-7652	710	1	journal	journal	PROPN
ap-7652	710	2	of	of	ADP
ap-7652	710	3	physics	physics	PROPN
ap-7652	710	4	a	a	PRON
ap-7652	710	5	:	:	PUNCT
ap-7652	710	6	mathematical	mathematical	ADJ
ap-7652	710	7	and	and	CCONJ
ap-7652	710	8	theoretical	theoretical	ADJ
ap-7652	710	9	51(34):345201	51(34):345201	NUM
ap-7652	710	10	,	,	PUNCT
ap-7652	710	11	2018	2018	NUM
ap-7652	710	12	.	.	PUNCT
ap-7652	711	1	https://doi.org/10.1088/1751-8121/aace4b	https://doi.org/10.1088/1751-8121/aace4b	INTJ
ap-7652	711	2	.	.	PUNCT
ap-7652	712	1	[	[	X
ap-7652	712	2	34	34	NUM
ap-7652	712	3	]	]	X
ap-7652	712	4	l.	l.	PROPN
ap-7652	712	5	e.	e.	PROPN
ap-7652	712	6	gendenshtein	gendenshtein	PROPN
ap-7652	712	7	.	.	PUNCT
ap-7652	713	1	derivation	derivation	NOUN
ap-7652	713	2	of	of	ADP
ap-7652	713	3	exact	exact	ADJ
ap-7652	713	4	spectra	spectra	NOUN
ap-7652	713	5	of	of	ADP
ap-7652	713	6	the	the	DET
ap-7652	713	7	schrödinger	schrödinger	ADJ
ap-7652	713	8	equation	equation	NOUN
ap-7652	713	9	by	by	ADP
ap-7652	713	10	means	mean	NOUN
ap-7652	713	11	of	of	ADP
ap-7652	713	12	supersymmetry	supersymmetry	NOUN
ap-7652	713	13	.	.	PUNCT
ap-7652	714	1	journal	journal	NOUN
ap-7652	714	2	of	of	ADP
ap-7652	714	3	experimental	experimental	ADJ
ap-7652	714	4	and	and	CCONJ
ap-7652	714	5	theoretical	theoretical	ADJ
ap-7652	714	6	physics	physics	NOUN
ap-7652	714	7	letters	letter	NOUN
ap-7652	714	8	38:356–359	38:356–359	PROPN
ap-7652	714	9	,	,	PUNCT
ap-7652	714	10	1983	1983	NUM
ap-7652	714	11	.	.	PUNCT
ap-7652	715	1	[	[	X
ap-7652	715	2	35	35	NUM
ap-7652	715	3	]	]	X
ap-7652	715	4	l.	l.	PROPN
ap-7652	715	5	e.	e.	PROPN
ap-7652	715	6	gendenshtein	gendenshtein	PROPN
ap-7652	715	7	,	,	PUNCT
ap-7652	715	8	i.	i.	PROPN
ap-7652	715	9	v.	v.	PROPN
ap-7652	715	10	krive	krive	PROPN
ap-7652	715	11	.	.	PUNCT
ap-7652	716	1	supersymmetry	supersymmetry	NOUN
ap-7652	716	2	in	in	ADP
ap-7652	716	3	quantum	quantum	ADJ
ap-7652	716	4	mechanics	mechanic	NOUN
ap-7652	716	5	.	.	PUNCT
ap-7652	717	1	soviet	soviet	PROPN
ap-7652	717	2	physics	physics	PROPN
ap-7652	717	3	uspekhi	uspekhi	PROPN
ap-7652	717	4	28(8):645–666	28(8):645–666	PROPN
ap-7652	717	5	,	,	PUNCT
ap-7652	717	6	1985	1985	NUM
ap-7652	717	7	.	.	PUNCT
ap-7652	718	1	https://doi.org/10.1070/pu1985v028n08abeh003882	https://doi.org/10.1070/pu1985v028n08abeh003882	PROPN
ap-7652	718	2	.	.	PUNCT
ap-7652	719	1	[	[	X
ap-7652	719	2	36	36	NUM
ap-7652	719	3	]	]	X
ap-7652	719	4	b.	b.	PROPN
ap-7652	719	5	f.	f.	PROPN
ap-7652	719	6	samsonov	samsonov	PROPN
ap-7652	719	7	.	.	PUNCT
ap-7652	720	1	on	on	ADP
ap-7652	720	2	the	the	DET
ap-7652	720	3	equivalence	equivalence	NOUN
ap-7652	720	4	of	of	ADP
ap-7652	720	5	the	the	DET
ap-7652	720	6	integral	integral	ADJ
ap-7652	720	7	and	and	CCONJ
ap-7652	720	8	the	the	DET
ap-7652	720	9	differential	differential	ADJ
ap-7652	720	10	exact	exact	ADJ
ap-7652	720	11	solution	solution	NOUN
ap-7652	720	12	generation	generation	NOUN
ap-7652	720	13	methods	method	NOUN
ap-7652	720	14	for	for	ADP
ap-7652	720	15	the	the	DET
ap-7652	720	16	one	one	NUM
ap-7652	720	17	-	-	PUNCT
ap-7652	720	18	dimensional	dimensional	ADJ
ap-7652	720	19	schrodinger	schrodinger	NOUN
ap-7652	720	20	equation	equation	NOUN
ap-7652	720	21	.	.	PUNCT
ap-7652	721	1	journal	journal	PROPN
ap-7652	721	2	of	of	ADP
ap-7652	721	3	physics	physics	PROPN
ap-7652	721	4	a	a	PRON
ap-7652	721	5	:	:	PUNCT
ap-7652	721	6	mathematical	mathematical	ADJ
ap-7652	721	7	and	and	CCONJ
ap-7652	721	8	general	general	ADJ
ap-7652	721	9	28(23):6989–6998	28(23):6989–6998	NUM
ap-7652	721	10	,	,	PUNCT
ap-7652	721	11	1995	1995	NUM
ap-7652	721	12	.	.	PUNCT
ap-7652	722	1	https://doi.org/10.1088/0305-4470/28/23/036	https://doi.org/10.1088/0305-4470/28/23/036	NOUN
ap-7652	722	2	.	.	PUNCT
ap-7652	723	1	[	[	X
ap-7652	723	2	37	37	NUM
ap-7652	723	3	]	]	X
ap-7652	723	4	b.	b.	PROPN
ap-7652	723	5	f.	f.	PROPN
ap-7652	723	6	samsonov	samsonov	PROPN
ap-7652	723	7	.	.	PUNCT
ap-7652	724	1	new	new	ADJ
ap-7652	724	2	features	feature	NOUN
ap-7652	724	3	in	in	ADP
ap-7652	724	4	supersymmetry	supersymmetry	NOUN
ap-7652	724	5	breakdown	breakdown	NOUN
ap-7652	724	6	in	in	ADP
ap-7652	724	7	quantum	quantum	ADJ
ap-7652	724	8	mechanics	mechanic	NOUN
ap-7652	724	9	.	.	PUNCT
ap-7652	725	1	modern	modern	ADJ
ap-7652	725	2	physics	physics	NOUN
ap-7652	725	3	letters	letter	NOUN
ap-7652	725	4	a	a	DET
ap-7652	725	5	11(19):1563–1567	11(19):1563–1567	NUM
ap-7652	725	6	,	,	PUNCT
ap-7652	725	7	1996	1996	NUM
ap-7652	725	8	.	.	PUNCT
ap-7652	726	1	https://doi.org/10.1142/s0217732396001557	https://doi.org/10.1142/s0217732396001557	X
ap-7652	726	2	.	.	PUNCT
ap-7652	727	1	[	[	X
ap-7652	727	2	38	38	NUM
ap-7652	727	3	]	]	PUNCT
ap-7652	727	4	v.	v.	PROPN
ap-7652	727	5	g.	g.	PROPN
ap-7652	727	6	bagrov	bagrov	PROPN
ap-7652	727	7	,	,	PUNCT
ap-7652	727	8	b.	b.	PROPN
ap-7652	727	9	f.	f.	PROPN
ap-7652	727	10	samsonov	samsonov	PROPN
ap-7652	727	11	.	.	PUNCT
ap-7652	728	1	darboux	darboux	VERB
ap-7652	728	2	transformation	transformation	NOUN
ap-7652	728	3	and	and	CCONJ
ap-7652	728	4	elementary	elementary	ADJ
ap-7652	728	5	exact	exact	ADJ
ap-7652	728	6	solutions	solution	NOUN
ap-7652	728	7	of	of	ADP
ap-7652	728	8	the	the	DET
ap-7652	728	9	schrödinger	schrödinger	ADJ
ap-7652	728	10	equation	equation	NOUN
ap-7652	728	11	.	.	PUNCT
ap-7652	729	1	pramana	pramana	PROPN
ap-7652	729	2	49:563–580	49:563–580	PROPN
ap-7652	729	3	,	,	PUNCT
ap-7652	729	4	1997	1997	NUM
ap-7652	729	5	.	.	PUNCT
ap-7652	730	1	https://doi.org/10.1007/bf02848330	https://doi.org/10.1007/bf02848330	PRON
ap-7652	730	2	.	.	PUNCT
ap-7652	731	1	[	[	X
ap-7652	731	2	39	39	NUM
ap-7652	731	3	]	]	PUNCT
ap-7652	731	4	f.	f.	PROPN
ap-7652	731	5	brafman	brafman	PROPN
ap-7652	731	6	.	.	PUNCT
ap-7652	732	1	a	a	DET
ap-7652	732	2	set	set	NOUN
ap-7652	732	3	of	of	ADP
ap-7652	732	4	generating	generating	NOUN
ap-7652	732	5	functions	function	NOUN
ap-7652	732	6	for	for	ADP
ap-7652	732	7	bessel	bessel	ADJ
ap-7652	732	8	polynomials	polynomial	NOUN
ap-7652	732	9	.	.	PUNCT
ap-7652	733	1	proceedings	proceeding	NOUN
ap-7652	733	2	of	of	ADP
ap-7652	733	3	the	the	DET
ap-7652	733	4	american	american	PROPN
ap-7652	733	5	mathematical	mathematical	PROPN
ap-7652	733	6	society	society	PROPN
ap-7652	733	7	4:275–277	4:275–277	NOUN
ap-7652	733	8	,	,	PUNCT
ap-7652	733	9	1953	1953	NUM
ap-7652	733	10	.	.	PUNCT
ap-7652	734	1	https://doi.org/10.1090/s0002-9939-1953-0054100-x	https://doi.org/10.1090/s0002-9939-1953-0054100-x	NOUN
ap-7652	734	2	.	.	PUNCT
ap-7652	735	1	[	[	X
ap-7652	735	2	40	40	NUM
ap-7652	735	3	]	]	PUNCT
ap-7652	735	4	k.	k.	PROPN
ap-7652	735	5	h.	h.	PROPN
ap-7652	735	6	kwon	kwon	PROPN
ap-7652	735	7	,	,	PUNCT
ap-7652	735	8	l.	l.	PROPN
ap-7652	735	9	l.	l.	PROPN
ap-7652	735	10	littlejohn	littlejohn	PROPN
ap-7652	735	11	.	.	PUNCT
ap-7652	736	1	classification	classification	NOUN
ap-7652	736	2	of	of	ADP
ap-7652	736	3	classical	classical	ADJ
ap-7652	736	4	orthogonal	orthogonal	ADJ
ap-7652	736	5	polynomials	polynomial	NOUN
ap-7652	736	6	.	.	PUNCT
ap-7652	737	1	journal	journal	NOUN
ap-7652	737	2	of	of	ADP
ap-7652	737	3	the	the	DET
ap-7652	737	4	korean	korean	PROPN
ap-7652	737	5	mathematical	mathematical	ADJ
ap-7652	737	6	society	society	NOUN
ap-7652	737	7	34(4):973–1008	34(4):973–1008	PROPN
ap-7652	737	8	,	,	PUNCT
ap-7652	737	9	1997	1997	NUM
ap-7652	737	10	.	.	PUNCT
ap-7652	738	1	[	[	X
ap-7652	738	2	41	41	NUM
ap-7652	738	3	]	]	PUNCT
ap-7652	738	4	a.	a.	NOUN
ap-7652	738	5	f.	f.	PROPN
ap-7652	738	6	nikiforov	nikiforov	PROPN
ap-7652	738	7	,	,	PUNCT
ap-7652	738	8	v.	v.	PROPN
ap-7652	738	9	b.	b.	PROPN
ap-7652	738	10	uvarov	uvarov	PROPN
ap-7652	738	11	.	.	PUNCT
ap-7652	739	1	special	special	ADJ
ap-7652	739	2	functions	function	NOUN
ap-7652	739	3	of	of	ADP
ap-7652	739	4	mathematical	mathematical	ADJ
ap-7652	739	5	physics	physics	NOUN
ap-7652	739	6	.	.	PUNCT
ap-7652	740	1	birkhauser	birkhauser	PROPN
ap-7652	740	2	,	,	PUNCT
ap-7652	740	3	basel	basel	PROPN
ap-7652	740	4	,	,	PUNCT
ap-7652	740	5	1988	1988	NUM
ap-7652	740	6	.	.	PUNCT
ap-7652	741	1	https://doi.org/10.1007/978-1-4757-1595-8	https://doi.org/10.1007/978-1-4757-1595-8	PROPN
ap-7652	741	2	.	.	PUNCT
ap-7652	742	1	[	[	X
ap-7652	742	2	42	42	NUM
ap-7652	742	3	]	]	X
ap-7652	742	4	g.	g.	PROPN
ap-7652	742	5	natanson	natanson	PROPN
ap-7652	742	6	.	.	PUNCT
ap-7652	742	7	darboux	darboux	VERB
ap-7652	742	8	-	-	PUNCT
ap-7652	742	9	crum	crum	NOUN
ap-7652	742	10	nets	net	NOUN
ap-7652	742	11	of	of	ADP
ap-7652	742	12	sturm	sturm	NOUN
ap-7652	742	13	-	-	PUNCT
ap-7652	742	14	liouville	liouville	NOUN
ap-7652	742	15	problems	problem	NOUN
ap-7652	742	16	solvable	solvable	ADJ
ap-7652	742	17	by	by	ADP
ap-7652	742	18	quasi	quasi	ADJ
ap-7652	742	19	-	-	ADJ
ap-7652	742	20	rational	rational	ADJ
ap-7652	742	21	functions	function	NOUN
ap-7652	742	22	i.	i.	PROPN
ap-7652	742	23	general	general	PROPN
ap-7652	742	24	theory	theory	NOUN
ap-7652	742	25	,	,	PUNCT
ap-7652	742	26	2018	2018	NUM
ap-7652	742	27	.	.	PUNCT
ap-7652	743	1	https://doi.org/10.13140/rg.2.2.31016.06405/1	https://doi.org/10.13140/rg.2.2.31016.06405/1	PROPN
ap-7652	743	2	.	.	PUNCT
ap-7652	744	1	116	116	NUM
ap-7652	744	2	https://doi.org/10.1088/1751-8113/46/23/235205	https://doi.org/10.1088/1751-8113/46/23/235205	VERB
ap-7652	744	3	https://doi.org/10.1088/1751-8113/46/24/245201	https://doi.org/10.1088/1751-8113/46/24/245201	NOUN
ap-7652	744	4	https://doi.org/10.1093/qmath/6.1.121	https://doi.org/10.1093/qmath/6.1.121	ADV
ap-7652	744	5	https://www.researchgate.net/publication/353131294	https://www.researchgate.net/publication/353131294	VERB
ap-7652	744	6	https://doi.org/10.1111/sapm.12225	https://doi.org/10.1111/sapm.12225	X
ap-7652	745	1	https://doi.org/10.1016/s0377-0427(00)00636-1	https://doi.org/10.1016/s0377-0427(00)00636-1	NOUN
ap-7652	745	2	https://doi.org/10.1007/bf02735890	https://doi.org/10.1007/bf02735890	VERB
ap-7652	745	3	https://arxiv.org/ps_cache/physics/pdf/9907/9907032v1.pdf	https://arxiv.org/ps_cache/physics/pdf/9907/9907032v1.pdf	NOUN
ap-7652	745	4	https://doi.org/10.1088/0266-5611/3/1/014	https://doi.org/10.1088/0266-5611/3/1/014	PROPN
ap-7652	745	5	https://doi.org/10.1063/1.1703891	https://doi.org/10.1063/1.1703891	PROPN
ap-7652	745	6	https://doi.org/10.1088/0305-4470/26/19/041	https://doi.org/10.1088/0305-4470/26/19/041	NOUN
ap-7652	745	7	https://doi.org/10.1088/0305-4470/27/7/035	https://doi.org/10.1088/0305-4470/27/7/035	PROPN
ap-7652	746	1	https://doi.org/10.1088/1751-8121/aace4b	https://doi.org/10.1088/1751-8121/aace4b	PROPN
ap-7652	746	2	https://doi.org/10.1070/pu1985v028n08abeh003882	https://doi.org/10.1070/pu1985v028n08abeh003882	PROPN
ap-7652	746	3	https://doi.org/10.1088/0305-4470/28/23/036	https://doi.org/10.1088/0305-4470/28/23/036	PROPN
ap-7652	747	1	https://doi.org/10.1142/s0217732396001557	https://doi.org/10.1142/s0217732396001557	NUM
ap-7652	747	2	https://doi.org/10.1007/bf02848330	https://doi.org/10.1007/bf02848330	NUM
ap-7652	747	3	https://doi.org/10.1090/s0002-9939-1953-0054100-x	https://doi.org/10.1090/s0002-9939-1953-0054100-x	NOUN
ap-7652	747	4	https://doi.org/10.1007/978-1-4757-1595-8	https://doi.org/10.1007/978-1-4757-1595-8	ADJ
ap-7652	747	5	https://doi.org/10.13140/rg.2.2.31016.06405/1	https://doi.org/10.13140/rg.2.2.31016.06405/1	PROPN
ap-7652	747	6	vol	vol	NOUN
ap-7652	747	7	.	.	PROPN
ap-7652	748	1	62	62	NUM
ap-7652	748	2	no	no	INTJ
ap-7652	748	3	.	.	PUNCT
ap-7652	749	1	1/2022	1/2022	NUM
ap-7652	749	2	quantization	quantization	NOUN
ap-7652	749	3	of	of	ADP
ap-7652	749	4	rationally	rationally	ADV
ap-7652	749	5	deformed	deform	VERB
ap-7652	749	6	morse	morse	ADJ
ap-7652	749	7	potentials	potential	NOUN
ap-7652	749	8	.	.	PUNCT
ap-7652	749	9	.	.	PUNCT
ap-7652	749	10	.	.	PUNCT
ap-7652	750	1	[	[	X
ap-7652	750	2	43	43	NUM
ap-7652	750	3	]	]	X
ap-7652	750	4	f.	f.	PROPN
ap-7652	750	5	gesztesy	gesztesy	PROPN
ap-7652	750	6	,	,	PUNCT
ap-7652	750	7	b.	b.	PROPN
ap-7652	750	8	simon	simon	PROPN
ap-7652	750	9	,	,	PUNCT
ap-7652	750	10	g.	g.	PROPN
ap-7652	750	11	teschl	teschl	PROPN
ap-7652	750	12	.	.	PUNCT
ap-7652	751	1	zeros	zero	NOUN
ap-7652	751	2	of	of	ADP
ap-7652	751	3	the	the	DET
ap-7652	751	4	wronskian	wronskian	NOUN
ap-7652	751	5	and	and	CCONJ
ap-7652	751	6	renormalized	renormalize	VERB
ap-7652	751	7	oscillation	oscillation	NOUN
ap-7652	751	8	theory	theory	NOUN
ap-7652	751	9	.	.	PUNCT
ap-7652	752	1	american	american	PROPN
ap-7652	752	2	journal	journal	PROPN
ap-7652	752	3	of	of	ADP
ap-7652	752	4	mathematics	mathematics	PROPN
ap-7652	752	5	118(3):571–594	118(3):571–594	NUM
ap-7652	752	6	,	,	PUNCT
ap-7652	752	7	1996	1996	NUM
ap-7652	752	8	.	.	PUNCT
ap-7652	753	1	https://doi.org/10.1353/ajm.1996.0024	https://doi.org/10.1353/ajm.1996.0024	NOUN
ap-7652	753	2	.	.	PUNCT
ap-7652	754	1	[	[	X
ap-7652	754	2	44	44	NUM
ap-7652	754	3	]	]	X
ap-7652	754	4	g.	g.	PROPN
ap-7652	754	5	natanson	natanson	PROPN
ap-7652	754	6	.	.	PUNCT
ap-7652	755	1	exact	exact	ADJ
ap-7652	755	2	quantization	quantization	NOUN
ap-7652	755	3	of	of	ADP
ap-7652	755	4	the	the	DET
ap-7652	755	5	milson	milson	NOUN
ap-7652	755	6	potential	potential	NOUN
ap-7652	755	7	via	via	ADP
ap-7652	755	8	romanovski	romanovski	PROPN
ap-7652	755	9	-	-	PUNCT
ap-7652	755	10	routh	routh	PROPN
ap-7652	755	11	polynomials	polynomial	NOUN
ap-7652	755	12	,	,	PUNCT
ap-7652	755	13	2015	2015	NUM
ap-7652	755	14	.	.	PUNCT
ap-7652	756	1	https://doi.org/10.13140/rg.2.2.24354.09928	https://doi.org/10.13140/rg.2.2.24354.09928	NOUN
ap-7652	756	2	.	.	PUNCT
ap-7652	757	1	[	[	X
ap-7652	757	2	45	45	NUM
ap-7652	757	3	]	]	PUNCT
ap-7652	757	4	a.	a.	NOUN
ap-7652	757	5	schulze	schulze	PROPN
ap-7652	757	6	-	-	PUNCT
ap-7652	757	7	halberg	halberg	PROPN
ap-7652	757	8	.	.	PUNCT
ap-7652	758	1	higher	high	ADJ
ap-7652	758	2	-	-	PUNCT
ap-7652	758	3	order	order	NOUN
ap-7652	758	4	darboux	darboux	VERB
ap-7652	758	5	transformations	transformation	NOUN
ap-7652	758	6	with	with	ADP
ap-7652	758	7	foreign	foreign	ADJ
ap-7652	758	8	auxiliary	auxiliary	ADJ
ap-7652	758	9	equations	equation	NOUN
ap-7652	758	10	and	and	CCONJ
ap-7652	758	11	equivalence	equivalence	NOUN
ap-7652	758	12	with	with	ADP
ap-7652	758	13	generalized	generalized	ADJ
ap-7652	758	14	darboux	darboux	ADJ
ap-7652	758	15	transformations	transformation	NOUN
ap-7652	758	16	.	.	PUNCT
ap-7652	759	1	applied	apply	VERB
ap-7652	759	2	mathematics	mathematics	NOUN
ap-7652	759	3	letters	letter	NOUN
ap-7652	759	4	25(10):1520–1527	25(10):1520–1527	NUM
ap-7652	759	5	,	,	PUNCT
ap-7652	759	6	2012	2012	NUM
ap-7652	759	7	.	.	PUNCT
ap-7652	760	1	https://doi.org/10.1016/j.aml.2012.01.008	https://doi.org/10.1016/j.aml.2012.01.008	NOUN
ap-7652	760	2	.	.	PUNCT
ap-7652	761	1	[	[	X
ap-7652	761	2	46	46	NUM
ap-7652	761	3	]	]	X
ap-7652	761	4	d.	d.	PROPN
ap-7652	761	5	gomez	gomez	PROPN
ap-7652	761	6	-	-	PUNCT
ap-7652	761	7	ullate	ullate	PROPN
ap-7652	761	8	,	,	PUNCT
ap-7652	761	9	n.	n.	PROPN
ap-7652	761	10	kamran	kamran	PROPN
ap-7652	761	11	,	,	PUNCT
ap-7652	761	12	r.	r.	PROPN
ap-7652	761	13	milson	milson	PROPN
ap-7652	761	14	.	.	PUNCT
ap-7652	762	1	an	an	DET
ap-7652	762	2	extension	extension	NOUN
ap-7652	762	3	of	of	ADP
ap-7652	762	4	bochner	bochner	NOUN
ap-7652	762	5	’s	’s	PART
ap-7652	762	6	problem	problem	NOUN
ap-7652	762	7	:	:	PUNCT
ap-7652	762	8	exceptional	exceptional	ADJ
ap-7652	762	9	invariant	invariant	ADJ
ap-7652	762	10	subspaces	subspace	NOUN
ap-7652	762	11	.	.	PUNCT
ap-7652	763	1	journal	journal	NOUN
ap-7652	763	2	of	of	ADP
ap-7652	763	3	approximation	approximation	NOUN
ap-7652	763	4	theory	theory	NOUN
ap-7652	763	5	162(5):987–1006	162(5):987–1006	NUM
ap-7652	763	6	,	,	PUNCT
ap-7652	763	7	2010	2010	NUM
ap-7652	763	8	.	.	PUNCT
ap-7652	764	1	https://doi.org/10.1016/j.jat.2009.11.002	https://doi.org/10.1016/j.jat.2009.11.002	NOUN
ap-7652	764	2	.	.	PUNCT
ap-7652	765	1	[	[	X
ap-7652	765	2	47	47	NUM
ap-7652	765	3	]	]	X
ap-7652	765	4	s.	s.	PROPN
ap-7652	765	5	bochner	bochner	PROPN
ap-7652	765	6	.	.	PUNCT
ap-7652	766	1	über	über	PROPN
ap-7652	766	2	sturm	sturm	PROPN
ap-7652	766	3	-	-	PUNCT
ap-7652	766	4	liouvillesche	liouvillesche	PROPN
ap-7652	766	5	polynomsysteme	polynomsysteme	NOUN
ap-7652	766	6	.	.	PUNCT
ap-7652	767	1	mathematische	mathematische	PROPN
ap-7652	767	2	zeitschrift	zeitschrift	PROPN
ap-7652	767	3	29:730–736	29:730–736	PROPN
ap-7652	767	4	,	,	PUNCT
ap-7652	767	5	1929	1929	NUM
ap-7652	767	6	.	.	PUNCT
ap-7652	768	1	https://doi.org/10.1007/bf01180560	https://doi.org/10.1007/bf01180560	X
ap-7652	768	2	.	.	PUNCT
ap-7652	769	1	[	[	X
ap-7652	769	2	48	48	NUM
ap-7652	769	3	]	]	PUNCT
ap-7652	769	4	v.	v.	PROPN
ap-7652	769	5	g.	g.	PROPN
ap-7652	769	6	bagrov	bagrov	PROPN
ap-7652	769	7	,	,	PUNCT
ap-7652	769	8	b.	b.	PROPN
ap-7652	769	9	f.	f.	PROPN
ap-7652	769	10	samsonov	samsonov	PROPN
ap-7652	769	11	.	.	PUNCT
ap-7652	770	1	darboux	darboux	VERB
ap-7652	770	2	transformation	transformation	NOUN
ap-7652	770	3	of	of	ADP
ap-7652	770	4	the	the	DET
ap-7652	770	5	schrödinger	schrödinger	ADJ
ap-7652	770	6	equation	equation	NOUN
ap-7652	770	7	.	.	PUNCT
ap-7652	771	1	physics	physics	NOUN
ap-7652	771	2	of	of	ADP
ap-7652	771	3	particles	particle	NOUN
ap-7652	771	4	and	and	CCONJ
ap-7652	771	5	nuclei	nucleus	NOUN
ap-7652	771	6	28(4):374–397	28(4):374–397	PROPN
ap-7652	771	7	,	,	PUNCT
ap-7652	771	8	1997	1997	NUM
ap-7652	771	9	.	.	PUNCT
ap-7652	772	1	https://doi.org/10.1134/1.953045	https://doi.org/10.1134/1.953045	NOUN
ap-7652	772	2	.	.	PUNCT
ap-7652	773	1	[	[	X
ap-7652	773	2	49	49	NUM
ap-7652	773	3	]	]	PUNCT
ap-7652	773	4	m.	m.	NOUN
ap-7652	773	5	g.	g.	PROPN
ap-7652	773	6	krein	krein	PROPN
ap-7652	773	7	.	.	PUNCT
ap-7652	774	1	on	on	ADP
ap-7652	774	2	a	a	DET
ap-7652	774	3	continuous	continuous	ADJ
ap-7652	774	4	analogue	analogue	NOUN
ap-7652	774	5	of	of	ADP
ap-7652	774	6	the	the	DET
ap-7652	774	7	christoffel	christoffel	ADJ
ap-7652	774	8	formula	formula	NOUN
ap-7652	774	9	from	from	ADP
ap-7652	774	10	the	the	DET
ap-7652	774	11	theory	theory	NOUN
ap-7652	774	12	of	of	ADP
ap-7652	774	13	orthogonal	orthogonal	ADJ
ap-7652	774	14	polynomials	polynomial	NOUN
ap-7652	774	15	.	.	PUNCT
ap-7652	775	1	doklady	doklady	PROPN
ap-7652	775	2	akademii	akademii	NOUN
ap-7652	775	3	nauk	nauk	NOUN
ap-7652	775	4	sssr	sssr	NOUN
ap-7652	775	5	113(5):970–973	113(5):970–973	NUM
ap-7652	775	6	,	,	PUNCT
ap-7652	775	7	1957	1957	NUM
ap-7652	775	8	.	.	PUNCT
ap-7652	776	1	[	[	X
ap-7652	776	2	50	50	NUM
ap-7652	776	3	]	]	PUNCT
ap-7652	776	4	v.	v.	PROPN
ap-7652	776	5	e.	e.	PROPN
ap-7652	776	6	adler	adler	PROPN
ap-7652	776	7	.	.	PUNCT
ap-7652	777	1	a	a	DET
ap-7652	777	2	modification	modification	NOUN
ap-7652	777	3	of	of	ADP
ap-7652	777	4	crum	crum	PROPN
ap-7652	777	5	’s	’s	PART
ap-7652	777	6	method	method	NOUN
ap-7652	777	7	.	.	PUNCT
ap-7652	778	1	theoretical	theoretical	ADJ
ap-7652	778	2	and	and	CCONJ
ap-7652	778	3	mathematical	mathematical	ADJ
ap-7652	778	4	physics	physics	NOUN
ap-7652	778	5	101:1381–1386	101:1381–1386	NUM
ap-7652	778	6	,	,	PUNCT
ap-7652	778	7	1994	1994	NUM
ap-7652	778	8	.	.	PUNCT
ap-7652	779	1	https://doi.org/10.1007/bf01035458	https://doi.org/10.1007/bf01035458	NOUN
ap-7652	779	2	.	.	PUNCT
ap-7652	780	1	[	[	X
ap-7652	780	2	51	51	NUM
ap-7652	780	3	]	]	PUNCT
ap-7652	780	4	a.	a.	NOUN
ap-7652	780	5	j.	j.	PROPN
ap-7652	780	6	durán	durán	PROPN
ap-7652	780	7	,	,	PUNCT
ap-7652	780	8	m.	m.	NOUN
ap-7652	780	9	pérez	pérez	NOUN
ap-7652	780	10	,	,	PUNCT
ap-7652	780	11	j.	j.	PROPN
ap-7652	780	12	l.	l.	PROPN
ap-7652	780	13	varona	varona	PROPN
ap-7652	780	14	.	.	PUNCT
ap-7652	781	1	some	some	DET
ap-7652	781	2	conjecture	conjecture	NOUN
ap-7652	781	3	on	on	ADP
ap-7652	781	4	wronskian	wronskian	NOUN
ap-7652	781	5	and	and	CCONJ
ap-7652	781	6	casorati	casorati	PROPN
ap-7652	781	7	determinants	determinant	NOUN
ap-7652	781	8	of	of	ADP
ap-7652	781	9	orthogonal	orthogonal	ADJ
ap-7652	781	10	polynomials	polynomial	NOUN
ap-7652	781	11	.	.	PUNCT
ap-7652	782	1	experimental	experimental	ADJ
ap-7652	782	2	mathematics	mathematics	PROPN
ap-7652	782	3	24(1):123–132	24(1):123–132	PROPN
ap-7652	782	4	,	,	PUNCT
ap-7652	782	5	2015	2015	NUM
ap-7652	782	6	.	.	PUNCT
ap-7652	783	1	https://doi.org/10.1080/10586458.2014.958786	https://doi.org/10.1080/10586458.2014.958786	X
ap-7652	783	2	.	.	PUNCT
ap-7652	784	1	[	[	X
ap-7652	784	2	52	52	NUM
ap-7652	784	3	]	]	PUNCT
ap-7652	784	4	a.	a.	NOUN
ap-7652	784	5	kienast	kienast	NOUN
ap-7652	784	6	.	.	PUNCT
ap-7652	785	1	untersuchungen	untersuchungen	PROPN
ap-7652	785	2	über	über	PROPN
ap-7652	785	3	die	die	PROPN
ap-7652	785	4	lösungen	lösungen	PROPN
ap-7652	785	5	der	der	PROPN
ap-7652	785	6	differentialgleichung	differentialgleichung	VERB
ap-7652	785	7	xy	xy	PROPN
ap-7652	785	8	′′	′′	PROPN
ap-7652	785	9	+	+	CCONJ
ap-7652	785	10	(	(	PUNCT
ap-7652	785	11	γ	γ	PROPN
ap-7652	785	12	−	−	PROPN
ap-7652	785	13	x)y	x)y	PUNCT
ap-7652	786	1	′	′	NUM
ap-7652	787	1	−	−	PROPN
ap-7652	788	1	βy	βy	PROPN
ap-7652	788	2	.	.	PUNCT
ap-7652	788	3	denkschriften	denkschriften	PROPN
ap-7652	788	4	der	der	PROPN
ap-7652	788	5	schweizerischen	schweizerischen	ADP
ap-7652	788	6	naturforschenden	naturforschenden	PROPN
ap-7652	788	7	gesellschaft	gesellschaft	PROPN
ap-7652	788	8	57:247	57:247	PROPN
ap-7652	788	9	,	,	PUNCT
ap-7652	788	10	79	79	NUM
ap-7652	788	11	pages	page	NOUN
ap-7652	788	12	,	,	PUNCT
ap-7652	788	13	1921	1921	NUM
ap-7652	788	14	.	.	PUNCT
ap-7652	789	1	[	[	X
ap-7652	789	2	53	53	NUM
ap-7652	789	3	]	]	PUNCT
ap-7652	789	4	w.	w.	PROPN
ap-7652	789	5	lawton	lawton	PROPN
ap-7652	789	6	.	.	PUNCT
ap-7652	790	1	on	on	ADP
ap-7652	790	2	the	the	DET
ap-7652	790	3	zeros	zero	NOUN
ap-7652	790	4	of	of	ADP
ap-7652	790	5	certain	certain	ADJ
ap-7652	790	6	polynomials	polynomial	NOUN
ap-7652	790	7	related	relate	VERB
ap-7652	790	8	to	to	ADP
ap-7652	790	9	jacobi	jacobi	PROPN
ap-7652	790	10	and	and	CCONJ
ap-7652	790	11	laguerre	laguerre	NOUN
ap-7652	790	12	polynomials	polynomial	NOUN
ap-7652	790	13	.	.	PUNCT
ap-7652	791	1	bulletin	bulletin	NOUN
ap-7652	791	2	of	of	ADP
ap-7652	791	3	the	the	DET
ap-7652	791	4	american	american	PROPN
ap-7652	791	5	mathematical	mathematical	PROPN
ap-7652	791	6	society	society	NOUN
ap-7652	791	7	38:442–448	38:442–448	PROPN
ap-7652	791	8	,	,	PUNCT
ap-7652	791	9	1932	1932	NUM
ap-7652	791	10	.	.	PUNCT
ap-7652	792	1	https://doi.org/10.1090/s0002-9904-1932-05418-0	https://doi.org/10.1090/s0002-9904-1932-05418-0	PROPN
ap-7652	792	2	.	.	PUNCT
ap-7652	793	1	[	[	X
ap-7652	793	2	54	54	NUM
ap-7652	793	3	]	]	PUNCT
ap-7652	793	4	w.	w.	PROPN
ap-7652	793	5	hahn	hahn	PROPN
ap-7652	793	6	.	.	PUNCT
ap-7652	794	1	bericht	bericht	PROPN
ap-7652	794	2	über	über	PROPN
ap-7652	794	3	die	die	VERB
ap-7652	794	4	nullstellen	nullstellen	ADJ
ap-7652	794	5	der	der	NOUN
ap-7652	794	6	laguerreschen	laguerreschen	SCONJ
ap-7652	794	7	und	und	VERB
ap-7652	794	8	der	der	NOUN
ap-7652	794	9	hermiteschen	hermiteschen	PROPN
ap-7652	794	10	polynome	polynome	PROPN
ap-7652	794	11	.	.	PUNCT
ap-7652	795	1	jahresbericht	jahresbericht	PROPN
ap-7652	795	2	der	der	PROPN
ap-7652	795	3	deutschen	deutschen	PROPN
ap-7652	795	4	mathematiker	mathematiker	PROPN
ap-7652	795	5	-	-	PUNCT
ap-7652	795	6	vereinigung	vereinigung	PROPN
ap-7652	795	7	1:215–236	1:215–236	NUM
ap-7652	795	8	,	,	PUNCT
ap-7652	795	9	1933	1933	NUM
ap-7652	795	10	.	.	PUNCT
ap-7652	796	1	[	[	X
ap-7652	796	2	55	55	NUM
ap-7652	796	3	]	]	X
ap-7652	796	4	r.	r.	PROPN
ap-7652	796	5	courant	courant	PROPN
ap-7652	796	6	,	,	PUNCT
ap-7652	796	7	d.	d.	PROPN
ap-7652	796	8	hilbert	hilbert	PROPN
ap-7652	796	9	.	.	PUNCT
ap-7652	797	1	methods	method	NOUN
ap-7652	797	2	of	of	ADP
ap-7652	797	3	mathematical	mathematical	ADJ
ap-7652	797	4	physics	physics	NOUN
ap-7652	797	5	,	,	PUNCT
ap-7652	797	6	vol	vol	NOUN
ap-7652	797	7	.	.	PROPN
ap-7652	797	8	1	1	NUM
ap-7652	797	9	,	,	PUNCT
ap-7652	797	10	.	.	PUNCT
ap-7652	798	1	interscience	interscience	NOUN
ap-7652	798	2	,	,	PUNCT
ap-7652	798	3	new	new	PROPN
ap-7652	798	4	york	york	PROPN
ap-7652	798	5	,	,	PUNCT
ap-7652	798	6	1953	1953	NUM
ap-7652	798	7	.	.	PUNCT
ap-7652	799	1	117	117	NUM
ap-7652	799	2	https://doi.org/10.1353/ajm.1996.0024	https://doi.org/10.1353/ajm.1996.0024	ADJ
ap-7652	799	3	https://doi.org/10.13140/rg.2.2.24354.09928	https://doi.org/10.13140/rg.2.2.24354.09928	PROPN
ap-7652	799	4	https://doi.org/10.1016/j.aml.2012.01.008	https://doi.org/10.1016/j.aml.2012.01.008	NOUN
ap-7652	799	5	https://doi.org/10.1016/j.jat.2009.11.002	https://doi.org/10.1016/j.jat.2009.11.002	NOUN
ap-7652	799	6	https://doi.org/10.1007/bf01180560	https://doi.org/10.1007/bf01180560	PROPN
ap-7652	800	1	https://doi.org/10.1134/1.953045	https://doi.org/10.1134/1.953045	ADJ
ap-7652	800	2	https://doi.org/10.1007/bf01035458	https://doi.org/10.1007/bf01035458	NOUN
ap-7652	800	3	https://doi.org/10.1080/10586458.2014.958786	https://doi.org/10.1080/10586458.2014.958786	PROPN
ap-7652	801	1	https://doi.org/10.1090/s0002-9904-1932-05418-0	https://doi.org/10.1090/s0002-9904-1932-05418-0	PROPN
ap-7652	801	2	acta	acta	PROPN
ap-7652	801	3	polytechnica	polytechnica	PROPN
ap-7652	801	4	62(1):100–117	62(1):100–117	PROPN
ap-7652	801	5	,	,	PUNCT
ap-7652	801	6	2022	2022	NUM
ap-7652	801	7	1	1	NUM
ap-7652	801	8	introduction	introduction	NOUN
ap-7652	801	9	2	2	NUM
ap-7652	801	10	tfi	tfi	X
ap-7652	801	11	sturm	sturm	NOUN
ap-7652	801	12	-	-	PUNCT
ap-7652	801	13	liouville	liouville	NOUN
ap-7652	801	14	equations	equation	NOUN
ap-7652	801	15	2.1	2.1	NUM
ap-7652	801	16	liouville	liouville	NOUN
ap-7652	801	17	-	-	PUNCT
ap-7652	801	18	darboux	darboux	VERB
ap-7652	801	19	transformations	transformation	NOUN
ap-7652	801	20	2.2	2.2	NUM
ap-7652	801	21	translational	translational	ADJ
ap-7652	801	22	from	from	ADP
ap-7652	801	23	-	-	PUNCT
ap-7652	801	24	invariance	invariance	NOUN
ap-7652	801	25	of	of	ADP
ap-7652	801	26	sturm	sturm	NOUN
ap-7652	801	27	-	-	PUNCT
ap-7652	801	28	liouville	liouville	NOUN
ap-7652	801	29	equation	equation	NOUN
ap-7652	801	30	2.3	2.3	NUM
ap-7652	801	31	equivalence	equivalence	NOUN
ap-7652	801	32	theorem	theorem	VERB
ap-7652	801	33	for	for	ADP
ap-7652	801	34	darboux	darboux	ADJ
ap-7652	801	35	-	-	PUNCT
ap-7652	801	36	crum	crum	NOUN
ap-7652	801	37	transforms	transform	NOUN
ap-7652	801	38	of	of	ADP
ap-7652	801	39	a	a	DET
ap-7652	801	40	tfi	tfi	NOUN
ap-7652	801	41	csle	csle	NOUN
ap-7652	801	42	with	with	ADP
ap-7652	801	43	two	two	NUM
ap-7652	801	44	basic	basic	ADJ
ap-7652	801	45	solutions	solution	NOUN
ap-7652	801	46	3	3	NUM
ap-7652	801	47	quantization	quantization	NOUN
ap-7652	801	48	of	of	ADP
ap-7652	801	49	rationally	rationally	ADV
ap-7652	801	50	deformed	deform	VERB
ap-7652	801	51	morse	morse	ADJ
ap-7652	801	52	potentials	potential	NOUN
ap-7652	801	53	by	by	ADP
ap-7652	801	54	wronskian	wronskian	ADJ
ap-7652	801	55	transforms	transform	NOUN
ap-7652	801	56	of	of	ADP
ap-7652	801	57	r	r	NOUN
ap-7652	801	58	-	-	PUNCT
ap-7652	801	59	bessel	bessel	ADJ
ap-7652	801	60	polynomials	polynomial	VERB
ap-7652	801	61	3.1	3.1	NUM
ap-7652	801	62	schrödinger	schrödinger	ADJ
ap-7652	801	63	equation	equation	NOUN
ap-7652	801	64	with	with	ADP
ap-7652	801	65	morse	morse	ADJ
ap-7652	801	66	potential	potential	NOUN
ap-7652	801	67	in	in	ADP
ap-7652	801	68	bessel	bessel	NOUN
ap-7652	801	69	form	form	NOUN
ap-7652	801	70	3.2	3.2	NUM
ap-7652	801	71	rdcts	rdct	NOUN
ap-7652	801	72	of	of	ADP
ap-7652	801	73	principal	principal	ADJ
ap-7652	801	74	solutions	solution	NOUN
ap-7652	801	75	near	near	ADP
ap-7652	801	76	singular	singular	PROPN
ap-7652	801	77	end	end	NOUN
ap-7652	801	78	points	point	VERB
ap-7652	801	79	3.3	3.3	NUM
ap-7652	801	80	isospectral	isospectral	ADJ
ap-7652	801	81	family	family	NOUN
ap-7652	801	82	of	of	ADP
ap-7652	801	83	rationally	rationally	ADV
ap-7652	801	84	deformed	deform	VERB
ap-7652	801	85	morse	morse	NOUN
ap-7652	801	86	potentials	potential	NOUN
ap-7652	801	87	with	with	ADP
ap-7652	801	88	a	a	DET
ap-7652	801	89	regular	regular	ADJ
ap-7652	801	90	spectrum	spectrum	NOUN
ap-7652	801	91	3.4	3.4	NUM
ap-7652	801	92	subnet	subnet	NOUN
ap-7652	801	93	of	of	ADP
ap-7652	801	94	rationally	rationally	ADV
ap-7652	801	95	deformed	deform	VERB
ap-7652	801	96	morse	morse	ADJ
ap-7652	801	97	potentials	potential	NOUN
ap-7652	801	98	quantized	quantize	VERB
ap-7652	801	99	via	via	ADP
ap-7652	801	100	wronskians	wronskian	NOUN
ap-7652	801	101	of	of	ADP
ap-7652	801	102	r	r	NOUN
ap-7652	801	103	-	-	PUNCT
ap-7652	801	104	bessel	bessel	ADJ
ap-7652	801	105	polynomials	polynomial	VERB
ap-7652	801	106	3.5	3.5	NUM
ap-7652	801	107	isospectral	isospectral	ADJ
ap-7652	801	108	rational	rational	ADJ
ap-7652	801	109	extensions	extension	NOUN
ap-7652	801	110	of	of	ADP
ap-7652	801	111	krein	krein	NOUN
ap-7652	801	112	-	-	PUNCT
ap-7652	801	113	adler	adler	PROPN
ap-7652	801	114	susy	susy	PROPN
ap-7652	801	115	partners	partner	NOUN
ap-7652	801	116	of	of	ADP
ap-7652	801	117	morse	morse	ADJ
ap-7652	801	118	potential	potential	ADJ
ap-7652	801	119	4	4	NUM
ap-7652	801	120	conclusions	conclusion	NOUN
ap-7652	801	121	acknowledgements	acknowledgement	NOUN
ap-7652	801	122	references	reference	NOUN