id	sid	tid	token	lemma	pos
ap-4476	1	1	acta	acta	PROPN
ap-4476	1	2	polytechnica	polytechnica	PROPN
ap-4476	1	3	doi:10.14311	doi:10.14311	PROPN
ap-4476	1	4	/	/	SYM
ap-4476	1	5	ap.2017.57.0477	ap.2017.57.0477	PROPN
ap-4476	1	6	acta	acta	PROPN
ap-4476	1	7	polytechnica	polytechnica	PROPN
ap-4476	1	8	57(6):477–487	57(6):477–487	PROPN
ap-4476	1	9	,	,	PUNCT
ap-4476	1	10	2017	2017	NUM
ap-4476	1	11	©	©	PROPN
ap-4476	1	12	czech	czech	PROPN
ap-4476	1	13	technical	technical	PROPN
ap-4476	1	14	university	university	PROPN
ap-4476	1	15	in	in	ADP
ap-4476	1	16	prague	prague	PROPN
ap-4476	1	17	,	,	PUNCT
ap-4476	1	18	2017	2017	NUM
ap-4476	1	19	available	available	ADJ
ap-4476	1	20	online	online	ADV
ap-4476	1	21	at	at	ADP
ap-4476	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4476	1	23	rationally	rationally	ADV
ap-4476	1	24	extended	extended	ADJ
ap-4476	1	25	shape	shape	NOUN
ap-4476	1	26	invariant	invariant	ADJ
ap-4476	1	27	potentials	potential	NOUN
ap-4476	1	28	in	in	ADP
ap-4476	1	29	arbitrary	arbitrary	ADJ
ap-4476	1	30	d	d	NOUN
ap-4476	1	31	dimensions	dimension	NOUN
ap-4476	1	32	associated	associate	VERB
ap-4476	1	33	with	with	ADP
ap-4476	1	34	exceptional	exceptional	ADJ
ap-4476	1	35	xm	xm	PROPN
ap-4476	1	36	polynomials	polynomials	PROPN
ap-4476	1	37	rajesh	rajesh	PROPN
ap-4476	1	38	kumar	kumar	PROPN
ap-4476	1	39	yadava	yadava	PROPN
ap-4476	1	40	,	,	PUNCT
ap-4476	1	41	nisha	nisha	PROPN
ap-4476	1	42	kumarib	kumarib	PROPN
ap-4476	1	43	,	,	PUNCT
ap-4476	1	44	avinash	avinash	PROPN
ap-4476	1	45	kharec	kharec	PROPN
ap-4476	1	46	,	,	PUNCT
ap-4476	1	47	bhabani	bhabani	PROPN
ap-4476	1	48	prasad	prasad	PROPN
ap-4476	1	49	mandalb,∗	mandalb,∗	PROPN
ap-4476	1	50	a	a	DET
ap-4476	1	51	department	department	NOUN
ap-4476	1	52	of	of	ADP
ap-4476	1	53	physics	physics	PROPN
ap-4476	1	54	,	,	PUNCT
ap-4476	1	55	s.	s.	PROPN
ap-4476	1	56	p.	p.	PROPN
ap-4476	1	57	college	college	PROPN
ap-4476	1	58	,	,	PUNCT
ap-4476	1	59	dumka	dumka	PROPN
ap-4476	1	60	(	(	PUNCT
ap-4476	1	61	skmu	skmu	PROPN
ap-4476	1	62	dumka)-814101	dumka)-814101	PROPN
ap-4476	1	63	,	,	PUNCT
ap-4476	1	64	india	india	PROPN
ap-4476	1	65	b	b	PROPN
ap-4476	1	66	department	department	PROPN
ap-4476	1	67	of	of	ADP
ap-4476	1	68	physics	physics	PROPN
ap-4476	1	69	,	,	PUNCT
ap-4476	1	70	banaras	banaras	PROPN
ap-4476	1	71	hindu	hindu	PROPN
ap-4476	1	72	university	university	NOUN
ap-4476	1	73	,	,	PUNCT
ap-4476	1	74	varanasi-221005	varanasi-221005	NOUN
ap-4476	1	75	,	,	PUNCT
ap-4476	1	76	india	india	PROPN
ap-4476	1	77	c	c	PROPN
ap-4476	1	78	raja	raja	PROPN
ap-4476	1	79	ramanna	ramanna	PROPN
ap-4476	1	80	fellow	fellow	PROPN
ap-4476	1	81	,	,	PUNCT
ap-4476	1	82	indian	indian	PROPN
ap-4476	1	83	institute	institute	PROPN
ap-4476	1	84	of	of	ADP
ap-4476	1	85	science	science	PROPN
ap-4476	1	86	education	education	NOUN
ap-4476	1	87	and	and	CCONJ
ap-4476	1	88	research	research	NOUN
ap-4476	1	89	(	(	PUNCT
ap-4476	1	90	iiser	iiser	NOUN
ap-4476	1	91	)	)	PUNCT
ap-4476	1	92	,	,	PUNCT
ap-4476	1	93	pune-411021	pune-411021	NOUN
ap-4476	1	94	,	,	PUNCT
ap-4476	1	95	india	india	PROPN
ap-4476	1	96	∗	∗	NOUN
ap-4476	1	97	corresponding	correspond	VERB
ap-4476	1	98	author	author	NOUN
ap-4476	1	99	:	:	PUNCT
ap-4476	1	100	bhabani.mandal@gmail.com	bhabani.mandal@gmail.com	X
ap-4476	1	101	abstract	abstract	ADJ
ap-4476	1	102	.	.	PUNCT
ap-4476	2	1	rationally	rationally	ADV
ap-4476	2	2	extended	extend	VERB
ap-4476	2	3	shape	shape	NOUN
ap-4476	2	4	invariant	invariant	ADJ
ap-4476	2	5	potentials	potential	NOUN
ap-4476	2	6	in	in	ADP
ap-4476	2	7	arbitrary	arbitrary	ADJ
ap-4476	2	8	d	d	NOUN
ap-4476	2	9	-	-	PUNCT
ap-4476	2	10	dimensions	dimension	NOUN
ap-4476	2	11	are	be	AUX
ap-4476	2	12	obtained	obtain	VERB
ap-4476	2	13	by	by	ADP
ap-4476	2	14	using	use	VERB
ap-4476	2	15	point	point	NOUN
ap-4476	2	16	canonical	canonical	ADJ
ap-4476	2	17	transformation	transformation	NOUN
ap-4476	2	18	(	(	PUNCT
ap-4476	2	19	pct	pct	NOUN
ap-4476	2	20	)	)	PUNCT
ap-4476	2	21	method	method	NOUN
ap-4476	2	22	.	.	PUNCT
ap-4476	3	1	the	the	DET
ap-4476	3	2	bound	bind	VERB
ap-4476	3	3	-	-	PUNCT
ap-4476	3	4	state	state	NOUN
ap-4476	3	5	solutions	solution	NOUN
ap-4476	3	6	of	of	ADP
ap-4476	3	7	these	these	DET
ap-4476	3	8	exactly	exactly	ADV
ap-4476	3	9	solvable	solvable	ADJ
ap-4476	3	10	potentials	potential	NOUN
ap-4476	3	11	can	can	AUX
ap-4476	3	12	be	be	AUX
ap-4476	3	13	written	write	VERB
ap-4476	3	14	in	in	ADP
ap-4476	3	15	terms	term	NOUN
ap-4476	3	16	of	of	ADP
ap-4476	3	17	xm	xm	PROPN
ap-4476	3	18	laguerre	laguerre	NOUN
ap-4476	3	19	or	or	CCONJ
ap-4476	3	20	xm	xm	PROPN
ap-4476	3	21	jacobi	jacobi	PROPN
ap-4476	3	22	exceptional	exceptional	ADJ
ap-4476	3	23	orthogonal	orthogonal	ADJ
ap-4476	3	24	polynomials	polynomial	NOUN
ap-4476	3	25	.	.	PUNCT
ap-4476	4	1	these	these	DET
ap-4476	4	2	potentials	potential	NOUN
ap-4476	4	3	are	be	AUX
ap-4476	4	4	isospectral	isospectral	ADJ
ap-4476	4	5	to	to	ADP
ap-4476	4	6	their	their	PRON
ap-4476	4	7	usual	usual	ADJ
ap-4476	4	8	counterparts	counterpart	NOUN
ap-4476	4	9	and	and	CCONJ
ap-4476	4	10	possess	possess	VERB
ap-4476	4	11	translationally	translationally	ADJ
ap-4476	4	12	shape	shape	NOUN
ap-4476	4	13	invariance	invariance	NOUN
ap-4476	4	14	property	property	NOUN
ap-4476	4	15	.	.	PUNCT
ap-4476	5	1	keywords	keyword	NOUN
ap-4476	5	2	:	:	PUNCT
ap-4476	5	3	exceptional	exceptional	ADJ
ap-4476	5	4	orthogonal	orthogonal	ADJ
ap-4476	5	5	polynomial	polynomial	NOUN
ap-4476	5	6	;	;	PUNCT
ap-4476	5	7	point	point	VERB
ap-4476	5	8	canonical	canonical	ADJ
ap-4476	5	9	transformation	transformation	NOUN
ap-4476	5	10	;	;	PUNCT
ap-4476	5	11	rationally	rationally	ADV
ap-4476	5	12	extended	extend	VERB
ap-4476	5	13	potential	potential	NOUN
ap-4476	5	14	;	;	PUNCT
ap-4476	5	15	shape	shape	VERB
ap-4476	5	16	invariance	invariance	NOUN
ap-4476	5	17	property	property	NOUN
ap-4476	5	18	.	.	PUNCT
ap-4476	6	1	1	1	X
ap-4476	6	2	.	.	X
ap-4476	6	3	introduction	introduction	NOUN
ap-4476	6	4	in	in	ADP
ap-4476	6	5	recent	recent	ADJ
ap-4476	6	6	years	year	NOUN
ap-4476	6	7	the	the	DET
ap-4476	6	8	discovery	discovery	NOUN
ap-4476	6	9	of	of	ADP
ap-4476	6	10	exceptional	exceptional	ADJ
ap-4476	6	11	orthogonal	orthogonal	ADJ
ap-4476	6	12	polynomials	polynomial	NOUN
ap-4476	6	13	(	(	PUNCT
ap-4476	6	14	eops	eop	NOUN
ap-4476	6	15	)	)	PUNCT
ap-4476	6	16	(	(	PUNCT
ap-4476	6	17	also	also	ADV
ap-4476	6	18	known	know	VERB
ap-4476	6	19	as	as	ADP
ap-4476	6	20	x1	x1	PROPN
ap-4476	6	21	laguerre	laguerre	NOUN
ap-4476	6	22	and	and	CCONJ
ap-4476	6	23	x1	x1	PROPN
ap-4476	6	24	jacobi	jacobi	PROPN
ap-4476	6	25	polynomials	polynomials	PROPN
ap-4476	6	26	)	)	PUNCT
ap-4476	7	1	[	[	X
ap-4476	7	2	1	1	NUM
ap-4476	7	3	,	,	PUNCT
ap-4476	7	4	2	2	NUM
ap-4476	7	5	]	]	PUNCT
ap-4476	7	6	has	have	AUX
ap-4476	7	7	increased	increase	VERB
ap-4476	7	8	the	the	DET
ap-4476	7	9	list	list	NOUN
ap-4476	7	10	of	of	ADP
ap-4476	7	11	exactly	exactly	ADV
ap-4476	7	12	solvable	solvable	ADJ
ap-4476	7	13	potentials	potential	NOUN
ap-4476	7	14	.	.	PUNCT
ap-4476	8	1	the	the	DET
ap-4476	8	2	eops	eop	NOUN
ap-4476	8	3	are	be	AUX
ap-4476	8	4	the	the	DET
ap-4476	8	5	solutions	solution	NOUN
ap-4476	8	6	of	of	ADP
ap-4476	8	7	secondorder	secondorder	NOUN
ap-4476	8	8	sturm	sturm	PROPN
ap-4476	8	9	-	-	PUNCT
ap-4476	8	10	liouvilli	liouvilli	PROPN
ap-4476	8	11	eigenvalue	eigenvalue	NOUN
ap-4476	8	12	problem	problem	NOUN
ap-4476	8	13	with	with	ADP
ap-4476	8	14	rational	rational	ADJ
ap-4476	8	15	coefficients	coefficient	NOUN
ap-4476	8	16	.	.	PUNCT
ap-4476	9	1	unlike	unlike	ADP
ap-4476	9	2	the	the	DET
ap-4476	9	3	usual	usual	ADJ
ap-4476	9	4	orthogonal	orthogonal	ADJ
ap-4476	9	5	polynomials	polynomial	NOUN
ap-4476	9	6	,	,	PUNCT
ap-4476	9	7	the	the	DET
ap-4476	9	8	eops	eop	NOUN
ap-4476	9	9	starts	start	VERB
ap-4476	9	10	with	with	ADP
ap-4476	9	11	degree	degree	NOUN
ap-4476	9	12	n	n	CCONJ
ap-4476	9	13	≥	≥	NOUN
ap-4476	9	14	1	1	NUM
ap-4476	9	15	and	and	CCONJ
ap-4476	9	16	still	still	ADV
ap-4476	9	17	form	form	VERB
ap-4476	9	18	a	a	DET
ap-4476	9	19	complete	complete	ADJ
ap-4476	9	20	orthonormal	orthonormal	ADJ
ap-4476	9	21	set	set	NOUN
ap-4476	9	22	with	with	ADP
ap-4476	9	23	respect	respect	NOUN
ap-4476	9	24	to	to	ADP
ap-4476	9	25	a	a	DET
ap-4476	9	26	positive	positive	ADJ
ap-4476	9	27	definite	definite	ADJ
ap-4476	9	28	innerproduct	innerproduct	NOUN
ap-4476	9	29	defined	define	VERB
ap-4476	9	30	over	over	ADP
ap-4476	9	31	a	a	DET
ap-4476	9	32	compact	compact	ADJ
ap-4476	9	33	interval	interval	NOUN
ap-4476	9	34	.	.	PUNCT
ap-4476	10	1	after	after	SCONJ
ap-4476	10	2	the	the	DET
ap-4476	10	3	discovery	discovery	NOUN
ap-4476	10	4	of	of	ADP
ap-4476	10	5	these	these	DET
ap-4476	10	6	two	two	NUM
ap-4476	10	7	polynomials	polynomial	NOUN
ap-4476	10	8	quesne	quesne	NOUN
ap-4476	10	9	et.al	et.al	PROPN
ap-4476	10	10	.	.	PUNCT
ap-4476	10	11	reported	report	VERB
ap-4476	10	12	three	three	NUM
ap-4476	10	13	shape	shape	NOUN
ap-4476	10	14	invariant	invariant	ADJ
ap-4476	10	15	potentials	potential	NOUN
ap-4476	10	16	whose	whose	DET
ap-4476	10	17	solutions	solution	NOUN
ap-4476	10	18	are	be	AUX
ap-4476	10	19	in	in	ADP
ap-4476	10	20	terms	term	NOUN
ap-4476	10	21	of	of	ADP
ap-4476	10	22	x1	x1	PROPN
ap-4476	10	23	laguerre	laguerre	NOUN
ap-4476	10	24	polynomial	polynomial	ADJ
ap-4476	10	25	(	(	PUNCT
ap-4476	10	26	extended	extended	ADJ
ap-4476	10	27	radial	radial	ADJ
ap-4476	10	28	oscillator	oscillator	NOUN
ap-4476	10	29	potentials	potential	NOUN
ap-4476	10	30	)	)	PUNCT
ap-4476	10	31	and	and	CCONJ
ap-4476	10	32	x1	x1	PROPN
ap-4476	10	33	jacobi	jacobi	PROPN
ap-4476	10	34	polynomials	polynomial	VERB
ap-4476	10	35	(	(	PUNCT
ap-4476	10	36	extended	extend	VERB
ap-4476	10	37	trigonometric	trigonometric	ADJ
ap-4476	10	38	scarf	scarf	NOUN
ap-4476	10	39	and	and	CCONJ
ap-4476	10	40	generalized	generalized	ADJ
ap-4476	10	41	pöschl	pöschl	NOUN
ap-4476	10	42	teller	teller	NOUN
ap-4476	10	43	(	(	PUNCT
ap-4476	10	44	gpt	gpt	NOUN
ap-4476	10	45	)	)	PUNCT
ap-4476	10	46	potentials	potential	VERB
ap-4476	10	47	)	)	PUNCT
ap-4476	11	1	[	[	X
ap-4476	11	2	3	3	NUM
ap-4476	11	3	,	,	PUNCT
ap-4476	11	4	4	4	NUM
ap-4476	11	5	]	]	PUNCT
ap-4476	11	6	.	.	PUNCT
ap-4476	12	1	subsequently	subsequently	ADV
ap-4476	12	2	odake	odake	VERB
ap-4476	12	3	and	and	CCONJ
ap-4476	12	4	sasaki	sasaki	PROPN
ap-4476	12	5	generalize	generalize	VERB
ap-4476	12	6	these	these	PRON
ap-4476	12	7	and	and	CCONJ
ap-4476	12	8	obtain	obtain	VERB
ap-4476	12	9	the	the	DET
ap-4476	12	10	solutions	solution	NOUN
ap-4476	12	11	in	in	ADP
ap-4476	12	12	terms	term	NOUN
ap-4476	12	13	of	of	ADP
ap-4476	12	14	exceptional	exceptional	ADJ
ap-4476	12	15	xm	xm	PROPN
ap-4476	12	16	orthogonal	orthogonal	ADJ
ap-4476	12	17	polynomials	polynomial	NOUN
ap-4476	12	18	[	[	X
ap-4476	12	19	5	5	NUM
ap-4476	12	20	]	]	PUNCT
ap-4476	12	21	.	.	PUNCT
ap-4476	13	1	the	the	DET
ap-4476	13	2	properties	property	NOUN
ap-4476	13	3	of	of	ADP
ap-4476	13	4	these	these	DET
ap-4476	13	5	xm	xm	PROPN
ap-4476	13	6	exceptional	exceptional	ADJ
ap-4476	13	7	orthogonal	orthogonal	ADJ
ap-4476	13	8	polynomials	polynomial	NOUN
ap-4476	13	9	have	have	AUX
ap-4476	13	10	been	be	AUX
ap-4476	13	11	studied	study	VERB
ap-4476	13	12	in	in	ADP
ap-4476	13	13	detail	detail	NOUN
ap-4476	13	14	in	in	ADP
ap-4476	13	15	ref	ref	NOUN
ap-4476	13	16	.	.	PUNCT
ap-4476	14	1	[	[	X
ap-4476	14	2	6–9	6–9	X
ap-4476	14	3	]	]	PUNCT
ap-4476	14	4	.	.	PUNCT
ap-4476	15	1	subsequently	subsequently	ADV
ap-4476	15	2	,	,	PUNCT
ap-4476	15	3	the	the	DET
ap-4476	15	4	extension	extension	NOUN
ap-4476	15	5	of	of	ADP
ap-4476	15	6	other	other	ADJ
ap-4476	15	7	exactly	exactly	ADV
ap-4476	15	8	solvable	solvable	ADJ
ap-4476	15	9	shape	shape	NOUN
ap-4476	15	10	invariant	invariant	ADJ
ap-4476	15	11	potentials	potential	NOUN
ap-4476	15	12	have	have	AUX
ap-4476	15	13	also	also	ADV
ap-4476	15	14	been	be	AUX
ap-4476	15	15	done	do	VERB
ap-4476	15	16	[	[	X
ap-4476	15	17	10–13	10–13	NUM
ap-4476	15	18	]	]	PUNCT
ap-4476	15	19	by	by	ADP
ap-4476	15	20	using	use	VERB
ap-4476	15	21	different	different	ADJ
ap-4476	15	22	approaches	approach	NOUN
ap-4476	15	23	such	such	ADJ
ap-4476	15	24	as	as	ADP
ap-4476	15	25	supersymmetry	supersymmetry	NOUN
ap-4476	15	26	quantum	quantum	NOUN
ap-4476	15	27	mechanics	mechanic	NOUN
ap-4476	15	28	(	(	PUNCT
ap-4476	15	29	susyqm	susyqm	PROPN
ap-4476	15	30	)	)	PUNCT
ap-4476	16	1	[	[	X
ap-4476	16	2	17	17	NUM
ap-4476	16	3	,	,	PUNCT
ap-4476	16	4	18	18	NUM
ap-4476	16	5	]	]	PUNCT
ap-4476	16	6	,	,	PUNCT
ap-4476	16	7	point	point	VERB
ap-4476	16	8	canonical	canonical	ADJ
ap-4476	16	9	transformation	transformation	NOUN
ap-4476	16	10	(	(	PUNCT
ap-4476	16	11	pct	pct	NOUN
ap-4476	16	12	)	)	PUNCT
ap-4476	17	1	[	[	X
ap-4476	17	2	21	21	NUM
ap-4476	17	3	]	]	PUNCT
ap-4476	17	4	,	,	PUNCT
ap-4476	17	5	darboux	darboux	VERB
ap-4476	17	6	-	-	PUNCT
ap-4476	17	7	crum	crum	NOUN
ap-4476	17	8	transformation	transformation	NOUN
ap-4476	17	9	(	(	PUNCT
ap-4476	17	10	dct	dct	PROPN
ap-4476	17	11	)	)	PUNCT
ap-4476	18	1	[	[	X
ap-4476	18	2	22	22	NUM
ap-4476	18	3	]	]	PUNCT
ap-4476	18	4	etc	etc	X
ap-4476	18	5	.	.	X
ap-4476	18	6	the	the	DET
ap-4476	18	7	scattering	scatter	VERB
ap-4476	18	8	amplitude	amplitude	NOUN
ap-4476	18	9	of	of	ADP
ap-4476	18	10	some	some	PRON
ap-4476	18	11	of	of	ADP
ap-4476	18	12	the	the	DET
ap-4476	18	13	newly	newly	ADV
ap-4476	18	14	found	find	VERB
ap-4476	18	15	exactly	exactly	ADV
ap-4476	18	16	solvable	solvable	ADJ
ap-4476	18	17	potentials	potential	NOUN
ap-4476	18	18	in	in	ADP
ap-4476	18	19	terms	term	NOUN
ap-4476	18	20	of	of	ADP
ap-4476	18	21	xm	xm	PROPN
ap-4476	18	22	eops	eop	NOUN
ap-4476	18	23	are	be	AUX
ap-4476	18	24	studied	study	VERB
ap-4476	18	25	in	in	ADP
ap-4476	18	26	ref	ref	NOUN
ap-4476	18	27	.	.	PUNCT
ap-4476	19	1	[	[	X
ap-4476	19	2	14–16	14–16	NUM
ap-4476	19	3	]	]	PUNCT
ap-4476	19	4	.	.	PUNCT
ap-4476	20	1	the	the	DET
ap-4476	20	2	bound	bind	VERB
ap-4476	20	3	state	state	NOUN
ap-4476	20	4	solutions	solution	NOUN
ap-4476	20	5	of	of	ADP
ap-4476	20	6	these	these	DET
ap-4476	20	7	extended	extend	VERB
ap-4476	20	8	(	(	PUNCT
ap-4476	20	9	deformed	deform	VERB
ap-4476	20	10	)	)	PUNCT
ap-4476	20	11	potentials	potential	NOUN
ap-4476	20	12	are	be	AUX
ap-4476	20	13	in	in	ADP
ap-4476	20	14	terms	term	NOUN
ap-4476	20	15	of	of	ADP
ap-4476	20	16	eops	eop	NOUN
ap-4476	20	17	or	or	CCONJ
ap-4476	20	18	some	some	DET
ap-4476	20	19	type	type	NOUN
ap-4476	20	20	of	of	ADP
ap-4476	20	21	new	new	ADJ
ap-4476	20	22	polynomials	polynomial	NOUN
ap-4476	20	23	(	(	PUNCT
ap-4476	20	24	yn	yn	NOUN
ap-4476	20	25	)	)	PUNCT
ap-4476	20	26	(	(	PUNCT
ap-4476	20	27	which	which	PRON
ap-4476	20	28	can	can	AUX
ap-4476	20	29	be	be	AUX
ap-4476	20	30	expressed	express	VERB
ap-4476	20	31	in	in	ADP
ap-4476	20	32	terms	term	NOUN
ap-4476	20	33	of	of	ADP
ap-4476	20	34	combination	combination	NOUN
ap-4476	20	35	of	of	ADP
ap-4476	20	36	usual	usual	ADJ
ap-4476	20	37	laguerre	laguerre	NOUN
ap-4476	20	38	or	or	CCONJ
ap-4476	20	39	jacobi	jacobi	PROPN
ap-4476	20	40	orthogonal	orthogonal	ADJ
ap-4476	20	41	polynomials	polynomial	NOUN
ap-4476	20	42	)	)	PUNCT
ap-4476	20	43	.	.	PUNCT
ap-4476	21	1	the	the	DET
ap-4476	21	2	bound	bind	VERB
ap-4476	21	3	state	state	NOUN
ap-4476	21	4	spectrum	spectrum	NOUN
ap-4476	21	5	of	of	ADP
ap-4476	21	6	all	all	DET
ap-4476	21	7	these	these	DET
ap-4476	21	8	extended	extended	ADJ
ap-4476	21	9	potentials	potential	NOUN
ap-4476	21	10	are	be	AUX
ap-4476	21	11	investigated	investigate	VERB
ap-4476	21	12	in	in	ADP
ap-4476	21	13	a	a	DET
ap-4476	21	14	fixed	fix	VERB
ap-4476	21	15	dimension	dimension	NOUN
ap-4476	21	16	(	(	PUNCT
ap-4476	21	17	d	d	NOUN
ap-4476	21	18	=	=	SYM
ap-4476	21	19	1	1	NUM
ap-4476	21	20	or	or	CCONJ
ap-4476	21	21	3	3	NUM
ap-4476	21	22	)	)	PUNCT
ap-4476	21	23	.	.	PUNCT
ap-4476	22	1	recently	recently	ADV
ap-4476	22	2	the	the	DET
ap-4476	22	3	extension	extension	NOUN
ap-4476	22	4	of	of	ADP
ap-4476	22	5	some	some	DET
ap-4476	22	6	exactly	exactly	ADV
ap-4476	22	7	solvable	solvable	ADJ
ap-4476	22	8	potentials	potential	NOUN
ap-4476	22	9	have	have	AUX
ap-4476	22	10	been	be	AUX
ap-4476	22	11	made	make	VERB
ap-4476	22	12	in	in	ADP
ap-4476	22	13	arbitrary	arbitrary	ADJ
ap-4476	22	14	d	d	NOUN
ap-4476	22	15	dimensions	dimension	NOUN
ap-4476	22	16	whose	whose	DET
ap-4476	22	17	solutions	solution	NOUN
ap-4476	22	18	are	be	AUX
ap-4476	22	19	in	in	ADP
ap-4476	22	20	terms	term	NOUN
ap-4476	22	21	of	of	ADP
ap-4476	22	22	x1	x1	PROPN
ap-4476	22	23	eops	eop	NOUN
ap-4476	22	24	[	[	X
ap-4476	22	25	26	26	NUM
ap-4476	22	26	]	]	PUNCT
ap-4476	22	27	.	.	PUNCT
ap-4476	23	1	the	the	DET
ap-4476	23	2	obvious	obvious	ADJ
ap-4476	23	3	question	question	NOUN
ap-4476	23	4	then	then	ADV
ap-4476	23	5	if	if	SCONJ
ap-4476	23	6	one	one	PRON
ap-4476	23	7	can	can	AUX
ap-4476	23	8	extend	extend	VERB
ap-4476	23	9	this	this	DET
ap-4476	23	10	discussion	discussion	NOUN
ap-4476	23	11	and	and	CCONJ
ap-4476	23	12	obtain	obtain	VERB
ap-4476	23	13	potentials	potential	NOUN
ap-4476	23	14	whose	whose	DET
ap-4476	23	15	solutions	solution	NOUN
ap-4476	23	16	are	be	AUX
ap-4476	23	17	in	in	ADP
ap-4476	23	18	terms	term	NOUN
ap-4476	23	19	of	of	ADP
ap-4476	23	20	xm	xm	PROPN
ap-4476	23	21	eops	eop	NOUN
ap-4476	23	22	in	in	ADP
ap-4476	23	23	arbitrary	arbitrary	ADJ
ap-4476	23	24	dimensions	dimension	NOUN
ap-4476	23	25	.	.	PUNCT
ap-4476	24	1	the	the	DET
ap-4476	24	2	purpose	purpose	NOUN
ap-4476	24	3	of	of	ADP
ap-4476	24	4	this	this	DET
ap-4476	24	5	paper	paper	NOUN
ap-4476	24	6	is	be	AUX
ap-4476	24	7	to	to	PART
ap-4476	24	8	answer	answer	VERB
ap-4476	24	9	this	this	DET
ap-4476	24	10	question	question	NOUN
ap-4476	24	11	.	.	PUNCT
ap-4476	25	1	in	in	ADP
ap-4476	25	2	particular	particular	ADJ
ap-4476	25	3	,	,	PUNCT
ap-4476	25	4	in	in	ADP
ap-4476	25	5	this	this	DET
ap-4476	25	6	paper	paper	NOUN
ap-4476	25	7	we	we	PRON
ap-4476	25	8	apply	apply	VERB
ap-4476	25	9	the	the	DET
ap-4476	25	10	pct	pct	NOUN
ap-4476	25	11	approach	approach	NOUN
ap-4476	25	12	,	,	PUNCT
ap-4476	25	13	which	which	PRON
ap-4476	25	14	consists	consist	VERB
ap-4476	25	15	of	of	ADP
ap-4476	25	16	a	a	DET
ap-4476	25	17	coordinate	coordinate	NOUN
ap-4476	25	18	transformation	transformation	NOUN
ap-4476	25	19	and	and	CCONJ
ap-4476	25	20	a	a	DET
ap-4476	25	21	functional	functional	ADJ
ap-4476	25	22	transformation	transformation	NOUN
ap-4476	25	23	,	,	PUNCT
ap-4476	25	24	that	that	PRON
ap-4476	25	25	allows	allow	VERB
ap-4476	25	26	generation	generation	NOUN
ap-4476	25	27	of	of	ADP
ap-4476	25	28	normalized	normalize	VERB
ap-4476	25	29	exact	exact	ADJ
ap-4476	25	30	analytic	analytic	ADJ
ap-4476	25	31	bound	bind	VERB
ap-4476	25	32	state	state	NOUN
ap-4476	25	33	solutions	solution	NOUN
ap-4476	25	34	of	of	ADP
ap-4476	25	35	the	the	DET
ap-4476	25	36	schrödinger	schrödinger	ADJ
ap-4476	25	37	equation	equation	NOUN
ap-4476	25	38	,	,	PUNCT
ap-4476	25	39	starting	start	VERB
ap-4476	25	40	from	from	ADP
ap-4476	25	41	an	an	DET
ap-4476	25	42	analytically	analytically	ADV
ap-4476	25	43	solvable	solvable	ADJ
ap-4476	25	44	conventional	conventional	ADJ
ap-4476	25	45	potential	potential	NOUN
ap-4476	25	46	.	.	PUNCT
ap-4476	26	1	here	here	ADV
ap-4476	26	2	we	we	PRON
ap-4476	26	3	consider	consider	VERB
ap-4476	26	4	two	two	NUM
ap-4476	26	5	analytically	analytically	ADV
ap-4476	26	6	solved	solve	VERB
ap-4476	26	7	conventional	conventional	ADJ
ap-4476	26	8	potentials	potential	NOUN
ap-4476	26	9	(	(	PUNCT
ap-4476	26	10	they	they	PRON
ap-4476	26	11	are	be	AUX
ap-4476	26	12	isotropic	isotropic	ADJ
ap-4476	26	13	oscillator	oscillator	NOUN
ap-4476	26	14	and	and	CCONJ
ap-4476	26	15	gpt	gpt	NOUN
ap-4476	26	16	potential	potential	NOUN
ap-4476	26	17	)	)	PUNCT
ap-4476	27	1	[	[	X
ap-4476	27	2	3	3	NUM
ap-4476	27	3	,	,	PUNCT
ap-4476	27	4	28	28	NUM
ap-4476	27	5	]	]	PUNCT
ap-4476	27	6	corresponding	correspond	VERB
ap-4476	27	7	to	to	ADP
ap-4476	27	8	which	which	PRON
ap-4476	27	9	d	d	ADJ
ap-4476	27	10	-	-	ADJ
ap-4476	27	11	dimensional	dimensional	ADJ
ap-4476	27	12	rationally	rationally	ADV
ap-4476	27	13	extended	extended	ADJ
ap-4476	27	14	potentials	potential	NOUN
ap-4476	27	15	are	be	AUX
ap-4476	27	16	obtained	obtain	VERB
ap-4476	27	17	whose	whose	DET
ap-4476	27	18	solutions	solution	NOUN
ap-4476	27	19	are	be	AUX
ap-4476	27	20	in	in	ADP
ap-4476	27	21	terms	term	NOUN
ap-4476	27	22	of	of	ADP
ap-4476	27	23	xm	xm	PROPN
ap-4476	27	24	exceptional	exceptional	ADJ
ap-4476	27	25	laguerre	laguerre	NOUN
ap-4476	27	26	or	or	CCONJ
ap-4476	27	27	jacobi	jacobi	PROPN
ap-4476	27	28	polynomials	polynomial	NOUN
ap-4476	27	29	.	.	PUNCT
ap-4476	28	1	this	this	DET
ap-4476	28	2	paper	paper	NOUN
ap-4476	28	3	is	be	AUX
ap-4476	28	4	organized	organize	VERB
ap-4476	28	5	as	as	SCONJ
ap-4476	28	6	follows	follow	VERB
ap-4476	28	7	.	.	PUNCT
ap-4476	29	1	in	in	ADP
ap-4476	29	2	§	§	PROPN
ap-4476	29	3	2	2	NUM
ap-4476	29	4	,	,	PUNCT
ap-4476	29	5	detail	detail	NOUN
ap-4476	29	6	about	about	ADP
ap-4476	29	7	the	the	DET
ap-4476	29	8	point	point	NOUN
ap-4476	29	9	canonical	canonical	ADJ
ap-4476	29	10	transformation	transformation	NOUN
ap-4476	29	11	(	(	PUNCT
ap-4476	29	12	pct	pct	NOUN
ap-4476	29	13	)	)	PUNCT
ap-4476	29	14	method	method	NOUN
ap-4476	29	15	for	for	ADP
ap-4476	29	16	arbitrary	arbitrary	ADJ
ap-4476	29	17	d	d	NOUN
ap-4476	29	18	-	-	PUNCT
ap-4476	29	19	dimensions	dimension	NOUN
ap-4476	29	20	is	be	AUX
ap-4476	29	21	given	give	VERB
ap-4476	29	22	.	.	PUNCT
ap-4476	30	1	in	in	ADP
ap-4476	30	2	§	§	PROPN
ap-4476	30	3	3	3	NUM
ap-4476	30	4	,	,	PUNCT
ap-4476	30	5	we	we	PRON
ap-4476	30	6	have	have	AUX
ap-4476	30	7	written	write	VERB
ap-4476	30	8	the	the	DET
ap-4476	30	9	differential	differential	ADJ
ap-4476	30	10	equation	equation	NOUN
ap-4476	30	11	corresponding	correspond	VERB
ap-4476	30	12	to	to	ADP
ap-4476	30	13	xm	xm	PROPN
ap-4476	30	14	eops	eop	NOUN
ap-4476	30	15	and	and	CCONJ
ap-4476	30	16	discussed	discuss	VERB
ap-4476	30	17	some	some	DET
ap-4476	30	18	important	important	ADJ
ap-4476	30	19	properties	property	NOUN
ap-4476	30	20	for	for	ADP
ap-4476	30	21	eops	eop	NOUN
ap-4476	30	22	.	.	PUNCT
ap-4476	31	1	arbitrary	arbitrary	ADJ
ap-4476	31	2	d	d	ADJ
ap-4476	31	3	-	-	ADJ
ap-4476	31	4	dimensional	dimensional	ADJ
ap-4476	31	5	rationally	rationally	ADV
ap-4476	31	6	extended	extend	VERB
ap-4476	31	7	exactly	exactly	ADV
ap-4476	31	8	solvable	solvable	ADJ
ap-4476	31	9	potentials	potential	VERB
ap-4476	31	10	whose	whose	DET
ap-4476	31	11	solutions	solution	NOUN
ap-4476	31	12	are	be	AUX
ap-4476	31	13	in	in	ADP
ap-4476	31	14	terms	term	NOUN
ap-4476	31	15	of	of	ADP
ap-4476	31	16	xm	xm	PROPN
ap-4476	31	17	laguerre	laguerre	NOUN
ap-4476	31	18	or	or	CCONJ
ap-4476	31	19	xm	xm	PROPN
ap-4476	31	20	jacobi	jacobi	PROPN
ap-4476	31	21	eops	eop	NOUN
ap-4476	31	22	are	be	AUX
ap-4476	31	23	obtained	obtain	VERB
ap-4476	31	24	in	in	ADP
ap-4476	31	25	§	§	PROPN
ap-4476	31	26	4	4	NUM
ap-4476	31	27	.	.	PUNCT
ap-4476	32	1	the	the	DET
ap-4476	32	2	approximate	approximate	ADJ
ap-4476	32	3	solutions	solution	NOUN
ap-4476	32	4	corresponding	correspond	VERB
ap-4476	32	5	to	to	ADP
ap-4476	32	6	xm	xm	PROPN
ap-4476	32	7	jacobi	jacobi	PROPN
ap-4476	32	8	case	case	NOUN
ap-4476	32	9	are	be	AUX
ap-4476	32	10	also	also	ADV
ap-4476	32	11	discussed	discuss	VERB
ap-4476	32	12	in	in	ADP
ap-4476	32	13	this	this	DET
ap-4476	32	14	section	section	NOUN
ap-4476	32	15	.	.	PUNCT
ap-4476	33	1	in	in	ADP
ap-4476	33	2	§	§	PROPN
ap-4476	33	3	5	5	NUM
ap-4476	33	4	,	,	PUNCT
ap-4476	33	5	new	new	ADJ
ap-4476	33	6	shape	shape	NOUN
ap-4476	33	7	invariant	invariant	ADJ
ap-4476	33	8	potentials	potential	NOUN
ap-4476	33	9	for	for	ADP
ap-4476	33	10	the	the	DET
ap-4476	33	11	rationally	rationally	ADV
ap-4476	33	12	extended	extended	ADJ
ap-4476	33	13	xm	xm	PROPN
ap-4476	33	14	laguerre	laguerre	NOUN
ap-4476	33	15	and	and	CCONJ
ap-4476	33	16	xm	xm	PROPN
ap-4476	33	17	jacobi	jacobi	PROPN
ap-4476	33	18	polynomials	polynomial	NOUN
ap-4476	33	19	are	be	AUX
ap-4476	33	20	obtained	obtain	VERB
ap-4476	33	21	in	in	ADP
ap-4476	33	22	arbitrary	arbitrary	ADJ
ap-4476	33	23	d	d	NOUN
ap-4476	33	24	dimensions	dimension	NOUN
ap-4476	33	25	.	.	PUNCT
ap-4476	34	1	in	in	ADP
ap-4476	34	2	particular	particular	ADJ
ap-4476	34	3	,	,	PUNCT
ap-4476	34	4	for	for	ADP
ap-4476	34	5	d	d	PROPN
ap-4476	34	6	=	=	SYM
ap-4476	34	7	2	2	NUM
ap-4476	34	8	and	and	CCONJ
ap-4476	34	9	d	d	NOUN
ap-4476	34	10	=	=	SYM
ap-4476	34	11	4	4	NUM
ap-4476	34	12	,	,	PUNCT
ap-4476	34	13	the	the	DET
ap-4476	34	14	shape	shape	NOUN
ap-4476	34	15	invariant	invariant	ADJ
ap-4476	34	16	partner	partner	NOUN
ap-4476	34	17	potentials	potential	VERB
ap-4476	34	18	for	for	SCONJ
ap-4476	34	19	the	the	DET
ap-4476	34	20	extended	extend	VERB
ap-4476	34	21	radial	radial	ADJ
ap-4476	34	22	oscillator	oscillator	NOUN
ap-4476	34	23	are	be	AUX
ap-4476	34	24	obtained	obtain	VERB
ap-4476	34	25	explicitly	explicitly	ADV
ap-4476	34	26	.	.	PUNCT
ap-4476	35	1	§	§	PROPN
ap-4476	35	2	6	6	NUM
ap-4476	35	3	,	,	PUNCT
ap-4476	35	4	is	be	AUX
ap-4476	35	5	reserved	reserve	VERB
ap-4476	35	6	for	for	ADP
ap-4476	35	7	results	result	NOUN
ap-4476	35	8	and	and	CCONJ
ap-4476	35	9	discussions	discussion	NOUN
ap-4476	35	10	.	.	PUNCT
ap-4476	36	1	477	477	NUM
ap-4476	37	1	http://dx.doi.org/10.14311/ap.2017.57.0477	http://dx.doi.org/10.14311/ap.2017.57.0477	PRON
ap-4476	37	2	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4476	37	3	r.	r.	PROPN
ap-4476	37	4	k.	k.	PROPN
ap-4476	37	5	yadav	yadav	PROPN
ap-4476	37	6	,	,	PUNCT
ap-4476	37	7	n.	n.	PROPN
ap-4476	37	8	kumari	kumari	PROPN
ap-4476	37	9	,	,	PUNCT
ap-4476	37	10	a.	a.	PROPN
ap-4476	37	11	khare	khare	PROPN
ap-4476	37	12	,	,	PUNCT
ap-4476	37	13	b.	b.	PROPN
ap-4476	37	14	p.	p.	PROPN
ap-4476	37	15	mandal	mandal	PROPN
ap-4476	37	16	acta	acta	PROPN
ap-4476	37	17	polytechnica	polytechnica	PROPN
ap-4476	37	18	2	2	NUM
ap-4476	37	19	.	.	PUNCT
ap-4476	37	20	point	point	NOUN
ap-4476	37	21	canonical	canonical	ADJ
ap-4476	37	22	transformation	transformation	NOUN
ap-4476	37	23	(	(	PUNCT
ap-4476	37	24	pct	pct	NOUN
ap-4476	37	25	)	)	PUNCT
ap-4476	37	26	method	method	NOUN
ap-4476	37	27	for	for	ADP
ap-4476	37	28	arbitrary	arbitrary	ADJ
ap-4476	37	29	d	d	NOUN
ap-4476	37	30	-	-	PUNCT
ap-4476	37	31	dimensions	dimension	NOUN
ap-4476	37	32	in	in	ADP
ap-4476	37	33	this	this	DET
ap-4476	37	34	section	section	NOUN
ap-4476	37	35	,	,	PUNCT
ap-4476	37	36	we	we	PRON
ap-4476	37	37	discuss	discuss	VERB
ap-4476	37	38	a	a	DET
ap-4476	37	39	more	more	ADV
ap-4476	37	40	traditional	traditional	ADJ
ap-4476	37	41	approach	approach	NOUN
ap-4476	37	42	,	,	PUNCT
ap-4476	37	43	the	the	DET
ap-4476	37	44	pct	pct	NOUN
ap-4476	37	45	approach	approach	NOUN
ap-4476	37	46	[	[	X
ap-4476	37	47	21	21	NUM
ap-4476	37	48	]	]	PUNCT
ap-4476	37	49	to	to	PART
ap-4476	37	50	get	get	VERB
ap-4476	37	51	the	the	DET
ap-4476	37	52	extension	extension	NOUN
ap-4476	37	53	of	of	ADP
ap-4476	37	54	conventional	conventional	ADJ
ap-4476	37	55	potentials	potential	NOUN
ap-4476	37	56	by	by	ADP
ap-4476	37	57	considering	consider	VERB
ap-4476	37	58	the	the	DET
ap-4476	37	59	radial	radial	ADJ
ap-4476	37	60	schrödinger	schrödinger	ADJ
ap-4476	37	61	equation	equation	NOUN
ap-4476	37	62	in	in	ADP
ap-4476	37	63	arbitrary	arbitrary	ADJ
ap-4476	37	64	d	d	ADJ
ap-4476	37	65	-	-	ADJ
ap-4476	37	66	dimensional	dimensional	ADJ
ap-4476	37	67	euclidean	euclidean	ADJ
ap-4476	37	68	space	space	NOUN
ap-4476	37	69	[	[	X
ap-4476	37	70	19	19	NUM
ap-4476	37	71	,	,	PUNCT
ap-4476	37	72	20	20	NUM
ap-4476	37	73	]	]	PUNCT
ap-4476	37	74	given	give	VERB
ap-4476	37	75	by	by	ADP
ap-4476	37	76	(	(	PUNCT
ap-4476	37	77	~	~	PUNCT
ap-4476	37	78	=	=	SYM
ap-4476	37	79	2	2	NUM
ap-4476	37	80	m	m	NOUN
ap-4476	37	81	=	=	SYM
ap-4476	37	82	1	1	X
ap-4476	37	83	)	)	PUNCT
ap-4476	37	84	d2ψ(r	d2ψ(r	PROPN
ap-4476	37	85	)	)	PUNCT
ap-4476	37	86	dr2	dr2	PROPN
ap-4476	38	1	+	+	X
ap-4476	38	2	(	(	PUNCT
ap-4476	38	3	d	d	NOUN
ap-4476	38	4	−	−	PROPN
ap-4476	38	5	1	1	X
ap-4476	38	6	)	)	PUNCT
ap-4476	38	7	r	r	NOUN
ap-4476	38	8	dψ(r	dψ(r	NOUN
ap-4476	38	9	)	)	PUNCT
ap-4476	38	10	dr	dr	PROPN
ap-4476	38	11	+	+	CCONJ
ap-4476	38	12	(	(	PUNCT
ap-4476	38	13	en	en	ADP
ap-4476	38	14	−	−	PROPN
ap-4476	38	15	v	v	NOUN
ap-4476	38	16	(	(	PUNCT
ap-4476	38	17	r)−	r)−	PROPN
ap-4476	38	18	`	`	PUNCT
ap-4476	38	19	(	(	PUNCT
ap-4476	38	20	`	`	PUNCT
ap-4476	38	21	+	+	NOUN
ap-4476	38	22	d	d	NOUN
ap-4476	38	23	−	−	ADJ
ap-4476	38	24	2	2	NUM
ap-4476	38	25	)	)	PUNCT
ap-4476	38	26	r2	r2	NOUN
ap-4476	38	27	)	)	PUNCT
ap-4476	38	28	ψ(r	ψ(r	PROPN
ap-4476	38	29	)	)	PUNCT
ap-4476	38	30	=	=	SYM
ap-4476	39	1	0	0	X
ap-4476	39	2	.	.	PUNCT
ap-4476	40	1	(	(	PUNCT
ap-4476	40	2	1	1	X
ap-4476	40	3	)	)	PUNCT
ap-4476	40	4	to	to	PART
ap-4476	40	5	solve	solve	VERB
ap-4476	40	6	this	this	DET
ap-4476	40	7	equation	equation	NOUN
ap-4476	40	8	,	,	PUNCT
ap-4476	40	9	we	we	PRON
ap-4476	40	10	apply	apply	VERB
ap-4476	40	11	pct	pct	NOUN
ap-4476	40	12	approach	approach	NOUN
ap-4476	40	13	and	and	CCONJ
ap-4476	40	14	assume	assume	VERB
ap-4476	40	15	the	the	DET
ap-4476	40	16	solution	solution	NOUN
ap-4476	40	17	of	of	ADP
ap-4476	40	18	the	the	DET
ap-4476	40	19	form	form	NOUN
ap-4476	40	20	ψ(r	ψ(r	NOUN
ap-4476	40	21	)	)	PUNCT
ap-4476	41	1	=	=	SYM
ap-4476	41	2	f(r)f	f(r)f	PROPN
ap-4476	41	3	(	(	PUNCT
ap-4476	41	4	g(r	g(r	NOUN
ap-4476	41	5	)	)	PUNCT
ap-4476	41	6	)	)	PUNCT
ap-4476	41	7	,	,	PUNCT
ap-4476	41	8	(	(	PUNCT
ap-4476	41	9	2	2	X
ap-4476	41	10	)	)	PUNCT
ap-4476	41	11	where	where	SCONJ
ap-4476	41	12	f(r	f(r	NOUN
ap-4476	41	13	)	)	PUNCT
ap-4476	41	14	and	and	CCONJ
ap-4476	41	15	g(r	g(r	PROPN
ap-4476	41	16	)	)	PUNCT
ap-4476	41	17	are	be	AUX
ap-4476	41	18	two	two	NUM
ap-4476	41	19	undetermined	undetermined	ADJ
ap-4476	41	20	functions	function	NOUN
ap-4476	41	21	and	and	CCONJ
ap-4476	41	22	f	f	PROPN
ap-4476	41	23	(	(	PUNCT
ap-4476	41	24	g(r	g(r	NOUN
ap-4476	41	25	)	)	PUNCT
ap-4476	41	26	)	)	PUNCT
ap-4476	41	27	will	will	AUX
ap-4476	41	28	be	be	AUX
ap-4476	41	29	later	later	ADV
ap-4476	41	30	identified	identify	VERB
ap-4476	41	31	as	as	ADP
ap-4476	41	32	one	one	NUM
ap-4476	41	33	of	of	ADP
ap-4476	41	34	the	the	DET
ap-4476	41	35	orthogonal	orthogonal	ADJ
ap-4476	41	36	polynomials	polynomial	NOUN
ap-4476	41	37	which	which	PRON
ap-4476	41	38	satisfy	satisfy	VERB
ap-4476	41	39	a	a	DET
ap-4476	41	40	second	second	ADJ
ap-4476	41	41	-	-	PUNCT
ap-4476	41	42	order	order	NOUN
ap-4476	41	43	differential	differential	NOUN
ap-4476	41	44	equation	equation	NOUN
ap-4476	41	45	f	f	PROPN
ap-4476	41	46	′′(g(r	′′(g(r	PROPN
ap-4476	41	47	)	)	PUNCT
ap-4476	41	48	)	)	PUNCT
ap-4476	42	1	+	+	ADP
ap-4476	42	2	q(g(r))f	q(g(r))f	NUM
ap-4476	42	3	′(g(r	′(g(r	NOUN
ap-4476	42	4	)	)	PUNCT
ap-4476	42	5	)	)	PUNCT
ap-4476	43	1	+	+	PUNCT
ap-4476	43	2	r(g(r))f	r(g(r))f	X
ap-4476	43	3	(	(	PUNCT
ap-4476	43	4	g(r	g(r	NOUN
ap-4476	43	5	)	)	PUNCT
ap-4476	43	6	)	)	PUNCT
ap-4476	44	1	=	=	PUNCT
ap-4476	44	2	0	0	X
ap-4476	44	3	.	.	PUNCT
ap-4476	45	1	(	(	PUNCT
ap-4476	45	2	3	3	X
ap-4476	45	3	)	)	PUNCT
ap-4476	45	4	here	here	ADV
ap-4476	45	5	a	a	DET
ap-4476	45	6	prime	prime	ADJ
ap-4476	45	7	denotes	denote	NOUN
ap-4476	45	8	derivative	derivative	ADJ
ap-4476	45	9	with	with	ADP
ap-4476	45	10	respect	respect	NOUN
ap-4476	45	11	to	to	ADP
ap-4476	45	12	g(r	g(r	NOUN
ap-4476	45	13	)	)	PUNCT
ap-4476	45	14	.	.	PUNCT
ap-4476	46	1	using	use	VERB
ap-4476	46	2	(	(	PUNCT
ap-4476	46	3	2	2	NUM
ap-4476	46	4	)	)	PUNCT
ap-4476	46	5	in	in	ADP
ap-4476	46	6	(	(	PUNCT
ap-4476	46	7	1	1	NUM
ap-4476	46	8	)	)	PUNCT
ap-4476	46	9	and	and	CCONJ
ap-4476	46	10	comparing	compare	VERB
ap-4476	46	11	the	the	DET
ap-4476	46	12	results	result	NOUN
ap-4476	46	13	with	with	ADP
ap-4476	46	14	(	(	PUNCT
ap-4476	46	15	3	3	NUM
ap-4476	46	16	)	)	PUNCT
ap-4476	46	17	,	,	PUNCT
ap-4476	46	18	we	we	PRON
ap-4476	46	19	get	get	VERB
ap-4476	46	20	f(r	f(r	NOUN
ap-4476	46	21	)	)	PUNCT
ap-4476	47	1	=	=	SYM
ap-4476	47	2	n	n	NUM
ap-4476	47	3	×	×	PROPN
ap-4476	47	4	r−	r−	PROPN
ap-4476	47	5	(	(	PUNCT
ap-4476	47	6	d−1	d−1	PROPN
ap-4476	47	7	)	)	PUNCT
ap-4476	47	8	2	2	NUM
ap-4476	47	9	(	(	PUNCT
ap-4476	47	10	g′(r))−	g′(r))−	NOUN
ap-4476	47	11	1	1	NUM
ap-4476	47	12	2	2	NUM
ap-4476	47	13	exp	exp	NOUN
ap-4476	47	14	(	(	PUNCT
ap-4476	47	15	1	1	NUM
ap-4476	47	16	2	2	NUM
ap-4476	47	17	∫	∫	NOUN
ap-4476	47	18	q(g)dg	q(g)dg	NOUN
ap-4476	47	19	)	)	PUNCT
ap-4476	47	20	(	(	PUNCT
ap-4476	47	21	4	4	NUM
ap-4476	47	22	)	)	PUNCT
ap-4476	47	23	and	and	CCONJ
ap-4476	47	24	en	en	ADP
ap-4476	47	25	−	−	PROPN
ap-4476	47	26	v	v	NOUN
ap-4476	47	27	(	(	PUNCT
ap-4476	47	28	r)−	r)−	PROPN
ap-4476	47	29	`	`	PUNCT
ap-4476	47	30	(	(	PUNCT
ap-4476	47	31	`	`	PUNCT
ap-4476	47	32	+	+	NOUN
ap-4476	47	33	d	d	NOUN
ap-4476	47	34	−	−	ADJ
ap-4476	47	35	2	2	NUM
ap-4476	47	36	)	)	PUNCT
ap-4476	47	37	r2	r2	NOUN
ap-4476	47	38	=	=	SYM
ap-4476	47	39	1	1	NUM
ap-4476	47	40	2{g(r	2{g(r	NUM
ap-4476	47	41	)	)	PUNCT
ap-4476	47	42	,	,	PUNCT
ap-4476	47	43	r}+	r}+	NOUN
ap-4476	47	44	g(r)′2	g(r)′2	NOUN
ap-4476	47	45	(	(	PUNCT
ap-4476	47	46	r(g)−	r(g)−	PROPN
ap-4476	47	47	1	1	NUM
ap-4476	47	48	2q	2q	NUM
ap-4476	47	49	′(g)−	′(g)−	NOUN
ap-4476	47	50	1	1	NUM
ap-4476	47	51	4q	4q	NOUN
ap-4476	47	52	2(g	2(g	NUM
ap-4476	47	53	)	)	PUNCT
ap-4476	47	54	)	)	PUNCT
ap-4476	48	1	+	+	CCONJ
ap-4476	48	2	(	(	PUNCT
ap-4476	48	3	d	d	X
ap-4476	48	4	−	−	PROPN
ap-4476	48	5	1)(d	1)(d	NUM
ap-4476	48	6	−	−	NOUN
ap-4476	48	7	3	3	NUM
ap-4476	48	8	)	)	PUNCT
ap-4476	48	9	4r2	4r2	NUM
ap-4476	48	10	,	,	PUNCT
ap-4476	48	11	(	(	PUNCT
ap-4476	48	12	5	5	X
ap-4476	48	13	)	)	PUNCT
ap-4476	48	14	where	where	SCONJ
ap-4476	48	15	n	n	PRON
ap-4476	48	16	is	be	AUX
ap-4476	48	17	the	the	DET
ap-4476	48	18	integration	integration	NOUN
ap-4476	48	19	constant	constant	ADJ
ap-4476	48	20	and	and	CCONJ
ap-4476	48	21	plays	play	VERB
ap-4476	48	22	the	the	DET
ap-4476	48	23	role	role	NOUN
ap-4476	48	24	of	of	ADP
ap-4476	48	25	the	the	DET
ap-4476	48	26	normalization	normalization	NOUN
ap-4476	48	27	constant	constant	ADJ
ap-4476	48	28	of	of	ADP
ap-4476	48	29	the	the	DET
ap-4476	48	30	wavefunctions	wavefunction	NOUN
ap-4476	48	31	and	and	CCONJ
ap-4476	48	32	{	{	PUNCT
ap-4476	48	33	g(r	g(r	NOUN
ap-4476	48	34	)	)	PUNCT
ap-4476	48	35	,	,	PUNCT
ap-4476	48	36	r	r	X
ap-4476	48	37	}	}	PUNCT
ap-4476	48	38	is	be	AUX
ap-4476	48	39	the	the	DET
ap-4476	48	40	schwartzian	schwartzian	ADJ
ap-4476	48	41	derivative	derivative	ADJ
ap-4476	48	42	symbol	symbol	NOUN
ap-4476	48	43	[	[	X
ap-4476	48	44	29	29	NUM
ap-4476	48	45	]	]	PUNCT
ap-4476	48	46	,	,	PUNCT
ap-4476	48	47	{	{	PUNCT
ap-4476	48	48	g	g	NOUN
ap-4476	48	49	,	,	PUNCT
ap-4476	48	50	r	r	NOUN
ap-4476	48	51	}	}	PUNCT
ap-4476	48	52	defined	define	VERB
ap-4476	48	53	as	as	ADP
ap-4476	48	54	{	{	PUNCT
ap-4476	48	55	g(r	g(r	NOUN
ap-4476	48	56	)	)	PUNCT
ap-4476	48	57	,	,	PUNCT
ap-4476	48	58	r	r	NOUN
ap-4476	48	59	}	}	PUNCT
ap-4476	48	60	=	=	SYM
ap-4476	48	61	g′′′(r	g′′′(r	NOUN
ap-4476	48	62	)	)	PUNCT
ap-4476	48	63	g′(r	g′(r	NOUN
ap-4476	48	64	)	)	PUNCT
ap-4476	48	65	−	−	NOUN
ap-4476	48	66	3	3	NUM
ap-4476	48	67	2	2	NUM
ap-4476	48	68	g′′2(r	g′′2(r	NOUN
ap-4476	48	69	)	)	PUNCT
ap-4476	48	70	g′2(r	g′2(r	NOUN
ap-4476	48	71	)	)	PUNCT
ap-4476	48	72	.	.	PUNCT
ap-4476	49	1	(	(	PUNCT
ap-4476	49	2	6	6	NUM
ap-4476	49	3	)	)	PUNCT
ap-4476	49	4	here	here	ADV
ap-4476	49	5	the	the	DET
ap-4476	49	6	prime	prime	ADJ
ap-4476	49	7	denotes	denote	NOUN
ap-4476	49	8	derivative	derivative	ADJ
ap-4476	49	9	with	with	ADP
ap-4476	49	10	respect	respect	NOUN
ap-4476	49	11	to	to	ADP
ap-4476	49	12	r.	r.	PROPN
ap-4476	49	13	from	from	ADP
ap-4476	49	14	(	(	PUNCT
ap-4476	49	15	2	2	NUM
ap-4476	49	16	)	)	PUNCT
ap-4476	49	17	and	and	CCONJ
ap-4476	49	18	(	(	PUNCT
ap-4476	49	19	4	4	NUM
ap-4476	49	20	)	)	PUNCT
ap-4476	49	21	,	,	PUNCT
ap-4476	49	22	the	the	DET
ap-4476	49	23	normalizable	normalizable	ADJ
ap-4476	49	24	wavefunction	wavefunction	NOUN
ap-4476	49	25	is	be	AUX
ap-4476	49	26	given	give	VERB
ap-4476	49	27	by	by	ADP
ap-4476	49	28	ψ(r	ψ(r	NOUN
ap-4476	49	29	)	)	PUNCT
ap-4476	49	30	=	=	SYM
ap-4476	50	1	χ(r	χ(r	X
ap-4476	50	2	)	)	PUNCT
ap-4476	50	3	r(d−1)/2	r(d−1)/2	PROPN
ap-4476	50	4	,	,	PUNCT
ap-4476	50	5	(	(	PUNCT
ap-4476	50	6	7	7	X
ap-4476	50	7	)	)	PUNCT
ap-4476	50	8	where	where	SCONJ
ap-4476	50	9	χ(r	χ(r	VERB
ap-4476	50	10	)	)	PUNCT
ap-4476	50	11	=	=	SYM
ap-4476	50	12	n	n	NUM
ap-4476	50	13	×	×	NOUN
ap-4476	50	14	(	(	PUNCT
ap-4476	50	15	g′(r))−	g′(r))−	NOUN
ap-4476	50	16	1	1	NUM
ap-4476	50	17	2	2	NUM
ap-4476	50	18	exp	exp	NOUN
ap-4476	50	19	(	(	PUNCT
ap-4476	50	20	1	1	NUM
ap-4476	50	21	2	2	NUM
ap-4476	50	22	∫	∫	NOUN
ap-4476	50	23	q(g)dg	q(g)dg	NOUN
ap-4476	50	24	)	)	PUNCT
ap-4476	50	25	f	f	PROPN
ap-4476	50	26	(	(	PUNCT
ap-4476	50	27	g(r	g(r	NOUN
ap-4476	50	28	)	)	PUNCT
ap-4476	50	29	)	)	PUNCT
ap-4476	50	30	.	.	PUNCT
ap-4476	51	1	(	(	PUNCT
ap-4476	51	2	8)	8)	NUM
ap-4476	51	3	the	the	DET
ap-4476	51	4	radial	radial	ADJ
ap-4476	51	5	wavefunction	wavefunction	NOUN
ap-4476	51	6	ψ(r	ψ(r	NOUN
ap-4476	51	7	)	)	PUNCT
ap-4476	51	8	=	=	SYM
ap-4476	52	1	χ(r	χ(r	X
ap-4476	52	2	)	)	PUNCT
ap-4476	52	3	r(d−1)/2	r(d−1)/2	PROPN
ap-4476	52	4	has	have	VERB
ap-4476	52	5	to	to	PART
ap-4476	52	6	satisfies	satisfies	VERB
ap-4476	52	7	the	the	DET
ap-4476	52	8	boundary	boundary	ADJ
ap-4476	52	9	condition	condition	NOUN
ap-4476	52	10	χ(r	χ(r	X
ap-4476	52	11	)	)	PUNCT
ap-4476	53	1	=	=	SYM
ap-4476	53	2	0	0	PUNCT
ap-4476	53	3	to	to	PART
ap-4476	53	4	be	be	AUX
ap-4476	53	5	more	more	ADV
ap-4476	53	6	precise	precise	ADJ
ap-4476	53	7	,	,	PUNCT
ap-4476	53	8	it	it	PRON
ap-4476	53	9	must	must	AUX
ap-4476	53	10	at	at	ADV
ap-4476	53	11	least	least	ADJ
ap-4476	53	12	vanish	vanish	VERB
ap-4476	53	13	as	as	ADV
ap-4476	53	14	fast	fast	ADV
ap-4476	53	15	as	as	ADP
ap-4476	53	16	r(d−1)/2	r(d−1)/2	PROPN
ap-4476	53	17	as	as	SCONJ
ap-4476	53	18	r	r	NOUN
ap-4476	53	19	goes	go	VERB
ap-4476	53	20	to	to	ADP
ap-4476	53	21	zero	zero	NUM
ap-4476	53	22	in	in	ADP
ap-4476	53	23	order	order	NOUN
ap-4476	53	24	to	to	PART
ap-4476	53	25	rule	rule	VERB
ap-4476	53	26	out	out	ADP
ap-4476	53	27	singular	singular	ADJ
ap-4476	53	28	solutions	solution	NOUN
ap-4476	53	29	[	[	X
ap-4476	53	30	30	30	NUM
ap-4476	53	31	]	]	PUNCT
ap-4476	53	32	.	.	PUNCT
ap-4476	54	1	for	for	ADP
ap-4476	54	2	(	(	PUNCT
ap-4476	54	3	5	5	NUM
ap-4476	54	4	)	)	PUNCT
ap-4476	54	5	to	to	PART
ap-4476	54	6	be	be	AUX
ap-4476	54	7	satisfied	satisfied	ADJ
ap-4476	54	8	,	,	PUNCT
ap-4476	54	9	one	one	PRON
ap-4476	54	10	needs	need	VERB
ap-4476	54	11	to	to	PART
ap-4476	54	12	find	find	VERB
ap-4476	54	13	some	some	DET
ap-4476	54	14	function	function	NOUN
ap-4476	54	15	g(r	g(r	NOUN
ap-4476	54	16	)	)	PUNCT
ap-4476	54	17	ensuring	ensure	VERB
ap-4476	54	18	the	the	DET
ap-4476	54	19	presence	presence	NOUN
ap-4476	54	20	of	of	ADP
ap-4476	54	21	a	a	DET
ap-4476	54	22	constant	constant	ADJ
ap-4476	54	23	term	term	NOUN
ap-4476	54	24	on	on	ADP
ap-4476	54	25	its	its	PRON
ap-4476	54	26	right	right	ADJ
ap-4476	54	27	hand	hand	NOUN
ap-4476	54	28	side	side	NOUN
ap-4476	54	29	to	to	PART
ap-4476	54	30	compensate	compensate	VERB
ap-4476	54	31	en	en	ADV
ap-4476	54	32	on	on	ADP
ap-4476	54	33	its	its	PRON
ap-4476	54	34	left	left	ADJ
ap-4476	54	35	hand	hand	NOUN
ap-4476	54	36	one	one	NUM
ap-4476	54	37	,	,	PUNCT
ap-4476	54	38	while	while	SCONJ
ap-4476	54	39	giving	give	VERB
ap-4476	54	40	rise	rise	NOUN
ap-4476	54	41	to	to	ADP
ap-4476	54	42	a	a	DET
ap-4476	54	43	potential	potential	ADJ
ap-4476	54	44	v	v	NOUN
ap-4476	54	45	(	(	PUNCT
ap-4476	54	46	r	r	NOUN
ap-4476	54	47	)	)	PUNCT
ap-4476	54	48	with	with	ADP
ap-4476	54	49	well	well	ADV
ap-4476	54	50	behaved	behave	VERB
ap-4476	54	51	wavefunctions	wavefunction	NOUN
ap-4476	54	52	.	.	PUNCT
ap-4476	55	1	3	3	X
ap-4476	55	2	.	.	X
ap-4476	55	3	exceptional	exceptional	ADJ
ap-4476	55	4	xm	xm	PROPN
ap-4476	55	5	orthogonal	orthogonal	ADJ
ap-4476	55	6	polynomials	polynomial	NOUN
ap-4476	55	7	for	for	ADP
ap-4476	55	8	completeness	completeness	NOUN
ap-4476	55	9	,	,	PUNCT
ap-4476	55	10	we	we	PRON
ap-4476	55	11	now	now	ADV
ap-4476	55	12	give	give	VERB
ap-4476	55	13	the	the	DET
ap-4476	55	14	differential	differential	ADJ
ap-4476	55	15	equations	equation	NOUN
ap-4476	55	16	corresponding	correspond	VERB
ap-4476	55	17	to	to	ADP
ap-4476	55	18	the	the	DET
ap-4476	55	19	xm	xm	PROPN
ap-4476	55	20	eops	eop	NOUN
ap-4476	55	21	and	and	CCONJ
ap-4476	55	22	summarize	summarize	VERB
ap-4476	55	23	the	the	DET
ap-4476	55	24	important	important	ADJ
ap-4476	55	25	properties	property	NOUN
ap-4476	55	26	for	for	ADP
ap-4476	55	27	these	these	DET
ap-4476	55	28	two	two	NUM
ap-4476	55	29	polynomials	polynomial	NOUN
ap-4476	55	30	.	.	PUNCT
ap-4476	56	1	3.1	3.1	NUM
ap-4476	56	2	.	.	PUNCT
ap-4476	56	3	exceptional	exceptional	PROPN
ap-4476	56	4	xm	xm	PROPN
ap-4476	56	5	laguerre	laguerre	PROPN
ap-4476	56	6	orthogonal	orthogonal	ADJ
ap-4476	56	7	polynomials	polynomial	NOUN
ap-4476	56	8	for	for	ADP
ap-4476	56	9	an	an	DET
ap-4476	56	10	integer	integer	NOUN
ap-4476	56	11	m	m	PROPN
ap-4476	56	12	≥	≥	NOUN
ap-4476	56	13	0	0	NUM
ap-4476	56	14	,	,	PUNCT
ap-4476	56	15	n	n	PRON
ap-4476	56	16	≥	≥	NOUN
ap-4476	56	17	m	m	PROPN
ap-4476	56	18	and	and	CCONJ
ap-4476	56	19	k	k	X
ap-4476	56	20	>	>	X
ap-4476	56	21	m	m	PROPN
ap-4476	56	22	,	,	PUNCT
ap-4476	56	23	the	the	DET
ap-4476	56	24	xm	xm	PROPN
ap-4476	56	25	laguerre	laguerre	PROPN
ap-4476	56	26	orthogonal	orthogonal	PROPN
ap-4476	56	27	polynomial	polynomial	ADJ
ap-4476	56	28	l̂(α	l̂(α	NOUN
ap-4476	56	29	)	)	PUNCT
ap-4476	56	30	n	n	CCONJ
ap-4476	56	31	,	,	PUNCT
ap-4476	56	32	m(g(r	m(g(r	PROPN
ap-4476	56	33	)	)	PUNCT
ap-4476	56	34	)	)	PUNCT
ap-4476	56	35	satisfies	satisfy	VERB
ap-4476	56	36	the	the	DET
ap-4476	56	37	differential	differential	ADJ
ap-4476	56	38	equation	equation	NOUN
ap-4476	56	39	[	[	X
ap-4476	56	40	23	23	NUM
ap-4476	56	41	]	]	PUNCT
ap-4476	56	42	l̂	l̂	X
ap-4476	56	43	′′(α	′′(α	NOUN
ap-4476	56	44	)	)	PUNCT
ap-4476	56	45	n	n	CCONJ
ap-4476	56	46	,	,	PUNCT
ap-4476	56	47	m	m	PROPN
ap-4476	56	48	(	(	PUNCT
ap-4476	56	49	g(r	g(r	NOUN
ap-4476	56	50	)	)	PUNCT
ap-4476	56	51	)	)	PUNCT
ap-4476	57	1	+	+	CCONJ
ap-4476	57	2	1	1	NUM
ap-4476	57	3	g	g	NOUN
ap-4476	57	4	(	(	PUNCT
ap-4476	57	5	(	(	PUNCT
ap-4476	57	6	α+	α+	X
ap-4476	57	7	1−	1−	NUM
ap-4476	57	8	g)−	g)−	NOUN
ap-4476	57	9	2	2	NUM
ap-4476	57	10	g	g	NOUN
ap-4476	57	11	l	l	NOUN
ap-4476	57	12	(	(	PUNCT
ap-4476	57	13	α	α	NOUN
ap-4476	57	14	)	)	PUNCT
ap-4476	57	15	m−1(−g(r	m−1(−g(r	NOUN
ap-4476	57	16	)	)	PUNCT
ap-4476	57	17	)	)	PUNCT
ap-4476	58	1	l	l	NOUN
ap-4476	58	2	(	(	PUNCT
ap-4476	58	3	α−1	α−1	NOUN
ap-4476	58	4	)	)	PUNCT
ap-4476	58	5	m	m	PROPN
ap-4476	58	6	(	(	PUNCT
ap-4476	58	7	−g(r	−g(r	PROPN
ap-4476	58	8	)	)	PUNCT
ap-4476	58	9	)	)	PUNCT
ap-4476	58	10	)	)	PUNCT
ap-4476	59	1	l̂	l̂	PROPN
ap-4476	59	2	′(α	′(α	NUM
ap-4476	59	3	)	)	PUNCT
ap-4476	59	4	n	n	CCONJ
ap-4476	59	5	,	,	PUNCT
ap-4476	59	6	m(g(r	m(g(r	PROPN
ap-4476	59	7	)	)	PUNCT
ap-4476	59	8	)	)	PUNCT
ap-4476	60	1	+	+	CCONJ
ap-4476	60	2	1	1	NUM
ap-4476	60	3	g	g	NOUN
ap-4476	60	4	(	(	PUNCT
ap-4476	60	5	n−	n−	NOUN
ap-4476	60	6	2α	2α	NOUN
ap-4476	60	7	l	l	NOUN
ap-4476	60	8	(	(	PUNCT
ap-4476	60	9	α	α	NOUN
ap-4476	60	10	)	)	PUNCT
ap-4476	60	11	m−1(−g(r	m−1(−g(r	NOUN
ap-4476	60	12	)	)	PUNCT
ap-4476	60	13	)	)	PUNCT
ap-4476	61	1	l	l	NOUN
ap-4476	61	2	(	(	PUNCT
ap-4476	61	3	α−1	α−1	NOUN
ap-4476	61	4	)	)	PUNCT
ap-4476	61	5	m	m	PROPN
ap-4476	61	6	(	(	PUNCT
ap-4476	61	7	−g(r	−g(r	PROPN
ap-4476	61	8	)	)	PUNCT
ap-4476	61	9	)	)	PUNCT
ap-4476	61	10	)	)	PUNCT
ap-4476	62	1	l̂(α	l̂(α	PROPN
ap-4476	62	2	)	)	PUNCT
ap-4476	62	3	n	n	CCONJ
ap-4476	62	4	,	,	PUNCT
ap-4476	62	5	m(g(r	m(g(r	PROPN
ap-4476	62	6	)	)	PUNCT
ap-4476	62	7	)	)	PUNCT
ap-4476	63	1	=	=	SYM
ap-4476	63	2	0	0	PUNCT
ap-4476	63	3	(	(	PUNCT
ap-4476	63	4	9	9	NUM
ap-4476	63	5	)	)	PUNCT
ap-4476	63	6	478	478	NUM
ap-4476	63	7	vol	vol	NOUN
ap-4476	63	8	.	.	PUNCT
ap-4476	64	1	57	57	NUM
ap-4476	64	2	no	no	NOUN
ap-4476	64	3	.	.	PUNCT
ap-4476	65	1	6/2017	6/2017	NUM
ap-4476	65	2	rationally	rationally	ADV
ap-4476	65	3	extended	extend	VERB
ap-4476	65	4	shape	shape	NOUN
ap-4476	65	5	invariant	invariant	ADJ
ap-4476	65	6	potentials	potential	VERB
ap-4476	65	7	the	the	DET
ap-4476	65	8	l2	l2	NOUN
ap-4476	65	9	norms	norm	NOUN
ap-4476	65	10	of	of	ADP
ap-4476	65	11	the	the	DET
ap-4476	65	12	xm	xm	PROPN
ap-4476	65	13	laguerre	laguerre	PROPN
ap-4476	65	14	polynomials	polynomial	NOUN
ap-4476	65	15	are	be	AUX
ap-4476	65	16	given	give	VERB
ap-4476	65	17	by∫	by∫	PROPN
ap-4476	65	18	∞	∞	PROPN
ap-4476	65	19	0	0	NUM
ap-4476	66	1	(	(	PUNCT
ap-4476	66	2	l̂(α	l̂(α	PROPN
ap-4476	66	3	)	)	PUNCT
ap-4476	66	4	n	n	CCONJ
ap-4476	66	5	,	,	PUNCT
ap-4476	66	6	m(g	m(g	PROPN
ap-4476	66	7	)	)	PUNCT
ap-4476	66	8	)	)	PUNCT
ap-4476	66	9	2	2	NUM
ap-4476	66	10	wα	wα	NOUN
ap-4476	66	11	m(g)dg	m(g)dg	NOUN
ap-4476	67	1	=	=	SYM
ap-4476	67	2	(	(	PUNCT
ap-4476	67	3	α+	α+	X
ap-4476	67	4	n)γ(α+	n)γ(α+	NOUN
ap-4476	67	5	n−m	n−m	PROPN
ap-4476	67	6	)	)	PUNCT
ap-4476	67	7	(	(	PUNCT
ap-4476	67	8	n−m	n−m	PROPN
ap-4476	67	9	)	)	PUNCT
ap-4476	67	10	!	!	PUNCT
ap-4476	68	1	,	,	PUNCT
ap-4476	68	2	(	(	PUNCT
ap-4476	68	3	10	10	NUM
ap-4476	68	4	)	)	PUNCT
ap-4476	68	5	where	where	SCONJ
ap-4476	68	6	wα	wα	NOUN
ap-4476	68	7	m(g	m(g	PROPN
ap-4476	68	8	)	)	PUNCT
ap-4476	68	9	=	=	SYM
ap-4476	68	10	gαe−g	gαe−g	NOUN
ap-4476	68	11	(	(	PUNCT
ap-4476	68	12	l	l	PROPN
ap-4476	68	13	(	(	PUNCT
ap-4476	68	14	α−1	α−1	NOUN
ap-4476	68	15	)	)	PUNCT
ap-4476	68	16	m	m	PROPN
ap-4476	68	17	(	(	PUNCT
ap-4476	68	18	−g	−g	NOUN
ap-4476	68	19	)	)	PUNCT
ap-4476	68	20	)	)	PUNCT
ap-4476	68	21	2	2	NUM
ap-4476	68	22	(	(	PUNCT
ap-4476	68	23	11	11	NUM
ap-4476	68	24	)	)	PUNCT
ap-4476	68	25	is	be	AUX
ap-4476	68	26	the	the	DET
ap-4476	68	27	weight	weight	NOUN
ap-4476	68	28	factor	factor	NOUN
ap-4476	68	29	for	for	ADP
ap-4476	68	30	the	the	DET
ap-4476	68	31	xm	xm	PROPN
ap-4476	68	32	laguerre	laguerre	NOUN
ap-4476	68	33	polynomials	polynomial	NOUN
ap-4476	68	34	.	.	PUNCT
ap-4476	69	1	in	in	ADP
ap-4476	69	2	terms	term	NOUN
ap-4476	69	3	of	of	ADP
ap-4476	69	4	classical	classical	ADJ
ap-4476	69	5	laguerre	laguerre	NOUN
ap-4476	69	6	polynomials	polynomial	VERB
ap-4476	69	7	the	the	DET
ap-4476	69	8	xm	xm	PROPN
ap-4476	69	9	laguerre	laguerre	NOUN
ap-4476	69	10	polynomials	polynomial	NOUN
ap-4476	69	11	can	can	AUX
ap-4476	69	12	be	be	AUX
ap-4476	69	13	written	write	VERB
ap-4476	69	14	as	as	ADP
ap-4476	69	15	l̂(α	l̂(α	NOUN
ap-4476	69	16	)	)	PUNCT
ap-4476	69	17	n	n	CCONJ
ap-4476	69	18	,	,	PUNCT
ap-4476	69	19	m(g	m(g	NOUN
ap-4476	69	20	)	)	PUNCT
ap-4476	69	21	=	=	SYM
ap-4476	70	1	l(α	l(α	PROPN
ap-4476	70	2	)	)	PUNCT
ap-4476	70	3	m	m	PROPN
ap-4476	70	4	(	(	PUNCT
ap-4476	70	5	−g)l(α−1	−g)l(α−1	ADJ
ap-4476	70	6	)	)	PUNCT
ap-4476	70	7	n−m	n−m	PROPN
ap-4476	70	8	(	(	PUNCT
ap-4476	70	9	g	g	NOUN
ap-4476	70	10	)	)	PUNCT
ap-4476	70	11	+	+	SYM
ap-4476	70	12	l(α−1	l(α−1	X
ap-4476	70	13	)	)	PUNCT
ap-4476	70	14	m	m	VERB
ap-4476	70	15	(	(	PUNCT
ap-4476	70	16	−g)l(α	−g)l(α	NOUN
ap-4476	70	17	)	)	PUNCT
ap-4476	70	18	n−m−1(g	n−m−1(g	ADV
ap-4476	70	19	)	)	PUNCT
ap-4476	70	20	;	;	PUNCT
ap-4476	70	21	n	n	PRON
ap-4476	70	22	≥	≥	NOUN
ap-4476	70	23	m.	m.	NOUN
ap-4476	70	24	(	(	PUNCT
ap-4476	70	25	12	12	NUM
ap-4476	70	26	)	)	PUNCT
ap-4476	70	27	for	for	ADP
ap-4476	70	28	m	m	PROPN
ap-4476	70	29	=	=	SYM
ap-4476	70	30	0	0	NUM
ap-4476	70	31	,	,	PUNCT
ap-4476	70	32	the	the	DET
ap-4476	70	33	above	above	ADJ
ap-4476	70	34	definitions	definition	NOUN
ap-4476	70	35	reduce	reduce	VERB
ap-4476	70	36	to	to	ADP
ap-4476	70	37	their	their	PRON
ap-4476	70	38	classical	classical	ADJ
ap-4476	70	39	counterparts	counterpart	NOUN
ap-4476	70	40	i.e.	i.e.	X
ap-4476	70	41	l̂	l̂	X
ap-4476	70	42	(	(	PUNCT
ap-4476	70	43	α	α	NOUN
ap-4476	70	44	)	)	PUNCT
ap-4476	70	45	0,n(g	0,n(g	NUM
ap-4476	70	46	)	)	PUNCT
ap-4476	70	47	=	=	SYM
ap-4476	70	48	l(α	l(α	PROPN
ap-4476	70	49	)	)	PUNCT
ap-4476	71	1	n	n	CCONJ
ap-4476	71	2	(	(	PUNCT
ap-4476	71	3	g	g	NOUN
ap-4476	71	4	)	)	PUNCT
ap-4476	71	5	(	(	PUNCT
ap-4476	71	6	13	13	NUM
ap-4476	71	7	)	)	PUNCT
ap-4476	71	8	wα	wα	NOUN
ap-4476	71	9	0	0	PUNCT
ap-4476	72	1	(	(	PUNCT
ap-4476	72	2	g	g	NOUN
ap-4476	72	3	)	)	PUNCT
ap-4476	72	4	=	=	NOUN
ap-4476	72	5	gαe−g	gαe−g	NOUN
ap-4476	72	6	,	,	PUNCT
ap-4476	72	7	(	(	PUNCT
ap-4476	72	8	14	14	NUM
ap-4476	72	9	)	)	PUNCT
ap-4476	72	10	and	and	CCONJ
ap-4476	72	11	for	for	ADP
ap-4476	72	12	m	m	PROPN
ap-4476	72	13	=	=	NOUN
ap-4476	72	14	1	1	NUM
ap-4476	72	15	this	this	DET
ap-4476	72	16	satisfies	satisfie	NOUN
ap-4476	72	17	[	[	X
ap-4476	72	18	1	1	NUM
ap-4476	72	19	,	,	PUNCT
ap-4476	72	20	eq	eq	NOUN
ap-4476	72	21	.	.	PROPN
ap-4476	72	22	80	80	NUM
ap-4476	72	23	]	]	PUNCT
ap-4476	72	24	.	.	PUNCT
ap-4476	73	1	the	the	DET
ap-4476	73	2	other	other	ADJ
ap-4476	73	3	properties	property	NOUN
ap-4476	73	4	related	relate	VERB
ap-4476	73	5	to	to	ADP
ap-4476	73	6	the	the	DET
ap-4476	73	7	xm	xm	PROPN
ap-4476	73	8	laguerre	laguerre	PROPN
ap-4476	73	9	polynomials	polynomial	NOUN
ap-4476	73	10	are	be	AUX
ap-4476	73	11	discussed	discuss	VERB
ap-4476	73	12	in	in	ADP
ap-4476	73	13	detail	detail	NOUN
ap-4476	73	14	in	in	ADP
ap-4476	73	15	ref	ref	NOUN
ap-4476	73	16	.	.	PUNCT
ap-4476	74	1	[	[	X
ap-4476	74	2	23	23	NUM
ap-4476	74	3	]	]	PUNCT
ap-4476	74	4	.	.	PUNCT
ap-4476	75	1	3.2	3.2	NUM
ap-4476	75	2	.	.	PUNCT
ap-4476	76	1	exceptional	exceptional	ADJ
ap-4476	76	2	xm	xm	PROPN
ap-4476	76	3	jacobi	jacobi	PROPN
ap-4476	76	4	orthogonal	orthogonal	PROPN
ap-4476	76	5	polynomials	polynomial	NOUN
ap-4476	76	6	for	for	ADP
ap-4476	76	7	an	an	DET
ap-4476	76	8	integer	integer	NOUN
ap-4476	76	9	m	m	PROPN
ap-4476	76	10	≥	≥	NOUN
ap-4476	76	11	1	1	NUM
ap-4476	76	12	and	and	CCONJ
ap-4476	76	13	α	α	NOUN
ap-4476	76	14	,	,	PUNCT
ap-4476	76	15	β	β	X
ap-4476	76	16	>	>	X
ap-4476	76	17	−1	−1	NOUN
ap-4476	76	18	the	the	DET
ap-4476	76	19	exceptional	exceptional	ADJ
ap-4476	76	20	xm	xm	PROPN
ap-4476	76	21	jacobi	jacobi	PROPN
ap-4476	76	22	orthogonal	orthogonal	PROPN
ap-4476	76	23	polynomials	polynomial	NOUN
ap-4476	76	24	p̂	p̂	NOUN
ap-4476	76	25	(	(	PUNCT
ap-4476	76	26	α	α	NOUN
ap-4476	76	27	,	,	PUNCT
ap-4476	76	28	β	β	NOUN
ap-4476	76	29	)	)	PUNCT
ap-4476	76	30	n	n	CCONJ
ap-4476	76	31	,	,	PUNCT
ap-4476	76	32	m	m	PROPN
ap-4476	76	33	(	(	PUNCT
ap-4476	76	34	g(r	g(r	NOUN
ap-4476	76	35	)	)	PUNCT
ap-4476	76	36	)	)	PUNCT
ap-4476	77	1	[	[	X
ap-4476	77	2	24	24	NUM
ap-4476	77	3	,	,	PUNCT
ap-4476	77	4	27	27	NUM
ap-4476	77	5	]	]	PUNCT
ap-4476	77	6	satisfies	satisfy	VERB
ap-4476	77	7	the	the	DET
ap-4476	77	8	differential	differential	ADJ
ap-4476	77	9	equation	equation	NOUN
ap-4476	77	10	p̂	p̂	X
ap-4476	77	11	′′(α	′′(α	VERB
ap-4476	77	12	,	,	PUNCT
ap-4476	77	13	β	β	NOUN
ap-4476	77	14	)	)	PUNCT
ap-4476	77	15	n	n	CCONJ
ap-4476	77	16	,	,	PUNCT
ap-4476	77	17	m	m	PROPN
ap-4476	77	18	(	(	PUNCT
ap-4476	77	19	g(r	g(r	NOUN
ap-4476	77	20	)	)	PUNCT
ap-4476	77	21	)	)	PUNCT
ap-4476	78	1	+	+	CCONJ
ap-4476	78	2	(	(	PUNCT
ap-4476	78	3	(	(	PUNCT
ap-4476	78	4	α−	α−	ADP
ap-4476	78	5	β	β	X
ap-4476	78	6	−m+	−m+	NOUN
ap-4476	78	7	1	1	NUM
ap-4476	78	8	)	)	PUNCT
ap-4476	78	9	p	p	NOUN
ap-4476	78	10	(	(	PUNCT
ap-4476	78	11	−α	−α	PROPN
ap-4476	78	12	,	,	PUNCT
ap-4476	78	13	β	β	NOUN
ap-4476	78	14	)	)	PUNCT
ap-4476	78	15	m−1	m−1	PROPN
ap-4476	78	16	(	(	PUNCT
ap-4476	78	17	g(r	g(r	NOUN
ap-4476	78	18	)	)	PUNCT
ap-4476	78	19	)	)	PUNCT
ap-4476	79	1	p	p	NOUN
ap-4476	79	2	(	(	PUNCT
ap-4476	79	3	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	79	4	)	)	PUNCT
ap-4476	79	5	m	m	PROPN
ap-4476	79	6	(	(	PUNCT
ap-4476	79	7	g(r	g(r	NOUN
ap-4476	79	8	)	)	PUNCT
ap-4476	79	9	)	)	PUNCT
ap-4476	80	1	−	−	ADP
ap-4476	80	2	α+	α+	PUNCT
ap-4476	80	3	1	1	NUM
ap-4476	80	4	1−	1−	NUM
ap-4476	80	5	g(r	g(r	PROPN
ap-4476	80	6	)	)	PUNCT
ap-4476	81	1	+	+	SYM
ap-4476	81	2	β	β	X
ap-4476	81	3	+	+	CCONJ
ap-4476	81	4	1	1	NUM
ap-4476	81	5	1	1	NUM
ap-4476	81	6	+	+	NUM
ap-4476	81	7	g(r	g(r	NOUN
ap-4476	81	8	)	)	PUNCT
ap-4476	81	9	)	)	PUNCT
ap-4476	81	10	p̂	p̂	X
ap-4476	81	11	′(α	′(α	PROPN
ap-4476	81	12	,	,	PUNCT
ap-4476	81	13	β	β	NOUN
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ap-4476	81	17	m	m	PROPN
ap-4476	81	18	(	(	PUNCT
ap-4476	81	19	g(r	g(r	NOUN
ap-4476	81	20	)	)	PUNCT
ap-4476	81	21	)	)	PUNCT
ap-4476	82	1	+	+	CCONJ
ap-4476	82	2	1	1	NUM
ap-4476	82	3	(	(	PUNCT
ap-4476	82	4	1−	1−	NUM
ap-4476	82	5	g2(r	g2(r	NOUN
ap-4476	82	6	)	)	PUNCT
ap-4476	82	7	)	)	PUNCT
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ap-4476	82	10	β	β	X
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ap-4476	82	12	1)(1−	1)(1−	NUM
ap-4476	82	13	g(r	g(r	PROPN
ap-4476	82	14	)	)	PUNCT
ap-4476	82	15	)	)	PUNCT
ap-4476	83	1	p	p	X
ap-4476	83	2	(	(	PUNCT
ap-4476	83	3	−α	−α	PROPN
ap-4476	83	4	,	,	PUNCT
ap-4476	83	5	β	β	NOUN
ap-4476	83	6	)	)	PUNCT
ap-4476	83	7	m−1	m−1	PROPN
ap-4476	83	8	(	(	PUNCT
ap-4476	83	9	g(r	g(r	NOUN
ap-4476	83	10	)	)	PUNCT
ap-4476	83	11	)	)	PUNCT
ap-4476	84	1	p	p	NOUN
ap-4476	84	2	(	(	PUNCT
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ap-4476	84	4	)	)	PUNCT
ap-4476	84	5	m	m	PROPN
ap-4476	84	6	(	(	PUNCT
ap-4476	84	7	g(r	g(r	NOUN
ap-4476	84	8	)	)	PUNCT
ap-4476	84	9	)	)	PUNCT
ap-4476	85	1	+	+	X
ap-4476	85	2	m(α−	m(α−	NOUN
ap-4476	85	3	β	β	X
ap-4476	85	4	−m+	−m+	X
ap-4476	85	5	1	1	NUM
ap-4476	85	6	)	)	PUNCT
ap-4476	85	7	+	+	CCONJ
ap-4476	85	8	(	(	PUNCT
ap-4476	85	9	n−m)(α+	n−m)(α+	PRON
ap-4476	85	10	β	β	NOUN
ap-4476	85	11	+	+	CCONJ
ap-4476	85	12	n−m+	n−m+	PROPN
ap-4476	85	13	1	1	NUM
ap-4476	85	14	)	)	PUNCT
ap-4476	85	15	)	)	PUNCT
ap-4476	85	16	p̂	p̂	X
ap-4476	85	17	(	(	PUNCT
ap-4476	85	18	α	α	X
ap-4476	85	19	,	,	PUNCT
ap-4476	85	20	β	β	NOUN
ap-4476	85	21	)	)	PUNCT
ap-4476	85	22	n	n	CCONJ
ap-4476	85	23	,	,	PUNCT
ap-4476	85	24	m	m	PROPN
ap-4476	85	25	(	(	PUNCT
ap-4476	85	26	g(r	g(r	NOUN
ap-4476	85	27	)	)	PUNCT
ap-4476	85	28	)	)	PUNCT
ap-4476	86	1	=	=	PUNCT
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ap-4476	87	2	15	15	NUM
ap-4476	87	3	)	)	PUNCT
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ap-4476	87	5	l2	l2	NOUN
ap-4476	87	6	norms	norm	NOUN
ap-4476	87	7	of	of	ADP
ap-4476	87	8	the	the	DET
ap-4476	87	9	xm	xm	PROPN
ap-4476	87	10	jacobi	jacobi	PROPN
ap-4476	87	11	polynomials	polynomial	NOUN
ap-4476	87	12	are	be	AUX
ap-4476	87	13	given	give	VERB
ap-4476	87	14	by∫	by∫	PROPN
ap-4476	87	15	1	1	NUM
ap-4476	87	16	−1	−1	NOUN
ap-4476	87	17	[	[	X
ap-4476	87	18	p̂	p̂	X
ap-4476	87	19	(	(	PUNCT
ap-4476	87	20	α	α	NOUN
ap-4476	87	21	,	,	PUNCT
ap-4476	87	22	β	β	NOUN
ap-4476	87	23	)	)	PUNCT
ap-4476	87	24	n	n	CCONJ
ap-4476	87	25	,	,	PUNCT
ap-4476	87	26	m	m	VERB
ap-4476	87	27	(	(	PUNCT
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ap-4476	87	29	,	,	PUNCT
ap-4476	87	30	β	β	X
ap-4476	87	31	m	m	VERB
ap-4476	87	32	dg	dg	NOUN
ap-4476	87	33	=	=	SYM
ap-4476	87	34	2α+β+1(1	2α+β+1(1	NUM
ap-4476	87	35	+	+	CCONJ
ap-4476	87	36	α+	α+	PRON
ap-4476	87	37	n−	n−	NOUN
ap-4476	87	38	2m)(β	2m)(β	NUM
ap-4476	87	39	+	+	CCONJ
ap-4476	87	40	n)γ(α+	n)γ(α+	PROPN
ap-4476	87	41	1	1	NUM
ap-4476	87	42	+	+	CCONJ
ap-4476	87	43	n−m)γ(β	n−m)γ(β	PROPN
ap-4476	87	44	+	+	SYM
ap-4476	87	45	n−m	n−m	PROPN
ap-4476	87	46	)	)	PUNCT
ap-4476	87	47	(	(	PUNCT
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ap-4476	87	49	1	1	NUM
ap-4476	87	50	+	+	NUM
ap-4476	87	51	n−m)(α+	n−m)(α+	NUM
ap-4476	87	52	β	β	NOUN
ap-4476	87	53	+	+	X
ap-4476	88	1	2n−	2n−	PROPN
ap-4476	88	2	2m+	2m+	NUM
ap-4476	88	3	1)γ(α+	1)γ(α+	PROPN
ap-4476	88	4	β	β	X
ap-4476	88	5	+	+	CCONJ
ap-4476	88	6	n−m+	n−m+	PROPN
ap-4476	88	7	1	1	NUM
ap-4476	88	8	)	)	PUNCT
ap-4476	88	9	,	,	PUNCT
ap-4476	88	10	(	(	PUNCT
ap-4476	88	11	16	16	NUM
ap-4476	88	12	)	)	PUNCT
ap-4476	88	13	where	where	SCONJ
ap-4476	88	14	ŵα	ŵα	PROPN
ap-4476	88	15	,	,	PUNCT
ap-4476	88	16	β	β	NOUN
ap-4476	88	17	m	m	NOUN
ap-4476	88	18	=	=	SYM
ap-4476	88	19	(	(	PUNCT
ap-4476	88	20	1−	1−	NUM
ap-4476	88	21	g)α(1	g)α(1	PROPN
ap-4476	88	22	+	+	CCONJ
ap-4476	88	23	g)β	g)β	ADJ
ap-4476	88	24	(	(	PUNCT
ap-4476	88	25	p	p	X
ap-4476	88	26	(	(	PUNCT
ap-4476	88	27	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	88	28	)	)	PUNCT
ap-4476	88	29	m	m	PROPN
ap-4476	88	30	(	(	PUNCT
ap-4476	88	31	g(r	g(r	NOUN
ap-4476	88	32	)	)	PUNCT
ap-4476	88	33	)	)	PUNCT
ap-4476	88	34	)	)	PUNCT
ap-4476	88	35	2	2	NUM
ap-4476	88	36	(	(	PUNCT
ap-4476	88	37	17	17	NUM
ap-4476	88	38	)	)	PUNCT
ap-4476	88	39	is	be	AUX
ap-4476	88	40	the	the	DET
ap-4476	88	41	weight	weight	NOUN
ap-4476	88	42	factor	factor	NOUN
ap-4476	88	43	for	for	ADP
ap-4476	88	44	the	the	DET
ap-4476	88	45	xm	xm	PROPN
ap-4476	88	46	jacobi	jacobi	PROPN
ap-4476	88	47	polynomials	polynomials	PROPN
ap-4476	88	48	.	.	PUNCT
ap-4476	89	1	the	the	DET
ap-4476	89	2	above	above	ADJ
ap-4476	89	3	l2	l2	NOUN
ap-4476	89	4	norms	norm	NOUN
ap-4476	89	5	of	of	ADP
ap-4476	89	6	the	the	DET
ap-4476	89	7	xm	xm	PROPN
ap-4476	89	8	jacobi	jacobi	PROPN
ap-4476	89	9	polynomials	polynomial	NOUN
ap-4476	89	10	hold	hold	VERB
ap-4476	89	11	,	,	PUNCT
ap-4476	89	12	when	when	SCONJ
ap-4476	89	13	the	the	DET
ap-4476	89	14	denominator	denominator	NOUN
ap-4476	89	15	of	of	ADP
ap-4476	89	16	the	the	DET
ap-4476	89	17	above	above	ADJ
ap-4476	89	18	weight	weight	NOUN
ap-4476	89	19	factor	factor	NOUN
ap-4476	89	20	is	be	AUX
ap-4476	89	21	non	non	ADJ
ap-4476	89	22	-	-	ADJ
ap-4476	89	23	zero	zero	NUM
ap-4476	89	24	for	for	ADP
ap-4476	89	25	−1	−1	NOUN
ap-4476	89	26	≤	≤	NOUN
ap-4476	89	27	g	g	NOUN
ap-4476	89	28	≤	≤	NUM
ap-4476	89	29	1	1	NUM
ap-4476	89	30	.	.	PUNCT
ap-4476	89	31	to	to	PART
ap-4476	89	32	ensure	ensure	VERB
ap-4476	89	33	this	this	PRON
ap-4476	89	34	,	,	PUNCT
ap-4476	89	35	the	the	DET
ap-4476	89	36	following	follow	VERB
ap-4476	89	37	two	two	NUM
ap-4476	89	38	conditions	condition	NOUN
ap-4476	89	39	must	must	AUX
ap-4476	89	40	be	be	AUX
ap-4476	89	41	satisfied	satisfied	ADJ
ap-4476	89	42	simultaneously	simultaneously	ADV
ap-4476	89	43	:	:	PUNCT
ap-4476	89	44	(	(	PUNCT
ap-4476	89	45	i	i	NOUN
ap-4476	89	46	)	)	PUNCT
ap-4476	89	47	β	β	PROPN
ap-4476	89	48	6=	6=	ADP
ap-4476	89	49	0	0	NUM
ap-4476	89	50	,	,	PUNCT
ap-4476	89	51	α	α	NOUN
ap-4476	89	52	,	,	PUNCT
ap-4476	89	53	α−	α−	ADP
ap-4476	89	54	β	β	X
ap-4476	89	55	−m+	−m+	VERB
ap-4476	89	56	1	1	NUM
ap-4476	89	57	6∈	6∈	PROPN
ap-4476	89	58	{	{	PUNCT
ap-4476	89	59	0	0	NUM
ap-4476	89	60	,	,	PUNCT
ap-4476	89	61	1	1	NUM
ap-4476	89	62	,	,	PUNCT
ap-4476	89	63	.	.	PUNCT
ap-4476	89	64	.	.	PUNCT
ap-4476	89	65	.	.	PUNCT
ap-4476	90	1	,	,	PUNCT
ap-4476	90	2	m−	m−	PROPN
ap-4476	90	3	1	1	NUM
ap-4476	90	4	}	}	PUNCT
ap-4476	90	5	,	,	PUNCT
ap-4476	90	6	(	(	PUNCT
ap-4476	90	7	ii	ii	NOUN
ap-4476	90	8	)	)	PUNCT
ap-4476	90	9	α	α	PROPN
ap-4476	90	10	>	>	X
ap-4476	90	11	m−	m−	PROPN
ap-4476	90	12	2	2	NUM
ap-4476	90	13	,	,	PUNCT
ap-4476	90	14	sgn(α−m+	sgn(α−m+	NOUN
ap-4476	90	15	1	1	NUM
ap-4476	90	16	)	)	PUNCT
ap-4476	90	17	=	=	SYM
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ap-4476	90	19	)	)	PUNCT
ap-4476	90	20	,	,	PUNCT
ap-4476	90	21	(	(	PUNCT
ap-4476	90	22	18	18	NUM
ap-4476	90	23	)	)	PUNCT
ap-4476	90	24	where	where	SCONJ
ap-4476	90	25	sgn(g	sgn(g	X
ap-4476	90	26	)	)	PUNCT
ap-4476	90	27	is	be	AUX
ap-4476	90	28	the	the	DET
ap-4476	90	29	signum	signum	PROPN
ap-4476	90	30	function	function	NOUN
ap-4476	90	31	.	.	PUNCT
ap-4476	91	1	in	in	ADP
ap-4476	91	2	terms	term	NOUN
ap-4476	91	3	of	of	ADP
ap-4476	91	4	classical	classical	ADJ
ap-4476	91	5	jacobi	jacobi	NOUN
ap-4476	91	6	polynomials	polynomials	PROPN
ap-4476	91	7	p	p	X
ap-4476	91	8	(	(	PUNCT
ap-4476	91	9	α	α	X
ap-4476	91	10	,	,	PUNCT
ap-4476	91	11	β	β	NOUN
ap-4476	91	12	)	)	PUNCT
ap-4476	91	13	n	n	PROPN
ap-4476	91	14	(	(	PUNCT
ap-4476	91	15	g	g	NOUN
ap-4476	91	16	)	)	PUNCT
ap-4476	91	17	,	,	PUNCT
ap-4476	91	18	the	the	DET
ap-4476	91	19	xm	xm	PROPN
ap-4476	91	20	jacobi	jacobi	PROPN
ap-4476	91	21	polynomials	polynomial	NOUN
ap-4476	91	22	can	can	AUX
ap-4476	91	23	be	be	AUX
ap-4476	91	24	written	write	VERB
ap-4476	91	25	as	as	ADP
ap-4476	91	26	p̂	p̂	X
ap-4476	91	27	(	(	PUNCT
ap-4476	91	28	α	α	NOUN
ap-4476	91	29	,	,	PUNCT
ap-4476	91	30	β	β	NOUN
ap-4476	91	31	)	)	PUNCT
ap-4476	91	32	n	n	CCONJ
ap-4476	91	33	,	,	PUNCT
ap-4476	91	34	m	m	PROPN
ap-4476	91	35	(	(	PUNCT
ap-4476	91	36	g	g	NOUN
ap-4476	91	37	)	)	PUNCT
ap-4476	91	38	=	=	SYM
ap-4476	92	1	(	(	PUNCT
ap-4476	92	2	−1)m	−1)m	PROPN
ap-4476	92	3	(	(	PUNCT
ap-4476	92	4	1	1	NUM
ap-4476	92	5	+	+	CCONJ
ap-4476	92	6	α+	α+	X
ap-4476	92	7	β	β	NOUN
ap-4476	92	8	+	+	X
ap-4476	92	9	j	j	PROPN
ap-4476	92	10	2(1	2(1	NUM
ap-4476	92	11	+	+	CCONJ
ap-4476	92	12	α+	α+	PROPN
ap-4476	92	13	j	j	NOUN
ap-4476	92	14	)	)	PUNCT
ap-4476	92	15	(	(	PUNCT
ap-4476	92	16	g	g	PROPN
ap-4476	92	17	−	−	PROPN
ap-4476	92	18	1)p	1)p	PROPN
ap-4476	92	19	(	(	PUNCT
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ap-4476	92	21	)	)	PUNCT
ap-4476	92	22	m	m	PROPN
ap-4476	92	23	(	(	PUNCT
ap-4476	92	24	g)p	g)p	X
ap-4476	92	25	(	(	PUNCT
ap-4476	92	26	α+2,β	α+2,β	NOUN
ap-4476	92	27	)	)	PUNCT
ap-4476	92	28	j−1	j−1	NOUN
ap-4476	92	29	(	(	PUNCT
ap-4476	92	30	g	g	NOUN
ap-4476	92	31	)	)	PUNCT
ap-4476	93	1	+	+	CCONJ
ap-4476	93	2	1	1	NUM
ap-4476	93	3	+	+	NUM
ap-4476	93	4	α−m	α−m	NOUN
ap-4476	93	5	α+	α+	X
ap-4476	93	6	1	1	NUM
ap-4476	94	1	+	+	NUM
ap-4476	94	2	j	j	PROPN
ap-4476	94	3	p	p	X
ap-4476	94	4	(	(	PUNCT
ap-4476	94	5	−2−α	−2−α	PROPN
ap-4476	94	6	,	,	PUNCT
ap-4476	94	7	β	β	X
ap-4476	94	8	)	)	PUNCT
ap-4476	94	9	m	m	VERB
ap-4476	94	10	(	(	PUNCT
ap-4476	94	11	g)p	g)p	X
ap-4476	94	12	(	(	PUNCT
ap-4476	94	13	α+1,β−1	α+1,β−1	NUM
ap-4476	94	14	)	)	PUNCT
ap-4476	94	15	j	j	PROPN
ap-4476	94	16	(	(	PUNCT
ap-4476	94	17	g	g	NOUN
ap-4476	94	18	)	)	PUNCT
ap-4476	94	19	)	)	PUNCT
ap-4476	94	20	,	,	PUNCT
ap-4476	94	21	j	j	PROPN
ap-4476	94	22	=	=	PRON
ap-4476	94	23	n−m	n−m	VERB
ap-4476	94	24	≥	≥	NOUN
ap-4476	94	25	0	0	NUM
ap-4476	94	26	.	.	PUNCT
ap-4476	95	1	(	(	PUNCT
ap-4476	95	2	19	19	NUM
ap-4476	95	3	)	)	PUNCT
ap-4476	95	4	for	for	ADP
ap-4476	95	5	m	m	PROPN
ap-4476	95	6	=	=	SYM
ap-4476	95	7	0	0	NUM
ap-4476	95	8	,	,	PUNCT
ap-4476	95	9	the	the	DET
ap-4476	95	10	above	above	ADJ
ap-4476	95	11	definitions	definition	NOUN
ap-4476	95	12	reduces	reduce	VERB
ap-4476	95	13	to	to	ADP
ap-4476	95	14	their	their	PRON
ap-4476	95	15	classical	classical	ADJ
ap-4476	95	16	counterparts	counterpart	NOUN
ap-4476	95	17	i.e.	i.e.	X
ap-4476	95	18	p̂	p̂	X
ap-4476	95	19	(	(	PUNCT
ap-4476	95	20	αβ	αβ	INTJ
ap-4476	95	21	)	)	PUNCT
ap-4476	95	22	0,n	0,n	NOUN
ap-4476	95	23	(	(	PUNCT
ap-4476	95	24	g	g	NOUN
ap-4476	95	25	)	)	PUNCT
ap-4476	96	1	=	=	SYM
ap-4476	97	1	p	p	X
ap-4476	97	2	(	(	PUNCT
ap-4476	97	3	α	α	X
ap-4476	97	4	,	,	PUNCT
ap-4476	97	5	β	β	NOUN
ap-4476	97	6	)	)	PUNCT
ap-4476	97	7	n	n	PROPN
ap-4476	97	8	(	(	PUNCT
ap-4476	97	9	g	g	NOUN
ap-4476	97	10	)	)	PUNCT
ap-4476	97	11	,	,	PUNCT
ap-4476	97	12	wα	wα	NOUN
ap-4476	97	13	,	,	PUNCT
ap-4476	97	14	β	β	X
ap-4476	97	15	0	0	NUM
ap-4476	98	1	(	(	PUNCT
ap-4476	98	2	g	g	NOUN
ap-4476	98	3	)	)	PUNCT
ap-4476	98	4	=	=	SYM
ap-4476	98	5	(	(	PUNCT
ap-4476	98	6	1−	1−	NUM
ap-4476	98	7	g)α(1	g)α(1	PROPN
ap-4476	98	8	+	+	CCONJ
ap-4476	98	9	g)β	g)β	ADJ
ap-4476	98	10	,	,	PUNCT
ap-4476	98	11	(	(	PUNCT
ap-4476	98	12	20	20	NUM
ap-4476	98	13	)	)	PUNCT
ap-4476	98	14	and	and	CCONJ
ap-4476	98	15	for	for	ADP
ap-4476	98	16	m	m	PROPN
ap-4476	98	17	=	=	NOUN
ap-4476	98	18	1	1	NUM
ap-4476	98	19	this	this	DET
ap-4476	98	20	satisfies	satisfie	NOUN
ap-4476	98	21	ref	ref	VERB
ap-4476	98	22	.	.	PUNCT
ap-4476	99	1	[	[	X
ap-4476	99	2	1	1	NUM
ap-4476	99	3	,	,	PUNCT
ap-4476	99	4	eq	eq	NOUN
ap-4476	99	5	.	.	PROPN
ap-4476	99	6	56	56	NUM
ap-4476	99	7	]	]	PUNCT
ap-4476	99	8	.	.	PUNCT
ap-4476	100	1	the	the	DET
ap-4476	100	2	other	other	ADJ
ap-4476	100	3	properties	property	NOUN
ap-4476	100	4	related	relate	VERB
ap-4476	100	5	to	to	ADP
ap-4476	100	6	the	the	DET
ap-4476	100	7	xm	xm	PROPN
ap-4476	100	8	jacobi	jacobi	PROPN
ap-4476	100	9	polynomials	polynomial	NOUN
ap-4476	100	10	are	be	AUX
ap-4476	100	11	discussed	discuss	VERB
ap-4476	100	12	in	in	ADP
ap-4476	100	13	detail	detail	NOUN
ap-4476	100	14	in	in	ADP
ap-4476	100	15	ref	ref	NOUN
ap-4476	100	16	.	.	PUNCT
ap-4476	101	1	[	[	X
ap-4476	101	2	24	24	NUM
ap-4476	101	3	]	]	SYM
ap-4476	101	4	479	479	PROPN
ap-4476	101	5	r.	r.	PROPN
ap-4476	101	6	k.	k.	PROPN
ap-4476	101	7	yadav	yadav	PROPN
ap-4476	101	8	,	,	PUNCT
ap-4476	101	9	n.	n.	PROPN
ap-4476	101	10	kumari	kumari	PROPN
ap-4476	101	11	,	,	PUNCT
ap-4476	101	12	a.	a.	PROPN
ap-4476	101	13	khare	khare	PROPN
ap-4476	101	14	,	,	PUNCT
ap-4476	101	15	b.	b.	PROPN
ap-4476	101	16	p.	p.	PROPN
ap-4476	101	17	mandal	mandal	PROPN
ap-4476	101	18	acta	acta	PROPN
ap-4476	101	19	polytechnica	polytechnica	PROPN
ap-4476	101	20	4	4	NUM
ap-4476	101	21	.	.	PUNCT
ap-4476	101	22	extended	extend	VERB
ap-4476	101	23	potentials	potential	NOUN
ap-4476	101	24	in	in	ADP
ap-4476	101	25	d	d	NOUN
ap-4476	101	26	-	-	PUNCT
ap-4476	101	27	dimensions	dimension	NOUN
ap-4476	101	28	4.1	4.1	NUM
ap-4476	101	29	.	.	PUNCT
ap-4476	102	1	potentials	potential	NOUN
ap-4476	102	2	associated	associate	VERB
ap-4476	102	3	with	with	ADP
ap-4476	102	4	xm	xm	PROPN
ap-4476	102	5	exceptional	exceptional	ADJ
ap-4476	102	6	laguerre	laguerre	NOUN
ap-4476	102	7	polynomial	polynomial	ADJ
ap-4476	102	8	in	in	ADP
ap-4476	102	9	this	this	DET
ap-4476	102	10	section	section	NOUN
ap-4476	102	11	,	,	PUNCT
ap-4476	102	12	we	we	PRON
ap-4476	102	13	consider	consider	VERB
ap-4476	102	14	the	the	DET
ap-4476	102	15	extension	extension	NOUN
ap-4476	102	16	of	of	ADP
ap-4476	102	17	the	the	DET
ap-4476	102	18	usual	usual	ADJ
ap-4476	102	19	radial	radial	ADJ
ap-4476	102	20	oscillator	oscillator	NOUN
ap-4476	102	21	potential	potential	NOUN
ap-4476	102	22	.	.	PUNCT
ap-4476	103	1	for	for	ADP
ap-4476	103	2	this	this	DET
ap-4476	103	3	potential	potential	NOUN
ap-4476	103	4	let	let	VERB
ap-4476	103	5	us	we	PRON
ap-4476	103	6	define	define	VERB
ap-4476	103	7	the	the	DET
ap-4476	103	8	function	function	NOUN
ap-4476	103	9	f	f	PROPN
ap-4476	103	10	(	(	PUNCT
ap-4476	103	11	g	g	NOUN
ap-4476	103	12	)	)	PUNCT
ap-4476	103	13	as	as	ADP
ap-4476	103	14	an	an	DET
ap-4476	103	15	xm	xm	PROPN
ap-4476	103	16	(	(	PUNCT
ap-4476	103	17	m	m	PROPN
ap-4476	103	18	≥	≥	NOUN
ap-4476	103	19	1	1	NUM
ap-4476	103	20	)	)	PUNCT
ap-4476	103	21	exceptional	exceptional	ADJ
ap-4476	103	22	laguerre	laguerre	NOUN
ap-4476	103	23	polynomial	polynomial	PROPN
ap-4476	103	24	l̂(α	l̂(α	PROPN
ap-4476	103	25	)	)	PUNCT
ap-4476	103	26	n	n	CCONJ
ap-4476	103	27	,	,	PUNCT
ap-4476	103	28	m(g	m(g	PROPN
ap-4476	103	29	)	)	PUNCT
ap-4476	103	30	,	,	PUNCT
ap-4476	103	31	where	where	SCONJ
ap-4476	103	32	n	n	X
ap-4476	103	33	=	=	SYM
ap-4476	103	34	0	0	NUM
ap-4476	103	35	,	,	PUNCT
ap-4476	103	36	1	1	NUM
ap-4476	103	37	,	,	PUNCT
ap-4476	103	38	2	2	NUM
ap-4476	103	39	,	,	PUNCT
ap-4476	103	40	3	3	NUM
ap-4476	103	41	,	,	PUNCT
ap-4476	103	42	.	.	PUNCT
ap-4476	103	43	.	.	PUNCT
ap-4476	104	1	.	.	PUNCT
ap-4476	105	1	,	,	PUNCT
ap-4476	105	2	and	and	CCONJ
ap-4476	105	3	α	α	X
ap-4476	105	4	>	>	X
ap-4476	105	5	0	0	PROPN
ap-4476	105	6	,	,	PUNCT
ap-4476	105	7	the	the	DET
ap-4476	105	8	associated	associated	ADJ
ap-4476	105	9	second	second	ADJ
ap-4476	105	10	order	order	NOUN
ap-4476	105	11	differential	differential	NOUN
ap-4476	105	12	equation	equation	NOUN
ap-4476	105	13	(	(	PUNCT
ap-4476	105	14	3	3	X
ap-4476	105	15	)	)	PUNCT
ap-4476	105	16	is	be	AUX
ap-4476	105	17	equivalent	equivalent	ADJ
ap-4476	105	18	to	to	ADP
ap-4476	105	19	xm	xm	PROPN
ap-4476	105	20	laguerre	laguerre	PROPN
ap-4476	105	21	differential	differential	ADJ
ap-4476	105	22	equation	equation	NOUN
ap-4476	105	23	(	(	PUNCT
ap-4476	105	24	9	9	NUM
ap-4476	105	25	)	)	PUNCT
ap-4476	105	26	where	where	SCONJ
ap-4476	105	27	the	the	DET
ap-4476	105	28	functions	function	NOUN
ap-4476	105	29	q(g	q(g	ADJ
ap-4476	105	30	)	)	PUNCT
ap-4476	105	31	and	and	CCONJ
ap-4476	105	32	r(g	r(g	NUM
ap-4476	105	33	)	)	PUNCT
ap-4476	105	34	are	be	AUX
ap-4476	105	35	q(g	q(g	ADJ
ap-4476	105	36	)	)	PUNCT
ap-4476	106	1	=	=	SYM
ap-4476	106	2	1	1	NUM
ap-4476	106	3	g	g	NOUN
ap-4476	106	4	(	(	PUNCT
ap-4476	106	5	(	(	PUNCT
ap-4476	106	6	α+	α+	X
ap-4476	106	7	1−	1−	NUM
ap-4476	106	8	g)−	g)−	NOUN
ap-4476	106	9	2	2	NUM
ap-4476	106	10	g	g	NOUN
ap-4476	106	11	l	l	NOUN
ap-4476	106	12	(	(	PUNCT
ap-4476	106	13	α	α	NOUN
ap-4476	106	14	)	)	PUNCT
ap-4476	106	15	m−1(−g	m−1(−g	PROPN
ap-4476	106	16	)	)	PUNCT
ap-4476	106	17	l	l	NOUN
ap-4476	106	18	(	(	PUNCT
ap-4476	106	19	α−1	α−1	NOUN
ap-4476	106	20	)	)	PUNCT
ap-4476	106	21	m	m	PROPN
ap-4476	106	22	(	(	PUNCT
ap-4476	106	23	−g	−g	NOUN
ap-4476	106	24	)	)	PUNCT
ap-4476	106	25	)	)	PUNCT
ap-4476	106	26	,	,	PUNCT
ap-4476	106	27	r(g	r(g	NUM
ap-4476	106	28	)	)	PUNCT
ap-4476	106	29	=	=	SYM
ap-4476	106	30	1	1	NUM
ap-4476	106	31	g	g	NOUN
ap-4476	106	32	(	(	PUNCT
ap-4476	106	33	n−	n−	NOUN
ap-4476	106	34	2α	2α	NOUN
ap-4476	106	35	l	l	NOUN
ap-4476	106	36	(	(	PUNCT
ap-4476	106	37	α	α	NOUN
ap-4476	106	38	)	)	PUNCT
ap-4476	106	39	m−1(−g	m−1(−g	PROPN
ap-4476	106	40	)	)	PUNCT
ap-4476	106	41	l	l	NOUN
ap-4476	106	42	(	(	PUNCT
ap-4476	106	43	α−1	α−1	NOUN
ap-4476	106	44	)	)	PUNCT
ap-4476	106	45	m	m	PROPN
ap-4476	106	46	(	(	PUNCT
ap-4476	106	47	−g	−g	NOUN
ap-4476	106	48	)	)	PUNCT
ap-4476	106	49	)	)	PUNCT
ap-4476	106	50	.	.	PUNCT
ap-4476	107	1	(	(	PUNCT
ap-4476	107	2	21	21	NUM
ap-4476	107	3	)	)	PUNCT
ap-4476	107	4	using	use	VERB
ap-4476	107	5	q(g	q(g	PROPN
ap-4476	107	6	)	)	PUNCT
ap-4476	107	7	and	and	CCONJ
ap-4476	107	8	r(g	r(g	NUM
ap-4476	107	9	)	)	PUNCT
ap-4476	107	10	in	in	ADP
ap-4476	107	11	(	(	PUNCT
ap-4476	107	12	5	5	NUM
ap-4476	107	13	)	)	PUNCT
ap-4476	107	14	,	,	PUNCT
ap-4476	107	15	we	we	PRON
ap-4476	107	16	get	get	VERB
ap-4476	107	17	en	en	ADP
ap-4476	107	18	−	−	NOUN
ap-4476	107	19	vm(r	vm(r	NOUN
ap-4476	107	20	)	)	PUNCT
ap-4476	107	21	=	=	SYM
ap-4476	107	22	1	1	NUM
ap-4476	107	23	2{g	2{g	NUM
ap-4476	107	24	,	,	PUNCT
ap-4476	107	25	r}+	r}+	NOUN
ap-4476	107	26	(	(	PUNCT
ap-4476	107	27	g′)2	g′)2	PROPN
ap-4476	107	28	(	(	PUNCT
ap-4476	107	29	−1	−1	NOUN
ap-4476	107	30	4	4	NUM
ap-4476	107	31	+	+	CCONJ
ap-4476	107	32	n	n	PRON
ap-4476	107	33	g	g	NOUN
ap-4476	108	1	+	+	CCONJ
ap-4476	108	2	(	(	PUNCT
ap-4476	108	3	α+	α+	NOUN
ap-4476	108	4	1	1	NUM
ap-4476	108	5	)	)	PUNCT
ap-4476	108	6	2	2	NUM
ap-4476	108	7	g	g	NOUN
ap-4476	108	8	−	−	PROPN
ap-4476	108	9	(	(	PUNCT
ap-4476	108	10	α+	α+	PROPN
ap-4476	108	11	1)(α−	1)(α−	NUM
ap-4476	108	12	1	1	NUM
ap-4476	108	13	)	)	PUNCT
ap-4476	108	14	4g2	4g2	NUM
ap-4476	109	1	+	+	CCONJ
ap-4476	109	2	l	l	NOUN
ap-4476	109	3	(	(	PUNCT
ap-4476	109	4	α+1	α+1	NUM
ap-4476	109	5	)	)	PUNCT
ap-4476	109	6	m−2	m−2	PROPN
ap-4476	109	7	(	(	PUNCT
ap-4476	109	8	−g	−g	NOUN
ap-4476	109	9	)	)	PUNCT
ap-4476	109	10	l	l	NOUN
ap-4476	109	11	(	(	PUNCT
ap-4476	109	12	α−1	α−1	NOUN
ap-4476	109	13	)	)	PUNCT
ap-4476	109	14	m	m	PROPN
ap-4476	109	15	(	(	PUNCT
ap-4476	109	16	−g	−g	NOUN
ap-4476	109	17	)	)	PUNCT
ap-4476	109	18	−	−	PROPN
ap-4476	109	19	(	(	PUNCT
ap-4476	109	20	α+	α+	NOUN
ap-4476	109	21	g	g	NOUN
ap-4476	109	22	−	−	PROPN
ap-4476	109	23	1	1	NUM
ap-4476	109	24	)	)	PUNCT
ap-4476	109	25	g	g	NOUN
ap-4476	109	26	l	l	NOUN
ap-4476	109	27	(	(	PUNCT
ap-4476	109	28	α	α	NOUN
ap-4476	109	29	)	)	PUNCT
ap-4476	109	30	m−1(−g	m−1(−g	PROPN
ap-4476	109	31	)	)	PUNCT
ap-4476	109	32	l	l	NOUN
ap-4476	109	33	(	(	PUNCT
ap-4476	109	34	α−1	α−1	NOUN
ap-4476	109	35	)	)	PUNCT
ap-4476	109	36	m	m	PROPN
ap-4476	109	37	(	(	PUNCT
ap-4476	109	38	−g	−g	NOUN
ap-4476	109	39	)	)	PUNCT
ap-4476	109	40	−	−	PROPN
ap-4476	109	41	2	2	NUM
ap-4476	109	42	(	(	PUNCT
ap-4476	109	43	l(α	l(α	PROPN
ap-4476	109	44	)	)	PUNCT
ap-4476	109	45	m−1(−g	m−1(−g	PROPN
ap-4476	109	46	)	)	PUNCT
ap-4476	109	47	l	l	NOUN
ap-4476	109	48	(	(	PUNCT
ap-4476	109	49	α−1	α−1	NOUN
ap-4476	109	50	)	)	PUNCT
ap-4476	109	51	m	m	PROPN
ap-4476	109	52	(	(	PUNCT
ap-4476	109	53	−g	−g	NOUN
ap-4476	109	54	)	)	PUNCT
ap-4476	109	55	)	)	PUNCT
ap-4476	109	56	2	2	X
ap-4476	109	57	)	)	PUNCT
ap-4476	109	58	+	+	CCONJ
ap-4476	109	59	(	(	PUNCT
ap-4476	109	60	d	d	X
ap-4476	109	61	−	−	PROPN
ap-4476	109	62	1)(d	1)(d	NUM
ap-4476	109	63	−	−	NOUN
ap-4476	109	64	3	3	NUM
ap-4476	109	65	)	)	PUNCT
ap-4476	109	66	4r2	4r2	NUM
ap-4476	109	67	.	.	PUNCT
ap-4476	110	1	(	(	PUNCT
ap-4476	110	2	22	22	NUM
ap-4476	110	3	)	)	PUNCT
ap-4476	110	4	to	to	PART
ap-4476	110	5	get	get	VERB
ap-4476	110	6	en	en	ADP
ap-4476	110	7	as	as	SCONJ
ap-4476	110	8	explained	explain	VERB
ap-4476	110	9	in	in	ADP
ap-4476	110	10	the	the	DET
ap-4476	110	11	above	above	ADJ
ap-4476	110	12	section	section	NOUN
ap-4476	110	13	,	,	PUNCT
ap-4476	110	14	here	here	ADV
ap-4476	110	15	we	we	PRON
ap-4476	110	16	assume	assume	VERB
ap-4476	110	17	(	(	PUNCT
ap-4476	110	18	g′(r))2	g′(r))2	NOUN
ap-4476	110	19	g(r	g(r	PROPN
ap-4476	110	20	)	)	PUNCT
ap-4476	111	1	=	=	PROPN
ap-4476	111	2	c1	c1	PROPN
ap-4476	111	3	(	(	PUNCT
ap-4476	111	4	a	a	DET
ap-4476	111	5	constant	constant	ADJ
ap-4476	111	6	not	not	PART
ap-4476	111	7	equal	equal	ADJ
ap-4476	111	8	to	to	ADP
ap-4476	111	9	zero	zero	NUM
ap-4476	111	10	)	)	PUNCT
ap-4476	111	11	,	,	PUNCT
ap-4476	111	12	and	and	CCONJ
ap-4476	111	13	for	for	ADP
ap-4476	111	14	the	the	DET
ap-4476	111	15	radial	radial	ADJ
ap-4476	111	16	oscillator	oscillator	NOUN
ap-4476	111	17	potential	potential	NOUN
ap-4476	111	18	this	this	DET
ap-4476	111	19	constant	constant	ADJ
ap-4476	111	20	c1	c1	NOUN
ap-4476	111	21	can	can	AUX
ap-4476	111	22	be	be	AUX
ap-4476	111	23	obtained	obtain	VERB
ap-4476	111	24	by	by	ADP
ap-4476	111	25	setting	set	VERB
ap-4476	111	26	g(r	g(r	NOUN
ap-4476	111	27	)	)	PUNCT
ap-4476	111	28	=	=	SYM
ap-4476	111	29	1	1	NUM
ap-4476	111	30	4c1r	4c1r	NOUN
ap-4476	111	31	2	2	NUM
ap-4476	111	32	.	.	PUNCT
ap-4476	111	33	(	(	PUNCT
ap-4476	111	34	23	23	NUM
ap-4476	111	35	)	)	PUNCT
ap-4476	111	36	putting	put	VERB
ap-4476	111	37	g(r	g(r	NOUN
ap-4476	111	38	)	)	PUNCT
ap-4476	111	39	in	in	ADP
ap-4476	111	40	(	(	PUNCT
ap-4476	111	41	22	22	NUM
ap-4476	111	42	)	)	PUNCT
ap-4476	111	43	above	above	ADV
ap-4476	111	44	and	and	CCONJ
ap-4476	111	45	defining	define	VERB
ap-4476	111	46	the	the	DET
ap-4476	111	47	quantum	quantum	ADJ
ap-4476	111	48	number	number	NOUN
ap-4476	111	49	n→	n→	PUNCT
ap-4476	111	50	n+m	n+m	NUM
ap-4476	111	51	,	,	PUNCT
ap-4476	111	52	we	we	PRON
ap-4476	111	53	get	get	VERB
ap-4476	111	54	en	en	ADP
ap-4476	111	55	=	=	SYM
ap-4476	111	56	nc1	nc1	PROPN
ap-4476	111	57	,	,	PUNCT
ap-4476	111	58	n	n	NOUN
ap-4476	111	59	=	=	SYM
ap-4476	111	60	0	0	NUM
ap-4476	111	61	,	,	PUNCT
ap-4476	111	62	1	1	NUM
ap-4476	111	63	,	,	PUNCT
ap-4476	111	64	2	2	NUM
ap-4476	111	65	,	,	PUNCT
ap-4476	111	66	.	.	PUNCT
ap-4476	111	67	.	.	PUNCT
ap-4476	111	68	.	.	PUNCT
ap-4476	112	1	,	,	PUNCT
ap-4476	112	2	(	(	PUNCT
ap-4476	112	3	24	24	NUM
ap-4476	112	4	)	)	PUNCT
ap-4476	112	5	vm(r	vm(r	NOUN
ap-4476	112	6	)	)	PUNCT
ap-4476	113	1	=	=	SYM
ap-4476	113	2	1	1	NUM
ap-4476	113	3	16c	16c	NOUN
ap-4476	113	4	2	2	NUM
ap-4476	113	5	1r	1r	NUM
ap-4476	113	6	2	2	NUM
ap-4476	113	7	+	+	CCONJ
ap-4476	113	8	(	(	PUNCT
ap-4476	113	9	α+	α+	PROPN
ap-4476	113	10	1	1	NUM
ap-4476	113	11	2	2	NUM
ap-4476	113	12	)	)	PUNCT
ap-4476	113	13	(	(	PUNCT
ap-4476	113	14	α−	α−	ADP
ap-4476	113	15	1	1	NUM
ap-4476	113	16	2	2	NUM
ap-4476	113	17	)	)	PUNCT
ap-4476	113	18	r2	r2	NOUN
ap-4476	113	19	−	−	PROPN
ap-4476	113	20	c2	c2	PROPN
ap-4476	113	21	1r	1r	NUM
ap-4476	113	22	2	2	NUM
ap-4476	113	23	4	4	NUM
ap-4476	113	24	l	l	NOUN
ap-4476	113	25	(	(	PUNCT
ap-4476	113	26	α+1	α+1	NUM
ap-4476	113	27	)	)	PUNCT
ap-4476	113	28	m−2	m−2	PROPN
ap-4476	113	29	(	(	PUNCT
ap-4476	113	30	−g	−g	NOUN
ap-4476	113	31	)	)	PUNCT
ap-4476	113	32	l	l	NOUN
ap-4476	113	33	(	(	PUNCT
ap-4476	113	34	α−1	α−1	NOUN
ap-4476	113	35	)	)	PUNCT
ap-4476	113	36	m	m	PROPN
ap-4476	113	37	(	(	PUNCT
ap-4476	113	38	−g	−g	NOUN
ap-4476	113	39	)	)	PUNCT
ap-4476	113	40	+	+	SYM
ap-4476	113	41	c	c	X
ap-4476	113	42	(	(	PUNCT
ap-4476	113	43	α+	α+	PUNCT
ap-4476	113	44	cr2	cr2	NOUN
ap-4476	113	45	4	4	NUM
ap-4476	113	46	−	−	NOUN
ap-4476	113	47	1	1	NUM
ap-4476	113	48	)	)	PUNCT
ap-4476	113	49	×	×	NOUN
ap-4476	113	50	l	l	NOUN
ap-4476	113	51	(	(	PUNCT
ap-4476	113	52	α	α	NOUN
ap-4476	113	53	)	)	PUNCT
ap-4476	113	54	m−1(−g	m−1(−g	PROPN
ap-4476	113	55	)	)	PUNCT
ap-4476	113	56	l	l	NOUN
ap-4476	113	57	(	(	PUNCT
ap-4476	113	58	α−1	α−1	NOUN
ap-4476	113	59	)	)	PUNCT
ap-4476	113	60	m	m	PROPN
ap-4476	113	61	(	(	PUNCT
ap-4476	113	62	−g	−g	NOUN
ap-4476	113	63	)	)	PUNCT
ap-4476	113	64	+	+	CCONJ
ap-4476	113	65	c2r2	c2r2	PROPN
ap-4476	113	66	2	2	X
ap-4476	113	67	(	(	PUNCT
ap-4476	113	68	l	l	X
ap-4476	113	69	(	(	PUNCT
ap-4476	113	70	α	α	NOUN
ap-4476	113	71	)	)	PUNCT
ap-4476	113	72	m−1(−g	m−1(−g	PROPN
ap-4476	113	73	)	)	PUNCT
ap-4476	113	74	l	l	NOUN
ap-4476	113	75	(	(	PUNCT
ap-4476	113	76	α−1	α−1	NOUN
ap-4476	113	77	)	)	PUNCT
ap-4476	113	78	m	m	PROPN
ap-4476	113	79	(	(	PUNCT
ap-4476	113	80	−g	−g	NOUN
ap-4476	113	81	)	)	PUNCT
ap-4476	113	82	)	)	PUNCT
ap-4476	113	83	2	2	NUM
ap-4476	113	84	−	−	NOUN
ap-4476	113	85	c	c	NOUN
ap-4476	113	86	2	2	NUM
ap-4476	113	87	(	(	PUNCT
ap-4476	113	88	2m+	2m+	NUM
ap-4476	113	89	α+	α+	PUNCT
ap-4476	113	90	1)−	1)−	NUM
ap-4476	113	91	(	(	PUNCT
ap-4476	113	92	d	d	NOUN
ap-4476	113	93	−	−	PROPN
ap-4476	113	94	1)(d	1)(d	NUM
ap-4476	113	95	−	−	NOUN
ap-4476	113	96	3	3	NUM
ap-4476	113	97	)	)	PUNCT
ap-4476	113	98	4r2	4r2	NUM
ap-4476	113	99	.	.	PUNCT
ap-4476	114	1	(	(	PUNCT
ap-4476	114	2	25	25	NUM
ap-4476	114	3	)	)	PUNCT
ap-4476	114	4	the	the	DET
ap-4476	114	5	wavefunction	wavefunction	NOUN
ap-4476	114	6	can	can	AUX
ap-4476	114	7	be	be	AUX
ap-4476	114	8	obtained	obtain	VERB
ap-4476	114	9	by	by	ADP
ap-4476	114	10	putting	put	VERB
ap-4476	114	11	q(g	q(g	PROPN
ap-4476	114	12	)	)	PUNCT
ap-4476	114	13	and	and	CCONJ
ap-4476	114	14	g(r	g(r	NOUN
ap-4476	114	15	)	)	PUNCT
ap-4476	114	16	in	in	ADP
ap-4476	114	17	(	(	PUNCT
ap-4476	114	18	8)	8)	NUM
ap-4476	114	19	and	and	CCONJ
ap-4476	114	20	is	be	AUX
ap-4476	114	21	given	give	VERB
ap-4476	114	22	by	by	ADP
ap-4476	114	23	χn	χn	NOUN
ap-4476	114	24	,	,	PUNCT
ap-4476	114	25	m(r	m(r	PROPN
ap-4476	114	26	)	)	PUNCT
ap-4476	115	1	=	=	SYM
ap-4476	115	2	nn	nn	PROPN
ap-4476	115	3	,	,	PUNCT
ap-4476	115	4	m	m	PROPN
ap-4476	115	5	r(α+	r(α+	VERB
ap-4476	115	6	1	1	NUM
ap-4476	115	7	2	2	NUM
ap-4476	115	8	)	)	PUNCT
ap-4476	115	9	exp(−c1r	exp(−c1r	NOUN
ap-4476	115	10	2	2	NUM
ap-4476	115	11	8	8	NUM
ap-4476	115	12	)	)	PUNCT
ap-4476	116	1	l	l	NOUN
ap-4476	116	2	(	(	PUNCT
ap-4476	116	3	α−1	α−1	NOUN
ap-4476	116	4	)	)	PUNCT
ap-4476	116	5	m	m	VERB
ap-4476	116	6	(	(	PUNCT
ap-4476	116	7	−	−	PROPN
ap-4476	116	8	1	1	NUM
ap-4476	116	9	4cr	4cr	ADJ
ap-4476	116	10	2	2	NUM
ap-4476	116	11	)	)	PUNCT
ap-4476	116	12	l̂	l̂	X
ap-4476	116	13	(	(	PUNCT
ap-4476	116	14	α	α	NOUN
ap-4476	116	15	)	)	PUNCT
ap-4476	116	16	n+m	n+m	PROPN
ap-4476	116	17	,	,	PUNCT
ap-4476	116	18	m	m	PROPN
ap-4476	116	19	(	(	PUNCT
ap-4476	116	20	c1r	c1r	NOUN
ap-4476	116	21	2	2	NUM
ap-4476	116	22	4	4	NUM
ap-4476	116	23	)	)	PUNCT
ap-4476	116	24	,	,	PUNCT
ap-4476	116	25	(	(	PUNCT
ap-4476	116	26	26	26	NUM
ap-4476	116	27	)	)	PUNCT
ap-4476	116	28	where	where	SCONJ
ap-4476	116	29	nn	nn	X
ap-4476	116	30	,	,	PUNCT
ap-4476	116	31	m	m	VERB
ap-4476	116	32	is	be	AUX
ap-4476	116	33	the	the	DET
ap-4476	116	34	normalization	normalization	NOUN
ap-4476	116	35	constant	constant	ADJ
ap-4476	116	36	given	give	VERB
ap-4476	116	37	by	by	ADP
ap-4476	116	38	nn	nn	PROPN
ap-4476	116	39	,	,	PUNCT
ap-4476	116	40	m	m	NOUN
ap-4476	116	41	=	=	PUNCT
ap-4476	116	42	(	(	PUNCT
ap-4476	116	43	n	n	X
ap-4476	116	44	!	!	PUNCT
ap-4476	117	1	(	(	PUNCT
ap-4476	117	2	α+	α+	X
ap-4476	117	3	n+m)γ(α+	n+m)γ(α+	NOUN
ap-4476	117	4	n	n	CCONJ
ap-4476	117	5	)	)	PUNCT
ap-4476	117	6	)	)	PUNCT
ap-4476	117	7	1	1	NUM
ap-4476	117	8	2	2	NUM
ap-4476	117	9	.	.	PUNCT
ap-4476	118	1	(	(	PUNCT
ap-4476	118	2	27	27	NUM
ap-4476	118	3	)	)	PUNCT
ap-4476	118	4	to	to	PART
ap-4476	118	5	get	get	VERB
ap-4476	118	6	the	the	DET
ap-4476	118	7	correct	correct	ADJ
ap-4476	118	8	centrifugal	centrifugal	ADJ
ap-4476	118	9	barrier	barrier	NOUN
ap-4476	118	10	term	term	NOUN
ap-4476	118	11	in	in	ADP
ap-4476	118	12	d	d	ADJ
ap-4476	118	13	-	-	ADJ
ap-4476	118	14	dimensional	dimensional	ADJ
ap-4476	118	15	euclidean	euclidean	ADJ
ap-4476	118	16	space	space	NOUN
ap-4476	118	17	,	,	PUNCT
ap-4476	118	18	we	we	PRON
ap-4476	118	19	have	have	VERB
ap-4476	118	20	to	to	PART
ap-4476	118	21	identify	identify	VERB
ap-4476	118	22	the	the	DET
ap-4476	118	23	coefficient	coefficient	NOUN
ap-4476	118	24	of	of	ADP
ap-4476	118	25	1	1	NUM
ap-4476	118	26	r2	r2	NOUN
ap-4476	118	27	in	in	ADP
ap-4476	118	28	(	(	PUNCT
ap-4476	118	29	25	25	NUM
ap-4476	118	30	)	)	PUNCT
ap-4476	118	31	to	to	PART
ap-4476	118	32	be	be	AUX
ap-4476	118	33	equal	equal	ADJ
ap-4476	118	34	to	to	ADP
ap-4476	118	35	`	`	PUNCT
ap-4476	118	36	(	(	PUNCT
ap-4476	118	37	`	`	PUNCT
ap-4476	118	38	+	+	NOUN
ap-4476	118	39	d	d	NOUN
ap-4476	118	40	−	−	NOUN
ap-4476	118	41	2	2	NUM
ap-4476	118	42	)	)	PUNCT
ap-4476	118	43	,	,	PUNCT
ap-4476	118	44	which	which	PRON
ap-4476	118	45	fixes	fix	VERB
ap-4476	118	46	the	the	DET
ap-4476	118	47	value	value	NOUN
ap-4476	118	48	of	of	ADP
ap-4476	118	49	α	α	NOUN
ap-4476	118	50	as	as	ADP
ap-4476	118	51	α	α	NOUN
ap-4476	118	52	=	=	PUNCT
ap-4476	119	1	`	`	PUNCT
ap-4476	119	2	+	+	NUM
ap-4476	120	1	d	d	NOUN
ap-4476	120	2	−	−	NOUN
ap-4476	120	3	2	2	NUM
ap-4476	120	4	2	2	NUM
ap-4476	120	5	(	(	PUNCT
ap-4476	120	6	28	28	NUM
ap-4476	120	7	)	)	PUNCT
ap-4476	120	8	and	and	CCONJ
ap-4476	120	9	identifying	identify	VERB
ap-4476	120	10	the	the	DET
ap-4476	120	11	constant	constant	ADJ
ap-4476	120	12	c1	c1	NOUN
ap-4476	120	13	=	=	PUNCT
ap-4476	120	14	2ω	2ω	PROPN
ap-4476	120	15	,	,	PUNCT
ap-4476	120	16	the	the	DET
ap-4476	120	17	energy	energy	NOUN
ap-4476	120	18	eigenvalues	eigenvalue	VERB
ap-4476	120	19	(	(	PUNCT
ap-4476	120	20	24	24	NUM
ap-4476	120	21	)	)	PUNCT
ap-4476	120	22	,	,	PUNCT
ap-4476	120	23	extended	extend	VERB
ap-4476	120	24	potential	potential	NOUN
ap-4476	120	25	(	(	PUNCT
ap-4476	120	26	25	25	NUM
ap-4476	120	27	)	)	PUNCT
ap-4476	120	28	and	and	CCONJ
ap-4476	120	29	the	the	DET
ap-4476	120	30	corresponding	corresponding	ADJ
ap-4476	120	31	wavefunction	wavefunction	NOUN
ap-4476	120	32	(	(	PUNCT
ap-4476	120	33	26	26	NUM
ap-4476	120	34	)	)	PUNCT
ap-4476	120	35	in	in	ADP
ap-4476	120	36	any	any	DET
ap-4476	120	37	arbitrary	arbitrary	ADJ
ap-4476	120	38	d	d	NOUN
ap-4476	120	39	-	-	PUNCT
ap-4476	120	40	dimensions	dimension	NOUN
ap-4476	120	41	are	be	AUX
ap-4476	120	42	en	en	ADV
ap-4476	120	43	=	=	NOUN
ap-4476	120	44	2nω	2nω	NOUN
ap-4476	120	45	,	,	PUNCT
ap-4476	120	46	(	(	PUNCT
ap-4476	120	47	29	29	NUM
ap-4476	120	48	)	)	PUNCT
ap-4476	120	49	vm(r	vm(r	NOUN
ap-4476	120	50	)	)	PUNCT
ap-4476	121	1	=	=	SYM
ap-4476	121	2	v	v	ADP
ap-4476	121	3	drad(r)−	drad(r)−	NOUN
ap-4476	121	4	ω2r2	ω2r2	X
ap-4476	121	5	l	l	NOUN
ap-4476	121	6	(	(	PUNCT
ap-4476	121	7	l+	l+	NOUN
ap-4476	121	8	d	d	NOUN
ap-4476	121	9	2	2	X
ap-4476	121	10	)	)	PUNCT
ap-4476	121	11	m−2	m−2	PROPN
ap-4476	121	12	(	(	PUNCT
ap-4476	121	13	−ωr	−ωr	NOUN
ap-4476	121	14	2	2	NUM
ap-4476	121	15	2	2	NUM
ap-4476	121	16	)	)	PUNCT
ap-4476	121	17	l	l	NOUN
ap-4476	121	18	(	(	PUNCT
ap-4476	121	19	l+	l+	NOUN
ap-4476	121	20	d−4	d−4	PROPN
ap-4476	121	21	2	2	NUM
ap-4476	121	22	)	)	PUNCT
ap-4476	121	23	m	m	VERB
ap-4476	121	24	(	(	PUNCT
ap-4476	121	25	−ωr2	−ωr2	X
ap-4476	121	26	2	2	NUM
ap-4476	121	27	)	)	PUNCT
ap-4476	121	28	+	+	CCONJ
ap-4476	122	1	ω(ωr2	ω(ωr2	ADJ
ap-4476	122	2	+	+	CCONJ
ap-4476	122	3	2l	2l	NUM
ap-4476	123	1	+	+	ADJ
ap-4476	123	2	d	d	NOUN
ap-4476	123	3	−	−	NOUN
ap-4476	123	4	4	4	NUM
ap-4476	123	5	)	)	PUNCT
ap-4476	123	6	l	l	NOUN
ap-4476	123	7	(	(	PUNCT
ap-4476	123	8	l+	l+	NOUN
ap-4476	123	9	d−2	d−2	PROPN
ap-4476	123	10	2	2	NUM
ap-4476	123	11	)	)	PUNCT
ap-4476	123	12	m−1	m−1	PROPN
ap-4476	123	13	(	(	PUNCT
ap-4476	123	14	−ωr	−ωr	NOUN
ap-4476	123	15	2	2	NUM
ap-4476	123	16	2	2	NUM
ap-4476	123	17	)	)	PUNCT
ap-4476	123	18	l	l	NOUN
ap-4476	123	19	(	(	PUNCT
ap-4476	123	20	l+	l+	NOUN
ap-4476	123	21	d−4	d−4	PROPN
ap-4476	123	22	2	2	NUM
ap-4476	123	23	)	)	PUNCT
ap-4476	123	24	m	m	VERB
ap-4476	123	25	(	(	PUNCT
ap-4476	123	26	−ωr2	−ωr2	X
ap-4476	123	27	2	2	NUM
ap-4476	123	28	)	)	PUNCT
ap-4476	123	29	+	+	NUM
ap-4476	123	30	2ω2r2	2ω2r2	NUM
ap-4476	123	31	(	(	PUNCT
ap-4476	123	32	l	l	NOUN
ap-4476	123	33	(	(	PUNCT
ap-4476	123	34	l+	l+	NOUN
ap-4476	123	35	d−2	d−2	PROPN
ap-4476	123	36	2	2	NUM
ap-4476	123	37	)	)	PUNCT
ap-4476	123	38	m−1	m−1	PROPN
ap-4476	123	39	(	(	PUNCT
ap-4476	123	40	−ωr	−ωr	NOUN
ap-4476	123	41	2	2	NUM
ap-4476	123	42	2	2	NUM
ap-4476	123	43	)	)	PUNCT
ap-4476	123	44	l	l	NOUN
ap-4476	123	45	(	(	PUNCT
ap-4476	123	46	l+	l+	NOUN
ap-4476	123	47	d−4	d−4	PROPN
ap-4476	123	48	2	2	NUM
ap-4476	123	49	)	)	PUNCT
ap-4476	123	50	m	m	VERB
ap-4476	123	51	(	(	PUNCT
ap-4476	123	52	−ωr2	−ωr2	X
ap-4476	123	53	2	2	NUM
ap-4476	123	54	)	)	PUNCT
ap-4476	123	55	)	)	PUNCT
ap-4476	124	1	2	2	NUM
ap-4476	124	2	−	−	NOUN
ap-4476	124	3	2mω	2mω	ADJ
ap-4476	124	4	(	(	PUNCT
ap-4476	124	5	30	30	NUM
ap-4476	124	6	)	)	PUNCT
ap-4476	124	7	480	480	NUM
ap-4476	124	8	vol	vol	NOUN
ap-4476	124	9	.	.	PUNCT
ap-4476	124	10	57	57	NUM
ap-4476	125	1	no	no	NOUN
ap-4476	125	2	.	.	PUNCT
ap-4476	126	1	6/2017	6/2017	NUM
ap-4476	126	2	rationally	rationally	ADV
ap-4476	126	3	extended	extend	VERB
ap-4476	126	4	shape	shape	NOUN
ap-4476	126	5	invariant	invariant	ADJ
ap-4476	126	6	potentials	potential	NOUN
ap-4476	126	7	and	and	CCONJ
ap-4476	126	8	χn	χn	NOUN
ap-4476	126	9	,	,	PUNCT
ap-4476	126	10	m(r	m(r	PROPN
ap-4476	126	11	)	)	PUNCT
ap-4476	126	12	=	=	SYM
ap-4476	126	13	nn	nn	PROPN
ap-4476	126	14	,	,	PUNCT
ap-4476	126	15	m	m	VERB
ap-4476	126	16	×	×	NOUN
ap-4476	126	17	r`+	r`+	NOUN
ap-4476	126	18	d−1	d−1	PROPN
ap-4476	126	19	2	2	NUM
ap-4476	126	20	exp(−ωr	exp(−ωr	ADJ
ap-4476	126	21	2	2	NUM
ap-4476	126	22	4	4	NUM
ap-4476	126	23	)	)	PUNCT
ap-4476	126	24	l	l	NOUN
ap-4476	126	25	(	(	PUNCT
ap-4476	126	26	l+	l+	NOUN
ap-4476	126	27	d−4	d−4	PROPN
ap-4476	126	28	2	2	NUM
ap-4476	126	29	)	)	PUNCT
ap-4476	126	30	m	m	VERB
ap-4476	126	31	(	(	PUNCT
ap-4476	126	32	−ωr2	−ωr2	X
ap-4476	126	33	2	2	NUM
ap-4476	126	34	)	)	PUNCT
ap-4476	126	35	l̂	l̂	VERB
ap-4476	126	36	(	(	PUNCT
ap-4476	126	37	`	`	PUNCT
ap-4476	126	38	+	+	CCONJ
ap-4476	126	39	d−2	d−2	PROPN
ap-4476	126	40	2	2	NUM
ap-4476	126	41	)	)	PUNCT
ap-4476	126	42	n+m	n+m	PROPN
ap-4476	126	43	,	,	PUNCT
ap-4476	126	44	m	m	PROPN
ap-4476	126	45	(	(	PUNCT
ap-4476	126	46	ωr2	ωr2	NOUN
ap-4476	126	47	2	2	NUM
ap-4476	126	48	)	)	PUNCT
ap-4476	126	49	(	(	PUNCT
ap-4476	126	50	31	31	NUM
ap-4476	126	51	)	)	PUNCT
ap-4476	126	52	respectively	respectively	ADV
ap-4476	126	53	,	,	PUNCT
ap-4476	126	54	where	where	SCONJ
ap-4476	126	55	v	v	ADP
ap-4476	126	56	drad(r	drad(r	PROPN
ap-4476	126	57	)	)	PUNCT
ap-4476	126	58	=	=	SYM
ap-4476	126	59	1	1	NUM
ap-4476	126	60	4ω	4ω	NOUN
ap-4476	126	61	2r2	2r2	NUM
ap-4476	127	1	+	+	CCONJ
ap-4476	127	2	`	`	PUNCT
ap-4476	127	3	(	(	PUNCT
ap-4476	127	4	`	`	PUNCT
ap-4476	127	5	+	+	ADJ
ap-4476	127	6	d−2	d−2	PROPN
ap-4476	127	7	)	)	PUNCT
ap-4476	127	8	r2	r2	PROPN
ap-4476	127	9	−ω(`+	−ω(`+	PROPN
ap-4476	127	10	d	d	PROPN
ap-4476	127	11	2	2	NUM
ap-4476	127	12	)	)	PUNCT
ap-4476	127	13	is	be	AUX
ap-4476	127	14	conventional	conventional	ADJ
ap-4476	127	15	radial	radial	ADJ
ap-4476	127	16	oscillator	oscillator	NOUN
ap-4476	127	17	potential	potential	NOUN
ap-4476	127	18	in	in	ADP
ap-4476	127	19	arbitrary	arbitrary	ADJ
ap-4476	127	20	d	d	ADJ
ap-4476	127	21	-	-	ADJ
ap-4476	127	22	dimensional	dimensional	ADJ
ap-4476	127	23	space	space	NOUN
ap-4476	127	24	[	[	X
ap-4476	127	25	31	31	NUM
ap-4476	127	26	]	]	PUNCT
ap-4476	127	27	.	.	PUNCT
ap-4476	128	1	note	note	VERB
ap-4476	128	2	that	that	SCONJ
ap-4476	128	3	the	the	DET
ap-4476	128	4	full	full	ADJ
ap-4476	128	5	eigenfunction	eigenfunction	NOUN
ap-4476	128	6	ψ	ψ	ADP
ap-4476	128	7	as	as	SCONJ
ap-4476	128	8	given	give	VERB
ap-4476	128	9	by	by	ADP
ap-4476	128	10	(	(	PUNCT
ap-4476	128	11	7	7	NUM
ap-4476	128	12	)	)	PUNCT
ap-4476	128	13	with	with	ADP
ap-4476	128	14	χ	χ	PRON
ap-4476	128	15	as	as	SCONJ
ap-4476	128	16	given	give	VERB
ap-4476	128	17	by	by	ADP
ap-4476	128	18	(	(	PUNCT
ap-4476	128	19	31	31	NUM
ap-4476	128	20	)	)	PUNCT
ap-4476	128	21	.	.	PUNCT
ap-4476	129	1	for	for	ADP
ap-4476	129	2	a	a	DET
ap-4476	129	3	check	check	NOUN
ap-4476	129	4	on	on	ADP
ap-4476	129	5	our	our	PRON
ap-4476	129	6	calculations	calculation	NOUN
ap-4476	129	7	,	,	PUNCT
ap-4476	129	8	we	we	PRON
ap-4476	129	9	now	now	ADV
ap-4476	129	10	discuss	discuss	VERB
ap-4476	129	11	few	few	ADJ
ap-4476	129	12	special	special	ADJ
ap-4476	129	13	cases	case	NOUN
ap-4476	129	14	of	of	ADP
ap-4476	129	15	the	the	DET
ap-4476	129	16	results	result	NOUN
ap-4476	129	17	obtained	obtain	VERB
ap-4476	129	18	in	in	ADP
ap-4476	129	19	(	(	PUNCT
ap-4476	129	20	30	30	NUM
ap-4476	129	21	)	)	PUNCT
ap-4476	129	22	and	and	CCONJ
ap-4476	129	23	(	(	PUNCT
ap-4476	129	24	31	31	NUM
ap-4476	129	25	)	)	PUNCT
ap-4476	129	26	.	.	PUNCT
ap-4476	130	1	case	case	NOUN
ap-4476	130	2	(	(	PUNCT
ap-4476	130	3	a	a	NOUN
ap-4476	130	4	)	)	PUNCT
ap-4476	130	5	.	.	PUNCT
ap-4476	131	1	form	form	NOUN
ap-4476	131	2	=	=	SYM
ap-4476	131	3	0	0	NUM
ap-4476	131	4	,	,	PUNCT
ap-4476	131	5	from	from	ADP
ap-4476	131	6	(	(	PUNCT
ap-4476	131	7	30	30	NUM
ap-4476	131	8	)	)	PUNCT
ap-4476	131	9	and	and	CCONJ
ap-4476	131	10	(	(	PUNCT
ap-4476	131	11	31	31	NUM
ap-4476	131	12	)	)	PUNCT
ap-4476	131	13	we	we	PRON
ap-4476	131	14	get	get	VERB
ap-4476	131	15	the	the	DET
ap-4476	131	16	well	well	ADV
ap-4476	131	17	known	know	VERB
ap-4476	131	18	usual	usual	ADJ
ap-4476	131	19	radial	radial	ADJ
ap-4476	131	20	oscillator	oscillator	NOUN
ap-4476	131	21	potential	potential	NOUN
ap-4476	131	22	in	in	ADP
ap-4476	131	23	d	d	NOUN
ap-4476	131	24	-	-	PUNCT
ap-4476	131	25	dimensions	dimension	NOUN
ap-4476	131	26	[	[	X
ap-4476	131	27	31	31	NUM
ap-4476	131	28	]	]	PUNCT
ap-4476	131	29	,	,	PUNCT
ap-4476	131	30	v0(r	v0(r	PROPN
ap-4476	131	31	)	)	PUNCT
ap-4476	131	32	=	=	NOUN
ap-4476	131	33	v	v	NUM
ap-4476	131	34	drad(r	drad(r	PROPN
ap-4476	131	35	)	)	PUNCT
ap-4476	131	36	=	=	SYM
ap-4476	131	37	1	1	NUM
ap-4476	131	38	4ω	4ω	NOUN
ap-4476	131	39	2r2	2r2	NUM
ap-4476	132	1	+	+	CCONJ
ap-4476	132	2	`	`	PUNCT
ap-4476	132	3	(	(	PUNCT
ap-4476	132	4	`	`	PUNCT
ap-4476	132	5	+	+	NOUN
ap-4476	132	6	d	d	NOUN
ap-4476	132	7	−	−	ADJ
ap-4476	132	8	2	2	NUM
ap-4476	132	9	)	)	PUNCT
ap-4476	132	10	r2	r2	NOUN
ap-4476	132	11	−	−	PROPN
ap-4476	132	12	ω	ω	PROPN
ap-4476	132	13	(	(	PUNCT
ap-4476	132	14	`	`	PUNCT
ap-4476	132	15	+	+	CCONJ
ap-4476	132	16	d	d	NOUN
ap-4476	132	17	2	2	NUM
ap-4476	132	18	)	)	PUNCT
ap-4476	132	19	(	(	PUNCT
ap-4476	132	20	32	32	NUM
ap-4476	132	21	)	)	PUNCT
ap-4476	132	22	and	and	CCONJ
ap-4476	132	23	the	the	DET
ap-4476	132	24	corresponding	correspond	VERB
ap-4476	132	25	wavefunctions	wavefunction	NOUN
ap-4476	132	26	which	which	PRON
ap-4476	132	27	can	can	AUX
ap-4476	132	28	be	be	AUX
ap-4476	132	29	written	write	VERB
ap-4476	132	30	in	in	ADP
ap-4476	132	31	terms	term	NOUN
ap-4476	132	32	of	of	ADP
ap-4476	132	33	usual	usual	ADJ
ap-4476	132	34	laguerre	laguerre	NOUN
ap-4476	132	35	polynomials	polynomials	PROPN
ap-4476	132	36	χn,0(r	χn,0(r	NOUN
ap-4476	132	37	)	)	PUNCT
ap-4476	132	38	=	=	PUNCT
ap-4476	133	1	nn,0	nn,0	NOUN
ap-4476	133	2	×	×	PROPN
ap-4476	133	3	r`+	r`+	NOUN
ap-4476	133	4	d−1	d−1	PROPN
ap-4476	133	5	2	2	NUM
ap-4476	133	6	exp	exp	NOUN
ap-4476	133	7	(	(	PUNCT
ap-4476	133	8	−ωr	−ωr	PROPN
ap-4476	133	9	2	2	NUM
ap-4476	133	10	4	4	NUM
ap-4476	133	11	)	)	PUNCT
ap-4476	133	12	l	l	NOUN
ap-4476	133	13	(	(	PUNCT
ap-4476	133	14	`	`	PUNCT
ap-4476	133	15	+	+	CCONJ
ap-4476	133	16	d−2	d−2	PROPN
ap-4476	133	17	2	2	NUM
ap-4476	133	18	)	)	PUNCT
ap-4476	133	19	n	n	CCONJ
ap-4476	133	20	(	(	PUNCT
ap-4476	133	21	ωr2	ωr2	NOUN
ap-4476	133	22	2	2	NUM
ap-4476	133	23	)	)	PUNCT
ap-4476	133	24	.	.	PUNCT
ap-4476	134	1	(	(	PUNCT
ap-4476	134	2	33	33	NUM
ap-4476	134	3	)	)	PUNCT
ap-4476	134	4	for	for	ADP
ap-4476	134	5	d	d	NOUN
ap-4476	134	6	=	=	SYM
ap-4476	134	7	3	3	NUM
ap-4476	134	8	above	above	ADP
ap-4476	134	9	expressions	expression	NOUN
ap-4476	134	10	reduces	reduce	VERB
ap-4476	134	11	to	to	ADP
ap-4476	134	12	the	the	DET
ap-4476	134	13	well	well	ADV
ap-4476	134	14	known	know	VERB
ap-4476	134	15	3	3	NUM
ap-4476	134	16	-	-	SYM
ap-4476	134	17	d	d	ADJ
ap-4476	134	18	harmonic	harmonic	ADJ
ap-4476	134	19	oscillator	oscillator	NOUN
ap-4476	134	20	potential	potential	NOUN
ap-4476	134	21	.	.	PUNCT
ap-4476	135	1	case	case	NOUN
ap-4476	135	2	(	(	PUNCT
ap-4476	135	3	b	b	NOUN
ap-4476	135	4	)	)	PUNCT
ap-4476	135	5	.	.	PUNCT
ap-4476	136	1	for	for	ADP
ap-4476	136	2	m	m	PROPN
ap-4476	136	3	=	=	SYM
ap-4476	136	4	1	1	NUM
ap-4476	136	5	,	,	PUNCT
ap-4476	136	6	the	the	DET
ap-4476	136	7	obtained	obtain	VERB
ap-4476	136	8	potential	potential	ADJ
ap-4476	136	9	v1(r	v1(r	NOUN
ap-4476	136	10	)	)	PUNCT
ap-4476	136	11	=	=	SYM
ap-4476	136	12	1	1	NUM
ap-4476	136	13	4ω	4ω	NOUN
ap-4476	136	14	2r2	2r2	NUM
ap-4476	137	1	+	+	CCONJ
ap-4476	137	2	`	`	PUNCT
ap-4476	137	3	(	(	PUNCT
ap-4476	137	4	`	`	PUNCT
ap-4476	137	5	+	+	NOUN
ap-4476	137	6	d	d	NOUN
ap-4476	137	7	−	−	ADJ
ap-4476	137	8	2	2	NUM
ap-4476	137	9	)	)	PUNCT
ap-4476	137	10	r2	r2	NOUN
ap-4476	137	11	−	−	PROPN
ap-4476	137	12	ω	ω	PROPN
ap-4476	137	13	(	(	PUNCT
ap-4476	137	14	`	`	PUNCT
ap-4476	137	15	+	+	CCONJ
ap-4476	137	16	d	d	NOUN
ap-4476	137	17	2	2	NUM
ap-4476	137	18	)	)	PUNCT
ap-4476	137	19	+	+	NUM
ap-4476	137	20	4ω	4ω	NOUN
ap-4476	137	21	(	(	PUNCT
ap-4476	137	22	ωr2	ωr2	NOUN
ap-4476	138	1	+	+	CCONJ
ap-4476	138	2	2`+d	2`+d	NUM
ap-4476	138	3	−	−	NOUN
ap-4476	138	4	2	2	NUM
ap-4476	138	5	)	)	PUNCT
ap-4476	138	6	−	−	NOUN
ap-4476	138	7	8ω(2`+d	8ω(2`+d	NUM
ap-4476	138	8	−	−	PROPN
ap-4476	138	9	2	2	NUM
ap-4476	138	10	)	)	PUNCT
ap-4476	138	11	(	(	PUNCT
ap-4476	138	12	ωr2	ωr2	NOUN
ap-4476	139	1	+	+	CCONJ
ap-4476	139	2	2`+d	2`+d	NUM
ap-4476	139	3	−	−	PROPN
ap-4476	139	4	2)2	2)2	NUM
ap-4476	139	5	(	(	PUNCT
ap-4476	139	6	34	34	NUM
ap-4476	139	7	)	)	PUNCT
ap-4476	139	8	is	be	AUX
ap-4476	139	9	the	the	DET
ap-4476	139	10	rationally	rationally	ADV
ap-4476	139	11	extended	extended	ADJ
ap-4476	139	12	d	d	ADJ
ap-4476	139	13	dimensional	dimensional	ADJ
ap-4476	139	14	oscillator	oscillator	NOUN
ap-4476	139	15	potential	potential	NOUN
ap-4476	139	16	studied	study	VERB
ap-4476	139	17	earlier	early	ADV
ap-4476	139	18	in	in	ADP
ap-4476	139	19	ref	ref	NOUN
ap-4476	139	20	.	.	PUNCT
ap-4476	140	1	[	[	X
ap-4476	140	2	26	26	NUM
ap-4476	140	3	]	]	PUNCT
ap-4476	140	4	the	the	DET
ap-4476	140	5	corresponding	correspond	VERB
ap-4476	140	6	wavefunctions	wavefunction	NOUN
ap-4476	140	7	in	in	ADP
ap-4476	140	8	terms	term	NOUN
ap-4476	140	9	of	of	ADP
ap-4476	140	10	exceptional	exceptional	ADJ
ap-4476	140	11	x1	x1	PROPN
ap-4476	140	12	laguerre	laguerre	NOUN
ap-4476	140	13	orthogonal	orthogonal	ADJ
ap-4476	140	14	polynomial	polynomial	NOUN
ap-4476	140	15	can	can	AUX
ap-4476	140	16	be	be	AUX
ap-4476	140	17	written	write	VERB
ap-4476	140	18	as	as	ADP
ap-4476	140	19	χn,1(r	χn,1(r	ADJ
ap-4476	140	20	)	)	PUNCT
ap-4476	141	1	=	=	SYM
ap-4476	142	1	nn,1	nn,1	PROPN
ap-4476	142	2	×	×	PROPN
ap-4476	142	3	r`+	r`+	NOUN
ap-4476	142	4	d−1	d−1	PROPN
ap-4476	142	5	2	2	NUM
ap-4476	142	6	exp(−ωr	exp(−ωr	ADJ
ap-4476	142	7	2	2	NUM
ap-4476	142	8	4	4	NUM
ap-4476	142	9	)	)	PUNCT
ap-4476	142	10	(	(	PUNCT
ap-4476	142	11	ωr2	ωr2	NOUN
ap-4476	143	1	+	+	CCONJ
ap-4476	143	2	2`+d	2`+d	NUM
ap-4476	143	3	−	−	NOUN
ap-4476	143	4	2	2	NUM
ap-4476	143	5	)	)	PUNCT
ap-4476	143	6	l̂	l̂	VERB
ap-4476	143	7	(	(	PUNCT
ap-4476	143	8	`	`	PUNCT
ap-4476	143	9	+	+	CCONJ
ap-4476	143	10	d−2	d−2	PROPN
ap-4476	143	11	2	2	NUM
ap-4476	143	12	)	)	PUNCT
ap-4476	143	13	n+1,1	n+1,1	NOUN
ap-4476	143	14	(	(	PUNCT
ap-4476	143	15	ωr2	ωr2	NOUN
ap-4476	143	16	2	2	NUM
ap-4476	143	17	)	)	PUNCT
ap-4476	143	18	.	.	PUNCT
ap-4476	144	1	(	(	PUNCT
ap-4476	144	2	35	35	NUM
ap-4476	144	3	)	)	PUNCT
ap-4476	144	4	for	for	ADP
ap-4476	144	5	d	d	PROPN
ap-4476	144	6	=	=	SYM
ap-4476	144	7	3	3	NUM
ap-4476	144	8	,	,	PUNCT
ap-4476	144	9	the	the	DET
ap-4476	144	10	above	above	ADJ
ap-4476	144	11	expressions	expression	NOUN
ap-4476	144	12	match	match	VERB
ap-4476	144	13	exactly	exactly	ADV
ap-4476	144	14	with	with	ADP
ap-4476	144	15	the	the	DET
ap-4476	144	16	expressions	expression	NOUN
ap-4476	144	17	given	give	VERB
ap-4476	144	18	in	in	ADP
ap-4476	144	19	ref	ref	NOUN
ap-4476	144	20	.	.	PUNCT
ap-4476	145	1	[	[	X
ap-4476	145	2	3	3	NUM
ap-4476	145	3	]	]	PUNCT
ap-4476	145	4	.	.	PUNCT
ap-4476	146	1	case	case	NOUN
ap-4476	146	2	(	(	PUNCT
ap-4476	146	3	c	c	NOUN
ap-4476	146	4	)	)	PUNCT
ap-4476	146	5	.	.	PUNCT
ap-4476	147	1	for	for	ADP
ap-4476	147	2	m	m	PROPN
ap-4476	147	3	=	=	SYM
ap-4476	147	4	2	2	NUM
ap-4476	147	5	,	,	PUNCT
ap-4476	147	6	in	in	ADP
ap-4476	147	7	this	this	DET
ap-4476	147	8	case	case	NOUN
ap-4476	147	9	the	the	DET
ap-4476	147	10	extended	extended	ADJ
ap-4476	147	11	potential	potential	NOUN
ap-4476	147	12	and	and	CCONJ
ap-4476	147	13	the	the	DET
ap-4476	147	14	corresponding	correspond	VERB
ap-4476	147	15	wavefunctions	wavefunction	NOUN
ap-4476	147	16	in	in	ADP
ap-4476	147	17	terms	term	NOUN
ap-4476	147	18	of	of	ADP
ap-4476	147	19	x2	x2	PROPN
ap-4476	147	20	laguerre	laguerre	PROPN
ap-4476	147	21	orthogonal	orthogonal	ADJ
ap-4476	147	22	polynomials	polynomial	NOUN
ap-4476	147	23	are	be	AUX
ap-4476	147	24	given	give	VERB
ap-4476	147	25	by	by	ADP
ap-4476	147	26	v2(r	v2(r	PRON
ap-4476	147	27	)	)	PUNCT
ap-4476	147	28	=	=	SYM
ap-4476	147	29	1	1	NUM
ap-4476	147	30	4ω	4ω	NOUN
ap-4476	147	31	2r2	2r2	NUM
ap-4476	148	1	+	+	CCONJ
ap-4476	148	2	`	`	PUNCT
ap-4476	148	3	(	(	PUNCT
ap-4476	148	4	`	`	PUNCT
ap-4476	148	5	+	+	NOUN
ap-4476	148	6	d	d	NOUN
ap-4476	148	7	−	−	ADJ
ap-4476	148	8	2	2	NUM
ap-4476	148	9	)	)	PUNCT
ap-4476	148	10	r2	r2	NOUN
ap-4476	148	11	−	−	PROPN
ap-4476	148	12	ω	ω	PROPN
ap-4476	148	13	(	(	PUNCT
ap-4476	148	14	`	`	PUNCT
ap-4476	148	15	+	+	CCONJ
ap-4476	148	16	d	d	NOUN
ap-4476	148	17	2	2	NUM
ap-4476	148	18	)	)	PUNCT
ap-4476	148	19	+	+	NUM
ap-4476	148	20	8ω	8ω	NOUN
ap-4476	148	21	(	(	PUNCT
ap-4476	148	22	ωr2	ωr2	NOUN
ap-4476	148	23	−	−	PROPN
ap-4476	148	24	(	(	PUNCT
ap-4476	148	25	2`+d	2`+d	NUM
ap-4476	148	26	)	)	PUNCT
ap-4476	148	27	)	)	PUNCT
ap-4476	149	1	ω2r4	ω2r4	PUNCT
ap-4476	149	2	+	+	NUM
ap-4476	149	3	2ωr2(2`+d	2ωr2(2`+d	NUM
ap-4476	149	4	)	)	PUNCT
ap-4476	150	1	+	+	CCONJ
ap-4476	150	2	(	(	PUNCT
ap-4476	150	3	2`+d	2`+d	NUM
ap-4476	150	4	−	−	NOUN
ap-4476	150	5	2)(2`+d	2)(2`+d	NUM
ap-4476	150	6	)	)	PUNCT
ap-4476	151	1	+	+	CCONJ
ap-4476	151	2	64ω2r2(2`+d	64ω2r2(2`+d	NUM
ap-4476	151	3	)	)	PUNCT
ap-4476	151	4	(	(	PUNCT
ap-4476	151	5	ω2r4	ω2r4	X
ap-4476	151	6	+	+	X
ap-4476	151	7	2ωr2(2`+d	2ωr2(2`+d	NUM
ap-4476	151	8	)	)	PUNCT
ap-4476	151	9	+	+	CCONJ
ap-4476	151	10	(	(	PUNCT
ap-4476	151	11	2`+d	2`+d	NUM
ap-4476	151	12	−	−	NOUN
ap-4476	151	13	2)(2`+d	2)(2`+d	NUM
ap-4476	151	14	)	)	PUNCT
ap-4476	151	15	)	)	PUNCT
ap-4476	151	16	2	2	NUM
ap-4476	151	17	,	,	PUNCT
ap-4476	151	18	(	(	PUNCT
ap-4476	151	19	36	36	NUM
ap-4476	151	20	)	)	PUNCT
ap-4476	151	21	and	and	CCONJ
ap-4476	151	22	χn,2(r	χn,2(r	NOUN
ap-4476	151	23	)	)	PUNCT
ap-4476	152	1	=	=	PUNCT
ap-4476	152	2	nn,2	nn,2	ADJ
ap-4476	152	3	×	×	NOUN
ap-4476	152	4	r`+	r`+	NOUN
ap-4476	152	5	d−1	d−1	PROPN
ap-4476	152	6	2	2	NUM
ap-4476	152	7	exp(−ωr	exp(−ωr	ADJ
ap-4476	152	8	2	2	NUM
ap-4476	152	9	4	4	NUM
ap-4476	152	10	)	)	PUNCT
ap-4476	152	11	ω2r4	ω2r4	PROPN
ap-4476	153	1	+	+	NUM
ap-4476	153	2	2ωr2(2`+d	2ωr2(2`+d	NUM
ap-4476	153	3	)	)	PUNCT
ap-4476	153	4	+	+	CCONJ
ap-4476	153	5	(	(	PUNCT
ap-4476	153	6	2`+d	2`+d	NUM
ap-4476	153	7	−	−	NOUN
ap-4476	153	8	2)(2`+d	2)(2`+d	NUM
ap-4476	153	9	)	)	PUNCT
ap-4476	153	10	l̂	l̂	VERB
ap-4476	153	11	(	(	PUNCT
ap-4476	153	12	`	`	PUNCT
ap-4476	153	13	+	+	CCONJ
ap-4476	153	14	d−2	d−2	PROPN
ap-4476	153	15	2	2	NUM
ap-4476	153	16	)	)	PUNCT
ap-4476	153	17	n+2,2	n+2,2	PROPN
ap-4476	153	18	(	(	PUNCT
ap-4476	153	19	ωr2	ωr2	NOUN
ap-4476	153	20	2	2	NUM
ap-4476	153	21	)	)	PUNCT
ap-4476	153	22	.	.	PUNCT
ap-4476	154	1	(	(	PUNCT
ap-4476	154	2	37	37	NUM
ap-4476	154	3	)	)	PUNCT
ap-4476	154	4	4.2	4.2	NUM
ap-4476	154	5	.	.	PUNCT
ap-4476	155	1	potentials	potential	NOUN
ap-4476	155	2	associated	associate	VERB
ap-4476	155	3	with	with	ADP
ap-4476	155	4	xm	xm	PROPN
ap-4476	155	5	exceptional	exceptional	ADJ
ap-4476	155	6	jacobi	jacobi	PROPN
ap-4476	155	7	polynomials	polynomial	NOUN
ap-4476	155	8	let	let	VERB
ap-4476	155	9	us	we	PRON
ap-4476	155	10	consider	consider	VERB
ap-4476	155	11	the	the	DET
ap-4476	155	12	case	case	NOUN
ap-4476	155	13	where	where	SCONJ
ap-4476	155	14	the	the	DET
ap-4476	155	15	second	second	ADJ
ap-4476	155	16	order	order	NOUN
ap-4476	155	17	differential	differential	NOUN
ap-4476	155	18	equation	equation	NOUN
ap-4476	155	19	(	(	PUNCT
ap-4476	155	20	3	3	X
ap-4476	155	21	)	)	PUNCT
ap-4476	155	22	coincides	coincide	VERB
ap-4476	155	23	with	with	ADP
ap-4476	155	24	that	that	PRON
ap-4476	155	25	satisfied	satisfy	VERB
ap-4476	155	26	by	by	ADP
ap-4476	155	27	xm	xm	PROPN
ap-4476	155	28	jacobi	jacobi	PROPN
ap-4476	155	29	polynomial	polynomial	PROPN
ap-4476	155	30	p̂	p̂	PROPN
ap-4476	155	31	(	(	PUNCT
ap-4476	155	32	α	α	NOUN
ap-4476	155	33	,	,	PUNCT
ap-4476	155	34	β	β	NOUN
ap-4476	155	35	)	)	PUNCT
ap-4476	155	36	n	n	CCONJ
ap-4476	155	37	,	,	PUNCT
ap-4476	155	38	m	m	VERB
ap-4476	155	39	,	,	PUNCT
ap-4476	155	40	where	where	SCONJ
ap-4476	155	41	n	n	NOUN
ap-4476	155	42	=	=	SYM
ap-4476	155	43	1	1	NUM
ap-4476	155	44	,	,	PUNCT
ap-4476	155	45	2	2	NUM
ap-4476	155	46	,	,	PUNCT
ap-4476	155	47	3	3	NUM
ap-4476	155	48	,	,	PUNCT
ap-4476	155	49	.	.	PUNCT
ap-4476	155	50	.	.	PUNCT
ap-4476	156	1	.	.	PUNCT
ap-4476	157	1	,	,	PUNCT
ap-4476	157	2	m	m	VERB
ap-4476	157	3	≥	≥	NOUN
ap-4476	157	4	1	1	NUM
ap-4476	157	5	,	,	PUNCT
ap-4476	157	6	α	α	X
ap-4476	157	7	,	,	PUNCT
ap-4476	157	8	β	β	X
ap-4476	157	9	>	>	X
ap-4476	157	10	−1	−1	NOUN
ap-4476	157	11	and	and	CCONJ
ap-4476	157	12	α	α	NOUN
ap-4476	157	13	6=	6=	ADP
ap-4476	157	14	β	β	X
ap-4476	157	15	.	.	PUNCT
ap-4476	158	1	thus	thus	ADV
ap-4476	158	2	the	the	DET
ap-4476	158	3	function	function	NOUN
ap-4476	158	4	f	f	X
ap-4476	158	5	(	(	PUNCT
ap-4476	158	6	g	g	NOUN
ap-4476	158	7	)	)	PUNCT
ap-4476	158	8	in	in	ADP
ap-4476	158	9	(	(	PUNCT
ap-4476	158	10	3	3	X
ap-4476	158	11	)	)	PUNCT
ap-4476	158	12	is	be	AUX
ap-4476	158	13	equivalent	equivalent	ADJ
ap-4476	158	14	to	to	ADP
ap-4476	158	15	p̂	p̂	X
ap-4476	158	16	(	(	PUNCT
ap-4476	158	17	α	α	X
ap-4476	158	18	,	,	PUNCT
ap-4476	158	19	β	β	NOUN
ap-4476	158	20	)	)	PUNCT
ap-4476	158	21	n	n	CCONJ
ap-4476	158	22	,	,	PUNCT
ap-4476	158	23	m	m	PROPN
ap-4476	158	24	(	(	PUNCT
ap-4476	158	25	g	g	NOUN
ap-4476	158	26	)	)	PUNCT
ap-4476	158	27	and	and	CCONJ
ap-4476	158	28	the	the	DET
ap-4476	158	29	other	other	ADJ
ap-4476	158	30	two	two	NUM
ap-4476	158	31	functions	function	NOUN
ap-4476	158	32	q(g	q(g	ADJ
ap-4476	158	33	)	)	PUNCT
ap-4476	158	34	and	and	CCONJ
ap-4476	158	35	r(g	r(g	NUM
ap-4476	158	36	)	)	PUNCT
ap-4476	158	37	are	be	AUX
ap-4476	158	38	given	give	VERB
ap-4476	158	39	by	by	ADP
ap-4476	158	40	(	(	PUNCT
ap-4476	158	41	15	15	NUM
ap-4476	158	42	)	)	PUNCT
ap-4476	158	43	q(g	q(g	ADJ
ap-4476	158	44	)	)	PUNCT
ap-4476	159	1	=	=	SYM
ap-4476	159	2	(	(	PUNCT
ap-4476	159	3	α−	α−	ADP
ap-4476	159	4	β	β	X
ap-4476	159	5	−m−	−m−	NOUN
ap-4476	159	6	1	1	NUM
ap-4476	159	7	)	)	PUNCT
ap-4476	159	8	p	p	NOUN
ap-4476	159	9	(	(	PUNCT
ap-4476	159	10	−α	−α	PROPN
ap-4476	159	11	,	,	PUNCT
ap-4476	159	12	β	β	NOUN
ap-4476	159	13	)	)	PUNCT
ap-4476	160	1	m−1	m−1	PROPN
ap-4476	160	2	(	(	PUNCT
ap-4476	160	3	g	g	NOUN
ap-4476	160	4	)	)	PUNCT
ap-4476	160	5	p	p	NOUN
ap-4476	160	6	(	(	PUNCT
ap-4476	160	7	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	160	8	)	)	PUNCT
ap-4476	160	9	m	m	PROPN
ap-4476	160	10	(	(	PUNCT
ap-4476	160	11	g	g	NOUN
ap-4476	160	12	)	)	PUNCT
ap-4476	160	13	−	−	NOUN
ap-4476	160	14	α+	α+	PUNCT
ap-4476	160	15	1	1	NUM
ap-4476	160	16	1−	1−	NUM
ap-4476	160	17	g	g	NOUN
ap-4476	160	18	+	+	X
ap-4476	160	19	β	β	X
ap-4476	160	20	+	+	CCONJ
ap-4476	160	21	1	1	NUM
ap-4476	160	22	1	1	NUM
ap-4476	160	23	+	+	CCONJ
ap-4476	160	24	g	g	NOUN
ap-4476	160	25	,	,	PUNCT
ap-4476	160	26	r(g	r(g	NUM
ap-4476	160	27	)	)	PUNCT
ap-4476	160	28	=	=	PUNCT
ap-4476	160	29	β(α−	β(α−	PUNCT
ap-4476	160	30	β	β	X
ap-4476	160	31	−m+	−m+	NOUN
ap-4476	160	32	1	1	NUM
ap-4476	160	33	)	)	PUNCT
ap-4476	160	34	1	1	NUM
ap-4476	160	35	+	+	CCONJ
ap-4476	160	36	g	g	PROPN
ap-4476	160	37	p	p	X
ap-4476	160	38	(	(	PUNCT
ap-4476	160	39	−α	−α	PROPN
ap-4476	160	40	,	,	PUNCT
ap-4476	160	41	β	β	NOUN
ap-4476	160	42	)	)	PUNCT
ap-4476	160	43	m−1	m−1	PROPN
ap-4476	160	44	(	(	PUNCT
ap-4476	160	45	g	g	NOUN
ap-4476	160	46	)	)	PUNCT
ap-4476	160	47	p	p	NOUN
ap-4476	160	48	(	(	PUNCT
ap-4476	160	49	−α−1,β−1)(g	−α−1,β−1)(g	NOUN
ap-4476	160	50	)	)	PUNCT
ap-4476	160	51	m	m	VERB
ap-4476	161	1	+	+	ADJ
ap-4476	161	2	1	1	NUM
ap-4476	161	3	1−	1−	NUM
ap-4476	161	4	g2	g2	PROPN
ap-4476	161	5	(	(	PUNCT
ap-4476	161	6	(	(	PUNCT
ap-4476	161	7	α−	α−	ADP
ap-4476	161	8	β	β	X
ap-4476	161	9	−m+	−m+	X
ap-4476	161	10	1	1	NUM
ap-4476	161	11	)	)	PUNCT
ap-4476	161	12	+	+	CCONJ
ap-4476	161	13	(	(	PUNCT
ap-4476	161	14	n−m)(α+	n−m)(α+	PRON
ap-4476	161	15	β	β	NOUN
ap-4476	161	16	+	+	CCONJ
ap-4476	161	17	n−m+	n−m+	PROPN
ap-4476	161	18	1	1	NUM
ap-4476	161	19	)	)	PUNCT
ap-4476	161	20	)	)	PUNCT
ap-4476	161	21	.	.	PUNCT
ap-4476	162	1	(	(	PUNCT
ap-4476	162	2	38	38	NUM
ap-4476	162	3	)	)	PUNCT
ap-4476	162	4	481	481	NUM
ap-4476	162	5	r.	r.	PROPN
ap-4476	162	6	k.	k.	PROPN
ap-4476	162	7	yadav	yadav	PROPN
ap-4476	162	8	,	,	PUNCT
ap-4476	162	9	n.	n.	PROPN
ap-4476	162	10	kumari	kumari	PROPN
ap-4476	162	11	,	,	PUNCT
ap-4476	162	12	a.	a.	PROPN
ap-4476	162	13	khare	khare	PROPN
ap-4476	162	14	,	,	PUNCT
ap-4476	162	15	b.	b.	PROPN
ap-4476	162	16	p.	p.	PROPN
ap-4476	162	17	mandal	mandal	PROPN
ap-4476	162	18	acta	acta	PROPN
ap-4476	162	19	polytechnica	polytechnica	PROPN
ap-4476	162	20	using	use	VERB
ap-4476	162	21	the	the	DET
ap-4476	162	22	above	above	ADJ
ap-4476	162	23	equations	equation	NOUN
ap-4476	162	24	in	in	ADP
ap-4476	162	25	(	(	PUNCT
ap-4476	162	26	5	5	NUM
ap-4476	162	27	)	)	PUNCT
ap-4476	162	28	and	and	CCONJ
ap-4476	162	29	after	after	ADP
ap-4476	162	30	doing	do	VERB
ap-4476	162	31	some	some	DET
ap-4476	162	32	straightforward	straightforward	ADJ
ap-4476	162	33	calculations	calculation	NOUN
ap-4476	162	34	for	for	ADP
ap-4476	162	35	s	s	NOUN
ap-4476	162	36	-	-	NOUN
ap-4476	162	37	wave	wave	NOUN
ap-4476	162	38	(	(	PUNCT
ap-4476	162	39	`	`	PUNCT
ap-4476	162	40	=	=	SYM
ap-4476	162	41	0	0	NUM
ap-4476	162	42	)	)	PUNCT
ap-4476	162	43	,	,	PUNCT
ap-4476	162	44	we	we	PRON
ap-4476	162	45	get	get	VERB
ap-4476	162	46	en	en	ADP
ap-4476	162	47	−	−	PROPN
ap-4476	162	48	veff	veff	NOUN
ap-4476	162	49	,	,	PUNCT
ap-4476	162	50	m(r	m(r	PROPN
ap-4476	162	51	)	)	PUNCT
ap-4476	162	52	=	=	SYM
ap-4476	162	53	1	1	NUM
ap-4476	162	54	2{g(r	2{g(r	NUM
ap-4476	162	55	)	)	PUNCT
ap-4476	162	56	,	,	PUNCT
ap-4476	162	57	r}+	r}+	NOUN
ap-4476	162	58	1−	1−	NUM
ap-4476	162	59	α2	α2	ADJ
ap-4476	162	60	4	4	NUM
ap-4476	162	61	g′(r)2	g′(r)2	NOUN
ap-4476	162	62	(	(	PUNCT
ap-4476	162	63	1−	1−	NUM
ap-4476	162	64	g(r))2	g(r))2	NOUN
ap-4476	162	65	+	+	CCONJ
ap-4476	162	66	1−	1−	NUM
ap-4476	162	67	β2	β2	NOUN
ap-4476	162	68	4	4	NUM
ap-4476	162	69	g′(r)2	g′(r)2	NOUN
ap-4476	162	70	(	(	PUNCT
ap-4476	162	71	1	1	NUM
ap-4476	162	72	+	+	CCONJ
ap-4476	162	73	g(r))2	g(r))2	NOUN
ap-4476	162	74	+	+	CCONJ
ap-4476	162	75	2n2	2n2	NUM
ap-4476	162	76	+	+	CCONJ
ap-4476	162	77	2n(α+	2n(α+	NUM
ap-4476	162	78	β	β	NOUN
ap-4476	162	79	−	−	NUM
ap-4476	162	80	2m+	2m+	NUM
ap-4476	162	81	1	1	NUM
ap-4476	162	82	)	)	PUNCT
ap-4476	163	1	+	+	CCONJ
ap-4476	163	2	2m(α−	2m(α−	NUM
ap-4476	163	3	3β	3β	NUM
ap-4476	163	4	−m+	−m+	X
ap-4476	163	5	1	1	NUM
ap-4476	163	6	)	)	PUNCT
ap-4476	163	7	+	+	CCONJ
ap-4476	163	8	(	(	PUNCT
ap-4476	163	9	α+	α+	NUM
ap-4476	163	10	1)(β	1)(β	NUM
ap-4476	163	11	+	+	NOUN
ap-4476	163	12	1	1	NUM
ap-4476	163	13	)	)	SYM
ap-4476	163	14	2	2	NUM
ap-4476	163	15	×	×	NOUN
ap-4476	163	16	g′(r)2	g′(r)2	NOUN
ap-4476	163	17	1−	1−	NUM
ap-4476	164	1	g(r)2	g(r)2	NOUN
ap-4476	164	2	+	+	CCONJ
ap-4476	164	3	(	(	PUNCT
ap-4476	164	4	α−	α−	ADP
ap-4476	164	5	β	β	X
ap-4476	164	6	−m+	−m+	X
ap-4476	164	7	1	1	NUM
ap-4476	164	8	)	)	PUNCT
ap-4476	164	9	(	(	PUNCT
ap-4476	164	10	α+	α+	X
ap-4476	164	11	β	β	X
ap-4476	164	12	+	+	CCONJ
ap-4476	164	13	(	(	PUNCT
ap-4476	164	14	α−	α−	ADP
ap-4476	164	15	β	β	X
ap-4476	164	16	+	+	NOUN
ap-4476	164	17	1)g(r	1)g(r	NUM
ap-4476	164	18	)	)	PUNCT
ap-4476	164	19	)	)	PUNCT
ap-4476	165	1	g′(r)2	g′(r)2	NOUN
ap-4476	165	2	1−	1−	NUM
ap-4476	166	1	g(r)2	g(r)2	NOUN
ap-4476	166	2	×	×	PROPN
ap-4476	166	3	p	p	X
ap-4476	166	4	(	(	PUNCT
ap-4476	166	5	−α	−α	PROPN
ap-4476	166	6	,	,	PUNCT
ap-4476	166	7	β	β	NOUN
ap-4476	166	8	)	)	PUNCT
ap-4476	167	1	m−1	m−1	PROPN
ap-4476	167	2	(	(	PUNCT
ap-4476	167	3	g	g	NOUN
ap-4476	167	4	)	)	PUNCT
ap-4476	167	5	p	p	NOUN
ap-4476	167	6	(	(	PUNCT
ap-4476	167	7	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	167	8	)	)	PUNCT
ap-4476	167	9	m	m	PROPN
ap-4476	167	10	(	(	PUNCT
ap-4476	167	11	g	g	NOUN
ap-4476	167	12	)	)	PUNCT
ap-4476	167	13	−	−	PROPN
ap-4476	167	14	(	(	PUNCT
ap-4476	167	15	α−	α−	ADP
ap-4476	167	16	β	β	X
ap-4476	167	17	−m+	−m+	VERB
ap-4476	167	18	1)2g′(r)2	1)2g′(r)2	NUM
ap-4476	167	19	2	2	NUM
ap-4476	167	20	(	(	PUNCT
ap-4476	167	21	p	p	X
ap-4476	167	22	(	(	PUNCT
ap-4476	167	23	−α	−α	PROPN
ap-4476	167	24	,	,	PUNCT
ap-4476	167	25	β	β	NOUN
ap-4476	167	26	)	)	PUNCT
ap-4476	167	27	m−1	m−1	PROPN
ap-4476	167	28	(	(	PUNCT
ap-4476	167	29	g	g	NOUN
ap-4476	167	30	)	)	PUNCT
ap-4476	167	31	p	p	NOUN
ap-4476	167	32	(	(	PUNCT
ap-4476	167	33	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	167	34	)	)	PUNCT
ap-4476	167	35	m	m	PROPN
ap-4476	168	1	(	(	PUNCT
ap-4476	168	2	g	g	NOUN
ap-4476	168	3	)	)	PUNCT
ap-4476	168	4	)	)	PUNCT
ap-4476	168	5	2	2	NUM
ap-4476	168	6	,	,	PUNCT
ap-4476	168	7	(	(	PUNCT
ap-4476	168	8	39	39	NUM
ap-4476	168	9	)	)	PUNCT
ap-4476	168	10	and	and	CCONJ
ap-4476	168	11	the	the	DET
ap-4476	168	12	wavefunction	wavefunction	NOUN
ap-4476	168	13	(	(	PUNCT
ap-4476	168	14	8)	8)	NUM
ap-4476	168	15	becomes	become	VERB
ap-4476	168	16	χn	χn	NOUN
ap-4476	168	17	,	,	PUNCT
ap-4476	168	18	m(r	m(r	PROPN
ap-4476	168	19	)	)	PUNCT
ap-4476	168	20	=	=	SYM
ap-4476	168	21	nn	nn	PROPN
ap-4476	168	22	,	,	PUNCT
ap-4476	168	23	m	m	VERB
ap-4476	168	24	×	×	ADJ
ap-4476	168	25	g′(r)−	g′(r)−	NOUN
ap-4476	168	26	1	1	NUM
ap-4476	168	27	2	2	NUM
ap-4476	168	28	(	(	PUNCT
ap-4476	168	29	1	1	NUM
ap-4476	168	30	+	+	CCONJ
ap-4476	168	31	g)(β+1)/2(1−	g)(β+1)/2(1−	PROPN
ap-4476	168	32	g)(α+1)/2	g)(α+1)/2	NOUN
ap-4476	168	33	p	p	NOUN
ap-4476	168	34	(	(	PUNCT
ap-4476	168	35	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	168	36	)	)	PUNCT
ap-4476	168	37	m	m	PROPN
ap-4476	168	38	(	(	PUNCT
ap-4476	168	39	g	g	NOUN
ap-4476	168	40	)	)	PUNCT
ap-4476	168	41	p̂	p̂	NOUN
ap-4476	168	42	(	(	PUNCT
ap-4476	168	43	α	α	X
ap-4476	168	44	,	,	PUNCT
ap-4476	168	45	β	β	NOUN
ap-4476	168	46	)	)	PUNCT
ap-4476	168	47	n	n	CCONJ
ap-4476	168	48	,	,	PUNCT
ap-4476	168	49	m	m	PROPN
ap-4476	168	50	(	(	PUNCT
ap-4476	168	51	g	g	NOUN
ap-4476	168	52	)	)	PUNCT
ap-4476	168	53	,	,	PUNCT
ap-4476	168	54	(	(	PUNCT
ap-4476	168	55	40	40	NUM
ap-4476	168	56	)	)	PUNCT
ap-4476	168	57	where	where	SCONJ
ap-4476	168	58	the	the	DET
ap-4476	168	59	effective	effective	ADJ
ap-4476	168	60	potential	potential	NOUN
ap-4476	168	61	,	,	PUNCT
ap-4476	168	62	veff	veff	NOUN
ap-4476	168	63	,	,	PUNCT
ap-4476	168	64	m(r	m(r	PROPN
ap-4476	168	65	)	)	PUNCT
ap-4476	168	66	is	be	AUX
ap-4476	168	67	given	give	VERB
ap-4476	168	68	by	by	ADP
ap-4476	168	69	veff	veff	NOUN
ap-4476	168	70	,	,	PUNCT
ap-4476	168	71	m(r	m(r	PROPN
ap-4476	168	72	)	)	PUNCT
ap-4476	168	73	=	=	SYM
ap-4476	168	74	vm(r	vm(r	NOUN
ap-4476	168	75	)	)	PUNCT
ap-4476	169	1	+	+	CCONJ
ap-4476	169	2	(	(	PUNCT
ap-4476	169	3	d	d	X
ap-4476	169	4	−	−	PROPN
ap-4476	169	5	1)(d	1)(d	NUM
ap-4476	169	6	−	−	NOUN
ap-4476	169	7	3	3	NUM
ap-4476	169	8	)	)	PUNCT
ap-4476	169	9	4r2	4r2	NUM
ap-4476	169	10	,	,	PUNCT
ap-4476	169	11	(	(	PUNCT
ap-4476	169	12	41	41	NUM
ap-4476	169	13	)	)	PUNCT
ap-4476	169	14	and	and	CCONJ
ap-4476	169	15	the	the	DET
ap-4476	169	16	normalization	normalization	NOUN
ap-4476	169	17	constant	constant	ADJ
ap-4476	169	18	nn	nn	PROPN
ap-4476	169	19	,	,	PUNCT
ap-4476	169	20	m	m	NOUN
ap-4476	169	21	=	=	PUNCT
ap-4476	169	22	(	(	PUNCT
ap-4476	169	23	n!(α+	n!(α+	NOUN
ap-4476	169	24	n+	n+	NUM
ap-4476	169	25	1)2(α+	1)2(α+	NUM
ap-4476	169	26	β	β	X
ap-4476	169	27	+	+	CCONJ
ap-4476	169	28	2n+	2n+	NUM
ap-4476	169	29	1)γ(α+	1)γ(α+	PROPN
ap-4476	169	30	β	β	X
ap-4476	169	31	+	+	CCONJ
ap-4476	169	32	n+	n+	NUM
ap-4476	169	33	1	1	NUM
ap-4476	169	34	)	)	PUNCT
ap-4476	169	35	2α+β+1(1	2α+β+1(1	NUM
ap-4476	169	36	+	+	CCONJ
ap-4476	169	37	α+	α+	PUNCT
ap-4476	169	38	n−m)(β	n−m)(β	NOUN
ap-4476	169	39	+	+	NUM
ap-4476	169	40	n+m)γ(α+	n+m)γ(α+	NOUN
ap-4476	169	41	n+	n+	NUM
ap-4476	169	42	2)γ(β	2)γ(β	NUM
ap-4476	169	43	+	+	CCONJ
ap-4476	169	44	n	n	CCONJ
ap-4476	169	45	)	)	PUNCT
ap-4476	169	46	)	)	PUNCT
ap-4476	169	47	1	1	NUM
ap-4476	169	48	2	2	NUM
ap-4476	169	49	.	.	PUNCT
ap-4476	170	1	(	(	PUNCT
ap-4476	170	2	42	42	NUM
ap-4476	170	3	)	)	PUNCT
ap-4476	170	4	it	it	PRON
ap-4476	170	5	is	be	AUX
ap-4476	170	6	interesting	interesting	ADJ
ap-4476	170	7	here	here	ADV
ap-4476	170	8	to	to	PART
ap-4476	170	9	note	note	VERB
ap-4476	170	10	that	that	SCONJ
ap-4476	170	11	when	when	SCONJ
ap-4476	170	12	this	this	DET
ap-4476	170	13	extended	extended	ADJ
ap-4476	170	14	potential	potential	NOUN
ap-4476	170	15	is	be	AUX
ap-4476	170	16	purely	purely	ADV
ap-4476	170	17	non	non	ADJ
ap-4476	170	18	-	-	ADJ
ap-4476	170	19	power	power	ADJ
ap-4476	170	20	law	law	NOUN
ap-4476	170	21	,	,	PUNCT
ap-4476	170	22	the	the	DET
ap-4476	170	23	potential	potential	NOUN
ap-4476	170	24	given	give	VERB
ap-4476	170	25	by	by	ADP
ap-4476	170	26	(	(	PUNCT
ap-4476	170	27	41	41	NUM
ap-4476	170	28	)	)	PUNCT
ap-4476	170	29	has	have	VERB
ap-4476	170	30	an	an	DET
ap-4476	170	31	extra	extra	ADJ
ap-4476	170	32	term	term	NOUN
ap-4476	170	33	(	(	PUNCT
ap-4476	170	34	d−1)(d−3	d−1)(d−3	NOUN
ap-4476	170	35	)	)	PUNCT
ap-4476	170	36	4r2	4r2	NUM
ap-4476	170	37	which	which	PRON
ap-4476	170	38	behaves	behave	VERB
ap-4476	170	39	as	as	ADP
ap-4476	170	40	constant	constant	ADJ
ap-4476	170	41	background	background	NOUN
ap-4476	170	42	attractive	attractive	ADJ
ap-4476	170	43	inverse	inverse	NOUN
ap-4476	170	44	square	square	ADJ
ap-4476	170	45	potential	potential	NOUN
ap-4476	170	46	in	in	ADP
ap-4476	170	47	any	any	DET
ap-4476	170	48	arbitrary	arbitrary	ADJ
ap-4476	170	49	dimensions	dimension	NOUN
ap-4476	170	50	except	except	SCONJ
ap-4476	170	51	for	for	ADP
ap-4476	170	52	d	d	PROPN
ap-4476	170	53	=	=	SYM
ap-4476	170	54	1	1	NUM
ap-4476	170	55	or	or	CCONJ
ap-4476	170	56	3	3	NUM
ap-4476	170	57	.	.	X
ap-4476	171	1	for	for	ADP
ap-4476	171	2	power	power	NOUN
ap-4476	171	3	law	law	NOUN
ap-4476	171	4	cases	case	NOUN
ap-4476	171	5	(	(	PUNCT
ap-4476	171	6	e.g.	e.g.	ADV
ap-4476	171	7	radial	radial	ADJ
ap-4476	171	8	oscillator	oscillator	NOUN
ap-4476	171	9	potential	potential	NOUN
ap-4476	171	10	)	)	PUNCT
ap-4476	171	11	,	,	PUNCT
ap-4476	171	12	this	this	DET
ap-4476	171	13	background	background	NOUN
ap-4476	171	14	potential	potential	NOUN
ap-4476	171	15	gives	give	VERB
ap-4476	171	16	the	the	DET
ap-4476	171	17	correct	correct	ADJ
ap-4476	171	18	barrier	barrier	NOUN
ap-4476	171	19	potential	potential	NOUN
ap-4476	171	20	in	in	ADP
ap-4476	171	21	arbitrary	arbitrary	ADJ
ap-4476	171	22	dimensions	dimension	NOUN
ap-4476	171	23	(	(	PUNCT
ap-4476	171	24	as	as	SCONJ
ap-4476	171	25	shown	show	VERB
ap-4476	171	26	in	in	ADP
ap-4476	171	27	(	(	PUNCT
ap-4476	171	28	30	30	NUM
ap-4476	171	29	)	)	PUNCT
ap-4476	171	30	)	)	PUNCT
ap-4476	171	31	.	.	PUNCT
ap-4476	172	1	on	on	ADP
ap-4476	172	2	using	use	VERB
ap-4476	172	3	(	(	PUNCT
ap-4476	172	4	6	6	NUM
ap-4476	172	5	)	)	PUNCT
ap-4476	172	6	in	in	ADP
ap-4476	172	7	(	(	PUNCT
ap-4476	172	8	39	39	NUM
ap-4476	172	9	)	)	PUNCT
ap-4476	172	10	and	and	CCONJ
ap-4476	172	11	assume	assume	VERB
ap-4476	172	12	a	a	DET
ap-4476	172	13	term	term	NOUN
ap-4476	172	14	g′2(r	g′2(r	NOUN
ap-4476	172	15	)	)	PUNCT
ap-4476	172	16	1−g2(r	1−g2(r	NUM
ap-4476	172	17	)	)	PUNCT
ap-4476	172	18	=	=	SYM
ap-4476	172	19	c2	c2	PROPN
ap-4476	172	20	(	(	PUNCT
ap-4476	172	21	a	a	DET
ap-4476	172	22	real	real	ADV
ap-4476	172	23	constant	constant	ADJ
ap-4476	172	24	not	not	PART
ap-4476	172	25	equal	equal	ADJ
ap-4476	172	26	to	to	ADP
ap-4476	172	27	zero	zero	NUM
ap-4476	172	28	)	)	PUNCT
ap-4476	172	29	,	,	PUNCT
ap-4476	172	30	we	we	PRON
ap-4476	172	31	get	get	VERB
ap-4476	172	32	a	a	DET
ap-4476	172	33	constant	constant	ADJ
ap-4476	172	34	term	term	NOUN
ap-4476	172	35	on	on	ADP
ap-4476	172	36	right	right	ADJ
ap-4476	172	37	hand	hand	NOUN
ap-4476	172	38	side	side	NOUN
ap-4476	172	39	which	which	PRON
ap-4476	172	40	gives	give	VERB
ap-4476	172	41	the	the	DET
ap-4476	172	42	energy	energy	NOUN
ap-4476	172	43	eigenvalue	eigenvalue	NOUN
ap-4476	172	44	en	en	X
ap-4476	172	45	.	.	PUNCT
ap-4476	173	1	there	there	PRON
ap-4476	173	2	are	be	VERB
ap-4476	173	3	several	several	ADJ
ap-4476	173	4	possibilities	possibility	NOUN
ap-4476	173	5	of	of	ADP
ap-4476	173	6	g(r	g(r	NOUN
ap-4476	173	7	)	)	PUNCT
ap-4476	173	8	which	which	PRON
ap-4476	173	9	produces	produce	VERB
ap-4476	173	10	this	this	DET
ap-4476	173	11	constant	constant	ADJ
ap-4476	173	12	c2	c2	PROPN
ap-4476	173	13	.	.	PUNCT
ap-4476	174	1	if	if	SCONJ
ap-4476	174	2	we	we	PRON
ap-4476	174	3	consider	consider	VERB
ap-4476	174	4	g(r	g(r	NOUN
ap-4476	174	5	)	)	PUNCT
ap-4476	175	1	=	=	SYM
ap-4476	175	2	cosh	cosh	PROPN
ap-4476	175	3	r	r	NOUN
ap-4476	175	4	,	,	PUNCT
ap-4476	175	5	0	0	NUM
ap-4476	175	6	≤	≤	NUM
ap-4476	175	7	r	r	NOUN
ap-4476	175	8	≤	≤	NUM
ap-4476	175	9	∞	∞	NUM
ap-4476	175	10	and	and	CCONJ
ap-4476	175	11	define	define	VERB
ap-4476	175	12	the	the	DET
ap-4476	175	13	parameters	parameter	NOUN
ap-4476	175	14	α	α	NOUN
ap-4476	175	15	=	=	SYM
ap-4476	175	16	b	b	PROPN
ap-4476	175	17	−	−	PROPN
ap-4476	175	18	a	a	DET
ap-4476	175	19	−	−	PROPN
ap-4476	175	20	1	1	NUM
ap-4476	175	21	2	2	NUM
ap-4476	175	22	,	,	PUNCT
ap-4476	175	23	β	β	NOUN
ap-4476	175	24	=	=	PUNCT
ap-4476	175	25	−b	−b	ADP
ap-4476	175	26	−	−	PROPN
ap-4476	175	27	a	a	DET
ap-4476	175	28	−	−	PROPN
ap-4476	175	29	1	1	NUM
ap-4476	175	30	2	2	NUM
ap-4476	175	31	,	,	PUNCT
ap-4476	175	32	b	b	X
ap-4476	175	33	>	>	X
ap-4476	175	34	a+	a+	PUNCT
ap-4476	175	35	(	(	PUNCT
ap-4476	175	36	d−1	d−1	PROPN
ap-4476	175	37	)	)	PUNCT
ap-4476	175	38	2	2	NUM
ap-4476	175	39	>	>	X
ap-4476	175	40	(	(	PUNCT
ap-4476	175	41	d−1	d−1	PROPN
ap-4476	175	42	)	)	PUNCT
ap-4476	175	43	2	2	NUM
ap-4476	175	44	and	and	CCONJ
ap-4476	175	45	the	the	DET
ap-4476	175	46	quantum	quantum	ADJ
ap-4476	175	47	number	number	NOUN
ap-4476	175	48	n→	n→	PUNCT
ap-4476	175	49	n+m	n+m	NUM
ap-4476	175	50	,	,	PUNCT
ap-4476	175	51	m	m	VERB
ap-4476	175	52	≥	≥	NOUN
ap-4476	175	53	1	1	NUM
ap-4476	175	54	,	,	PUNCT
ap-4476	175	55	(	(	PUNCT
ap-4476	175	56	39	39	NUM
ap-4476	175	57	)	)	PUNCT
ap-4476	175	58	and	and	CCONJ
ap-4476	175	59	(	(	PUNCT
ap-4476	175	60	40	40	NUM
ap-4476	175	61	)	)	PUNCT
ap-4476	175	62	give	give	NOUN
ap-4476	175	63	,	,	PUNCT
ap-4476	175	64	en	en	NOUN
ap-4476	175	65	=	=	NOUN
ap-4476	175	66	−(a−	−(a−	PROPN
ap-4476	175	67	n)2	n)2	PROPN
ap-4476	175	68	,	,	PUNCT
ap-4476	175	69	n	n	NOUN
ap-4476	175	70	=	=	SYM
ap-4476	175	71	0	0	NUM
ap-4476	175	72	,	,	PUNCT
ap-4476	175	73	1	1	NUM
ap-4476	175	74	,	,	PUNCT
ap-4476	175	75	2	2	NUM
ap-4476	175	76	,	,	PUNCT
ap-4476	175	77	......	......	PUNCT
ap-4476	175	78	,	,	PUNCT
ap-4476	175	79	nmax	nmax	ADJ
ap-4476	175	80	a−	a−	PROPN
ap-4476	175	81	1	1	NUM
ap-4476	175	82	≤	≤	NOUN
ap-4476	175	83	nmax	nmax	ADV
ap-4476	175	84	<	<	X
ap-4476	175	85	a	a	PRON
ap-4476	175	86	,	,	PUNCT
ap-4476	175	87	(	(	PUNCT
ap-4476	175	88	43	43	NUM
ap-4476	175	89	)	)	PUNCT
ap-4476	175	90	veff	veff	PROPN
ap-4476	175	91	,	,	PUNCT
ap-4476	175	92	m(r	m(r	PROPN
ap-4476	175	93	)	)	PUNCT
ap-4476	175	94	=	=	SYM
ap-4476	176	1	vm(r	vm(r	NOUN
ap-4476	176	2	)	)	PUNCT
ap-4476	177	1	+	+	CCONJ
ap-4476	177	2	(	(	PUNCT
ap-4476	177	3	d	d	X
ap-4476	177	4	−	−	PROPN
ap-4476	177	5	1)(d	1)(d	NUM
ap-4476	177	6	−	−	NOUN
ap-4476	177	7	3	3	NUM
ap-4476	177	8	)	)	PUNCT
ap-4476	177	9	4r2	4r2	NUM
ap-4476	177	10	=	=	NOUN
ap-4476	177	11	vgpt	vgpt	NOUN
ap-4476	177	12	(	(	PUNCT
ap-4476	177	13	r	r	NOUN
ap-4476	177	14	)	)	PUNCT
ap-4476	177	15	+	+	CCONJ
ap-4476	177	16	2m(2b	2m(2b	AUX
ap-4476	177	17	−m+	−m+	NOUN
ap-4476	177	18	1	1	NUM
ap-4476	177	19	)	)	PUNCT
ap-4476	177	20	−	−	PROPN
ap-4476	177	21	(	(	PUNCT
ap-4476	177	22	2b	2b	NOUN
ap-4476	177	23	−m+	−m+	PRON
ap-4476	177	24	1	1	NUM
ap-4476	177	25	)	)	PUNCT
ap-4476	177	26	(	(	PUNCT
ap-4476	177	27	(	(	PUNCT
ap-4476	177	28	2a+	2a+	NUM
ap-4476	177	29	1−	1−	NUM
ap-4476	177	30	(	(	PUNCT
ap-4476	177	31	2b	2b	NUM
ap-4476	177	32	+	+	SYM
ap-4476	177	33	1	1	X
ap-4476	177	34	)	)	PUNCT
ap-4476	177	35	cosh	cosh	NOUN
ap-4476	177	36	r	r	NOUN
ap-4476	177	37	)	)	PUNCT
ap-4476	177	38	)	)	PUNCT
ap-4476	177	39	×	×	NOUN
ap-4476	177	40	p	p	X
ap-4476	177	41	(	(	PUNCT
ap-4476	177	42	−α	−α	PROPN
ap-4476	177	43	,	,	PUNCT
ap-4476	177	44	β	β	NOUN
ap-4476	177	45	)	)	PUNCT
ap-4476	177	46	m−1	m−1	PROPN
ap-4476	177	47	(	(	PUNCT
ap-4476	177	48	cosh	cosh	PROPN
ap-4476	177	49	r	r	NOUN
ap-4476	177	50	)	)	PUNCT
ap-4476	177	51	p	p	NOUN
ap-4476	177	52	(	(	PUNCT
ap-4476	177	53	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	177	54	)	)	PUNCT
ap-4476	177	55	m	m	PROPN
ap-4476	178	1	(	(	PUNCT
ap-4476	178	2	cosh	cosh	PROPN
ap-4476	178	3	r	r	NOUN
ap-4476	178	4	)	)	PUNCT
ap-4476	179	1	+	+	CCONJ
ap-4476	179	2	(	(	PUNCT
ap-4476	179	3	2b	2b	NOUN
ap-4476	179	4	−m+	−m+	PRON
ap-4476	179	5	1)2	1)2	NUM
ap-4476	179	6	sinh2	sinh2	NOUN
ap-4476	180	1	r	r	NOUN
ap-4476	180	2	2	2	NUM
ap-4476	180	3	(	(	PUNCT
ap-4476	180	4	p	p	X
ap-4476	180	5	(	(	PUNCT
ap-4476	180	6	−α	−α	PROPN
ap-4476	180	7	,	,	PUNCT
ap-4476	180	8	β	β	NOUN
ap-4476	180	9	)	)	PUNCT
ap-4476	180	10	m−1	m−1	PROPN
ap-4476	180	11	(	(	PUNCT
ap-4476	180	12	cosh	cosh	PROPN
ap-4476	180	13	r	r	NOUN
ap-4476	180	14	)	)	PUNCT
ap-4476	180	15	p	p	NOUN
ap-4476	180	16	(	(	PUNCT
ap-4476	180	17	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	180	18	)	)	PUNCT
ap-4476	180	19	m	m	PROPN
ap-4476	180	20	(	(	PUNCT
ap-4476	180	21	cosh	cosh	PROPN
ap-4476	180	22	r	r	NOUN
ap-4476	180	23	)	)	PUNCT
ap-4476	180	24	)	)	PUNCT
ap-4476	180	25	2	2	NUM
ap-4476	180	26	(	(	PUNCT
ap-4476	180	27	44	44	NUM
ap-4476	180	28	)	)	PUNCT
ap-4476	180	29	and	and	CCONJ
ap-4476	180	30	the	the	DET
ap-4476	180	31	wave	wave	NOUN
ap-4476	180	32	function	function	PROPN
ap-4476	180	33	χn	χn	PROPN
ap-4476	180	34	,	,	PUNCT
ap-4476	180	35	m(r	m(r	PROPN
ap-4476	180	36	)	)	PUNCT
ap-4476	180	37	=	=	SYM
ap-4476	180	38	nn	nn	PROPN
ap-4476	180	39	,	,	PUNCT
ap-4476	180	40	m	m	VERB
ap-4476	180	41	×	×	NOUN
ap-4476	180	42	(	(	PUNCT
ap-4476	180	43	cosh	cosh	NOUN
ap-4476	180	44	r	r	NOUN
ap-4476	180	45	−	−	PROPN
ap-4476	180	46	1)(b−a)/2(cosh	1)(b−a)/2(cosh	NUM
ap-4476	180	47	r	r	NOUN
ap-4476	180	48	+	+	NUM
ap-4476	180	49	1)−(b+a)/2	1)−(b+a)/2	NUM
ap-4476	180	50	p	p	NOUN
ap-4476	180	51	(	(	PUNCT
ap-4476	180	52	−b+a−	−b+a−	NUM
ap-4476	180	53	1	1	NUM
ap-4476	180	54	2	2	NUM
ap-4476	180	55	,	,	PUNCT
ap-4476	180	56	−b−a−	−b−a−	X
ap-4476	180	57	3	3	NUM
ap-4476	180	58	2	2	NUM
ap-4476	180	59	)	)	PUNCT
ap-4476	180	60	m	m	PROPN
ap-4476	180	61	(	(	PUNCT
ap-4476	180	62	cosh	cosh	PROPN
ap-4476	180	63	r	r	NOUN
ap-4476	180	64	)	)	PUNCT
ap-4476	180	65	p̂	p̂	NOUN
ap-4476	180	66	(	(	PUNCT
ap-4476	180	67	b−a−	b−a−	VERB
ap-4476	180	68	1	1	NUM
ap-4476	180	69	2	2	NUM
ap-4476	180	70	,	,	PUNCT
ap-4476	180	71	−b−a−	−b−a−	X
ap-4476	180	72	1	1	NUM
ap-4476	180	73	2	2	NUM
ap-4476	180	74	)	)	PUNCT
ap-4476	180	75	n+m	n+m	PROPN
ap-4476	180	76	,	,	PUNCT
ap-4476	180	77	m	m	PROPN
ap-4476	180	78	(	(	PUNCT
ap-4476	180	79	cosh	cosh	PROPN
ap-4476	180	80	r	r	NOUN
ap-4476	180	81	)	)	PUNCT
ap-4476	180	82	.	.	PUNCT
ap-4476	181	1	(	(	PUNCT
ap-4476	181	2	45	45	NUM
ap-4476	181	3	)	)	PUNCT
ap-4476	181	4	where	where	SCONJ
ap-4476	181	5	vgpt	vgpt	NOUN
ap-4476	181	6	(	(	PUNCT
ap-4476	181	7	r	r	NOUN
ap-4476	181	8	)	)	PUNCT
ap-4476	181	9	=	=	SYM
ap-4476	181	10	(	(	PUNCT
ap-4476	181	11	b2	b2	NOUN
ap-4476	181	12	+	+	NOUN
ap-4476	181	13	a(a+	a(a+	NOUN
ap-4476	181	14	1	1	NUM
ap-4476	181	15	)	)	PUNCT
ap-4476	181	16	)	)	PUNCT
ap-4476	182	1	cosech2	cosech2	NOUN
ap-4476	182	2	r	r	NOUN
ap-4476	182	3	−b(2a+	−b(2a+	NOUN
ap-4476	182	4	1	1	NUM
ap-4476	182	5	)	)	PUNCT
ap-4476	182	6	cosech	cosech	NOUN
ap-4476	182	7	r	r	NOUN
ap-4476	182	8	coth	coth	NOUN
ap-4476	182	9	r	r	NOUN
ap-4476	182	10	(	(	PUNCT
ap-4476	182	11	46	46	NUM
ap-4476	182	12	)	)	PUNCT
ap-4476	182	13	is	be	AUX
ap-4476	182	14	the	the	DET
ap-4476	182	15	conventional	conventional	ADJ
ap-4476	182	16	generalized	generalize	VERB
ap-4476	182	17	pöschl	pöschl	NOUN
ap-4476	182	18	teller	teller	NOUN
ap-4476	182	19	(	(	PUNCT
ap-4476	182	20	gpt	gpt	NOUN
ap-4476	182	21	)	)	PUNCT
ap-4476	182	22	potential	potential	NOUN
ap-4476	182	23	.	.	PUNCT
ap-4476	183	1	note	note	VERB
ap-4476	183	2	that	that	SCONJ
ap-4476	183	3	the	the	DET
ap-4476	183	4	full	full	ADJ
ap-4476	183	5	eigenfunction	eigenfunction	NOUN
ap-4476	183	6	is	be	AUX
ap-4476	183	7	given	give	VERB
ap-4476	183	8	by	by	ADP
ap-4476	183	9	(	(	PUNCT
ap-4476	183	10	7	7	NUM
ap-4476	183	11	)	)	PUNCT
ap-4476	183	12	with	with	ADP
ap-4476	183	13	χ	χ	PRON
ap-4476	183	14	as	as	SCONJ
ap-4476	183	15	given	give	VERB
ap-4476	183	16	by	by	ADP
ap-4476	183	17	(	(	PUNCT
ap-4476	183	18	45	45	NUM
ap-4476	183	19	)	)	PUNCT
ap-4476	183	20	.	.	PUNCT
ap-4476	184	1	here	here	ADV
ap-4476	184	2	we	we	PRON
ap-4476	184	3	see	see	VERB
ap-4476	184	4	that	that	SCONJ
ap-4476	184	5	the	the	DET
ap-4476	184	6	energy	energy	NOUN
ap-4476	184	7	eigenvalues	eigenvalue	NOUN
ap-4476	184	8	of	of	ADP
ap-4476	184	9	conventional	conventional	ADJ
ap-4476	184	10	potentials	potential	NOUN
ap-4476	184	11	are	be	AUX
ap-4476	184	12	same	same	ADJ
ap-4476	184	13	as	as	ADP
ap-4476	184	14	the	the	DET
ap-4476	184	15	rationally	rationally	ADV
ap-4476	184	16	extended	extended	ADJ
ap-4476	184	17	d	d	ADJ
ap-4476	184	18	-	-	ADJ
ap-4476	184	19	dimensional	dimensional	ADJ
ap-4476	184	20	potentials	potential	NOUN
ap-4476	184	21	(	(	PUNCT
ap-4476	184	22	i.e	i.e	CCONJ
ap-4476	184	23	they	they	PRON
ap-4476	184	24	are	be	AUX
ap-4476	184	25	isospectral	isospectral	ADJ
ap-4476	184	26	)	)	PUNCT
ap-4476	184	27	.	.	PUNCT
ap-4476	185	1	it	it	PRON
ap-4476	185	2	is	be	AUX
ap-4476	185	3	interesting	interesting	ADJ
ap-4476	185	4	to	to	PART
ap-4476	185	5	note	note	VERB
ap-4476	185	6	that	that	SCONJ
ap-4476	185	7	compared	compare	VERB
ap-4476	185	8	to	to	ADP
ap-4476	185	9	d	d	PROPN
ap-4476	185	10	=	=	SYM
ap-4476	185	11	3	3	NUM
ap-4476	185	12	,	,	PUNCT
ap-4476	185	13	the	the	DET
ap-4476	185	14	only	only	ADJ
ap-4476	185	15	change	change	NOUN
ap-4476	185	16	in	in	ADP
ap-4476	185	17	the	the	DET
ap-4476	185	18	potential	potential	NOUN
ap-4476	185	19	in	in	ADP
ap-4476	185	20	d	d	NOUN
ap-4476	185	21	-	-	PUNCT
ap-4476	185	22	dimensions	dimension	NOUN
ap-4476	185	23	is	be	AUX
ap-4476	185	24	the	the	DET
ap-4476	185	25	extra	extra	ADJ
ap-4476	185	26	centrifugal	centrifugal	ADJ
ap-4476	185	27	barrier	barrier	NOUN
ap-4476	185	28	term	term	NOUN
ap-4476	185	29	(	(	PUNCT
ap-4476	185	30	d−1)(d−3	d−1)(d−3	NOUN
ap-4476	185	31	)	)	PUNCT
ap-4476	185	32	4r2	4r2	NUM
ap-4476	185	33	,	,	PUNCT
ap-4476	185	34	and	and	CCONJ
ap-4476	185	35	χ(r	χ(r	PROPN
ap-4476	185	36	)	)	PUNCT
ap-4476	185	37	is	be	AUX
ap-4476	185	38	unaltered	unaltere	VERB
ap-4476	185	39	while	while	SCONJ
ap-4476	185	40	only	only	ADV
ap-4476	185	41	ψ(r	ψ(r	PROPN
ap-4476	185	42	)	)	PUNCT
ap-4476	185	43	is	be	AUX
ap-4476	185	44	slightly	slightly	ADV
ap-4476	185	45	different	different	ADJ
ap-4476	185	46	due	due	ADP
ap-4476	185	47	to	to	ADP
ap-4476	185	48	r(d−1)/2	r(d−1)/2	PROPN
ap-4476	185	49	.	.	PUNCT
ap-4476	186	1	it	it	PRON
ap-4476	186	2	is	be	AUX
ap-4476	186	3	also	also	ADV
ap-4476	186	4	worth	worth	ADJ
ap-4476	186	5	pointing	point	VERB
ap-4476	186	6	out	out	ADP
ap-4476	186	7	that	that	SCONJ
ap-4476	186	8	even	even	ADV
ap-4476	186	9	in	in	ADP
ap-4476	186	10	three	three	NUM
ap-4476	186	11	dimensions	dimension	NOUN
ap-4476	186	12	,	,	PUNCT
ap-4476	186	13	the	the	DET
ap-4476	186	14	gpt	gpt	NOUN
ap-4476	186	15	potential	potential	NOUN
ap-4476	186	16	(	(	PUNCT
ap-4476	186	17	46	46	NUM
ap-4476	186	18	)	)	PUNCT
ap-4476	186	19	can	can	AUX
ap-4476	186	20	be	be	AUX
ap-4476	186	21	analytically	analytically	ADV
ap-4476	186	22	solved	solve	VERB
ap-4476	186	23	only	only	ADV
ap-4476	186	24	in	in	ADP
ap-4476	186	25	the	the	DET
ap-4476	186	26	case	case	NOUN
ap-4476	186	27	of	of	ADP
ap-4476	186	28	s	s	NOUN
ap-4476	186	29	-	-	NOUN
ap-4476	186	30	wave	wave	NOUN
ap-4476	186	31	,	,	PUNCT
ap-4476	186	32	i.e.	i.e.	X
ap-4476	186	33	l	l	X
ap-4476	187	1	=	=	SYM
ap-4476	188	1	0	0	X
ap-4476	188	2	.	.	PUNCT
ap-4476	189	1	we	we	PRON
ap-4476	189	2	now	now	ADV
ap-4476	189	3	show	show	VERB
ap-4476	189	4	that	that	SCONJ
ap-4476	189	5	approximate	approximate	ADJ
ap-4476	189	6	solution	solution	NOUN
ap-4476	189	7	of	of	ADP
ap-4476	189	8	the	the	DET
ap-4476	189	9	gpt	gpt	NOUN
ap-4476	189	10	potential	potential	ADJ
ap-4476	189	11	problem	problem	NOUN
ap-4476	189	12	for	for	ADP
ap-4476	189	13	arbitrary	arbitrary	ADJ
ap-4476	189	14	l	l	NOUN
ap-4476	189	15	can	can	AUX
ap-4476	189	16	,	,	PUNCT
ap-4476	189	17	however	however	ADV
ap-4476	189	18	,	,	PUNCT
ap-4476	189	19	be	be	AUX
ap-4476	189	20	obtained	obtain	VERB
ap-4476	189	21	in	in	ADP
ap-4476	189	22	d	d	PROPN
ap-4476	189	23	dimensions	dimension	NOUN
ap-4476	189	24	.	.	PUNCT
ap-4476	190	1	482	482	NUM
ap-4476	190	2	vol	vol	NOUN
ap-4476	190	3	.	.	PUNCT
ap-4476	190	4	57	57	NUM
ap-4476	190	5	no	no	NOUN
ap-4476	190	6	.	.	PUNCT
ap-4476	191	1	6/2017	6/2017	NUM
ap-4476	191	2	rationally	rationally	ADV
ap-4476	191	3	extended	extend	VERB
ap-4476	191	4	shape	shape	NOUN
ap-4476	191	5	invariant	invariant	ADJ
ap-4476	191	6	potentials	potential	VERB
ap-4476	191	7	4.2.1	4.2.1	NUM
ap-4476	191	8	.	.	PUNCT
ap-4476	191	9	approximate	approximate	ADJ
ap-4476	191	10	solutions	solution	NOUN
ap-4476	191	11	for	for	ADP
ap-4476	191	12	arbitrary	arbitrary	ADJ
ap-4476	191	13	`	`	PUNCT
ap-4476	191	14	in	in	ADP
ap-4476	191	15	this	this	DET
ap-4476	191	16	section	section	NOUN
ap-4476	191	17	,	,	PUNCT
ap-4476	191	18	we	we	PRON
ap-4476	191	19	solve	solve	VERB
ap-4476	191	20	the	the	DET
ap-4476	191	21	d	d	ADJ
ap-4476	191	22	-	-	ADJ
ap-4476	191	23	dimensional	dimensional	ADJ
ap-4476	191	24	schödringer	schödringer	ADJ
ap-4476	191	25	equation	equation	NOUN
ap-4476	191	26	(	(	PUNCT
ap-4476	191	27	1	1	NUM
ap-4476	191	28	)	)	PUNCT
ap-4476	191	29	with	with	ADP
ap-4476	191	30	arbitrary	arbitrary	ADJ
ap-4476	191	31	`	`	PUNCT
ap-4476	191	32	and	and	CCONJ
ap-4476	191	33	obtain	obtain	VERB
ap-4476	191	34	the	the	DET
ap-4476	191	35	effective	effective	ADJ
ap-4476	191	36	potential	potential	NOUN
ap-4476	191	37	(	(	PUNCT
ap-4476	191	38	as	as	SCONJ
ap-4476	191	39	given	give	VERB
ap-4476	191	40	in	in	ADP
ap-4476	191	41	(	(	PUNCT
ap-4476	191	42	39	39	NUM
ap-4476	191	43	)	)	PUNCT
ap-4476	191	44	)	)	PUNCT
ap-4476	191	45	with	with	ADP
ap-4476	191	46	an	an	DET
ap-4476	191	47	extra	extra	ADJ
ap-4476	191	48	`	`	PUNCT
ap-4476	191	49	dependent	dependent	ADJ
ap-4476	191	50	term	term	NOUN
ap-4476	191	51	i.e.	i.e.	X
ap-4476	191	52	,	,	PUNCT
ap-4476	191	53	veff	veff	PROPN
ap-4476	191	54	,	,	PUNCT
ap-4476	191	55	m(r	m(r	PROPN
ap-4476	191	56	)	)	PUNCT
ap-4476	191	57	=	=	SYM
ap-4476	191	58	vm(r	vm(r	NOUN
ap-4476	191	59	)	)	PUNCT
ap-4476	192	1	+	+	CCONJ
ap-4476	192	2	(	(	PUNCT
ap-4476	192	3	(	(	PUNCT
ap-4476	192	4	d	d	NOUN
ap-4476	192	5	−	−	PROPN
ap-4476	192	6	1)(d	1)(d	NUM
ap-4476	192	7	−	−	NOUN
ap-4476	192	8	3	3	NUM
ap-4476	192	9	)	)	PUNCT
ap-4476	192	10	4r2	4r2	NUM
ap-4476	193	1	+	+	CCONJ
ap-4476	193	2	`	`	PUNCT
ap-4476	193	3	(	(	PUNCT
ap-4476	193	4	`	`	PUNCT
ap-4476	193	5	+	+	NOUN
ap-4476	193	6	d	d	NOUN
ap-4476	193	7	−	−	ADJ
ap-4476	193	8	2	2	NUM
ap-4476	193	9	)	)	PUNCT
ap-4476	193	10	r2	r2	PROPN
ap-4476	193	11	)	)	PUNCT
ap-4476	193	12	.	.	PUNCT
ap-4476	194	1	(	(	PUNCT
ap-4476	194	2	47	47	NUM
ap-4476	194	3	)	)	PUNCT
ap-4476	195	1	so	so	ADV
ap-4476	195	2	,	,	PUNCT
ap-4476	195	3	in	in	ADP
ap-4476	195	4	order	order	NOUN
ap-4476	195	5	to	to	PART
ap-4476	195	6	get	get	VERB
ap-4476	195	7	the	the	DET
ap-4476	195	8	appropriate	appropriate	ADJ
ap-4476	195	9	centrifugal	centrifugal	ADJ
ap-4476	195	10	barrier	barrier	NOUN
ap-4476	195	11	terms	term	NOUN
ap-4476	195	12	in	in	ADP
ap-4476	195	13	the	the	DET
ap-4476	195	14	above	above	ADJ
ap-4476	195	15	effective	effective	ADJ
ap-4476	195	16	potential	potential	NOUN
ap-4476	195	17	,	,	PUNCT
ap-4476	195	18	we	we	PRON
ap-4476	195	19	have	have	VERB
ap-4476	195	20	to	to	PART
ap-4476	195	21	apply	apply	VERB
ap-4476	195	22	some	some	DET
ap-4476	195	23	approximation	approximation	NOUN
ap-4476	195	24	.	.	PUNCT
ap-4476	196	1	following	follow	VERB
ap-4476	196	2	[	[	X
ap-4476	196	3	25	25	NUM
ap-4476	196	4	]	]	PUNCT
ap-4476	196	5	,	,	PUNCT
ap-4476	196	6	we	we	PRON
ap-4476	196	7	consider	consider	VERB
ap-4476	196	8	the	the	DET
ap-4476	196	9	approximation	approximation	NOUN
ap-4476	196	10	1	1	NUM
ap-4476	196	11	r2	r2	NOUN
ap-4476	196	12	'	'	PART
ap-4476	196	13	1	1	NUM
ap-4476	196	14	sinh2	sinh2	NOUN
ap-4476	196	15	r	r	NOUN
ap-4476	196	16	.	.	PUNCT
ap-4476	197	1	(	(	PUNCT
ap-4476	197	2	48	48	NUM
ap-4476	197	3	)	)	PUNCT
ap-4476	197	4	thus	thus	ADV
ap-4476	197	5	effectively	effectively	ADV
ap-4476	197	6	,	,	PUNCT
ap-4476	197	7	one	one	PRON
ap-4476	197	8	has	have	AUX
ap-4476	197	9	approximated	approximate	VERB
ap-4476	197	10	a	a	DET
ap-4476	197	11	problem	problem	NOUN
ap-4476	197	12	for	for	ADP
ap-4476	197	13	the	the	DET
ap-4476	197	14	l’th	l’th	PROPN
ap-4476	197	15	partial	partial	ADJ
ap-4476	197	16	wave	wave	NOUN
ap-4476	197	17	to	to	ADP
ap-4476	197	18	that	that	PRON
ap-4476	197	19	of	of	ADP
ap-4476	197	20	l	l	NOUN
ap-4476	197	21	=	=	SYM
ap-4476	197	22	0	0	PUNCT
ap-4476	198	1	but	but	CCONJ
ap-4476	198	2	with	with	ADP
ap-4476	198	3	different	different	ADJ
ap-4476	198	4	set	set	NOUN
ap-4476	198	5	of	of	ADP
ap-4476	198	6	parameters	parameter	NOUN
ap-4476	198	7	compared	compare	VERB
ap-4476	198	8	to	to	ADP
ap-4476	198	9	the	the	DET
ap-4476	198	10	usual	usual	ADJ
ap-4476	198	11	l	l	NOUN
ap-4476	198	12	=	=	SYM
ap-4476	198	13	0	0	NUM
ap-4476	198	14	case	case	NOUN
ap-4476	198	15	.	.	PUNCT
ap-4476	199	1	in	in	ADP
ap-4476	199	2	that	that	DET
ap-4476	199	3	case	case	NOUN
ap-4476	199	4	,	,	PUNCT
ap-4476	199	5	the	the	DET
ap-4476	199	6	effective	effective	ADJ
ap-4476	199	7	potential	potential	NOUN
ap-4476	199	8	(	(	PUNCT
ap-4476	199	9	41	41	NUM
ap-4476	199	10	)	)	PUNCT
ap-4476	199	11	becomes	become	VERB
ap-4476	199	12	veff	veff	NOUN
ap-4476	199	13	,	,	PUNCT
ap-4476	199	14	m	m	VERB
ap-4476	199	15	=	=	SYM
ap-4476	199	16	vm(r	vm(r	NOUN
ap-4476	199	17	)	)	PUNCT
ap-4476	200	1	+	+	CCONJ
ap-4476	200	2	(	(	PUNCT
ap-4476	200	3	(	(	PUNCT
ap-4476	200	4	d	d	NOUN
ap-4476	200	5	−	−	PROPN
ap-4476	200	6	1)(d	1)(d	NUM
ap-4476	200	7	−	−	NOUN
ap-4476	200	8	3	3	NUM
ap-4476	200	9	)	)	PUNCT
ap-4476	200	10	4	4	NUM
ap-4476	200	11	+	+	CCONJ
ap-4476	200	12	`	`	PUNCT
ap-4476	200	13	(	(	PUNCT
ap-4476	200	14	`	`	PUNCT
ap-4476	200	15	+	+	NOUN
ap-4476	200	16	d	d	NOUN
ap-4476	200	17	−	−	PROPN
ap-4476	200	18	2	2	NUM
ap-4476	200	19	)	)	PUNCT
ap-4476	200	20	)	)	PUNCT
ap-4476	200	21	cosech2r	cosech2r	PROPN
ap-4476	200	22	.	.	PUNCT
ap-4476	201	1	(	(	PUNCT
ap-4476	201	2	49	49	NUM
ap-4476	201	3	)	)	PUNCT
ap-4476	201	4	now	now	ADV
ap-4476	201	5	we	we	PRON
ap-4476	201	6	define	define	VERB
ap-4476	201	7	the	the	DET
ap-4476	201	8	parameters	parameter	NOUN
ap-4476	201	9	α	α	PROPN
ap-4476	201	10	and	and	CCONJ
ap-4476	201	11	β	β	X
ap-4476	201	12	in	in	ADP
ap-4476	201	13	terms	term	NOUN
ap-4476	201	14	of	of	ADP
ap-4476	201	15	modified	modified	ADJ
ap-4476	201	16	parameters1	parameters1	NOUN
ap-4476	201	17	b′	b′	NUM
ap-4476	201	18	and	and	CCONJ
ap-4476	201	19	a′	a′	PROPN
ap-4476	201	20	i.e.	i.e.	X
ap-4476	201	21	,	,	PUNCT
ap-4476	201	22	α	α	PROPN
ap-4476	201	23	=	=	SYM
ap-4476	201	24	b′	b′	NUM
ap-4476	201	25	−	−	PROPN
ap-4476	201	26	a′	a′	NOUN
ap-4476	201	27	−	−	PROPN
ap-4476	201	28	1	1	NUM
ap-4476	201	29	2	2	NUM
ap-4476	201	30	,	,	PUNCT
ap-4476	201	31	β	β	X
ap-4476	201	32	=	=	PUNCT
ap-4476	201	33	−b′	−b′	VERB
ap-4476	202	1	−a′	−a′	ADV
ap-4476	202	2	−	−	NUM
ap-4476	202	3	1	1	NUM
ap-4476	202	4	2	2	NUM
ap-4476	202	5	,	,	PUNCT
ap-4476	202	6	b	b	NOUN
ap-4476	202	7	′	′	NOUN
ap-4476	202	8	>	>	X
ap-4476	202	9	a′	a′	PROPN
ap-4476	203	1	+	+	CCONJ
ap-4476	203	2	d−1	d−1	PROPN
ap-4476	203	3	2	2	NUM
ap-4476	203	4	>	>	PUNCT
ap-4476	203	5	d−1	d−1	PROPN
ap-4476	203	6	2	2	NUM
ap-4476	203	7	,	,	PUNCT
ap-4476	203	8	where	where	SCONJ
ap-4476	203	9	b′	b′	NOUN
ap-4476	203	10	=	=	SYM
ap-4476	203	11	(	(	PUNCT
ap-4476	203	12	(	(	PUNCT
ap-4476	203	13	ζ	ζ	NOUN
ap-4476	203	14	+	+	NOUN
ap-4476	203	15	1	1	NUM
ap-4476	203	16	4	4	NUM
ap-4476	203	17	)	)	PUNCT
ap-4476	203	18	+	+	CCONJ
ap-4476	203	19	(	(	PUNCT
ap-4476	203	20	(	(	PUNCT
ap-4476	203	21	ζ	ζ	NOUN
ap-4476	203	22	+	+	NOUN
ap-4476	203	23	1	1	NUM
ap-4476	203	24	4	4	NUM
ap-4476	203	25	+	+	NOUN
ap-4476	203	26	b(2a+	b(2a+	NOUN
ap-4476	203	27	1))(ζ	1))(ζ	NUM
ap-4476	203	28	+	+	CCONJ
ap-4476	203	29	1	1	NUM
ap-4476	203	30	4	4	NUM
ap-4476	203	31	−b(2a+	−b(2a+	NOUN
ap-4476	203	32	1	1	NUM
ap-4476	203	33	)	)	PUNCT
ap-4476	203	34	)	)	PUNCT
ap-4476	203	35	)	)	PUNCT
ap-4476	203	36	1	1	NUM
ap-4476	203	37	2	2	NUM
ap-4476	203	38	2	2	NUM
ap-4476	203	39	)	)	PUNCT
ap-4476	203	40	1	1	NUM
ap-4476	203	41	2	2	NUM
ap-4476	203	42	(	(	PUNCT
ap-4476	203	43	50	50	NUM
ap-4476	203	44	)	)	PUNCT
ap-4476	203	45	and	and	CCONJ
ap-4476	203	46	a′	a′	PROPN
ap-4476	203	47	=	=	SYM
ap-4476	203	48	1	1	NUM
ap-4476	203	49	2	2	NUM
ap-4476	203	50	(	(	PUNCT
ap-4476	203	51	2b(a+	2b(a+	PROPN
ap-4476	203	52	1	1	NUM
ap-4476	203	53	2	2	NUM
ap-4476	203	54	)	)	PUNCT
ap-4476	203	55	b′	b′	NUM
ap-4476	203	56	−	−	NOUN
ap-4476	203	57	1	1	NUM
ap-4476	203	58	)	)	PUNCT
ap-4476	203	59	,	,	PUNCT
ap-4476	203	60	(	(	PUNCT
ap-4476	203	61	51	51	NUM
ap-4476	203	62	)	)	PUNCT
ap-4476	203	63	while	while	SCONJ
ap-4476	203	64	ζ	ζ	NOUN
ap-4476	203	65	=	=	SYM
ap-4476	203	66	b2	b2	NOUN
ap-4476	204	1	+	+	NOUN
ap-4476	204	2	a(a+	a(a+	NOUN
ap-4476	204	3	1	1	NUM
ap-4476	204	4	)	)	PUNCT
ap-4476	205	1	+	+	CCONJ
ap-4476	205	2	`	`	PUNCT
ap-4476	205	3	(	(	PUNCT
ap-4476	205	4	`	`	PUNCT
ap-4476	205	5	+	+	NOUN
ap-4476	205	6	d	d	NOUN
ap-4476	205	7	−	−	NOUN
ap-4476	205	8	2	2	NUM
ap-4476	205	9	)	)	PUNCT
ap-4476	205	10	+	+	CCONJ
ap-4476	205	11	(	(	PUNCT
ap-4476	205	12	d	d	X
ap-4476	205	13	−	−	PROPN
ap-4476	205	14	1)(d	1)(d	NUM
ap-4476	205	15	−	−	NOUN
ap-4476	205	16	3	3	NUM
ap-4476	205	17	)	)	PUNCT
ap-4476	205	18	4	4	NUM
ap-4476	205	19	.	.	PUNCT
ap-4476	205	20	(	(	PUNCT
ap-4476	205	21	52	52	NUM
ap-4476	205	22	)	)	PUNCT
ap-4476	205	23	for	for	ADP
ap-4476	205	24	d	d	PROPN
ap-4476	205	25	=	=	SYM
ap-4476	205	26	3	3	NUM
ap-4476	205	27	and	and	CCONJ
ap-4476	205	28	`	`	PUNCT
ap-4476	205	29	=	=	SYM
ap-4476	205	30	0	0	NUM
ap-4476	205	31	;	;	PUNCT
ap-4476	205	32	we	we	PRON
ap-4476	205	33	get	get	VERB
ap-4476	205	34	the	the	DET
ap-4476	205	35	usual	usual	ADJ
ap-4476	205	36	parameters	parameter	NOUN
ap-4476	205	37	as	as	SCONJ
ap-4476	205	38	defined	define	VERB
ap-4476	205	39	in	in	ADP
ap-4476	205	40	the	the	DET
ap-4476	205	41	above	above	ADJ
ap-4476	205	42	section	section	NOUN
ap-4476	205	43	i.e.	i.e.	X
ap-4476	205	44	,	,	PUNCT
ap-4476	205	45	b′	b′	NUM
ap-4476	205	46	→	→	SYM
ap-4476	205	47	b	b	NOUN
ap-4476	205	48	and	and	CCONJ
ap-4476	205	49	a′	a′	PROPN
ap-4476	205	50	→	→	SYM
ap-4476	205	51	a.	a.	NOUN
ap-4476	205	52	on	on	ADP
ap-4476	205	53	using	use	VERB
ap-4476	205	54	these	these	DET
ap-4476	205	55	new	new	ADJ
ap-4476	205	56	parameters	parameter	NOUN
ap-4476	205	57	α	α	NOUN
ap-4476	205	58	and	and	CCONJ
ap-4476	205	59	β	β	X
ap-4476	205	60	,	,	PUNCT
ap-4476	205	61	quantum	quantum	ADJ
ap-4476	205	62	number	number	NOUN
ap-4476	205	63	n→	n→	PUNCT
ap-4476	205	64	n+m;m	n+m;m	PROPN
ap-4476	205	65	≥	≥	NUM
ap-4476	205	66	1	1	NUM
ap-4476	205	67	,	,	PUNCT
ap-4476	205	68	(	(	PUNCT
ap-4476	205	69	39	39	NUM
ap-4476	205	70	)	)	PUNCT
ap-4476	205	71	and	and	CCONJ
ap-4476	205	72	(	(	PUNCT
ap-4476	205	73	40	40	NUM
ap-4476	205	74	)	)	PUNCT
ap-4476	205	75	give	give	VERB
ap-4476	205	76	en	en	PRON
ap-4476	205	77	=	=	SYM
ap-4476	205	78	−(a′	−(a′	NOUN
ap-4476	205	79	−	−	PROPN
ap-4476	205	80	n)2	n)2	NOUN
ap-4476	205	81	,	,	PUNCT
ap-4476	205	82	n	n	NOUN
ap-4476	205	83	=	=	SYM
ap-4476	205	84	0	0	NUM
ap-4476	205	85	,	,	PUNCT
ap-4476	205	86	1	1	NUM
ap-4476	205	87	,	,	PUNCT
ap-4476	205	88	2	2	NUM
ap-4476	205	89	,	,	PUNCT
ap-4476	205	90	.	.	PUNCT
ap-4476	205	91	.	.	PUNCT
ap-4476	206	1	.	.	PUNCT
ap-4476	207	1	,	,	PUNCT
ap-4476	207	2	nmax	nmax	PROPN
ap-4476	207	3	a′	a′	NOUN
ap-4476	207	4	−	−	PROPN
ap-4476	207	5	1	1	NUM
ap-4476	207	6	≤	≤	NOUN
ap-4476	207	7	nmax	nmax	ADV
ap-4476	207	8	<	<	X
ap-4476	207	9	a′	a′	PROPN
ap-4476	207	10	,	,	PUNCT
ap-4476	207	11	(	(	PUNCT
ap-4476	207	12	53	53	NUM
ap-4476	207	13	)	)	PUNCT
ap-4476	207	14	veff	veff	NOUN
ap-4476	207	15	,	,	PUNCT
ap-4476	207	16	m(r	m(r	PROPN
ap-4476	207	17	)	)	PUNCT
ap-4476	207	18	=	=	SYM
ap-4476	207	19	v	v	NOUN
ap-4476	207	20	(	(	PUNCT
ap-4476	207	21	a′,b′	a′,b′	PROPN
ap-4476	207	22	)	)	PUNCT
ap-4476	207	23	gpt	gpt	NOUN
ap-4476	207	24	(	(	PUNCT
ap-4476	207	25	r)+2m(2b′−m+1)−	r)+2m(2b′−m+1)−	PROPN
ap-4476	207	26	(	(	PUNCT
ap-4476	207	27	2b′−m+1)[(2a′+1−	2b′−m+1)[(2a′+1−	PROPN
ap-4476	207	28	(	(	PUNCT
ap-4476	207	29	2b′+1	2b′+1	NUM
ap-4476	207	30	)	)	PUNCT
ap-4476	207	31	cosh	cosh	NOUN
ap-4476	207	32	r)]×	r)]×	NOUN
ap-4476	208	1	p	p	X
ap-4476	208	2	(	(	PUNCT
ap-4476	208	3	−α	−α	PROPN
ap-4476	208	4	,	,	PUNCT
ap-4476	208	5	β	β	NOUN
ap-4476	208	6	)	)	PUNCT
ap-4476	209	1	m−1	m−1	PROPN
ap-4476	209	2	(	(	PUNCT
ap-4476	209	3	cosh	cosh	PROPN
ap-4476	209	4	r	r	NOUN
ap-4476	209	5	)	)	PUNCT
ap-4476	209	6	p	p	NOUN
ap-4476	209	7	(	(	PUNCT
ap-4476	209	8	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	209	9	)	)	PUNCT
ap-4476	209	10	m	m	PROPN
ap-4476	209	11	(	(	PUNCT
ap-4476	209	12	cosh	cosh	PROPN
ap-4476	209	13	r	r	NOUN
ap-4476	209	14	)	)	PUNCT
ap-4476	209	15	+	+	CCONJ
ap-4476	209	16	(	(	PUNCT
ap-4476	209	17	2b′	2b′	NUM
ap-4476	209	18	−m+	−m+	NOUN
ap-4476	209	19	1)2	1)2	NUM
ap-4476	209	20	sinh2	sinh2	NOUN
ap-4476	210	1	r	r	NOUN
ap-4476	210	2	2	2	NUM
ap-4476	210	3	(	(	PUNCT
ap-4476	210	4	p	p	X
ap-4476	210	5	(	(	PUNCT
ap-4476	210	6	−α	−α	PROPN
ap-4476	210	7	,	,	PUNCT
ap-4476	210	8	β	β	NOUN
ap-4476	210	9	)	)	PUNCT
ap-4476	210	10	m−1	m−1	PROPN
ap-4476	210	11	(	(	PUNCT
ap-4476	210	12	cosh	cosh	PROPN
ap-4476	210	13	r	r	NOUN
ap-4476	210	14	)	)	PUNCT
ap-4476	210	15	p	p	NOUN
ap-4476	210	16	(	(	PUNCT
ap-4476	210	17	−α−1,β−1	−α−1,β−1	NOUN
ap-4476	210	18	)	)	PUNCT
ap-4476	210	19	m	m	PROPN
ap-4476	210	20	(	(	PUNCT
ap-4476	210	21	cosh	cosh	PROPN
ap-4476	210	22	r	r	NOUN
ap-4476	210	23	)	)	PUNCT
ap-4476	210	24	)	)	PUNCT
ap-4476	210	25	2	2	NUM
ap-4476	210	26	(	(	PUNCT
ap-4476	210	27	54	54	NUM
ap-4476	210	28	)	)	PUNCT
ap-4476	210	29	and	and	CCONJ
ap-4476	210	30	the	the	DET
ap-4476	210	31	wave	wave	NOUN
ap-4476	210	32	functions	function	NOUN
ap-4476	210	33	χn	χn	X
ap-4476	210	34	,	,	PUNCT
ap-4476	210	35	m(r	m(r	PROPN
ap-4476	210	36	)	)	PUNCT
ap-4476	210	37	=	=	SYM
ap-4476	210	38	nn	nn	PROPN
ap-4476	210	39	,	,	PUNCT
ap-4476	210	40	m	m	VERB
ap-4476	210	41	×	×	NOUN
ap-4476	210	42	(	(	PUNCT
ap-4476	210	43	cosh	cosh	NOUN
ap-4476	210	44	r	r	NOUN
ap-4476	210	45	−	−	NUM
ap-4476	210	46	1)(b′−a′)/2(cosh	1)(b′−a′)/2(cosh	NUM
ap-4476	210	47	r	r	NOUN
ap-4476	210	48	+	+	NUM
ap-4476	210	49	1)−(b′+a′)/2	1)−(b′+a′)/2	NUM
ap-4476	210	50	p	p	NOUN
ap-4476	210	51	(	(	PUNCT
ap-4476	210	52	−b′+a′−	−b′+a′−	PROPN
ap-4476	210	53	1	1	NUM
ap-4476	210	54	2	2	NUM
ap-4476	210	55	,	,	PUNCT
ap-4476	210	56	−b′−a′−	−b′−a′−	PROPN
ap-4476	210	57	3	3	NUM
ap-4476	210	58	2	2	NUM
ap-4476	210	59	)	)	PUNCT
ap-4476	210	60	m	m	PROPN
ap-4476	210	61	(	(	PUNCT
ap-4476	210	62	cosh	cosh	PROPN
ap-4476	210	63	r	r	NOUN
ap-4476	210	64	)	)	PUNCT
ap-4476	210	65	p̂	p̂	NOUN
ap-4476	210	66	(	(	PUNCT
ap-4476	210	67	b′−a′−	b′−a′−	NOUN
ap-4476	210	68	1	1	NUM
ap-4476	210	69	2	2	NUM
ap-4476	210	70	,	,	PUNCT
ap-4476	210	71	−b	−b	ADV
ap-4476	210	72	′−a′−	′−a′−	ADP
ap-4476	210	73	1	1	NUM
ap-4476	210	74	2	2	NUM
ap-4476	210	75	)	)	PUNCT
ap-4476	210	76	n+m	n+m	PROPN
ap-4476	210	77	,	,	PUNCT
ap-4476	210	78	m	m	PROPN
ap-4476	210	79	(	(	PUNCT
ap-4476	210	80	cosh	cosh	PROPN
ap-4476	210	81	r	r	NOUN
ap-4476	210	82	)	)	PUNCT
ap-4476	210	83	.	.	PUNCT
ap-4476	211	1	(	(	PUNCT
ap-4476	211	2	55	55	NUM
ap-4476	211	3	)	)	PUNCT
ap-4476	211	4	where	where	SCONJ
ap-4476	211	5	v	v	X
ap-4476	211	6	(	(	PUNCT
ap-4476	211	7	a′,b′	a′,b′	PROPN
ap-4476	211	8	)	)	PUNCT
ap-4476	211	9	gpt	gpt	NOUN
ap-4476	211	10	(	(	PUNCT
ap-4476	211	11	r	r	NOUN
ap-4476	211	12	)	)	PUNCT
ap-4476	211	13	=	=	SYM
ap-4476	211	14	(	(	PUNCT
ap-4476	211	15	b′2	b′2	NOUN
ap-4476	212	1	+	+	NOUN
ap-4476	212	2	a′(a′	a′(a′	NOUN
ap-4476	212	3	+	+	NOUN
ap-4476	212	4	1	1	NUM
ap-4476	212	5	)	)	PUNCT
ap-4476	212	6	)	)	PUNCT
ap-4476	213	1	cosech2	cosech2	NOUN
ap-4476	213	2	r	r	NOUN
ap-4476	213	3	−b′(2a′	−b′(2a′	NOUN
ap-4476	213	4	+	+	CCONJ
ap-4476	213	5	1	1	X
ap-4476	213	6	)	)	PUNCT
ap-4476	213	7	cosech	cosech	NOUN
ap-4476	213	8	r	r	NOUN
ap-4476	213	9	coth	coth	NOUN
ap-4476	213	10	r	r	NOUN
ap-4476	213	11	(	(	PUNCT
ap-4476	213	12	56	56	NUM
ap-4476	213	13	)	)	PUNCT
ap-4476	213	14	is	be	AUX
ap-4476	213	15	the	the	DET
ap-4476	213	16	conventional	conventional	ADJ
ap-4476	213	17	generalized	generalize	VERB
ap-4476	213	18	pöschl	pöschl	NOUN
ap-4476	213	19	teller	teller	NOUN
ap-4476	213	20	(	(	PUNCT
ap-4476	213	21	gpt	gpt	NOUN
ap-4476	213	22	)	)	PUNCT
ap-4476	213	23	potential	potential	NOUN
ap-4476	213	24	in	in	ADP
ap-4476	213	25	arbitrary	arbitrary	ADJ
ap-4476	213	26	d	d	NOUN
ap-4476	213	27	and	and	CCONJ
ap-4476	213	28	`	`	PUNCT
ap-4476	213	29	.	.	PUNCT
ap-4476	214	1	similar	similar	ADJ
ap-4476	214	2	to	to	ADP
ap-4476	214	3	the	the	DET
ap-4476	214	4	extended	extended	ADJ
ap-4476	214	5	oscillator	oscillator	NOUN
ap-4476	214	6	case	case	NOUN
ap-4476	214	7	,	,	PUNCT
ap-4476	214	8	we	we	PRON
ap-4476	214	9	now	now	ADV
ap-4476	214	10	consider	consider	VERB
ap-4476	214	11	few	few	ADJ
ap-4476	214	12	special	special	ADJ
ap-4476	214	13	cases	case	NOUN
ap-4476	214	14	of	of	ADP
ap-4476	214	15	the	the	DET
ap-4476	214	16	results	result	NOUN
ap-4476	214	17	of	of	ADP
ap-4476	214	18	extended	extended	ADJ
ap-4476	214	19	gpt	gpt	NOUN
ap-4476	214	20	potential	potential	NOUN
ap-4476	214	21	obtained	obtain	VERB
ap-4476	214	22	in	in	ADP
ap-4476	214	23	equations	equation	NOUN
ap-4476	214	24	(	(	PUNCT
ap-4476	214	25	54	54	NUM
ap-4476	214	26	)	)	PUNCT
ap-4476	214	27	and	and	CCONJ
ap-4476	214	28	(	(	PUNCT
ap-4476	214	29	55	55	NUM
ap-4476	214	30	)	)	PUNCT
ap-4476	214	31	.	.	PUNCT
ap-4476	215	1	1when	1when	ADV
ap-4476	215	2	we	we	PRON
ap-4476	215	3	solve	solve	VERB
ap-4476	215	4	the	the	DET
ap-4476	215	5	schrödinger	schrödinger	ADJ
ap-4476	215	6	equation	equation	NOUN
ap-4476	215	7	for	for	ADP
ap-4476	215	8	usual	usual	ADJ
ap-4476	215	9	gpt	gpt	NOUN
ap-4476	215	10	potential	potential	NOUN
ap-4476	215	11	,	,	PUNCT
ap-4476	215	12	vgp	vgp	PROPN
ap-4476	215	13	t	t	PROPN
ap-4476	215	14	(	(	PUNCT
ap-4476	215	15	r	r	NOUN
ap-4476	215	16	)	)	PUNCT
ap-4476	215	17	=	=	SYM
ap-4476	215	18	(	(	PUNCT
ap-4476	215	19	b2	b2	NOUN
ap-4476	215	20	+	+	NOUN
ap-4476	215	21	a(a+1))cosech2r−b(2a+1	a(a+1))cosech2r−b(2a+1	ADJ
ap-4476	215	22	)	)	PUNCT
ap-4476	215	23	coth	coth	PROPN
ap-4476	215	24	rcosechr	rcosechr	NOUN
ap-4476	215	25	,	,	PUNCT
ap-4476	215	26	we	we	PRON
ap-4476	215	27	define	define	VERB
ap-4476	215	28	the	the	DET
ap-4476	215	29	parameters	parameter	NOUN
ap-4476	215	30	α	α	PROPN
ap-4476	215	31	and	and	CCONJ
ap-4476	215	32	β	β	X
ap-4476	215	33	in	in	ADP
ap-4476	215	34	terms	term	NOUN
ap-4476	215	35	of	of	ADP
ap-4476	215	36	a	a	PRON
ap-4476	215	37	and	and	CCONJ
ap-4476	215	38	b.	b.	PROPN
ap-4476	215	39	but	but	CCONJ
ap-4476	215	40	,	,	PUNCT
ap-4476	215	41	in	in	ADP
ap-4476	215	42	the	the	DET
ap-4476	215	43	above	above	ADJ
ap-4476	215	44	d	d	ADJ
ap-4476	215	45	-	-	ADJ
ap-4476	215	46	dimensional	dimensional	ADJ
ap-4476	215	47	effective	effective	ADJ
ap-4476	215	48	potential	potential	NOUN
ap-4476	215	49	the	the	DET
ap-4476	215	50	parameters	parameter	NOUN
ap-4476	215	51	α	α	PROPN
ap-4476	215	52	and	and	CCONJ
ap-4476	215	53	β	β	PROPN
ap-4476	215	54	have	have	AUX
ap-4476	215	55	been	be	AUX
ap-4476	215	56	modified	modify	VERB
ap-4476	215	57	due	due	ADP
ap-4476	215	58	to	to	ADP
ap-4476	215	59	the	the	DET
ap-4476	215	60	presence	presence	NOUN
ap-4476	215	61	of	of	ADP
ap-4476	215	62	an	an	DET
ap-4476	215	63	extra	extra	ADJ
ap-4476	215	64	d	d	NOUN
ap-4476	215	65	-	-	ADJ
ap-4476	215	66	dependent	dependent	ADJ
ap-4476	215	67	term	term	NOUN
ap-4476	215	68	.	.	PUNCT
ap-4476	216	1	483	483	NUM
ap-4476	216	2	r.	r.	PROPN
ap-4476	216	3	k.	k.	PROPN
ap-4476	216	4	yadav	yadav	PROPN
ap-4476	216	5	,	,	PUNCT
ap-4476	216	6	n.	n.	PROPN
ap-4476	216	7	kumari	kumari	PROPN
ap-4476	216	8	,	,	PUNCT
ap-4476	216	9	a.	a.	PROPN
ap-4476	216	10	khare	khare	PROPN
ap-4476	216	11	,	,	PUNCT
ap-4476	216	12	b.	b.	PROPN
ap-4476	216	13	p.	p.	PROPN
ap-4476	216	14	mandal	mandal	PROPN
ap-4476	216	15	acta	acta	PROPN
ap-4476	216	16	polytechnica	polytechnica	PROPN
ap-4476	216	17	case	case	NOUN
ap-4476	216	18	(	(	PUNCT
ap-4476	216	19	a	a	NOUN
ap-4476	216	20	)	)	PUNCT
ap-4476	216	21	.	.	PUNCT
ap-4476	217	1	for	for	ADP
ap-4476	217	2	m	m	PROPN
ap-4476	217	3	=	=	SYM
ap-4476	217	4	0	0	NUM
ap-4476	217	5	,	,	PUNCT
ap-4476	217	6	from	from	ADP
ap-4476	217	7	eqs	eqs	PROPN
ap-4476	217	8	.	.	PUNCT
ap-4476	218	1	(	(	PUNCT
ap-4476	218	2	54	54	NUM
ap-4476	218	3	)	)	PUNCT
ap-4476	218	4	and	and	CCONJ
ap-4476	218	5	(	(	PUNCT
ap-4476	218	6	55	55	NUM
ap-4476	218	7	)	)	PUNCT
ap-4476	218	8	,	,	PUNCT
ap-4476	218	9	the	the	DET
ap-4476	218	10	potential	potential	NOUN
ap-4476	218	11	and	and	CCONJ
ap-4476	218	12	the	the	DET
ap-4476	218	13	corresponding	correspond	VERB
ap-4476	218	14	wavefunctions	wavefunction	NOUN
ap-4476	218	15	in	in	ADP
ap-4476	218	16	terms	term	NOUN
ap-4476	218	17	of	of	ADP
ap-4476	218	18	usual	usual	ADJ
ap-4476	218	19	jacobi	jacobi	NOUN
ap-4476	218	20	polynomials	polynomial	NOUN
ap-4476	218	21	are	be	AUX
ap-4476	218	22	veff,0(r	veff,0(r	NOUN
ap-4476	218	23	)	)	PUNCT
ap-4476	219	1	=	=	SYM
ap-4476	219	2	v	v	NOUN
ap-4476	219	3	(	(	PUNCT
ap-4476	219	4	a′,b′	a′,b′	PROPN
ap-4476	219	5	)	)	PUNCT
ap-4476	219	6	gpt	gpt	NOUN
ap-4476	219	7	(	(	PUNCT
ap-4476	219	8	r	r	NOUN
ap-4476	219	9	)	)	PUNCT
ap-4476	219	10	(	(	PUNCT
ap-4476	219	11	57	57	NUM
ap-4476	219	12	)	)	PUNCT
ap-4476	219	13	and	and	CCONJ
ap-4476	219	14	χn,0(r	χn,0(r	NOUN
ap-4476	219	15	)	)	PUNCT
ap-4476	219	16	=	=	PUNCT
ap-4476	220	1	nn,0	nn,0	PROPN
ap-4476	220	2	×	×	NOUN
ap-4476	220	3	(	(	PUNCT
ap-4476	220	4	cosh	cosh	NOUN
ap-4476	220	5	r	r	NOUN
ap-4476	220	6	−	−	NUM
ap-4476	220	7	1)(b′−a′)/2(cosh	1)(b′−a′)/2(cosh	NUM
ap-4476	220	8	r	r	NOUN
ap-4476	220	9	+	+	NUM
ap-4476	220	10	1)−(b′+a′)/2p	1)−(b′+a′)/2p	NUM
ap-4476	220	11	(	(	PUNCT
ap-4476	220	12	b′−a′−	b′−a′−	NOUN
ap-4476	220	13	1	1	NUM
ap-4476	220	14	2	2	NUM
ap-4476	220	15	,	,	PUNCT
ap-4476	220	16	−b	−b	ADV
ap-4476	220	17	′−a′−	′−a′−	ADP
ap-4476	220	18	1	1	NUM
ap-4476	220	19	2	2	NUM
ap-4476	220	20	)	)	PUNCT
ap-4476	220	21	n	n	CCONJ
ap-4476	220	22	(	(	PUNCT
ap-4476	220	23	cosh	cosh	PROPN
ap-4476	220	24	r	r	NOUN
ap-4476	220	25	)	)	PUNCT
ap-4476	220	26	.	.	PUNCT
ap-4476	221	1	(	(	PUNCT
ap-4476	221	2	58	58	NUM
ap-4476	221	3	)	)	PUNCT
ap-4476	221	4	for	for	ADP
ap-4476	221	5	d	d	PROPN
ap-4476	221	6	=	=	SYM
ap-4476	221	7	3	3	NUM
ap-4476	221	8	and	and	CCONJ
ap-4476	221	9	`	`	PUNCT
ap-4476	221	10	=	=	SYM
ap-4476	221	11	0	0	PUNCT
ap-4476	221	12	the	the	DET
ap-4476	221	13	effective	effective	ADJ
ap-4476	221	14	potential	potential	ADJ
ap-4476	221	15	veff,0	veff,0	NOUN
ap-4476	221	16	=	=	SYM
ap-4476	221	17	vgpt	vgpt	NOUN
ap-4476	221	18	(	(	PUNCT
ap-4476	221	19	r	r	NOUN
ap-4476	221	20	)	)	PUNCT
ap-4476	221	21	.	.	PUNCT
ap-4476	222	1	case	case	NOUN
ap-4476	222	2	(	(	PUNCT
ap-4476	222	3	b	b	NOUN
ap-4476	222	4	)	)	PUNCT
ap-4476	222	5	.	.	PUNCT
ap-4476	223	1	for	for	ADP
ap-4476	223	2	m	m	PROPN
ap-4476	223	3	=	=	SYM
ap-4476	223	4	1	1	NUM
ap-4476	223	5	,	,	PUNCT
ap-4476	223	6	the	the	PRON
ap-4476	223	7	obtained	obtain	VERB
ap-4476	223	8	potential	potential	ADJ
ap-4476	223	9	veff,1(r	veff,1(r	NOUN
ap-4476	223	10	)	)	PUNCT
ap-4476	223	11	=	=	SYM
ap-4476	223	12	v	v	X
ap-4476	223	13	(	(	PUNCT
ap-4476	223	14	a′,b′	a′,b′	PROPN
ap-4476	223	15	)	)	PUNCT
ap-4476	223	16	gpt	gpt	NOUN
ap-4476	223	17	(	(	PUNCT
ap-4476	223	18	r	r	NOUN
ap-4476	223	19	)	)	PUNCT
ap-4476	223	20	+	+	NOUN
ap-4476	223	21	2(2a′	2(2a′	NUM
ap-4476	223	22	+	+	NOUN
ap-4476	223	23	1	1	NUM
ap-4476	223	24	)	)	PUNCT
ap-4476	223	25	(	(	PUNCT
ap-4476	223	26	2b′	2b′	NUM
ap-4476	223	27	cosh	cosh	NOUN
ap-4476	223	28	r	r	NOUN
ap-4476	223	29	−	−	PROPN
ap-4476	223	30	2a′	2a′	NUM
ap-4476	223	31	−	−	NOUN
ap-4476	223	32	1	1	NUM
ap-4476	223	33	)	)	PUNCT
ap-4476	223	34	−	−	PROPN
ap-4476	223	35	2	2	NUM
ap-4476	223	36	(	(	PUNCT
ap-4476	223	37	4b′2	4b′2	NOUN
ap-4476	223	38	−	−	PROPN
ap-4476	223	39	(	(	PUNCT
ap-4476	223	40	2a′	2a′	NUM
ap-4476	223	41	+	+	CCONJ
ap-4476	223	42	1)2	1)2	NUM
ap-4476	223	43	)	)	PUNCT
ap-4476	223	44	(	(	PUNCT
ap-4476	223	45	2b′	2b′	NUM
ap-4476	223	46	cosh	cosh	NOUN
ap-4476	223	47	r	r	NOUN
ap-4476	223	48	−	−	PROPN
ap-4476	223	49	2a′	2a′	NUM
ap-4476	224	1	−	−	PROPN
ap-4476	224	2	1)2	1)2	NUM
ap-4476	224	3	(	(	PUNCT
ap-4476	224	4	59	59	NUM
ap-4476	224	5	)	)	PUNCT
ap-4476	224	6	is	be	AUX
ap-4476	224	7	the	the	DET
ap-4476	224	8	rationally	rationally	ADV
ap-4476	224	9	extended	extended	ADJ
ap-4476	224	10	d	d	ADJ
ap-4476	224	11	dimensional	dimensional	ADJ
ap-4476	224	12	gpt	gpt	NOUN
ap-4476	224	13	potential	potential	NOUN
ap-4476	224	14	.	.	PUNCT
ap-4476	225	1	the	the	DET
ap-4476	225	2	corresponding	correspond	VERB
ap-4476	225	3	wavefunctions	wavefunction	NOUN
ap-4476	225	4	in	in	ADP
ap-4476	225	5	terms	term	NOUN
ap-4476	225	6	of	of	ADP
ap-4476	225	7	exceptional	exceptional	ADJ
ap-4476	225	8	x1	x1	PROPN
ap-4476	225	9	jacobi	jacobi	PROPN
ap-4476	225	10	orthogonal	orthogonal	ADJ
ap-4476	225	11	polynomials	polynomial	NOUN
ap-4476	225	12	can	can	AUX
ap-4476	225	13	be	be	AUX
ap-4476	225	14	written	write	VERB
ap-4476	225	15	as	as	ADP
ap-4476	225	16	χn,1(r	χn,1(r	ADJ
ap-4476	225	17	)	)	PUNCT
ap-4476	226	1	=	=	SYM
ap-4476	226	2	nn,1	nn,1	PROPN
ap-4476	226	3	×	×	NOUN
ap-4476	226	4	(	(	PUNCT
ap-4476	226	5	cosh	cosh	NOUN
ap-4476	226	6	r	r	NOUN
ap-4476	227	1	−	−	NUM
ap-4476	227	2	1)(b′−a′)/2(cosh	1)(b′−a′)/2(cosh	NUM
ap-4476	227	3	r	r	NOUN
ap-4476	227	4	+	+	NUM
ap-4476	227	5	1)−(b′+a′)/2	1)−(b′+a′)/2	NUM
ap-4476	227	6	(	(	PUNCT
ap-4476	227	7	2b′	2b′	NUM
ap-4476	227	8	cosh	cosh	NOUN
ap-4476	227	9	r	r	NOUN
ap-4476	227	10	−	−	PROPN
ap-4476	227	11	2a′	2a′	NUM
ap-4476	227	12	−	−	NOUN
ap-4476	227	13	1	1	NUM
ap-4476	227	14	)	)	PUNCT
ap-4476	227	15	p̂	p̂	NOUN
ap-4476	227	16	(	(	PUNCT
ap-4476	227	17	b′−a′−	b′−a′−	NOUN
ap-4476	227	18	1	1	NUM
ap-4476	227	19	2	2	NUM
ap-4476	227	20	,	,	PUNCT
ap-4476	227	21	−b	−b	ADV
ap-4476	227	22	′−a′−	′−a′−	ADP
ap-4476	227	23	1	1	NUM
ap-4476	227	24	2	2	NUM
ap-4476	227	25	)	)	PUNCT
ap-4476	227	26	n+1,1	n+1,1	NOUN
ap-4476	227	27	(	(	PUNCT
ap-4476	227	28	cosh	cosh	PROPN
ap-4476	227	29	r	r	NOUN
ap-4476	227	30	)	)	PUNCT
ap-4476	227	31	.	.	PUNCT
ap-4476	228	1	(	(	PUNCT
ap-4476	228	2	60	60	NUM
ap-4476	228	3	)	)	PUNCT
ap-4476	228	4	for	for	ADP
ap-4476	228	5	d	d	PROPN
ap-4476	228	6	=	=	SYM
ap-4476	228	7	3	3	NUM
ap-4476	228	8	and	and	CCONJ
ap-4476	228	9	`	`	PUNCT
ap-4476	228	10	=	=	SYM
ap-4476	228	11	0	0	NUM
ap-4476	228	12	,	,	PUNCT
ap-4476	228	13	the	the	DET
ap-4476	228	14	above	above	ADJ
ap-4476	228	15	expressions	expression	NOUN
ap-4476	228	16	match	match	VERB
ap-4476	228	17	exactly	exactly	ADV
ap-4476	228	18	with	with	ADP
ap-4476	228	19	the	the	DET
ap-4476	228	20	results	result	NOUN
ap-4476	228	21	obtained	obtain	VERB
ap-4476	228	22	in	in	ADP
ap-4476	228	23	[	[	X
ap-4476	228	24	4	4	NUM
ap-4476	228	25	,	,	PUNCT
ap-4476	228	26	15	15	NUM
ap-4476	228	27	]	]	PUNCT
ap-4476	228	28	.	.	PUNCT
ap-4476	229	1	case	case	NOUN
ap-4476	229	2	(	(	PUNCT
ap-4476	229	3	c	c	NOUN
ap-4476	229	4	)	)	PUNCT
ap-4476	229	5	.	.	PUNCT
ap-4476	230	1	in	in	ADP
ap-4476	230	2	this	this	DET
ap-4476	230	3	case	case	NOUN
ap-4476	230	4	the	the	DET
ap-4476	230	5	potential	potential	NOUN
ap-4476	230	6	and	and	CCONJ
ap-4476	230	7	its	its	PRON
ap-4476	230	8	wavefunctions	wavefunction	NOUN
ap-4476	230	9	in	in	ADP
ap-4476	230	10	terms	term	NOUN
ap-4476	230	11	of	of	ADP
ap-4476	230	12	x2	x2	PROPN
ap-4476	230	13	jacobi	jacobi	PROPN
ap-4476	230	14	polynomials	polynomial	NOUN
ap-4476	230	15	are	be	AUX
ap-4476	230	16	given	give	VERB
ap-4476	230	17	by	by	ADP
ap-4476	230	18	veff,2(r	veff,2(r	PROPN
ap-4476	230	19	)	)	PUNCT
ap-4476	230	20	=	=	SYM
ap-4476	230	21	v	v	NOUN
ap-4476	230	22	(	(	PUNCT
ap-4476	230	23	a′,b′	a′,b′	PROPN
ap-4476	230	24	)	)	PUNCT
ap-4476	230	25	gpt	gpt	NOUN
ap-4476	230	26	(	(	PUNCT
ap-4476	230	27	r	r	NOUN
ap-4476	230	28	)	)	PUNCT
ap-4476	230	29	+	+	CCONJ
ap-4476	230	30	4(2b′	4(2b′	NUM
ap-4476	230	31	−	−	PROPN
ap-4476	230	32	1	1	NUM
ap-4476	230	33	)	)	PUNCT
ap-4476	230	34	−	−	PROPN
ap-4476	230	35	4	4	NUM
ap-4476	230	36	(	(	PUNCT
ap-4476	230	37	3(2b′	3(2b′	NUM
ap-4476	230	38	−	−	NOUN
ap-4476	230	39	1)(2a′	1)(2a′	NOUN
ap-4476	231	1	+	+	CCONJ
ap-4476	231	2	1	1	X
ap-4476	231	3	)	)	PUNCT
ap-4476	231	4	cosh	cosh	NOUN
ap-4476	231	5	r	r	NOUN
ap-4476	231	6	−	−	NOUN
ap-4476	231	7	2b′(2b′	2b′(2b′	NUM
ap-4476	232	1	−	−	PROPN
ap-4476	232	2	1)−	1)−	PROPN
ap-4476	232	3	8a′(a′	8a′(a′	PROPN
ap-4476	232	4	+	+	CCONJ
ap-4476	232	5	1	1	NUM
ap-4476	232	6	)	)	PUNCT
ap-4476	232	7	)	)	PUNCT
ap-4476	233	1	(	(	PUNCT
ap-4476	233	2	2b′	2b′	NUM
ap-4476	233	3	−	−	NOUN
ap-4476	233	4	1)(2b′	1)(2b′	NUM
ap-4476	234	1	−	−	NOUN
ap-4476	234	2	2	2	NUM
ap-4476	234	3	)	)	PUNCT
ap-4476	234	4	cosh2	cosh2	VERB
ap-4476	235	1	r	r	NOUN
ap-4476	235	2	−	−	NOUN
ap-4476	235	3	2(2b′	2(2b′	NUM
ap-4476	235	4	−	−	NOUN
ap-4476	235	5	1)(2a′	1)(2a′	NOUN
ap-4476	236	1	+	+	CCONJ
ap-4476	236	2	1	1	X
ap-4476	236	3	)	)	PUNCT
ap-4476	236	4	cosh	cosh	NOUN
ap-4476	236	5	r	r	NOUN
ap-4476	236	6	+	+	PROPN
ap-4476	236	7	4a′(a′	4a′(a′	NOUN
ap-4476	237	1	+	+	NOUN
ap-4476	237	2	1	1	NUM
ap-4476	237	3	)	)	PUNCT
ap-4476	237	4	+	+	CCONJ
ap-4476	237	5	2b′	2b′	NUM
ap-4476	237	6	−	−	NOUN
ap-4476	237	7	1	1	NUM
ap-4476	238	1	+	+	NUM
ap-4476	238	2	8(2b′	8(2b′	NUM
ap-4476	238	3	−	−	NOUN
ap-4476	238	4	1)2	1)2	NUM
ap-4476	238	5	sinh2	sinh2	NOUN
ap-4476	239	1	r	r	NOUN
ap-4476	239	2	(	(	PUNCT
ap-4476	239	3	(	(	PUNCT
ap-4476	239	4	2a′	2a′	NUM
ap-4476	239	5	+	+	NUM
ap-4476	239	6	1)−	1)−	NUM
ap-4476	239	7	(	(	PUNCT
ap-4476	239	8	2b′	2b′	NUM
ap-4476	239	9	−	−	NOUN
ap-4476	239	10	2	2	X
ap-4476	239	11	)	)	PUNCT
ap-4476	239	12	cosh	cosh	NOUN
ap-4476	239	13	r	r	NOUN
ap-4476	239	14	)	)	PUNCT
ap-4476	239	15	2	2	NUM
ap-4476	239	16	(	(	PUNCT
ap-4476	239	17	(	(	PUNCT
ap-4476	239	18	2b′	2b′	NUM
ap-4476	239	19	−	−	NOUN
ap-4476	239	20	1)(2b′	1)(2b′	NUM
ap-4476	240	1	−	−	NOUN
ap-4476	240	2	2	2	NUM
ap-4476	240	3	)	)	PUNCT
ap-4476	240	4	cosh2	cosh2	VERB
ap-4476	241	1	r	r	NOUN
ap-4476	241	2	−	−	NOUN
ap-4476	241	3	2(2b′	2(2b′	NUM
ap-4476	241	4	−	−	NOUN
ap-4476	241	5	1)(2a′	1)(2a′	NOUN
ap-4476	242	1	+	+	CCONJ
ap-4476	242	2	1	1	X
ap-4476	242	3	)	)	PUNCT
ap-4476	242	4	cosh	cosh	NOUN
ap-4476	242	5	r	r	NOUN
ap-4476	242	6	+	+	PROPN
ap-4476	242	7	4a′(a′	4a′(a′	NOUN
ap-4476	243	1	+	+	NOUN
ap-4476	243	2	1	1	NUM
ap-4476	243	3	)	)	PUNCT
ap-4476	243	4	+	+	CCONJ
ap-4476	243	5	2b′	2b′	NUM
ap-4476	244	1	−	−	NOUN
ap-4476	244	2	1	1	NUM
ap-4476	244	3	)	)	SYM
ap-4476	244	4	2	2	NUM
ap-4476	244	5	−	−	NOUN
ap-4476	244	6	8	8	NUM
ap-4476	244	7	(	(	PUNCT
ap-4476	244	8	61	61	NUM
ap-4476	244	9	)	)	PUNCT
ap-4476	244	10	and	and	CCONJ
ap-4476	244	11	χn,2(r	χn,2(r	NOUN
ap-4476	244	12	)	)	PUNCT
ap-4476	245	1	=	=	SYM
ap-4476	245	2	nn,2	nn,2	PROPN
ap-4476	245	3	(	(	PUNCT
ap-4476	245	4	cosh	cosh	NOUN
ap-4476	245	5	r	r	NOUN
ap-4476	245	6	−	−	NUM
ap-4476	245	7	1)(b′−a′)/2(cosh	1)(b′−a′)/2(cosh	NUM
ap-4476	245	8	r	r	NOUN
ap-4476	245	9	+	+	NUM
ap-4476	245	10	1)−(b′+a′)/2	1)−(b′+a′)/2	NUM
ap-4476	245	11	(	(	PUNCT
ap-4476	245	12	2b′	2b′	NUM
ap-4476	245	13	−	−	NOUN
ap-4476	245	14	1)(2b′	1)(2b′	NUM
ap-4476	245	15	−	−	NOUN
ap-4476	245	16	2	2	NUM
ap-4476	245	17	)	)	PUNCT
ap-4476	245	18	cosh2	cosh2	VERB
ap-4476	246	1	r	r	NOUN
ap-4476	246	2	−	−	NOUN
ap-4476	246	3	2(2b′	2(2b′	NUM
ap-4476	246	4	−	−	NOUN
ap-4476	246	5	1)(2a′	1)(2a′	NOUN
ap-4476	247	1	+	+	CCONJ
ap-4476	247	2	1	1	X
ap-4476	247	3	)	)	PUNCT
ap-4476	247	4	cosh	cosh	NOUN
ap-4476	247	5	r	r	NOUN
ap-4476	247	6	+	+	PROPN
ap-4476	247	7	4a′(a′	4a′(a′	NOUN
ap-4476	248	1	+	+	NOUN
ap-4476	248	2	1	1	NUM
ap-4476	248	3	)	)	PUNCT
ap-4476	248	4	+	+	CCONJ
ap-4476	248	5	2b′	2b′	NUM
ap-4476	248	6	−	−	NUM
ap-4476	248	7	1	1	NUM
ap-4476	248	8	×	×	NOUN
ap-4476	248	9	p̂	p̂	NOUN
ap-4476	248	10	(	(	PUNCT
ap-4476	248	11	b′−a′−	b′−a′−	NOUN
ap-4476	248	12	1	1	NUM
ap-4476	248	13	2	2	NUM
ap-4476	248	14	,	,	PUNCT
ap-4476	248	15	−b	−b	ADV
ap-4476	248	16	′−a′−	′−a′−	ADP
ap-4476	248	17	1	1	NUM
ap-4476	248	18	2	2	NUM
ap-4476	248	19	)	)	PUNCT
ap-4476	248	20	n+2,2	n+2,2	PROPN
ap-4476	248	21	(	(	PUNCT
ap-4476	248	22	cosh	cosh	PROPN
ap-4476	248	23	r	r	NOUN
ap-4476	248	24	)	)	PUNCT
ap-4476	248	25	.	.	PUNCT
ap-4476	249	1	(	(	PUNCT
ap-4476	249	2	62	62	NUM
ap-4476	249	3	)	)	PUNCT
ap-4476	249	4	5	5	NUM
ap-4476	249	5	.	.	PUNCT
ap-4476	250	1	new	new	ADJ
ap-4476	250	2	shape	shape	NOUN
ap-4476	250	3	invariant	invariant	ADJ
ap-4476	250	4	potentials	potential	NOUN
ap-4476	250	5	(	(	PUNCT
ap-4476	250	6	sips	sip	NOUN
ap-4476	250	7	)	)	PUNCT
ap-4476	250	8	in	in	ADP
ap-4476	250	9	higher	high	ADJ
ap-4476	250	10	dimensions	dimension	NOUN
ap-4476	250	11	a	a	DET
ap-4476	250	12	quantum	quantum	ADJ
ap-4476	250	13	mechanical	mechanical	ADJ
ap-4476	250	14	system	system	NOUN
ap-4476	250	15	is	be	AUX
ap-4476	250	16	termed	term	VERB
ap-4476	250	17	as	as	ADP
ap-4476	250	18	si	si	PROPN
ap-4476	250	19	when	when	SCONJ
ap-4476	250	20	the	the	DET
ap-4476	250	21	partner	partner	NOUN
ap-4476	250	22	potentials	potential	VERB
ap-4476	250	23	in	in	ADP
ap-4476	250	24	a	a	DET
ap-4476	250	25	unbroken	unbroken	ADJ
ap-4476	250	26	susy	susy	NOUN
ap-4476	251	1	[	[	X
ap-4476	251	2	17	17	NUM
ap-4476	251	3	,	,	PUNCT
ap-4476	251	4	18	18	NUM
ap-4476	251	5	]	]	PUNCT
ap-4476	251	6	satisfy	satisfy	VERB
ap-4476	251	7	the	the	DET
ap-4476	251	8	si	si	PROPN
ap-4476	251	9	property	property	NOUN
ap-4476	251	10	v	v	NOUN
ap-4476	251	11	(	(	PUNCT
ap-4476	251	12	+	+	NOUN
ap-4476	251	13	)	)	PUNCT
ap-4476	251	14	(	(	PUNCT
ap-4476	251	15	x	x	X
ap-4476	251	16	;	;	PUNCT
ap-4476	251	17	a	a	X
ap-4476	251	18	)	)	PUNCT
ap-4476	251	19	=	=	SYM
ap-4476	251	20	v	v	NOUN
ap-4476	251	21	(	(	PUNCT
ap-4476	251	22	−)(x	−)(x	NOUN
ap-4476	251	23	;	;	PUNCT
ap-4476	251	24	b	b	X
ap-4476	251	25	)	)	PUNCT
ap-4476	251	26	+	+	NOUN
ap-4476	251	27	r(a	r(a	NOUN
ap-4476	251	28	)	)	PUNCT
ap-4476	251	29	,	,	PUNCT
ap-4476	251	30	(	(	PUNCT
ap-4476	251	31	63	63	NUM
ap-4476	251	32	)	)	PUNCT
ap-4476	251	33	where	where	SCONJ
ap-4476	251	34	a	a	PRON
ap-4476	251	35	is	be	AUX
ap-4476	251	36	a	a	DET
ap-4476	251	37	set	set	NOUN
ap-4476	251	38	of	of	ADP
ap-4476	251	39	parameters	parameter	NOUN
ap-4476	251	40	,	,	PUNCT
ap-4476	251	41	b	b	PROPN
ap-4476	251	42	is	be	AUX
ap-4476	251	43	a	a	DET
ap-4476	251	44	function	function	NOUN
ap-4476	251	45	of	of	ADP
ap-4476	251	46	a	a	DET
ap-4476	251	47	(	(	PUNCT
ap-4476	251	48	say	say	INTJ
ap-4476	251	49	b	b	PROPN
ap-4476	251	50	=	=	SYM
ap-4476	251	51	f(a	f(a	PROPN
ap-4476	251	52	)	)	PUNCT
ap-4476	251	53	)	)	PUNCT
ap-4476	251	54	and	and	CCONJ
ap-4476	251	55	the	the	DET
ap-4476	251	56	remainder	remainder	NOUN
ap-4476	251	57	r(a	r(a	PROPN
ap-4476	251	58	)	)	PUNCT
ap-4476	251	59	is	be	AUX
ap-4476	251	60	independent	independent	ADJ
ap-4476	251	61	of	of	ADP
ap-4476	251	62	x.	x.	NOUN
ap-4476	251	63	the	the	DET
ap-4476	251	64	partner	partner	NOUN
ap-4476	251	65	potentials	potential	VERB
ap-4476	251	66	,	,	PUNCT
ap-4476	251	67	v	v	NOUN
ap-4476	251	68	±(x	±(x	NOUN
ap-4476	251	69	)	)	PUNCT
ap-4476	251	70	are	be	AUX
ap-4476	251	71	obtained	obtain	VERB
ap-4476	251	72	from	from	ADP
ap-4476	251	73	the	the	DET
ap-4476	251	74	superpotential	superpotential	ADJ
ap-4476	251	75	,	,	PUNCT
ap-4476	251	76	w	w	NOUN
ap-4476	251	77	(	(	PUNCT
ap-4476	251	78	x	x	NOUN
ap-4476	251	79	)	)	PUNCT
ap-4476	251	80	through	through	ADP
ap-4476	251	81	v	v	NOUN
ap-4476	251	82	±(x	±(x	NOUN
ap-4476	251	83	)	)	PUNCT
ap-4476	252	1	=	=	PUNCT
ap-4476	253	1	w	w	PROPN
ap-4476	253	2	2(x)±w	2(x)±w	NUM
ap-4476	253	3	′(x	′(x	NOUN
ap-4476	253	4	)	)	PUNCT
ap-4476	253	5	+	+	CCONJ
ap-4476	253	6	e0	e0	PROPN
ap-4476	253	7	,	,	PUNCT
ap-4476	253	8	~	~	PUNCT
ap-4476	253	9	=	=	SYM
ap-4476	253	10	2	2	NUM
ap-4476	253	11	m	m	NOUN
ap-4476	253	12	=	=	SYM
ap-4476	253	13	1	1	NUM
ap-4476	253	14	,	,	PUNCT
ap-4476	253	15	(	(	PUNCT
ap-4476	253	16	64	64	NUM
ap-4476	253	17	)	)	PUNCT
ap-4476	253	18	where	where	SCONJ
ap-4476	253	19	e0	e0	PROPN
ap-4476	253	20	is	be	AUX
ap-4476	253	21	factorization	factorization	ADJ
ap-4476	253	22	energy2	energy2	NOUN
ap-4476	253	23	.	.	PUNCT
ap-4476	254	1	the	the	DET
ap-4476	254	2	eigenstates	eigenstate	NOUN
ap-4476	254	3	of	of	ADP
ap-4476	254	4	these	these	DET
ap-4476	254	5	partner	partner	NOUN
ap-4476	254	6	potentials	potential	NOUN
ap-4476	254	7	are	be	AUX
ap-4476	254	8	related	relate	VERB
ap-4476	254	9	by	by	ADP
ap-4476	254	10	e(+	e(+	NOUN
ap-4476	254	11	)	)	PUNCT
ap-4476	254	12	n	n	NOUN
ap-4476	254	13	=	=	SYM
ap-4476	254	14	e	e	X
ap-4476	254	15	(	(	PUNCT
ap-4476	254	16	−	−	NOUN
ap-4476	254	17	)	)	PUNCT
ap-4476	254	18	n+1	n+1	PROPN
ap-4476	254	19	,	,	PUNCT
ap-4476	254	20	e	e	X
ap-4476	254	21	(	(	PUNCT
ap-4476	254	22	0	0	NUM
ap-4476	254	23	)	)	PUNCT
ap-4476	254	24	0	0	NUM
ap-4476	255	1	=	=	SYM
ap-4476	255	2	0	0	NUM
ap-4476	255	3	,	,	PUNCT
ap-4476	255	4	ψ(+	ψ(+	NUM
ap-4476	255	5	)	)	PUNCT
ap-4476	256	1	n	n	CCONJ
ap-4476	256	2	∝	∝	PROPN
ap-4476	256	3	aψ(−	aψ(−	NOUN
ap-4476	256	4	)	)	PUNCT
ap-4476	256	5	n+1	n+1	PROPN
ap-4476	256	6	,	,	PUNCT
ap-4476	256	7	ψ	ψ	X
ap-4476	256	8	(	(	PUNCT
ap-4476	256	9	−	−	NOUN
ap-4476	256	10	)	)	PUNCT
ap-4476	256	11	n+1	n+1	PROPN
ap-4476	256	12	∝	∝	PROPN
ap-4476	256	13	a†ψ(+	a†ψ(+	NOUN
ap-4476	256	14	)	)	PUNCT
ap-4476	256	15	n	n	NOUN
ap-4476	256	16	,	,	PUNCT
ap-4476	256	17	(	(	PUNCT
ap-4476	256	18	65	65	NUM
ap-4476	256	19	)	)	PUNCT
ap-4476	256	20	where	where	SCONJ
ap-4476	256	21	a	a	PRON
ap-4476	256	22	,	,	PUNCT
ap-4476	256	23	a†	a†	NOUN
ap-4476	256	24	and	and	CCONJ
ap-4476	256	25	superpotential	superpotential	ADJ
ap-4476	256	26	w	w	NOUN
ap-4476	256	27	(	(	PUNCT
ap-4476	256	28	x	x	NOUN
ap-4476	256	29	)	)	PUNCT
ap-4476	256	30	are	be	AUX
ap-4476	256	31	defined	define	VERB
ap-4476	256	32	as	as	ADP
ap-4476	256	33	a	a	PRON
ap-4476	256	34	=	=	SYM
ap-4476	256	35	d	d	X
ap-4476	256	36	dx	dx	PROPN
ap-4476	257	1	+	+	PROPN
ap-4476	257	2	w	w	PROPN
ap-4476	257	3	(	(	PUNCT
ap-4476	257	4	x	x	NOUN
ap-4476	257	5	)	)	PUNCT
ap-4476	257	6	,	,	PUNCT
ap-4476	257	7	a†	a†	NOUN
ap-4476	257	8	=	=	SYM
ap-4476	257	9	−	−	PROPN
ap-4476	258	1	d	d	X
ap-4476	258	2	dx	dx	PROPN
ap-4476	259	1	+	+	PROPN
ap-4476	259	2	w	w	PROPN
ap-4476	259	3	(	(	PUNCT
ap-4476	259	4	x	x	NOUN
ap-4476	259	5	)	)	PUNCT
ap-4476	259	6	,	,	PUNCT
ap-4476	259	7	w	w	PROPN
ap-4476	259	8	(	(	PUNCT
ap-4476	259	9	x	x	NOUN
ap-4476	259	10	)	)	PUNCT
ap-4476	259	11	=	=	SYM
ap-4476	260	1	−	−	PROPN
ap-4476	260	2	d	d	X
ap-4476	260	3	dx	dx	PROPN
ap-4476	260	4	lnψ(−	lnψ(−	PROPN
ap-4476	260	5	)	)	PUNCT
ap-4476	260	6	0	0	PUNCT
ap-4476	261	1	(	(	PUNCT
ap-4476	261	2	x	x	NOUN
ap-4476	261	3	)	)	PUNCT
ap-4476	261	4	.	.	PUNCT
ap-4476	262	1	(	(	PUNCT
ap-4476	262	2	66	66	NUM
ap-4476	262	3	)	)	PUNCT
ap-4476	262	4	the	the	DET
ap-4476	262	5	factorized	factorize	VERB
ap-4476	262	6	hamiltonians	hamiltonian	NOUN
ap-4476	262	7	in	in	ADP
ap-4476	262	8	terms	term	NOUN
ap-4476	262	9	of	of	ADP
ap-4476	262	10	a	a	PRON
ap-4476	262	11	and	and	CCONJ
ap-4476	262	12	a†	a†	NOUN
ap-4476	262	13	or	or	CCONJ
ap-4476	262	14	in	in	ADP
ap-4476	262	15	terms	term	NOUN
ap-4476	262	16	of	of	ADP
ap-4476	262	17	partner	partner	NOUN
ap-4476	262	18	potentials	potential	NOUN
ap-4476	262	19	are	be	AUX
ap-4476	262	20	given	give	VERB
ap-4476	262	21	by	by	ADP
ap-4476	262	22	h(−	h(−	PRON
ap-4476	262	23	)	)	PUNCT
ap-4476	262	24	=	=	PUNCT
ap-4476	262	25	a†a	a†a	PART
ap-4476	262	26	=	=	SYM
ap-4476	262	27	−	−	PROPN
ap-4476	262	28	d2	d2	PROPN
ap-4476	262	29	dx2	dx2	PROPN
ap-4476	262	30	+	+	CCONJ
ap-4476	262	31	v	v	PROPN
ap-4476	262	32	(	(	PUNCT
ap-4476	262	33	−)(x)−	−)(x)−	PROPN
ap-4476	262	34	e	e	PROPN
ap-4476	262	35	,	,	PUNCT
ap-4476	262	36	h(+	h(+	NOUN
ap-4476	262	37	)	)	PUNCT
ap-4476	263	1	=	=	PUNCT
ap-4476	263	2	aa†	aa†	PUNCT
ap-4476	263	3	=	=	SYM
ap-4476	264	1	−	−	PROPN
ap-4476	264	2	d2	d2	PROPN
ap-4476	264	3	dx2	dx2	PROPN
ap-4476	264	4	+	+	CCONJ
ap-4476	264	5	v	v	PROPN
ap-4476	264	6	(	(	PUNCT
ap-4476	264	7	+	+	NOUN
ap-4476	264	8	)	)	PUNCT
ap-4476	264	9	(	(	PUNCT
ap-4476	264	10	x)−	x)−	PROPN
ap-4476	264	11	e.	e.	PROPN
ap-4476	264	12	(	(	PUNCT
ap-4476	264	13	67	67	NUM
ap-4476	264	14	)	)	PUNCT
ap-4476	264	15	in	in	ADP
ap-4476	264	16	this	this	DET
ap-4476	264	17	section	section	NOUN
ap-4476	264	18	,	,	PUNCT
ap-4476	264	19	we	we	PRON
ap-4476	264	20	will	will	AUX
ap-4476	264	21	show	show	VERB
ap-4476	264	22	that	that	SCONJ
ap-4476	264	23	various	various	ADJ
ap-4476	264	24	rationally	rationally	ADV
ap-4476	264	25	extended	extended	ADJ
ap-4476	264	26	d	d	ADJ
ap-4476	264	27	-	-	ADJ
ap-4476	264	28	dimensional	dimensional	ADJ
ap-4476	264	29	potentials	potential	NOUN
ap-4476	264	30	satisfy	satisfy	VERB
ap-4476	264	31	such	such	ADJ
ap-4476	264	32	si	si	NOUN
ap-4476	264	33	property	property	NOUN
ap-4476	264	34	.	.	PUNCT
ap-4476	265	1	2for	2for	DET
ap-4476	265	2	radial	radial	ADJ
ap-4476	265	3	oscillator	oscillator	NOUN
ap-4476	265	4	potential	potential	NOUN
ap-4476	265	5	the	the	DET
ap-4476	265	6	factorization	factorization	NOUN
ap-4476	265	7	energy	energy	NOUN
ap-4476	265	8	e0	e0	NOUN
ap-4476	265	9	=	=	PUNCT
ap-4476	266	1	ω(l	ω(l	PROPN
ap-4476	266	2	+	+	CCONJ
ap-4476	266	3	d	d	PROPN
ap-4476	266	4	2	2	NUM
ap-4476	266	5	)	)	PUNCT
ap-4476	266	6	and	and	CCONJ
ap-4476	266	7	for	for	ADP
ap-4476	266	8	gpt	gpt	NOUN
ap-4476	266	9	potential	potential	ADJ
ap-4476	266	10	e0	e0	PROPN
ap-4476	266	11	=	=	PROPN
ap-4476	266	12	−a2	−a2	PROPN
ap-4476	266	13	.	.	PUNCT
ap-4476	267	1	484	484	NUM
ap-4476	267	2	vol	vol	NOUN
ap-4476	267	3	.	.	PUNCT
ap-4476	267	4	57	57	NUM
ap-4476	267	5	no	no	NOUN
ap-4476	267	6	.	.	PUNCT
ap-4476	268	1	6/2017	6/2017	NUM
ap-4476	268	2	rationally	rationally	ADV
ap-4476	268	3	extended	extend	VERB
ap-4476	268	4	shape	shape	NOUN
ap-4476	268	5	invariant	invariant	ADJ
ap-4476	268	6	potentials	potential	VERB
ap-4476	268	7	5.1	5.1	NUM
ap-4476	268	8	.	.	PUNCT
ap-4476	269	1	extended	extend	VERB
ap-4476	269	2	radial	radial	ADJ
ap-4476	269	3	oscillator	oscillator	NOUN
ap-4476	269	4	potentials	potential	VERB
ap-4476	269	5	we	we	PRON
ap-4476	269	6	now	now	ADV
ap-4476	269	7	show	show	VERB
ap-4476	269	8	that	that	SCONJ
ap-4476	269	9	the	the	DET
ap-4476	269	10	extended	extended	ADJ
ap-4476	269	11	radial	radial	ADJ
ap-4476	269	12	oscillator	oscillator	NOUN
ap-4476	269	13	potentials	potential	VERB
ap-4476	269	14	that	that	SCONJ
ap-4476	269	15	we	we	PRON
ap-4476	269	16	have	have	AUX
ap-4476	269	17	obtained	obtain	VERB
ap-4476	269	18	in	in	ADP
ap-4476	269	19	d	d	PROPN
ap-4476	269	20	dimensions	dimension	NOUN
ap-4476	269	21	in	in	ADP
ap-4476	269	22	sec	sec	PROPN
ap-4476	269	23	.	.	PROPN
ap-4476	269	24	4	4	NUM
ap-4476	269	25	provide	provide	VERB
ap-4476	269	26	us	we	PRON
ap-4476	269	27	with	with	ADP
ap-4476	269	28	yet	yet	ADV
ap-4476	269	29	another	another	PRON
ap-4476	269	30	example	example	NOUN
ap-4476	269	31	of	of	ADP
ap-4476	269	32	shape	shape	NOUN
ap-4476	269	33	invariant	invariant	ADJ
ap-4476	269	34	potentials	potential	NOUN
ap-4476	269	35	with	with	ADP
ap-4476	269	36	translation	translation	NOUN
ap-4476	269	37	.	.	PUNCT
ap-4476	270	1	for	for	ADP
ap-4476	270	2	the	the	DET
ap-4476	270	3	radial	radial	ADJ
ap-4476	270	4	oscillator	oscillator	NOUN
ap-4476	270	5	case	case	NOUN
ap-4476	270	6	the	the	DET
ap-4476	270	7	ground	ground	NOUN
ap-4476	270	8	state	state	NOUN
ap-4476	270	9	wave	wave	NOUN
ap-4476	270	10	function	function	NOUN
ap-4476	270	11	χ(−	χ(−	ADP
ap-4476	270	12	)	)	PUNCT
ap-4476	270	13	0,m(r	0,m(r	NUM
ap-4476	270	14	)	)	PUNCT
ap-4476	270	15	is	be	AUX
ap-4476	270	16	given	give	VERB
ap-4476	270	17	by	by	ADP
ap-4476	270	18	(	(	PUNCT
ap-4476	270	19	31	31	NUM
ap-4476	270	20	)	)	PUNCT
ap-4476	270	21	i.e.	i.e.	X
ap-4476	270	22	χ	χ	X
ap-4476	270	23	(	(	PUNCT
ap-4476	270	24	−	−	PROPN
ap-4476	270	25	)	)	PUNCT
ap-4476	270	26	0,m(r	0,m(r	NUM
ap-4476	270	27	)	)	PUNCT
ap-4476	270	28	∝	∝	PROPN
ap-4476	270	29	φ0(r)φm(r	φ0(r)φm(r	NUM
ap-4476	270	30	)	)	PUNCT
ap-4476	270	31	,	,	PUNCT
ap-4476	270	32	(	(	PUNCT
ap-4476	270	33	68	68	NUM
ap-4476	270	34	)	)	PUNCT
ap-4476	270	35	where	where	SCONJ
ap-4476	270	36	φ0(r	φ0(r	NOUN
ap-4476	270	37	)	)	PUNCT
ap-4476	270	38	∝	∝	PROPN
ap-4476	270	39	rl+	rl+	NOUN
ap-4476	270	40	d−1	d−1	PROPN
ap-4476	270	41	2	2	NUM
ap-4476	270	42	exp	exp	NOUN
ap-4476	270	43	(	(	PUNCT
ap-4476	270	44	−ωr	−ωr	PROPN
ap-4476	270	45	2	2	NUM
ap-4476	270	46	4	4	NUM
ap-4476	270	47	)	)	PUNCT
ap-4476	270	48	and	and	CCONJ
ap-4476	270	49	φm(r	φm(r	NUM
ap-4476	270	50	)	)	PUNCT
ap-4476	270	51	∝	∝	PROPN
ap-4476	270	52	l	l	NOUN
ap-4476	270	53	(	(	PUNCT
ap-4476	270	54	l+	l+	NOUN
ap-4476	270	55	d−2	d−2	PROPN
ap-4476	270	56	2	2	NUM
ap-4476	270	57	)	)	PUNCT
ap-4476	270	58	m	m	PROPN
ap-4476	270	59	(	(	PUNCT
ap-4476	270	60	−ωr	−ωr	PROPN
ap-4476	270	61	2	2	NUM
ap-4476	270	62	2	2	NUM
ap-4476	270	63	)	)	PUNCT
ap-4476	270	64	l	l	NOUN
ap-4476	270	65	(	(	PUNCT
ap-4476	270	66	l+	l+	NOUN
ap-4476	270	67	d−4	d−4	PROPN
ap-4476	270	68	2	2	NUM
ap-4476	270	69	)	)	PUNCT
ap-4476	270	70	m	m	VERB
ap-4476	270	71	(	(	PUNCT
ap-4476	270	72	−ωr2	−ωr2	X
ap-4476	270	73	2	2	NUM
ap-4476	270	74	)	)	PUNCT
ap-4476	270	75	.	.	PUNCT
ap-4476	271	1	(	(	PUNCT
ap-4476	271	2	69	69	NUM
ap-4476	271	3	)	)	PUNCT
ap-4476	271	4	here	here	ADV
ap-4476	271	5	we	we	PRON
ap-4476	271	6	see	see	VERB
ap-4476	271	7	that	that	SCONJ
ap-4476	271	8	the	the	DET
ap-4476	271	9	ground	ground	NOUN
ap-4476	271	10	state	state	NOUN
ap-4476	271	11	wave	wave	NOUN
ap-4476	271	12	function	function	NOUN
ap-4476	271	13	of	of	ADP
ap-4476	271	14	the	the	DET
ap-4476	271	15	extended	extend	VERB
ap-4476	271	16	radial	radial	ADJ
ap-4476	271	17	oscillator	oscillator	NOUN
ap-4476	271	18	potential	potential	NOUN
ap-4476	271	19	in	in	ADP
ap-4476	271	20	higher	high	ADJ
ap-4476	271	21	dimensions	dimension	NOUN
ap-4476	271	22	whose	whose	DET
ap-4476	271	23	solutions	solution	NOUN
ap-4476	271	24	are	be	AUX
ap-4476	271	25	in	in	ADP
ap-4476	271	26	terms	term	NOUN
ap-4476	271	27	of	of	ADP
ap-4476	271	28	eops	eop	NOUN
ap-4476	271	29	differs	differ	VERB
ap-4476	271	30	from	from	ADP
ap-4476	271	31	that	that	PRON
ap-4476	271	32	of	of	ADP
ap-4476	271	33	the	the	DET
ap-4476	271	34	usual	usual	ADJ
ap-4476	271	35	potential	potential	NOUN
ap-4476	271	36	by	by	ADP
ap-4476	271	37	an	an	DET
ap-4476	271	38	extra	extra	ADJ
ap-4476	271	39	term	term	NOUN
ap-4476	271	40	φm(r	φm(r	PUNCT
ap-4476	271	41	)	)	PUNCT
ap-4476	271	42	and	and	CCONJ
ap-4476	271	43	the	the	DET
ap-4476	271	44	corresponding	correspond	VERB
ap-4476	271	45	superpotential	superpotential	ADJ
ap-4476	271	46	w	w	NOUN
ap-4476	271	47	(	(	PUNCT
ap-4476	271	48	r)(=	r)(=	PROPN
ap-4476	271	49	−	−	PROPN
ap-4476	272	1	d	d	X
ap-4476	272	2	dr	dr	PROPN
ap-4476	272	3	[	[	X
ap-4476	272	4	lnχ(−	lnχ(−	PROPN
ap-4476	272	5	)	)	PUNCT
ap-4476	272	6	0,m(r	0,m(r	NUM
ap-4476	272	7	)	)	PUNCT
ap-4476	272	8	]	]	PUNCT
ap-4476	272	9	)	)	PUNCT
ap-4476	272	10	is	be	AUX
ap-4476	272	11	given	give	VERB
ap-4476	272	12	by	by	ADP
ap-4476	272	13	w	w	PROPN
ap-4476	272	14	(	(	PUNCT
ap-4476	272	15	r	r	NOUN
ap-4476	272	16	)	)	PUNCT
ap-4476	272	17	=	=	SYM
ap-4476	272	18	w1(r	w1(r	PROPN
ap-4476	272	19	)	)	PUNCT
ap-4476	272	20	+	+	NOUN
ap-4476	272	21	w2(r	w2(r	NOUN
ap-4476	272	22	)	)	PUNCT
ap-4476	272	23	,	,	PUNCT
ap-4476	272	24	(	(	PUNCT
ap-4476	272	25	70	70	NUM
ap-4476	272	26	)	)	PUNCT
ap-4476	272	27	where	where	SCONJ
ap-4476	272	28	w1(r	w1(r	NOUN
ap-4476	272	29	)	)	PUNCT
ap-4476	272	30	=	=	SYM
ap-4476	273	1	−φ	−φ	NOUN
ap-4476	273	2	′	′	NUM
ap-4476	273	3	0(r	0(r	NOUN
ap-4476	273	4	)	)	PUNCT
ap-4476	273	5	φ0(r	φ0(r	NOUN
ap-4476	273	6	)	)	PUNCT
ap-4476	273	7	and	and	CCONJ
ap-4476	273	8	w2(r	w2(r	NOUN
ap-4476	273	9	)	)	PUNCT
ap-4476	273	10	=	=	PUNCT
ap-4476	273	11	−φ	−φ	NOUN
ap-4476	273	12	′	′	NUM
ap-4476	273	13	m(r	m(r	NOUN
ap-4476	273	14	)	)	PUNCT
ap-4476	273	15	φm(r	φm(r	NUM
ap-4476	273	16	)	)	PUNCT
ap-4476	273	17	.	.	PUNCT
ap-4476	274	1	(	(	PUNCT
ap-4476	274	2	71	71	NUM
ap-4476	274	3	)	)	PUNCT
ap-4476	274	4	using	use	VERB
ap-4476	274	5	w	w	PROPN
ap-4476	274	6	(	(	PUNCT
ap-4476	274	7	r	r	NOUN
ap-4476	274	8	)	)	PUNCT
ap-4476	274	9	,	,	PUNCT
ap-4476	274	10	we	we	PRON
ap-4476	274	11	get	get	VERB
ap-4476	274	12	v	v	ADP
ap-4476	274	13	(	(	PUNCT
ap-4476	274	14	−	−	NOUN
ap-4476	274	15	)	)	PUNCT
ap-4476	274	16	m	m	PROPN
ap-4476	274	17	(	(	PUNCT
ap-4476	274	18	r)(=	r)(=	PROPN
ap-4476	274	19	w	w	PROPN
ap-4476	274	20	(	(	PUNCT
ap-4476	274	21	r)2	r)2	X
ap-4476	274	22	−w	−w	ADV
ap-4476	274	23	′(r	′(r	ADV
ap-4476	274	24	)	)	PUNCT
ap-4476	274	25	)	)	PUNCT
ap-4476	274	26	same	same	ADJ
ap-4476	274	27	as	as	ADP
ap-4476	274	28	in	in	ADP
ap-4476	274	29	(	(	PUNCT
ap-4476	274	30	30	30	NUM
ap-4476	274	31	)	)	PUNCT
ap-4476	274	32	and	and	CCONJ
ap-4476	274	33	v	v	X
ap-4476	274	34	(	(	PUNCT
ap-4476	274	35	+	+	NOUN
ap-4476	274	36	)	)	PUNCT
ap-4476	274	37	m	m	VERB
ap-4476	274	38	(	(	PUNCT
ap-4476	274	39	r)(=	r)(=	PROPN
ap-4476	274	40	w	w	PROPN
ap-4476	274	41	(	(	PUNCT
ap-4476	274	42	r)2	r)2	NOUN
ap-4476	274	43	+	+	NOUN
ap-4476	274	44	w	w	NOUN
ap-4476	274	45	′(r	′(r	NOUN
ap-4476	274	46	)	)	PUNCT
ap-4476	274	47	)	)	PUNCT
ap-4476	274	48	is	be	AUX
ap-4476	274	49	given	give	VERB
ap-4476	274	50	by	by	ADP
ap-4476	274	51	v	v	NOUN
ap-4476	274	52	(	(	PUNCT
ap-4476	274	53	+	+	NOUN
ap-4476	274	54	)	)	PUNCT
ap-4476	274	55	m	m	VERB
ap-4476	274	56	(	(	PUNCT
ap-4476	275	1	r	r	NOUN
ap-4476	275	2	)	)	PUNCT
ap-4476	275	3	=	=	NOUN
ap-4476	275	4	v	v	NUM
ap-4476	275	5	d	d	NOUN
ap-4476	275	6	,	,	PUNCT
ap-4476	275	7	l+1	l+1	PROPN
ap-4476	275	8	rad	rad	INTJ
ap-4476	275	9	(	(	PUNCT
ap-4476	275	10	r)−	r)−	PROPN
ap-4476	275	11	ω2r2l	ω2r2l	NUM
ap-4476	275	12	(	(	PUNCT
ap-4476	275	13	l+	l+	X
ap-4476	275	14	d+2	d+2	NOUN
ap-4476	275	15	2	2	X
ap-4476	275	16	)	)	PUNCT
ap-4476	275	17	m−2	m−2	PROPN
ap-4476	275	18	(	(	PUNCT
ap-4476	275	19	−ωr	−ωr	NOUN
ap-4476	275	20	2	2	NUM
ap-4476	275	21	2	2	NUM
ap-4476	275	22	)	)	PUNCT
ap-4476	275	23	l	l	NOUN
ap-4476	275	24	(	(	PUNCT
ap-4476	275	25	l+	l+	NOUN
ap-4476	275	26	d−2	d−2	PROPN
ap-4476	275	27	2	2	NUM
ap-4476	275	28	)	)	PUNCT
ap-4476	275	29	m	m	VERB
ap-4476	275	30	(	(	PUNCT
ap-4476	275	31	−ωr2	−ωr2	X
ap-4476	275	32	2	2	NUM
ap-4476	275	33	)	)	PUNCT
ap-4476	275	34	+	+	CCONJ
ap-4476	276	1	ω(ωr2	ω(ωr2	ADJ
ap-4476	276	2	+	+	CCONJ
ap-4476	276	3	2l	2l	NUM
ap-4476	277	1	+	+	ADJ
ap-4476	277	2	d	d	NOUN
ap-4476	277	3	−	−	ADJ
ap-4476	277	4	2	2	NUM
ap-4476	277	5	)	)	PUNCT
ap-4476	277	6	l	l	NOUN
ap-4476	277	7	(	(	PUNCT
ap-4476	277	8	l+	l+	NOUN
ap-4476	277	9	d	d	NOUN
ap-4476	277	10	2	2	X
ap-4476	277	11	)	)	PUNCT
ap-4476	277	12	m−1	m−1	PROPN
ap-4476	277	13	(	(	PUNCT
ap-4476	277	14	−ωr	−ωr	NOUN
ap-4476	277	15	2	2	NUM
ap-4476	277	16	2	2	NUM
ap-4476	277	17	)	)	PUNCT
ap-4476	277	18	l	l	NOUN
ap-4476	277	19	(	(	PUNCT
ap-4476	277	20	l+	l+	NOUN
ap-4476	277	21	d−2	d−2	PROPN
ap-4476	277	22	2	2	NUM
ap-4476	277	23	)	)	PUNCT
ap-4476	277	24	m	m	VERB
ap-4476	277	25	(	(	PUNCT
ap-4476	277	26	−ωr2	−ωr2	X
ap-4476	277	27	2	2	NUM
ap-4476	277	28	)	)	PUNCT
ap-4476	277	29	+	+	NUM
ap-4476	277	30	2ω2r2	2ω2r2	NUM
ap-4476	277	31	(	(	PUNCT
ap-4476	277	32	l	l	NOUN
ap-4476	277	33	(	(	PUNCT
ap-4476	277	34	l+	l+	NOUN
ap-4476	277	35	d	d	NOUN
ap-4476	277	36	2	2	X
ap-4476	277	37	)	)	PUNCT
ap-4476	277	38	m−1	m−1	PROPN
ap-4476	277	39	(	(	PUNCT
ap-4476	277	40	−ωr	−ωr	NOUN
ap-4476	277	41	2	2	NUM
ap-4476	277	42	2	2	NUM
ap-4476	277	43	)	)	PUNCT
ap-4476	277	44	l	l	NOUN
ap-4476	277	45	(	(	PUNCT
ap-4476	277	46	l+	l+	NOUN
ap-4476	277	47	d−2	d−2	PROPN
ap-4476	277	48	2	2	NUM
ap-4476	277	49	)	)	PUNCT
ap-4476	277	50	m	m	VERB
ap-4476	277	51	(	(	PUNCT
ap-4476	277	52	−ωr2	−ωr2	X
ap-4476	277	53	2	2	NUM
ap-4476	277	54	)	)	PUNCT
ap-4476	277	55	)	)	PUNCT
ap-4476	277	56	2	2	NUM
ap-4476	277	57	−	−	NOUN
ap-4476	277	58	2mω	2mω	ADJ
ap-4476	277	59	−	−	PROPN
ap-4476	277	60	(	(	PUNCT
ap-4476	277	61	l	l	NOUN
ap-4476	278	1	+	+	CCONJ
ap-4476	278	2	d	d	NOUN
ap-4476	278	3	−	−	NOUN
ap-4476	278	4	2	2	NUM
ap-4476	278	5	2	2	NUM
ap-4476	278	6	)	)	PUNCT
ap-4476	278	7	(	(	PUNCT
ap-4476	278	8	72	72	NUM
ap-4476	278	9	)	)	PUNCT
ap-4476	278	10	from	from	ADP
ap-4476	278	11	the	the	DET
ap-4476	278	12	above	above	ADJ
ap-4476	278	13	equations	equation	NOUN
ap-4476	278	14	(	(	PUNCT
ap-4476	278	15	30	30	NUM
ap-4476	278	16	)	)	PUNCT
ap-4476	278	17	and	and	CCONJ
ap-4476	278	18	(	(	PUNCT
ap-4476	278	19	72	72	NUM
ap-4476	278	20	)	)	PUNCT
ap-4476	278	21	,	,	PUNCT
ap-4476	278	22	the	the	DET
ap-4476	278	23	potential	potential	ADJ
ap-4476	278	24	v	v	X
ap-4476	278	25	(	(	PUNCT
ap-4476	278	26	+	+	NOUN
ap-4476	278	27	)	)	PUNCT
ap-4476	278	28	m	m	VERB
ap-4476	278	29	(	(	PUNCT
ap-4476	278	30	r	r	NOUN
ap-4476	278	31	)	)	PUNCT
ap-4476	278	32	can	can	AUX
ap-4476	278	33	be	be	AUX
ap-4476	278	34	obtained	obtain	VERB
ap-4476	278	35	directly	directly	ADV
ap-4476	278	36	by	by	ADP
ap-4476	278	37	replacing	replace	VERB
ap-4476	278	38	l	l	NOUN
ap-4476	278	39	−→	−→	NOUN
ap-4476	278	40	l	l	NOUN
ap-4476	279	1	+	+	CCONJ
ap-4476	279	2	1	1	NUM
ap-4476	279	3	in	in	ADP
ap-4476	279	4	v	v	NUM
ap-4476	279	5	(	(	PUNCT
ap-4476	279	6	−	−	NOUN
ap-4476	279	7	)	)	PUNCT
ap-4476	279	8	m	m	VERB
ap-4476	279	9	(	(	PUNCT
ap-4476	279	10	r	r	NOUN
ap-4476	279	11	)	)	PUNCT
ap-4476	279	12	and	and	CCONJ
ap-4476	279	13	satisfy	satisfy	VERB
ap-4476	279	14	(	(	PUNCT
ap-4476	279	15	63	63	NUM
ap-4476	279	16	)	)	PUNCT
ap-4476	279	17	.	.	PUNCT
ap-4476	280	1	this	this	PRON
ap-4476	280	2	means	mean	VERB
ap-4476	280	3	these	these	DET
ap-4476	280	4	two	two	NUM
ap-4476	280	5	partner	partner	NOUN
ap-4476	280	6	potentials	potential	NOUN
ap-4476	280	7	are	be	AUX
ap-4476	280	8	shape	shape	NOUN
ap-4476	280	9	invariant	invariant	ADJ
ap-4476	280	10	potentials	potential	NOUN
ap-4476	280	11	(	(	PUNCT
ap-4476	280	12	with	with	ADP
ap-4476	280	13	translation	translation	NOUN
ap-4476	280	14	)	)	PUNCT
ap-4476	280	15	.	.	PUNCT
ap-4476	281	1	thus	thus	ADV
ap-4476	281	2	we	we	PRON
ap-4476	281	3	see	see	VERB
ap-4476	281	4	that	that	SCONJ
ap-4476	281	5	the	the	DET
ap-4476	281	6	same	same	ADJ
ap-4476	281	7	oscillator	oscillator	NOUN
ap-4476	281	8	potential	potential	NOUN
ap-4476	281	9	v	v	ADP
ap-4476	281	10	(	(	PUNCT
ap-4476	281	11	r	r	NOUN
ap-4476	281	12	)	)	PUNCT
ap-4476	281	13	=	=	SYM
ap-4476	281	14	1	1	NUM
ap-4476	281	15	4ω	4ω	NOUN
ap-4476	281	16	2r2	2r2	NUM
ap-4476	281	17	,	,	PUNCT
ap-4476	281	18	where	where	SCONJ
ap-4476	281	19	r	r	NOUN
ap-4476	281	20	=	=	PUNCT
ap-4476	281	21	√	√	NUM
ap-4476	281	22	x2	x2	NOUN
ap-4476	281	23	1	1	NUM
ap-4476	282	1	+	+	NUM
ap-4476	282	2	x2	x2	PROPN
ap-4476	282	3	2	2	NUM
ap-4476	282	4	+	+	CCONJ
ap-4476	282	5	·	·	PUNCT
ap-4476	282	6	·	·	PUNCT
ap-4476	282	7	·	·	PUNCT
ap-4476	282	8	+	+	NUM
ap-4476	282	9	x2	x2	PROPN
ap-4476	282	10	d	d	PROPN
ap-4476	282	11	,	,	PUNCT
ap-4476	282	12	gives	give	VERB
ap-4476	282	13	different	different	ADJ
ap-4476	282	14	sips	sip	NOUN
ap-4476	282	15	in	in	ADP
ap-4476	282	16	different	different	ADJ
ap-4476	282	17	dimensions	dimension	NOUN
ap-4476	282	18	.	.	PUNCT
ap-4476	283	1	for	for	ADP
ap-4476	283	2	example	example	NOUN
ap-4476	283	3	:	:	PUNCT
ap-4476	283	4	for	for	ADP
ap-4476	283	5	d	d	PROPN
ap-4476	283	6	=	=	SYM
ap-4476	283	7	2	2	NUM
ap-4476	283	8	v	v	NOUN
ap-4476	283	9	(	(	PUNCT
ap-4476	283	10	−	−	NOUN
ap-4476	283	11	)	)	PUNCT
ap-4476	283	12	m	m	VERB
ap-4476	283	13	(	(	PUNCT
ap-4476	283	14	r	r	NOUN
ap-4476	283	15	)	)	PUNCT
ap-4476	283	16	=	=	SYM
ap-4476	283	17	1	1	NUM
ap-4476	283	18	4ω	4ω	NOUN
ap-4476	283	19	2r2	2r2	NUM
ap-4476	283	20	+	+	CCONJ
ap-4476	283	21	l2	l2	NOUN
ap-4476	283	22	r2	r2	NOUN
ap-4476	283	23	−	−	PROPN
ap-4476	283	24	ω	ω	PROPN
ap-4476	283	25	2r2l	2r2l	NUM
ap-4476	283	26	(	(	PUNCT
ap-4476	283	27	l+1	l+1	NOUN
ap-4476	283	28	)	)	PUNCT
ap-4476	283	29	m−2	m−2	PROPN
ap-4476	283	30	(	(	PUNCT
ap-4476	283	31	−ωr	−ωr	NOUN
ap-4476	283	32	2	2	NUM
ap-4476	283	33	2	2	NUM
ap-4476	283	34	)	)	PUNCT
ap-4476	283	35	l	l	NOUN
ap-4476	283	36	(	(	PUNCT
ap-4476	283	37	l−1	l−1	PROPN
ap-4476	283	38	)	)	PUNCT
ap-4476	283	39	m	m	VERB
ap-4476	283	40	(	(	PUNCT
ap-4476	283	41	−ωr2	−ωr2	X
ap-4476	283	42	2	2	NUM
ap-4476	283	43	)	)	PUNCT
ap-4476	283	44	+	+	CCONJ
ap-4476	283	45	ω(ωr2	ω(ωr2	ADJ
ap-4476	283	46	+	+	CCONJ
ap-4476	283	47	2l	2l	NUM
ap-4476	283	48	−	−	NOUN
ap-4476	283	49	2	2	NUM
ap-4476	283	50	)	)	PUNCT
ap-4476	283	51	l	l	NOUN
ap-4476	283	52	(	(	PUNCT
ap-4476	283	53	l	l	NOUN
ap-4476	283	54	)	)	PUNCT
ap-4476	283	55	m−1(−ωr	m−1(−ωr	NOUN
ap-4476	283	56	2	2	NUM
ap-4476	283	57	2	2	NUM
ap-4476	283	58	)	)	PUNCT
ap-4476	283	59	l	l	NOUN
ap-4476	283	60	(	(	PUNCT
ap-4476	283	61	l−1	l−1	PROPN
ap-4476	283	62	)	)	PUNCT
ap-4476	283	63	m	m	VERB
ap-4476	283	64	(	(	PUNCT
ap-4476	283	65	−ωr2	−ωr2	X
ap-4476	283	66	2	2	NUM
ap-4476	283	67	)	)	PUNCT
ap-4476	283	68	+	+	NUM
ap-4476	283	69	2ω2r2	2ω2r2	NUM
ap-4476	283	70	(	(	PUNCT
ap-4476	283	71	l	l	NOUN
ap-4476	283	72	(	(	PUNCT
ap-4476	283	73	l	l	NOUN
ap-4476	283	74	)	)	PUNCT
ap-4476	283	75	m−1(−ωr	m−1(−ωr	NOUN
ap-4476	283	76	2	2	NUM
ap-4476	283	77	2	2	NUM
ap-4476	283	78	)	)	PUNCT
ap-4476	283	79	l	l	NOUN
ap-4476	283	80	(	(	PUNCT
ap-4476	283	81	l−1	l−1	PROPN
ap-4476	283	82	)	)	PUNCT
ap-4476	283	83	m	m	VERB
ap-4476	283	84	(	(	PUNCT
ap-4476	283	85	−ωr2	−ωr2	X
ap-4476	283	86	2	2	NUM
ap-4476	283	87	)	)	PUNCT
ap-4476	283	88	)	)	PUNCT
ap-4476	283	89	2	2	NUM
ap-4476	283	90	−	−	NOUN
ap-4476	283	91	2mω	2mω	ADJ
ap-4476	283	92	−	−	ADP
ap-4476	283	93	ω(l	ω(l	NUM
ap-4476	283	94	+	+	CCONJ
ap-4476	283	95	1	1	NUM
ap-4476	283	96	)	)	PUNCT
ap-4476	283	97	(	(	PUNCT
ap-4476	283	98	73	73	NUM
ap-4476	283	99	)	)	PUNCT
ap-4476	283	100	and	and	CCONJ
ap-4476	283	101	v	v	X
ap-4476	283	102	(	(	PUNCT
ap-4476	283	103	+	+	NOUN
ap-4476	283	104	)	)	PUNCT
ap-4476	283	105	m	m	VERB
ap-4476	283	106	(	(	PUNCT
ap-4476	283	107	r	r	NOUN
ap-4476	283	108	)	)	PUNCT
ap-4476	283	109	=	=	SYM
ap-4476	283	110	1	1	NUM
ap-4476	283	111	4ω	4ω	NOUN
ap-4476	283	112	2r2	2r2	NUM
ap-4476	283	113	+	+	CCONJ
ap-4476	283	114	(	(	PUNCT
ap-4476	283	115	l	l	NOUN
ap-4476	283	116	+	+	NOUN
ap-4476	283	117	1	1	X
ap-4476	283	118	)	)	PUNCT
ap-4476	283	119	r2	r2	NOUN
ap-4476	283	120	−	−	PROPN
ap-4476	283	121	ω2r2l	ω2r2l	NUM
ap-4476	283	122	(	(	PUNCT
ap-4476	283	123	l+2	l+2	NOUN
ap-4476	283	124	)	)	PUNCT
ap-4476	283	125	m−2	m−2	PROPN
ap-4476	283	126	(	(	PUNCT
ap-4476	283	127	−ωr	−ωr	NOUN
ap-4476	283	128	2	2	NUM
ap-4476	283	129	2	2	NUM
ap-4476	283	130	)	)	PUNCT
ap-4476	283	131	l	l	NOUN
ap-4476	283	132	(	(	PUNCT
ap-4476	283	133	l	l	NOUN
ap-4476	283	134	)	)	PUNCT
ap-4476	283	135	m	m	VERB
ap-4476	283	136	(	(	PUNCT
ap-4476	283	137	−ωr2	−ωr2	X
ap-4476	283	138	2	2	NUM
ap-4476	283	139	)	)	PUNCT
ap-4476	283	140	+	+	CCONJ
ap-4476	283	141	ω(ωr2	ω(ωr2	ADJ
ap-4476	283	142	+	+	CCONJ
ap-4476	283	143	2l	2l	NUM
ap-4476	283	144	)	)	PUNCT
ap-4476	283	145	l	l	NOUN
ap-4476	283	146	(	(	PUNCT
ap-4476	283	147	l+1	l+1	PROPN
ap-4476	283	148	)	)	PUNCT
ap-4476	283	149	m−1	m−1	PROPN
ap-4476	283	150	(	(	PUNCT
ap-4476	283	151	−ωr	−ωr	PROPN
ap-4476	283	152	2	2	NUM
ap-4476	283	153	2	2	NUM
ap-4476	283	154	)	)	PUNCT
ap-4476	283	155	l	l	NOUN
ap-4476	283	156	(	(	PUNCT
ap-4476	283	157	l	l	NOUN
ap-4476	283	158	)	)	PUNCT
ap-4476	283	159	m	m	VERB
ap-4476	283	160	(	(	PUNCT
ap-4476	283	161	−ωr2	−ωr2	X
ap-4476	283	162	2	2	NUM
ap-4476	283	163	)	)	PUNCT
ap-4476	283	164	+	+	NUM
ap-4476	283	165	2ω2r2	2ω2r2	NUM
ap-4476	283	166	(	(	PUNCT
ap-4476	283	167	l	l	NOUN
ap-4476	283	168	(	(	PUNCT
ap-4476	283	169	l+1	l+1	PROPN
ap-4476	283	170	)	)	PUNCT
ap-4476	283	171	m−1	m−1	PROPN
ap-4476	283	172	(	(	PUNCT
ap-4476	283	173	−ωr	−ωr	PROPN
ap-4476	283	174	2	2	NUM
ap-4476	283	175	2	2	NUM
ap-4476	283	176	)	)	PUNCT
ap-4476	283	177	l	l	NOUN
ap-4476	283	178	(	(	PUNCT
ap-4476	283	179	l	l	NOUN
ap-4476	283	180	)	)	PUNCT
ap-4476	283	181	m	m	VERB
ap-4476	283	182	(	(	PUNCT
ap-4476	283	183	−ωr2	−ωr2	X
ap-4476	283	184	2	2	NUM
ap-4476	283	185	)	)	PUNCT
ap-4476	283	186	)	)	PUNCT
ap-4476	283	187	2	2	NUM
ap-4476	283	188	−	−	NOUN
ap-4476	283	189	2mω	2mω	ADJ
ap-4476	283	190	−	−	PROPN
ap-4476	283	191	ωl	ωl	NOUN
ap-4476	283	192	.	.	PUNCT
ap-4476	284	1	(	(	PUNCT
ap-4476	284	2	74	74	NUM
ap-4476	284	3	)	)	PUNCT
ap-4476	284	4	for	for	ADP
ap-4476	284	5	d	d	NOUN
ap-4476	284	6	=	=	SYM
ap-4476	284	7	4	4	NUM
ap-4476	284	8	v	v	NOUN
ap-4476	284	9	(	(	PUNCT
ap-4476	284	10	−	−	NOUN
ap-4476	284	11	)	)	PUNCT
ap-4476	284	12	m	m	VERB
ap-4476	284	13	(	(	PUNCT
ap-4476	284	14	r	r	NOUN
ap-4476	284	15	)	)	PUNCT
ap-4476	284	16	=	=	SYM
ap-4476	284	17	1	1	NUM
ap-4476	284	18	4ω	4ω	NOUN
ap-4476	284	19	2r2	2r2	NUM
ap-4476	285	1	+	+	CCONJ
ap-4476	285	2	l(l	l(l	ADJ
ap-4476	285	3	+	+	CCONJ
ap-4476	285	4	2	2	X
ap-4476	285	5	)	)	PUNCT
ap-4476	285	6	r2	r2	NOUN
ap-4476	285	7	−	−	PROPN
ap-4476	285	8	ω2r2l	ω2r2l	NUM
ap-4476	285	9	(	(	PUNCT
ap-4476	285	10	l+2	l+2	NOUN
ap-4476	285	11	)	)	PUNCT
ap-4476	285	12	m−2	m−2	PROPN
ap-4476	285	13	(	(	PUNCT
ap-4476	285	14	−ωr	−ωr	NOUN
ap-4476	285	15	2	2	NUM
ap-4476	285	16	2	2	NUM
ap-4476	285	17	)	)	PUNCT
ap-4476	285	18	l	l	NOUN
ap-4476	285	19	(	(	PUNCT
ap-4476	285	20	l	l	NOUN
ap-4476	285	21	)	)	PUNCT
ap-4476	285	22	m	m	VERB
ap-4476	285	23	(	(	PUNCT
ap-4476	285	24	−ωr2	−ωr2	X
ap-4476	285	25	2	2	NUM
ap-4476	285	26	)	)	PUNCT
ap-4476	285	27	+	+	CCONJ
ap-4476	285	28	ω(ωr2	ω(ωr2	ADJ
ap-4476	285	29	+	+	CCONJ
ap-4476	285	30	2l	2l	NUM
ap-4476	285	31	)	)	PUNCT
ap-4476	285	32	l	l	NOUN
ap-4476	285	33	(	(	PUNCT
ap-4476	285	34	l+1	l+1	PROPN
ap-4476	285	35	)	)	PUNCT
ap-4476	285	36	m−1	m−1	PROPN
ap-4476	285	37	(	(	PUNCT
ap-4476	285	38	−ωr	−ωr	PROPN
ap-4476	285	39	2	2	NUM
ap-4476	285	40	2	2	NUM
ap-4476	285	41	)	)	PUNCT
ap-4476	285	42	l	l	NOUN
ap-4476	285	43	(	(	PUNCT
ap-4476	285	44	l	l	NOUN
ap-4476	285	45	)	)	PUNCT
ap-4476	285	46	m	m	VERB
ap-4476	285	47	(	(	PUNCT
ap-4476	285	48	−ωr2	−ωr2	X
ap-4476	285	49	2	2	NUM
ap-4476	285	50	)	)	PUNCT
ap-4476	285	51	+	+	NUM
ap-4476	285	52	2ω2r2	2ω2r2	NUM
ap-4476	285	53	(	(	PUNCT
ap-4476	285	54	l	l	NOUN
ap-4476	285	55	(	(	PUNCT
ap-4476	285	56	l+2	l+2	NOUN
ap-4476	285	57	)	)	PUNCT
ap-4476	285	58	m−1	m−1	PROPN
ap-4476	285	59	(	(	PUNCT
ap-4476	285	60	−ωr	−ωr	PROPN
ap-4476	285	61	2	2	NUM
ap-4476	285	62	2	2	NUM
ap-4476	285	63	)	)	PUNCT
ap-4476	285	64	l	l	NOUN
ap-4476	285	65	(	(	PUNCT
ap-4476	285	66	l	l	NOUN
ap-4476	285	67	)	)	PUNCT
ap-4476	285	68	m	m	VERB
ap-4476	285	69	(	(	PUNCT
ap-4476	285	70	−ωr2	−ωr2	X
ap-4476	285	71	2	2	NUM
ap-4476	285	72	)	)	PUNCT
ap-4476	285	73	)	)	PUNCT
ap-4476	285	74	2	2	NUM
ap-4476	285	75	−	−	NOUN
ap-4476	285	76	2mω	2mω	ADJ
ap-4476	285	77	−	−	ADP
ap-4476	285	78	ω(l	ω(l	NUM
ap-4476	285	79	+	+	CCONJ
ap-4476	285	80	2	2	NUM
ap-4476	285	81	)	)	PUNCT
ap-4476	285	82	(	(	PUNCT
ap-4476	285	83	75	75	NUM
ap-4476	285	84	)	)	PUNCT
ap-4476	285	85	and	and	CCONJ
ap-4476	285	86	v	v	X
ap-4476	285	87	(	(	PUNCT
ap-4476	285	88	+	+	NOUN
ap-4476	285	89	)	)	PUNCT
ap-4476	285	90	m	m	VERB
ap-4476	285	91	(	(	PUNCT
ap-4476	285	92	r	r	NOUN
ap-4476	285	93	)	)	PUNCT
ap-4476	285	94	=	=	SYM
ap-4476	285	95	1	1	NUM
ap-4476	285	96	4ω	4ω	NOUN
ap-4476	285	97	2r2	2r2	NUM
ap-4476	285	98	+	+	CCONJ
ap-4476	285	99	(	(	PUNCT
ap-4476	285	100	l	l	NOUN
ap-4476	285	101	+	+	NOUN
ap-4476	285	102	1)(l	1)(l	NUM
ap-4476	285	103	+	+	CCONJ
ap-4476	285	104	3	3	NUM
ap-4476	285	105	)	)	PUNCT
ap-4476	285	106	r2	r2	PROPN
ap-4476	285	107	−ω2r2l	−ω2r2l	X
ap-4476	285	108	(	(	PUNCT
ap-4476	285	109	l+3	l+3	X
ap-4476	285	110	)	)	PUNCT
ap-4476	285	111	m−2	m−2	PROPN
ap-4476	285	112	(	(	PUNCT
ap-4476	285	113	−ωr	−ωr	NOUN
ap-4476	285	114	2	2	NUM
ap-4476	285	115	2	2	NUM
ap-4476	285	116	)	)	PUNCT
ap-4476	285	117	l	l	NOUN
ap-4476	285	118	(	(	PUNCT
ap-4476	285	119	l+1	l+1	PROPN
ap-4476	285	120	)	)	PUNCT
ap-4476	285	121	m	m	VERB
ap-4476	285	122	(	(	PUNCT
ap-4476	285	123	−ωr2	−ωr2	X
ap-4476	285	124	2	2	NUM
ap-4476	285	125	)	)	PUNCT
ap-4476	286	1	+	+	PUNCT
ap-4476	286	2	ω(ωr2	ω(ωr2	ADJ
ap-4476	286	3	+	+	ADJ
ap-4476	286	4	2l+2	2l+2	NOUN
ap-4476	286	5	)	)	PUNCT
ap-4476	286	6	l	l	NOUN
ap-4476	286	7	(	(	PUNCT
ap-4476	286	8	l+2	l+2	NOUN
ap-4476	286	9	)	)	PUNCT
ap-4476	286	10	m−1	m−1	PROPN
ap-4476	286	11	(	(	PUNCT
ap-4476	286	12	−ωr	−ωr	PROPN
ap-4476	286	13	2	2	NUM
ap-4476	286	14	2	2	NUM
ap-4476	286	15	)	)	PUNCT
ap-4476	286	16	l	l	NOUN
ap-4476	286	17	(	(	PUNCT
ap-4476	286	18	l+1	l+1	PROPN
ap-4476	286	19	)	)	PUNCT
ap-4476	286	20	m	m	VERB
ap-4476	286	21	(	(	PUNCT
ap-4476	286	22	−ωr2	−ωr2	X
ap-4476	286	23	2	2	NUM
ap-4476	286	24	)	)	PUNCT
ap-4476	286	25	+2ω2r2	+2ω2r2	PROPN
ap-4476	287	1	(	(	PUNCT
ap-4476	287	2	l	l	NOUN
ap-4476	287	3	(	(	PUNCT
ap-4476	287	4	l+2	l+2	NOUN
ap-4476	287	5	)	)	PUNCT
ap-4476	287	6	m−1	m−1	PROPN
ap-4476	287	7	(	(	PUNCT
ap-4476	287	8	−ωr	−ωr	PROPN
ap-4476	287	9	2	2	NUM
ap-4476	287	10	2	2	NUM
ap-4476	287	11	)	)	PUNCT
ap-4476	287	12	l	l	NOUN
ap-4476	287	13	(	(	PUNCT
ap-4476	287	14	l+1	l+1	PROPN
ap-4476	287	15	)	)	PUNCT
ap-4476	287	16	m	m	VERB
ap-4476	287	17	(	(	PUNCT
ap-4476	287	18	−ωr2	−ωr2	X
ap-4476	287	19	2	2	NUM
ap-4476	287	20	)	)	PUNCT
ap-4476	287	21	)	)	PUNCT
ap-4476	287	22	2	2	NUM
ap-4476	287	23	−	−	NOUN
ap-4476	287	24	2mω	2mω	ADJ
ap-4476	287	25	−	−	PROPN
ap-4476	287	26	(	(	PUNCT
ap-4476	287	27	l	l	NOUN
ap-4476	287	28	+	+	NOUN
ap-4476	287	29	1	1	NUM
ap-4476	287	30	)	)	PUNCT
ap-4476	287	31	.	.	PUNCT
ap-4476	288	1	(	(	PUNCT
ap-4476	288	2	76	76	NUM
ap-4476	288	3	)	)	PUNCT
ap-4476	288	4	485	485	NUM
ap-4476	288	5	r.	r.	PROPN
ap-4476	288	6	k.	k.	PROPN
ap-4476	288	7	yadav	yadav	PROPN
ap-4476	288	8	,	,	PUNCT
ap-4476	288	9	n.	n.	PROPN
ap-4476	288	10	kumari	kumari	PROPN
ap-4476	288	11	,	,	PUNCT
ap-4476	288	12	a.	a.	PROPN
ap-4476	288	13	khare	khare	PROPN
ap-4476	288	14	,	,	PUNCT
ap-4476	288	15	b.	b.	PROPN
ap-4476	288	16	p.	p.	PROPN
ap-4476	288	17	mandal	mandal	PROPN
ap-4476	288	18	acta	acta	PROPN
ap-4476	288	19	polytechnica	polytechnica	PROPN
ap-4476	288	20	5.2	5.2	NUM
ap-4476	288	21	.	.	PUNCT
ap-4476	289	1	extended	extend	VERB
ap-4476	289	2	pöschl	pöschl	NOUN
ap-4476	289	3	-	-	PUNCT
ap-4476	289	4	teller	teller	NOUN
ap-4476	289	5	potentials	potential	NOUN
ap-4476	289	6	let	let	VERB
ap-4476	289	7	us	we	PRON
ap-4476	289	8	first	first	ADV
ap-4476	289	9	discuss	discuss	VERB
ap-4476	289	10	the	the	DET
ap-4476	289	11	extended	extended	ADJ
ap-4476	289	12	gpt	gpt	NOUN
ap-4476	289	13	(	(	PUNCT
ap-4476	289	14	with	with	ADP
ap-4476	289	15	l	l	NOUN
ap-4476	289	16	=	=	SYM
ap-4476	289	17	0	0	NUM
ap-4476	289	18	)	)	PUNCT
ap-4476	289	19	as	as	SCONJ
ap-4476	289	20	discussed	discuss	VERB
ap-4476	289	21	in	in	ADP
ap-4476	289	22	sec	sec	PROPN
ap-4476	289	23	.	.	PROPN
ap-4476	289	24	4.2	4.2	NUM
ap-4476	289	25	.	.	PUNCT
ap-4476	290	1	in	in	ADP
ap-4476	290	2	this	this	DET
ap-4476	290	3	case	case	NOUN
ap-4476	290	4	,	,	PUNCT
ap-4476	290	5	the	the	DET
ap-4476	290	6	ground	ground	NOUN
ap-4476	290	7	state	state	NOUN
ap-4476	290	8	wave	wave	NOUN
ap-4476	290	9	function	function	NOUN
ap-4476	290	10	χ(−	χ(−	ADP
ap-4476	290	11	)	)	PUNCT
ap-4476	290	12	0,m(r	0,m(r	NUM
ap-4476	290	13	)	)	PUNCT
ap-4476	290	14	is	be	AUX
ap-4476	290	15	given	give	VERB
ap-4476	290	16	by	by	ADP
ap-4476	290	17	(	(	PUNCT
ap-4476	290	18	45	45	NUM
ap-4476	290	19	)	)	PUNCT
ap-4476	290	20	i.e.	i.e.	X
ap-4476	290	21	χ	χ	X
ap-4476	290	22	(	(	PUNCT
ap-4476	290	23	−	−	PROPN
ap-4476	290	24	)	)	PUNCT
ap-4476	290	25	0,m(r	0,m(r	NUM
ap-4476	290	26	)	)	PUNCT
ap-4476	290	27	∝	∝	PROPN
ap-4476	290	28	φ0(r)φm(r	φ0(r)φm(r	NUM
ap-4476	290	29	)	)	PUNCT
ap-4476	290	30	(	(	PUNCT
ap-4476	290	31	77	77	NUM
ap-4476	290	32	)	)	PUNCT
ap-4476	290	33	where	where	SCONJ
ap-4476	290	34	φ0(r	φ0(r	NOUN
ap-4476	290	35	)	)	PUNCT
ap-4476	290	36	∝	∝	PROPN
ap-4476	290	37	(	(	PUNCT
ap-4476	290	38	cosh	cosh	NOUN
ap-4476	290	39	r	r	NOUN
ap-4476	290	40	−	−	PROPN
ap-4476	290	41	1)(b−a)/2(cosh	1)(b−a)/2(cosh	NUM
ap-4476	290	42	r	r	NOUN
ap-4476	290	43	+	+	NUM
ap-4476	290	44	1)−(b+a)/2	1)−(b+a)/2	NUM
ap-4476	290	45	and	and	CCONJ
ap-4476	290	46	φm(r	φm(r	NUM
ap-4476	290	47	)	)	PUNCT
ap-4476	290	48	∝	∝	PROPN
ap-4476	290	49	p	p	X
ap-4476	290	50	(	(	PUNCT
ap-4476	290	51	−b+a−	−b+a−	NUM
ap-4476	290	52	3	3	NUM
ap-4476	290	53	2	2	NUM
ap-4476	290	54	,	,	PUNCT
ap-4476	290	55	−b−a−	−b−a−	X
ap-4476	290	56	1	1	NUM
ap-4476	290	57	2	2	NUM
ap-4476	290	58	)	)	PUNCT
ap-4476	290	59	m	m	PROPN
ap-4476	290	60	(	(	PUNCT
ap-4476	290	61	cosh	cosh	PROPN
ap-4476	290	62	r	r	NOUN
ap-4476	290	63	)	)	PUNCT
ap-4476	290	64	p	p	NOUN
ap-4476	290	65	(	(	PUNCT
ap-4476	290	66	−b+a−	−b+a−	NUM
ap-4476	290	67	1	1	NUM
ap-4476	290	68	2	2	NUM
ap-4476	290	69	,	,	PUNCT
ap-4476	290	70	−b−a−	−b−a−	X
ap-4476	290	71	3	3	NUM
ap-4476	290	72	2	2	NUM
ap-4476	290	73	)	)	PUNCT
ap-4476	290	74	m	m	PROPN
ap-4476	290	75	(	(	PUNCT
ap-4476	290	76	cosh	cosh	PROPN
ap-4476	290	77	r	r	NOUN
ap-4476	290	78	)	)	PUNCT
ap-4476	290	79	.	.	PUNCT
ap-4476	291	1	(	(	PUNCT
ap-4476	291	2	78	78	X
ap-4476	291	3	)	)	PUNCT
ap-4476	291	4	it	it	PRON
ap-4476	291	5	is	be	AUX
ap-4476	291	6	easy	easy	ADJ
ap-4476	291	7	to	to	PART
ap-4476	291	8	check	check	VERB
ap-4476	291	9	that	that	PRON
ap-4476	291	10	due	due	ADP
ap-4476	291	11	to	to	ADP
ap-4476	291	12	the	the	DET
ap-4476	291	13	extra	extra	ADJ
ap-4476	291	14	centrifugal	centrifugal	ADJ
ap-4476	291	15	term	term	NOUN
ap-4476	291	16	(	(	PUNCT
ap-4476	291	17	d	d	NOUN
ap-4476	291	18	−	−	PROPN
ap-4476	291	19	1)(d	1)(d	NUM
ap-4476	291	20	−	−	NOUN
ap-4476	291	21	3)/4r2	3)/4r2	NUM
ap-4476	291	22	,	,	PUNCT
ap-4476	291	23	the	the	DET
ap-4476	291	24	corresponding	corresponding	ADJ
ap-4476	291	25	potentials	potential	NOUN
ap-4476	291	26	in	in	ADP
ap-4476	291	27	d	d	PROPN
ap-4476	291	28	dimensions	dimension	NOUN
ap-4476	291	29	are	be	AUX
ap-4476	291	30	not	not	PART
ap-4476	291	31	shape	shape	NOUN
ap-4476	291	32	invariant	invariant	ADJ
ap-4476	291	33	except	except	SCONJ
ap-4476	291	34	when	when	SCONJ
ap-4476	291	35	d	d	PROPN
ap-4476	291	36	=	=	SYM
ap-4476	291	37	3	3	X
ap-4476	291	38	.	.	PUNCT
ap-4476	292	1	however	however	ADV
ap-4476	292	2	,	,	PUNCT
ap-4476	292	3	if	if	SCONJ
ap-4476	292	4	we	we	PRON
ap-4476	292	5	consider	consider	VERB
ap-4476	292	6	the	the	DET
ap-4476	292	7	approximate	approximate	ADJ
ap-4476	292	8	extended	extended	ADJ
ap-4476	292	9	pöschl	pöschl	NOUN
ap-4476	292	10	-	-	PUNCT
ap-4476	292	11	teller	teller	NOUN
ap-4476	292	12	potentials	potential	NOUN
ap-4476	292	13	as	as	SCONJ
ap-4476	292	14	discussed	discuss	VERB
ap-4476	292	15	in	in	ADP
ap-4476	292	16	sec	sec	PROPN
ap-4476	292	17	.	.	PROPN
ap-4476	292	18	4.2.1	4.2.1	NUM
ap-4476	292	19	,	,	PUNCT
ap-4476	292	20	then	then	ADV
ap-4476	292	21	as	as	SCONJ
ap-4476	292	22	we	we	PRON
ap-4476	292	23	now	now	ADV
ap-4476	292	24	show	show	VERB
ap-4476	292	25	,	,	PUNCT
ap-4476	292	26	one	one	PRON
ap-4476	292	27	gets	get	VERB
ap-4476	292	28	shape	shape	NOUN
ap-4476	292	29	invariant	invariant	ADJ
ap-4476	292	30	potentials	potential	NOUN
ap-4476	292	31	with	with	ADP
ap-4476	292	32	translation	translation	NOUN
ap-4476	292	33	.	.	PUNCT
ap-4476	293	1	in	in	ADP
ap-4476	293	2	that	that	DET
ap-4476	293	3	case	case	NOUN
ap-4476	293	4	the	the	DET
ap-4476	293	5	corresponding	correspond	VERB
ap-4476	293	6	superpotential	superpotential	ADJ
ap-4476	293	7	(	(	PUNCT
ap-4476	293	8	w	w	NOUN
ap-4476	293	9	(	(	PUNCT
ap-4476	293	10	r	r	NOUN
ap-4476	293	11	)	)	PUNCT
ap-4476	293	12	=	=	SYM
ap-4476	294	1	−	−	PROPN
ap-4476	294	2	d	d	X
ap-4476	294	3	dr	dr	PROPN
ap-4476	295	1	[	[	X
ap-4476	295	2	lnχ(−	lnχ(−	PROPN
ap-4476	295	3	)	)	PUNCT
ap-4476	295	4	0,m(r	0,m(r	NUM
ap-4476	295	5	)	)	PUNCT
ap-4476	295	6	]	]	PUNCT
ap-4476	295	7	)	)	PUNCT
ap-4476	295	8	is	be	AUX
ap-4476	295	9	given	give	VERB
ap-4476	295	10	by	by	ADP
ap-4476	295	11	w	w	PROPN
ap-4476	295	12	(	(	PUNCT
ap-4476	295	13	r	r	NOUN
ap-4476	295	14	)	)	PUNCT
ap-4476	295	15	=	=	SYM
ap-4476	295	16	w1(r	w1(r	PROPN
ap-4476	295	17	)	)	PUNCT
ap-4476	295	18	+	+	NOUN
ap-4476	295	19	w2(r	w2(r	NOUN
ap-4476	295	20	)	)	PUNCT
ap-4476	295	21	,	,	PUNCT
ap-4476	295	22	(	(	PUNCT
ap-4476	295	23	79	79	NUM
ap-4476	295	24	)	)	PUNCT
ap-4476	295	25	where	where	SCONJ
ap-4476	295	26	w1(r	w1(r	NOUN
ap-4476	295	27	)	)	PUNCT
ap-4476	295	28	=	=	SYM
ap-4476	296	1	−φ	−φ	NOUN
ap-4476	296	2	′	′	NUM
ap-4476	296	3	0(r	0(r	NOUN
ap-4476	296	4	)	)	PUNCT
ap-4476	296	5	φ0(r	φ0(r	NOUN
ap-4476	296	6	)	)	PUNCT
ap-4476	296	7	and	and	CCONJ
ap-4476	296	8	w2(r	w2(r	NOUN
ap-4476	296	9	)	)	PUNCT
ap-4476	296	10	=	=	PUNCT
ap-4476	296	11	−φ	−φ	NOUN
ap-4476	296	12	′	′	NUM
ap-4476	296	13	m(r	m(r	NOUN
ap-4476	296	14	)	)	PUNCT
ap-4476	296	15	φm(r	φm(r	NUM
ap-4476	296	16	)	)	PUNCT
ap-4476	296	17	.	.	PUNCT
ap-4476	297	1	(	(	PUNCT
ap-4476	297	2	80	80	NUM
ap-4476	297	3	)	)	PUNCT
ap-4476	297	4	using	use	VERB
ap-4476	297	5	w	w	PROPN
ap-4476	297	6	(	(	PUNCT
ap-4476	297	7	r	r	NOUN
ap-4476	297	8	)	)	PUNCT
ap-4476	297	9	,	,	PUNCT
ap-4476	297	10	the	the	DET
ap-4476	297	11	partner	partner	NOUN
ap-4476	297	12	potential	potential	NOUN
ap-4476	297	13	v	v	ADP
ap-4476	297	14	(	(	PUNCT
ap-4476	297	15	−	−	NOUN
ap-4476	297	16	)	)	PUNCT
ap-4476	297	17	eff	eff	PROPN
ap-4476	297	18	,	,	PUNCT
ap-4476	297	19	m(r	m(r	PROPN
ap-4476	297	20	)	)	PUNCT
ap-4476	297	21	is	be	AUX
ap-4476	297	22	same	same	ADJ
ap-4476	297	23	as	as	SCONJ
ap-4476	297	24	given	give	VERB
ap-4476	297	25	in	in	ADP
ap-4476	297	26	(	(	PUNCT
ap-4476	297	27	54	54	NUM
ap-4476	297	28	)	)	PUNCT
ap-4476	297	29	and	and	CCONJ
ap-4476	297	30	v	v	X
ap-4476	297	31	(	(	PUNCT
ap-4476	297	32	+	+	NOUN
ap-4476	297	33	)	)	PUNCT
ap-4476	297	34	eff	eff	PROPN
ap-4476	297	35	,	,	PUNCT
ap-4476	297	36	m(r	m(r	PROPN
ap-4476	297	37	)	)	PUNCT
ap-4476	297	38	is	be	AUX
ap-4476	297	39	obtained	obtain	VERB
ap-4476	297	40	by	by	ADP
ap-4476	297	41	using	use	VERB
ap-4476	297	42	v	v	NOUN
ap-4476	297	43	(	(	PUNCT
ap-4476	297	44	+	+	NOUN
ap-4476	297	45	)	)	PUNCT
ap-4476	297	46	m	m	VERB
ap-4476	297	47	(	(	PUNCT
ap-4476	297	48	r	r	NOUN
ap-4476	297	49	)	)	PUNCT
ap-4476	297	50	=	=	PUNCT
ap-4476	298	1	w	w	PROPN
ap-4476	298	2	2(r	2(r	NUM
ap-4476	298	3	)	)	PUNCT
ap-4476	299	1	+	+	ADJ
ap-4476	299	2	w	w	NOUN
ap-4476	299	3	′(r	′(r	ADV
ap-4476	299	4	)	)	PUNCT
ap-4476	299	5	or	or	CCONJ
ap-4476	299	6	simply	simply	ADV
ap-4476	299	7	by	by	ADP
ap-4476	299	8	replacing	replace	VERB
ap-4476	299	9	a′	a′	NOUN
ap-4476	299	10	−→	−→	NOUN
ap-4476	299	11	a′	a′	PROPN
ap-4476	299	12	−	−	PROPN
ap-4476	299	13	1	1	NUM
ap-4476	299	14	in	in	ADP
ap-4476	299	15	v	v	NUM
ap-4476	299	16	(	(	PUNCT
ap-4476	299	17	−	−	NOUN
ap-4476	299	18	)	)	PUNCT
ap-4476	299	19	eff	eff	PROPN
ap-4476	299	20	,	,	PUNCT
ap-4476	299	21	m(r	m(r	PROPN
ap-4476	299	22	)	)	PUNCT
ap-4476	299	23	.	.	PUNCT
ap-4476	300	1	hence	hence	ADV
ap-4476	300	2	the	the	DET
ap-4476	300	3	potentials	potential	NOUN
ap-4476	300	4	v	v	X
ap-4476	300	5	(	(	PUNCT
ap-4476	300	6	−	−	NOUN
ap-4476	300	7	)	)	PUNCT
ap-4476	300	8	eff	eff	PROPN
ap-4476	300	9	,	,	PUNCT
ap-4476	300	10	m(r	m(r	PROPN
ap-4476	300	11	)	)	PUNCT
ap-4476	300	12	is	be	AUX
ap-4476	300	13	shape	shape	ADJ
ap-4476	300	14	invariant	invariant	ADJ
ap-4476	300	15	potential	potential	NOUN
ap-4476	300	16	(	(	PUNCT
ap-4476	300	17	with	with	ADP
ap-4476	300	18	translation	translation	NOUN
ap-4476	300	19	)	)	PUNCT
ap-4476	300	20	and	and	CCONJ
ap-4476	300	21	satisfy	satisfy	NOUN
ap-4476	300	22	(	(	PUNCT
ap-4476	300	23	63	63	NUM
ap-4476	300	24	)	)	PUNCT
ap-4476	300	25	for	for	ADP
ap-4476	300	26	any	any	DET
ap-4476	300	27	arbitrary	arbitrary	ADJ
ap-4476	300	28	values	value	NOUN
ap-4476	300	29	of	of	ADP
ap-4476	300	30	d	d	PROPN
ap-4476	300	31	and	and	CCONJ
ap-4476	300	32	`	`	PUNCT
ap-4476	300	33	.	.	PUNCT
ap-4476	301	1	for	for	ADP
ap-4476	301	2	a	a	DET
ap-4476	301	3	check	check	NOUN
ap-4476	301	4	we	we	PRON
ap-4476	301	5	are	be	AUX
ap-4476	301	6	giving	give	VERB
ap-4476	301	7	here	here	ADV
ap-4476	301	8	some	some	DET
ap-4476	301	9	simple	simple	ADJ
ap-4476	301	10	cases	case	NOUN
ap-4476	301	11	for	for	ADP
ap-4476	301	12	v	v	NOUN
ap-4476	301	13	(	(	PUNCT
ap-4476	301	14	−	−	NOUN
ap-4476	301	15	)	)	PUNCT
ap-4476	301	16	eff	eff	PROPN
ap-4476	301	17	,	,	PUNCT
ap-4476	301	18	m(r	m(r	PROPN
ap-4476	301	19	)	)	PUNCT
ap-4476	301	20	and	and	CCONJ
ap-4476	301	21	v	v	X
ap-4476	301	22	(	(	PUNCT
ap-4476	301	23	+	+	NOUN
ap-4476	301	24	)	)	PUNCT
ap-4476	301	25	eff	eff	PROPN
ap-4476	301	26	,	,	PUNCT
ap-4476	301	27	m(r	m(r	PROPN
ap-4476	301	28	)	)	PUNCT
ap-4476	301	29	.	.	PUNCT
ap-4476	302	1	case	case	NOUN
ap-4476	302	2	(	(	PUNCT
ap-4476	302	3	a	a	NOUN
ap-4476	302	4	)	)	PUNCT
ap-4476	302	5	.	.	PUNCT
ap-4476	303	1	for	for	ADP
ap-4476	303	2	m	m	PROPN
ap-4476	303	3	=	=	SYM
ap-4476	303	4	0	0	NUM
ap-4476	303	5	and	and	CCONJ
ap-4476	303	6	any	any	DET
ap-4476	303	7	arbitrary	arbitrary	ADJ
ap-4476	303	8	values	value	NOUN
ap-4476	303	9	of	of	ADP
ap-4476	303	10	d	d	PROPN
ap-4476	303	11	and	and	CCONJ
ap-4476	303	12	`	`	PUNCT
ap-4476	303	13	,	,	PUNCT
ap-4476	303	14	(	(	PUNCT
ap-4476	303	15	54	54	NUM
ap-4476	303	16	)	)	PUNCT
ap-4476	303	17	gives	give	VERB
ap-4476	303	18	v	v	NOUN
ap-4476	303	19	(	(	PUNCT
ap-4476	303	20	−	−	NOUN
ap-4476	303	21	)	)	PUNCT
ap-4476	303	22	eff,0(r	eff,0(r	NUM
ap-4476	303	23	)	)	PUNCT
ap-4476	303	24	as	as	ADP
ap-4476	303	25	v	v	X
ap-4476	303	26	(	(	PUNCT
ap-4476	303	27	−	−	NOUN
ap-4476	303	28	)	)	PUNCT
ap-4476	303	29	eff,0(r	eff,0(r	NUM
ap-4476	303	30	)	)	PUNCT
ap-4476	304	1	=	=	PRON
ap-4476	304	2	(	(	PUNCT
ap-4476	304	3	b′2	b′2	NOUN
ap-4476	305	1	+	+	NOUN
ap-4476	305	2	a′(a′	a′(a′	NOUN
ap-4476	305	3	+	+	NOUN
ap-4476	305	4	1	1	NUM
ap-4476	305	5	)	)	PUNCT
ap-4476	305	6	)	)	PUNCT
ap-4476	306	1	cosech2	cosech2	NOUN
ap-4476	306	2	r	r	NOUN
ap-4476	306	3	−b′(2a′	−b′(2a′	NOUN
ap-4476	306	4	+	+	CCONJ
ap-4476	306	5	1	1	X
ap-4476	306	6	)	)	PUNCT
ap-4476	306	7	cosech	cosech	NOUN
ap-4476	306	8	r	r	NOUN
ap-4476	306	9	+	+	NOUN
ap-4476	306	10	a′2	a′2	ADJ
ap-4476	306	11	coth	coth	NOUN
ap-4476	306	12	r	r	NOUN
ap-4476	306	13	(	(	PUNCT
ap-4476	306	14	81	81	NUM
ap-4476	306	15	)	)	PUNCT
ap-4476	306	16	and	and	CCONJ
ap-4476	306	17	the	the	DET
ap-4476	306	18	partner	partner	NOUN
ap-4476	306	19	potential	potential	NOUN
ap-4476	306	20	v	v	ADP
ap-4476	306	21	(	(	PUNCT
ap-4476	306	22	+	+	NOUN
ap-4476	306	23	)	)	PUNCT
ap-4476	306	24	eff,0(r	eff,0(r	PRON
ap-4476	306	25	)	)	PUNCT
ap-4476	306	26	is	be	AUX
ap-4476	306	27	given	give	VERB
ap-4476	306	28	by	by	ADP
ap-4476	306	29	v	v	NOUN
ap-4476	306	30	(	(	PUNCT
ap-4476	306	31	+	+	NOUN
ap-4476	306	32	)	)	PUNCT
ap-4476	306	33	eff,0(r	eff,0(r	NUM
ap-4476	306	34	)	)	PUNCT
ap-4476	307	1	=	=	PRON
ap-4476	308	1	(	(	PUNCT
ap-4476	308	2	b′2	b′2	NOUN
ap-4476	309	1	+	+	NOUN
ap-4476	309	2	a′(a′	a′(a′	NOUN
ap-4476	309	3	−	−	NOUN
ap-4476	309	4	1	1	NUM
ap-4476	309	5	)	)	PUNCT
ap-4476	309	6	)	)	PUNCT
ap-4476	310	1	cosech2	cosech2	NOUN
ap-4476	310	2	r	r	NOUN
ap-4476	310	3	−b′(2a′	−b′(2a′	NOUN
ap-4476	310	4	−	−	NOUN
ap-4476	310	5	1	1	NUM
ap-4476	310	6	)	)	PUNCT
ap-4476	310	7	cosech	cosech	NOUN
ap-4476	310	8	r	r	NOUN
ap-4476	310	9	coth	coth	NOUN
ap-4476	310	10	r	r	NOUN
ap-4476	310	11	+	+	NOUN
ap-4476	310	12	a′2	a′2	NOUN
ap-4476	310	13	.	.	PUNCT
ap-4476	311	1	(	(	PUNCT
ap-4476	311	2	82	82	NUM
ap-4476	311	3	)	)	PUNCT
ap-4476	311	4	the	the	DET
ap-4476	311	5	potential	potential	ADJ
ap-4476	311	6	v	v	X
ap-4476	311	7	(	(	PUNCT
ap-4476	311	8	+	+	NOUN
ap-4476	311	9	)	)	PUNCT
ap-4476	311	10	eff,0(r	eff,0(r	PRON
ap-4476	311	11	)	)	PUNCT
ap-4476	311	12	can	can	AUX
ap-4476	311	13	also	also	ADV
ap-4476	311	14	be	be	AUX
ap-4476	311	15	obtained	obtain	VERB
ap-4476	311	16	simply	simply	ADV
ap-4476	311	17	by	by	ADP
ap-4476	311	18	replacing	replace	VERB
ap-4476	311	19	a′	a′	NOUN
ap-4476	311	20	→	→	SYM
ap-4476	311	21	a′	a′	NOUN
ap-4476	311	22	−	−	PROPN
ap-4476	311	23	1	1	NUM
ap-4476	311	24	in	in	ADP
ap-4476	311	25	v	v	NUM
ap-4476	311	26	(	(	PUNCT
ap-4476	311	27	−	−	NOUN
ap-4476	311	28	)	)	PUNCT
ap-4476	311	29	eff,0(r	eff,0(r	NUM
ap-4476	311	30	)	)	PUNCT
ap-4476	311	31	and	and	CCONJ
ap-4476	311	32	satisfies	satisfie	NOUN
ap-4476	311	33	(	(	PUNCT
ap-4476	311	34	63	63	NUM
ap-4476	311	35	)	)	PUNCT
ap-4476	311	36	.	.	PUNCT
ap-4476	312	1	for	for	ADP
ap-4476	312	2	d	d	PROPN
ap-4476	312	3	=	=	SYM
ap-4476	312	4	3	3	NUM
ap-4476	312	5	and	and	CCONJ
ap-4476	312	6	`	`	PUNCT
ap-4476	312	7	=	=	SYM
ap-4476	312	8	0	0	PUNCT
ap-4476	312	9	the	the	DET
ap-4476	312	10	parameters	parameter	NOUN
ap-4476	312	11	a′	a′	PROPN
ap-4476	312	12	→	→	SYM
ap-4476	312	13	a	a	DET
ap-4476	312	14	,	,	PUNCT
ap-4476	312	15	b′	b′	NUM
ap-4476	312	16	→	→	SYM
ap-4476	312	17	b	b	NOUN
ap-4476	312	18	and	and	CCONJ
ap-4476	312	19	thus	thus	ADV
ap-4476	312	20	these	these	DET
ap-4476	312	21	potentials	potential	NOUN
ap-4476	312	22	corresponds	correspond	VERB
ap-4476	312	23	to	to	ADP
ap-4476	312	24	the	the	DET
ap-4476	312	25	conventional	conventional	ADJ
ap-4476	312	26	shape	shape	NOUN
ap-4476	312	27	invariant	invariant	ADJ
ap-4476	312	28	pöschl	pöschl	NOUN
ap-4476	312	29	teller	teller	NOUN
ap-4476	312	30	potentials	potential	NOUN
ap-4476	312	31	given	give	VERB
ap-4476	312	32	in	in	ADP
ap-4476	312	33	ref	ref	NOUN
ap-4476	312	34	.	.	PUNCT
ap-4476	313	1	[	[	X
ap-4476	313	2	18	18	NUM
ap-4476	313	3	]	]	PUNCT
ap-4476	313	4	.	.	PUNCT
ap-4476	314	1	case	case	NOUN
ap-4476	314	2	(	(	PUNCT
ap-4476	314	3	b	b	NOUN
ap-4476	314	4	)	)	PUNCT
ap-4476	314	5	.	.	PUNCT
ap-4476	315	1	for	for	ADP
ap-4476	315	2	m	m	PROPN
ap-4476	315	3	=	=	SYM
ap-4476	315	4	1	1	NUM
ap-4476	315	5	and	and	CCONJ
ap-4476	315	6	arbitrary	arbitrary	ADJ
ap-4476	315	7	`	`	PUNCT
ap-4476	315	8	,	,	PUNCT
ap-4476	315	9	the	the	DET
ap-4476	315	10	partner	partner	NOUN
ap-4476	315	11	potentials	potential	VERB
ap-4476	315	12	v	v	ADP
ap-4476	315	13	(	(	PUNCT
ap-4476	315	14	−	−	NOUN
ap-4476	315	15	)	)	PUNCT
ap-4476	315	16	eff,1(a′	eff,1(a′	NOUN
ap-4476	315	17	,	,	PUNCT
ap-4476	315	18	b′	b′	NUM
ap-4476	315	19	,	,	PUNCT
ap-4476	315	20	r	r	NOUN
ap-4476	315	21	)	)	PUNCT
ap-4476	315	22	=	=	NOUN
ap-4476	315	23	v	v	NOUN
ap-4476	315	24	(	(	PUNCT
ap-4476	315	25	a′,b′	a′,b′	PROPN
ap-4476	315	26	)	)	PUNCT
ap-4476	315	27	gpt	gpt	NOUN
ap-4476	315	28	(	(	PUNCT
ap-4476	315	29	r	r	NOUN
ap-4476	315	30	)	)	PUNCT
ap-4476	316	1	+	+	NOUN
ap-4476	317	1	2(2a′	2(2a′	NUM
ap-4476	318	1	+	+	NOUN
ap-4476	318	2	1	1	NUM
ap-4476	318	3	)	)	PUNCT
ap-4476	318	4	(	(	PUNCT
ap-4476	318	5	2b′	2b′	NUM
ap-4476	318	6	cosh	cosh	NOUN
ap-4476	318	7	r	r	NOUN
ap-4476	318	8	−	−	PROPN
ap-4476	318	9	2a′	2a′	NUM
ap-4476	318	10	−	−	NOUN
ap-4476	318	11	1	1	NUM
ap-4476	318	12	)	)	PUNCT
ap-4476	318	13	−	−	PROPN
ap-4476	318	14	2	2	NUM
ap-4476	318	15	(	(	PUNCT
ap-4476	318	16	4b′2	4b′2	NOUN
ap-4476	318	17	−	−	PROPN
ap-4476	318	18	(	(	PUNCT
ap-4476	318	19	2a′	2a′	NUM
ap-4476	318	20	+	+	CCONJ
ap-4476	318	21	1)2	1)2	NUM
ap-4476	318	22	)	)	PUNCT
ap-4476	318	23	(	(	PUNCT
ap-4476	318	24	2b′	2b′	NUM
ap-4476	318	25	cosh	cosh	NOUN
ap-4476	318	26	r	r	NOUN
ap-4476	318	27	−	−	PROPN
ap-4476	318	28	2a′	2a′	NUM
ap-4476	318	29	−	−	PROPN
ap-4476	318	30	1)2	1)2	NUM
ap-4476	318	31	+	+	NOUN
ap-4476	318	32	a′2	a′2	ADJ
ap-4476	318	33	(	(	PUNCT
ap-4476	318	34	83	83	NUM
ap-4476	318	35	)	)	PUNCT
ap-4476	318	36	and	and	CCONJ
ap-4476	318	37	v	v	X
ap-4476	318	38	(	(	PUNCT
ap-4476	318	39	+	+	ADJ
ap-4476	318	40	)	)	PUNCT
ap-4476	318	41	eff,1(a′	eff,1(a′	NOUN
ap-4476	318	42	,	,	PUNCT
ap-4476	318	43	b′	b′	NUM
ap-4476	318	44	,	,	PUNCT
ap-4476	318	45	,	,	PUNCT
ap-4476	318	46	r	r	NOUN
ap-4476	318	47	)	)	PUNCT
ap-4476	318	48	=	=	NOUN
ap-4476	318	49	v	v	X
ap-4476	318	50	(	(	PUNCT
ap-4476	318	51	a′−1,b′	a′−1,b′	PROPN
ap-4476	318	52	)	)	PUNCT
ap-4476	318	53	gpt	gpt	NOUN
ap-4476	318	54	(	(	PUNCT
ap-4476	318	55	r	r	NOUN
ap-4476	318	56	)	)	PUNCT
ap-4476	318	57	+	+	NOUN
ap-4476	319	1	2(2a′	2(2a′	NUM
ap-4476	319	2	−	−	NOUN
ap-4476	319	3	1	1	NUM
ap-4476	319	4	)	)	PUNCT
ap-4476	319	5	(	(	PUNCT
ap-4476	319	6	2b′	2b′	NUM
ap-4476	319	7	cosh	cosh	NOUN
ap-4476	319	8	r	r	NOUN
ap-4476	319	9	−	−	PROPN
ap-4476	319	10	2a′	2a′	NUM
ap-4476	320	1	+	+	CCONJ
ap-4476	320	2	1	1	X
ap-4476	320	3	)	)	PUNCT
ap-4476	320	4	−	−	PROPN
ap-4476	320	5	2	2	NUM
ap-4476	320	6	(	(	PUNCT
ap-4476	320	7	4b′2	4b′2	NUM
ap-4476	321	1	−	−	PROPN
ap-4476	321	2	(	(	PUNCT
ap-4476	321	3	2a′	2a′	NUM
ap-4476	321	4	−	−	NOUN
ap-4476	321	5	1)2	1)2	NUM
ap-4476	321	6	)	)	PUNCT
ap-4476	321	7	(	(	PUNCT
ap-4476	321	8	2b′	2b′	NUM
ap-4476	321	9	cosh	cosh	NOUN
ap-4476	321	10	r	r	NOUN
ap-4476	321	11	−	−	NOUN
ap-4476	321	12	2a′	2a′	NUM
ap-4476	322	1	+	+	CCONJ
ap-4476	322	2	1)2	1)2	NUM
ap-4476	322	3	+	+	NOUN
ap-4476	322	4	a′2	a′2	NOUN
ap-4476	322	5	.	.	PUNCT
ap-4476	323	1	(	(	PUNCT
ap-4476	323	2	84	84	NUM
ap-4476	323	3	)	)	PUNCT
ap-4476	323	4	these	these	DET
ap-4476	323	5	potentials	potential	VERB
ap-4476	323	6	satisfy	satisfy	VERB
ap-4476	323	7	the	the	DET
ap-4476	323	8	shape	shape	NOUN
ap-4476	323	9	invariant	invariant	ADJ
ap-4476	323	10	property	property	NOUN
ap-4476	323	11	(	(	PUNCT
ap-4476	323	12	63	63	NUM
ap-4476	323	13	)	)	PUNCT
ap-4476	323	14	i.e.	i.e.	X
ap-4476	323	15	,	,	PUNCT
ap-4476	323	16	v	v	INTJ
ap-4476	323	17	(	(	PUNCT
ap-4476	323	18	+	+	ADJ
ap-4476	323	19	)	)	PUNCT
ap-4476	323	20	eff,1(a′	eff,1(a′	NOUN
ap-4476	323	21	,	,	PUNCT
ap-4476	323	22	b′	b′	NUM
ap-4476	323	23	,	,	PUNCT
ap-4476	323	24	r	r	NOUN
ap-4476	323	25	)	)	PUNCT
ap-4476	323	26	=	=	NOUN
ap-4476	323	27	v	v	NOUN
ap-4476	323	28	(	(	PUNCT
ap-4476	323	29	−	−	NOUN
ap-4476	323	30	)	)	PUNCT
ap-4476	323	31	eff,1(a′	eff,1(a′	NOUN
ap-4476	323	32	−	−	NOUN
ap-4476	323	33	1	1	NUM
ap-4476	323	34	,	,	PUNCT
ap-4476	323	35	b′	b′	NUM
ap-4476	323	36	,	,	PUNCT
ap-4476	323	37	r	r	NOUN
ap-4476	323	38	)	)	PUNCT
ap-4476	324	1	+	+	NOUN
ap-4476	324	2	2a′	2a′	NUM
ap-4476	324	3	−	−	NOUN
ap-4476	324	4	1	1	NUM
ap-4476	324	5	.	.	PUNCT
ap-4476	324	6	(	(	PUNCT
ap-4476	324	7	85	85	NUM
ap-4476	324	8	)	)	PUNCT
ap-4476	324	9	for	for	ADP
ap-4476	324	10	d	d	PROPN
ap-4476	324	11	=	=	SYM
ap-4476	324	12	3	3	NUM
ap-4476	324	13	and	and	CCONJ
ap-4476	324	14	`	`	PUNCT
ap-4476	324	15	=	=	SYM
ap-4476	324	16	0	0	NUM
ap-4476	324	17	,	,	PUNCT
ap-4476	324	18	the	the	DET
ap-4476	324	19	above	above	ADJ
ap-4476	324	20	expressions	expression	NOUN
ap-4476	324	21	matches	match	VERB
ap-4476	324	22	exactly	exactly	ADV
ap-4476	324	23	with	with	ADP
ap-4476	324	24	the	the	DET
ap-4476	324	25	results	result	NOUN
ap-4476	324	26	obtained	obtain	VERB
ap-4476	324	27	in	in	ADP
ap-4476	324	28	[	[	X
ap-4476	324	29	4	4	NUM
ap-4476	324	30	,	,	PUNCT
ap-4476	324	31	14	14	NUM
ap-4476	324	32	,	,	PUNCT
ap-4476	324	33	15	15	NUM
ap-4476	324	34	]	]	PUNCT
ap-4476	324	35	.	.	PUNCT
ap-4476	325	1	6	6	X
ap-4476	325	2	.	.	X
ap-4476	325	3	results	result	NOUN
ap-4476	325	4	and	and	CCONJ
ap-4476	325	5	discussions	discussion	NOUN
ap-4476	325	6	in	in	ADP
ap-4476	325	7	the	the	DET
ap-4476	325	8	present	present	ADJ
ap-4476	325	9	manuscript	manuscript	NOUN
ap-4476	325	10	by	by	ADP
ap-4476	325	11	using	use	VERB
ap-4476	325	12	pct	pct	NOUN
ap-4476	325	13	approach	approach	NOUN
ap-4476	325	14	we	we	PRON
ap-4476	325	15	have	have	AUX
ap-4476	325	16	generated	generate	VERB
ap-4476	325	17	exactly	exactly	ADV
ap-4476	325	18	solvable	solvable	ADJ
ap-4476	325	19	rationally	rationally	ADV
ap-4476	325	20	extended	extended	ADJ
ap-4476	325	21	d	d	ADJ
ap-4476	325	22	-	-	ADJ
ap-4476	325	23	dimensional	dimensional	ADJ
ap-4476	325	24	radial	radial	ADJ
ap-4476	325	25	oscillator	oscillator	NOUN
ap-4476	325	26	and	and	CCONJ
ap-4476	325	27	gpt	gpt	NOUN
ap-4476	325	28	potential	potential	NOUN
ap-4476	325	29	and	and	CCONJ
ap-4476	325	30	constructed	construct	VERB
ap-4476	325	31	their	their	PRON
ap-4476	325	32	bound	bind	VERB
ap-4476	325	33	state	state	NOUN
ap-4476	325	34	wavefunctions	wavefunction	NOUN
ap-4476	325	35	in	in	ADP
ap-4476	325	36	terms	term	NOUN
ap-4476	325	37	of	of	ADP
ap-4476	325	38	xm	xm	PROPN
ap-4476	325	39	exceptional	exceptional	ADJ
ap-4476	325	40	laguerre	laguerre	NOUN
ap-4476	325	41	and	and	CCONJ
ap-4476	325	42	jacobi	jacobi	PROPN
ap-4476	325	43	orthogonal	orthogonal	PROPN
ap-4476	325	44	polynomials	polynomial	NOUN
ap-4476	325	45	respectively	respectively	ADV
ap-4476	325	46	.	.	PUNCT
ap-4476	326	1	the	the	DET
ap-4476	326	2	extended	extended	ADJ
ap-4476	326	3	potentials	potential	NOUN
ap-4476	326	4	are	be	AUX
ap-4476	326	5	isospectral	isospectral	ADJ
ap-4476	326	6	to	to	ADP
ap-4476	326	7	their	their	PRON
ap-4476	326	8	conventional	conventional	ADJ
ap-4476	326	9	counterparts	counterpart	NOUN
ap-4476	326	10	.	.	PUNCT
ap-4476	327	1	for	for	ADP
ap-4476	327	2	the	the	DET
ap-4476	327	3	oscillator	oscillator	NOUN
ap-4476	327	4	case	case	NOUN
ap-4476	327	5	we	we	PRON
ap-4476	327	6	have	have	AUX
ap-4476	327	7	shown	show	VERB
ap-4476	327	8	that	that	SCONJ
ap-4476	327	9	the	the	DET
ap-4476	327	10	rationally	rationally	ADV
ap-4476	327	11	extended	extended	ADJ
ap-4476	327	12	d	d	ADJ
ap-4476	327	13	-	-	ADJ
ap-4476	327	14	dimensional	dimensional	ADJ
ap-4476	327	15	oscillator	oscillator	NOUN
ap-4476	327	16	potentials	potential	NOUN
ap-4476	327	17	are	be	AUX
ap-4476	327	18	shape	shape	NOUN
ap-4476	327	19	invariant	invariant	ADJ
ap-4476	327	20	with	with	ADP
ap-4476	327	21	translation	translation	NOUN
ap-4476	327	22	.	.	PUNCT
ap-4476	328	1	for	for	ADP
ap-4476	328	2	the	the	DET
ap-4476	328	3	jacobi	jacobi	PROPN
ap-4476	328	4	case	case	NOUN
ap-4476	328	5	,	,	PUNCT
ap-4476	328	6	this	this	PRON
ap-4476	328	7	is	be	AUX
ap-4476	328	8	not	not	PART
ap-4476	328	9	true	true	ADJ
ap-4476	328	10	unless	unless	SCONJ
ap-4476	328	11	d	d	PROPN
ap-4476	328	12	=	=	SYM
ap-4476	328	13	3	3	X
ap-4476	328	14	.	.	X
ap-4476	329	1	for	for	ADP
ap-4476	329	2	l	l	PROPN
ap-4476	329	3	6=	6=	ADP
ap-4476	329	4	0	0	NUM
ap-4476	329	5	we	we	PRON
ap-4476	329	6	also	also	ADV
ap-4476	329	7	obtained	obtain	VERB
ap-4476	329	8	approximate	approximate	ADJ
ap-4476	329	9	extended	extend	VERB
ap-4476	329	10	gpt	gpt	NOUN
ap-4476	329	11	potentials	potential	NOUN
ap-4476	329	12	and	and	CCONJ
ap-4476	329	13	these	these	PRON
ap-4476	329	14	have	have	AUX
ap-4476	329	15	been	be	AUX
ap-4476	329	16	shown	show	VERB
ap-4476	329	17	to	to	PART
ap-4476	329	18	be	be	AUX
ap-4476	329	19	shape	shape	NOUN
ap-4476	329	20	invariant	invariant	ADJ
ap-4476	329	21	.	.	PUNCT
ap-4476	330	1	for	for	ADP
ap-4476	330	2	the	the	DET
ap-4476	330	3	particular	particular	ADJ
ap-4476	330	4	case	case	NOUN
ap-4476	330	5	(	(	PUNCT
ap-4476	330	6	d	d	NOUN
ap-4476	330	7	=	=	SYM
ap-4476	330	8	3	3	NUM
ap-4476	330	9	)	)	PUNCT
ap-4476	330	10	the	the	DET
ap-4476	330	11	potentials	potential	NOUN
ap-4476	330	12	corresponds	correspond	VERB
ap-4476	330	13	to	to	ADP
ap-4476	330	14	the	the	DET
ap-4476	330	15	potentials	potential	NOUN
ap-4476	330	16	obtained	obtain	VERB
ap-4476	330	17	by	by	ADP
ap-4476	330	18	quesne	quesne	NOUN
ap-4476	330	19	et.al	et.al	NOUN
ap-4476	330	20	[	[	X
ap-4476	330	21	3	3	NUM
ap-4476	330	22	,	,	PUNCT
ap-4476	330	23	4	4	NUM
ap-4476	330	24	]	]	PUNCT
ap-4476	330	25	and	and	CCONJ
ap-4476	330	26	others	other	NOUN
ap-4476	330	27	and	and	CCONJ
ap-4476	330	28	thus	thus	ADV
ap-4476	330	29	provide	provide	VERB
ap-4476	330	30	a	a	DET
ap-4476	330	31	powerful	powerful	ADJ
ap-4476	330	32	check	check	NOUN
ap-4476	330	33	on	on	ADP
ap-4476	330	34	our	our	PRON
ap-4476	330	35	calculations	calculation	NOUN
ap-4476	330	36	.	.	PUNCT
ap-4476	331	1	486	486	NUM
ap-4476	331	2	vol	vol	NOUN
ap-4476	331	3	.	.	PUNCT
ap-4476	331	4	57	57	NUM
ap-4476	331	5	no	no	NOUN
ap-4476	331	6	.	.	PUNCT
ap-4476	332	1	6/2017	6/2017	NUM
ap-4476	332	2	rationally	rationally	ADV
ap-4476	332	3	extended	extend	VERB
ap-4476	332	4	shape	shape	NOUN
ap-4476	332	5	invariant	invariant	ADJ
ap-4476	332	6	potentials	potential	VERB
ap-4476	332	7	acknowledgements	acknowledgement	VERB
ap-4476	332	8	one	one	NUM
ap-4476	332	9	of	of	ADP
ap-4476	332	10	us	we	PRON
ap-4476	332	11	(	(	PUNCT
ap-4476	332	12	nk	nk	PROPN
ap-4476	332	13	)	)	PUNCT
ap-4476	332	14	acknowledges	acknowledge	VERB
ap-4476	332	15	financial	financial	ADJ
ap-4476	332	16	support	support	NOUN
ap-4476	332	17	from	from	ADP
ap-4476	332	18	ugc	ugc	PROPN
ap-4476	332	19	under	under	ADP
ap-4476	332	20	the	the	DET
ap-4476	332	21	bhu	bhu	NOUN
ap-4476	332	22	-	-	PUNCT
ap-4476	332	23	cret	cret	NOUN
ap-4476	332	24	fellowship	fellowship	NOUN
ap-4476	332	25	.	.	PUNCT
ap-4476	333	1	b.p.m	b.p.m	PROPN
ap-4476	333	2	.	.	PUNCT
ap-4476	333	3	acknowledges	acknowledge	VERB
ap-4476	333	4	the	the	DET
ap-4476	333	5	financial	financial	ADJ
ap-4476	333	6	support	support	NOUN
ap-4476	333	7	from	from	ADP
ap-4476	333	8	the	the	DET
ap-4476	333	9	department	department	NOUN
ap-4476	333	10	of	of	ADP
ap-4476	333	11	science	science	NOUN
ap-4476	333	12	and	and	CCONJ
ap-4476	333	13	technology	technology	NOUN
ap-4476	333	14	(	(	PUNCT
ap-4476	333	15	dst	dst	PROPN
ap-4476	333	16	)	)	PUNCT
ap-4476	333	17	,	,	PUNCT
ap-4476	333	18	gov	gov	PROPN
ap-4476	333	19	.	.	PROPN
ap-4476	333	20	of	of	ADP
ap-4476	333	21	india	india	PROPN
ap-4476	333	22	under	under	ADP
ap-4476	333	23	serc	serc	NOUN
ap-4476	333	24	project	project	NOUN
ap-4476	333	25	sanction	sanction	NOUN
ap-4476	333	26	grant	grant	NOUN
ap-4476	333	27	no	no	INTJ
ap-4476	333	28	.	.	PUNCT
ap-4476	334	1	sr	sr	PROPN
ap-4476	334	2	/	/	SYM
ap-4476	334	3	s2	s2	PROPN
ap-4476	334	4	/	/	SYM
ap-4476	334	5	hep/0009/2012	hep/0009/2012	NOUN
ap-4476	334	6	.	.	PUNCT
ap-4476	335	1	references	reference	NOUN
ap-4476	335	2	[	[	X
ap-4476	335	3	1	1	X
ap-4476	335	4	]	]	PUNCT
ap-4476	335	5	d.	d.	PROPN
ap-4476	335	6	gomez	gomez	PROPN
ap-4476	335	7	-	-	PUNCT
ap-4476	335	8	ullate	ullate	PROPN
ap-4476	335	9	,	,	PUNCT
ap-4476	335	10	n.	n.	PROPN
ap-4476	335	11	kamran	kamran	PROPN
ap-4476	335	12	and	and	CCONJ
ap-4476	335	13	r.	r.	PROPN
ap-4476	335	14	milson	milson	PROPN
ap-4476	335	15	,	,	PUNCT
ap-4476	335	16	j.	j.	PROPN
ap-4476	335	17	math	math	PROPN
ap-4476	335	18	.	.	PUNCT
ap-4476	336	1	anal.appl	anal.appl	PROPN
ap-4476	336	2	.	.	PROPN
ap-4476	336	3	359	359	NUM
ap-4476	336	4	(	(	PUNCT
ap-4476	336	5	2009	2009	NUM
ap-4476	336	6	)	)	PUNCT
ap-4476	336	7	352	352	NUM
ap-4476	336	8	.	.	PUNCT
ap-4476	337	1	[	[	X
ap-4476	337	2	2	2	X
ap-4476	337	3	]	]	PUNCT
ap-4476	337	4	d.	d.	PROPN
ap-4476	337	5	gomez	gomez	PROPN
ap-4476	337	6	-	-	PUNCT
ap-4476	337	7	ullate	ullate	PROPN
ap-4476	337	8	,	,	PUNCT
ap-4476	337	9	n.	n.	PROPN
ap-4476	337	10	kamran	kamran	PROPN
ap-4476	337	11	and	and	CCONJ
ap-4476	337	12	r.	r.	PROPN
ap-4476	337	13	milson	milson	PROPN
ap-4476	337	14	,	,	PUNCT
ap-4476	337	15	j.	j.	PROPN
ap-4476	337	16	phys	phys	PROPN
ap-4476	337	17	.	.	PUNCT
ap-4476	338	1	a	a	DET
ap-4476	338	2	43	43	NUM
ap-4476	338	3	(	(	PUNCT
ap-4476	338	4	2010	2010	NUM
ap-4476	338	5	)	)	PUNCT
ap-4476	338	6	434016	434016	NUM
ap-4476	338	7	.	.	PUNCT
ap-4476	339	1	[	[	X
ap-4476	339	2	3	3	X
ap-4476	339	3	]	]	X
ap-4476	339	4	c.	c.	NOUN
ap-4476	339	5	quesne	quesne	NOUN
ap-4476	339	6	,	,	PUNCT
ap-4476	339	7	j.phys.a	j.phys.a	PROPN
ap-4476	339	8	41	41	NUM
ap-4476	339	9	(	(	PUNCT
ap-4476	339	10	2008	2008	NUM
ap-4476	339	11	)	)	PUNCT
ap-4476	339	12	392001	392001	NUM
ap-4476	339	13	.	.	PUNCT
ap-4476	340	1	[	[	X
ap-4476	340	2	4	4	X
ap-4476	340	3	]	]	X
ap-4476	340	4	b.	b.	PROPN
ap-4476	340	5	bagchi	bagchi	PROPN
ap-4476	340	6	,	,	PUNCT
ap-4476	340	7	c.	c.	PROPN
ap-4476	340	8	quesne	quesne	NOUN
ap-4476	340	9	and	and	CCONJ
ap-4476	340	10	r.	r.	PROPN
ap-4476	340	11	roychoudhary	roychoudhary	PROPN
ap-4476	340	12	,	,	PUNCT
ap-4476	340	13	pramana	pramana	PROPN
ap-4476	340	14	j.	j.	PROPN
ap-4476	340	15	phys	phys	PROPN
ap-4476	340	16	.	.	PUNCT
ap-4476	341	1	73(2009	73(2009	X
ap-4476	341	2	)	)	PUNCT
ap-4476	341	3	337	337	NUM
ap-4476	341	4	,	,	PUNCT
ap-4476	342	1	c.	c.	NOUN
ap-4476	342	2	quesne	quesne	NOUN
ap-4476	342	3	,	,	PUNCT
ap-4476	342	4	sigma	sigma	NOUN
ap-4476	342	5	5	5	NUM
ap-4476	342	6	(	(	PUNCT
ap-4476	342	7	2009	2009	NUM
ap-4476	342	8	)	)	PUNCT
ap-4476	342	9	84	84	NUM
ap-4476	342	10	;	;	PUNCT
ap-4476	342	11	a.	a.	NOUN
ap-4476	342	12	khare	khare	PROPN
ap-4476	342	13	,	,	PUNCT
ap-4476	342	14	unpublished	unpublished	ADJ
ap-4476	342	15	.	.	PUNCT
ap-4476	343	1	[	[	X
ap-4476	343	2	5	5	X
ap-4476	343	3	]	]	PUNCT
ap-4476	343	4	s.	s.	PROPN
ap-4476	343	5	odake	odake	PROPN
ap-4476	343	6	and	and	CCONJ
ap-4476	343	7	r.	r.	PROPN
ap-4476	343	8	sasaki	sasaki	PROPN
ap-4476	343	9	,	,	PUNCT
ap-4476	343	10	phys	phy	NOUN
ap-4476	343	11	.	.	PUNCT
ap-4476	344	1	lett	lett	PROPN
ap-4476	344	2	.	.	PUNCT
ap-4476	345	1	b	b	X
ap-4476	345	2	,	,	PUNCT
ap-4476	345	3	684	684	NUM
ap-4476	345	4	(	(	PUNCT
ap-4476	345	5	2010	2010	NUM
ap-4476	345	6	)	)	PUNCT
ap-4476	345	7	173	173	NUM
ap-4476	345	8	;	;	PUNCT
ap-4476	345	9	ibid	ibid	NOUN
ap-4476	345	10	679	679	NUM
ap-4476	345	11	(	(	PUNCT
ap-4476	345	12	2009	2009	NUM
ap-4476	345	13	)	)	PUNCT
ap-4476	345	14	414	414	NUM
ap-4476	345	15	.	.	PUNCT
ap-4476	346	1	j.	j.	PROPN
ap-4476	346	2	math	math	PROPN
ap-4476	346	3	.	.	PUNCT
ap-4476	347	1	phys	phy	NOUN
ap-4476	347	2	,	,	PUNCT
ap-4476	347	3	51	51	NUM
ap-4476	347	4	,	,	PUNCT
ap-4476	347	5	053513	053513	NUM
ap-4476	347	6	(	(	PUNCT
ap-4476	347	7	2010	2010	NUM
ap-4476	347	8	)	)	PUNCT
ap-4476	347	9	.	.	PUNCT
ap-4476	348	1	[	[	X
ap-4476	348	2	6	6	NUM
ap-4476	348	3	]	]	SYM
ap-4476	348	4	c	c	X
ap-4476	348	5	-	-	PUNCT
ap-4476	348	6	l.	l.	PROPN
ap-4476	348	7	ho	ho	PROPN
ap-4476	348	8	,	,	PUNCT
ap-4476	348	9	s	s	PART
ap-4476	348	10	odake	odake	NOUN
ap-4476	348	11	and	and	CCONJ
ap-4476	348	12	r	r	PROPN
ap-4476	348	13	sasaki	sasaki	NOUN
ap-4476	348	14	,	,	PUNCT
ap-4476	348	15	sigma	sigma	NOUN
ap-4476	348	16	7	7	NUM
ap-4476	348	17	(	(	PUNCT
ap-4476	348	18	2011	2011	NUM
ap-4476	348	19	)	)	PUNCT
ap-4476	348	20	107	107	NUM
ap-4476	348	21	.	.	PUNCT
ap-4476	349	1	[	[	X
ap-4476	349	2	7	7	NUM
ap-4476	349	3	]	]	SYM
ap-4476	349	4	c	c	X
ap-4476	349	5	-	-	PUNCT
ap-4476	349	6	l.	l.	PROPN
ap-4476	349	7	ho	ho	PROPN
ap-4476	349	8	and	and	CCONJ
ap-4476	349	9	r	r	PROPN
ap-4476	349	10	sasaki	sasaki	PROPN
ap-4476	349	11	,	,	PUNCT
ap-4476	349	12	arxiv	arxiv	PROPN
ap-4476	349	13	:	:	PUNCT
ap-4476	349	14	1102.5669	1102.5669	NUM
ap-4476	349	15	.	.	PUNCT
ap-4476	350	1	[	[	X
ap-4476	350	2	8	8	NUM
ap-4476	350	3	]	]	X
ap-4476	350	4	d.	d.	PROPN
ap-4476	350	5	gomez	gomez	PROPN
ap-4476	350	6	-	-	PUNCT
ap-4476	350	7	ullate	ullate	PROPN
ap-4476	350	8	,	,	PUNCT
ap-4476	350	9	n.	n.	PROPN
ap-4476	350	10	kamran	kamran	PROPN
ap-4476	350	11	and	and	CCONJ
ap-4476	350	12	r.	r.	PROPN
ap-4476	350	13	milson	milson	PROPN
ap-4476	350	14	,	,	PUNCT
ap-4476	350	15	arxiv	arxiv	PROPN
ap-4476	350	16	:	:	PUNCT
ap-4476	350	17	1204.2282	1204.2282	PROPN
ap-4476	350	18	.	.	PUNCT
ap-4476	351	1	[	[	X
ap-4476	351	2	9	9	NUM
ap-4476	351	3	]	]	PUNCT
ap-4476	351	4	c.	c.	NOUN
ap-4476	351	5	quesne	quesne	NOUN
ap-4476	351	6	,	,	PUNCT
ap-4476	351	7	int	int	NOUN
ap-4476	351	8	.	.	PUNCT
ap-4476	352	1	j.	j.	PROPN
ap-4476	352	2	mod	mod	PROPN
ap-4476	352	3	.	.	PUNCT
ap-4476	353	1	phys	phys	PROPN
ap-4476	353	2	.	.	PUNCT
ap-4476	354	1	a	a	DET
ap-4476	354	2	26	26	NUM
ap-4476	354	3	(	(	PUNCT
ap-4476	354	4	2011	2011	NUM
ap-4476	354	5	)	)	PUNCT
ap-4476	354	6	5337	5337	NUM
ap-4476	354	7	.	.	PUNCT
ap-4476	355	1	[	[	X
ap-4476	355	2	10	10	NUM
ap-4476	355	3	]	]	X
ap-4476	355	4	y.	y.	PROPN
ap-4476	355	5	grandati	grandati	PROPN
ap-4476	355	6	,	,	PUNCT
ap-4476	355	7	j.	j.	PROPN
ap-4476	355	8	math	math	PROPN
ap-4476	355	9	.	.	PUNCT
ap-4476	356	1	phys	phy	NOUN
ap-4476	356	2	.	.	PUNCT
ap-4476	357	1	52	52	NUM
ap-4476	357	2	103505	103505	NUM
ap-4476	357	3	(	(	PUNCT
ap-4476	357	4	2011	2011	NUM
ap-4476	357	5	)	)	PUNCT
ap-4476	357	6	.	.	PUNCT
ap-4476	358	1	[	[	X
ap-4476	358	2	11	11	NUM
ap-4476	358	3	]	]	X
ap-4476	358	4	y.	y.	PROPN
ap-4476	358	5	grandati	grandati	PROPN
ap-4476	358	6	,	,	PUNCT
ap-4476	358	7	ann	ann	PROPN
ap-4476	358	8	.	.	PUNCT
ap-4476	358	9	phys	phys	PROPN
ap-4476	358	10	.	.	PUNCT
ap-4476	359	1	327	327	NUM
ap-4476	359	2	185	185	NUM
ap-4476	359	3	(	(	PUNCT
ap-4476	359	4	2012	2012	NUM
ap-4476	359	5	)	)	PUNCT
ap-4476	359	6	.	.	PUNCT
ap-4476	360	1	[	[	X
ap-4476	360	2	12	12	NUM
ap-4476	360	3	]	]	X
ap-4476	360	4	y.	y.	PROPN
ap-4476	360	5	grandati	grandati	PROPN
ap-4476	360	6	,	,	PUNCT
ap-4476	360	7	ann	ann	PROPN
ap-4476	360	8	.	.	PUNCT
ap-4476	361	1	phys	phys	PROPN
ap-4476	361	2	.	.	PUNCT
ap-4476	362	1	326	326	NUM
ap-4476	362	2	2074	2074	NUM
ap-4476	362	3	(	(	PUNCT
ap-4476	362	4	2011	2011	NUM
ap-4476	362	5	)	)	PUNCT
ap-4476	362	6	.	.	PUNCT
ap-4476	363	1	[	[	X
ap-4476	363	2	13	13	NUM
ap-4476	363	3	]	]	PUNCT
ap-4476	363	4	c.	c.	NOUN
ap-4476	363	5	quesne	quesne	NOUN
ap-4476	363	6	,	,	PUNCT
ap-4476	363	7	sigma	sigma	VERB
ap-4476	363	8	8	8	NUM
ap-4476	363	9	080	080	NUM
ap-4476	363	10	(	(	PUNCT
ap-4476	363	11	2012	2012	NUM
ap-4476	363	12	)	)	PUNCT
ap-4476	363	13	.	.	PUNCT
ap-4476	364	1	[	[	X
ap-4476	364	2	14	14	NUM
ap-4476	364	3	]	]	PUNCT
ap-4476	364	4	r.	r.	PROPN
ap-4476	364	5	k.	k.	PROPN
ap-4476	364	6	yadav	yadav	PROPN
ap-4476	364	7	,	,	PUNCT
ap-4476	364	8	a.	a.	PROPN
ap-4476	364	9	khare	khare	PROPN
ap-4476	364	10	and	and	CCONJ
ap-4476	364	11	b.	b.	PROPN
ap-4476	364	12	p.	p.	PROPN
ap-4476	364	13	mandal	mandal	PROPN
ap-4476	364	14	,	,	PUNCT
ap-4476	364	15	phys	phy	NOUN
ap-4476	364	16	.	.	PUNCT
ap-4476	365	1	lett	lett	PROPN
ap-4476	365	2	.	.	PUNCT
ap-4476	366	1	b	b	ADP
ap-4476	366	2	723	723	NUM
ap-4476	366	3	(	(	PUNCT
ap-4476	366	4	2013	2013	NUM
ap-4476	366	5	)	)	PUNCT
ap-4476	366	6	433	433	NUM
ap-4476	366	7	.	.	PUNCT
ap-4476	367	1	[	[	X
ap-4476	367	2	15	15	NUM
ap-4476	367	3	]	]	X
ap-4476	367	4	r.	r.	PROPN
ap-4476	367	5	k.	k.	PROPN
ap-4476	367	6	yadav	yadav	PROPN
ap-4476	367	7	,	,	PUNCT
ap-4476	367	8	a.	a.	PROPN
ap-4476	367	9	khare	khare	PROPN
ap-4476	367	10	and	and	CCONJ
ap-4476	367	11	b.	b.	PROPN
ap-4476	367	12	p.	p.	PROPN
ap-4476	367	13	mandal	mandal	PROPN
ap-4476	367	14	,	,	PUNCT
ap-4476	367	15	annals	annal	NOUN
ap-4476	367	16	of	of	ADP
ap-4476	367	17	physics	physics	NOUN
ap-4476	367	18	331	331	NUM
ap-4476	367	19	(	(	PUNCT
ap-4476	367	20	2013	2013	NUM
ap-4476	367	21	)	)	PUNCT
ap-4476	367	22	313	313	NUM
ap-4476	367	23	.	.	PUNCT
ap-4476	368	1	[	[	X
ap-4476	368	2	16	16	NUM
ap-4476	368	3	]	]	PUNCT
ap-4476	368	4	r.	r.	PROPN
ap-4476	368	5	k.	k.	PROPN
ap-4476	368	6	yadav	yadav	PROPN
ap-4476	368	7	,	,	PUNCT
ap-4476	368	8	a.	a.	PROPN
ap-4476	368	9	khare	khare	PROPN
ap-4476	368	10	and	and	CCONJ
ap-4476	368	11	b.	b.	PROPN
ap-4476	368	12	p.	p.	PROPN
ap-4476	368	13	mandal	mandal	PROPN
ap-4476	368	14	,	,	PUNCT
ap-4476	368	15	arxiv:1309.6755	arxiv:1309.6755	VERB
ap-4476	368	16	.	.	PUNCT
ap-4476	369	1	[	[	X
ap-4476	369	2	17	17	NUM
ap-4476	369	3	]	]	X
ap-4476	369	4	e.	e.	PROPN
ap-4476	369	5	witten	witten	PROPN
ap-4476	369	6	nucl	nucl	PROPN
ap-4476	369	7	.	.	PUNCT
ap-4476	370	1	phys	phy	NOUN
ap-4476	370	2	.	.	PUNCT
ap-4476	371	1	a	a	DET
ap-4476	371	2	188	188	NUM
ap-4476	371	3	513	513	NUM
ap-4476	371	4	.	.	PUNCT
ap-4476	372	1	[	[	X
ap-4476	372	2	18	18	NUM
ap-4476	372	3	]	]	X
ap-4476	372	4	f.	f.	PROPN
ap-4476	372	5	cooper	cooper	PROPN
ap-4476	372	6	,	,	PUNCT
ap-4476	372	7	a.	a.	PROPN
ap-4476	372	8	khare	khare	PROPN
ap-4476	372	9	,	,	PUNCT
ap-4476	372	10	u.	u.	PROPN
ap-4476	372	11	sukhatme	sukhatme	PROPN
ap-4476	372	12	phys	phys	PROPN
ap-4476	372	13	.	.	PUNCT
ap-4476	373	1	rep	rep	PROPN
ap-4476	373	2	.	.	PROPN
ap-4476	373	3	251	251	NUM
ap-4476	373	4	(	(	PUNCT
ap-4476	373	5	1995	1995	NUM
ap-4476	373	6	)	)	PUNCT
ap-4476	373	7	267	267	NUM
ap-4476	373	8	;	;	PUNCT
ap-4476	373	9	"	"	PUNCT
ap-4476	373	10	susy	susy	NOUN
ap-4476	373	11	in	in	ADP
ap-4476	373	12	quantum	quantum	ADJ
ap-4476	373	13	mechanics	mechanic	NOUN
ap-4476	373	14	"	"	PUNCT
ap-4476	373	15	world	world	NOUN
ap-4476	373	16	scientific	scientific	ADJ
ap-4476	373	17	(	(	PUNCT
ap-4476	373	18	2001	2001	NUM
ap-4476	373	19	)	)	PUNCT
ap-4476	373	20	.	.	PUNCT
ap-4476	374	1	[	[	X
ap-4476	374	2	19	19	NUM
ap-4476	374	3	]	]	PUNCT
ap-4476	374	4	k.	k.	PROPN
ap-4476	374	5	j.	j.	PROPN
ap-4476	374	6	oyewumi	oyewumi	PROPN
ap-4476	374	7	,	,	PUNCT
ap-4476	374	8	f.	f.	PROPN
ap-4476	374	9	o.	o.	PROPN
ap-4476	374	10	akinpelu	akinpelu	PROPN
ap-4476	374	11	and	and	CCONJ
ap-4476	374	12	d.	d.	PROPN
ap-4476	374	13	agboola	agboola	PROPN
ap-4476	374	14	,	,	PUNCT
ap-4476	374	15	int	int	PROPN
ap-4476	374	16	.	.	PUNCT
ap-4476	375	1	j.	j.	PROPN
ap-4476	375	2	theor	theor	PROPN
ap-4476	375	3	.	.	PUNCT
ap-4476	376	1	phys	phy	NOUN
ap-4476	376	2	.	.	PUNCT
ap-4476	377	1	,47	,47	PROPN
ap-4476	377	2	(	(	PUNCT
ap-4476	377	3	2008	2008	NUM
ap-4476	377	4	)	)	PUNCT
ap-4476	377	5	1039	1039	NUM
ap-4476	377	6	.	.	PUNCT
ap-4476	378	1	[	[	X
ap-4476	378	2	20	20	NUM
ap-4476	378	3	]	]	PUNCT
ap-4476	378	4	e	e	NOUN
ap-4476	378	5	schrödinger	schrödinger	NOUN
ap-4476	378	6	,	,	PUNCT
ap-4476	378	7	proc	proc	NOUN
ap-4476	378	8	.	.	PUNCT
ap-4476	378	9	r.	r.	PROPN
ap-4476	378	10	irish	irish	PROPN
ap-4476	378	11	acad	acad	PROPN
ap-4476	378	12	.	.	PUNCT
ap-4476	379	1	a,46	a,46	ADP
ap-4476	379	2	(	(	PUNCT
ap-4476	379	3	1940	1940	NUM
ap-4476	379	4	)	)	PUNCT
ap-4476	379	5	183	183	NUM
ap-4476	379	6	.	.	PUNCT
ap-4476	380	1	[	[	X
ap-4476	380	2	21	21	NUM
ap-4476	380	3	]	]	PUNCT
ap-4476	380	4	a.	a.	NOUN
ap-4476	380	5	bhattacharjie	bhattacharjie	NOUN
ap-4476	380	6	and	and	CCONJ
ap-4476	380	7	e.	e.	PROPN
ap-4476	380	8	c.	c.	PROPN
ap-4476	380	9	g.	g.	PROPN
ap-4476	380	10	sudarshan	sudarshan	PROPN
ap-4476	380	11	,	,	PUNCT
ap-4476	380	12	nuovo	nuovo	PROPN
ap-4476	380	13	cimento	cimento	PROPN
ap-4476	380	14	25	25	NUM
ap-4476	380	15	864	864	NUM
ap-4476	380	16	.	.	PUNCT
ap-4476	381	1	[	[	X
ap-4476	381	2	22	22	NUM
ap-4476	381	3	]	]	X
ap-4476	381	4	g.	g.	PROPN
ap-4476	381	5	darboux	darboux	NOUN
ap-4476	381	6	,	,	PUNCT
ap-4476	381	7	theorie	theorie	PROPN
ap-4476	381	8	generale	generale	PROPN
ap-4476	381	9	des	des	PROPN
ap-4476	381	10	surfaces	surface	NOUN
ap-4476	381	11	vol	vol	VERB
ap-4476	381	12	2	2	NUM
ap-4476	381	13	(	(	PUNCT
ap-4476	381	14	paris	paris	PROPN
ap-4476	381	15	:	:	PUNCT
ap-4476	381	16	gauthier	gauthier	NOUN
ap-4476	381	17	-	-	PUNCT
ap-4476	381	18	villars	villar	NOUN
ap-4476	381	19	)	)	PUNCT
ap-4476	381	20	(	(	PUNCT
ap-4476	381	21	1988	1988	NUM
ap-4476	381	22	)	)	PUNCT
ap-4476	381	23	.	.	PUNCT
ap-4476	382	1	[	[	X
ap-4476	382	2	23	23	NUM
ap-4476	382	3	]	]	X
ap-4476	382	4	d.	d.	PROPN
ap-4476	382	5	gomez	gomez	PROPN
ap-4476	382	6	-	-	PUNCT
ap-4476	382	7	ullate	ullate	PROPN
ap-4476	382	8	,	,	PUNCT
ap-4476	382	9	n.	n.	PROPN
ap-4476	382	10	kamran	kamran	PROPN
ap-4476	382	11	and	and	CCONJ
ap-4476	382	12	r.	r.	PROPN
ap-4476	382	13	milson	milson	PROPN
ap-4476	382	14	,	,	PUNCT
ap-4476	382	15	arxiv	arxiv	PROPN
ap-4476	382	16	:	:	PUNCT
ap-4476	382	17	1002.2666v2	1002.2666v2	X
ap-4476	382	18	.	.	PUNCT
ap-4476	383	1	[	[	X
ap-4476	383	2	24	24	NUM
ap-4476	383	3	]	]	X
ap-4476	383	4	d.	d.	PROPN
ap-4476	383	5	gomez	gomez	PROPN
ap-4476	383	6	-	-	PUNCT
ap-4476	383	7	ullate	ullate	PROPN
ap-4476	383	8	,	,	PUNCT
ap-4476	383	9	n.	n.	PROPN
ap-4476	383	10	kamran	kamran	PROPN
ap-4476	383	11	and	and	CCONJ
ap-4476	383	12	r.	r.	PROPN
ap-4476	383	13	milson	milson	PROPN
ap-4476	383	14	,	,	PUNCT
ap-4476	383	15	contemporary	contemporary	ADJ
ap-4476	383	16	mathematics	mathematic	NOUN
ap-4476	383	17	563	563	NUM
ap-4476	383	18	51	51	NUM
ap-4476	383	19	2012	2012	NUM
ap-4476	383	20	.	.	PUNCT
ap-4476	384	1	[	[	X
ap-4476	384	2	25	25	NUM
ap-4476	384	3	]	]	X
ap-4476	384	4	gao	gao	PROPN
ap-4476	384	5	-	-	PUNCT
ap-4476	384	6	feng	feng	PROPN
ap-4476	384	7	wei	wei	PROPN
ap-4476	384	8	,	,	PUNCT
ap-4476	384	9	chao	chao	PROPN
ap-4476	384	10	-	-	PUNCT
ap-4476	384	11	yun	yun	PROPN
ap-4476	384	12	long	long	ADJ
ap-4476	384	13	and	and	CCONJ
ap-4476	384	14	shi	shi	PROPN
ap-4476	384	15	-	-	PUNCT
ap-4476	384	16	hai	hai	PROPN
ap-4476	384	17	dong	dong	PROPN
ap-4476	384	18	,	,	PUNCT
ap-4476	384	19	phys	phy	NOUN
ap-4476	384	20	.	.	PUNCT
ap-4476	385	1	lett	lett	PROPN
ap-4476	385	2	.	.	PUNCT
ap-4476	386	1	a	a	DET
ap-4476	386	2	372	372	NUM
ap-4476	386	3	(	(	PUNCT
ap-4476	386	4	2008	2008	NUM
ap-4476	386	5	)	)	PUNCT
ap-4476	386	6	2592	2592	NUM
ap-4476	386	7	.	.	PUNCT
ap-4476	387	1	[	[	X
ap-4476	387	2	26	26	NUM
ap-4476	387	3	]	]	X
ap-4476	387	4	n.	n.	PROPN
ap-4476	387	5	bhagawati	bhagawati	PROPN
ap-4476	387	6	,	,	PUNCT
ap-4476	387	7	arxiv:1402.1265	arxiv:1402.1265	PROPN
ap-4476	387	8	;	;	PUNCT
ap-4476	387	9	r.	r.	PROPN
ap-4476	387	10	k.	k.	PROPN
ap-4476	387	11	yadav	yadav	PROPN
ap-4476	387	12	et.al	et.al	PROPN
ap-4476	387	13	.	.	PUNCT
ap-4476	388	1	(	(	PUNCT
ap-4476	388	2	unpublished	unpublished	ADJ
ap-4476	388	3	)	)	PUNCT
ap-4476	388	4	.	.	PUNCT
ap-4476	389	1	[	[	X
ap-4476	389	2	27	27	NUM
ap-4476	389	3	]	]	X
ap-4476	389	4	b.	b.	PROPN
ap-4476	389	5	midya	midya	PROPN
ap-4476	389	6	and	and	CCONJ
ap-4476	389	7	b.	b.	PROPN
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ap-4476	389	9	,	,	PUNCT
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ap-4476	389	11	.	.	PUNCT
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ap-4476	390	3	]	]	X
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ap-4476	390	5	khare	khare	PROPN
ap-4476	390	6	and	and	CCONJ
ap-4476	390	7	u.	u.	PROPN
ap-4476	390	8	p.	p.	PROPN
ap-4476	390	9	sukhatme	sukhatme	PROPN
ap-4476	390	10	j.	j.	PROPN
ap-4476	390	11	phys	phys	PROPN
ap-4476	390	12	.	.	PUNCT
ap-4476	391	1	a	a	DET
ap-4476	391	2	:	:	PUNCT
ap-4476	391	3	math	math	NOUN
ap-4476	391	4	.	.	PUNCT
ap-4476	392	1	gen	gen	PROPN
ap-4476	392	2	21	21	NUM
ap-4476	392	3	(	(	PUNCT
ap-4476	392	4	1988	1988	NUM
ap-4476	392	5	)	)	PUNCT
ap-4476	392	6	l501	l501	PROPN
ap-4476	392	7	.	.	PUNCT
ap-4476	393	1	[	[	X
ap-4476	393	2	29	29	NUM
ap-4476	393	3	]	]	X
ap-4476	393	4	e.	e.	PROPN
ap-4476	393	5	hille	hille	PROPN
ap-4476	393	6	,	,	PUNCT
ap-4476	393	7	"	"	PUNCT
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ap-4476	393	9	on	on	ADP
ap-4476	393	10	ordinary	ordinary	ADJ
ap-4476	393	11	differential	differential	ADJ
ap-4476	393	12	equations	equation	NOUN
ap-4476	393	13	"	"	PUNCT
ap-4476	393	14	addision	addision	PROPN
ap-4476	393	15	-	-	PUNCT
ap-4476	393	16	wesley	wesley	PROPN
ap-4476	393	17	(	(	PUNCT
ap-4476	393	18	1969	1969	NUM
ap-4476	393	19	)	)	PUNCT
ap-4476	393	20	p	p	X
ap-4476	393	21	647	647	NUM
ap-4476	393	22	.	.	PUNCT
ap-4476	394	1	[	[	X
ap-4476	394	2	30	30	NUM
ap-4476	394	3	]	]	PUNCT
ap-4476	394	4	a.	a.	NOUN
ap-4476	394	5	a.	a.	NOUN
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ap-4476	394	7	,	,	PUNCT
ap-4476	394	8	t.	t.	PROPN
ap-4476	394	9	p.	p.	PROPN
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ap-4476	394	11	,	,	PUNCT
ap-4476	394	12	am	be	AUX
ap-4476	394	13	.	.	PUNCT
ap-4476	395	1	j.	j.	PROPN
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ap-4476	395	4	(	(	PUNCT
ap-4476	395	5	2011	2011	NUM
ap-4476	395	6	)	)	PUNCT
ap-4476	395	7	668	668	NUM
ap-4476	395	8	.	.	PUNCT
ap-4476	396	1	[	[	X
ap-4476	396	2	31	31	NUM
ap-4476	396	3	]	]	PUNCT
ap-4476	396	4	s.	s.	PROPN
ap-4476	396	5	a.	a.	PROPN
ap-4476	396	6	s.	s.	PROPN
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ap-4476	396	8	,	,	PUNCT
ap-4476	396	9	int	int	PROPN
ap-4476	396	10	.	.	PUNCT
ap-4476	397	1	j.	j.	PROPN
ap-4476	397	2	theor	theor	PROPN
ap-4476	397	3	.	.	PUNCT
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ap-4476	398	2	.	.	PUNCT
ap-4476	398	3	,36	,36	PUNCT
ap-4476	398	4	(	(	PUNCT
ap-4476	398	5	1997	1997	NUM
ap-4476	398	6	)	)	PUNCT
ap-4476	398	7	8	8	NUM
ap-4476	398	8	.	.	X
ap-4476	398	9	487	487	NUM
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ap-4476	398	11	polytechnica	polytechnica	PROPN
ap-4476	398	12	57(6):477–487	57(6):477–487	PROPN
ap-4476	398	13	,	,	PUNCT
ap-4476	398	14	2017	2017	NUM
ap-4476	398	15	1	1	NUM
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ap-4476	398	17	2	2	NUM
ap-4476	398	18	point	point	NOUN
ap-4476	398	19	canonical	canonical	ADJ
ap-4476	398	20	transformation	transformation	NOUN
ap-4476	398	21	(	(	PUNCT
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ap-4476	398	23	)	)	PUNCT
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ap-4476	398	25	for	for	ADP
ap-4476	398	26	arbitrary	arbitrary	ADJ
ap-4476	398	27	d	d	NOUN
ap-4476	398	28	-	-	PUNCT
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ap-4476	398	30	3	3	NUM
ap-4476	398	31	exceptional	exceptional	ADJ
ap-4476	398	32	xm	xm	PROPN
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ap-4476	398	34	polynomials	polynomial	NOUN
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ap-4476	398	37	xm	xm	PROPN
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ap-4476	398	40	polynomials	polynomial	NOUN
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ap-4476	398	47	4	4	NUM
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ap-4476	398	50	in	in	ADP
ap-4476	398	51	d	d	NOUN
ap-4476	398	52	-	-	PUNCT
ap-4476	398	53	dimensions	dimension	NOUN
ap-4476	398	54	4.1	4.1	NUM
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ap-4476	398	57	with	with	ADP
ap-4476	398	58	xm	xm	PROPN
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ap-4476	398	61	polynomial	polynomial	ADJ
ap-4476	398	62	4.2	4.2	NUM
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ap-4476	398	64	associated	associate	VERB
ap-4476	398	65	with	with	ADP
ap-4476	398	66	xm	xm	PROPN
ap-4476	398	67	exceptional	exceptional	ADJ
ap-4476	398	68	jacobi	jacobi	PROPN
ap-4476	398	69	polynomials	polynomial	VERB
ap-4476	398	70	4.2.1	4.2.1	NUM
ap-4476	398	71	approximate	approximate	ADJ
ap-4476	398	72	solutions	solution	NOUN
ap-4476	398	73	for	for	ADP
ap-4476	398	74	arbitrary	arbitrary	ADJ
ap-4476	398	75	5	5	NUM
ap-4476	398	76	new	new	ADJ
ap-4476	398	77	shape	shape	NOUN
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ap-4476	398	79	potentials	potential	NOUN
ap-4476	398	80	(	(	PUNCT
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ap-4476	398	82	)	)	PUNCT
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ap-4476	398	84	higher	high	ADJ
ap-4476	398	85	dimensions	dimension	NOUN
ap-4476	398	86	5.1	5.1	NUM
ap-4476	398	87	extended	extend	VERB
ap-4476	398	88	radial	radial	ADJ
ap-4476	398	89	oscillator	oscillator	NOUN
ap-4476	398	90	potentials	potential	VERB
ap-4476	398	91	5.2	5.2	NUM
ap-4476	398	92	extended	extended	ADJ
ap-4476	398	93	pöschl	pöschl	NOUN
ap-4476	398	94	-	-	PUNCT
ap-4476	398	95	teller	teller	NOUN
ap-4476	398	96	potentials	potential	VERB
ap-4476	398	97	6	6	NUM
ap-4476	398	98	results	result	NOUN
ap-4476	398	99	and	and	CCONJ
ap-4476	398	100	discussions	discussion	NOUN
ap-4476	398	101	acknowledgements	acknowledgement	NOUN
ap-4476	398	102	references	reference	NOUN