id	sid	tid	token	lemma	pos
ap-7659	1	1	acta	acta	PROPN
ap-7659	1	2	polytechnica	polytechnica	PROPN
ap-7659	1	3	https://doi.org/10.14311/ap.2022.62.0157	https://doi.org/10.14311/ap.2022.62.0157	PROPN
ap-7659	1	4	acta	acta	PROPN
ap-7659	1	5	polytechnica	polytechnica	PROPN
ap-7659	1	6	62(1):157–164	62(1):157–164	PROPN
ap-7659	1	7	,	,	PUNCT
ap-7659	1	8	2022	2022	NUM
ap-7659	1	9	©	©	ADP
ap-7659	1	10	2022	2022	NUM
ap-7659	1	11	the	the	DET
ap-7659	1	12	author(s	author(s	NOUN
ap-7659	1	13	)	)	PUNCT
ap-7659	1	14	.	.	PUNCT
ap-7659	2	1	licensed	license	VERB
ap-7659	2	2	under	under	ADP
ap-7659	2	3	a	a	DET
ap-7659	2	4	cc	cc	NOUN
ap-7659	2	5	-	-	PUNCT
ap-7659	2	6	by	by	ADP
ap-7659	2	7	4.0	4.0	NUM
ap-7659	2	8	licence	licence	NOUN
ap-7659	2	9	published	publish	VERB
ap-7659	2	10	by	by	ADP
ap-7659	2	11	the	the	DET
ap-7659	2	12	czech	czech	PROPN
ap-7659	2	13	technical	technical	PROPN
ap-7659	2	14	university	university	PROPN
ap-7659	2	15	in	in	ADP
ap-7659	2	16	prague	prague	PROPN
ap-7659	2	17	swanson	swanson	PROPN
ap-7659	2	18	hamiltonian	hamiltonian	PROPN
ap-7659	2	19	revisited	revisit	VERB
ap-7659	2	20	through	through	ADP
ap-7659	2	21	the	the	DET
ap-7659	2	22	complex	complex	ADJ
ap-7659	2	23	scaling	scaling	NOUN
ap-7659	2	24	method	method	NOUN
ap-7659	2	25	marta	marta	PROPN
ap-7659	2	26	reboiroa	reboiroa	PROPN
ap-7659	2	27	,	,	PUNCT
ap-7659	2	28	b,∗	b,∗	PROPN
ap-7659	2	29	,	,	PUNCT
ap-7659	2	30	romina	romina	PROPN
ap-7659	2	31	ramírezc	ramírezc	PROPN
ap-7659	2	32	,	,	PUNCT
ap-7659	2	33	d	d	PROPN
ap-7659	2	34	,	,	PUNCT
ap-7659	2	35	viviano	viviano	NOUN
ap-7659	2	36	fernándezc	fernándezc	VERB
ap-7659	2	37	a	a	DET
ap-7659	2	38	university	university	NOUN
ap-7659	2	39	of	of	ADP
ap-7659	2	40	la	la	PROPN
ap-7659	2	41	plata	plata	PROPN
ap-7659	2	42	,	,	PUNCT
ap-7659	2	43	faculty	faculty	NOUN
ap-7659	2	44	of	of	ADP
ap-7659	2	45	exact	exact	ADJ
ap-7659	2	46	science	science	NOUN
ap-7659	2	47	,	,	PUNCT
ap-7659	2	48	department	department	NOUN
ap-7659	2	49	of	of	ADP
ap-7659	2	50	physics	physics	PROPN
ap-7659	2	51	,	,	PUNCT
ap-7659	2	52	49	49	NUM
ap-7659	2	53	&	&	CCONJ
ap-7659	2	54	115	115	NUM
ap-7659	2	55	,	,	PUNCT
ap-7659	2	56	1900	1900	NUM
ap-7659	2	57	la	la	PROPN
ap-7659	2	58	plata	plata	PROPN
ap-7659	2	59	,	,	PUNCT
ap-7659	2	60	argentine	argentine	PROPN
ap-7659	2	61	b	b	PROPN
ap-7659	2	62	conicet	conicet	PROPN
ap-7659	2	63	,	,	PUNCT
ap-7659	2	64	institute	institute	PROPN
ap-7659	2	65	of	of	ADP
ap-7659	2	66	physics	physics	PROPN
ap-7659	2	67	of	of	ADP
ap-7659	2	68	la	la	PROPN
ap-7659	2	69	plata	plata	PROPN
ap-7659	2	70	.	.	PUNCT
ap-7659	3	1	63	63	NUM
ap-7659	3	2	&	&	CCONJ
ap-7659	3	3	diag	diag	NOUN
ap-7659	3	4	.	.	PROPN
ap-7659	4	1	113	113	NUM
ap-7659	4	2	,	,	PUNCT
ap-7659	4	3	1900	1900	NUM
ap-7659	4	4	la	la	PROPN
ap-7659	4	5	plata	plata	PROPN
ap-7659	4	6	,	,	PUNCT
ap-7659	4	7	argentine	argentine	PROPN
ap-7659	4	8	c	c	PROPN
ap-7659	4	9	university	university	PROPN
ap-7659	4	10	of	of	ADP
ap-7659	4	11	la	la	PROPN
ap-7659	4	12	plata	plata	PROPN
ap-7659	4	13	,	,	PUNCT
ap-7659	4	14	faculty	faculty	NOUN
ap-7659	4	15	of	of	ADP
ap-7659	4	16	exact	exact	ADJ
ap-7659	4	17	science	science	NOUN
ap-7659	4	18	,	,	PUNCT
ap-7659	4	19	department	department	NOUN
ap-7659	4	20	of	of	ADP
ap-7659	4	21	mathematics	mathematic	NOUN
ap-7659	4	22	,	,	PUNCT
ap-7659	4	23	50	50	NUM
ap-7659	4	24	&	&	CCONJ
ap-7659	4	25	115	115	NUM
ap-7659	4	26	,	,	PUNCT
ap-7659	4	27	1900	1900	NUM
ap-7659	4	28	la	la	PROPN
ap-7659	4	29	plata	plata	PROPN
ap-7659	4	30	,	,	PUNCT
ap-7659	4	31	argentine	argentine	PROPN
ap-7659	4	32	d	d	PROPN
ap-7659	4	33	conicet	conicet	PROPN
ap-7659	4	34	,	,	PUNCT
ap-7659	4	35	institute	institute	NOUN
ap-7659	4	36	argentine	argentine	NOUN
ap-7659	4	37	of	of	ADP
ap-7659	4	38	mathematics	mathematic	NOUN
ap-7659	4	39	.	.	PUNCT
ap-7659	5	1	saavedra	saavedra	PROPN
ap-7659	5	2	15	15	NUM
ap-7659	5	3	3º	3º	NUM
ap-7659	5	4	,	,	PUNCT
ap-7659	5	5	c1083aca	c1083aca	PROPN
ap-7659	5	6	buenos	buenos	PROPN
ap-7659	5	7	aires	aires	PROPN
ap-7659	5	8	,	,	PUNCT
ap-7659	5	9	argentine	argentine	ADJ
ap-7659	5	10	∗	∗	NOUN
ap-7659	5	11	corresponding	correspond	VERB
ap-7659	5	12	author	author	NOUN
ap-7659	5	13	:	:	PUNCT
ap-7659	5	14	reboiro@fisica.unlp.edu.ar	reboiro@fisica.unlp.edu.ar	X
ap-7659	5	15	abstract	abstract	ADJ
ap-7659	5	16	.	.	PUNCT
ap-7659	6	1	in	in	ADP
ap-7659	6	2	this	this	DET
ap-7659	6	3	work	work	NOUN
ap-7659	6	4	,	,	PUNCT
ap-7659	6	5	we	we	PRON
ap-7659	6	6	study	study	VERB
ap-7659	6	7	the	the	DET
ap-7659	6	8	non	non	ADJ
ap-7659	6	9	-	-	ADJ
ap-7659	6	10	hermitian	hermitian	ADJ
ap-7659	6	11	pt	pt	PROPN
ap-7659	6	12	-	-	PUNCT
ap-7659	6	13	symmetry	symmetry	NOUN
ap-7659	6	14	swanson	swanson	PROPN
ap-7659	6	15	hamiltonian	hamiltonian	NOUN
ap-7659	6	16	in	in	ADP
ap-7659	6	17	the	the	DET
ap-7659	6	18	framework	framework	NOUN
ap-7659	6	19	of	of	ADP
ap-7659	6	20	the	the	DET
ap-7659	6	21	complex	complex	ADJ
ap-7659	6	22	scaling	scaling	NOUN
ap-7659	6	23	method	method	NOUN
ap-7659	6	24	.	.	PUNCT
ap-7659	7	1	we	we	PRON
ap-7659	7	2	show	show	VERB
ap-7659	7	3	that	that	SCONJ
ap-7659	7	4	by	by	ADP
ap-7659	7	5	applying	apply	VERB
ap-7659	7	6	this	this	DET
ap-7659	7	7	method	method	NOUN
ap-7659	7	8	we	we	PRON
ap-7659	7	9	can	can	AUX
ap-7659	7	10	work	work	VERB
ap-7659	7	11	with	with	ADP
ap-7659	7	12	eigenfunctions	eigenfunction	NOUN
ap-7659	7	13	that	that	PRON
ap-7659	7	14	are	be	AUX
ap-7659	7	15	square	square	ADJ
ap-7659	7	16	-	-	PUNCT
ap-7659	7	17	integrable	integrable	ADJ
ap-7659	7	18	both	both	PRON
ap-7659	7	19	in	in	ADP
ap-7659	7	20	the	the	DET
ap-7659	7	21	pt	pt	NOUN
ap-7659	7	22	and	and	CCONJ
ap-7659	7	23	in	in	ADP
ap-7659	7	24	the	the	DET
ap-7659	7	25	non	non	ADJ
ap-7659	7	26	-	-	ADJ
ap-7659	7	27	pt	pt	ADJ
ap-7659	7	28	symmetry	symmetry	NOUN
ap-7659	7	29	phase	phase	NOUN
ap-7659	7	30	.	.	PUNCT
ap-7659	8	1	keywords	keyword	NOUN
ap-7659	8	2	:	:	PUNCT
ap-7659	8	3	pt	pt	ADJ
ap-7659	8	4	-	-	ADJ
ap-7659	8	5	symmetric	symmetric	ADJ
ap-7659	8	6	hamiltonians	hamiltonian	NOUN
ap-7659	8	7	,	,	PUNCT
ap-7659	8	8	swanson	swanson	PROPN
ap-7659	8	9	model	model	NOUN
ap-7659	8	10	,	,	PUNCT
ap-7659	8	11	complex	complex	ADJ
ap-7659	8	12	scaling	scaling	NOUN
ap-7659	8	13	method	method	NOUN
ap-7659	8	14	.	.	PUNCT
ap-7659	9	1	1	1	X
ap-7659	9	2	.	.	X
ap-7659	9	3	introduction	introduction	NOUN
ap-7659	9	4	the	the	DET
ap-7659	9	5	swanson	swanson	PROPN
ap-7659	9	6	model	model	NOUN
ap-7659	9	7	has	have	AUX
ap-7659	9	8	been	be	AUX
ap-7659	9	9	introduced	introduce	VERB
ap-7659	9	10	in	in	ADP
ap-7659	9	11	[	[	X
ap-7659	9	12	1	1	NUM
ap-7659	9	13	]	]	PUNCT
ap-7659	9	14	as	as	ADP
ap-7659	9	15	an	an	DET
ap-7659	9	16	example	example	NOUN
ap-7659	9	17	of	of	ADP
ap-7659	9	18	a	a	DET
ap-7659	9	19	pt	pt	NOUN
ap-7659	9	20	-	-	PUNCT
ap-7659	9	21	symmetry	symmetry	NOUN
ap-7659	9	22	hamiltonian	hamiltonian	NOUN
ap-7659	10	1	[	[	X
ap-7659	10	2	2–8	2–8	NUM
ap-7659	10	3	]	]	PUNCT
ap-7659	10	4	.	.	PUNCT
ap-7659	11	1	since	since	SCONJ
ap-7659	11	2	then	then	ADV
ap-7659	11	3	it	it	PRON
ap-7659	11	4	has	have	AUX
ap-7659	11	5	been	be	AUX
ap-7659	11	6	extensively	extensively	ADV
ap-7659	11	7	studied	study	VERB
ap-7659	11	8	,	,	PUNCT
ap-7659	11	9	allowing	allow	VERB
ap-7659	11	10	for	for	ADP
ap-7659	11	11	several	several	ADJ
ap-7659	11	12	interesting	interesting	ADJ
ap-7659	11	13	extensions	extension	NOUN
ap-7659	11	14	[	[	X
ap-7659	11	15	9–25	9–25	NUM
ap-7659	11	16	]	]	PUNCT
ap-7659	11	17	.	.	PUNCT
ap-7659	12	1	among	among	ADP
ap-7659	12	2	recent	recent	ADJ
ap-7659	12	3	works	work	NOUN
ap-7659	12	4	,	,	PUNCT
ap-7659	12	5	let	let	VERB
ap-7659	12	6	us	we	PRON
ap-7659	12	7	mention	mention	VERB
ap-7659	12	8	an	an	DET
ap-7659	12	9	extension	extension	NOUN
ap-7659	12	10	of	of	ADP
ap-7659	12	11	the	the	DET
ap-7659	12	12	swanson	swanson	PROPN
ap-7659	12	13	model	model	NOUN
ap-7659	12	14	with	with	ADP
ap-7659	12	15	complex	complex	ADJ
ap-7659	12	16	parameters	parameter	NOUN
ap-7659	12	17	[	[	X
ap-7659	12	18	23	23	NUM
ap-7659	12	19	,	,	PUNCT
ap-7659	12	20	25	25	NUM
ap-7659	12	21	]	]	PUNCT
ap-7659	12	22	,	,	PUNCT
ap-7659	12	23	this	this	DET
ap-7659	12	24	work	work	NOUN
ap-7659	12	25	introduces	introduce	VERB
ap-7659	12	26	bicoherent	bicoherent	ADJ
ap-7659	12	27	-	-	PUNCT
ap-7659	12	28	state	state	NOUN
ap-7659	12	29	path	path	NOUN
ap-7659	12	30	integration	integration	NOUN
ap-7659	12	31	as	as	ADP
ap-7659	12	32	a	a	DET
ap-7659	12	33	method	method	NOUN
ap-7659	12	34	to	to	PART
ap-7659	12	35	quantify	quantify	VERB
ap-7659	12	36	non	non	ADJ
ap-7659	12	37	-	-	ADJ
ap-7659	12	38	hermitian	hermitian	ADJ
ap-7659	12	39	systems	system	NOUN
ap-7659	12	40	.	.	PUNCT
ap-7659	13	1	though	though	SCONJ
ap-7659	13	2	the	the	DET
ap-7659	13	3	swanson	swanson	PROPN
ap-7659	13	4	model	model	NOUN
ap-7659	13	5	is	be	AUX
ap-7659	13	6	described	describe	VERB
ap-7659	13	7	by	by	ADP
ap-7659	13	8	quadratic	quadratic	ADJ
ap-7659	13	9	operators	operator	NOUN
ap-7659	13	10	,	,	PUNCT
ap-7659	13	11	the	the	DET
ap-7659	13	12	underlying	underlie	VERB
ap-7659	13	13	physics	physics	NOUN
ap-7659	13	14	is	be	AUX
ap-7659	13	15	nevertheless	nevertheless	ADV
ap-7659	13	16	very	very	ADV
ap-7659	13	17	rich	rich	ADJ
ap-7659	13	18	.	.	PUNCT
ap-7659	14	1	depending	depend	VERB
ap-7659	14	2	on	on	ADP
ap-7659	14	3	the	the	DET
ap-7659	14	4	region	region	NOUN
ap-7659	14	5	in	in	ADP
ap-7659	14	6	the	the	DET
ap-7659	14	7	model	model	NOUN
ap-7659	14	8	parameter	parameter	PROPN
ap-7659	14	9	space	space	NOUN
ap-7659	14	10	,	,	PUNCT
ap-7659	14	11	the	the	DET
ap-7659	14	12	swanson	swanson	PROPN
ap-7659	14	13	model	model	NOUN
ap-7659	14	14	is	be	AUX
ap-7659	14	15	similar	similar	ADJ
ap-7659	14	16	to	to	ADP
ap-7659	14	17	the	the	DET
ap-7659	14	18	hamiltonian	hamiltonian	NOUN
ap-7659	14	19	of	of	ADP
ap-7659	14	20	a	a	DET
ap-7659	14	21	parabolic	parabolic	ADJ
ap-7659	14	22	barrier	barrier	NOUN
ap-7659	14	23	or	or	CCONJ
ap-7659	14	24	the	the	DET
ap-7659	14	25	hamiltonian	hamiltonian	NOUN
ap-7659	14	26	of	of	ADP
ap-7659	14	27	a	a	DET
ap-7659	14	28	harmonic	harmonic	ADJ
ap-7659	14	29	oscillator	oscillator	NOUN
ap-7659	14	30	[	[	X
ap-7659	14	31	26	26	NUM
ap-7659	14	32	]	]	PUNCT
ap-7659	14	33	.	.	PUNCT
ap-7659	15	1	from	from	ADP
ap-7659	15	2	the	the	DET
ap-7659	15	3	mathematical	mathematical	ADJ
ap-7659	15	4	point	point	NOUN
ap-7659	15	5	of	of	ADP
ap-7659	15	6	view	view	NOUN
ap-7659	15	7	,	,	PUNCT
ap-7659	15	8	it	it	PRON
ap-7659	15	9	is	be	AUX
ap-7659	15	10	an	an	DET
ap-7659	15	11	example	example	NOUN
ap-7659	15	12	of	of	ADP
ap-7659	15	13	a	a	DET
ap-7659	15	14	hamiltonian	hamiltonian	NOUN
ap-7659	15	15	with	with	ADP
ap-7659	15	16	eigenfunctions	eigenfunction	NOUN
ap-7659	15	17	that	that	PRON
ap-7659	15	18	do	do	AUX
ap-7659	15	19	not	not	PART
ap-7659	15	20	belong	belong	VERB
ap-7659	15	21	to	to	ADP
ap-7659	15	22	l2(r	l2(r	NOUN
ap-7659	15	23	)	)	PUNCT
ap-7659	15	24	in	in	ADP
ap-7659	15	25	some	some	DET
ap-7659	15	26	regions	region	NOUN
ap-7659	15	27	of	of	ADP
ap-7659	15	28	the	the	DET
ap-7659	15	29	space	space	NOUN
ap-7659	15	30	of	of	ADP
ap-7659	15	31	parameters	parameter	NOUN
ap-7659	15	32	.	.	PUNCT
ap-7659	16	1	among	among	ADP
ap-7659	16	2	the	the	DET
ap-7659	16	3	methods	method	NOUN
ap-7659	16	4	that	that	PRON
ap-7659	16	5	are	be	AUX
ap-7659	16	6	employed	employ	VERB
ap-7659	16	7	to	to	PART
ap-7659	16	8	describe	describe	VERB
ap-7659	16	9	the	the	DET
ap-7659	16	10	physics	physics	NOUN
ap-7659	16	11	of	of	ADP
ap-7659	16	12	resonances	resonance	NOUN
ap-7659	16	13	with	with	ADP
ap-7659	16	14	complex	complex	ADJ
ap-7659	16	15	energy	energy	NOUN
ap-7659	16	16	,	,	PUNCT
ap-7659	16	17	the	the	DET
ap-7659	16	18	complex	complex	ADJ
ap-7659	16	19	scaling	scaling	NOUN
ap-7659	16	20	method	method	NOUN
ap-7659	16	21	(	(	PUNCT
ap-7659	16	22	csm	csm	X
ap-7659	16	23	)	)	PUNCT
ap-7659	17	1	[	[	X
ap-7659	17	2	27–32	27–32	NUM
ap-7659	17	3	]	]	X
ap-7659	17	4	is	be	AUX
ap-7659	17	5	one	one	NUM
ap-7659	17	6	of	of	ADP
ap-7659	17	7	the	the	DET
ap-7659	17	8	most	most	ADV
ap-7659	17	9	powerful	powerful	ADJ
ap-7659	17	10	.	.	PUNCT
ap-7659	18	1	it	it	PRON
ap-7659	18	2	has	have	AUX
ap-7659	18	3	been	be	AUX
ap-7659	18	4	extensively	extensively	ADV
ap-7659	18	5	used	use	VERB
ap-7659	18	6	in	in	ADP
ap-7659	18	7	the	the	DET
ap-7659	18	8	description	description	NOUN
ap-7659	18	9	of	of	ADP
ap-7659	18	10	many	many	ADJ
ap-7659	18	11	-	-	PUNCT
ap-7659	18	12	body	body	NOUN
ap-7659	18	13	resonant	resonant	NOUN
ap-7659	18	14	states	state	NOUN
ap-7659	18	15	and	and	CCONJ
ap-7659	18	16	non	non	ADJ
ap-7659	18	17	-	-	ADJ
ap-7659	18	18	resonant	resonant	ADJ
ap-7659	18	19	continuum	continuum	ADJ
ap-7659	18	20	states	state	NOUN
ap-7659	18	21	observed	observe	VERB
ap-7659	18	22	in	in	ADP
ap-7659	18	23	unstable	unstable	ADJ
ap-7659	18	24	nuclei	nucleus	NOUN
ap-7659	18	25	[	[	X
ap-7659	18	26	32	32	NUM
ap-7659	18	27	]	]	PUNCT
ap-7659	18	28	.	.	PUNCT
ap-7659	19	1	in	in	ADP
ap-7659	19	2	this	this	DET
ap-7659	19	3	work	work	NOUN
ap-7659	19	4	,	,	PUNCT
ap-7659	19	5	we	we	PRON
ap-7659	19	6	propose	propose	VERB
ap-7659	19	7	the	the	DET
ap-7659	19	8	use	use	NOUN
ap-7659	19	9	of	of	ADP
ap-7659	19	10	the	the	DET
ap-7659	19	11	csm	csm	NOUN
ap-7659	19	12	to	to	PART
ap-7659	19	13	describe	describe	VERB
ap-7659	19	14	the	the	DET
ap-7659	19	15	dynamics	dynamic	NOUN
ap-7659	19	16	of	of	ADP
ap-7659	19	17	the	the	DET
ap-7659	19	18	swanson	swanson	PROPN
ap-7659	19	19	model	model	NOUN
ap-7659	19	20	,	,	PUNCT
ap-7659	19	21	particularly	particularly	ADV
ap-7659	19	22	in	in	ADP
ap-7659	19	23	the	the	DET
ap-7659	19	24	region	region	NOUN
ap-7659	19	25	of	of	ADP
ap-7659	19	26	non	non	ADJ
ap-7659	19	27	-	-	ADJ
ap-7659	19	28	pt	pt	NOUN
ap-7659	19	29	-	-	PUNCT
ap-7659	19	30	symmetry	symmetry	NOUN
ap-7659	19	31	.	.	PUNCT
ap-7659	20	1	the	the	DET
ap-7659	20	2	work	work	NOUN
ap-7659	20	3	is	be	AUX
ap-7659	20	4	organized	organize	VERB
ap-7659	20	5	as	as	SCONJ
ap-7659	20	6	follows	follow	VERB
ap-7659	20	7	.	.	PUNCT
ap-7659	21	1	in	in	ADP
ap-7659	21	2	section	section	NOUN
ap-7659	21	3	2	2	NUM
ap-7659	21	4	we	we	PRON
ap-7659	21	5	describe	describe	VERB
ap-7659	21	6	the	the	DET
ap-7659	21	7	application	application	NOUN
ap-7659	21	8	of	of	ADP
ap-7659	21	9	the	the	DET
ap-7659	21	10	csm	csm	NOUN
ap-7659	21	11	to	to	ADP
ap-7659	21	12	the	the	DET
ap-7659	21	13	swanson	swanson	PROPN
ap-7659	21	14	hamiltonian	hamiltonian	NOUN
ap-7659	21	15	.	.	PUNCT
ap-7659	22	1	we	we	PRON
ap-7659	22	2	establish	establish	VERB
ap-7659	22	3	a	a	DET
ap-7659	22	4	similarity	similarity	NOUN
ap-7659	22	5	transformation	transformation	NOUN
ap-7659	22	6	between	between	ADP
ap-7659	22	7	the	the	DET
ap-7659	22	8	transformed	transform	VERB
ap-7659	22	9	hamiltonian	hamiltonian	NOUN
ap-7659	22	10	and	and	CCONJ
ap-7659	22	11	its	its	PRON
ap-7659	22	12	adjoint	adjoint	NOUN
ap-7659	22	13	operator	operator	NOUN
ap-7659	22	14	.	.	PUNCT
ap-7659	23	1	we	we	PRON
ap-7659	23	2	discuss	discuss	VERB
ap-7659	23	3	,	,	PUNCT
ap-7659	23	4	according	accord	VERB
ap-7659	23	5	to	to	ADP
ap-7659	23	6	the	the	DET
ap-7659	23	7	space	space	NOUN
ap-7659	23	8	of	of	ADP
ap-7659	23	9	parameters	parameter	NOUN
ap-7659	23	10	of	of	ADP
ap-7659	23	11	the	the	DET
ap-7659	23	12	model	model	NOUN
ap-7659	23	13	,	,	PUNCT
ap-7659	23	14	the	the	DET
ap-7659	23	15	possibility	possibility	NOUN
ap-7659	23	16	of	of	ADP
ap-7659	23	17	having	have	VERB
ap-7659	23	18	square	square	NOUN
ap-7659	23	19	-	-	PUNCT
ap-7659	23	20	integrable	integrable	ADJ
ap-7659	23	21	eigenfunctions	eigenfunction	NOUN
ap-7659	23	22	.	.	PUNCT
ap-7659	24	1	we	we	PRON
ap-7659	24	2	present	present	VERB
ap-7659	24	3	the	the	DET
ap-7659	24	4	mean	mean	ADJ
ap-7659	24	5	values	value	NOUN
ap-7659	24	6	of	of	ADP
ap-7659	24	7	some	some	DET
ap-7659	24	8	observables	observable	NOUN
ap-7659	24	9	.	.	PUNCT
ap-7659	25	1	in	in	ADP
ap-7659	25	2	section	section	NOUN
ap-7659	25	3	3	3	NUM
ap-7659	25	4	,	,	PUNCT
ap-7659	25	5	we	we	PRON
ap-7659	25	6	analyse	analyse	VERB
ap-7659	25	7	with	with	ADP
ap-7659	25	8	an	an	DET
ap-7659	25	9	example	example	NOUN
ap-7659	25	10	,	,	PUNCT
ap-7659	25	11	the	the	DET
ap-7659	25	12	survival	survival	NOUN
ap-7659	25	13	probability	probability	NOUN
ap-7659	25	14	as	as	ADP
ap-7659	25	15	a	a	DET
ap-7659	25	16	function	function	NOUN
ap-7659	25	17	of	of	ADP
ap-7659	25	18	time	time	NOUN
ap-7659	25	19	for	for	ADP
ap-7659	25	20	an	an	DET
ap-7659	25	21	initial	initial	ADJ
ap-7659	25	22	coherent	coherent	ADJ
ap-7659	25	23	state	state	NOUN
ap-7659	25	24	.	.	PUNCT
ap-7659	26	1	conclusions	conclusion	NOUN
ap-7659	26	2	are	be	AUX
ap-7659	26	3	drawn	draw	VERB
ap-7659	26	4	in	in	ADP
ap-7659	26	5	section	section	NOUN
ap-7659	26	6	4	4	NUM
ap-7659	26	7	.	.	NOUN
ap-7659	26	8	2	2	NUM
ap-7659	26	9	.	.	X
ap-7659	26	10	formalism	formalism	VERB
ap-7659	26	11	the	the	DET
ap-7659	26	12	hamiltonian	hamiltonian	NOUN
ap-7659	26	13	of	of	ADP
ap-7659	26	14	swanson	swanson	PROPN
ap-7659	27	1	[	[	X
ap-7659	27	2	1	1	NUM
ap-7659	27	3	]	]	PUNCT
ap-7659	27	4	is	be	AUX
ap-7659	27	5	given	give	VERB
ap-7659	27	6	by	by	ADP
ap-7659	27	7	h	h	NOUN
ap-7659	27	8	=	=	NOUN
ap-7659	27	9	ℏω	ℏω	INTJ
ap-7659	27	10	(	(	PUNCT
ap-7659	27	11	a†a+	a†a+	PROPN
ap-7659	27	12	1	1	NUM
ap-7659	27	13	2	2	NUM
ap-7659	27	14	)	)	PUNCT
ap-7659	27	15	+	+	CCONJ
ap-7659	27	16	ℏα	ℏα	ADP
ap-7659	27	17	a2	a2	PROPN
ap-7659	27	18	+	+	X
ap-7659	27	19	ℏβ	ℏβ	NOUN
ap-7659	27	20	a†2	a†2	PROPN
ap-7659	27	21	,	,	PUNCT
ap-7659	27	22	(	(	PUNCT
ap-7659	27	23	1	1	X
ap-7659	27	24	)	)	PUNCT
ap-7659	27	25	with	with	ADP
ap-7659	27	26	ω	ω	PROPN
ap-7659	27	27	,	,	PUNCT
ap-7659	27	28	α	α	X
ap-7659	27	29	,	,	PUNCT
ap-7659	27	30	β	β	PROPN
ap-7659	27	31	∈	∈	PROPN
ap-7659	27	32	r.	r.	NOUN
ap-7659	27	33	the	the	DET
ap-7659	27	34	hamiltonian	hamiltonian	NOUN
ap-7659	27	35	of	of	ADP
ap-7659	27	36	eq	eq	PROPN
ap-7659	27	37	.	.	PUNCT
ap-7659	28	1	(	(	PUNCT
ap-7659	28	2	1	1	X
ap-7659	28	3	)	)	PUNCT
ap-7659	28	4	can	can	AUX
ap-7659	28	5	be	be	AUX
ap-7659	28	6	written	write	VERB
ap-7659	28	7	in	in	ADP
ap-7659	28	8	terms	term	NOUN
ap-7659	28	9	of	of	ADP
ap-7659	28	10	the	the	DET
ap-7659	28	11	coordinate	coordinate	NOUN
ap-7659	28	12	operator	operator	NOUN
ap-7659	28	13	,	,	PUNCT
ap-7659	28	14	x̂	x̂	NUM
ap-7659	28	15	,	,	PUNCT
ap-7659	28	16	and	and	CCONJ
ap-7659	28	17	the	the	DET
ap-7659	28	18	momentum	momentum	NOUN
ap-7659	28	19	operator	operator	NOUN
ap-7659	28	20	,	,	PUNCT
ap-7659	28	21	p̂	p̂	X
ap-7659	28	22	,	,	PUNCT
ap-7659	28	23	by	by	ADP
ap-7659	28	24	implementing	implement	VERB
ap-7659	28	25	the	the	DET
ap-7659	28	26	following	follow	VERB
ap-7659	28	27	representation	representation	NOUN
ap-7659	28	28	a	a	DET
ap-7659	28	29	=	=	SYM
ap-7659	28	30	1√	1√	ADJ
ap-7659	28	31	2	2	NUM
ap-7659	28	32	(	(	PUNCT
ap-7659	28	33	x̂	x̂	NUM
ap-7659	28	34	b0	b0	NOUN
ap-7659	28	35	+	+	CCONJ
ap-7659	28	36	ib0	ib0	NOUN
ap-7659	28	37	ℏ	ℏ	PRON
ap-7659	28	38	p̂	p̂	NOUN
ap-7659	28	39	)	)	PUNCT
ap-7659	28	40	,	,	PUNCT
ap-7659	28	41	a†	a†	NOUN
ap-7659	28	42	=	=	SYM
ap-7659	28	43	1√	1√	PROPN
ap-7659	28	44	2	2	NUM
ap-7659	28	45	(	(	PUNCT
ap-7659	28	46	x̂	x̂	NUM
ap-7659	28	47	b0	b0	ADP
ap-7659	28	48	−	−	PROPN
ap-7659	28	49	ib0	ib0	ADP
ap-7659	28	50	ℏ	ℏ	NOUN
ap-7659	28	51	p̂	p̂	NOUN
ap-7659	28	52	)	)	PUNCT
ap-7659	28	53	,	,	PUNCT
ap-7659	28	54	(	(	PUNCT
ap-7659	28	55	2	2	X
ap-7659	28	56	)	)	PUNCT
ap-7659	28	57	being	be	AUX
ap-7659	28	58	b0	b0	VERB
ap-7659	28	59	the	the	DET
ap-7659	28	60	characteristic	characteristic	ADJ
ap-7659	28	61	length	length	NOUN
ap-7659	28	62	of	of	ADP
ap-7659	28	63	the	the	DET
ap-7659	28	64	noninteracting	noninteracting	NOUN
ap-7659	28	65	system	system	NOUN
ap-7659	28	66	.	.	PUNCT
ap-7659	29	1	the	the	DET
ap-7659	29	2	hamiltonian	hamiltonian	NOUN
ap-7659	29	3	in	in	ADP
ap-7659	29	4	eq	eq	PROPN
ap-7659	29	5	.	.	PUNCT
ap-7659	30	1	(	(	PUNCT
ap-7659	30	2	1	1	X
ap-7659	30	3	)	)	PUNCT
ap-7659	30	4	reads	read	VERB
ap-7659	30	5	h(ω	h(ω	PROPN
ap-7659	30	6	,	,	PUNCT
ap-7659	30	7	α	α	X
ap-7659	30	8	,	,	PUNCT
ap-7659	30	9	β	β	NOUN
ap-7659	30	10	)	)	PUNCT
ap-7659	30	11	=	=	SYM
ap-7659	30	12	1	1	NUM
ap-7659	30	13	2ℏ(ω	2ℏ(ω	NUM
ap-7659	30	14	+	+	CCONJ
ap-7659	30	15	α+	α+	X
ap-7659	30	16	β	β	X
ap-7659	30	17	)	)	PUNCT
ap-7659	30	18	(	(	PUNCT
ap-7659	30	19	x̂	x̂	NUM
ap-7659	30	20	b0	b0	NOUN
ap-7659	30	21	)	)	PUNCT
ap-7659	30	22	2	2	NUM
ap-7659	30	23	+1	+1	NOUN
ap-7659	30	24	2ℏ(ω	2ℏ(ω	NUM
ap-7659	30	25	−	−	NOUN
ap-7659	30	26	α−	α−	ADP
ap-7659	30	27	β	β	NOUN
ap-7659	30	28	)	)	PUNCT
ap-7659	30	29	(	(	PUNCT
ap-7659	30	30	b0	b0	VERB
ap-7659	30	31	p̂	p̂	NUM
ap-7659	30	32	ℏ	ℏ	NOUN
ap-7659	30	33	)	)	PUNCT
ap-7659	30	34	2	2	NUM
ap-7659	31	1	+	+	SYM
ap-7659	31	2	ℏ	ℏ	PROPN
ap-7659	31	3	(	(	PUNCT
ap-7659	31	4	α−	α−	ADP
ap-7659	31	5	β	β	NOUN
ap-7659	31	6	)	)	PUNCT
ap-7659	31	7	2	2	NUM
ap-7659	31	8	(	(	PUNCT
ap-7659	31	9	2	2	NUM
ap-7659	31	10	x̂	x̂	NUM
ap-7659	31	11	i	i	PRON
ap-7659	31	12	ℏ	ℏ	PROPN
ap-7659	31	13	p̂+	p̂+	NOUN
ap-7659	31	14	1	1	NUM
ap-7659	31	15	)	)	PUNCT
ap-7659	31	16	.	.	PUNCT
ap-7659	32	1	(	(	PUNCT
ap-7659	32	2	3	3	X
ap-7659	32	3	)	)	PUNCT
ap-7659	32	4	the	the	DET
ap-7659	32	5	adjoint	adjoint	PROPN
ap-7659	32	6	hamiltonian	hamiltonian	NOUN
ap-7659	32	7	of	of	ADP
ap-7659	32	8	h(ω	h(ω	PROPN
ap-7659	32	9	,	,	PUNCT
ap-7659	32	10	α	α	X
ap-7659	32	11	,	,	PUNCT
ap-7659	32	12	β	β	NOUN
ap-7659	32	13	)	)	PUNCT
ap-7659	32	14	is	be	AUX
ap-7659	32	15	hc	hc	PROPN
ap-7659	32	16	=	=	PUNCT
ap-7659	32	17	h(ω	h(ω	PROPN
ap-7659	32	18	,	,	PUNCT
ap-7659	32	19	β	β	X
ap-7659	32	20	,	,	PUNCT
ap-7659	32	21	α	α	NOUN
ap-7659	32	22	)	)	PUNCT
ap-7659	32	23	.	.	PUNCT
ap-7659	33	1	as	as	SCONJ
ap-7659	33	2	we	we	PRON
ap-7659	33	3	showed	show	VERB
ap-7659	33	4	in	in	ADP
ap-7659	33	5	[	[	X
ap-7659	33	6	26	26	NUM
ap-7659	33	7	]	]	PUNCT
ap-7659	33	8	,	,	PUNCT
ap-7659	33	9	some	some	PRON
ap-7659	33	10	of	of	ADP
ap-7659	33	11	the	the	DET
ap-7659	33	12	eigenfunctions	eigenfunction	NOUN
ap-7659	33	13	of	of	ADP
ap-7659	33	14	eq	eq	PROPN
ap-7659	33	15	.	.	PUNCT
ap-7659	34	1	(	(	PUNCT
ap-7659	34	2	3	3	X
ap-7659	34	3	)	)	PUNCT
ap-7659	34	4	do	do	AUX
ap-7659	34	5	not	not	PART
ap-7659	34	6	belong	belong	VERB
ap-7659	34	7	to	to	ADP
ap-7659	34	8	the	the	DET
ap-7659	34	9	usual	usual	ADJ
ap-7659	34	10	hilbert	hilbert	NOUN
ap-7659	34	11	space	space	NOUN
ap-7659	34	12	,	,	PUNCT
ap-7659	34	13	h	h	NOUN
ap-7659	34	14	=	=	SYM
ap-7659	34	15	l2(r	l2(r	PROPN
ap-7659	34	16	)	)	PUNCT
ap-7659	34	17	,	,	PUNCT
ap-7659	34	18	so	so	SCONJ
ap-7659	34	19	that	that	SCONJ
ap-7659	34	20	we	we	PRON
ap-7659	34	21	have	have	VERB
ap-7659	34	22	to	to	PART
ap-7659	34	23	work	work	VERB
ap-7659	34	24	in	in	ADP
ap-7659	34	25	a	a	DET
ap-7659	34	26	rigged	rig	VERB
ap-7659	34	27	hilbert	hilbert	NOUN
ap-7659	34	28	space	space	NOUN
ap-7659	34	29	[	[	X
ap-7659	34	30	33	33	NUM
ap-7659	34	31	,	,	PUNCT
ap-7659	34	32	34	34	NUM
ap-7659	34	33	]	]	PUNCT
ap-7659	34	34	.	.	PUNCT
ap-7659	35	1	an	an	DET
ap-7659	35	2	alternative	alternative	ADJ
ap-7659	35	3	approach	approach	NOUN
ap-7659	35	4	to	to	PART
ap-7659	35	5	solve	solve	VERB
ap-7659	35	6	the	the	DET
ap-7659	35	7	eigenvalue	eigenvalue	PROPN
ap-7659	35	8	problem	problem	NOUN
ap-7659	35	9	of	of	ADP
ap-7659	35	10	the	the	DET
ap-7659	35	11	hamiltonian	hamiltonian	NOUN
ap-7659	35	12	of	of	ADP
ap-7659	35	13	eq	eq	PROPN
ap-7659	35	14	.	.	PUNCT
ap-7659	36	1	(	(	PUNCT
ap-7659	36	2	1	1	NUM
ap-7659	36	3	)	)	PUNCT
ap-7659	36	4	,	,	PUNCT
ap-7659	36	5	is	be	AUX
ap-7659	36	6	the	the	DET
ap-7659	36	7	use	use	NOUN
ap-7659	36	8	of	of	ADP
ap-7659	36	9	the	the	DET
ap-7659	36	10	csm	csm	NOUN
ap-7659	36	11	method	method	NOUN
ap-7659	36	12	[	[	X
ap-7659	36	13	27–32	27–32	NUM
ap-7659	36	14	]	]	PUNCT
ap-7659	36	15	.	.	PUNCT
ap-7659	37	1	the	the	DET
ap-7659	37	2	aim	aim	NOUN
ap-7659	37	3	of	of	ADP
ap-7659	37	4	the	the	DET
ap-7659	37	5	csm	csm	NOUN
ap-7659	37	6	is	be	AUX
ap-7659	37	7	to	to	PART
ap-7659	37	8	make	make	VERB
ap-7659	37	9	a	a	DET
ap-7659	37	10	similarity	similarity	NOUN
ap-7659	37	11	transformation	transformation	NOUN
ap-7659	37	12	from	from	ADP
ap-7659	37	13	the	the	DET
ap-7659	37	14	original	original	ADJ
ap-7659	37	15	hamiltonian	hamiltonian	NOUN
ap-7659	37	16	to	to	ADP
ap-7659	37	17	a	a	DET
ap-7659	37	18	hamiltonian	hamiltonian	NOUN
ap-7659	37	19	which	which	PRON
ap-7659	37	20	has	have	VERB
ap-7659	37	21	eigenfunctions	eigenfunction	NOUN
ap-7659	37	22	157	157	NUM
ap-7659	37	23	https://doi.org/10.14311/ap.2022.62.0157	https://doi.org/10.14311/ap.2022.62.0157	PROPN
ap-7659	37	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7659	37	25	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7659	37	26	m.	m.	PROPN
ap-7659	37	27	reboiro	reboiro	PROPN
ap-7659	37	28	,	,	PUNCT
ap-7659	37	29	r.	r.	PROPN
ap-7659	37	30	ramírez	ramírez	PROPN
ap-7659	37	31	,	,	PUNCT
ap-7659	37	32	v.	v.	ADP
ap-7659	37	33	fernández	fernández	PROPN
ap-7659	37	34	acta	acta	PROPN
ap-7659	37	35	polytechnica	polytechnica	PROPN
ap-7659	37	36	that	that	PRON
ap-7659	37	37	belong	belong	VERB
ap-7659	37	38	to	to	ADP
ap-7659	37	39	l2(r	l2(r	NOUN
ap-7659	37	40	)	)	PUNCT
ap-7659	37	41	.	.	PUNCT
ap-7659	38	1	in	in	ADP
ap-7659	38	2	the	the	DET
ap-7659	38	3	framework	framework	NOUN
ap-7659	38	4	of	of	ADP
ap-7659	38	5	the	the	DET
ap-7659	38	6	csm	csm	NOUN
ap-7659	38	7	,	,	PUNCT
ap-7659	38	8	we	we	PRON
ap-7659	38	9	shall	shall	AUX
ap-7659	38	10	introduce	introduce	VERB
ap-7659	38	11	the	the	DET
ap-7659	38	12	transformation	transformation	NOUN
ap-7659	38	13	operator	operator	NOUN
ap-7659	38	14	v̂	v̂	X
ap-7659	38	15	(	(	PUNCT
ap-7659	38	16	θ	θ	NOUN
ap-7659	38	17	)	)	PUNCT
ap-7659	38	18	=	=	NOUN
ap-7659	39	1	e−	e−	PROPN
ap-7659	39	2	θ	θ	PROPN
ap-7659	39	3	2ℏ	2ℏ	NUM
ap-7659	39	4	(	(	PUNCT
ap-7659	39	5	x̂p̂+p̂x̂	x̂p̂+p̂x̂	PROPN
ap-7659	39	6	)	)	PUNCT
ap-7659	39	7	with	with	ADP
ap-7659	39	8	a	a	DET
ap-7659	39	9	real	real	ADJ
ap-7659	39	10	scaling	scaling	NOUN
ap-7659	39	11	parameter	parameter	NOUN
ap-7659	39	12	θ	θ	NOUN
ap-7659	39	13	:	:	PUNCT
ap-7659	39	14	v̂	v̂	PRON
ap-7659	39	15	(	(	PUNCT
ap-7659	39	16	θ)x̂v̂	θ)x̂v̂	NOUN
ap-7659	39	17	−1(θ	−1(θ	NOUN
ap-7659	39	18	)	)	PUNCT
ap-7659	39	19	=	=	SYM
ap-7659	39	20	e	e	NOUN
ap-7659	39	21	iθ	iθ	NOUN
ap-7659	39	22	x̂	x̂	PROPN
ap-7659	39	23	,	,	PUNCT
ap-7659	39	24	v̂	v̂	PRON
ap-7659	39	25	(	(	PUNCT
ap-7659	39	26	θ)p̂v̂	θ)p̂v̂	VERB
ap-7659	39	27	−1(θ	−1(θ	NOUN
ap-7659	39	28	)	)	PUNCT
ap-7659	39	29	=	=	SYM
ap-7659	39	30	e−iθ	e−iθ	PROPN
ap-7659	39	31	p̂.	p̂.	NOUN
ap-7659	39	32	(	(	PUNCT
ap-7659	39	33	4	4	NUM
ap-7659	39	34	)	)	PUNCT
ap-7659	39	35	the	the	DET
ap-7659	39	36	hamiltonian	hamiltonian	NOUN
ap-7659	39	37	of	of	ADP
ap-7659	39	38	eq	eq	PROPN
ap-7659	39	39	.	.	PUNCT
ap-7659	40	1	(	(	PUNCT
ap-7659	40	2	3	3	X
ap-7659	40	3	)	)	PUNCT
ap-7659	40	4	is	be	AUX
ap-7659	40	5	transformed	transform	VERB
ap-7659	40	6	as	as	ADP
ap-7659	40	7	h(θ	h(θ	PROPN
ap-7659	40	8	)	)	PUNCT
ap-7659	41	1	=	=	PUNCT
ap-7659	41	2	v̂	v̂	X
ap-7659	41	3	(	(	PUNCT
ap-7659	41	4	θ)hv̂	θ)hv̂	PROPN
ap-7659	41	5	−1(θ	−1(θ	NOUN
ap-7659	41	6	):	):	PUNCT
ap-7659	41	7	h(θ	h(θ	PROPN
ap-7659	41	8	)	)	PUNCT
ap-7659	41	9	=	=	SYM
ap-7659	41	10	h(θ	h(θ	PROPN
ap-7659	41	11	,	,	PUNCT
ap-7659	41	12	ω	ω	PROPN
ap-7659	41	13	,	,	PUNCT
ap-7659	41	14	α	α	NOUN
ap-7659	41	15	,	,	PUNCT
ap-7659	41	16	β	β	NOUN
ap-7659	41	17	)	)	PUNCT
ap-7659	41	18	=	=	SYM
ap-7659	41	19	1	1	NUM
ap-7659	41	20	2ℏ(ω	2ℏ(ω	NUM
ap-7659	41	21	+	+	CCONJ
ap-7659	41	22	α+	α+	X
ap-7659	41	23	β	β	X
ap-7659	41	24	)	)	PUNCT
ap-7659	41	25	(	(	PUNCT
ap-7659	41	26	e	e	X
ap-7659	41	27	iθ	iθ	NOUN
ap-7659	41	28	x̂	x̂	PROPN
ap-7659	41	29	b0	b0	NOUN
ap-7659	41	30	)	)	PUNCT
ap-7659	41	31	2	2	NUM
ap-7659	41	32	+1	+1	NOUN
ap-7659	41	33	2ℏ(ω	2ℏ(ω	NUM
ap-7659	41	34	−	−	NOUN
ap-7659	41	35	α−	α−	ADP
ap-7659	41	36	β	β	NOUN
ap-7659	41	37	)	)	PUNCT
ap-7659	41	38	(	(	PUNCT
ap-7659	41	39	b0	b0	NOUN
ap-7659	41	40	e	e	X
ap-7659	41	41	−iθ	−iθ	PROPN
ap-7659	41	42	p̂	p̂	X
ap-7659	41	43	ℏ	ℏ	NOUN
ap-7659	41	44	)	)	PUNCT
ap-7659	41	45	2	2	X
ap-7659	42	1	+	+	SYM
ap-7659	42	2	ℏ	ℏ	PROPN
ap-7659	42	3	(	(	PUNCT
ap-7659	42	4	α−	α−	ADP
ap-7659	42	5	β	β	NOUN
ap-7659	42	6	)	)	PUNCT
ap-7659	42	7	2	2	NUM
ap-7659	42	8	(	(	PUNCT
ap-7659	42	9	2	2	NUM
ap-7659	42	10	x̂	x̂	NUM
ap-7659	42	11	i	i	PRON
ap-7659	42	12	ℏ	ℏ	PROPN
ap-7659	42	13	p̂+	p̂+	NOUN
ap-7659	42	14	1	1	NUM
ap-7659	42	15	)	)	PUNCT
ap-7659	42	16	.	.	PUNCT
ap-7659	43	1	(	(	PUNCT
ap-7659	43	2	5	5	X
ap-7659	43	3	)	)	PUNCT
ap-7659	43	4	it	it	PRON
ap-7659	43	5	is	be	AUX
ap-7659	43	6	straightforward	straightforward	ADJ
ap-7659	43	7	to	to	PART
ap-7659	43	8	observe	observe	VERB
ap-7659	43	9	that	that	DET
ap-7659	43	10	h†(θ	h†(θ	NOUN
ap-7659	43	11	)	)	PUNCT
ap-7659	44	1	=	=	SYM
ap-7659	44	2	h(−θ	h(−θ	NOUN
ap-7659	44	3	,	,	PUNCT
ap-7659	44	4	ω	ω	PROPN
ap-7659	44	5	,	,	PUNCT
ap-7659	44	6	β	β	X
ap-7659	44	7	,	,	PUNCT
ap-7659	44	8	α	α	NOUN
ap-7659	44	9	)	)	PUNCT
ap-7659	44	10	.	.	PUNCT
ap-7659	45	1	(	(	PUNCT
ap-7659	45	2	6	6	X
ap-7659	45	3	)	)	PUNCT
ap-7659	45	4	notice	notice	NOUN
ap-7659	45	5	that	that	SCONJ
ap-7659	45	6	h(θ	h(θ	PROPN
ap-7659	45	7	)	)	PUNCT
ap-7659	45	8	is	be	AUX
ap-7659	45	9	not	not	PART
ap-7659	45	10	invariant	invariant	ADJ
ap-7659	45	11	under	under	ADP
ap-7659	45	12	the	the	DET
ap-7659	45	13	usual	usual	ADJ
ap-7659	45	14	pt	pt	NOUN
ap-7659	45	15	-	-	PUNCT
ap-7659	45	16	symmetry	symmetry	NOUN
ap-7659	45	17	given	give	VERB
ap-7659	45	18	by	by	ADP
ap-7659	45	19	x̂	x̂	PROPN
ap-7659	45	20	→	→	SYM
ap-7659	45	21	−x̂	−x̂	PROPN
ap-7659	45	22	,	,	PUNCT
ap-7659	45	23	and	and	CCONJ
ap-7659	45	24	p̂	p̂	NOUN
ap-7659	45	25	→	→	SYM
ap-7659	45	26	p̂	p̂	NOUN
ap-7659	45	27	,	,	PUNCT
ap-7659	45	28	and	and	CCONJ
ap-7659	45	29	i	i	PRON
ap-7659	45	30	→	→	PUNCT
ap-7659	45	31	−i	−i	ADJ
ap-7659	45	32	.	.	PUNCT
ap-7659	46	1	we	we	PRON
ap-7659	46	2	shall	shall	AUX
ap-7659	46	3	introduce	introduce	VERB
ap-7659	46	4	the	the	DET
ap-7659	46	5	following	follow	VERB
ap-7659	46	6	similarity	similarity	NOUN
ap-7659	46	7	transformation	transformation	NOUN
ap-7659	46	8	induced	induce	VERB
ap-7659	46	9	by	by	ADP
ap-7659	46	10	the	the	DET
ap-7659	46	11	operator	operator	NOUN
ap-7659	46	12	υ(θ	υ(θ	NOUN
ap-7659	46	13	)	)	PUNCT
ap-7659	47	1	=	=	SYM
ap-7659	47	2	e	e	X
ap-7659	47	3	−	−	PROPN
ap-7659	47	4	α−β	α−β	PROPN
ap-7659	47	5	ω−α−β	ω−α−β	PROPN
ap-7659	47	6	e2iθx2	e2iθx2	PROPN
ap-7659	47	7	2b2	2b2	NUM
ap-7659	47	8	0	0	NUM
ap-7659	47	9	.	.	PUNCT
ap-7659	48	1	it	it	PRON
ap-7659	48	2	reads	read	VERB
ap-7659	48	3	υ(θ	υ(θ	NOUN
ap-7659	48	4	)	)	PUNCT
ap-7659	48	5	h(θ)υ(θ)−1	h(θ)υ(θ)−1	NOUN
ap-7659	48	6	=	=	SYM
ap-7659	48	7	h(θ	h(θ	PROPN
ap-7659	48	8	)	)	PUNCT
ap-7659	48	9	,	,	PUNCT
ap-7659	48	10	(	(	PUNCT
ap-7659	48	11	7	7	X
ap-7659	48	12	)	)	PUNCT
ap-7659	48	13	where	where	SCONJ
ap-7659	48	14	h(θ	h(θ	PROPN
ap-7659	48	15	)	)	PUNCT
ap-7659	48	16	is	be	AUX
ap-7659	48	17	given	give	VERB
ap-7659	48	18	by	by	ADP
ap-7659	48	19	h(θ	h(θ	PROPN
ap-7659	48	20	)	)	PUNCT
ap-7659	48	21	=	=	NOUN
ap-7659	49	1	1	1	NUM
ap-7659	49	2	2	2	NUM
ap-7659	49	3	m	m	NOUN
ap-7659	49	4	(	(	PUNCT
ap-7659	49	5	e−iθp̂	e−iθp̂	PROPN
ap-7659	49	6	)	)	PUNCT
ap-7659	49	7	2	2	NUM
ap-7659	49	8	+	+	SYM
ap-7659	49	9	1	1	NUM
ap-7659	49	10	2k	2k	NUM
ap-7659	49	11	(	(	PUNCT
ap-7659	49	12	eiθx̂	eiθx̂	NOUN
ap-7659	49	13	)	)	PUNCT
ap-7659	49	14	2	2	X
ap-7659	49	15	.	.	PUNCT
ap-7659	50	1	(	(	PUNCT
ap-7659	50	2	8)	8)	NUM
ap-7659	50	3	we	we	PRON
ap-7659	50	4	have	have	AUX
ap-7659	50	5	defined	define	VERB
ap-7659	50	6	[	[	PUNCT
ap-7659	50	7	26	26	NUM
ap-7659	50	8	]	]	X
ap-7659	50	9	k	k	NOUN
ap-7659	51	1	=	=	PUNCT
ap-7659	51	2	m	m	VERB
ap-7659	51	3	ω2	ω2	ADJ
ap-7659	51	4	and	and	CCONJ
ap-7659	51	5	m	m	PROPN
ap-7659	51	6	=	=	SYM
ap-7659	51	7	m(ω	m(ω	PROPN
ap-7659	51	8	,	,	PUNCT
ap-7659	51	9	α	α	X
ap-7659	51	10	,	,	PUNCT
ap-7659	51	11	β	β	NOUN
ap-7659	51	12	,	,	PUNCT
ap-7659	51	13	b0	b0	NOUN
ap-7659	51	14	)	)	PUNCT
ap-7659	52	1	=	=	SYM
ap-7659	52	2	ℏ	ℏ	PROPN
ap-7659	52	3	(	(	PUNCT
ap-7659	52	4	ω	ω	NOUN
ap-7659	52	5	−	−	NOUN
ap-7659	52	6	α−	α−	ADP
ap-7659	52	7	β)b2	β)b2	PROPN
ap-7659	52	8	0	0	NUM
ap-7659	52	9	ω	ω	NUM
ap-7659	52	10	=	=	PUNCT
ap-7659	52	11	ω(ω	ω(ω	PROPN
ap-7659	52	12	,	,	PUNCT
ap-7659	52	13	α	α	X
ap-7659	52	14	,	,	PUNCT
ap-7659	52	15	β	β	NOUN
ap-7659	52	16	)	)	PUNCT
ap-7659	52	17	=	=	SYM
ap-7659	52	18	√	√	NUM
ap-7659	52	19	ω2	ω2	CCONJ
ap-7659	52	20	−	−	PROPN
ap-7659	52	21	4αβ	4αβ	NOUN
ap-7659	52	22	=	=	X
ap-7659	52	23	|ω|eiϕ.	|ω|eiϕ.	NOUN
ap-7659	52	24	(	(	PUNCT
ap-7659	52	25	9	9	NUM
ap-7659	52	26	)	)	PUNCT
ap-7659	52	27	though	though	SCONJ
ap-7659	52	28	h(θ	h(θ	PROPN
ap-7659	52	29	)	)	PUNCT
ap-7659	52	30	is	be	AUX
ap-7659	52	31	a	a	DET
ap-7659	52	32	non	non	ADJ
ap-7659	52	33	-	-	ADJ
ap-7659	52	34	hermitian	hermitian	ADJ
ap-7659	52	35	operator	operator	NOUN
ap-7659	52	36	,	,	PUNCT
ap-7659	52	37	h†(θ	h†(θ	NUM
ap-7659	52	38	)	)	PUNCT
ap-7659	52	39	=	=	SYM
ap-7659	52	40	h(−θ	h(−θ	X
ap-7659	52	41	)	)	PUNCT
ap-7659	52	42	=	=	SYM
ap-7659	52	43	v	v	X
ap-7659	52	44	(	(	PUNCT
ap-7659	52	45	−2θ)h(θ)v	−2θ)h(θ)v	PROPN
ap-7659	52	46	(	(	PUNCT
ap-7659	52	47	−2θ)−1	−2θ)−1	PROPN
ap-7659	52	48	.	.	PUNCT
ap-7659	52	49	consequently	consequently	ADV
ap-7659	52	50	υ(−θ)−1h†(θ)υ(−θ	υ(−θ)−1h†(θ)υ(−θ	NUM
ap-7659	52	51	)	)	PUNCT
ap-7659	52	52	=	=	SYM
ap-7659	53	1	h(θ)∗	h(θ)∗	NOUN
ap-7659	53	2	,	,	PUNCT
ap-7659	53	3	(	(	PUNCT
ap-7659	53	4	υ(−θ)v	υ(−θ)v	NOUN
ap-7659	53	5	(	(	PUNCT
ap-7659	53	6	−2θ))−1h†(θ)(υ(−θ)v	−2θ))−1h†(θ)(υ(−θ)v	PROPN
ap-7659	53	7	(	(	PUNCT
ap-7659	53	8	−2θ	−2θ	PROPN
ap-7659	53	9	)	)	PUNCT
ap-7659	53	10	)	)	PUNCT
ap-7659	53	11	=	=	SYM
ap-7659	53	12	h(θ	h(θ	PROPN
ap-7659	53	13	)	)	PUNCT
ap-7659	53	14	.	.	PUNCT
ap-7659	54	1	(	(	PUNCT
ap-7659	54	2	10	10	NUM
ap-7659	54	3	)	)	PUNCT
ap-7659	54	4	from	from	ADP
ap-7659	54	5	eqs	eqs	PROPN
ap-7659	54	6	.	.	PUNCT
ap-7659	55	1	(	(	PUNCT
ap-7659	55	2	7	7	NUM
ap-7659	55	3	)	)	PUNCT
ap-7659	55	4	and	and	CCONJ
ap-7659	55	5	(	(	PUNCT
ap-7659	55	6	10	10	NUM
ap-7659	55	7	)	)	PUNCT
ap-7659	55	8	,	,	PUNCT
ap-7659	55	9	it	it	PRON
ap-7659	55	10	results	result	VERB
ap-7659	55	11	h†(θ)s	h†(θ)	NOUN
ap-7659	55	12	=	=	SYM
ap-7659	55	13	sh(θ	sh(θ	NOUN
ap-7659	55	14	)	)	PUNCT
ap-7659	55	15	,	,	PUNCT
ap-7659	55	16	with	with	ADP
ap-7659	55	17	s	s	NOUN
ap-7659	55	18	=	=	VERB
ap-7659	55	19	υ(−θ)v	υ(−θ)v	PROPN
ap-7659	55	20	(	(	PUNCT
ap-7659	55	21	−2θ)υ(θ	−2θ)υ(θ	PROPN
ap-7659	55	22	)	)	PUNCT
ap-7659	56	1	[	[	X
ap-7659	56	2	35–37	35–37	NOUN
ap-7659	56	3	]	]	X
ap-7659	56	4	.	.	PUNCT
ap-7659	57	1	the	the	DET
ap-7659	57	2	eigenfunctions	eigenfunction	NOUN
ap-7659	57	3	and	and	CCONJ
ap-7659	57	4	eigenvalues	eigenvalue	NOUN
ap-7659	57	5	of	of	ADP
ap-7659	57	6	h(θ	h(θ	PROPN
ap-7659	57	7	)	)	PUNCT
ap-7659	57	8	,	,	PUNCT
ap-7659	57	9	ϕ(θ	ϕ(θ	PROPN
ap-7659	57	10	)	)	PUNCT
ap-7659	57	11	and	and	CCONJ
ap-7659	57	12	e(θ	e(θ	ADJ
ap-7659	57	13	)	)	PUNCT
ap-7659	57	14	,	,	PUNCT
ap-7659	57	15	are	be	AUX
ap-7659	57	16	related	relate	VERB
ap-7659	57	17	to	to	ADP
ap-7659	57	18	that	that	PRON
ap-7659	57	19	of	of	ADP
ap-7659	57	20	h	h	NOUN
ap-7659	57	21	and	and	CCONJ
ap-7659	57	22	h†	h†	NOUN
ap-7659	57	23	as	as	SCONJ
ap-7659	57	24	follows	follow	VERB
ap-7659	57	25	.	.	PUNCT
ap-7659	58	1	given	give	VERB
ap-7659	58	2	h(θ)ϕ(θ	h(θ)ϕ(θ	NOUN
ap-7659	58	3	,	,	PUNCT
ap-7659	58	4	x	x	X
ap-7659	58	5	)	)	PUNCT
ap-7659	58	6	=	=	SYM
ap-7659	58	7	e(θ)ϕ(θ	e(θ)ϕ(θ	NOUN
ap-7659	58	8	,	,	PUNCT
ap-7659	58	9	x	x	X
ap-7659	58	10	):	):	PUNCT
ap-7659	58	11	h	h	PROPN
ap-7659	58	12	ϕ(θ	ϕ(θ	PROPN
ap-7659	58	13	,	,	PUNCT
ap-7659	58	14	x	x	X
ap-7659	58	15	)	)	PUNCT
ap-7659	58	16	=	=	SYM
ap-7659	58	17	ẽ(θ	ẽ(θ	PROPN
ap-7659	58	18	)	)	PUNCT
ap-7659	58	19	ϕ(θ	ϕ(θ	PROPN
ap-7659	58	20	,	,	PUNCT
ap-7659	58	21	x	x	NOUN
ap-7659	58	22	)	)	PUNCT
ap-7659	58	23	,	,	PUNCT
ap-7659	58	24	h†	h†	PROPN
ap-7659	58	25	ψ(θ	ψ(θ	NOUN
ap-7659	58	26	,	,	PUNCT
ap-7659	58	27	x	x	X
ap-7659	58	28	)	)	PUNCT
ap-7659	58	29	=	=	SYM
ap-7659	58	30	e(θ	e(θ	ADJ
ap-7659	58	31	)	)	PUNCT
ap-7659	58	32	ψ(θ	ψ(θ	PROPN
ap-7659	58	33	,	,	PUNCT
ap-7659	58	34	x	x	NOUN
ap-7659	58	35	)	)	PUNCT
ap-7659	58	36	,	,	PUNCT
ap-7659	58	37	(	(	PUNCT
ap-7659	58	38	11	11	NUM
ap-7659	58	39	)	)	PUNCT
ap-7659	58	40	with	with	ADP
ap-7659	58	41	ϕ̃(θ	ϕ̃(θ	PROPN
ap-7659	58	42	,	,	PUNCT
ap-7659	58	43	x	x	NOUN
ap-7659	58	44	)	)	PUNCT
ap-7659	58	45	=	=	SYM
ap-7659	58	46	υ(θ)−1ϕ(θ	υ(θ)−1ϕ(θ	X
ap-7659	58	47	,	,	PUNCT
ap-7659	58	48	x	x	X
ap-7659	58	49	)	)	PUNCT
ap-7659	58	50	,	,	PUNCT
ap-7659	58	51	e(θ	e(θ	VERB
ap-7659	58	52	)	)	PUNCT
ap-7659	58	53	=	=	SYM
ap-7659	58	54	e(θ	e(θ	NOUN
ap-7659	58	55	)	)	PUNCT
ap-7659	58	56	,	,	PUNCT
ap-7659	58	57	ψ(θ	ψ(θ	PROPN
ap-7659	58	58	,	,	PUNCT
ap-7659	58	59	x	x	X
ap-7659	58	60	)	)	PUNCT
ap-7659	58	61	=	=	SYM
ap-7659	58	62	υ(−θ)(ϕ(θ	υ(−θ)(ϕ(θ	PROPN
ap-7659	58	63	,	,	PUNCT
ap-7659	58	64	x))∗	x))∗	PROPN
ap-7659	58	65	,	,	PUNCT
ap-7659	58	66	e(θ	e(θ	NOUN
ap-7659	58	67	)	)	PUNCT
ap-7659	59	1	=	=	SYM
ap-7659	59	2	e(θ)∗.	e(θ)∗.	NOUN
ap-7659	59	3	(	(	PUNCT
ap-7659	59	4	12	12	NUM
ap-7659	59	5	)	)	PUNCT
ap-7659	59	6	thus	thus	ADV
ap-7659	59	7	,	,	PUNCT
ap-7659	59	8	the	the	DET
ap-7659	59	9	eigenfunctions	eigenfunction	NOUN
ap-7659	59	10	of	of	ADP
ap-7659	59	11	h(θ	h(θ	PROPN
ap-7659	59	12	)	)	PUNCT
ap-7659	59	13	with	with	ADP
ap-7659	59	14	eigenvalue	eigenvalue	PROPN
ap-7659	59	15	ẽν(θ	ẽν(θ	NUM
ap-7659	59	16	)	)	PUNCT
ap-7659	59	17	=	=	SYM
ap-7659	59	18	eν(θ	eν(θ	X
ap-7659	59	19	)	)	PUNCT
ap-7659	59	20	are	be	AUX
ap-7659	59	21	given	give	VERB
ap-7659	59	22	by	by	ADP
ap-7659	59	23	ϕ̃ν(θ	ϕ̃ν(θ	PROPN
ap-7659	59	24	,	,	PUNCT
ap-7659	59	25	x	x	X
ap-7659	59	26	)	)	PUNCT
ap-7659	59	27	=	=	SYM
ap-7659	59	28	e	e	PROPN
ap-7659	59	29	α−β	α−β	PROPN
ap-7659	59	30	ω−α−β	ω−α−β	PROPN
ap-7659	59	31	e2iθx2	e2iθx2	PROPN
ap-7659	59	32	2b2	2b2	NUM
ap-7659	59	33	0	0	NUM
ap-7659	59	34	nνϕν(θ	nνϕν(θ	PROPN
ap-7659	59	35	,	,	PUNCT
ap-7659	59	36	x	x	PRON
ap-7659	59	37	)	)	PUNCT
ap-7659	59	38	(	(	PUNCT
ap-7659	59	39	13	13	NUM
ap-7659	59	40	)	)	PUNCT
ap-7659	59	41	with	with	ADP
ap-7659	59	42	nν	nν	INTJ
ap-7659	59	43	a	a	DET
ap-7659	59	44	normalization	normalization	NOUN
ap-7659	59	45	constant	constant	ADJ
ap-7659	59	46	.	.	PUNCT
ap-7659	60	1	it	it	PRON
ap-7659	60	2	can	can	AUX
ap-7659	60	3	be	be	AUX
ap-7659	60	4	shown	show	VERB
ap-7659	60	5	that	that	SCONJ
ap-7659	60	6	the	the	DET
ap-7659	60	7	eigenfunctions	eigenfunction	NOUN
ap-7659	60	8	of	of	ADP
ap-7659	60	9	h†(θ	h†(θ	NOUN
ap-7659	60	10	)	)	PUNCT
ap-7659	60	11	are	be	AUX
ap-7659	60	12	ψν(θ	ψν(θ	ADV
ap-7659	60	13	,	,	PUNCT
ap-7659	60	14	x	x	X
ap-7659	60	15	)	)	PUNCT
ap-7659	60	16	=	=	SYM
ap-7659	60	17	e	e	X
ap-7659	60	18	−	−	PROPN
ap-7659	60	19	α−β	α−β	PROPN
ap-7659	60	20	ω−α−β	ω−α−β	PROPN
ap-7659	60	21	e−2iθx2	e−2iθx2	PROPN
ap-7659	60	22	2b2	2b2	NUM
ap-7659	60	23	0	0	NUM
ap-7659	60	24	(	(	PUNCT
ap-7659	60	25	nνϕν(θ	nνϕν(θ	PROPN
ap-7659	60	26	,	,	PUNCT
ap-7659	60	27	x))∗	x))∗	PROPN
ap-7659	60	28	,	,	PUNCT
ap-7659	60	29	(	(	PUNCT
ap-7659	60	30	14	14	NUM
ap-7659	60	31	)	)	PUNCT
ap-7659	60	32	and	and	CCONJ
ap-7659	60	33	the	the	DET
ap-7659	60	34	corresponding	correspond	VERB
ap-7659	60	35	eigenvalue	eigenvalue	NOUN
ap-7659	60	36	is	be	AUX
ap-7659	60	37	given	give	VERB
ap-7659	60	38	by	by	ADP
ap-7659	60	39	eν(θ	eν(θ	NOUN
ap-7659	60	40	)	)	PUNCT
ap-7659	61	1	=	=	SYM
ap-7659	61	2	ẽν(θ)∗.	ẽν(θ)∗.	PROPN
ap-7659	61	3	a	a	DET
ap-7659	61	4	similar	similar	ADJ
ap-7659	61	5	structure	structure	NOUN
ap-7659	61	6	for	for	ADP
ap-7659	61	7	eqs	eqs	PROPN
ap-7659	61	8	.	.	PUNCT
ap-7659	62	1	(	(	PUNCT
ap-7659	62	2	10)-(14	10)-(14	NOUN
ap-7659	62	3	)	)	PUNCT
ap-7659	62	4	can	can	AUX
ap-7659	62	5	be	be	AUX
ap-7659	62	6	found	find	VERB
ap-7659	62	7	in	in	ADP
ap-7659	62	8	[	[	X
ap-7659	62	9	38	38	NUM
ap-7659	62	10	,	,	PUNCT
ap-7659	62	11	39	39	NUM
ap-7659	62	12	]	]	PUNCT
ap-7659	62	13	.	.	PUNCT
ap-7659	63	1	moreover	moreover	ADV
ap-7659	63	2	,	,	PUNCT
ap-7659	63	3	the	the	DET
ap-7659	63	4	relation	relation	NOUN
ap-7659	63	5	between	between	ADP
ap-7659	63	6	the	the	DET
ap-7659	63	7	eigenvalues	eigenvalue	NOUN
ap-7659	63	8	,	,	PUNCT
ap-7659	63	9	eq	eq	NOUN
ap-7659	63	10	.	.	PUNCT
ap-7659	64	1	(	(	PUNCT
ap-7659	64	2	12	12	NUM
ap-7659	64	3	)	)	PUNCT
ap-7659	64	4	,	,	PUNCT
ap-7659	64	5	is	be	AUX
ap-7659	64	6	a	a	DET
ap-7659	64	7	typical	typical	ADJ
ap-7659	64	8	feature	feature	NOUN
ap-7659	64	9	for	for	ADP
ap-7659	64	10	operators	operator	NOUN
ap-7659	64	11	which	which	PRON
ap-7659	64	12	are	be	AUX
ap-7659	64	13	self	self	NOUN
ap-7659	64	14	-	-	PUNCT
ap-7659	64	15	adjoint	adjoint	NOUN
ap-7659	64	16	in	in	ADP
ap-7659	64	17	krein	krein	PROPN
ap-7659	64	18	spaces	space	NOUN
ap-7659	64	19	[	[	X
ap-7659	64	20	39–41	39–41	NUM
ap-7659	64	21	]	]	PUNCT
ap-7659	64	22	.	.	PUNCT
ap-7659	65	1	it	it	PRON
ap-7659	65	2	should	should	AUX
ap-7659	65	3	be	be	AUX
ap-7659	65	4	mentioned	mention	VERB
ap-7659	65	5	that	that	SCONJ
ap-7659	65	6	the	the	DET
ap-7659	65	7	hamiltonian	hamiltonian	NOUN
ap-7659	65	8	of	of	ADP
ap-7659	65	9	eq	eq	PROPN
ap-7659	65	10	.	.	PUNCT
ap-7659	66	1	(	(	PUNCT
ap-7659	66	2	5	5	NUM
ap-7659	66	3	)	)	PUNCT
ap-7659	66	4	,	,	PUNCT
ap-7659	66	5	for	for	ADP
ap-7659	66	6	α	α	NOUN
ap-7659	66	7	=	=	SYM
ap-7659	66	8	β	β	X
ap-7659	66	9	=	=	SYM
ap-7659	66	10	0	0	NUM
ap-7659	66	11	and	and	CCONJ
ap-7659	66	12	ω	ω	NUM
ap-7659	66	13	=	=	SYM
ap-7659	66	14	1/	1/	NUM
ap-7659	66	15	cos(2θ	cos(2θ	PROPN
ap-7659	66	16	)	)	PUNCT
ap-7659	66	17	,	,	PUNCT
ap-7659	66	18	reduces	reduce	VERB
ap-7659	66	19	to	to	ADP
ap-7659	66	20	the	the	DET
ap-7659	66	21	one	one	NOUN
ap-7659	66	22	introduced	introduce	VERB
ap-7659	66	23	in	in	ADP
ap-7659	66	24	[	[	X
ap-7659	66	25	23–25	23–25	NUM
ap-7659	66	26	]	]	X
ap-7659	66	27	.	.	PUNCT
ap-7659	67	1	particularly	particularly	ADV
ap-7659	67	2	,	,	PUNCT
ap-7659	67	3	in	in	ADP
ap-7659	67	4	[	[	X
ap-7659	67	5	25	25	NUM
ap-7659	67	6	]	]	PUNCT
ap-7659	67	7	the	the	DET
ap-7659	67	8	dynamics	dynamic	NOUN
ap-7659	67	9	under	under	ADP
ap-7659	67	10	the	the	DET
ap-7659	67	11	action	action	NOUN
ap-7659	67	12	of	of	ADP
ap-7659	67	13	this	this	DET
ap-7659	67	14	hamiltonian	hamiltonian	NOUN
ap-7659	67	15	is	be	AUX
ap-7659	67	16	described	describe	VERB
ap-7659	67	17	for	for	ADP
ap-7659	67	18	values	value	NOUN
ap-7659	67	19	of	of	ADP
ap-7659	67	20	θ	θ	PROPN
ap-7659	67	21	∈	∈	PROPN
ap-7659	67	22	(	(	PUNCT
ap-7659	67	23	−π/4	−π/4	PROPN
ap-7659	67	24	,	,	PUNCT
ap-7659	67	25	π/4	π/4	NUM
ap-7659	67	26	)	)	PUNCT
ap-7659	67	27	.	.	PUNCT
ap-7659	68	1	for	for	ADP
ap-7659	68	2	further	further	ADJ
ap-7659	68	3	results	result	NOUN
ap-7659	68	4	,	,	PUNCT
ap-7659	68	5	the	the	DET
ap-7659	68	6	reader	reader	NOUN
ap-7659	68	7	is	be	AUX
ap-7659	68	8	kindly	kindly	ADV
ap-7659	68	9	referred	refer	VERB
ap-7659	68	10	to	to	ADP
ap-7659	68	11	[	[	X
ap-7659	68	12	23–25	23–25	NUM
ap-7659	68	13	]	]	PUNCT
ap-7659	68	14	.	.	PUNCT
ap-7659	69	1	in	in	ADP
ap-7659	69	2	what	what	PRON
ap-7659	69	3	follows	follow	VERB
ap-7659	69	4	,	,	PUNCT
ap-7659	69	5	we	we	PRON
ap-7659	69	6	aim	aim	VERB
ap-7659	69	7	to	to	PART
ap-7659	69	8	determine	determine	VERB
ap-7659	69	9	the	the	DET
ap-7659	69	10	range	range	NOUN
ap-7659	69	11	of	of	ADP
ap-7659	69	12	values	value	NOUN
ap-7659	69	13	of	of	ADP
ap-7659	69	14	θ	θ	PROPN
ap-7659	69	15	for	for	ADP
ap-7659	69	16	which	which	PRON
ap-7659	69	17	ϕ(θ	ϕ(θ	PROPN
ap-7659	69	18	,	,	PUNCT
ap-7659	69	19	x	x	X
ap-7659	69	20	)	)	PUNCT
ap-7659	69	21	belongs	belong	VERB
ap-7659	69	22	to	to	ADP
ap-7659	69	23	the	the	DET
ap-7659	69	24	hilbert	hilbert	NOUN
ap-7659	69	25	space	space	NOUN
ap-7659	69	26	l2(r	l2(r	PROPN
ap-7659	69	27	)	)	PUNCT
ap-7659	69	28	.	.	PUNCT
ap-7659	70	1	2.1	2.1	NUM
ap-7659	70	2	.	.	PUNCT
ap-7659	71	1	eigenfunctions	eigenfunction	NOUN
ap-7659	71	2	and	and	CCONJ
ap-7659	71	3	eigenvectors	eigenvector	NOUN
ap-7659	71	4	for	for	ADP
ap-7659	71	5	ω	ω	NUM
ap-7659	71	6	−	−	PROPN
ap-7659	71	7	(	(	PUNCT
ap-7659	71	8	α+	α+	X
ap-7659	71	9	β	β	X
ap-7659	71	10	)	)	PUNCT
ap-7659	71	11	̸=	̸=	PROPN
ap-7659	71	12	0	0	NUM
ap-7659	71	13	,	,	PUNCT
ap-7659	71	14	eq	eq	NOUN
ap-7659	71	15	.	.	PUNCT
ap-7659	72	1	(	(	PUNCT
ap-7659	72	2	8)	8)	NUM
ap-7659	72	3	can	can	AUX
ap-7659	72	4	be	be	AUX
ap-7659	72	5	also	also	ADV
ap-7659	72	6	written	write	VERB
ap-7659	72	7	as	as	ADP
ap-7659	72	8	−d2ϕ(y	−d2ϕ(y	PROPN
ap-7659	72	9	)	)	PUNCT
ap-7659	72	10	dy2	dy2	PROPN
ap-7659	73	1	+	+	CCONJ
ap-7659	73	2	(	(	PUNCT
ap-7659	73	3	1	1	NUM
ap-7659	73	4	4y	4y	NUM
ap-7659	73	5	2	2	NUM
ap-7659	73	6	−	−	NOUN
ap-7659	73	7	ϵ	ϵ	X
ap-7659	73	8	)	)	PUNCT
ap-7659	73	9	ϕ(y	ϕ(y	PROPN
ap-7659	73	10	)	)	PUNCT
ap-7659	73	11	=	=	SYM
ap-7659	73	12	0	0	NUM
ap-7659	73	13	,	,	PUNCT
ap-7659	73	14	(	(	PUNCT
ap-7659	73	15	15	15	NUM
ap-7659	73	16	)	)	PUNCT
ap-7659	73	17	with	with	ADP
ap-7659	73	18	ϵ	ϵ	PROPN
ap-7659	73	19	=	=	PUNCT
ap-7659	73	20	e	e	X
ap-7659	73	21	ℏω	ℏω	NOUN
ap-7659	73	22	=	=	SYM
ap-7659	73	23	e	e	NOUN
ap-7659	73	24	ℏ|ω|	ℏ|ω|	VERB
ap-7659	73	25	eiϕ	eiϕ	PROPN
ap-7659	73	26	(	(	PUNCT
ap-7659	73	27	16	16	NUM
ap-7659	73	28	)	)	PUNCT
ap-7659	73	29	and	and	CCONJ
ap-7659	73	30	y	y	PROPN
ap-7659	73	31	=	=	NOUN
ap-7659	73	32	√	√	PROPN
ap-7659	73	33	2	2	NUM
ap-7659	73	34	|σ|ei(θ+γ	|σ|ei(θ+γ	NOUN
ap-7659	73	35	)	)	PUNCT
ap-7659	73	36	x	x	SYM
ap-7659	73	37	b0	b0	NOUN
ap-7659	73	38	,	,	PUNCT
ap-7659	73	39	(	(	PUNCT
ap-7659	73	40	17	17	NUM
ap-7659	73	41	)	)	PUNCT
ap-7659	73	42	where	where	SCONJ
ap-7659	73	43	we	we	PRON
ap-7659	73	44	have	have	AUX
ap-7659	73	45	defined	define	VERB
ap-7659	73	46	σ	σ	NOUN
ap-7659	73	47	=	=	PUNCT
ap-7659	73	48	(	(	PUNCT
ap-7659	73	49	mω	mω	PROPN
ap-7659	73	50	ℏ	ℏ	PROPN
ap-7659	73	51	)	)	PUNCT
ap-7659	73	52	1/2	1/2	NUM
ap-7659	73	53	b0	b0	NOUN
ap-7659	73	54	=	=	SYM
ap-7659	73	55	eiγ	eiγ	NOUN
ap-7659	73	56	|σ|	|σ|	PROPN
ap-7659	73	57	.	.	PUNCT
ap-7659	73	58	(	(	PUNCT
ap-7659	73	59	18	18	NUM
ap-7659	73	60	)	)	PUNCT
ap-7659	73	61	158	158	NUM
ap-7659	73	62	vol	vol	NOUN
ap-7659	73	63	.	.	PUNCT
ap-7659	74	1	62	62	NUM
ap-7659	74	2	no	no	INTJ
ap-7659	74	3	.	.	PUNCT
ap-7659	75	1	1/2022	1/2022	NUM
ap-7659	75	2	swanson	swanson	PROPN
ap-7659	75	3	hamiltonian	hamiltonian	NOUN
ap-7659	75	4	revisited	revisit	VERB
ap-7659	75	5	through	through	ADP
ap-7659	75	6	the	the	DET
ap-7659	75	7	csm	csm	NOUN
ap-7659	75	8	(	(	PUNCT
ap-7659	75	9	a	a	X
ap-7659	75	10	)	)	PUNCT
ap-7659	75	11	0	0	NUM
ap-7659	76	1	π	π	SYM
ap-7659	76	2	2	2	NUM
ap-7659	76	3	π	π	SYM
ap-7659	76	4	3	3	NUM
ap-7659	76	5	π	π	SYM
ap-7659	76	6	2	2	NUM
ap-7659	76	7	2	2	NUM
ap-7659	76	8	π	π	NOUN
ap-7659	76	9	-1	-1	NOUN
ap-7659	76	10	0	0	NUM
ap-7659	76	11	1	1	NUM
ap-7659	76	12	θ	θ	NOUN
ap-7659	76	13	u	u	NOUN
ap-7659	76	14	(	(	PUNCT
ap-7659	76	15	x	x	NOUN
ap-7659	76	16	)	)	PUNCT
ap-7659	76	17	/	/	SYM
ap-7659	76	18	|u	|u	ADJ
ap-7659	76	19	(	(	PUNCT
ap-7659	76	20	x	x	X
ap-7659	76	21	)	)	PUNCT
ap-7659	76	22	|	|	CCONJ
ap-7659	76	23	(	(	PUNCT
ap-7659	76	24	b	b	NOUN
ap-7659	76	25	)	)	PUNCT
ap-7659	76	26	0	0	NUM
ap-7659	77	1	π	π	SYM
ap-7659	77	2	2	2	NUM
ap-7659	77	3	π	π	SYM
ap-7659	77	4	3	3	NUM
ap-7659	77	5	π	π	SYM
ap-7659	77	6	2	2	NUM
ap-7659	77	7	2	2	NUM
ap-7659	77	8	π	π	NOUN
ap-7659	77	9	-1	-1	NOUN
ap-7659	77	10	0	0	NUM
ap-7659	77	11	1	1	NUM
ap-7659	77	12	θ	θ	NOUN
ap-7659	77	13	u	u	NOUN
ap-7659	77	14	(	(	PUNCT
ap-7659	77	15	x	x	NOUN
ap-7659	77	16	)	)	PUNCT
ap-7659	77	17	/	/	SYM
ap-7659	77	18	|u	|u	ADJ
ap-7659	77	19	(	(	PUNCT
ap-7659	77	20	x	x	X
ap-7659	77	21	)	)	PUNCT
ap-7659	77	22	|	|	CCONJ
ap-7659	77	23	(	(	PUNCT
ap-7659	77	24	c	c	NOUN
ap-7659	77	25	)	)	PUNCT
ap-7659	77	26	0	0	NUM
ap-7659	78	1	π	π	SYM
ap-7659	78	2	2	2	NUM
ap-7659	78	3	π	π	SYM
ap-7659	78	4	3	3	NUM
ap-7659	78	5	π	π	SYM
ap-7659	78	6	2	2	NUM
ap-7659	78	7	2	2	NUM
ap-7659	78	8	π	π	NOUN
ap-7659	78	9	-1	-1	NOUN
ap-7659	78	10	0	0	NUM
ap-7659	78	11	1	1	NUM
ap-7659	78	12	θ	θ	NOUN
ap-7659	78	13	u	u	NOUN
ap-7659	78	14	(	(	PUNCT
ap-7659	78	15	x	x	NOUN
ap-7659	78	16	)	)	PUNCT
ap-7659	78	17	/	/	SYM
ap-7659	78	18	|u	|u	ADJ
ap-7659	78	19	(	(	PUNCT
ap-7659	78	20	x	x	X
ap-7659	78	21	)	)	PUNCT
ap-7659	78	22	|	|	ADV
ap-7659	78	23	(	(	PUNCT
ap-7659	78	24	d	d	NOUN
ap-7659	78	25	)	)	PUNCT
ap-7659	78	26	0	0	NUM
ap-7659	79	1	π	π	SYM
ap-7659	79	2	2	2	NUM
ap-7659	79	3	π	π	SYM
ap-7659	79	4	3	3	NUM
ap-7659	79	5	π	π	SYM
ap-7659	79	6	2	2	NUM
ap-7659	79	7	2	2	NUM
ap-7659	79	8	π	π	NOUN
ap-7659	79	9	-1	-1	NOUN
ap-7659	79	10	0	0	NUM
ap-7659	79	11	1	1	NUM
ap-7659	79	12	θ	θ	NOUN
ap-7659	79	13	u	u	NOUN
ap-7659	79	14	(	(	PUNCT
ap-7659	79	15	x	x	NOUN
ap-7659	79	16	)	)	PUNCT
ap-7659	79	17	/	/	SYM
ap-7659	79	18	|u	|u	ADJ
ap-7659	79	19	(	(	PUNCT
ap-7659	79	20	x	x	X
ap-7659	79	21	)	)	PUNCT
ap-7659	79	22	|	|	ADV
ap-7659	79	23	figure	figure	NOUN
ap-7659	79	24	1	1	NUM
ap-7659	79	25	.	.	PUNCT
ap-7659	79	26	effective	effective	ADJ
ap-7659	79	27	potential	potential	NOUN
ap-7659	79	28	of	of	ADP
ap-7659	79	29	eq	eq	PROPN
ap-7659	79	30	.	.	PUNCT
ap-7659	80	1	(	(	PUNCT
ap-7659	80	2	19	19	NUM
ap-7659	80	3	)	)	PUNCT
ap-7659	80	4	,	,	PUNCT
ap-7659	80	5	u(θ	u(θ	NOUN
ap-7659	80	6	,	,	PUNCT
ap-7659	80	7	x	x	NOUN
ap-7659	80	8	)	)	PUNCT
ap-7659	80	9	|u(θ	|u(θ	NOUN
ap-7659	80	10	,	,	PUNCT
ap-7659	80	11	x)|	x)|	PROPN
ap-7659	80	12	,	,	PUNCT
ap-7659	80	13	for	for	ADP
ap-7659	80	14	a	a	DET
ap-7659	80	15	fixed	fix	VERB
ap-7659	80	16	x	x	NOUN
ap-7659	80	17	in	in	ADP
ap-7659	80	18	the	the	DET
ap-7659	80	19	regions	region	NOUN
ap-7659	80	20	determined	determine	VERB
ap-7659	80	21	by	by	ADP
ap-7659	80	22	the	the	DET
ap-7659	80	23	signs	sign	NOUN
ap-7659	80	24	of	of	ADP
ap-7659	80	25	the	the	DET
ap-7659	80	26	parameters	parameter	NOUN
ap-7659	80	27	m(ω	m(ω	PROPN
ap-7659	80	28	,	,	PUNCT
ap-7659	80	29	α	α	X
ap-7659	80	30	,	,	PUNCT
ap-7659	80	31	β	β	NOUN
ap-7659	80	32	,	,	PUNCT
ap-7659	80	33	b0	b0	NOUN
ap-7659	80	34	)	)	PUNCT
ap-7659	80	35	and	and	CCONJ
ap-7659	80	36	ω2(ω	ω2(ω	PROPN
ap-7659	80	37	,	,	PUNCT
ap-7659	80	38	α	α	X
ap-7659	80	39	,	,	PUNCT
ap-7659	80	40	β	β	NOUN
ap-7659	80	41	,	,	PUNCT
ap-7659	80	42	b0	b0	NOUN
ap-7659	80	43	)	)	PUNCT
ap-7659	80	44	.	.	PUNCT
ap-7659	81	1	in	in	ADP
ap-7659	81	2	panel	panel	NOUN
ap-7659	81	3	(	(	PUNCT
ap-7659	81	4	a	a	NOUN
ap-7659	81	5	)	)	PUNCT
ap-7659	81	6	,	,	PUNCT
ap-7659	81	7	(	(	PUNCT
ap-7659	81	8	sg(m	sg(m	NOUN
ap-7659	81	9	)	)	PUNCT
ap-7659	81	10	,	,	PUNCT
ap-7659	81	11	sg(ω2	sg(ω2	NOUN
ap-7659	81	12	)	)	PUNCT
ap-7659	81	13	)	)	PUNCT
ap-7659	82	1	=	=	PUNCT
ap-7659	82	2	(	(	PUNCT
ap-7659	82	3	+	+	ADJ
ap-7659	82	4	,	,	PUNCT
ap-7659	82	5	+	+	ADJ
ap-7659	82	6	)	)	PUNCT
ap-7659	82	7	,	,	PUNCT
ap-7659	82	8	region	region	NOUN
ap-7659	82	9	i.	i.	PROPN
ap-7659	82	10	for	for	ADP
ap-7659	82	11	panel	panel	NOUN
ap-7659	82	12	(	(	PUNCT
ap-7659	82	13	b),(sg(m	b),(sg(m	PROPN
ap-7659	82	14	)	)	PUNCT
ap-7659	82	15	,	,	PUNCT
ap-7659	82	16	sg(ω2	sg(ω2	NOUN
ap-7659	82	17	)	)	PUNCT
ap-7659	82	18	)	)	PUNCT
ap-7659	82	19	=	=	PUNCT
ap-7659	83	1	(	(	PUNCT
ap-7659	83	2	+	+	ADJ
ap-7659	83	3	,	,	PUNCT
ap-7659	83	4	−	−	NOUN
ap-7659	83	5	)	)	PUNCT
ap-7659	83	6	,	,	PUNCT
ap-7659	83	7	region	region	PROPN
ap-7659	83	8	ii	ii	PROPN
ap-7659	83	9	.	.	PUNCT
ap-7659	84	1	while	while	SCONJ
ap-7659	84	2	,	,	PUNCT
ap-7659	84	3	(	(	PUNCT
ap-7659	84	4	sg(m	sg(m	NOUN
ap-7659	84	5	)	)	PUNCT
ap-7659	84	6	,	,	PUNCT
ap-7659	84	7	sg(ω2	sg(ω2	NOUN
ap-7659	84	8	)	)	PUNCT
ap-7659	84	9	)	)	PUNCT
ap-7659	85	1	=	=	PRON
ap-7659	85	2	(	(	PUNCT
ap-7659	85	3	−	−	PROPN
ap-7659	85	4	,	,	PUNCT
ap-7659	85	5	+	+	NOUN
ap-7659	85	6	)	)	PUNCT
ap-7659	85	7	in	in	ADP
ap-7659	85	8	panel	panel	NOUN
ap-7659	85	9	(	(	PUNCT
ap-7659	85	10	c	c	NOUN
ap-7659	85	11	)	)	PUNCT
ap-7659	85	12	,	,	PUNCT
ap-7659	85	13	region	region	NOUN
ap-7659	85	14	iii	iii	PROPN
ap-7659	85	15	.	.	PROPN
ap-7659	86	1	in	in	ADP
ap-7659	86	2	region	region	NOUN
ap-7659	86	3	iv	iv	NUM
ap-7659	86	4	(	(	PUNCT
ap-7659	86	5	sg(m	sg(m	NOUN
ap-7659	86	6	)	)	PUNCT
ap-7659	86	7	,	,	PUNCT
ap-7659	86	8	sg(ω2	sg(ω2	NOUN
ap-7659	86	9	)	)	PUNCT
ap-7659	86	10	)	)	PUNCT
ap-7659	87	1	=	=	PRON
ap-7659	87	2	(	(	PUNCT
ap-7659	87	3	−	−	NOUN
ap-7659	87	4	,	,	PUNCT
ap-7659	87	5	−	−	PROPN
ap-7659	87	6	)	)	PUNCT
ap-7659	87	7	,	,	PUNCT
ap-7659	87	8	for	for	ADP
ap-7659	87	9	panel	panel	NOUN
ap-7659	87	10	(	(	PUNCT
ap-7659	87	11	d	d	NOUN
ap-7659	87	12	)	)	PUNCT
ap-7659	87	13	.	.	PUNCT
ap-7659	88	1	the	the	DET
ap-7659	88	2	real	real	ADJ
ap-7659	88	3	part	part	NOUN
ap-7659	88	4	of	of	ADP
ap-7659	88	5	the	the	DET
ap-7659	88	6	effective	effective	ADJ
ap-7659	88	7	potential	potential	NOUN
ap-7659	88	8	,	,	PUNCT
ap-7659	88	9	re	re	X
ap-7659	88	10	(	(	PUNCT
ap-7659	88	11	u(θ	u(θ	NOUN
ap-7659	88	12	,	,	PUNCT
ap-7659	88	13	x	x	NOUN
ap-7659	88	14	)	)	PUNCT
ap-7659	88	15	|u(θ	|u(θ	NOUN
ap-7659	88	16	,	,	PUNCT
ap-7659	88	17	x)|	x)|	PROPN
ap-7659	88	18	)	)	PUNCT
ap-7659	88	19	,	,	PUNCT
ap-7659	88	20	is	be	AUX
ap-7659	88	21	displayed	display	VERB
ap-7659	88	22	in	in	ADP
ap-7659	88	23	solid	solid	ADJ
ap-7659	88	24	lines	line	NOUN
ap-7659	88	25	,	,	PUNCT
ap-7659	88	26	while	while	SCONJ
ap-7659	88	27	the	the	DET
ap-7659	88	28	imaginary	imaginary	ADJ
ap-7659	88	29	part	part	NOUN
ap-7659	88	30	of	of	ADP
ap-7659	88	31	the	the	DET
ap-7659	88	32	effective	effective	ADJ
ap-7659	88	33	potential	potential	NOUN
ap-7659	88	34	,	,	PUNCT
ap-7659	88	35	i	i	PRON
ap-7659	88	36	m	m	VERB
ap-7659	88	37	(	(	PUNCT
ap-7659	88	38	u(θ	u(θ	NOUN
ap-7659	88	39	,	,	PUNCT
ap-7659	88	40	x	x	NOUN
ap-7659	88	41	)	)	PUNCT
ap-7659	88	42	|u(θ	|u(θ	NOUN
ap-7659	88	43	,	,	PUNCT
ap-7659	88	44	x)|	x)|	PROPN
ap-7659	88	45	)	)	PUNCT
ap-7659	88	46	,	,	PUNCT
ap-7659	88	47	is	be	AUX
ap-7659	88	48	drawn	draw	VERB
ap-7659	88	49	with	with	ADP
ap-7659	88	50	dashed	dash	VERB
ap-7659	88	51	lines	line	NOUN
ap-7659	88	52	.	.	PUNCT
ap-7659	89	1	eq	eq	X
ap-7659	89	2	.	.	PUNCT
ap-7659	90	1	(	(	PUNCT
ap-7659	90	2	15	15	NUM
ap-7659	90	3	)	)	PUNCT
ap-7659	90	4	is	be	AUX
ap-7659	90	5	the	the	DET
ap-7659	90	6	schrödinger	schrödinger	ADJ
ap-7659	90	7	equation	equation	NOUN
ap-7659	90	8	corresponding	correspond	VERB
ap-7659	90	9	to	to	ADP
ap-7659	90	10	the	the	DET
ap-7659	90	11	effective	effective	ADJ
ap-7659	90	12	potential	potential	ADJ
ap-7659	90	13	u(θ	u(θ	NOUN
ap-7659	90	14	,	,	PUNCT
ap-7659	90	15	x	x	X
ap-7659	90	16	)	)	PUNCT
ap-7659	90	17	=	=	SYM
ap-7659	90	18	u(θ	u(θ	NOUN
ap-7659	90	19	,	,	PUNCT
ap-7659	90	20	x	x	NOUN
ap-7659	90	21	)	)	PUNCT
ap-7659	90	22	ℏω	ℏω	NOUN
ap-7659	90	23	=	=	SYM
ap-7659	90	24	e2i(θ+γ	e2i(θ+γ	PROPN
ap-7659	90	25	)	)	PUNCT
ap-7659	90	26	1	1	NUM
ap-7659	90	27	2	2	NUM
ap-7659	90	28	|σ|2x	|σ|2x	NOUN
ap-7659	90	29	2	2	NUM
ap-7659	90	30	b2	b2	NOUN
ap-7659	90	31	0	0	NUM
ap-7659	90	32	.	.	PUNCT
ap-7659	91	1	(	(	PUNCT
ap-7659	91	2	19	19	NUM
ap-7659	91	3	)	)	PUNCT
ap-7659	91	4	solutions	solution	NOUN
ap-7659	91	5	corresponding	correspond	VERB
ap-7659	91	6	to	to	ADP
ap-7659	91	7	eq	eq	PROPN
ap-7659	91	8	.	.	PUNCT
ap-7659	92	1	(	(	PUNCT
ap-7659	92	2	15	15	NUM
ap-7659	92	3	)	)	PUNCT
ap-7659	92	4	represent	represent	VERB
ap-7659	92	5	different	different	ADJ
ap-7659	92	6	physical	physical	ADJ
ap-7659	92	7	systems	system	NOUN
ap-7659	92	8	according	accord	VERB
ap-7659	92	9	to	to	ADP
ap-7659	92	10	the	the	DET
ap-7659	92	11	signs	sign	NOUN
ap-7659	92	12	of	of	ADP
ap-7659	92	13	m(ω	m(ω	PROPN
ap-7659	92	14	,	,	PUNCT
ap-7659	92	15	α	α	X
ap-7659	92	16	,	,	PUNCT
ap-7659	92	17	β	β	NOUN
ap-7659	92	18	,	,	PUNCT
ap-7659	92	19	b0	b0	NOUN
ap-7659	92	20	)	)	PUNCT
ap-7659	92	21	and	and	CCONJ
ap-7659	92	22	ω2(ω	ω2(ω	PROPN
ap-7659	92	23	,	,	PUNCT
ap-7659	92	24	α	α	X
ap-7659	92	25	,	,	PUNCT
ap-7659	92	26	β	β	NOUN
ap-7659	92	27	,	,	PUNCT
ap-7659	92	28	b0	b0	NOUN
ap-7659	92	29	)	)	PUNCT
ap-7659	93	1	[	[	X
ap-7659	93	2	26	26	NUM
ap-7659	93	3	]	]	PUNCT
ap-7659	93	4	.	.	PUNCT
ap-7659	94	1	in	in	ADP
ap-7659	94	2	what	what	PRON
ap-7659	94	3	follows	follow	VERB
ap-7659	94	4	,	,	PUNCT
ap-7659	94	5	we	we	PRON
ap-7659	94	6	shall	shall	AUX
ap-7659	94	7	refer	refer	VERB
ap-7659	94	8	to	to	ADP
ap-7659	94	9	region	region	NOUN
ap-7659	94	10	i	i	PRON
ap-7659	94	11	when	when	SCONJ
ap-7659	94	12	(	(	PUNCT
ap-7659	94	13	sg(m	sg(m	NUM
ap-7659	94	14	)	)	PUNCT
ap-7659	94	15	,	,	PUNCT
ap-7659	94	16	sg(ω2	sg(ω2	NOUN
ap-7659	94	17	)	)	PUNCT
ap-7659	94	18	)	)	PUNCT
ap-7659	95	1	=	=	PUNCT
ap-7659	95	2	(	(	PUNCT
ap-7659	95	3	+	+	ADJ
ap-7659	95	4	,	,	PUNCT
ap-7659	95	5	+	+	ADJ
ap-7659	95	6	)	)	PUNCT
ap-7659	95	7	,	,	PUNCT
ap-7659	95	8	region	region	NOUN
ap-7659	95	9	ii	ii	PROPN
ap-7659	95	10	for	for	ADP
ap-7659	95	11	the	the	DET
ap-7659	95	12	case	case	NOUN
ap-7659	95	13	(	(	PUNCT
ap-7659	95	14	sg(m	sg(m	NUM
ap-7659	95	15	)	)	PUNCT
ap-7659	95	16	,	,	PUNCT
ap-7659	95	17	sg(ω2	sg(ω2	NOUN
ap-7659	95	18	)	)	PUNCT
ap-7659	95	19	)	)	PUNCT
ap-7659	96	1	=	=	PUNCT
ap-7659	96	2	(	(	PUNCT
ap-7659	96	3	+	+	ADJ
ap-7659	96	4	,	,	PUNCT
ap-7659	96	5	−	−	NOUN
ap-7659	96	6	)	)	PUNCT
ap-7659	96	7	,	,	PUNCT
ap-7659	96	8	region	region	NOUN
ap-7659	96	9	iii	iii	PROPN
ap-7659	96	10	for	for	ADP
ap-7659	96	11	(	(	PUNCT
ap-7659	96	12	sg(m	sg(m	NOUN
ap-7659	96	13	)	)	PUNCT
ap-7659	96	14	,	,	PUNCT
ap-7659	96	15	sg(ω2	sg(ω2	NOUN
ap-7659	96	16	)	)	PUNCT
ap-7659	96	17	)	)	PUNCT
ap-7659	97	1	=	=	SYM
ap-7659	97	2	(	(	PUNCT
ap-7659	97	3	−,+	−,+	PROPN
ap-7659	97	4	)	)	PUNCT
ap-7659	97	5	,	,	PUNCT
ap-7659	97	6	and	and	CCONJ
ap-7659	97	7	region	region	NOUN
ap-7659	97	8	iv	iv	NUM
ap-7659	97	9	for	for	ADP
ap-7659	97	10	(	(	PUNCT
ap-7659	97	11	sg(m	sg(m	NOUN
ap-7659	97	12	)	)	PUNCT
ap-7659	97	13	,	,	PUNCT
ap-7659	97	14	sg(ω2	sg(ω2	NOUN
ap-7659	97	15	)	)	PUNCT
ap-7659	97	16	)	)	PUNCT
ap-7659	98	1	=	=	PRON
ap-7659	98	2	(	(	PUNCT
ap-7659	98	3	−,−	−,−	NOUN
ap-7659	98	4	)	)	PUNCT
ap-7659	98	5	,	,	PUNCT
ap-7659	98	6	respectively	respectively	ADV
ap-7659	98	7	.	.	PUNCT
ap-7659	99	1	in	in	ADP
ap-7659	99	2	figure	figure	NOUN
ap-7659	99	3	1	1	NUM
ap-7659	99	4	we	we	PRON
ap-7659	99	5	present	present	VERB
ap-7659	99	6	the	the	DET
ap-7659	99	7	behaviour	behaviour	NOUN
ap-7659	99	8	of	of	ADP
ap-7659	99	9	the	the	DET
ap-7659	99	10	effective	effective	ADJ
ap-7659	99	11	potential	potential	NOUN
ap-7659	99	12	of	of	ADP
ap-7659	99	13	eq	eq	PROPN
ap-7659	99	14	.	.	PUNCT
ap-7659	100	1	(	(	PUNCT
ap-7659	100	2	19	19	NUM
ap-7659	100	3	)	)	PUNCT
ap-7659	100	4	,	,	PUNCT
ap-7659	100	5	u(x	u(x	PROPN
ap-7659	100	6	)	)	PUNCT
ap-7659	101	1	|u(x)|	|u(x)|	NOUN
ap-7659	101	2	,	,	PUNCT
ap-7659	101	3	as	as	ADP
ap-7659	101	4	a	a	DET
ap-7659	101	5	function	function	NOUN
ap-7659	101	6	of	of	ADP
ap-7659	101	7	θ	θ	PROPN
ap-7659	101	8	,	,	PUNCT
ap-7659	101	9	for	for	ADP
ap-7659	101	10	x	x	SYM
ap-7659	101	11	,	,	PUNCT
ap-7659	101	12	|σ|	|σ|	PROPN
ap-7659	101	13	and	and	CCONJ
ap-7659	101	14	|ω|	|ω|	NUM
ap-7659	101	15	fixed	fix	VERB
ap-7659	101	16	,	,	PUNCT
ap-7659	101	17	in	in	ADP
ap-7659	101	18	the	the	DET
ap-7659	101	19	different	different	ADJ
ap-7659	101	20	regions	region	NOUN
ap-7659	101	21	of	of	ADP
ap-7659	101	22	the	the	DET
ap-7659	101	23	parameter	parameter	NOUN
ap-7659	101	24	model	model	NOUN
ap-7659	101	25	-	-	PUNCT
ap-7659	101	26	space	space	NOUN
ap-7659	101	27	.	.	PUNCT
ap-7659	102	1	the	the	DET
ap-7659	102	2	real	real	ADJ
ap-7659	102	3	part	part	NOUN
ap-7659	102	4	of	of	ADP
ap-7659	102	5	the	the	DET
ap-7659	102	6	effective	effective	ADJ
ap-7659	102	7	potential	potential	NOUN
ap-7659	102	8	,	,	PUNCT
ap-7659	102	9	re	re	ADP
ap-7659	102	10	(	(	PUNCT
ap-7659	102	11	u(x	u(x	NOUN
ap-7659	102	12	)	)	PUNCT
ap-7659	102	13	|u(x)|	|u(x)|	NOUN
ap-7659	102	14	)	)	PUNCT
ap-7659	102	15	,	,	PUNCT
ap-7659	102	16	is	be	AUX
ap-7659	102	17	displayed	display	VERB
ap-7659	102	18	in	in	ADP
ap-7659	102	19	solid	solid	ADJ
ap-7659	102	20	lines	line	NOUN
ap-7659	102	21	,	,	PUNCT
ap-7659	102	22	while	while	SCONJ
ap-7659	102	23	the	the	DET
ap-7659	102	24	imaginary	imaginary	ADJ
ap-7659	102	25	part	part	NOUN
ap-7659	102	26	of	of	ADP
ap-7659	102	27	the	the	DET
ap-7659	102	28	effective	effective	ADJ
ap-7659	102	29	potential	potential	NOUN
ap-7659	102	30	,	,	PUNCT
ap-7659	102	31	i	i	PRON
ap-7659	102	32	m	m	VERB
ap-7659	102	33	(	(	PUNCT
ap-7659	102	34	u(x	u(x	PROPN
ap-7659	102	35	)	)	PUNCT
ap-7659	102	36	|u(x)|	|u(x)|	NOUN
ap-7659	102	37	)	)	PUNCT
ap-7659	102	38	,	,	PUNCT
ap-7659	102	39	is	be	AUX
ap-7659	102	40	drawn	draw	VERB
ap-7659	102	41	with	with	ADP
ap-7659	102	42	dashed	dash	VERB
ap-7659	102	43	lines	line	NOUN
ap-7659	102	44	.	.	PUNCT
ap-7659	103	1	2.1.1	2.1.1	X
ap-7659	103	2	.	.	PUNCT
ap-7659	103	3	discrete	discrete	ADJ
ap-7659	103	4	spectrum	spectrum	NOUN
ap-7659	103	5	for	for	ADP
ap-7659	103	6	the	the	DET
ap-7659	103	7	discrete	discrete	ADJ
ap-7659	103	8	sector	sector	NOUN
ap-7659	103	9	of	of	ADP
ap-7659	103	10	the	the	DET
ap-7659	103	11	spectrum	spectrum	NOUN
ap-7659	103	12	,	,	PUNCT
ap-7659	103	13	eigenvalues	eigenvalue	VERB
ap-7659	103	14	and	and	CCONJ
ap-7659	103	15	the	the	DET
ap-7659	103	16	eigenfunctions	eigenfunction	NOUN
ap-7659	103	17	are	be	AUX
ap-7659	103	18	given	give	VERB
ap-7659	103	19	by	by	ADP
ap-7659	103	20	en	en	X
ap-7659	103	21	=	=	SYM
ap-7659	103	22	ℏ	ℏ	PROPN
ap-7659	103	23	ω	ω	X
ap-7659	104	1	[	[	X
ap-7659	104	2	n	n	X
ap-7659	104	3	]	]	X
ap-7659	104	4	=	=	SYM
ap-7659	104	5	ℏ	ℏ	PROPN
ap-7659	104	6	|ω|eiϕ	|ω|eiϕ	PUNCT
ap-7659	104	7	[	[	X
ap-7659	104	8	n	n	X
ap-7659	104	9	]	]	X
ap-7659	104	10	,	,	PUNCT
ap-7659	104	11	ϕ̃m(θ	ϕ̃m(θ	VERB
ap-7659	104	12	,	,	PUNCT
ap-7659	104	13	x	x	NOUN
ap-7659	104	14	)	)	PUNCT
ap-7659	104	15	=	=	SYM
ap-7659	104	16	e	e	PROPN
ap-7659	104	17	α−β	α−β	PROPN
ap-7659	104	18	ω−α−β	ω−α−β	PROPN
ap-7659	104	19	e2iθ	e2iθ	PROPN
ap-7659	105	1	x2	x2	PROPN
ap-7659	105	2	2b2	2b2	NUM
ap-7659	105	3	0	0	NUM
ap-7659	105	4	ϕm(θ	ϕm(θ	NOUN
ap-7659	105	5	,	,	PUNCT
ap-7659	105	6	x	x	X
ap-7659	105	7	)	)	PUNCT
ap-7659	105	8	,	,	PUNCT
ap-7659	105	9	(	(	PUNCT
ap-7659	105	10	20	20	NUM
ap-7659	105	11	)	)	PUNCT
ap-7659	105	12	ψm(θ	ψm(θ	NOUN
ap-7659	105	13	,	,	PUNCT
ap-7659	105	14	x	x	X
ap-7659	105	15	)	)	PUNCT
ap-7659	105	16	=	=	SYM
ap-7659	105	17	e	e	X
ap-7659	105	18	−	−	PROPN
ap-7659	105	19	α−β	α−β	PROPN
ap-7659	105	20	ω−α−β	ω−α−β	PROPN
ap-7659	105	21	e−2iθ	e−2iθ	PROPN
ap-7659	105	22	x2	x2	PROPN
ap-7659	106	1	2b2	2b2	NUM
ap-7659	106	2	0	0	NUM
ap-7659	106	3	(	(	PUNCT
ap-7659	106	4	ϕm(θ	ϕm(θ	NOUN
ap-7659	106	5	,	,	PUNCT
ap-7659	106	6	x))∗	x))∗	PROPN
ap-7659	106	7	,	,	PUNCT
ap-7659	106	8	(	(	PUNCT
ap-7659	106	9	21	21	NUM
ap-7659	106	10	)	)	PUNCT
ap-7659	106	11	where	where	SCONJ
ap-7659	106	12	ϕn(θ	ϕn(θ	NOUN
ap-7659	106	13	,	,	PUNCT
ap-7659	106	14	x	x	X
ap-7659	106	15	)	)	PUNCT
ap-7659	106	16	can	can	AUX
ap-7659	106	17	be	be	AUX
ap-7659	106	18	written	write	VERB
ap-7659	106	19	as	as	ADP
ap-7659	106	20	(	(	PUNCT
ap-7659	106	21	a	a	NOUN
ap-7659	106	22	)	)	PUNCT
ap-7659	106	23	0	0	NUM
ap-7659	107	1	π	π	SYM
ap-7659	107	2	2	2	NUM
ap-7659	107	3	π	π	SYM
ap-7659	107	4	3	3	NUM
ap-7659	107	5	π	π	SYM
ap-7659	107	6	2	2	NUM
ap-7659	107	7	2	2	NUM
ap-7659	107	8	π	π	NOUN
ap-7659	107	9	-1	-1	NOUN
ap-7659	107	10	0	0	NUM
ap-7659	107	11	1	1	NUM
ap-7659	107	12	θ	θ	NOUN
ap-7659	107	13	r	r	NOUN
ap-7659	107	14	e	e	X
ap-7659	107	15	(	(	PUNCT
ap-7659	107	16	u	u	NOUN
ap-7659	107	17	(	(	PUNCT
ap-7659	107	18	x	x	PROPN
ap-7659	107	19	)	)	PUNCT
ap-7659	107	20	/	/	SYM
ap-7659	107	21	|u	|u	ADJ
ap-7659	107	22	(	(	PUNCT
ap-7659	107	23	x	x	X
ap-7659	107	24	)	)	PUNCT
ap-7659	107	25	|	|	ADV
ap-7659	107	26	)	)	PUNCT
ap-7659	107	27	(	(	PUNCT
ap-7659	107	28	b	b	X
ap-7659	107	29	)	)	PUNCT
ap-7659	107	30	0	0	NUM
ap-7659	108	1	π	π	SYM
ap-7659	108	2	2	2	NUM
ap-7659	108	3	π	π	SYM
ap-7659	108	4	3	3	NUM
ap-7659	108	5	π	π	SYM
ap-7659	108	6	2	2	NUM
ap-7659	108	7	2	2	NUM
ap-7659	108	8	π	π	NOUN
ap-7659	108	9	-1	-1	NOUN
ap-7659	108	10	0	0	NUM
ap-7659	108	11	1	1	NUM
ap-7659	108	12	θ	θ	NOUN
ap-7659	108	13	r	r	NOUN
ap-7659	108	14	e	e	X
ap-7659	108	15	(	(	PUNCT
ap-7659	108	16	u	u	NOUN
ap-7659	108	17	(	(	PUNCT
ap-7659	108	18	x	x	PROPN
ap-7659	108	19	)	)	PUNCT
ap-7659	108	20	/	/	SYM
ap-7659	108	21	|u	|u	ADJ
ap-7659	108	22	(	(	PUNCT
ap-7659	108	23	x	x	X
ap-7659	108	24	)	)	PUNCT
ap-7659	108	25	|	|	ADV
ap-7659	108	26	)	)	PUNCT
ap-7659	108	27	(	(	PUNCT
ap-7659	108	28	c	c	X
ap-7659	108	29	)	)	PUNCT
ap-7659	108	30	0	0	NUM
ap-7659	109	1	π	π	SYM
ap-7659	109	2	2	2	NUM
ap-7659	109	3	π	π	SYM
ap-7659	109	4	3	3	NUM
ap-7659	109	5	π	π	SYM
ap-7659	109	6	2	2	NUM
ap-7659	109	7	2	2	NUM
ap-7659	109	8	π	π	NOUN
ap-7659	109	9	-1	-1	NOUN
ap-7659	109	10	0	0	NUM
ap-7659	109	11	1	1	NUM
ap-7659	109	12	θ	θ	NOUN
ap-7659	109	13	r	r	NOUN
ap-7659	109	14	e	e	X
ap-7659	109	15	(	(	PUNCT
ap-7659	109	16	u	u	NOUN
ap-7659	109	17	(	(	PUNCT
ap-7659	109	18	x	x	PROPN
ap-7659	109	19	)	)	PUNCT
ap-7659	109	20	/	/	SYM
ap-7659	109	21	|u	|u	ADJ
ap-7659	109	22	(	(	PUNCT
ap-7659	109	23	x	x	X
ap-7659	109	24	)	)	PUNCT
ap-7659	109	25	|	|	ADV
ap-7659	109	26	)	)	PUNCT
ap-7659	109	27	(	(	PUNCT
ap-7659	109	28	d	d	X
ap-7659	109	29	)	)	PUNCT
ap-7659	109	30	0	0	NUM
ap-7659	110	1	π	π	SYM
ap-7659	110	2	2	2	NUM
ap-7659	110	3	π	π	SYM
ap-7659	110	4	3	3	NUM
ap-7659	110	5	π	π	SYM
ap-7659	110	6	2	2	NUM
ap-7659	110	7	2	2	NUM
ap-7659	110	8	π	π	NOUN
ap-7659	110	9	-1	-1	NOUN
ap-7659	110	10	0	0	NUM
ap-7659	110	11	1	1	NUM
ap-7659	110	12	θ	θ	NOUN
ap-7659	110	13	r	r	NOUN
ap-7659	110	14	e	e	X
ap-7659	110	15	(	(	PUNCT
ap-7659	110	16	u	u	NOUN
ap-7659	110	17	(	(	PUNCT
ap-7659	110	18	x	x	PROPN
ap-7659	110	19	)	)	PUNCT
ap-7659	110	20	/	/	SYM
ap-7659	110	21	|u	|u	ADJ
ap-7659	110	22	(	(	PUNCT
ap-7659	110	23	x	x	NOUN
ap-7659	110	24	)	)	PUNCT
ap-7659	110	25	|	|	ADV
ap-7659	110	26	)	)	PUNCT
ap-7659	110	27	figure	figure	NOUN
ap-7659	110	28	2	2	NUM
ap-7659	110	29	.	.	PUNCT
ap-7659	110	30	real	real	ADJ
ap-7659	110	31	part	part	NOUN
ap-7659	110	32	of	of	ADP
ap-7659	110	33	the	the	DET
ap-7659	110	34	effective	effective	ADJ
ap-7659	110	35	potential	potential	NOUN
ap-7659	110	36	of	of	ADP
ap-7659	110	37	eq	eq	PROPN
ap-7659	110	38	.	.	PUNCT
ap-7659	111	1	(	(	PUNCT
ap-7659	111	2	19	19	NUM
ap-7659	111	3	)	)	PUNCT
ap-7659	111	4	,	,	PUNCT
ap-7659	111	5	u(θ	u(θ	NOUN
ap-7659	111	6	,	,	PUNCT
ap-7659	111	7	x	x	NOUN
ap-7659	111	8	)	)	PUNCT
ap-7659	111	9	|u(θ	|u(θ	NOUN
ap-7659	111	10	,	,	PUNCT
ap-7659	111	11	x)|	x)|	PROPN
ap-7659	111	12	.	.	PUNCT
ap-7659	112	1	the	the	DET
ap-7659	112	2	shadowed	shadow	VERB
ap-7659	112	3	sectors	sector	NOUN
ap-7659	112	4	correspond	correspond	VERB
ap-7659	112	5	to	to	ADP
ap-7659	112	6	the	the	DET
ap-7659	112	7	values	value	NOUN
ap-7659	112	8	of	of	ADP
ap-7659	112	9	θ	θ	PROPN
ap-7659	112	10	for	for	ADP
ap-7659	112	11	which	which	PRON
ap-7659	112	12	the	the	DET
ap-7659	112	13	solutions	solution	NOUN
ap-7659	112	14	of	of	ADP
ap-7659	112	15	eq	eq	PROPN
ap-7659	112	16	.	.	PUNCT
ap-7659	113	1	(	(	PUNCT
ap-7659	113	2	15	15	NUM
ap-7659	113	3	)	)	PUNCT
ap-7659	113	4	are	be	AUX
ap-7659	113	5	square	square	ADJ
ap-7659	113	6	-	-	PUNCT
ap-7659	113	7	integrable	integrable	ADJ
ap-7659	113	8	.	.	PUNCT
ap-7659	114	1	in	in	ADP
ap-7659	114	2	panels	panel	NOUN
ap-7659	114	3	(	(	PUNCT
ap-7659	114	4	a	a	X
ap-7659	114	5	)	)	PUNCT
ap-7659	114	6	,	,	PUNCT
ap-7659	114	7	(	(	PUNCT
ap-7659	114	8	b	b	NOUN
ap-7659	114	9	)	)	PUNCT
ap-7659	114	10	,	,	PUNCT
ap-7659	114	11	c	c	X
ap-7659	114	12	)	)	PUNCT
ap-7659	114	13	and	and	CCONJ
ap-7659	114	14	(	(	PUNCT
ap-7659	114	15	d	d	X
ap-7659	114	16	)	)	PUNCT
ap-7659	114	17	we	we	PRON
ap-7659	114	18	present	present	VERB
ap-7659	114	19	the	the	DET
ap-7659	114	20	results	result	NOUN
ap-7659	114	21	for	for	ADP
ap-7659	114	22	regions	region	NOUN
ap-7659	114	23	i	i	PROPN
ap-7659	114	24	,	,	PUNCT
ap-7659	114	25	ii	ii	PROPN
ap-7659	114	26	,	,	PUNCT
ap-7659	114	27	iii	iii	PROPN
ap-7659	114	28	and	and	CCONJ
ap-7659	114	29	iv	iv	NUM
ap-7659	114	30	,	,	PUNCT
ap-7659	114	31	respectively	respectively	ADV
ap-7659	114	32	.	.	PUNCT
ap-7659	115	1	ϕn(θ	ϕn(θ	NOUN
ap-7659	115	2	,	,	PUNCT
ap-7659	115	3	x	x	X
ap-7659	115	4	)	)	PUNCT
ap-7659	115	5	=	=	SYM
ap-7659	115	6	nne	nne	PROPN
ap-7659	115	7	−e2i(θ+γ	−e2i(θ+γ	PROPN
ap-7659	115	8	)	)	PUNCT
ap-7659	116	1	x2	x2	PROPN
ap-7659	116	2	2b2	2b2	NUM
ap-7659	116	3	0	0	X
ap-7659	117	1	|σ|2	|σ|2	ADJ
ap-7659	118	1	hn	hn	PROPN
ap-7659	118	2	(	(	PUNCT
ap-7659	118	3	ei(θ+γ	ei(θ+γ	PROPN
ap-7659	118	4	)	)	PUNCT
ap-7659	118	5	x	x	PUNCT
ap-7659	118	6	b0	b0	NOUN
ap-7659	118	7	|σ|	|σ|	PROPN
ap-7659	118	8	)	)	PUNCT
ap-7659	118	9	.	.	PUNCT
ap-7659	119	1	nn	nn	PROPN
ap-7659	119	2	2	2	NUM
ap-7659	119	3	=	=	SYM
ap-7659	119	4	ei(θ+γ	ei(θ+γ	PROPN
ap-7659	119	5	)	)	PUNCT
ap-7659	119	6	√	√	PROPN
ap-7659	119	7	πn!2n	πn!2n	NOUN
ap-7659	119	8	|σ|	|σ|	PROPN
ap-7659	119	9	b0	b0	PROPN
ap-7659	119	10	,	,	PUNCT
ap-7659	119	11	(	(	PUNCT
ap-7659	119	12	22	22	NUM
ap-7659	119	13	)	)	PUNCT
ap-7659	119	14	being	be	AUX
ap-7659	119	15	hn(z	hn(z	NOUN
ap-7659	119	16	)	)	PUNCT
ap-7659	119	17	the	the	DET
ap-7659	119	18	hermite	hermite	ADJ
ap-7659	119	19	polynomial	polynomial	NOUN
ap-7659	119	20	of	of	ADP
ap-7659	119	21	order	order	NOUN
ap-7659	119	22	n	n	CCONJ
ap-7659	119	23	,	,	PUNCT
ap-7659	119	24	and	and	CCONJ
ap-7659	119	25	[	[	X
ap-7659	119	26	n	n	X
ap-7659	119	27	]	]	X
ap-7659	119	28	=	=	SYM
ap-7659	119	29	n+	n+	PUNCT
ap-7659	119	30	1/2	1/2	NUM
ap-7659	119	31	.	.	PUNCT
ap-7659	120	1	eigenfunctions	eigenfunction	NOUN
ap-7659	120	2	ϕn(θ	ϕn(θ	PROPN
ap-7659	120	3	,	,	PUNCT
ap-7659	120	4	x	x	X
ap-7659	120	5	)	)	PUNCT
ap-7659	120	6	are	be	AUX
ap-7659	120	7	square	square	NOUN
ap-7659	120	8	-	-	PUNCT
ap-7659	120	9	integrable	integrable	ADJ
ap-7659	120	10	for	for	ADP
ap-7659	120	11	θintervals	θinterval	NOUN
ap-7659	120	12	where	where	SCONJ
ap-7659	120	13	re(u(θ	re(u(θ	NOUN
ap-7659	120	14	,	,	PUNCT
ap-7659	120	15	x	x	NOUN
ap-7659	120	16	)	)	PUNCT
ap-7659	120	17	)	)	PUNCT
ap-7659	120	18	takes	take	VERB
ap-7659	120	19	positive	positive	ADJ
ap-7659	120	20	values	value	NOUN
ap-7659	120	21	.	.	PUNCT
ap-7659	121	1	in	in	ADP
ap-7659	121	2	figure	figure	NOUN
ap-7659	121	3	2	2	NUM
ap-7659	121	4	,	,	PUNCT
ap-7659	121	5	we	we	PRON
ap-7659	121	6	plot	plot	VERB
ap-7659	121	7	re(u(θ	re(u(θ	NOUN
ap-7659	121	8	,	,	PUNCT
ap-7659	121	9	x)/|u(θ	x)/|u(θ	PROPN
ap-7659	121	10	,	,	PUNCT
ap-7659	121	11	x)|	x)|	PROPN
ap-7659	121	12	)	)	PUNCT
ap-7659	121	13	for	for	ADP
ap-7659	121	14	every	every	DET
ap-7659	121	15	region	region	NOUN
ap-7659	121	16	,	,	PUNCT
ap-7659	121	17	the	the	DET
ap-7659	121	18	gray	gray	ADJ
ap-7659	121	19	regions	region	NOUN
ap-7659	121	20	correspond	correspond	VERB
ap-7659	121	21	to	to	ADP
ap-7659	121	22	the	the	DET
ap-7659	121	23	intervals	interval	NOUN
ap-7659	121	24	for	for	ADP
ap-7659	121	25	which	which	PRON
ap-7659	121	26	the	the	DET
ap-7659	121	27	eigenfunctions	eigenfunction	NOUN
ap-7659	121	28	are	be	AUX
ap-7659	121	29	square	square	ADJ
ap-7659	121	30	integrable	integrable	ADJ
ap-7659	121	31	.	.	PUNCT
ap-7659	122	1	in	in	ADP
ap-7659	122	2	table	table	NOUN
ap-7659	122	3	(	(	PUNCT
ap-7659	122	4	1	1	NUM
ap-7659	122	5	)	)	PUNCT
ap-7659	122	6	,	,	PUNCT
ap-7659	122	7	we	we	PRON
ap-7659	122	8	summarize	summarize	VERB
ap-7659	122	9	the	the	DET
ap-7659	122	10	sign	sign	NOUN
ap-7659	122	11	of	of	ADP
ap-7659	122	12	the	the	DET
ap-7659	122	13	parameter	parameter	NOUN
ap-7659	122	14	m	m	PROPN
ap-7659	122	15	and	and	CCONJ
ap-7659	122	16	ω2	ω2	ADJ
ap-7659	122	17	,	,	PUNCT
ap-7659	122	18	which	which	PRON
ap-7659	122	19	characterize	characterize	VERB
ap-7659	122	20	the	the	DET
ap-7659	122	21	different	different	ADJ
ap-7659	122	22	regions	region	NOUN
ap-7659	122	23	of	of	ADP
ap-7659	122	24	the	the	DET
ap-7659	122	25	model	model	NOUN
ap-7659	122	26	,	,	PUNCT
ap-7659	122	27	and	and	CCONJ
ap-7659	122	28	for	for	ADP
ap-7659	122	29	each	each	DET
ap-7659	122	30	region	region	NOUN
ap-7659	122	31	we	we	PRON
ap-7659	122	32	present	present	VERB
ap-7659	122	33	the	the	DET
ap-7659	122	34	values	value	NOUN
ap-7659	122	35	of	of	ADP
ap-7659	122	36	phases	phase	NOUN
ap-7659	122	37	γ	γ	X
ap-7659	122	38	and	and	CCONJ
ap-7659	122	39	ϕ	ϕ	NOUN
ap-7659	122	40	,	,	PUNCT
ap-7659	122	41	and	and	CCONJ
ap-7659	122	42	the	the	DET
ap-7659	122	43	interval	interval	NOUN
ap-7659	122	44	where	where	SCONJ
ap-7659	122	45	the	the	DET
ap-7659	122	46	eigenfunctions	eigenfunction	NOUN
ap-7659	122	47	are	be	AUX
ap-7659	122	48	square	square	ADJ
ap-7659	122	49	-	-	PUNCT
ap-7659	122	50	integrable	integrable	ADJ
ap-7659	122	51	.	.	PUNCT
ap-7659	123	1	in	in	ADP
ap-7659	123	2	regions	region	NOUN
ap-7659	123	3	(	(	PUNCT
ap-7659	123	4	i	i	NOUN
ap-7659	123	5	)	)	PUNCT
ap-7659	123	6	and	and	CCONJ
ap-7659	123	7	(	(	PUNCT
ap-7659	123	8	iii	iii	NOUN
ap-7659	123	9	)	)	PUNCT
ap-7659	123	10	,	,	PUNCT
ap-7659	123	11	we	we	PRON
ap-7659	123	12	can	can	AUX
ap-7659	123	13	define	define	VERB
ap-7659	123	14	two	two	NUM
ap-7659	123	15	welldefined	welldefine	VERB
ap-7659	123	16	θ−domains	θ−domains	PROPN
ap-7659	123	17	:	:	PUNCT
ap-7659	123	18	i1	i1	PROPN
ap-7659	123	19	=	=	PUNCT
ap-7659	124	1	[	[	X
ap-7659	124	2	−π,−3π/4)∪(−π/4	−π,−3π/4)∪(−π/4	NOUN
ap-7659	124	3	,	,	PUNCT
ap-7659	124	4	π/4)∪	π/4)∪	PROPN
ap-7659	124	5	(	(	PUNCT
ap-7659	124	6	3π/4	3π/4	NUM
ap-7659	124	7	,	,	PUNCT
ap-7659	124	8	π	π	PROPN
ap-7659	124	9	]	]	X
ap-7659	124	10	and	and	CCONJ
ap-7659	124	11	i2	i2	PROPN
ap-7659	124	12	=	=	SYM
ap-7659	124	13	(	(	PUNCT
ap-7659	124	14	−3π/4,−π/4	−3π/4,−π/4	NOUN
ap-7659	124	15	)	)	PUNCT
ap-7659	124	16	∪	∪	X
ap-7659	124	17	(	(	PUNCT
ap-7659	124	18	π/4	π/4	NUM
ap-7659	124	19	,	,	PUNCT
ap-7659	124	20	3π/4	3π/4	NUM
ap-7659	124	21	)	)	PUNCT
ap-7659	124	22	.	.	PUNCT
ap-7659	125	1	while	while	SCONJ
ap-7659	125	2	,	,	PUNCT
ap-7659	125	3	in	in	ADP
ap-7659	125	4	regions	region	NOUN
ap-7659	125	5	(	(	PUNCT
ap-7659	125	6	ii	ii	NOUN
ap-7659	125	7	)	)	PUNCT
ap-7659	125	8	and	and	CCONJ
ap-7659	125	9	(	(	PUNCT
ap-7659	125	10	iv	iv	X
ap-7659	125	11	)	)	PUNCT
ap-7659	125	12	,	,	PUNCT
ap-7659	125	13	the	the	DET
ap-7659	125	14	θ	θ	PROPN
ap-7659	125	15	-	-	PUNCT
ap-7659	125	16	domains	domain	NOUN
ap-7659	125	17	are	be	AUX
ap-7659	125	18	:	:	PUNCT
ap-7659	125	19	i3	i3	NOUN
ap-7659	125	20	=	=	SYM
ap-7659	125	21	(	(	PUNCT
ap-7659	125	22	−π,−π/2	−π,−π/2	NUM
ap-7659	125	23	)	)	PUNCT
ap-7659	125	24	∪	∪	NOUN
ap-7659	125	25	(	(	PUNCT
ap-7659	125	26	0	0	NUM
ap-7659	125	27	,	,	PUNCT
ap-7659	125	28	π/2	π/2	NUM
ap-7659	125	29	)	)	PUNCT
ap-7659	125	30	and	and	CCONJ
ap-7659	125	31	i4	i4	PROPN
ap-7659	125	32	=	=	SYM
ap-7659	125	33	(	(	PUNCT
ap-7659	125	34	−π/2	−π/2	PROPN
ap-7659	125	35	,	,	PUNCT
ap-7659	125	36	0	0	NUM
ap-7659	125	37	)	)	PUNCT
ap-7659	125	38	∪	∪	NOUN
ap-7659	125	39	(	(	PUNCT
ap-7659	125	40	π/2	π/2	NUM
ap-7659	125	41	,	,	PUNCT
ap-7659	125	42	π	π	PROPN
ap-7659	125	43	)	)	PUNCT
ap-7659	125	44	.	.	PUNCT
ap-7659	126	1	the	the	DET
ap-7659	126	2	intervals	interval	NOUN
ap-7659	126	3	repeat	repeat	VERB
ap-7659	126	4	themselves	themselves	PRON
ap-7659	126	5	periodically	periodically	ADV
ap-7659	126	6	,	,	PUNCT
ap-7659	126	7	with	with	ADP
ap-7659	126	8	period	period	NOUN
ap-7659	126	9	π	π	NOUN
ap-7659	126	10	.	.	PUNCT
ap-7659	127	1	in	in	ADP
ap-7659	127	2	the	the	DET
ap-7659	127	3	domains	domain	NOUN
ap-7659	127	4	summarized	summarize	VERB
ap-7659	127	5	in	in	ADP
ap-7659	127	6	table	table	NOUN
ap-7659	127	7	1	1	NUM
ap-7659	127	8	,	,	PUNCT
ap-7659	127	9	eigenfunctions	eigenfunction	NOUN
ap-7659	127	10	{	{	PUNCT
ap-7659	127	11	ψν(θ	ψν(θ	ADV
ap-7659	127	12	,	,	PUNCT
ap-7659	127	13	x	x	NOUN
ap-7659	127	14	)	)	PUNCT
ap-7659	127	15	,	,	PUNCT
ap-7659	127	16	ϕ̃ν(θ	ϕ̃ν(θ	PROPN
ap-7659	127	17	,	,	PUNCT
ap-7659	127	18	x	x	NOUN
ap-7659	127	19	)	)	PUNCT
ap-7659	127	20	}	}	PUNCT
ap-7659	127	21	form	form	VERB
ap-7659	127	22	a	a	DET
ap-7659	127	23	biorthogonal	biorthogonal	ADJ
ap-7659	127	24	complete	complete	ADJ
ap-7659	127	25	set	set	NOUN
ap-7659	127	26	.	.	PUNCT
ap-7659	128	1	∫	∫	PROPN
ap-7659	128	2	∞	∞	PROPN
ap-7659	129	1	−∞	−∞	X
ap-7659	129	2	(	(	PUNCT
ap-7659	129	3	ψm(θ	ψm(θ	VERB
ap-7659	129	4	,	,	PUNCT
ap-7659	129	5	x))∗ϕ̃n(θ	x))∗ϕ̃n(θ	X
ap-7659	129	6	,	,	PUNCT
ap-7659	129	7	x	x	X
ap-7659	129	8	)	)	PUNCT
ap-7659	129	9	dx	dx	PROPN
ap-7659	130	1	=	=	NOUN
ap-7659	130	2	∫	∫	PROPN
ap-7659	130	3	∞	∞	PROPN
ap-7659	130	4	−∞	−∞	ADP
ap-7659	130	5	ϕm(θ	ϕm(θ	NOUN
ap-7659	130	6	,	,	PUNCT
ap-7659	130	7	x)ϕn(θ	x)ϕn(θ	NUM
ap-7659	130	8	,	,	PUNCT
ap-7659	130	9	x	x	X
ap-7659	130	10	)	)	PUNCT
ap-7659	130	11	dx	dx	PROPN
ap-7659	130	12	=	=	SYM
ap-7659	130	13	δmn	δmn	PROPN
ap-7659	130	14	.	.	PUNCT
ap-7659	131	1	(	(	PUNCT
ap-7659	131	2	23	23	NUM
ap-7659	131	3	)	)	PUNCT
ap-7659	131	4	it	it	PRON
ap-7659	131	5	should	should	AUX
ap-7659	131	6	be	be	AUX
ap-7659	131	7	noticed	notice	VERB
ap-7659	131	8	that	that	SCONJ
ap-7659	131	9	in	in	ADP
ap-7659	131	10	all	all	DET
ap-7659	131	11	regions	region	NOUN
ap-7659	131	12	,	,	PUNCT
ap-7659	131	13	the	the	DET
ap-7659	131	14	θ−domains	θ−domain	NOUN
ap-7659	131	15	of	of	ADP
ap-7659	131	16	positive	positive	ADJ
ap-7659	131	17	spectrum	spectrum	NOUN
ap-7659	131	18	are	be	AUX
ap-7659	131	19	different	different	ADJ
ap-7659	131	20	from	from	ADP
ap-7659	131	21	the	the	DET
ap-7659	131	22	domains	domain	NOUN
ap-7659	131	23	with	with	ADP
ap-7659	131	24	negative	negative	ADJ
ap-7659	131	25	spectrum	spectrum	NOUN
ap-7659	131	26	.	.	PUNCT
ap-7659	132	1	they	they	PRON
ap-7659	132	2	represent	represent	VERB
ap-7659	132	3	different	different	ADJ
ap-7659	132	4	physical	physical	ADJ
ap-7659	132	5	boundary	boundary	ADJ
ap-7659	132	6	conditions	condition	NOUN
ap-7659	132	7	.	.	PUNCT
ap-7659	133	1	159	159	NUM
ap-7659	133	2	m.	m.	NOUN
ap-7659	133	3	reboiro	reboiro	PROPN
ap-7659	133	4	,	,	PUNCT
ap-7659	133	5	r.	r.	PROPN
ap-7659	133	6	ramírez	ramírez	PROPN
ap-7659	133	7	,	,	PUNCT
ap-7659	133	8	v.	v.	ADP
ap-7659	133	9	fernández	fernández	PROPN
ap-7659	133	10	acta	acta	PROPN
ap-7659	133	11	polytechnica	polytechnica	PROPN
ap-7659	133	12	sg(m	sg(m	PUNCT
ap-7659	133	13	)	)	PUNCT
ap-7659	133	14	sg(ω2	sg(ω2	NOUN
ap-7659	133	15	)	)	PUNCT
ap-7659	133	16	γ	γ	X
ap-7659	133	17	ϕ	ϕ	X
ap-7659	134	1	i	i	PRON
ap-7659	134	2	θc	θc	VERB
ap-7659	134	3	i	i	PRON
ap-7659	134	4	+	+	PROPN
ap-7659	135	1	+	+	CCONJ
ap-7659	135	2	0	0	NUM
ap-7659	135	3	0	0	NUM
ap-7659	135	4	i1	i1	PROPN
ap-7659	135	5	±π/4π/2	±π/4π/2	PROPN
ap-7659	135	6	π	π	PROPN
ap-7659	135	7	i2	i2	PROPN
ap-7659	135	8	iii	iii	PROPN
ap-7659	136	1	+	+	CCONJ
ap-7659	136	2	π/2	π/2	NUM
ap-7659	136	3	0	0	NUM
ap-7659	136	4	i2	i2	PROPN
ap-7659	136	5	0	0	NUM
ap-7659	136	6	π	π	PROPN
ap-7659	136	7	i1	i1	PROPN
ap-7659	136	8	ii	ii	PROPN
ap-7659	136	9	+	+	CCONJ
ap-7659	136	10	π/4	π/4	PUNCT
ap-7659	136	11	π/2	π/2	PROPN
ap-7659	136	12	i4	i4	PROPN
ap-7659	136	13	0	0	NUM
ap-7659	136	14	±π/2	±π/2	PROPN
ap-7659	136	15	π	π	NOUN
ap-7659	136	16	−π/4	−π/4	VERB
ap-7659	136	17	−π/2	−π/2	PROPN
ap-7659	136	18	i3	i3	NOUN
ap-7659	136	19	iv	iv	NUM
ap-7659	136	20	−π/4	−π/4	PROPN
ap-7659	136	21	π/2	π/2	NUM
ap-7659	136	22	i3	i3	NOUN
ap-7659	136	23	π/4	π/4	PUNCT
ap-7659	136	24	−π/2	−π/2	PROPN
ap-7659	136	25	i4	i4	PROPN
ap-7659	136	26	table	table	NOUN
ap-7659	136	27	1	1	NUM
ap-7659	136	28	.	.	PUNCT
ap-7659	137	1	values	value	NOUN
ap-7659	137	2	of	of	ADP
ap-7659	137	3	the	the	DET
ap-7659	137	4	characteristic	characteristic	ADJ
ap-7659	137	5	parameters	parameter	NOUN
ap-7659	137	6	for	for	ADP
ap-7659	137	7	the	the	DET
ap-7659	137	8	different	different	ADJ
ap-7659	137	9	model	model	ADJ
ap-7659	137	10	-	-	PUNCT
ap-7659	137	11	space	space	NOUN
ap-7659	137	12	regions	region	NOUN
ap-7659	137	13	.	.	PUNCT
ap-7659	138	1	in	in	ADP
ap-7659	138	2	columns	column	NOUN
ap-7659	138	3	2	2	NUM
ap-7659	138	4	and	and	CCONJ
ap-7659	138	5	3	3	NUM
ap-7659	138	6	we	we	PRON
ap-7659	138	7	give	give	VERB
ap-7659	138	8	the	the	DET
ap-7659	138	9	sign	sign	NOUN
ap-7659	138	10	of	of	ADP
ap-7659	138	11	m	m	PROPN
ap-7659	138	12	and	and	CCONJ
ap-7659	138	13	ω2	ω2	ADJ
ap-7659	138	14	,	,	PUNCT
ap-7659	138	15	respectively	respectively	ADV
ap-7659	138	16	.	.	PUNCT
ap-7659	139	1	phases	phase	NOUN
ap-7659	139	2	γ	γ	PROPN
ap-7659	139	3	and	and	CCONJ
ap-7659	139	4	ϕ	ϕ	PROPN
ap-7659	139	5	,	,	PUNCT
ap-7659	139	6	for	for	ADP
ap-7659	139	7	the	the	DET
ap-7659	139	8	different	different	ADJ
ap-7659	139	9	regions	region	NOUN
ap-7659	139	10	,	,	PUNCT
ap-7659	139	11	are	be	AUX
ap-7659	139	12	given	give	VERB
ap-7659	139	13	in	in	ADP
ap-7659	139	14	columns	column	NOUN
ap-7659	139	15	4	4	NUM
ap-7659	139	16	and	and	CCONJ
ap-7659	139	17	5	5	NUM
ap-7659	139	18	,	,	PUNCT
ap-7659	139	19	respectively	respectively	ADV
ap-7659	139	20	.	.	PUNCT
ap-7659	140	1	in	in	ADP
ap-7659	140	2	column	column	NOUN
ap-7659	140	3	6	6	NUM
ap-7659	140	4	we	we	PRON
ap-7659	140	5	present	present	VERB
ap-7659	140	6	the	the	DET
ap-7659	140	7	θ	θ	NOUN
ap-7659	140	8	-	-	NOUN
ap-7659	140	9	interval	interval	NOUN
ap-7659	140	10	for	for	ADP
ap-7659	140	11	which	which	PRON
ap-7659	140	12	the	the	DET
ap-7659	140	13	different	different	ADJ
ap-7659	140	14	eigenfunctions	eigenfunction	NOUN
ap-7659	140	15	are	be	AUX
ap-7659	140	16	square	square	ADJ
ap-7659	140	17	-	-	PUNCT
ap-7659	140	18	integrable	integrable	ADJ
ap-7659	140	19	.	.	PUNCT
ap-7659	141	1	in	in	ADP
ap-7659	141	2	the	the	DET
ap-7659	141	3	table	table	NOUN
ap-7659	141	4	i1	i1	NOUN
ap-7659	142	1	=	=	PUNCT
ap-7659	143	1	[	[	X
ap-7659	143	2	−π	−π	PROPN
ap-7659	143	3	,	,	PUNCT
ap-7659	143	4	−3π/4	−3π/4	NOUN
ap-7659	143	5	)	)	PUNCT
ap-7659	143	6	∪	∪	NOUN
ap-7659	143	7	(	(	PUNCT
ap-7659	143	8	−π/4	−π/4	PROPN
ap-7659	143	9	,	,	PUNCT
ap-7659	143	10	π/4	π/4	NOUN
ap-7659	143	11	)	)	PUNCT
ap-7659	143	12	∪	∪	ADP
ap-7659	143	13	(	(	PUNCT
ap-7659	143	14	3π/4	3π/4	NUM
ap-7659	143	15	,	,	PUNCT
ap-7659	143	16	π	π	PROPN
ap-7659	143	17	]	]	X
ap-7659	143	18	,	,	PUNCT
ap-7659	143	19	i2	i2	PROPN
ap-7659	143	20	=	=	SYM
ap-7659	143	21	(	(	PUNCT
ap-7659	143	22	−3π/4	−3π/4	PROPN
ap-7659	143	23	,	,	PUNCT
ap-7659	143	24	−π/4	−π/4	NOUN
ap-7659	143	25	)	)	PUNCT
ap-7659	143	26	∪	∪	NOUN
ap-7659	143	27	(	(	PUNCT
ap-7659	143	28	π/4	π/4	NUM
ap-7659	143	29	,	,	PUNCT
ap-7659	143	30	3π/4	3π/4	NUM
ap-7659	143	31	)	)	PUNCT
ap-7659	143	32	,	,	PUNCT
ap-7659	143	33	i3	i3	NOUN
ap-7659	143	34	=	=	SYM
ap-7659	143	35	(	(	PUNCT
ap-7659	143	36	−π	−π	PROPN
ap-7659	143	37	,	,	PUNCT
ap-7659	143	38	−π/2	−π/2	PROPN
ap-7659	143	39	)	)	PUNCT
ap-7659	143	40	∪	∪	NOUN
ap-7659	143	41	(	(	PUNCT
ap-7659	143	42	0	0	NUM
ap-7659	143	43	,	,	PUNCT
ap-7659	143	44	π/2	π/2	NUM
ap-7659	143	45	)	)	PUNCT
ap-7659	143	46	and	and	CCONJ
ap-7659	143	47	i4	i4	PROPN
ap-7659	143	48	=	=	SYM
ap-7659	143	49	(	(	PUNCT
ap-7659	143	50	−π/2	−π/2	PROPN
ap-7659	143	51	,	,	PUNCT
ap-7659	143	52	0	0	NUM
ap-7659	143	53	)	)	PUNCT
ap-7659	143	54	∪	∪	NOUN
ap-7659	143	55	(	(	PUNCT
ap-7659	143	56	π/2	π/2	NUM
ap-7659	143	57	,	,	PUNCT
ap-7659	143	58	π	π	PROPN
ap-7659	143	59	)	)	PUNCT
ap-7659	143	60	.	.	PUNCT
ap-7659	144	1	in	in	ADP
ap-7659	144	2	the	the	DET
ap-7659	144	3	last	last	ADJ
ap-7659	144	4	column	column	NOUN
ap-7659	144	5	,	,	PUNCT
ap-7659	144	6	we	we	PRON
ap-7659	144	7	give	give	VERB
ap-7659	144	8	the	the	DET
ap-7659	144	9	values	value	NOUN
ap-7659	144	10	of	of	ADP
ap-7659	144	11	θc	θc	NOUN
ap-7659	144	12	for	for	ADP
ap-7659	144	13	which	which	PRON
ap-7659	144	14	the	the	DET
ap-7659	144	15	eigenfunctions	eigenfunction	NOUN
ap-7659	144	16	of	of	ADP
ap-7659	144	17	the	the	DET
ap-7659	144	18	continuous	continuous	ADJ
ap-7659	144	19	spectrum	spectrum	NOUN
ap-7659	144	20	are	be	AUX
ap-7659	144	21	square	square	NOUN
ap-7659	144	22	-	-	PUNCT
ap-7659	144	23	integrable	integrable	ADJ
ap-7659	144	24	.	.	PUNCT
ap-7659	145	1	the	the	DET
ap-7659	145	2	intervals	interval	NOUN
ap-7659	145	3	repeat	repeat	VERB
ap-7659	145	4	themselves	themselves	PRON
ap-7659	145	5	periodically	periodically	ADV
ap-7659	145	6	,	,	PUNCT
ap-7659	145	7	with	with	ADP
ap-7659	145	8	period	period	NOUN
ap-7659	145	9	π	π	NOUN
ap-7659	145	10	.	.	PUNCT
ap-7659	146	1	2.1.2	2.1.2	NUM
ap-7659	146	2	.	.	PUNCT
ap-7659	146	3	continuous	continuous	ADJ
ap-7659	146	4	spectrum	spectrum	NOUN
ap-7659	146	5	the	the	DET
ap-7659	146	6	eigenfunctions	eigenfunction	NOUN
ap-7659	146	7	associated	associate	VERB
ap-7659	146	8	to	to	ADP
ap-7659	146	9	the	the	DET
ap-7659	146	10	continuous	continuous	ADJ
ap-7659	146	11	spectrum	spectrum	NOUN
ap-7659	147	1	[	[	X
ap-7659	147	2	26	26	NUM
ap-7659	147	3	,	,	PUNCT
ap-7659	147	4	42–45	42–45	NUM
ap-7659	147	5	]	]	PUNCT
ap-7659	147	6	are	be	AUX
ap-7659	147	7	given	give	VERB
ap-7659	147	8	,	,	PUNCT
ap-7659	147	9	in	in	ADP
ap-7659	147	10	terms	term	NOUN
ap-7659	147	11	of	of	ADP
ap-7659	147	12	the	the	DET
ap-7659	147	13	eigenfunctions	eigenfunction	NOUN
ap-7659	147	14	of	of	ADP
ap-7659	147	15	h(θ	h(θ	PROPN
ap-7659	147	16	)	)	PUNCT
ap-7659	147	17	of	of	ADP
ap-7659	147	18	eq	eq	PROPN
ap-7659	147	19	.	.	PUNCT
ap-7659	148	1	(	(	PUNCT
ap-7659	148	2	8)	8)	NUM
ap-7659	148	3	,	,	PUNCT
ap-7659	148	4	ϕe	ϕe	NOUN
ap-7659	148	5	±(θ	±(θ	NOUN
ap-7659	148	6	,	,	PUNCT
ap-7659	148	7	x	x	NOUN
ap-7659	148	8	)	)	PUNCT
ap-7659	148	9	,	,	PUNCT
ap-7659	148	10	by	by	ADP
ap-7659	148	11	ϕ̃e	ϕ̃e	PROPN
ap-7659	148	12	±(θ	±(θ	VERB
ap-7659	148	13	,	,	PUNCT
ap-7659	148	14	x	x	X
ap-7659	148	15	)	)	PUNCT
ap-7659	148	16	=	=	SYM
ap-7659	148	17	e	e	PROPN
ap-7659	148	18	α−β	α−β	PROPN
ap-7659	148	19	ω−α−β	ω−α−β	PROPN
ap-7659	148	20	e2iθ	e2iθ	PROPN
ap-7659	149	1	x2	x2	PROPN
ap-7659	149	2	2b2	2b2	NUM
ap-7659	149	3	0	0	NUM
ap-7659	150	1	ϕe	ϕe	NOUN
ap-7659	150	2	±(θ	±(θ	NOUN
ap-7659	150	3	,	,	PUNCT
ap-7659	150	4	x	x	NOUN
ap-7659	150	5	)	)	PUNCT
ap-7659	150	6	,	,	PUNCT
ap-7659	150	7	(	(	PUNCT
ap-7659	150	8	24	24	NUM
ap-7659	150	9	)	)	PUNCT
ap-7659	150	10	ψ	ψ	NOUN
ap-7659	150	11	e	e	NOUN
ap-7659	150	12	±(θ	±(θ	X
ap-7659	150	13	,	,	PUNCT
ap-7659	150	14	x	x	X
ap-7659	150	15	)	)	PUNCT
ap-7659	151	1	=	=	SYM
ap-7659	151	2	e	e	X
ap-7659	151	3	−	−	PROPN
ap-7659	151	4	α−β	α−β	PROPN
ap-7659	151	5	ω−α−β	ω−α−β	PROPN
ap-7659	151	6	e−2iθ	e−2iθ	PROPN
ap-7659	151	7	x2	x2	PROPN
ap-7659	152	1	2b2	2b2	NUM
ap-7659	152	2	0	0	NUM
ap-7659	152	3	(	(	PUNCT
ap-7659	152	4	ϕe	ϕe	NOUN
ap-7659	152	5	±(θ	±(θ	NOUN
ap-7659	152	6	,	,	PUNCT
ap-7659	152	7	x))∗	x))∗	PROPN
ap-7659	152	8	,	,	PUNCT
ap-7659	152	9	(	(	PUNCT
ap-7659	152	10	25	25	NUM
ap-7659	152	11	)	)	PUNCT
ap-7659	152	12	with	with	ADP
ap-7659	152	13	ϕe	ϕe	NOUN
ap-7659	152	14	±(θ	±(θ	NOUN
ap-7659	152	15	,	,	PUNCT
ap-7659	152	16	x	x	X
ap-7659	152	17	)	)	PUNCT
ap-7659	152	18	=	=	PUNCT
ap-7659	152	19	c	c	X
ap-7659	152	20	γ(ν	γ(ν	PROPN
ap-7659	152	21	+	+	CCONJ
ap-7659	152	22	1)d−ν−1	1)d−ν−1	NUM
ap-7659	152	23	(	(	PUNCT
ap-7659	152	24	∓	∓	NOUN
ap-7659	152	25	√	√	PROPN
ap-7659	152	26	−2ei(θ+γ)|σ|	−2ei(θ+γ)|σ|	PROPN
ap-7659	152	27	x	x	SYM
ap-7659	152	28	b0	b0	NOUN
ap-7659	152	29	)	)	PUNCT
ap-7659	152	30	.	.	PUNCT
ap-7659	153	1	(	(	PUNCT
ap-7659	153	2	26	26	NUM
ap-7659	153	3	)	)	PUNCT
ap-7659	153	4	being	be	AUX
ap-7659	153	5	d−ν−1(y	d−ν−1(y	PRON
ap-7659	153	6	)	)	PUNCT
ap-7659	153	7	the	the	DET
ap-7659	153	8	parabolic	parabolic	ADJ
ap-7659	153	9	cylinder	cylinder	NOUN
ap-7659	153	10	functions	function	NOUN
ap-7659	153	11	and	and	CCONJ
ap-7659	153	12	ν	ν	X
ap-7659	153	13	=	=	PUNCT
ap-7659	154	1	ϵ−	ϵ−	NUM
ap-7659	154	2	1	1	NUM
ap-7659	154	3	2	2	NUM
ap-7659	154	4	.	.	PUNCT
ap-7659	155	1	the	the	DET
ap-7659	155	2	normalization	normalization	NOUN
ap-7659	155	3	constant	constant	ADJ
ap-7659	155	4	takes	take	VERB
ap-7659	155	5	the	the	DET
ap-7659	155	6	value	value	NOUN
ap-7659	155	7	c	c	NOUN
ap-7659	155	8	=	=	SYM
ap-7659	155	9	eiπ/8iν/2	eiπ/8iν/2	PROPN
ap-7659	155	10	(	(	PUNCT
ap-7659	155	11	|σ|	|σ|	PROPN
ap-7659	155	12	b0	b0	PROPN
ap-7659	155	13	ei(θ+γ	ei(θ+γ	PROPN
ap-7659	155	14	)	)	PUNCT
ap-7659	155	15	)	)	PUNCT
ap-7659	156	1	1/2	1/2	NUM
ap-7659	156	2	π23/4	π23/4	NOUN
ap-7659	156	3	.	.	PUNCT
ap-7659	157	1	the	the	DET
ap-7659	157	2	biorthogonality	biorthogonality	NOUN
ap-7659	157	3	and	and	CCONJ
ap-7659	157	4	the	the	DET
ap-7659	157	5	completeness	completeness	NOUN
ap-7659	157	6	relation	relation	NOUN
ap-7659	157	7	can	can	AUX
ap-7659	157	8	be	be	AUX
ap-7659	157	9	written	write	VERB
ap-7659	157	10	as	as	ADP
ap-7659	157	11	∫	∫	PROPN
ap-7659	157	12	∞	∞	PROPN
ap-7659	157	13	−∞	−∞	X
ap-7659	157	14	(	(	PUNCT
ap-7659	157	15	ψe	ψe	NOUN
ap-7659	157	16	±(θ	±(θ	NOUN
ap-7659	157	17	,	,	PUNCT
ap-7659	157	18	x))∗ϕ̃e′	x))∗ϕ̃e′	PROPN
ap-7659	157	19	±	±	PROPN
ap-7659	157	20	(	(	PUNCT
ap-7659	157	21	θ	θ	PROPN
ap-7659	157	22	,	,	PUNCT
ap-7659	157	23	x)dx	x)dx	PROPN
ap-7659	157	24	=	=	PUNCT
ap-7659	158	1	δ(e	δ(e	PROPN
ap-7659	158	2	−	−	VERB
ap-7659	158	3	e′),∑	e′),∑	PROPN
ap-7659	158	4	s=±	s=±	NOUN
ap-7659	158	5	∫	∫	PROPN
ap-7659	158	6	∞	∞	PROPN
ap-7659	158	7	−∞	−∞	X
ap-7659	158	8	(	(	PUNCT
ap-7659	158	9	ψe	ψe	PROPN
ap-7659	158	10	s	s	X
ap-7659	158	11	(	(	PUNCT
ap-7659	158	12	θ	θ	PROPN
ap-7659	158	13	,	,	PUNCT
ap-7659	158	14	x))∗ϕ̃e	x))∗ϕ̃e	PROPN
ap-7659	158	15	s	s	X
ap-7659	158	16	(	(	PUNCT
ap-7659	158	17	θ	θ	PROPN
ap-7659	158	18	,	,	PUNCT
ap-7659	158	19	x)de	x)de	PROPN
ap-7659	158	20	=	=	SYM
ap-7659	158	21	δ(x−	δ(x−	X
ap-7659	158	22	x′	x′	NUM
ap-7659	158	23	)	)	PUNCT
ap-7659	158	24	.	.	PUNCT
ap-7659	159	1	(	(	PUNCT
ap-7659	159	2	27	27	NUM
ap-7659	159	3	)	)	PUNCT
ap-7659	159	4	the	the	DET
ap-7659	159	5	possible	possible	ADJ
ap-7659	159	6	values	value	NOUN
ap-7659	159	7	that	that	SCONJ
ap-7659	159	8	the	the	DET
ap-7659	159	9	parameter	parameter	NOUN
ap-7659	159	10	θ	θ	PROPN
ap-7659	159	11	can	can	AUX
ap-7659	159	12	take	take	VERB
ap-7659	159	13	to	to	PART
ap-7659	159	14	fulfill	fulfill	VERB
ap-7659	159	15	the	the	DET
ap-7659	159	16	requirements	requirement	NOUN
ap-7659	159	17	of	of	ADP
ap-7659	159	18	biorthogonality	biorthogonality	NOUN
ap-7659	159	19	and	and	CCONJ
ap-7659	159	20	completeness	completeness	NOUN
ap-7659	159	21	of	of	ADP
ap-7659	159	22	eq	eq	PROPN
ap-7659	159	23	.	.	PUNCT
ap-7659	160	1	(	(	PUNCT
ap-7659	160	2	27	27	NUM
ap-7659	160	3	)	)	PUNCT
ap-7659	160	4	,	,	PUNCT
ap-7659	160	5	θc	θc	NOUN
ap-7659	160	6	,	,	PUNCT
ap-7659	160	7	are	be	AUX
ap-7659	160	8	presented	present	VERB
ap-7659	160	9	in	in	ADP
ap-7659	160	10	the	the	DET
ap-7659	160	11	last	last	ADJ
ap-7659	160	12	column	column	NOUN
ap-7659	160	13	of	of	ADP
ap-7659	160	14	table	table	NOUN
ap-7659	160	15	1	1	NUM
ap-7659	160	16	.	.	PUNCT
ap-7659	161	1	in	in	ADP
ap-7659	161	2	the	the	DET
ap-7659	161	3	framework	framework	NOUN
ap-7659	161	4	of	of	ADP
ap-7659	161	5	the	the	DET
ap-7659	161	6	csm	csm	NOUN
ap-7659	161	7	,	,	PUNCT
ap-7659	161	8	the	the	DET
ap-7659	161	9	continuous	continuous	ADJ
ap-7659	161	10	spectrum	spectrum	NOUN
ap-7659	161	11	lies	lie	VERB
ap-7659	161	12	along	along	ADP
ap-7659	161	13	the	the	DET
ap-7659	161	14	line	line	NOUN
ap-7659	161	15	2θ	2θ	NUM
ap-7659	161	16	.	.	PUNCT
ap-7659	162	1	in	in	ADP
ap-7659	162	2	regions	region	NOUN
ap-7659	162	3	ii	ii	PROPN
ap-7659	162	4	and	and	CCONJ
ap-7659	162	5	iv	iv	NUM
ap-7659	162	6	,	,	PUNCT
ap-7659	162	7	the	the	DET
ap-7659	162	8	2θc	2θc	NOUN
ap-7659	162	9	=	=	SYM
ap-7659	162	10	±	±	NUM
ap-7659	162	11	π	π	NOUN
ap-7659	162	12	so	so	SCONJ
ap-7659	162	13	that	that	SCONJ
ap-7659	162	14	e	e	PROPN
ap-7659	162	15	∈	∈	PROPN
ap-7659	162	16	(	(	PUNCT
ap-7659	162	17	−∞,+∞	−∞,+∞	NUM
ap-7659	162	18	)	)	PUNCT
ap-7659	162	19	meanwhile	meanwhile	ADV
ap-7659	162	20	,	,	PUNCT
ap-7659	162	21	in	in	ADP
ap-7659	162	22	region	region	NOUN
ap-7659	162	23	i	i	PROPN
ap-7659	162	24	and	and	CCONJ
ap-7659	162	25	iii	iii	PROPN
ap-7659	162	26	,	,	PUNCT
ap-7659	162	27	2θc	2θc	NOUN
ap-7659	162	28	=	=	SYM
ap-7659	162	29	±	±	NUM
ap-7659	162	30	π	π	NOUN
ap-7659	162	31	2	2	NUM
ap-7659	162	32	,	,	PUNCT
ap-7659	162	33	so	so	SCONJ
ap-7659	162	34	that	that	SCONJ
ap-7659	162	35	e	e	NOUN
ap-7659	162	36	takes	take	VERB
ap-7659	162	37	imaginary	imaginary	ADJ
ap-7659	162	38	values	value	NOUN
ap-7659	162	39	.	.	PUNCT
ap-7659	163	1	consequently	consequently	ADV
ap-7659	163	2	,	,	PUNCT
ap-7659	163	3	the	the	DET
ap-7659	163	4	parameter	parameter	NOUN
ap-7659	163	5	ν	ν	PROPN
ap-7659	163	6	associated	associate	VERB
ap-7659	163	7	to	to	ADP
ap-7659	163	8	the	the	DET
ap-7659	163	9	order	order	NOUN
ap-7659	163	10	of	of	ADP
ap-7659	163	11	the	the	DET
ap-7659	163	12	eigenfunctions	eigenfunction	NOUN
ap-7659	163	13	of	of	ADP
ap-7659	163	14	eq	eq	PROPN
ap-7659	163	15	.	.	PUNCT
ap-7659	164	1	(	(	PUNCT
ap-7659	164	2	26	26	NUM
ap-7659	164	3	)	)	PUNCT
ap-7659	164	4	takes	take	VERB
ap-7659	164	5	the	the	DET
ap-7659	164	6	value	value	NOUN
ap-7659	164	7	ν	ν	NOUN
ap-7659	164	8	=	=	PUNCT
ap-7659	165	1	−i|ϵ|	−i|ϵ|	PUNCT
ap-7659	165	2	−	−	NOUN
ap-7659	165	3	1	1	NUM
ap-7659	165	4	2	2	NUM
ap-7659	165	5	.	.	PUNCT
ap-7659	166	1	if	if	SCONJ
ap-7659	166	2	we	we	PRON
ap-7659	166	3	look	look	VERB
ap-7659	166	4	at	at	ADP
ap-7659	166	5	the	the	DET
ap-7659	166	6	effective	effective	ADJ
ap-7659	166	7	potential	potential	ADJ
ap-7659	166	8	u(θ	u(θ	NOUN
ap-7659	166	9	,	,	PUNCT
ap-7659	166	10	x	x	NOUN
ap-7659	166	11	)	)	PUNCT
ap-7659	166	12	,	,	PUNCT
ap-7659	166	13	the	the	DET
ap-7659	166	14	values	value	NOUN
ap-7659	166	15	of	of	ADP
ap-7659	166	16	θc	θc	NOUN
ap-7659	166	17	correspond	correspond	NOUN
ap-7659	166	18	to	to	ADP
ap-7659	166	19	the	the	DET
ap-7659	166	20	values	value	NOUN
ap-7659	166	21	of	of	ADP
ap-7659	166	22	θ	θ	PROPN
ap-7659	166	23	for	for	ADP
ap-7659	166	24	which	which	PRON
ap-7659	166	25	re(u(θ	re(u(θ	NOUN
ap-7659	166	26	,	,	PUNCT
ap-7659	166	27	x	x	NOUN
ap-7659	166	28	)	)	PUNCT
ap-7659	166	29	)	)	PUNCT
ap-7659	167	1	=	=	PUNCT
ap-7659	167	2	0	0	X
ap-7659	167	3	.	.	X
ap-7659	167	4	2.1.3	2.1.3	NUM
ap-7659	167	5	.	.	PUNCT
ap-7659	167	6	particular	particular	ADJ
ap-7659	167	7	cases	case	NOUN
ap-7659	167	8	case	case	NOUN
ap-7659	167	9	(	(	PUNCT
ap-7659	167	10	a	a	X
ap-7659	167	11	):	):	PUNCT
ap-7659	167	12	ω	ω	NOUN
ap-7659	167	13	=	=	SYM
ap-7659	167	14	0	0	PROPN
ap-7659	167	15	.	.	PUNCT
ap-7659	168	1	when	when	SCONJ
ap-7659	168	2	ω	ω	PROPN
ap-7659	168	3	=	=	SYM
ap-7659	168	4	0	0	NUM
ap-7659	168	5	and	and	CCONJ
ap-7659	168	6	ω	ω	NUM
ap-7659	168	7	−	−	PROPN
ap-7659	168	8	(	(	PUNCT
ap-7659	168	9	α	α	PROPN
ap-7659	168	10	+	+	X
ap-7659	168	11	β	β	X
ap-7659	168	12	)	)	PUNCT
ap-7659	168	13	̸=	̸=	PROPN
ap-7659	168	14	0	0	NUM
ap-7659	168	15	,	,	PUNCT
ap-7659	168	16	the	the	DET
ap-7659	168	17	problem	problem	NOUN
ap-7659	168	18	reduces	reduce	VERB
ap-7659	168	19	to	to	ADP
ap-7659	168	20	that	that	PRON
ap-7659	168	21	of	of	ADP
ap-7659	168	22	a	a	DET
ap-7659	168	23	free	free	ADJ
ap-7659	168	24	particle	particle	NOUN
ap-7659	168	25	of	of	ADP
ap-7659	168	26	energy	energy	NOUN
ap-7659	168	27	e	e	NOUN
ap-7659	168	28	=	=	PROPN
ap-7659	168	29	ε	ε	PROPN
ap-7659	168	30	e−2iθ	e−2iθ	PROPN
ap-7659	168	31	.	.	PUNCT
ap-7659	169	1	eq	eq	ADP
ap-7659	169	2	.	.	PUNCT
ap-7659	170	1	(	(	PUNCT
ap-7659	170	2	8)	8)	NUM
ap-7659	170	3	reduces	reduce	VERB
ap-7659	170	4	to	to	ADP
ap-7659	170	5	−	−	NOUN
ap-7659	170	6	ℏ2	ℏ2	NOUN
ap-7659	170	7	2	2	NUM
ap-7659	170	8	m	m	NOUN
ap-7659	171	1	e2iθ	e2iθ	PROPN
ap-7659	171	2	d2f(x	d2f(x	PROPN
ap-7659	171	3	)	)	PUNCT
ap-7659	171	4	dx2	dx2	PROPN
ap-7659	171	5	=	=	SYM
ap-7659	171	6	e	e	PROPN
ap-7659	171	7	f(x	f(x	PROPN
ap-7659	171	8	)	)	PUNCT
ap-7659	171	9	,	,	PUNCT
ap-7659	171	10	(	(	PUNCT
ap-7659	171	11	28	28	NUM
ap-7659	171	12	)	)	PUNCT
ap-7659	171	13	the	the	DET
ap-7659	171	14	wave	wave	NOUN
ap-7659	171	15	function	function	NOUN
ap-7659	171	16	can	can	AUX
ap-7659	171	17	be	be	AUX
ap-7659	171	18	written	write	VERB
ap-7659	171	19	as	as	ADP
ap-7659	171	20	f(x	f(x	PROPN
ap-7659	171	21	)	)	PUNCT
ap-7659	172	1	=	=	PUNCT
ap-7659	172	2	aeikx	aeikx	PROPN
ap-7659	172	3	+	+	CCONJ
ap-7659	172	4	ae−ikx	ae−ikx	PROPN
ap-7659	172	5	,	,	PUNCT
ap-7659	172	6	with	with	ADP
ap-7659	172	7	k	k	PROPN
ap-7659	172	8	=	=	PUNCT
ap-7659	172	9	√	√	PROPN
ap-7659	172	10	2ε	2ε	NUM
ap-7659	172	11	ℏ(ω−α−β)b2	ℏ(ω−α−β)b2	X
ap-7659	172	12	0	0	NUM
ap-7659	172	13	.	.	PUNCT
ap-7659	173	1	case	case	NOUN
ap-7659	173	2	(	(	PUNCT
ap-7659	173	3	b	b	NOUN
ap-7659	173	4	):	):	PUNCT
ap-7659	173	5	ω	ω	PROPN
ap-7659	173	6	−	−	PROPN
ap-7659	173	7	(	(	PUNCT
ap-7659	173	8	α+	α+	X
ap-7659	173	9	β	β	X
ap-7659	173	10	)	)	PUNCT
ap-7659	173	11	=	=	SYM
ap-7659	173	12	0	0	NUM
ap-7659	173	13	,	,	PUNCT
ap-7659	173	14	α	α	X
ap-7659	173	15	̸=	̸=	PROPN
ap-7659	173	16	β	β	NOUN
ap-7659	173	17	.	.	PUNCT
ap-7659	173	18	to	to	PART
ap-7659	173	19	study	study	VERB
ap-7659	173	20	this	this	DET
ap-7659	173	21	case	case	NOUN
ap-7659	173	22	we	we	PRON
ap-7659	173	23	have	have	VERB
ap-7659	173	24	to	to	PART
ap-7659	173	25	look	look	VERB
ap-7659	173	26	at	at	ADP
ap-7659	173	27	eq	eq	ADP
ap-7659	173	28	.	.	PUNCT
ap-7659	173	29	(	(	PUNCT
ap-7659	173	30	5	5	NUM
ap-7659	173	31	)	)	PUNCT
ap-7659	173	32	.	.	PUNCT
ap-7659	174	1	if	if	SCONJ
ap-7659	174	2	ω	ω	NUM
ap-7659	174	3	−	−	PROPN
ap-7659	174	4	(	(	PUNCT
ap-7659	174	5	α+	α+	X
ap-7659	174	6	β	β	X
ap-7659	174	7	)	)	PUNCT
ap-7659	174	8	=	=	SYM
ap-7659	174	9	0	0	NUM
ap-7659	174	10	,	,	PUNCT
ap-7659	174	11	it	it	PRON
ap-7659	174	12	reads	read	VERB
ap-7659	174	13	h(θ	h(θ	PROPN
ap-7659	174	14	)	)	PUNCT
ap-7659	175	1	=	=	PUNCT
ap-7659	175	2	ℏ(α+	ℏ(α+	X
ap-7659	175	3	β	β	X
ap-7659	175	4	)	)	PUNCT
ap-7659	175	5	(	(	PUNCT
ap-7659	175	6	e	e	X
ap-7659	175	7	iθ	iθ	NOUN
ap-7659	175	8	x̂	x̂	PROPN
ap-7659	175	9	b0	b0	NOUN
ap-7659	175	10	)	)	PUNCT
ap-7659	175	11	2	2	NUM
ap-7659	176	1	+	+	SYM
ap-7659	176	2	ℏ	ℏ	PROPN
ap-7659	176	3	(	(	PUNCT
ap-7659	176	4	α−	α−	ADP
ap-7659	176	5	β	β	NOUN
ap-7659	176	6	)	)	PUNCT
ap-7659	176	7	2	2	NUM
ap-7659	176	8	(	(	PUNCT
ap-7659	176	9	2	2	NUM
ap-7659	176	10	x̂	x̂	NUM
ap-7659	176	11	i	i	PRON
ap-7659	176	12	ℏ	ℏ	PROPN
ap-7659	176	13	p̂+	p̂+	NOUN
ap-7659	176	14	1	1	NUM
ap-7659	176	15	)	)	PUNCT
ap-7659	176	16	,	,	PUNCT
ap-7659	176	17	(	(	PUNCT
ap-7659	176	18	29	29	NUM
ap-7659	176	19	)	)	PUNCT
ap-7659	176	20	f(x	f(x	PROPN
ap-7659	176	21	)	)	PUNCT
ap-7659	176	22	=	=	PUNCT
ap-7659	177	1	e	e	X
ap-7659	177	2	−e2iθ	−e2iθ	NUM
ap-7659	177	3	x̂2	x̂2	NOUN
ap-7659	177	4	4b2	4b2	NUM
ap-7659	177	5	0	0	NUM
ap-7659	177	6	α+β	α+β	NUM
ap-7659	177	7	α−β	α−β	X
ap-7659	177	8	x−	x−	NOUN
ap-7659	177	9	1	1	NUM
ap-7659	177	10	2	2	NUM
ap-7659	177	11	+	+	CCONJ
ap-7659	177	12	εe−2iθ	εe−2iθ	NUM
ap-7659	177	13	ℏ(α−β	ℏ(α−β	NOUN
ap-7659	177	14	)	)	PUNCT
ap-7659	177	15	.	.	PUNCT
ap-7659	178	1	(	(	PUNCT
ap-7659	178	2	30	30	NUM
ap-7659	178	3	)	)	PUNCT
ap-7659	178	4	in	in	ADP
ap-7659	178	5	table	table	NOUN
ap-7659	178	6	2	2	NUM
ap-7659	178	7	we	we	PRON
ap-7659	178	8	present	present	VERB
ap-7659	178	9	the	the	DET
ap-7659	178	10	values	value	NOUN
ap-7659	178	11	of	of	ADP
ap-7659	178	12	e	e	NOUN
ap-7659	178	13	for	for	ADP
ap-7659	178	14	which	which	PRON
ap-7659	178	15	the	the	DET
ap-7659	178	16	wavefunction	wavefunction	NOUN
ap-7659	178	17	f(x	f(x	PROPN
ap-7659	178	18	)	)	PUNCT
ap-7659	178	19	is	be	AUX
ap-7659	178	20	square	square	ADV
ap-7659	178	21	-	-	PUNCT
ap-7659	178	22	integrable	integrable	ADJ
ap-7659	178	23	.	.	PUNCT
ap-7659	179	1	(	(	PUNCT
ap-7659	179	2	α+	α+	X
ap-7659	179	3	β)/(α−	β)/(α−	NOUN
ap-7659	179	4	β	β	X
ap-7659	179	5	)	)	PUNCT
ap-7659	179	6	(	(	PUNCT
ap-7659	179	7	α−	α−	ADP
ap-7659	179	8	β	β	NOUN
ap-7659	179	9	)	)	PUNCT
ap-7659	179	10	cos(2θ	cos(2θ	NOUN
ap-7659	179	11	)	)	PUNCT
ap-7659	179	12	ε	ε	PROPN
ap-7659	179	13	+	+	PROPN
ap-7659	180	1	+	+	PROPN
ap-7659	180	2	i1	i1	PROPN
ap-7659	180	3	ε|	ε|	PROPN
ap-7659	180	4	cos(2θ)|	cos(2θ)|	X
ap-7659	181	1	ℏ|α−β|	ℏ|α−β|	VERB
ap-7659	181	2	<	<	X
ap-7659	181	3	1	1	NUM
ap-7659	181	4	2	2	NUM
ap-7659	181	5	i2	i2	PROPN
ap-7659	181	6	+	+	CCONJ
ap-7659	181	7	i1	i1	PROPN
ap-7659	181	8	ε|	ε|	PROPN
ap-7659	181	9	cos(2θ)|	cos(2θ)|	X
ap-7659	182	1	ℏ|α−β|	ℏ|α−β|	VERB
ap-7659	182	2	>	>	X
ap-7659	182	3	1	1	NUM
ap-7659	182	4	2	2	NUM
ap-7659	182	5	+	+	NUM
ap-7659	182	6	i2	i2	NOUN
ap-7659	182	7	table	table	NOUN
ap-7659	182	8	2	2	NUM
ap-7659	182	9	.	.	PUNCT
ap-7659	182	10	regions	region	NOUN
ap-7659	182	11	for	for	ADP
ap-7659	182	12	which	which	PRON
ap-7659	182	13	the	the	DET
ap-7659	182	14	wave	wave	NOUN
ap-7659	182	15	function	function	NOUN
ap-7659	182	16	of	of	ADP
ap-7659	182	17	eq	eq	PROPN
ap-7659	182	18	.	.	PUNCT
ap-7659	183	1	(	(	PUNCT
ap-7659	183	2	30	30	NUM
ap-7659	183	3	)	)	PUNCT
ap-7659	183	4	is	be	AUX
ap-7659	183	5	square	square	ADV
ap-7659	183	6	-	-	PUNCT
ap-7659	183	7	integrable	integrable	ADJ
ap-7659	183	8	.	.	PUNCT
ap-7659	184	1	2.2	2.2	NUM
ap-7659	184	2	.	.	PUNCT
ap-7659	185	1	mean	mean	ADJ
ap-7659	185	2	values	value	NOUN
ap-7659	185	3	of	of	ADP
ap-7659	185	4	observables	observable	NOUN
ap-7659	185	5	to	to	PART
ap-7659	185	6	compute	compute	VERB
ap-7659	185	7	the	the	DET
ap-7659	185	8	mean	mean	ADJ
ap-7659	185	9	values	value	NOUN
ap-7659	185	10	,	,	PUNCT
ap-7659	185	11	we	we	PRON
ap-7659	185	12	use	use	VERB
ap-7659	185	13	operators	operator	NOUN
ap-7659	185	14	p̂	p̂	NOUN
ap-7659	185	15	and	and	CCONJ
ap-7659	185	16	x̂	x̂	NOUN
ap-7659	185	17	defined	define	VERB
ap-7659	185	18	as	as	ADP
ap-7659	185	19	[	[	X
ap-7659	185	20	19	19	NUM
ap-7659	185	21	,	,	PUNCT
ap-7659	185	22	46	46	NUM
ap-7659	185	23	,	,	PUNCT
ap-7659	185	24	47	47	NUM
ap-7659	185	25	]	]	PUNCT
ap-7659	185	26	p̂	p̂	X
ap-7659	186	1	=	=	PUNCT
ap-7659	186	2	υ−1v	υ−1v	NOUN
ap-7659	186	3	(	(	PUNCT
ap-7659	186	4	θ	θ	PROPN
ap-7659	186	5	+	+	X
ap-7659	186	6	γ)p̂v	γ)p̂v	PROPN
ap-7659	186	7	(	(	PUNCT
ap-7659	186	8	θ	θ	NOUN
ap-7659	186	9	+	+	PUNCT
ap-7659	186	10	γ)−1υ	γ)−1υ	NOUN
ap-7659	186	11	=	=	SYM
ap-7659	186	12	e−i(θ+γ)p̂+	e−i(θ+γ)p̂+	PROPN
ap-7659	186	13	iℏei(θ+γ	iℏei(θ+γ	NOUN
ap-7659	186	14	)	)	PUNCT
ap-7659	186	15	α−	α−	ADP
ap-7659	186	16	β	β	X
ap-7659	186	17	(	(	PUNCT
ap-7659	186	18	ω	ω	NOUN
ap-7659	186	19	−	−	X
ap-7659	186	20	α−	α−	ADP
ap-7659	186	21	β)b2	β)b2	PROPN
ap-7659	186	22	0	0	NUM
ap-7659	186	23	x̂	x̂	NUM
ap-7659	186	24	,	,	PUNCT
ap-7659	186	25	x̂	x̂	PUNCT
ap-7659	186	26	=	=	PUNCT
ap-7659	187	1	υ−1v	υ−1v	NOUN
ap-7659	187	2	(	(	PUNCT
ap-7659	187	3	θ	θ	PROPN
ap-7659	187	4	+	+	X
ap-7659	187	5	γ)x̂v	γ)x̂v	PROPN
ap-7659	187	6	(	(	PUNCT
ap-7659	187	7	θ	θ	NOUN
ap-7659	187	8	+	+	PUNCT
ap-7659	187	9	γ)−1υ	γ)−1υ	ADJ
ap-7659	187	10	=	=	SYM
ap-7659	187	11	ei(θ+γ)x̂	ei(θ+γ)x̂	NOUN
ap-7659	187	12	,	,	PUNCT
ap-7659	187	13	(	(	PUNCT
ap-7659	187	14	31	31	NUM
ap-7659	187	15	)	)	PUNCT
ap-7659	187	16	160	160	NUM
ap-7659	187	17	vol	vol	NOUN
ap-7659	187	18	.	.	PUNCT
ap-7659	188	1	62	62	NUM
ap-7659	188	2	no	no	INTJ
ap-7659	188	3	.	.	PUNCT
ap-7659	189	1	1/2022	1/2022	NUM
ap-7659	189	2	swanson	swanson	PROPN
ap-7659	189	3	hamiltonian	hamiltonian	NOUN
ap-7659	189	4	revisited	revisit	VERB
ap-7659	189	5	through	through	ADP
ap-7659	189	6	the	the	DET
ap-7659	189	7	csm	csm	NOUN
ap-7659	189	8	that	that	PRON
ap-7659	189	9	satisfy	satisfy	VERB
ap-7659	189	10	[	[	X
ap-7659	189	11	x̂	x̂	NOUN
ap-7659	189	12	,	,	PUNCT
ap-7659	189	13	p̂	p̂	X
ap-7659	189	14	]	]	PUNCT
ap-7659	190	1	=	=	SYM
ap-7659	190	2	iℏ.	iℏ.	NOUN
ap-7659	190	3	(	(	PUNCT
ap-7659	190	4	32	32	NUM
ap-7659	190	5	)	)	PUNCT
ap-7659	190	6	for	for	ADP
ap-7659	190	7	the	the	DET
ap-7659	190	8	discrete	discrete	ADJ
ap-7659	190	9	spectrum	spectrum	NOUN
ap-7659	190	10	of	of	ADP
ap-7659	190	11	h	h	NOUN
ap-7659	190	12	,	,	PUNCT
ap-7659	190	13	it	it	PRON
ap-7659	190	14	can	can	AUX
ap-7659	190	15	be	be	AUX
ap-7659	190	16	proved	prove	VERB
ap-7659	190	17	that	that	SCONJ
ap-7659	190	18	⟨m|p̂	⟨m|p̂	NOUN
ap-7659	190	19	|n⟩	|n⟩	PROPN
ap-7659	190	20	=	=	SYM
ap-7659	191	1	∫	∫	PROPN
ap-7659	191	2	∞	∞	PROPN
ap-7659	192	1	−∞	−∞	X
ap-7659	192	2	(	(	PUNCT
ap-7659	192	3	ψm(θ	ψm(θ	X
ap-7659	192	4	,	,	PUNCT
ap-7659	192	5	x))∗	x))∗	PROPN
ap-7659	192	6	p̂	p̂	NOUN
ap-7659	192	7	ϕ̃n(θ	ϕ̃n(θ	NOUN
ap-7659	192	8	,	,	PUNCT
ap-7659	192	9	x)dx	x)dx	PROPN
ap-7659	192	10	=	=	SYM
ap-7659	193	1	∫	∫	PROPN
ap-7659	193	2	∞	∞	PROPN
ap-7659	193	3	−∞	−∞	ADP
ap-7659	193	4	ϕm(θ	ϕm(θ	NOUN
ap-7659	193	5	,	,	PUNCT
ap-7659	193	6	x	x	X
ap-7659	193	7	)	)	PUNCT
ap-7659	193	8	e−i(θ+γ)p̂	e−i(θ+γ)p̂	X
ap-7659	194	1	ϕn(θ	ϕn(θ	NOUN
ap-7659	194	2	,	,	PUNCT
ap-7659	195	1	x)dx	x)dx	PROPN
ap-7659	195	2	=	=	SYM
ap-7659	196	1	iℏ√	iℏ√	PROPN
ap-7659	196	2	2b0r	2b0r	NOUN
ap-7659	196	3	(	(	PUNCT
ap-7659	196	4	√	√	NUM
ap-7659	196	5	n+	n+	NUM
ap-7659	196	6	1δm	1δm	ADJ
ap-7659	196	7	,	,	PUNCT
ap-7659	196	8	n+1	n+1	PROPN
ap-7659	196	9	−	−	NOUN
ap-7659	196	10	√	√	NUM
ap-7659	196	11	nδm	nδm	NOUN
ap-7659	196	12	,	,	PUNCT
ap-7659	196	13	n−1	n−1	PROPN
ap-7659	196	14	)	)	PUNCT
ap-7659	196	15	,	,	PUNCT
ap-7659	196	16	⟨m|p̂	⟨m|p̂	X
ap-7659	196	17	2|n⟩	2|n⟩	NUM
ap-7659	197	1	=	=	SYM
ap-7659	197	2	∫	∫	PROPN
ap-7659	197	3	∞	∞	PROPN
ap-7659	197	4	−∞	−∞	X
ap-7659	197	5	(	(	PUNCT
ap-7659	197	6	ψm(θ	ψm(θ	X
ap-7659	197	7	,	,	PUNCT
ap-7659	197	8	x))∗	x))∗	PROPN
ap-7659	197	9	p̂	p̂	NUM
ap-7659	197	10	2	2	NUM
ap-7659	197	11	ϕ̃n(θ	ϕ̃n(θ	NOUN
ap-7659	197	12	,	,	PUNCT
ap-7659	197	13	x)dx	x)dx	PROPN
ap-7659	197	14	=	=	SYM
ap-7659	198	1	∫	∫	PROPN
ap-7659	198	2	∞	∞	PROPN
ap-7659	198	3	−∞	−∞	ADP
ap-7659	198	4	ϕm(θ	ϕm(θ	NOUN
ap-7659	198	5	,	,	PUNCT
ap-7659	198	6	x	x	X
ap-7659	198	7	)	)	PUNCT
ap-7659	198	8	e−2i(θ+γ)p̂2	e−2i(θ+γ)p̂2	VERB
ap-7659	198	9	ϕn(θ	ϕn(θ	NOUN
ap-7659	198	10	,	,	PUNCT
ap-7659	198	11	x)dx	x)dx	PROPN
ap-7659	198	12	=	=	SYM
ap-7659	199	1	iℏ√	iℏ√	PROPN
ap-7659	199	2	2b0r	2b0r	NOUN
ap-7659	199	3	(	(	PUNCT
ap-7659	199	4	√	√	NUM
ap-7659	199	5	n+	n+	NUM
ap-7659	199	6	1δm	1δm	ADJ
ap-7659	199	7	,	,	PUNCT
ap-7659	199	8	n+1	n+1	PROPN
ap-7659	199	9	−	−	NOUN
ap-7659	199	10	√	√	NUM
ap-7659	199	11	nδm	nδm	NOUN
ap-7659	199	12	,	,	PUNCT
ap-7659	199	13	n−1	n−1	PROPN
ap-7659	199	14	)	)	PUNCT
ap-7659	199	15	=	=	SYM
ap-7659	200	1	−	−	NOUN
ap-7659	200	2	ℏ2	ℏ2	NOUN
ap-7659	200	3	2b2	2b2	NUM
ap-7659	200	4	0r	0r	X
ap-7659	200	5	(	(	PUNCT
ap-7659	200	6	√	√	NUM
ap-7659	200	7	(	(	PUNCT
ap-7659	200	8	n+	n+	NUM
ap-7659	200	9	2)(n+	2)(n+	NUM
ap-7659	200	10	1)δm	1)δm	NOUN
ap-7659	200	11	,	,	PUNCT
ap-7659	200	12	n+2	n+2	PROPN
ap-7659	201	1	−(2n+	−(2n+	ADP
ap-7659	201	2	1)δm	1)δm	PROPN
ap-7659	201	3	,	,	PUNCT
ap-7659	201	4	n	n	PROPN
ap-7659	201	5	+	+	CCONJ
ap-7659	201	6	√	√	PROPN
ap-7659	201	7	n(n−	n(n−	PROPN
ap-7659	201	8	1)δm	1)δm	PROPN
ap-7659	201	9	,	,	PUNCT
ap-7659	201	10	n−2	n−2	PROPN
ap-7659	201	11	)	)	PUNCT
ap-7659	201	12	,	,	PUNCT
ap-7659	201	13	(	(	PUNCT
ap-7659	201	14	33	33	NUM
ap-7659	201	15	)	)	PUNCT
ap-7659	201	16	and	and	CCONJ
ap-7659	201	17	⟨m|x̂|n⟩	⟨m|x̂|n⟩	NOUN
ap-7659	202	1	=	=	SYM
ap-7659	202	2	∫	∫	PROPN
ap-7659	202	3	∞	∞	PROPN
ap-7659	202	4	−∞	−∞	X
ap-7659	202	5	(	(	PUNCT
ap-7659	202	6	ψm(θ	ψm(θ	X
ap-7659	202	7	,	,	PUNCT
ap-7659	202	8	x))∗	x))∗	PROPN
ap-7659	202	9	x̂	x̂	PROPN
ap-7659	202	10	ϕ̃n(θ	ϕ̃n(θ	PROPN
ap-7659	202	11	,	,	PUNCT
ap-7659	202	12	x)dx	x)dx	PROPN
ap-7659	202	13	=	=	SYM
ap-7659	203	1	∫	∫	PROPN
ap-7659	203	2	∞	∞	PROPN
ap-7659	203	3	−∞	−∞	ADP
ap-7659	203	4	ϕ±	ϕ±	PROPN
ap-7659	203	5	m(θ	m(θ	PROPN
ap-7659	203	6	,	,	PUNCT
ap-7659	203	7	x	x	NOUN
ap-7659	203	8	)	)	PUNCT
ap-7659	203	9	ei(θ+γ)x̂	ei(θ+γ)x̂	NOUN
ap-7659	203	10	ϕ±	ϕ±	PROPN
ap-7659	203	11	n	n	CCONJ
ap-7659	203	12	(	(	PUNCT
ap-7659	203	13	θ	θ	PROPN
ap-7659	203	14	,	,	PUNCT
ap-7659	203	15	x)dx	x)dx	NOUN
ap-7659	203	16	=	=	PRON
ap-7659	204	1	b0r√	b0r√	ADP
ap-7659	204	2	2	2	NUM
ap-7659	204	3	(	(	PUNCT
ap-7659	204	4	√	√	NUM
ap-7659	204	5	n+	n+	NUM
ap-7659	204	6	1δm	1δm	ADJ
ap-7659	204	7	,	,	PUNCT
ap-7659	204	8	n+1	n+1	PROPN
ap-7659	204	9	+	+	NOUN
ap-7659	204	10	√	√	NUM
ap-7659	204	11	nδm	nδm	NOUN
ap-7659	204	12	,	,	PUNCT
ap-7659	204	13	n−1	n−1	PROPN
ap-7659	204	14	)	)	PUNCT
ap-7659	204	15	,	,	PUNCT
ap-7659	204	16	⟨m|x̂2|n⟩	⟨m|x̂2|n⟩	NOUN
ap-7659	204	17	=	=	SYM
ap-7659	204	18	∫	∫	PROPN
ap-7659	204	19	∞	∞	PROPN
ap-7659	205	1	−∞	−∞	X
ap-7659	205	2	(	(	PUNCT
ap-7659	205	3	ψm(θ	ψm(θ	X
ap-7659	205	4	,	,	PUNCT
ap-7659	205	5	x))∗	x))∗	PROPN
ap-7659	205	6	x̂2	x̂2	PROPN
ap-7659	205	7	ϕ̃n(θ	ϕ̃n(θ	PROPN
ap-7659	205	8	,	,	PUNCT
ap-7659	205	9	x)dx	x)dx	PROPN
ap-7659	205	10	=	=	SYM
ap-7659	206	1	∫	∫	PROPN
ap-7659	206	2	∞	∞	PROPN
ap-7659	206	3	−∞	−∞	ADP
ap-7659	206	4	ϕm(θ	ϕm(θ	NOUN
ap-7659	206	5	,	,	PUNCT
ap-7659	206	6	x	x	X
ap-7659	206	7	)	)	PUNCT
ap-7659	206	8	e2i(θ+γ)x̂2	e2i(θ+γ)x̂2	ADJ
ap-7659	206	9	ϕn(θ	ϕn(θ	NOUN
ap-7659	206	10	,	,	PUNCT
ap-7659	206	11	x)dx	x)dx	PROPN
ap-7659	206	12	=	=	SYM
ap-7659	206	13	b2	b2	PROPN
ap-7659	206	14	0r	0r	NUM
ap-7659	206	15	2	2	NUM
ap-7659	206	16	(	(	PUNCT
ap-7659	206	17	√	√	NUM
ap-7659	206	18	(	(	PUNCT
ap-7659	206	19	n+	n+	NUM
ap-7659	206	20	2)(n+	2)(n+	NUM
ap-7659	206	21	1)δm	1)δm	NOUN
ap-7659	206	22	,	,	PUNCT
ap-7659	206	23	n+2	n+2	PROPN
ap-7659	206	24	+	+	ADJ
ap-7659	206	25	(	(	PUNCT
ap-7659	206	26	2n+	2n+	NUM
ap-7659	206	27	1)δm	1)δm	NOUN
ap-7659	206	28	,	,	PUNCT
ap-7659	206	29	n	n	PROPN
ap-7659	206	30	+	+	CCONJ
ap-7659	206	31	√	√	PROPN
ap-7659	206	32	n(n−	n(n−	PROPN
ap-7659	206	33	1)δm	1)δm	PROPN
ap-7659	206	34	,	,	PUNCT
ap-7659	206	35	n−2	n−2	PROPN
ap-7659	206	36	)	)	PUNCT
ap-7659	206	37	,	,	PUNCT
ap-7659	206	38	(	(	PUNCT
ap-7659	206	39	34	34	NUM
ap-7659	206	40	)	)	PUNCT
ap-7659	206	41	with	with	ADP
ap-7659	206	42	b0r	b0r	PROPN
ap-7659	206	43	=	=	SYM
ap-7659	206	44	b0/|σ|	b0/|σ|	PROPN
ap-7659	206	45	.	.	PUNCT
ap-7659	207	1	2.3	2.3	NUM
ap-7659	207	2	.	.	PUNCT
ap-7659	207	3	time	time	NOUN
ap-7659	207	4	dependent	dependent	ADJ
ap-7659	207	5	mean	mean	ADJ
ap-7659	207	6	values	value	NOUN
ap-7659	207	7	from	from	ADP
ap-7659	207	8	the	the	DET
ap-7659	207	9	schrödinger	schrödinger	ADJ
ap-7659	207	10	equation	equation	NOUN
ap-7659	207	11	iℏ	iℏ	ADP
ap-7659	207	12	∂	∂	NOUN
ap-7659	207	13	∂t	∂t	PROPN
ap-7659	208	1	φ̃n(θ	φ̃n(θ	PROPN
ap-7659	208	2	,	,	PUNCT
ap-7659	208	3	x	x	X
ap-7659	208	4	,	,	PUNCT
ap-7659	208	5	t	t	PROPN
ap-7659	208	6	)	)	PUNCT
ap-7659	208	7	=	=	SYM
ap-7659	208	8	h(θ)φ̃n(θ	h(θ)φ̃n(θ	X
ap-7659	208	9	,	,	PUNCT
ap-7659	208	10	x	x	NOUN
ap-7659	208	11	,	,	PUNCT
ap-7659	208	12	t	t	PROPN
ap-7659	208	13	)	)	PUNCT
ap-7659	208	14	,	,	PUNCT
ap-7659	208	15	(	(	PUNCT
ap-7659	208	16	35	35	NUM
ap-7659	208	17	)	)	PUNCT
ap-7659	208	18	it	it	PRON
ap-7659	208	19	results	result	VERB
ap-7659	208	20	φ̃n(θ	φ̃n(θ	ADP
ap-7659	208	21	,	,	PUNCT
ap-7659	208	22	x	x	NOUN
ap-7659	208	23	,	,	PUNCT
ap-7659	208	24	t	t	PROPN
ap-7659	208	25	)	)	PUNCT
ap-7659	208	26	=	=	NOUN
ap-7659	209	1	e−iẽn	e−iẽn	NUM
ap-7659	209	2	t	t	NOUN
ap-7659	209	3	ℏ	ℏ	NOUN
ap-7659	209	4	ϕ̃n(θ	ϕ̃n(θ	NUM
ap-7659	209	5	,	,	PUNCT
ap-7659	209	6	x	x	NOUN
ap-7659	209	7	)	)	PUNCT
ap-7659	209	8	.	.	PUNCT
ap-7659	210	1	(	(	PUNCT
ap-7659	210	2	36	36	NUM
ap-7659	210	3	)	)	PUNCT
ap-7659	210	4	in	in	ADP
ap-7659	210	5	the	the	DET
ap-7659	210	6	same	same	ADJ
ap-7659	210	7	way	way	NOUN
ap-7659	210	8	iℏ	iℏ	ADP
ap-7659	210	9	∂	∂	NOUN
ap-7659	210	10	∂t	∂t	PROPN
ap-7659	210	11	ψn(θ	ψn(θ	PUNCT
ap-7659	210	12	,	,	PUNCT
ap-7659	210	13	x	x	PROPN
ap-7659	210	14	,	,	PUNCT
ap-7659	210	15	t	t	PROPN
ap-7659	210	16	)	)	PUNCT
ap-7659	210	17	=	=	SYM
ap-7659	210	18	h(θ)†ψn(θ	h(θ)†ψn(θ	PROPN
ap-7659	210	19	,	,	PUNCT
ap-7659	210	20	x	x	NOUN
ap-7659	210	21	,	,	PUNCT
ap-7659	210	22	t	t	PROPN
ap-7659	210	23	)	)	PUNCT
ap-7659	210	24	,	,	PUNCT
ap-7659	210	25	(	(	PUNCT
ap-7659	210	26	37	37	NUM
ap-7659	210	27	)	)	PUNCT
ap-7659	210	28	it	it	PRON
ap-7659	210	29	results	result	VERB
ap-7659	210	30	ψn(θ	ψn(θ	PUNCT
ap-7659	210	31	,	,	PUNCT
ap-7659	210	32	x	x	X
ap-7659	210	33	,	,	PUNCT
ap-7659	210	34	t	t	PROPN
ap-7659	210	35	)	)	PUNCT
ap-7659	210	36	=	=	PUNCT
ap-7659	211	1	e−ien	e−ien	NOUN
ap-7659	211	2	t	t	PROPN
ap-7659	211	3	ℏψn(θ	ℏψn(θ	PROPN
ap-7659	211	4	,	,	PUNCT
ap-7659	211	5	x	x	NOUN
ap-7659	211	6	)	)	PUNCT
ap-7659	211	7	.	.	PUNCT
ap-7659	212	1	(	(	PUNCT
ap-7659	212	2	38	38	NUM
ap-7659	212	3	)	)	PUNCT
ap-7659	212	4	2.3.1	2.3.1	NUM
ap-7659	212	5	.	.	PUNCT
ap-7659	213	1	reigions	reigion	NOUN
ap-7659	214	1	i	i	PRON
ap-7659	214	2	and	and	CCONJ
ap-7659	214	3	iii	iii	NUM
ap-7659	214	4	:	:	PUNCT
ap-7659	214	5	real	real	ADJ
ap-7659	214	6	spectrum	spectrum	NOUN
ap-7659	214	7	in	in	ADP
ap-7659	214	8	regions	region	NOUN
ap-7659	214	9	i	i	PRON
ap-7659	214	10	and	and	CCONJ
ap-7659	214	11	iii	iii	PROPN
ap-7659	214	12	,	,	PUNCT
ap-7659	214	13	the	the	DET
ap-7659	214	14	discrete	discrete	ADJ
ap-7659	214	15	eigenvalues	eigenvalue	NOUN
ap-7659	214	16	of	of	ADP
ap-7659	214	17	h(θ	h(θ	PROPN
ap-7659	214	18	)	)	PUNCT
ap-7659	214	19	take	take	VERB
ap-7659	214	20	the	the	DET
ap-7659	214	21	values	value	NOUN
ap-7659	214	22	e±	e±	PROPN
ap-7659	214	23	n	n	PROPN
ap-7659	214	24	=	=	PUNCT
ap-7659	214	25	±ℏ|ω|[n	±ℏ|ω|[n	NOUN
ap-7659	214	26	]	]	PUNCT
ap-7659	214	27	,	,	PUNCT
ap-7659	214	28	with	with	ADP
ap-7659	214	29	eigenfunctions	eigenfunction	NOUN
ap-7659	214	30	ϕ̃±	ϕ̃±	NOUN
ap-7659	214	31	n	n	X
ap-7659	214	32	(	(	PUNCT
ap-7659	214	33	θ	θ	PROPN
ap-7659	214	34	,	,	PUNCT
ap-7659	214	35	x	x	NOUN
ap-7659	214	36	)	)	PUNCT
ap-7659	214	37	.	.	PUNCT
ap-7659	215	1	in	in	ADP
ap-7659	215	2	region	region	NOUN
ap-7659	215	3	i	i	PRON
ap-7659	215	4	,	,	PUNCT
ap-7659	215	5	the	the	DET
ap-7659	215	6	eigenfunctions	eigenfunction	NOUN
ap-7659	215	7	of	of	ADP
ap-7659	215	8	the	the	DET
ap-7659	215	9	positive	positive	ADJ
ap-7659	215	10	(	(	PUNCT
ap-7659	215	11	negative	negative	ADJ
ap-7659	215	12	)	)	PUNCT
ap-7659	215	13	are	be	AUX
ap-7659	215	14	square	square	ADJ
ap-7659	215	15	integrable	integrable	ADJ
ap-7659	215	16	in	in	ADP
ap-7659	215	17	interval	interval	NOUN
ap-7659	215	18	i1	i1	PROPN
ap-7659	215	19	(	(	PUNCT
ap-7659	215	20	i2	i2	PROPN
ap-7659	215	21	)	)	PUNCT
ap-7659	215	22	,	,	PUNCT
ap-7659	215	23	see	see	VERB
ap-7659	215	24	table	table	NOUN
ap-7659	215	25	1	1	NUM
ap-7659	215	26	.	.	PUNCT
ap-7659	216	1	meanwhile	meanwhile	ADV
ap-7659	216	2	,	,	PUNCT
ap-7659	216	3	in	in	ADP
ap-7659	216	4	region	region	PROPN
ap-7659	216	5	iii	iii	PROPN
ap-7659	216	6	,	,	PUNCT
ap-7659	216	7	tthe	tthe	ADP
ap-7659	216	8	eigenfunctions	eigenfunction	NOUN
ap-7659	216	9	of	of	ADP
ap-7659	216	10	the	the	DET
ap-7659	216	11	positive	positive	ADJ
ap-7659	216	12	(	(	PUNCT
ap-7659	216	13	negative	negative	ADJ
ap-7659	216	14	)	)	PUNCT
ap-7659	216	15	are	be	AUX
ap-7659	216	16	square	square	ADJ
ap-7659	216	17	integrable	integrable	ADJ
ap-7659	216	18	in	in	ADP
ap-7659	216	19	interval	interval	NOUN
ap-7659	216	20	i2	i2	PROPN
ap-7659	216	21	(	(	PUNCT
ap-7659	216	22	i1	i1	PROPN
ap-7659	216	23	)	)	PUNCT
ap-7659	216	24	.	.	PUNCT
ap-7659	217	1	consequently	consequently	ADV
ap-7659	217	2	the	the	DET
ap-7659	217	3	time	time	NOUN
ap-7659	217	4	evolution	evolution	NOUN
ap-7659	217	5	of	of	ADP
ap-7659	217	6	the	the	DET
ap-7659	217	7	states	state	NOUN
ap-7659	217	8	is	be	AUX
ap-7659	217	9	given	give	VERB
ap-7659	217	10	by	by	ADP
ap-7659	217	11	φ̃±	φ̃±	PROPN
ap-7659	217	12	n	n	CCONJ
ap-7659	217	13	(	(	PUNCT
ap-7659	217	14	θ	θ	PROPN
ap-7659	217	15	,	,	PUNCT
ap-7659	217	16	x	x	PROPN
ap-7659	217	17	,	,	PUNCT
ap-7659	217	18	t	t	PROPN
ap-7659	217	19	)	)	PUNCT
ap-7659	218	1	=	=	SYM
ap-7659	218	2	e−i	e−i	NOUN
ap-7659	218	3	ẽnt	ẽnt	PROPN
ap-7659	218	4	ℏ	ℏ	NOUN
ap-7659	218	5	ϕ̃n(θ	ϕ̃n(θ	NUM
ap-7659	218	6	,	,	PUNCT
ap-7659	218	7	x	x	NOUN
ap-7659	218	8	)	)	PUNCT
ap-7659	218	9	,	,	PUNCT
ap-7659	218	10	=	=	SYM
ap-7659	218	11	e∓i(n+	e∓i(n+	NOUN
ap-7659	218	12	1	1	NUM
ap-7659	218	13	2	2	NUM
ap-7659	218	14	)	)	PUNCT
ap-7659	218	15	|ω|tϕ̃±	|ω|tϕ̃±	PROPN
ap-7659	218	16	n	n	CCONJ
ap-7659	218	17	(	(	PUNCT
ap-7659	218	18	θ	θ	PROPN
ap-7659	218	19	,	,	PUNCT
ap-7659	218	20	x	x	NOUN
ap-7659	218	21	)	)	PUNCT
ap-7659	218	22	.	.	PUNCT
ap-7659	219	1	ψ±	ψ±	PROPN
ap-7659	219	2	n	n	CCONJ
ap-7659	219	3	(	(	PUNCT
ap-7659	219	4	θ	θ	PROPN
ap-7659	219	5	,	,	PUNCT
ap-7659	219	6	x	x	PROPN
ap-7659	219	7	,	,	PUNCT
ap-7659	219	8	t	t	PROPN
ap-7659	219	9	)	)	PUNCT
ap-7659	220	1	=	=	PUNCT
ap-7659	220	2	e−i	e−i	VERB
ap-7659	220	3	ent	ent	NOUN
ap-7659	220	4	ℏ	ℏ	PROPN
ap-7659	220	5	ψn(θ	ψn(θ	PUNCT
ap-7659	220	6	,	,	PUNCT
ap-7659	220	7	x	x	NOUN
ap-7659	220	8	)	)	PUNCT
ap-7659	220	9	,	,	PUNCT
ap-7659	220	10	=	=	SYM
ap-7659	220	11	e∓i(n+	e∓i(n+	NOUN
ap-7659	220	12	1	1	NUM
ap-7659	220	13	2	2	NUM
ap-7659	220	14	)	)	PUNCT
ap-7659	220	15	|ω|tψ	|ω|tψ	NOUN
ap-7659	220	16	±	±	NUM
ap-7659	220	17	n	n	CCONJ
ap-7659	220	18	(	(	PUNCT
ap-7659	220	19	θ	θ	PROPN
ap-7659	220	20	,	,	PUNCT
ap-7659	220	21	x	x	NOUN
ap-7659	220	22	)	)	PUNCT
ap-7659	220	23	,	,	PUNCT
ap-7659	220	24	(	(	PUNCT
ap-7659	220	25	39	39	NUM
ap-7659	220	26	)	)	PUNCT
ap-7659	220	27	and	and	CCONJ
ap-7659	220	28	then	then	ADV
ap-7659	220	29	⟨m|ô|n⟩	⟨m|ô|n⟩	X
ap-7659	221	1	=	=	SYM
ap-7659	221	2	e∓i(n−m)|ω|t	e∓i(n−m)|ω|t	ADJ
ap-7659	221	3	∫	∫	PROPN
ap-7659	221	4	∞	∞	PROPN
ap-7659	222	1	−∞	−∞	X
ap-7659	222	2	(	(	PUNCT
ap-7659	222	3	ψ±	ψ±	PROPN
ap-7659	222	4	m(θ	m(θ	PROPN
ap-7659	222	5	,	,	PUNCT
ap-7659	222	6	x))∗ôϕ̃±	x))∗ôϕ̃±	NUM
ap-7659	222	7	n	n	CCONJ
ap-7659	222	8	(	(	PUNCT
ap-7659	222	9	θ	θ	NOUN
ap-7659	222	10	,	,	PUNCT
ap-7659	222	11	x)dx	x)dx	PROPN
ap-7659	222	12	.	.	PUNCT
ap-7659	223	1	(	(	PUNCT
ap-7659	223	2	40	40	NUM
ap-7659	223	3	)	)	PUNCT
ap-7659	223	4	2.3.2	2.3.2	NUM
ap-7659	223	5	.	.	PUNCT
ap-7659	224	1	region	region	PROPN
ap-7659	224	2	ii	ii	PROPN
ap-7659	224	3	and	and	CCONJ
ap-7659	224	4	iv	iv	NUM
ap-7659	224	5	:	:	PUNCT
ap-7659	224	6	complex	complex	ADJ
ap-7659	224	7	spectrum	spectrum	NOUN
ap-7659	224	8	in	in	ADP
ap-7659	224	9	regions	region	NOUN
ap-7659	224	10	ii	ii	PROPN
ap-7659	224	11	and	and	CCONJ
ap-7659	224	12	iv	iv	NUM
ap-7659	224	13	,	,	PUNCT
ap-7659	224	14	the	the	DET
ap-7659	224	15	discrete	discrete	ADJ
ap-7659	224	16	eigenvalues	eigenvalue	NOUN
ap-7659	224	17	of	of	ADP
ap-7659	224	18	h(θ	h(θ	PROPN
ap-7659	224	19	)	)	PUNCT
ap-7659	224	20	take	take	VERB
ap-7659	224	21	the	the	DET
ap-7659	224	22	values	value	NOUN
ap-7659	224	23	e±	e±	PROPN
ap-7659	224	24	n	n	X
ap-7659	224	25	=	=	PUNCT
ap-7659	224	26	±iℏ|ω|[n	±iℏ|ω|[n	PROPN
ap-7659	224	27	]	]	PUNCT
ap-7659	224	28	,	,	PUNCT
ap-7659	224	29	with	with	ADP
ap-7659	224	30	eigenfunctions	eigenfunction	NOUN
ap-7659	224	31	ϕ̃±	ϕ̃±	NOUN
ap-7659	224	32	n	n	X
ap-7659	224	33	(	(	PUNCT
ap-7659	224	34	θ	θ	PROPN
ap-7659	224	35	,	,	PUNCT
ap-7659	224	36	x	x	NOUN
ap-7659	224	37	)	)	PUNCT
ap-7659	224	38	.	.	PUNCT
ap-7659	225	1	in	in	ADP
ap-7659	225	2	region	region	PROPN
ap-7659	225	3	ii	ii	PROPN
ap-7659	225	4	,	,	PUNCT
ap-7659	225	5	the	the	DET
ap-7659	225	6	eigenfunctions	eigenfunction	NOUN
ap-7659	225	7	of	of	ADP
ap-7659	225	8	the	the	DET
ap-7659	225	9	positive	positive	ADJ
ap-7659	225	10	(	(	PUNCT
ap-7659	225	11	negative	negative	ADJ
ap-7659	225	12	)	)	PUNCT
ap-7659	225	13	are	be	AUX
ap-7659	225	14	square	square	ADJ
ap-7659	225	15	integrable	integrable	ADJ
ap-7659	225	16	in	in	ADP
ap-7659	225	17	interval	interval	NOUN
ap-7659	225	18	i4	i4	PROPN
ap-7659	225	19	(	(	PUNCT
ap-7659	225	20	i3	i3	PROPN
ap-7659	225	21	)	)	PUNCT
ap-7659	225	22	.	.	PUNCT
ap-7659	226	1	meanwhile	meanwhile	ADV
ap-7659	226	2	,	,	PUNCT
ap-7659	226	3	in	in	ADP
ap-7659	226	4	region	region	PROPN
ap-7659	226	5	iii	iii	PROPN
ap-7659	226	6	,	,	PUNCT
ap-7659	226	7	the	the	DET
ap-7659	226	8	eigenfunctions	eigenfunction	NOUN
ap-7659	226	9	of	of	ADP
ap-7659	226	10	the	the	DET
ap-7659	226	11	positive	positive	ADJ
ap-7659	226	12	(	(	PUNCT
ap-7659	226	13	negative	negative	ADJ
ap-7659	226	14	)	)	PUNCT
ap-7659	226	15	are	be	AUX
ap-7659	226	16	square	square	ADJ
ap-7659	226	17	integrable	integrable	ADJ
ap-7659	226	18	in	in	ADP
ap-7659	226	19	interval	interval	NOUN
ap-7659	226	20	i3	i3	NOUN
ap-7659	226	21	(	(	PUNCT
ap-7659	226	22	i4	i4	PROPN
ap-7659	226	23	)	)	PUNCT
ap-7659	226	24	.	.	PUNCT
ap-7659	227	1	so	so	ADV
ap-7659	227	2	that	that	SCONJ
ap-7659	227	3	the	the	DET
ap-7659	227	4	time	time	NOUN
ap-7659	227	5	evolution	evolution	NOUN
ap-7659	227	6	of	of	ADP
ap-7659	227	7	the	the	DET
ap-7659	227	8	eigenfunctions	eigenfunction	NOUN
ap-7659	227	9	are	be	AUX
ap-7659	227	10	given	give	VERB
ap-7659	227	11	by	by	ADP
ap-7659	227	12	φ̃±	φ̃±	PROPN
ap-7659	227	13	n	n	CCONJ
ap-7659	227	14	(	(	PUNCT
ap-7659	227	15	θ	θ	PROPN
ap-7659	227	16	,	,	PUNCT
ap-7659	227	17	x	x	PROPN
ap-7659	227	18	,	,	PUNCT
ap-7659	227	19	t	t	PROPN
ap-7659	227	20	)	)	PUNCT
ap-7659	228	1	=	=	PUNCT
ap-7659	228	2	e−i	e−i	VERB
ap-7659	228	3	ent	ent	NOUN
ap-7659	228	4	ℏ	ℏ	PROPN
ap-7659	228	5	ϕ̃±	ϕ̃±	NOUN
ap-7659	228	6	n	n	PROPN
ap-7659	228	7	(	(	PUNCT
ap-7659	228	8	θ	θ	PROPN
ap-7659	228	9	,	,	PUNCT
ap-7659	228	10	x	x	NOUN
ap-7659	228	11	)	)	PUNCT
ap-7659	228	12	,	,	PUNCT
ap-7659	228	13	=	=	PUNCT
ap-7659	228	14	e±(n+	e±(n+	X
ap-7659	228	15	1	1	NUM
ap-7659	228	16	2	2	NUM
ap-7659	228	17	)	)	PUNCT
ap-7659	228	18	|ω|tϕ̃n(θ	|ω|tϕ̃n(θ	NOUN
ap-7659	228	19	,	,	PUNCT
ap-7659	228	20	x	x	NOUN
ap-7659	228	21	)	)	PUNCT
ap-7659	228	22	.	.	PUNCT
ap-7659	229	1	(	(	PUNCT
ap-7659	229	2	41	41	NUM
ap-7659	229	3	)	)	PUNCT
ap-7659	229	4	and	and	CCONJ
ap-7659	229	5	ψ±	ψ±	PROPN
ap-7659	229	6	n	n	CCONJ
ap-7659	229	7	(	(	PUNCT
ap-7659	229	8	θ	θ	PROPN
ap-7659	229	9	,	,	PUNCT
ap-7659	229	10	x	x	PROPN
ap-7659	229	11	,	,	PUNCT
ap-7659	229	12	t	t	PROPN
ap-7659	229	13	)	)	PUNCT
ap-7659	229	14	=	=	PUNCT
ap-7659	229	15	e−i	e−i	VERB
ap-7659	229	16	e∗	e∗	PROPN
ap-7659	229	17	nt	not	PART
ap-7659	229	18	ℏ	ℏ	PROPN
ap-7659	229	19	ψn(θ	ψn(θ	PUNCT
ap-7659	229	20	,	,	PUNCT
ap-7659	229	21	x	x	NOUN
ap-7659	229	22	)	)	PUNCT
ap-7659	229	23	,	,	PUNCT
ap-7659	229	24	=	=	PRON
ap-7659	229	25	e∓(n+	e∓(n+	NOUN
ap-7659	229	26	1	1	NUM
ap-7659	229	27	2	2	NUM
ap-7659	229	28	)	)	PUNCT
ap-7659	229	29	|ω|tψ	|ω|tψ	NOUN
ap-7659	229	30	±	±	NUM
ap-7659	229	31	n	n	CCONJ
ap-7659	229	32	(	(	PUNCT
ap-7659	229	33	θ	θ	PROPN
ap-7659	229	34	,	,	PUNCT
ap-7659	229	35	x	x	NOUN
ap-7659	229	36	)	)	PUNCT
ap-7659	229	37	.	.	PUNCT
ap-7659	230	1	(	(	PUNCT
ap-7659	230	2	42	42	NUM
ap-7659	230	3	)	)	PUNCT
ap-7659	230	4	as	as	ADP
ap-7659	230	5	a	a	DET
ap-7659	230	6	result	result	NOUN
ap-7659	230	7	⟨m|ô|n⟩	⟨m|ô|n⟩	PUNCT
ap-7659	231	1	=	=	SYM
ap-7659	231	2	e±(n−m)|ω|t	e±(n−m)|ω|t	PROPN
ap-7659	231	3	∫	∫	PROPN
ap-7659	231	4	∞	∞	PROPN
ap-7659	232	1	−∞	−∞	X
ap-7659	232	2	(	(	PUNCT
ap-7659	232	3	ψ±	ψ±	PROPN
ap-7659	232	4	m(θ	m(θ	PROPN
ap-7659	232	5	,	,	PUNCT
ap-7659	232	6	x))∗ôϕ̃±	x))∗ôϕ̃±	NUM
ap-7659	232	7	n	n	CCONJ
ap-7659	232	8	(	(	PUNCT
ap-7659	232	9	θ	θ	NOUN
ap-7659	232	10	,	,	PUNCT
ap-7659	232	11	x)dx	x)dx	PROPN
ap-7659	232	12	.	.	PUNCT
ap-7659	233	1	(	(	PUNCT
ap-7659	233	2	43	43	NUM
ap-7659	233	3	)	)	PUNCT
ap-7659	233	4	161	161	NUM
ap-7659	233	5	m.	m.	NOUN
ap-7659	233	6	reboiro	reboiro	PROPN
ap-7659	233	7	,	,	PUNCT
ap-7659	233	8	r.	r.	PROPN
ap-7659	233	9	ramírez	ramírez	PROPN
ap-7659	233	10	,	,	PUNCT
ap-7659	233	11	v.	v.	ADP
ap-7659	233	12	fernández	fernández	PROPN
ap-7659	233	13	acta	acta	PROPN
ap-7659	233	14	polytechnica	polytechnica	PROPN
ap-7659	233	15	3	3	NUM
ap-7659	233	16	.	.	NOUN
ap-7659	233	17	results	result	NOUN
ap-7659	233	18	and	and	CCONJ
ap-7659	233	19	discussion	discussion	NOUN
ap-7659	233	20	in	in	ADP
ap-7659	233	21	order	order	NOUN
ap-7659	233	22	to	to	PART
ap-7659	233	23	evaluate	evaluate	VERB
ap-7659	233	24	the	the	DET
ap-7659	233	25	benefits	benefit	NOUN
ap-7659	233	26	of	of	ADP
ap-7659	233	27	the	the	DET
ap-7659	233	28	present	present	ADJ
ap-7659	233	29	approach	approach	NOUN
ap-7659	233	30	,	,	PUNCT
ap-7659	233	31	let	let	VERB
ap-7659	233	32	us	we	PRON
ap-7659	233	33	consider	consider	VERB
ap-7659	233	34	the	the	DET
ap-7659	233	35	time	time	NOUN
ap-7659	233	36	evolution	evolution	NOUN
ap-7659	233	37	of	of	ADP
ap-7659	233	38	a	a	DET
ap-7659	233	39	given	give	VERB
ap-7659	233	40	initial	initial	ADJ
ap-7659	233	41	state	state	NOUN
ap-7659	233	42	when	when	SCONJ
ap-7659	233	43	the	the	DET
ap-7659	233	44	parameters	parameter	NOUN
ap-7659	233	45	of	of	ADP
ap-7659	233	46	the	the	DET
ap-7659	233	47	model	model	NOUN
ap-7659	233	48	correspond	correspond	VERB
ap-7659	233	49	to	to	ADP
ap-7659	233	50	region	region	PROPN
ap-7659	233	51	ii	ii	PROPN
ap-7659	233	52	.	.	PUNCT
ap-7659	234	1	in	in	ADP
ap-7659	234	2	[	[	X
ap-7659	234	3	26	26	NUM
ap-7659	234	4	]	]	X
ap-7659	234	5	we	we	PRON
ap-7659	234	6	have	have	AUX
ap-7659	234	7	analysed	analyse	VERB
ap-7659	234	8	the	the	DET
ap-7659	234	9	swanson	swanson	PROPN
ap-7659	234	10	model	model	NOUN
ap-7659	234	11	by	by	ADP
ap-7659	234	12	solving	solve	VERB
ap-7659	234	13	its	its	PRON
ap-7659	234	14	eigenvalue	eigenvalue	ADJ
ap-7659	234	15	problem	problem	NOUN
ap-7659	234	16	in	in	ADP
ap-7659	234	17	the	the	DET
ap-7659	234	18	rigged	rig	VERB
ap-7659	234	19	hilbert	hilbert	NOUN
ap-7659	234	20	space	space	NOUN
ap-7659	234	21	.	.	PUNCT
ap-7659	235	1	we	we	PRON
ap-7659	235	2	have	have	AUX
ap-7659	235	3	found	find	VERB
ap-7659	235	4	that	that	SCONJ
ap-7659	235	5	in	in	ADP
ap-7659	235	6	region	region	NOUN
ap-7659	235	7	ii	ii	PROPN
ap-7659	235	8	the	the	DET
ap-7659	235	9	hamiltonian	hamiltonian	NOUN
ap-7659	235	10	was	be	AUX
ap-7659	235	11	similar	similar	ADJ
ap-7659	235	12	to	to	ADP
ap-7659	235	13	the	the	DET
ap-7659	235	14	one	one	NUM
ap-7659	235	15	of	of	ADP
ap-7659	235	16	a	a	DET
ap-7659	235	17	particle	particle	NOUN
ap-7659	235	18	in	in	ADP
ap-7659	235	19	a	a	DET
ap-7659	235	20	parabolic	parabolic	ADJ
ap-7659	235	21	barrier	barrier	NOUN
ap-7659	235	22	.	.	PUNCT
ap-7659	236	1	in	in	ADP
ap-7659	236	2	the	the	DET
ap-7659	236	3	framework	framework	NOUN
ap-7659	236	4	of	of	ADP
ap-7659	236	5	the	the	DET
ap-7659	236	6	csm	csm	NOUN
ap-7659	236	7	,	,	PUNCT
ap-7659	236	8	we	we	PRON
ap-7659	236	9	model	model	VERB
ap-7659	236	10	the	the	DET
ap-7659	236	11	effective	effective	ADJ
ap-7659	236	12	interaction	interaction	NOUN
ap-7659	236	13	by	by	ADP
ap-7659	236	14	a	a	DET
ap-7659	236	15	complex	complex	ADJ
ap-7659	236	16	potential	potential	NOUN
ap-7659	236	17	.	.	PUNCT
ap-7659	237	1	this	this	DET
ap-7659	237	2	fact	fact	NOUN
ap-7659	237	3	resembles	resemble	VERB
ap-7659	237	4	the	the	DET
ap-7659	237	5	spirit	spirit	NOUN
ap-7659	237	6	of	of	ADP
ap-7659	237	7	the	the	DET
ap-7659	237	8	optical	optical	ADJ
ap-7659	237	9	potential	potential	NOUN
ap-7659	237	10	in	in	ADP
ap-7659	237	11	nuclear	nuclear	ADJ
ap-7659	237	12	physics	physics	NOUN
ap-7659	237	13	[	[	X
ap-7659	237	14	48	48	NUM
ap-7659	237	15	,	,	PUNCT
ap-7659	237	16	49	49	NUM
ap-7659	237	17	]	]	PUNCT
ap-7659	237	18	,	,	PUNCT
ap-7659	237	19	as	as	SCONJ
ap-7659	237	20	the	the	DET
ap-7659	237	21	potential	potential	NOUN
ap-7659	237	22	seen	see	VERB
ap-7659	237	23	by	by	ADP
ap-7659	237	24	an	an	DET
ap-7659	237	25	incident	incident	NOUN
ap-7659	237	26	nucleon	nucleon	NOUN
ap-7659	237	27	on	on	ADP
ap-7659	237	28	a	a	DET
ap-7659	237	29	nucleus	nucleus	NOUN
ap-7659	237	30	is	be	AUX
ap-7659	237	31	modeled	model	VERB
ap-7659	237	32	by	by	ADP
ap-7659	237	33	a	a	DET
ap-7659	237	34	complex	complex	ADJ
ap-7659	237	35	effective	effective	ADJ
ap-7659	237	36	potential	potential	ADJ
ap-7659	237	37	accounting	accounting	NOUN
ap-7659	237	38	for	for	ADP
ap-7659	237	39	the	the	DET
ap-7659	237	40	loss	loss	NOUN
ap-7659	237	41	of	of	ADP
ap-7659	237	42	flux	flux	NOUN
ap-7659	237	43	due	due	ADP
ap-7659	237	44	to	to	ADP
ap-7659	237	45	the	the	DET
ap-7659	237	46	interaction	interaction	NOUN
ap-7659	237	47	of	of	ADP
ap-7659	237	48	an	an	DET
ap-7659	237	49	incident	incident	NOUN
ap-7659	237	50	particle	particle	NOUN
ap-7659	237	51	with	with	ADP
ap-7659	237	52	the	the	DET
ap-7659	237	53	nucleons	nucleon	NOUN
ap-7659	237	54	of	of	ADP
ap-7659	237	55	the	the	DET
ap-7659	237	56	nucleus	nucleus	NOUN
ap-7659	237	57	.	.	PUNCT
ap-7659	238	1	we	we	PRON
ap-7659	238	2	shall	shall	AUX
ap-7659	238	3	consider	consider	VERB
ap-7659	238	4	the	the	DET
ap-7659	238	5	solutions	solution	NOUN
ap-7659	238	6	with	with	ADP
ap-7659	238	7	eigenvalues	eigenvalue	NOUN
ap-7659	238	8	en	en	NOUN
ap-7659	238	9	=	=	PUNCT
ap-7659	238	10	−iℏ|ω|(n	−iℏ|ω|(n	NOUN
ap-7659	239	1	+	+	NOUN
ap-7659	239	2	1/2	1/2	NUM
ap-7659	239	3	)	)	PUNCT
ap-7659	239	4	,	,	PUNCT
ap-7659	239	5	which	which	PRON
ap-7659	239	6	evolve	evolve	VERB
ap-7659	239	7	in	in	ADP
ap-7659	239	8	time	time	NOUN
ap-7659	239	9	as	as	ADP
ap-7659	239	10	e−|ω|(n+1/2)t	e−|ω|(n+1/2)t	NOUN
ap-7659	239	11	.	.	PUNCT
ap-7659	240	1	they	they	PRON
ap-7659	240	2	correspond	correspond	VERB
ap-7659	240	3	to	to	ADP
ap-7659	240	4	the	the	DET
ap-7659	240	5	boundary	boundary	ADJ
ap-7659	240	6	problem	problem	NOUN
ap-7659	240	7	for	for	ADP
ap-7659	240	8	0	0	NUM
ap-7659	240	9	<	<	X
ap-7659	240	10	t	t	X
ap-7659	240	11	<	<	X
ap-7659	240	12	∞.	∞.	PROPN
ap-7659	240	13	in	in	ADP
ap-7659	240	14	this	this	DET
ap-7659	240	15	case	case	NOUN
ap-7659	240	16	γ	γ	X
ap-7659	240	17	=	=	SYM
ap-7659	240	18	−π/4	−π/4	PROPN
ap-7659	240	19	and	and	CCONJ
ap-7659	240	20	θ	θ	PROPN
ap-7659	240	21	∈	∈	PROPN
ap-7659	240	22	i3	i3	NOUN
ap-7659	240	23	.	.	PUNCT
ap-7659	241	1	for	for	ADP
ap-7659	241	2	simplicity	simplicity	NOUN
ap-7659	241	3	,	,	PUNCT
ap-7659	241	4	let	let	VERB
ap-7659	241	5	us	we	PRON
ap-7659	241	6	assume	assume	VERB
ap-7659	241	7	that	that	SCONJ
ap-7659	241	8	the	the	DET
ap-7659	241	9	initial	initial	ADJ
ap-7659	241	10	state	state	NOUN
ap-7659	241	11	is	be	AUX
ap-7659	241	12	a	a	DET
ap-7659	241	13	coherent	coherent	ADJ
ap-7659	241	14	state	state	NOUN
ap-7659	241	15	of	of	ADP
ap-7659	241	16	the	the	DET
ap-7659	241	17	form	form	NOUN
ap-7659	241	18	ϕi(z	ϕi(z	NOUN
ap-7659	241	19	,	,	PUNCT
ap-7659	241	20	θ	θ	NOUN
ap-7659	241	21	,	,	PUNCT
ap-7659	241	22	x	x	NOUN
ap-7659	241	23	)	)	PUNCT
ap-7659	241	24	=	=	SYM
ap-7659	241	25	e−|z|2/2	e−|z|2/2	VERB
ap-7659	241	26	∞∑	∞∑	NUM
ap-7659	241	27	k=0	k=0	PUNCT
ap-7659	241	28	zk	zk	PROPN
ap-7659	241	29	√	√	PROPN
ap-7659	241	30	k	k	PROPN
ap-7659	241	31	!	!	PROPN
ap-7659	241	32	ϕk(θ	ϕk(θ	PROPN
ap-7659	241	33	,	,	PUNCT
ap-7659	241	34	x	x	NOUN
ap-7659	241	35	)	)	PUNCT
ap-7659	241	36	,	,	PUNCT
ap-7659	241	37	(	(	PUNCT
ap-7659	241	38	44	44	NUM
ap-7659	241	39	)	)	PUNCT
ap-7659	241	40	where	where	SCONJ
ap-7659	241	41	ϕ̃k(θ	ϕ̃k(θ	PROPN
ap-7659	241	42	,	,	PUNCT
ap-7659	241	43	x	x	X
ap-7659	241	44	)	)	PUNCT
ap-7659	241	45	is	be	AUX
ap-7659	241	46	the	the	DET
ap-7659	241	47	k	k	NOUN
ap-7659	241	48	-	-	NOUN
ap-7659	241	49	eigenfunction	eigenfunction	NOUN
ap-7659	241	50	of	of	ADP
ap-7659	241	51	h(θ	h(θ	PROPN
ap-7659	241	52	)	)	PUNCT
ap-7659	241	53	.	.	PUNCT
ap-7659	242	1	the	the	DET
ap-7659	242	2	survival	survival	NOUN
ap-7659	242	3	probability	probability	NOUN
ap-7659	242	4	of	of	ADP
ap-7659	242	5	the	the	DET
ap-7659	242	6	state	state	NOUN
ap-7659	242	7	can	can	AUX
ap-7659	242	8	be	be	AUX
ap-7659	242	9	computed	compute	VERB
ap-7659	242	10	as	as	ADP
ap-7659	242	11	p(t	p(t	NOUN
ap-7659	242	12	)	)	PUNCT
ap-7659	243	1	=	=	SYM
ap-7659	243	2	∣∣∣∣∫	∣∣∣∣∫	PRON
ap-7659	243	3	∞	∞	NUM
ap-7659	244	1	−∞	−∞	X
ap-7659	244	2	(	(	PUNCT
ap-7659	244	3	ψi(z	ψi(z	X
ap-7659	244	4	,	,	PUNCT
ap-7659	244	5	θ	θ	NOUN
ap-7659	244	6	,	,	PUNCT
ap-7659	244	7	x))∗e−ih(θ)t/ℏϕi(z	x))∗e−ih(θ)t/ℏϕi(z	PROPN
ap-7659	244	8	,	,	PUNCT
ap-7659	244	9	θ	θ	PROPN
ap-7659	244	10	,	,	PUNCT
ap-7659	244	11	x)dx	x)dx	PROPN
ap-7659	244	12	∣∣∣∣2	∣∣∣∣2	NOUN
ap-7659	244	13	=	=	SYM
ap-7659	244	14	∣∣∣∣∣e−|z|2−|ω|t/2	∣∣∣∣∣e−|z|2−|ω|t/2	NOUN
ap-7659	245	1	∞∑	∞∑	NUM
ap-7659	245	2	k=0	k=0	PROPN
ap-7659	245	3	(	(	PUNCT
ap-7659	245	4	|z|2e−|ω|t)k	|z|2e−|ω|t)k	ADJ
ap-7659	245	5	k	k	X
ap-7659	245	6	!	!	PUNCT
ap-7659	246	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ap-7659	246	2	2	2	X
ap-7659	246	3	=	=	SYM
ap-7659	246	4	e−|ω|t+2|z|2(e−|ω|t−1	e−|ω|t+2|z|2(e−|ω|t−1	PROPN
ap-7659	246	5	)	)	PUNCT
ap-7659	246	6	.	.	PUNCT
ap-7659	247	1	(	(	PUNCT
ap-7659	247	2	45	45	NUM
ap-7659	247	3	)	)	PUNCT
ap-7659	247	4	notice	notice	VERB
ap-7659	247	5	that	that	SCONJ
ap-7659	247	6	,	,	PUNCT
ap-7659	247	7	in	in	ADP
ap-7659	247	8	this	this	DET
ap-7659	247	9	particular	particular	ADJ
ap-7659	247	10	case	case	NOUN
ap-7659	247	11	,	,	PUNCT
ap-7659	247	12	p(t	p(t	NOUN
ap-7659	247	13	)	)	PUNCT
ap-7659	247	14	is	be	AUX
ap-7659	247	15	independent	independent	ADJ
ap-7659	247	16	of	of	ADP
ap-7659	247	17	the	the	DET
ap-7659	247	18	parameter	parameter	PROPN
ap-7659	247	19	θ	θ	PROPN
ap-7659	247	20	.	.	PROPN
ap-7659	247	21	4	4	NUM
ap-7659	247	22	.	.	PUNCT
ap-7659	247	23	conclusions	conclusion	NOUN
ap-7659	247	24	in	in	ADP
ap-7659	247	25	this	this	DET
ap-7659	247	26	work	work	NOUN
ap-7659	247	27	we	we	PRON
ap-7659	247	28	analyse	analyse	VERB
ap-7659	247	29	the	the	DET
ap-7659	247	30	advantages	advantage	NOUN
ap-7659	247	31	of	of	ADP
ap-7659	247	32	the	the	DET
ap-7659	247	33	csm	csm	NOUN
ap-7659	247	34	for	for	ADP
ap-7659	247	35	describing	describe	VERB
ap-7659	247	36	the	the	DET
ap-7659	247	37	dynamics	dynamic	NOUN
ap-7659	247	38	of	of	ADP
ap-7659	247	39	a	a	DET
ap-7659	247	40	non	non	ADJ
ap-7659	247	41	-	-	ADJ
ap-7659	247	42	hermitian	hermitian	ADJ
ap-7659	247	43	system	system	NOUN
ap-7659	247	44	when	when	SCONJ
ap-7659	247	45	the	the	DET
ap-7659	247	46	eigenfunctions	eigenfunction	NOUN
ap-7659	247	47	of	of	ADP
ap-7659	247	48	the	the	DET
ap-7659	247	49	problem	problem	NOUN
ap-7659	247	50	do	do	AUX
ap-7659	247	51	not	not	PART
ap-7659	247	52	belong	belong	VERB
ap-7659	247	53	to	to	ADP
ap-7659	247	54	l2(r	l2(r	NOUN
ap-7659	247	55	)	)	PUNCT
ap-7659	247	56	.	.	PUNCT
ap-7659	248	1	we	we	PRON
ap-7659	248	2	have	have	AUX
ap-7659	248	3	shown	show	VERB
ap-7659	248	4	that	that	SCONJ
ap-7659	248	5	we	we	PRON
ap-7659	248	6	can	can	AUX
ap-7659	248	7	cast	cast	VERB
ap-7659	248	8	the	the	DET
ap-7659	248	9	original	original	ADJ
ap-7659	248	10	problem	problem	NOUN
ap-7659	248	11	into	into	ADP
ap-7659	248	12	a	a	DET
ap-7659	248	13	complex	complex	ADJ
ap-7659	248	14	potential	potential	NOUN
ap-7659	248	15	,	,	PUNCT
ap-7659	248	16	which	which	PRON
ap-7659	248	17	includes	include	VERB
ap-7659	248	18	absorption	absorption	NOUN
ap-7659	248	19	and	and	CCONJ
ap-7659	248	20	dissipation	dissipation	NOUN
ap-7659	248	21	effects	effect	NOUN
ap-7659	248	22	according	accord	VERB
ap-7659	248	23	to	to	ADP
ap-7659	248	24	the	the	DET
ap-7659	248	25	sign	sign	NOUN
ap-7659	248	26	of	of	ADP
ap-7659	248	27	its	its	PRON
ap-7659	248	28	imaginary	imaginary	ADJ
ap-7659	248	29	component	component	NOUN
ap-7659	248	30	.	.	PUNCT
ap-7659	249	1	we	we	PRON
ap-7659	249	2	have	have	AUX
ap-7659	249	3	shown	show	VERB
ap-7659	249	4	that	that	SCONJ
ap-7659	249	5	for	for	ADP
ap-7659	249	6	a	a	DET
ap-7659	249	7	range	range	NOUN
ap-7659	249	8	of	of	ADP
ap-7659	249	9	values	value	NOUN
ap-7659	249	10	of	of	ADP
ap-7659	249	11	θ	θ	PROPN
ap-7659	249	12	in	in	ADP
ap-7659	249	13	the	the	DET
ap-7659	249	14	different	different	ADJ
ap-7659	249	15	regions	region	NOUN
ap-7659	249	16	of	of	ADP
ap-7659	249	17	the	the	DET
ap-7659	249	18	model	model	NOUN
ap-7659	249	19	,	,	PUNCT
ap-7659	249	20	the	the	DET
ap-7659	249	21	resulting	result	VERB
ap-7659	249	22	eigenfunctions	eigenfunction	NOUN
ap-7659	249	23	are	be	AUX
ap-7659	249	24	square	square	ADJ
ap-7659	249	25	-	-	PUNCT
ap-7659	249	26	integrable	integrable	ADJ
ap-7659	249	27	.	.	PUNCT
ap-7659	250	1	this	this	DET
ap-7659	250	2	feature	feature	NOUN
ap-7659	250	3	facilitates	facilitate	VERB
ap-7659	250	4	the	the	DET
ap-7659	250	5	study	study	NOUN
ap-7659	250	6	of	of	ADP
ap-7659	250	7	the	the	DET
ap-7659	250	8	dynamics	dynamic	NOUN
ap-7659	250	9	of	of	ADP
ap-7659	250	10	the	the	DET
ap-7659	250	11	system	system	NOUN
ap-7659	250	12	from	from	ADP
ap-7659	250	13	the	the	DET
ap-7659	250	14	computational	computational	ADJ
ap-7659	250	15	point	point	NOUN
ap-7659	250	16	of	of	ADP
ap-7659	250	17	view	view	NOUN
ap-7659	250	18	.	.	PUNCT
ap-7659	251	1	the	the	DET
ap-7659	251	2	price	price	NOUN
ap-7659	251	3	we	we	PRON
ap-7659	251	4	have	have	VERB
ap-7659	251	5	to	to	PART
ap-7659	251	6	pay	pay	VERB
ap-7659	251	7	is	be	AUX
ap-7659	251	8	the	the	DET
ap-7659	251	9	lack	lack	NOUN
ap-7659	251	10	of	of	ADP
ap-7659	251	11	pt	pt	NOUN
ap-7659	251	12	-	-	PUNCT
ap-7659	251	13	symmetry	symmetry	NOUN
ap-7659	251	14	invariance	invariance	NOUN
ap-7659	251	15	of	of	ADP
ap-7659	251	16	the	the	DET
ap-7659	251	17	transformed	transform	VERB
ap-7659	251	18	hamiltonian	hamiltonian	NOUN
ap-7659	251	19	.	.	PUNCT
ap-7659	252	1	work	work	NOUN
ap-7659	252	2	is	be	AUX
ap-7659	252	3	in	in	ADP
ap-7659	252	4	progress	progress	NOUN
ap-7659	252	5	concerning	concern	VERB
ap-7659	252	6	the	the	DET
ap-7659	252	7	application	application	NOUN
ap-7659	252	8	of	of	ADP
ap-7659	252	9	the	the	DET
ap-7659	252	10	csm	csm	NOUN
ap-7659	252	11	to	to	ADP
ap-7659	252	12	a	a	DET
ap-7659	252	13	more	more	ADV
ap-7659	252	14	involved	involved	ADJ
ap-7659	252	15	problem	problem	NOUN
ap-7659	252	16	as	as	SCONJ
ap-7659	252	17	the	the	DET
ap-7659	252	18	one	one	NOUN
ap-7659	252	19	presented	present	VERB
ap-7659	252	20	in	in	ADP
ap-7659	252	21	[	[	X
ap-7659	252	22	50	50	NUM
ap-7659	252	23	]	]	PUNCT
ap-7659	252	24	.	.	PUNCT
ap-7659	253	1	acknowledgements	acknowledgement	NOUN
ap-7659	253	2	this	this	DET
ap-7659	253	3	work	work	NOUN
ap-7659	253	4	was	be	AUX
ap-7659	253	5	partially	partially	ADV
ap-7659	253	6	supported	support	VERB
ap-7659	253	7	by	by	ADP
ap-7659	253	8	the	the	DET
ap-7659	253	9	national	national	PROPN
ap-7659	253	10	research	research	PROPN
ap-7659	253	11	council	council	PROPN
ap-7659	253	12	of	of	ADP
ap-7659	253	13	argentine	argentine	PROPN
ap-7659	253	14	(	(	PUNCT
ap-7659	253	15	conicet	conicet	PROPN
ap-7659	253	16	)	)	PUNCT
ap-7659	253	17	(	(	PUNCT
ap-7659	253	18	pip	pip	NOUN
ap-7659	253	19	0616	0616	NUM
ap-7659	253	20	)	)	PUNCT
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ap-7659	253	22	by	by	ADP
ap-7659	253	23	the	the	DET
ap-7659	253	24	agencia	agencia	PROPN
ap-7659	253	25	nacional	nacional	PROPN
ap-7659	253	26	de	de	PROPN
ap-7659	253	27	promoción	promoción	PROPN
ap-7659	253	28	científica	científica	PROPN
ap-7659	253	29	(	(	PUNCT
ap-7659	253	30	anpcyt	anpcyt	PROPN
ap-7659	253	31	)	)	PUNCT
ap-7659	253	32	of	of	ADP
ap-7659	253	33	argentina	argentina	PROPN
ap-7659	253	34	.	.	PUNCT
ap-7659	254	1	references	reference	NOUN
ap-7659	254	2	[	[	X
ap-7659	254	3	1	1	NUM
ap-7659	254	4	]	]	PUNCT
ap-7659	254	5	m.	m.	NOUN
ap-7659	254	6	s.	s.	PROPN
ap-7659	254	7	swanson	swanson	PROPN
ap-7659	254	8	.	.	PUNCT
ap-7659	255	1	transition	transition	NOUN
ap-7659	255	2	elements	element	NOUN
ap-7659	255	3	for	for	ADP
ap-7659	255	4	a	a	DET
ap-7659	255	5	non	non	ADJ
ap-7659	255	6	-	-	ADJ
ap-7659	255	7	hermitian	hermitian	ADJ
ap-7659	255	8	quadratic	quadratic	ADJ
ap-7659	255	9	hamiltonian	hamiltonian	NOUN
ap-7659	255	10	.	.	PUNCT
ap-7659	256	1	journal	journal	NOUN
ap-7659	256	2	of	of	ADP
ap-7659	256	3	mathematical	mathematical	ADJ
ap-7659	256	4	physics	physics	NOUN
ap-7659	256	5	45(2):585–601	45(2):585–601	PROPN
ap-7659	256	6	,	,	PUNCT
ap-7659	256	7	2004	2004	NUM
ap-7659	256	8	.	.	PUNCT
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ap-7659	257	2	.	.	PUNCT
ap-7659	258	1	[	[	X
ap-7659	258	2	2	2	NUM
ap-7659	258	3	]	]	PUNCT
ap-7659	258	4	c.	c.	PROPN
ap-7659	258	5	m.	m.	PROPN
ap-7659	258	6	bender	bender	PROPN
ap-7659	258	7	,	,	PUNCT
ap-7659	258	8	s.	s.	PROPN
ap-7659	258	9	boettcher	boettcher	PROPN
ap-7659	258	10	.	.	PUNCT
ap-7659	259	1	real	real	ADJ
ap-7659	259	2	spectra	spectra	NOUN
ap-7659	259	3	in	in	ADP
ap-7659	259	4	non	non	ADJ
ap-7659	259	5	-	-	ADJ
ap-7659	259	6	hermitian	hermitian	ADJ
ap-7659	259	7	hamiltonians	hamiltonian	NOUN
ap-7659	259	8	having	have	VERB
ap-7659	259	9	pt	pt	PRON
ap-7659	259	10	symmetry	symmetry	NOUN
ap-7659	259	11	.	.	PUNCT
ap-7659	260	1	physical	physical	PROPN
ap-7659	260	2	review	review	PROPN
ap-7659	260	3	letters	letter	NOUN
ap-7659	260	4	80(24):5243–5246	80(24):5243–5246	NUM
ap-7659	260	5	,	,	PUNCT
ap-7659	260	6	1998	1998	NUM
ap-7659	260	7	.	.	PUNCT
ap-7659	261	1	https://doi.org/10.1103/physrevlett.80.5243	https://doi.org/10.1103/physrevlett.80.5243	NOUN
ap-7659	261	2	.	.	PUNCT
ap-7659	262	1	[	[	X
ap-7659	262	2	3	3	X
ap-7659	262	3	]	]	X
ap-7659	262	4	c.	c.	PROPN
ap-7659	262	5	m.	m.	PROPN
ap-7659	262	6	bender	bender	PROPN
ap-7659	262	7	,	,	PUNCT
ap-7659	262	8	m.	m.	NOUN
ap-7659	262	9	v.	v.	ADP
ap-7659	262	10	berry	berry	PROPN
ap-7659	262	11	,	,	PUNCT
ap-7659	262	12	a.	a.	PROPN
ap-7659	262	13	mandilara	mandilara	PROPN
ap-7659	262	14	.	.	PUNCT
ap-7659	263	1	generalized	generalize	VERB
ap-7659	263	2	pt	pt	NOUN
ap-7659	263	3	symmetry	symmetry	NOUN
ap-7659	263	4	and	and	CCONJ
ap-7659	263	5	real	real	ADJ
ap-7659	263	6	spectra	spectra	PROPN
ap-7659	263	7	.	.	PROPN
ap-7659	263	8	journal	journal	PROPN
ap-7659	263	9	of	of	ADP
ap-7659	263	10	physics	physics	PROPN
ap-7659	263	11	a	a	PRON
ap-7659	263	12	:	:	PUNCT
ap-7659	263	13	mathematical	mathematical	ADJ
ap-7659	263	14	and	and	CCONJ
ap-7659	263	15	general	general	ADJ
ap-7659	263	16	35(31):l467	35(31):l467	NUM
ap-7659	263	17	–	–	PUNCT
ap-7659	263	18	l471	l471	PROPN
ap-7659	263	19	,	,	PUNCT
ap-7659	263	20	2002	2002	NUM
ap-7659	263	21	.	.	PUNCT
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ap-7659	264	2	.	.	PUNCT
ap-7659	265	1	[	[	X
ap-7659	265	2	4	4	NUM
ap-7659	265	3	]	]	X
ap-7659	265	4	c.	c.	PROPN
ap-7659	265	5	bender	bender	PROPN
ap-7659	265	6	,	,	PUNCT
ap-7659	265	7	b.	b.	PROPN
ap-7659	265	8	berntson	berntson	PROPN
ap-7659	265	9	,	,	PUNCT
ap-7659	265	10	d.	d.	PROPN
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ap-7659	265	12	,	,	PUNCT
ap-7659	265	13	e.	e.	PROPN
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ap-7659	265	15	.	.	PUNCT
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ap-7659	266	2	of	of	ADP
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ap-7659	266	4	phase	phase	NOUN
ap-7659	266	5	transition	transition	NOUN
ap-7659	266	6	in	in	ADP
ap-7659	266	7	a	a	DET
ap-7659	266	8	simple	simple	ADJ
ap-7659	266	9	mechanical	mechanical	ADJ
ap-7659	266	10	system	system	NOUN
ap-7659	266	11	.	.	PUNCT
ap-7659	267	1	american	american	PROPN
ap-7659	267	2	journal	journal	PROPN
ap-7659	267	3	of	of	ADP
ap-7659	267	4	physics	physics	PROPN
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ap-7659	267	6	,	,	PUNCT
ap-7659	267	7	2013	2013	NUM
ap-7659	267	8	.	.	PUNCT
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ap-7659	268	2	.	.	PUNCT
ap-7659	269	1	[	[	X
ap-7659	269	2	5	5	NUM
ap-7659	269	3	]	]	PUNCT
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ap-7659	269	5	m.	m.	PROPN
ap-7659	269	6	bender	bender	PROPN
ap-7659	269	7	,	,	PUNCT
ap-7659	269	8	m.	m.	NOUN
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ap-7659	269	10	,	,	PUNCT
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ap-7659	269	13	k.	k.	PROPN
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ap-7659	269	18	.	.	PROPN
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ap-7659	269	26	.	.	PUNCT
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ap-7659	270	2	review	review	NOUN
ap-7659	270	3	a	a	DET
ap-7659	270	4	88(6):062111	88(6):062111	NUM
ap-7659	270	5	,	,	PUNCT
ap-7659	270	6	2013	2013	NUM
ap-7659	270	7	.	.	PUNCT
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ap-7659	271	2	.	.	PUNCT
ap-7659	272	1	[	[	X
ap-7659	272	2	6	6	NUM
ap-7659	272	3	]	]	PUNCT
ap-7659	272	4	a.	a.	NOUN
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ap-7659	272	6	,	,	PUNCT
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ap-7659	272	8	p.	p.	PROPN
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ap-7659	272	10	,	,	PUNCT
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ap-7659	272	12	m.	m.	PROPN
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ap-7659	272	14	.	.	PUNCT
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ap-7659	273	2	oscillator	oscillator	NOUN
ap-7659	273	3	systems	system	NOUN
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ap-7659	273	6	pt	pt	NOUN
ap-7659	273	7	symmetry	symmetry	NOUN
ap-7659	273	8	.	.	PUNCT
ap-7659	274	1	physical	physical	ADJ
ap-7659	274	2	review	review	NOUN
ap-7659	274	3	a	a	DET
ap-7659	274	4	91(6):062101	91(6):062101	NUM
ap-7659	274	5	,	,	PUNCT
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ap-7659	274	7	.	.	PUNCT
ap-7659	275	1	https://doi.org/10.1103/physreva.91.062101	https://doi.org/10.1103/physreva.91.062101	NOUN
ap-7659	275	2	.	.	PUNCT
ap-7659	276	1	[	[	X
ap-7659	276	2	7	7	X
ap-7659	276	3	]	]	PUNCT
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ap-7659	276	6	,	,	PUNCT
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ap-7659	276	8	m.	m.	PROPN
ap-7659	276	9	bender	bender	PROPN
ap-7659	276	10	.	.	PUNCT
ap-7659	277	1	pt	pt	PROPN
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ap-7659	277	3	potentials	potential	NOUN
ap-7659	277	4	having	have	VERB
ap-7659	277	5	continuous	continuous	ADJ
ap-7659	277	6	spectra	spectra	PROPN
ap-7659	277	7	.	.	PROPN
ap-7659	277	8	journal	journal	PROPN
ap-7659	277	9	of	of	ADP
ap-7659	277	10	physics	physics	PROPN
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ap-7659	277	12	:	:	PUNCT
ap-7659	277	13	mathematical	mathematical	ADJ
ap-7659	277	14	and	and	CCONJ
ap-7659	277	15	theoretical	theoretical	ADJ
ap-7659	277	16	53(37):375302	53(37):375302	NUM
ap-7659	277	17	,	,	PUNCT
ap-7659	277	18	2020	2020	NUM
ap-7659	277	19	.	.	PUNCT
ap-7659	278	1	https://doi.org/10.1088/1751-8121/aba468	https://doi.org/10.1088/1751-8121/aba468	PROPN
ap-7659	278	2	.	.	PUNCT
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ap-7659	279	2	8	8	NUM
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ap-7659	279	4	c.	c.	PROPN
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ap-7659	279	7	,	,	PUNCT
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ap-7659	279	9	f.	f.	PROPN
ap-7659	279	10	jones	jones	PROPN
ap-7659	279	11	.	.	PUNCT
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ap-7659	280	2	of	of	ADP
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ap-7659	280	5	non	non	ADJ
ap-7659	280	6	-	-	ADJ
ap-7659	280	7	hermitian	hermitian	ADJ
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ap-7659	280	9	.	.	PUNCT
ap-7659	281	1	journal	journal	PROPN
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ap-7659	281	5	:	:	PUNCT
ap-7659	281	6	mathematical	mathematical	ADJ
ap-7659	281	7	and	and	CCONJ
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ap-7659	281	10	,	,	PUNCT
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ap-7659	281	12	.	.	PUNCT
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ap-7659	282	2	.	.	PUNCT
ap-7659	283	1	[	[	X
ap-7659	283	2	9	9	NUM
ap-7659	283	3	]	]	PUNCT
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ap-7659	283	5	sinha	sinha	PROPN
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ap-7659	283	9	.	.	PUNCT
ap-7659	284	1	isospectral	isospectral	ADJ
ap-7659	284	2	partners	partner	NOUN
ap-7659	284	3	of	of	ADP
ap-7659	284	4	a	a	DET
ap-7659	284	5	complex	complex	ADJ
ap-7659	284	6	pt	pt	ADJ
ap-7659	284	7	-	-	PUNCT
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ap-7659	284	10	.	.	PUNCT
ap-7659	285	1	physics	physics	NOUN
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ap-7659	285	3	a	a	DET
ap-7659	285	4	301(3	301(3	NUM
ap-7659	285	5	-	-	SYM
ap-7659	285	6	4):163–172	4):163–172	NUM
ap-7659	285	7	,	,	PUNCT
ap-7659	285	8	2002	2002	NUM
ap-7659	285	9	.	.	PUNCT
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ap-7659	286	2	.	.	PUNCT
ap-7659	287	1	[	[	X
ap-7659	287	2	10	10	NUM
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ap-7659	287	4	a.	a.	NOUN
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ap-7659	287	6	,	,	PUNCT
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ap-7659	287	8	roy	roy	PROPN
ap-7659	287	9	.	.	PROPN
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ap-7659	288	2	swanson	swanson	PROPN
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ap-7659	288	6	solutions	solution	NOUN
ap-7659	288	7	.	.	PUNCT
ap-7659	289	1	journal	journal	PROPN
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ap-7659	289	10	,	,	PUNCT
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ap-7659	289	12	.	.	PUNCT
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ap-7659	291	2	11	11	NUM
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ap-7659	291	5	sinha	sinha	PROPN
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ap-7659	291	9	.	.	PROPN
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ap-7659	291	12	partners	partner	NOUN
ap-7659	291	13	for	for	ADP
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ap-7659	291	15	generalized	generalized	ADJ
ap-7659	291	16	swanson	swanson	PROPN
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ap-7659	291	18	.	.	PUNCT
ap-7659	292	1	journal	journal	PROPN
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ap-7659	292	4	a	a	PRON
ap-7659	292	5	:	:	PUNCT
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ap-7659	292	8	theoretical	theoretical	ADJ
ap-7659	292	9	41(33):335306	41(33):335306	NUM
ap-7659	292	10	,	,	PUNCT
ap-7659	292	11	2008	2008	NUM
ap-7659	292	12	.	.	PUNCT
ap-7659	293	1	https://doi.org/10.1088/1751-8113/41/33/335306	https://doi.org/10.1088/1751-8113/41/33/335306	PROPN
ap-7659	293	2	.	.	PUNCT
ap-7659	294	1	[	[	X
ap-7659	294	2	12	12	NUM
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ap-7659	294	4	h.	h.	PROPN
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ap-7659	294	7	.	.	PUNCT
ap-7659	295	1	on	on	ADP
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ap-7659	295	3	-	-	ADJ
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ap-7659	295	10	.	.	PUNCT
ap-7659	296	1	journal	journal	PROPN
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ap-7659	296	5	:	:	PUNCT
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ap-7659	296	7	and	and	CCONJ
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ap-7659	296	9	38(8):1741–1746	38(8):1741–1746	NUM
ap-7659	296	10	,	,	PUNCT
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ap-7659	296	12	.	.	PUNCT
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ap-7659	297	2	.	.	PUNCT
ap-7659	298	1	162	162	NUM
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ap-7659	298	5	https://doi.org/10.1119/1.4789549	https://doi.org/10.1119/1.4789549	PROPN
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ap-7659	298	7	https://doi.org/10.1103/physreva.91.062101	https://doi.org/10.1103/physreva.91.062101	PROPN
ap-7659	298	8	https://doi.org/10.1088/1751-8121/aba468	https://doi.org/10.1088/1751-8121/aba468	PROPN
ap-7659	298	9	https://doi.org/10.1088/1751-8113/41/24/244006	https://doi.org/10.1088/1751-8113/41/24/244006	PROPN
ap-7659	298	10	https://doi.org/10.1016/s0375-9601(02)00736-3	https://doi.org/10.1016/s0375-9601(02)00736-3	PROPN
ap-7659	298	11	https://doi.org/10.1088/1751-8113/40/34/015	https://doi.org/10.1088/1751-8113/40/34/015	PROPN
ap-7659	298	12	https://doi.org/10.1088/1751-8113/41/33/335306	https://doi.org/10.1088/1751-8113/41/33/335306	PROPN
ap-7659	298	13	https://doi.org/10.1088/0305-4470/38/8/010	https://doi.org/10.1088/0305-4470/38/8/010	PROPN
ap-7659	298	14	vol	vol	NOUN
ap-7659	298	15	.	.	PUNCT
ap-7659	299	1	62	62	NUM
ap-7659	299	2	no	no	INTJ
ap-7659	299	3	.	.	PUNCT
ap-7659	300	1	1/2022	1/2022	NUM
ap-7659	300	2	swanson	swanson	PROPN
ap-7659	300	3	hamiltonian	hamiltonian	NOUN
ap-7659	300	4	revisited	revisit	VERB
ap-7659	300	5	through	through	ADP
ap-7659	300	6	the	the	DET
ap-7659	300	7	csm	csm	NOUN
ap-7659	300	8	[	[	X
ap-7659	300	9	13	13	NUM
ap-7659	300	10	]	]	PUNCT
ap-7659	300	11	ö.	ö.	NOUN
ap-7659	300	12	yeşiltaş	yeşiltaş	NOUN
ap-7659	300	13	.	.	PUNCT
ap-7659	301	1	quantum	quantum	PROPN
ap-7659	301	2	isotonic	isotonic	ADJ
ap-7659	301	3	nonlinear	nonlinear	ADJ
ap-7659	301	4	oscillator	oscillator	NOUN
ap-7659	301	5	as	as	ADP
ap-7659	301	6	a	a	DET
ap-7659	301	7	hermitian	hermitian	ADJ
ap-7659	301	8	counterpart	counterpart	NOUN
ap-7659	301	9	of	of	ADP
ap-7659	301	10	swanson	swanson	PROPN
ap-7659	301	11	hamiltonian	hamiltonian	NOUN
ap-7659	301	12	and	and	CCONJ
ap-7659	301	13	pseudo	pseudo	NOUN
ap-7659	301	14	-	-	NOUN
ap-7659	301	15	supersymmetry	supersymmetry	NOUN
ap-7659	301	16	.	.	PUNCT
ap-7659	302	1	journal	journal	PROPN
ap-7659	302	2	of	of	ADP
ap-7659	302	3	physics	physics	PROPN
ap-7659	302	4	a	a	PRON
ap-7659	302	5	:	:	PUNCT
ap-7659	302	6	mathematical	mathematical	ADJ
ap-7659	302	7	and	and	CCONJ
ap-7659	302	8	theoretical	theoretical	ADJ
ap-7659	302	9	44(30):305305	44(30):305305	NUM
ap-7659	302	10	,	,	PUNCT
ap-7659	302	11	2011	2011	NUM
ap-7659	302	12	.	.	PUNCT
ap-7659	303	1	https://doi.org/10.1088/1751-8113/44/30/305305	https://doi.org/10.1088/1751-8113/44/30/305305	ADV
ap-7659	303	2	.	.	PUNCT
ap-7659	304	1	[	[	X
ap-7659	304	2	14	14	NUM
ap-7659	304	3	]	]	PUNCT
ap-7659	304	4	p.	p.	PROPN
ap-7659	304	5	e.	e.	PROPN
ap-7659	304	6	g.	g.	PROPN
ap-7659	304	7	assis	assis	PROPN
ap-7659	304	8	,	,	PUNCT
ap-7659	304	9	a.	a.	NOUN
ap-7659	304	10	fring	fring	NOUN
ap-7659	304	11	.	.	PUNCT
ap-7659	305	1	metrics	metric	NOUN
ap-7659	305	2	and	and	CCONJ
ap-7659	305	3	isospectral	isospectral	ADJ
ap-7659	305	4	partners	partner	NOUN
ap-7659	305	5	for	for	ADP
ap-7659	305	6	the	the	DET
ap-7659	305	7	most	most	ADV
ap-7659	305	8	generic	generic	ADJ
ap-7659	305	9	cubic	cubic	ADJ
ap-7659	305	10	pt	pt	NOUN
ap-7659	305	11	-symmetric	-symmetric	ADJ
ap-7659	305	12	non	non	ADJ
ap-7659	305	13	-	-	ADJ
ap-7659	305	14	hermitian	hermitian	ADJ
ap-7659	305	15	hamiltonian	hamiltonian	NOUN
ap-7659	305	16	.	.	PUNCT
ap-7659	306	1	journal	journal	PROPN
ap-7659	306	2	of	of	ADP
ap-7659	306	3	physics	physics	PROPN
ap-7659	306	4	a	a	PRON
ap-7659	306	5	:	:	PUNCT
ap-7659	306	6	mathematical	mathematical	ADJ
ap-7659	306	7	and	and	CCONJ
ap-7659	306	8	theoretical	theoretical	ADJ
ap-7659	306	9	41(24):244001	41(24):244001	NUM
ap-7659	306	10	,	,	PUNCT
ap-7659	306	11	2008	2008	NUM
ap-7659	306	12	.	.	PUNCT
ap-7659	307	1	https://doi.org/10.1088/1751-8113/41/24/244001	https://doi.org/10.1088/1751-8113/41/24/244001	NOUN
ap-7659	307	2	.	.	PUNCT
ap-7659	308	1	[	[	X
ap-7659	308	2	15	15	NUM
ap-7659	308	3	]	]	X
ap-7659	308	4	b.	b.	PROPN
ap-7659	308	5	midya	midya	PROPN
ap-7659	308	6	,	,	PUNCT
ap-7659	308	7	p.	p.	NOUN
ap-7659	308	8	p.	p.	PROPN
ap-7659	309	1	dube	dube	PROPN
ap-7659	309	2	,	,	PUNCT
ap-7659	309	3	r.	r.	PROPN
ap-7659	309	4	roychoudhury	roychoudhury	PROPN
ap-7659	309	5	.	.	PUNCT
ap-7659	310	1	nonisospectrality	nonisospectrality	NOUN
ap-7659	310	2	of	of	ADP
ap-7659	310	3	the	the	DET
ap-7659	310	4	generalized	generalize	VERB
ap-7659	310	5	swanson	swanson	PROPN
ap-7659	310	6	hamiltonian	hamiltonian	NOUN
ap-7659	310	7	and	and	CCONJ
ap-7659	310	8	harmonic	harmonic	ADJ
ap-7659	310	9	oscillator	oscillator	NOUN
ap-7659	310	10	.	.	PUNCT
ap-7659	311	1	journal	journal	PROPN
ap-7659	311	2	of	of	ADP
ap-7659	311	3	physics	physics	PROPN
ap-7659	311	4	a	a	PRON
ap-7659	311	5	:	:	PUNCT
ap-7659	311	6	mathematical	mathematical	ADJ
ap-7659	311	7	and	and	CCONJ
ap-7659	311	8	theoretical	theoretical	ADJ
ap-7659	311	9	44(6):062001	44(6):062001	PROPN
ap-7659	311	10	,	,	PUNCT
ap-7659	311	11	2011	2011	NUM
ap-7659	311	12	.	.	PUNCT
ap-7659	312	1	https://doi.org/10.1088/1751-8113/44/6/062001	https://doi.org/10.1088/1751-8113/44/6/062001	NOUN
ap-7659	312	2	.	.	PUNCT
ap-7659	313	1	[	[	X
ap-7659	313	2	16	16	NUM
ap-7659	313	3	]	]	PUNCT
ap-7659	313	4	a.	a.	NOUN
ap-7659	313	5	mostafazadeh	mostafazadeh	PROPN
ap-7659	313	6	.	.	PUNCT
ap-7659	314	1	metric	metric	ADJ
ap-7659	314	2	operators	operator	NOUN
ap-7659	314	3	for	for	ADP
ap-7659	314	4	quasi	quasi	ADJ
ap-7659	314	5	-	-	ADJ
ap-7659	314	6	hermitian	hermitian	ADJ
ap-7659	314	7	hamiltonians	hamiltonian	NOUN
ap-7659	314	8	and	and	CCONJ
ap-7659	314	9	symmetries	symmetry	NOUN
ap-7659	314	10	of	of	ADP
ap-7659	314	11	equivalent	equivalent	ADJ
ap-7659	314	12	hermitian	hermitian	ADJ
ap-7659	314	13	hamiltonians	hamiltonian	NOUN
ap-7659	314	14	.	.	PUNCT
ap-7659	315	1	journal	journal	PROPN
ap-7659	315	2	of	of	ADP
ap-7659	315	3	physics	physics	PROPN
ap-7659	315	4	a	a	PRON
ap-7659	315	5	:	:	PUNCT
ap-7659	315	6	mathematical	mathematical	ADJ
ap-7659	315	7	and	and	CCONJ
ap-7659	315	8	theoretical	theoretical	ADJ
ap-7659	315	9	41(24):244017	41(24):244017	NUM
ap-7659	315	10	,	,	PUNCT
ap-7659	315	11	2008	2008	NUM
ap-7659	315	12	.	.	PUNCT
ap-7659	316	1	https://doi.org/10.1088/1751-8113/41/24/244017	https://doi.org/10.1088/1751-8113/41/24/244017	NOUN
ap-7659	316	2	.	.	PUNCT
ap-7659	317	1	[	[	X
ap-7659	317	2	17	17	NUM
ap-7659	317	3	]	]	PUNCT
ap-7659	317	4	a.	a.	NOUN
ap-7659	317	5	mostafazadeh	mostafazadeh	PROPN
ap-7659	317	6	.	.	PUNCT
ap-7659	318	1	pseudo	pseudo	NOUN
ap-7659	318	2	-	-	ADJ
ap-7659	318	3	hermitian	hermitian	ADJ
ap-7659	318	4	representation	representation	NOUN
ap-7659	318	5	of	of	ADP
ap-7659	318	6	quantum	quantum	ADJ
ap-7659	318	7	mechanics	mechanic	NOUN
ap-7659	318	8	.	.	PUNCT
ap-7659	319	1	international	international	ADJ
ap-7659	319	2	journal	journal	PROPN
ap-7659	319	3	of	of	ADP
ap-7659	319	4	geometric	geometric	ADJ
ap-7659	319	5	methods	method	NOUN
ap-7659	319	6	in	in	ADP
ap-7659	319	7	modern	modern	ADJ
ap-7659	319	8	physics	physic	NOUN
ap-7659	319	9	07(07):1191–1306	07(07):1191–1306	PROPN
ap-7659	319	10	,	,	PUNCT
ap-7659	319	11	2010	2010	NUM
ap-7659	319	12	.	.	PUNCT
ap-7659	320	1	https://doi.org/10.1142/s0219887810004816	https://doi.org/10.1142/s0219887810004816	NUM
ap-7659	320	2	.	.	PUNCT
ap-7659	321	1	[	[	X
ap-7659	321	2	18	18	NUM
ap-7659	321	3	]	]	PUNCT
ap-7659	321	4	m.	m.	NOUN
ap-7659	321	5	znojil	znojil	PROPN
ap-7659	321	6	.	.	PUNCT
ap-7659	322	1	complete	complete	ADJ
ap-7659	322	2	set	set	NOUN
ap-7659	322	3	of	of	ADP
ap-7659	322	4	inner	inner	ADJ
ap-7659	322	5	products	product	NOUN
ap-7659	322	6	for	for	ADP
ap-7659	322	7	a	a	DET
ap-7659	322	8	discrete	discrete	ADJ
ap-7659	322	9	pt	pt	NOUN
ap-7659	322	10	-symmetric	-symmetric	ADJ
ap-7659	322	11	square	square	ADJ
ap-7659	322	12	-	-	PUNCT
ap-7659	322	13	well	well	NOUN
ap-7659	322	14	hamiltonian	hamiltonian	NOUN
ap-7659	322	15	.	.	PUNCT
ap-7659	323	1	journal	journal	PROPN
ap-7659	323	2	of	of	ADP
ap-7659	323	3	mathematical	mathematical	ADJ
ap-7659	323	4	physics	physics	NOUN
ap-7659	323	5	50(12):122105	50(12):122105	PROPN
ap-7659	323	6	,	,	PUNCT
ap-7659	323	7	2009	2009	NUM
ap-7659	323	8	.	.	PUNCT
ap-7659	324	1	https://doi.org/10.1063/1.3272002	https://doi.org/10.1063/1.3272002	X
ap-7659	324	2	.	.	PUNCT
ap-7659	325	1	[	[	X
ap-7659	325	2	19	19	NUM
ap-7659	325	3	]	]	PUNCT
ap-7659	325	4	b.	b.	PROPN
ap-7659	325	5	bagchi	bagchi	PROPN
ap-7659	325	6	,	,	PUNCT
ap-7659	325	7	a.	a.	NOUN
ap-7659	325	8	fring	fring	NOUN
ap-7659	325	9	.	.	PUNCT
ap-7659	326	1	minimal	minimal	ADJ
ap-7659	326	2	length	length	NOUN
ap-7659	326	3	in	in	ADP
ap-7659	326	4	quantum	quantum	ADJ
ap-7659	326	5	mechanics	mechanic	NOUN
ap-7659	326	6	and	and	CCONJ
ap-7659	326	7	non	non	ADJ
ap-7659	326	8	-	-	ADJ
ap-7659	326	9	hermitian	hermitian	ADJ
ap-7659	326	10	hamiltonian	hamiltonian	ADJ
ap-7659	326	11	systems	system	NOUN
ap-7659	326	12	.	.	PUNCT
ap-7659	327	1	physics	physics	NOUN
ap-7659	327	2	letters	letter	NOUN
ap-7659	327	3	a	a	DET
ap-7659	327	4	373(47):4307–4310	373(47):4307–4310	NUM
ap-7659	327	5	,	,	PUNCT
ap-7659	327	6	2009	2009	NUM
ap-7659	327	7	.	.	PUNCT
ap-7659	328	1	https://doi.org/10.1016/j.physleta.2009.09.054	https://doi.org/10.1016/j.physleta.2009.09.054	ADJ
ap-7659	328	2	.	.	PUNCT
ap-7659	329	1	[	[	X
ap-7659	329	2	20	20	NUM
ap-7659	329	3	]	]	PUNCT
ap-7659	329	4	a.	a.	NOUN
ap-7659	329	5	sinha	sinha	PROPN
ap-7659	329	6	,	,	PUNCT
ap-7659	329	7	p.	p.	PROPN
ap-7659	329	8	roy	roy	PROPN
ap-7659	329	9	.	.	PROPN
ap-7659	329	10	generalized	generalize	VERB
ap-7659	329	11	swanson	swanson	PROPN
ap-7659	329	12	model	model	NOUN
ap-7659	329	13	and	and	CCONJ
ap-7659	329	14	its	its	PRON
ap-7659	329	15	pseudo	pseudo	NOUN
ap-7659	329	16	supersymmetric	supersymmetric	ADJ
ap-7659	329	17	partners	partner	NOUN
ap-7659	329	18	.	.	PUNCT
ap-7659	330	1	in	in	ADP
ap-7659	330	2	recent	recent	ADJ
ap-7659	330	3	developments	development	NOUN
ap-7659	330	4	in	in	ADP
ap-7659	330	5	theoretical	theoretical	ADJ
ap-7659	330	6	physics	physics	NOUN
ap-7659	330	7	,	,	PUNCT
ap-7659	330	8	pp	pp	ADJ
ap-7659	330	9	.	.	PUNCT
ap-7659	331	1	222–234	222–234	NUM
ap-7659	331	2	.	.	PUNCT
ap-7659	332	1	indian	indian	ADJ
ap-7659	332	2	statistical	statistical	PROPN
ap-7659	332	3	institute	institute	PROPN
ap-7659	332	4	,	,	PUNCT
ap-7659	332	5	india	india	PROPN
ap-7659	332	6	,	,	PUNCT
ap-7659	332	7	2009	2009	NUM
ap-7659	332	8	.	.	PUNCT
ap-7659	333	1	https://doi.org/10.1142/9789814287333_0010	https://doi.org/10.1142/9789814287333_0010	X
ap-7659	333	2	.	.	PUNCT
ap-7659	334	1	[	[	X
ap-7659	334	2	21	21	NUM
ap-7659	334	3	]	]	X
ap-7659	334	4	b.	b.	PROPN
ap-7659	334	5	bagchi	bagchi	PROPN
ap-7659	334	6	,	,	PUNCT
ap-7659	334	7	i.	i.	PROPN
ap-7659	334	8	marquette	marquette	PROPN
ap-7659	334	9	.	.	PUNCT
ap-7659	335	1	new	new	ADJ
ap-7659	335	2	1	1	NUM
ap-7659	335	3	-	-	PUNCT
ap-7659	335	4	step	step	NOUN
ap-7659	335	5	extension	extension	NOUN
ap-7659	335	6	of	of	ADP
ap-7659	335	7	the	the	DET
ap-7659	335	8	swanson	swanson	PROPN
ap-7659	335	9	oscillator	oscillator	NOUN
ap-7659	335	10	and	and	CCONJ
ap-7659	335	11	superintegrability	superintegrability	NOUN
ap-7659	335	12	of	of	ADP
ap-7659	335	13	its	its	PRON
ap-7659	335	14	two	two	NUM
ap-7659	335	15	-	-	PUNCT
ap-7659	335	16	dimensional	dimensional	ADJ
ap-7659	335	17	generalization	generalization	NOUN
ap-7659	335	18	.	.	PUNCT
ap-7659	336	1	physics	physics	NOUN
ap-7659	336	2	letters	letter	NOUN
ap-7659	336	3	a	a	DET
ap-7659	336	4	379(26	379(26	NOUN
ap-7659	336	5	-	-	NOUN
ap-7659	336	6	27):1584–1588	27):1584–1588	NUM
ap-7659	336	7	,	,	PUNCT
ap-7659	336	8	2015	2015	NUM
ap-7659	336	9	.	.	PUNCT
ap-7659	337	1	https://doi.org/10.1016/j.physleta.2015.04.009	https://doi.org/10.1016/j.physleta.2015.04.009	NUM
ap-7659	337	2	.	.	PUNCT
ap-7659	338	1	[	[	X
ap-7659	338	2	22	22	NUM
ap-7659	338	3	]	]	PUNCT
ap-7659	338	4	s.	s.	PROPN
ap-7659	338	5	dey	dey	PROPN
ap-7659	338	6	,	,	PUNCT
ap-7659	338	7	a.	a.	NOUN
ap-7659	338	8	fring	fring	PROPN
ap-7659	338	9	,	,	PUNCT
ap-7659	338	10	l.	l.	PROPN
ap-7659	338	11	gouba	gouba	PROPN
ap-7659	338	12	.	.	PUNCT
ap-7659	339	1	milne	milne	PROPN
ap-7659	339	2	quantization	quantization	NOUN
ap-7659	339	3	for	for	ADP
ap-7659	339	4	non	non	ADJ
ap-7659	339	5	-	-	ADJ
ap-7659	339	6	hermitian	hermitian	ADJ
ap-7659	339	7	systems	system	NOUN
ap-7659	339	8	.	.	PUNCT
ap-7659	340	1	journal	journal	PROPN
ap-7659	340	2	of	of	ADP
ap-7659	340	3	physics	physics	PROPN
ap-7659	340	4	a	a	PRON
ap-7659	340	5	:	:	PUNCT
ap-7659	340	6	mathematical	mathematical	ADJ
ap-7659	340	7	and	and	CCONJ
ap-7659	340	8	theoretical	theoretical	ADJ
ap-7659	340	9	48(40):40ft01	48(40):40ft01	NUM
ap-7659	340	10	,	,	PUNCT
ap-7659	340	11	2015	2015	NUM
ap-7659	340	12	.	.	PUNCT
ap-7659	341	1	https://doi.org/10.1088/1751-8113/48/40/40ft01	https://doi.org/10.1088/1751-8113/48/40/40ft01	X
ap-7659	341	2	.	.	PUNCT
ap-7659	342	1	[	[	X
ap-7659	342	2	23	23	NUM
ap-7659	342	3	]	]	PUNCT
ap-7659	342	4	j.	j.	PROPN
ap-7659	342	5	da	da	PROPN
ap-7659	342	6	providência	providência	PROPN
ap-7659	342	7	,	,	PUNCT
ap-7659	342	8	n.	n.	PROPN
ap-7659	342	9	bebiano	bebiano	PROPN
ap-7659	342	10	,	,	PUNCT
ap-7659	342	11	j.	j.	PROPN
ap-7659	342	12	p.	p.	PROPN
ap-7659	342	13	da	da	PROPN
ap-7659	342	14	providência	providência	PROPN
ap-7659	342	15	.	.	PUNCT
ap-7659	343	1	non	non	ADJ
ap-7659	343	2	-	-	ADJ
ap-7659	343	3	hermitian	hermitian	ADJ
ap-7659	343	4	hamiltonians	hamiltonian	NOUN
ap-7659	343	5	with	with	ADP
ap-7659	343	6	real	real	ADJ
ap-7659	343	7	spectrum	spectrum	NOUN
ap-7659	343	8	in	in	ADP
ap-7659	343	9	quantum	quantum	ADJ
ap-7659	343	10	mechanics	mechanic	NOUN
ap-7659	343	11	.	.	PUNCT
ap-7659	344	1	brazilian	brazilian	ADJ
ap-7659	344	2	journal	journal	PROPN
ap-7659	344	3	of	of	ADP
ap-7659	344	4	physics	physics	PROPN
ap-7659	344	5	41:78–85	41:78–85	PROPN
ap-7659	344	6	,	,	PUNCT
ap-7659	344	7	2011	2011	NUM
ap-7659	344	8	.	.	PUNCT
ap-7659	345	1	https://doi.org/10.1007/s13538-011-0010-9	https://doi.org/10.1007/s13538-011-0010-9	NUM
ap-7659	345	2	.	.	PUNCT
ap-7659	346	1	[	[	X
ap-7659	346	2	24	24	NUM
ap-7659	346	3	]	]	PUNCT
ap-7659	346	4	f.	f.	PROPN
ap-7659	346	5	bagarello	bagarello	PROPN
ap-7659	346	6	.	.	PUNCT
ap-7659	347	1	examples	example	NOUN
ap-7659	347	2	of	of	ADP
ap-7659	347	3	pseudo	pseudo	NOUN
ap-7659	347	4	-	-	NOUN
ap-7659	347	5	bosons	bosons	NOUN
ap-7659	347	6	in	in	ADP
ap-7659	347	7	quantum	quantum	ADJ
ap-7659	347	8	mechanics	mechanic	NOUN
ap-7659	347	9	.	.	PUNCT
ap-7659	348	1	physics	physics	NOUN
ap-7659	348	2	letters	letter	NOUN
ap-7659	348	3	a	a	DET
ap-7659	348	4	374(37):3823–3827	374(37):3823–3827	NUM
ap-7659	348	5	,	,	PUNCT
ap-7659	348	6	2010	2010	NUM
ap-7659	348	7	.	.	PUNCT
ap-7659	349	1	https://doi.org/10.1016/j.physleta.2010.07.044	https://doi.org/10.1016/j.physleta.2010.07.044	PROPN
ap-7659	349	2	.	.	PUNCT
ap-7659	350	1	[	[	X
ap-7659	350	2	25	25	NUM
ap-7659	350	3	]	]	PUNCT
ap-7659	350	4	f.	f.	PROPN
ap-7659	350	5	bagarello	bagarello	PROPN
ap-7659	350	6	,	,	PUNCT
ap-7659	350	7	j.	j.	PROPN
ap-7659	350	8	feinberg	feinberg	PROPN
ap-7659	350	9	.	.	PUNCT
ap-7659	350	10	bicoherent	bicoherent	ADJ
ap-7659	350	11	-	-	PUNCT
ap-7659	350	12	state	state	NOUN
ap-7659	350	13	path	path	NOUN
ap-7659	350	14	integral	integral	ADJ
ap-7659	350	15	quantization	quantization	NOUN
ap-7659	350	16	of	of	ADP
ap-7659	350	17	a	a	DET
ap-7659	350	18	non	non	ADJ
ap-7659	350	19	-	-	ADJ
ap-7659	350	20	hermitian	hermitian	ADJ
ap-7659	350	21	hamiltonian	hamiltonian	NOUN
ap-7659	350	22	.	.	PUNCT
ap-7659	351	1	annals	annal	NOUN
ap-7659	351	2	of	of	ADP
ap-7659	351	3	physics	physics	NOUN
ap-7659	351	4	422:168313	422:168313	NUM
ap-7659	351	5	,	,	PUNCT
ap-7659	351	6	2020	2020	NUM
ap-7659	351	7	.	.	PUNCT
ap-7659	352	1	https://doi.org/10.1016/j.aop.2020.168313	https://doi.org/10.1016/j.aop.2020.168313	PROPN
ap-7659	352	2	.	.	PUNCT
ap-7659	353	1	[	[	X
ap-7659	353	2	26	26	NUM
ap-7659	353	3	]	]	X
ap-7659	353	4	v.	v.	ADP
ap-7659	353	5	fernández	fernández	PROPN
ap-7659	353	6	,	,	PUNCT
ap-7659	353	7	r.	r.	PROPN
ap-7659	353	8	ramírez	ramírez	PROPN
ap-7659	353	9	,	,	PUNCT
ap-7659	353	10	m.	m.	NOUN
ap-7659	353	11	reboiro	reboiro	PROPN
ap-7659	353	12	.	.	PUNCT
ap-7659	354	1	swanson	swanson	PROPN
ap-7659	354	2	hamiltonian	hamiltonian	PROPN
ap-7659	354	3	:	:	PUNCT
ap-7659	354	4	non	non	ADJ
ap-7659	354	5	-	-	ADJ
ap-7659	354	6	pt	pt	ADJ
ap-7659	354	7	-	-	PUNCT
ap-7659	354	8	symmetry	symmetry	NOUN
ap-7659	354	9	phase	phase	NOUN
ap-7659	354	10	.	.	PUNCT
ap-7659	355	1	journal	journal	PROPN
ap-7659	355	2	of	of	ADP
ap-7659	355	3	physics	physics	PROPN
ap-7659	355	4	a	a	PRON
ap-7659	355	5	:	:	PUNCT
ap-7659	355	6	mathematical	mathematical	ADJ
ap-7659	355	7	and	and	CCONJ
ap-7659	355	8	theoretical	theoretical	ADJ
ap-7659	355	9	55(1):015303	55(1):015303	NUM
ap-7659	355	10	,	,	PUNCT
ap-7659	355	11	2022	2022	NUM
ap-7659	355	12	.	.	PUNCT
ap-7659	356	1	https://doi.org/10.1088/1751-8121/ac3a35	https://doi.org/10.1088/1751-8121/ac3a35	NOUN
ap-7659	356	2	.	.	PUNCT
ap-7659	357	1	[	[	X
ap-7659	357	2	27	27	NUM
ap-7659	357	3	]	]	PUNCT
ap-7659	357	4	j.	j.	PROPN
ap-7659	357	5	aguilar	aguilar	PROPN
ap-7659	357	6	,	,	PUNCT
ap-7659	357	7	j.	j.	PROPN
ap-7659	357	8	m.	m.	PROPN
ap-7659	357	9	combes	combes	PROPN
ap-7659	357	10	.	.	PUNCT
ap-7659	358	1	a	a	DET
ap-7659	358	2	class	class	NOUN
ap-7659	358	3	of	of	ADP
ap-7659	358	4	analytic	analytic	ADJ
ap-7659	358	5	perturbations	perturbation	NOUN
ap-7659	358	6	for	for	ADP
ap-7659	358	7	one	one	NUM
ap-7659	358	8	-	-	PUNCT
ap-7659	358	9	body	body	NOUN
ap-7659	358	10	schrödinger	schrödinger	ADJ
ap-7659	358	11	hamiltonians	hamiltonian	NOUN
ap-7659	358	12	.	.	PUNCT
ap-7659	359	1	communications	communication	NOUN
ap-7659	359	2	in	in	ADP
ap-7659	359	3	mathematical	mathematical	ADJ
ap-7659	359	4	physics	physics	NOUN
ap-7659	359	5	22:269–279	22:269–279	PROPN
ap-7659	359	6	,	,	PUNCT
ap-7659	359	7	1971	1971	NUM
ap-7659	359	8	.	.	PUNCT
ap-7659	360	1	https://doi.org/10.1007/bf01877510	https://doi.org/10.1007/bf01877510	VERB
ap-7659	360	2	.	.	PUNCT
ap-7659	361	1	[	[	X
ap-7659	361	2	28	28	NUM
ap-7659	361	3	]	]	X
ap-7659	361	4	e.	e.	PROPN
ap-7659	361	5	balslev	balslev	PROPN
ap-7659	361	6	,	,	PUNCT
ap-7659	361	7	j.	j.	PROPN
ap-7659	361	8	m.	m.	PROPN
ap-7659	361	9	combes	combes	PROPN
ap-7659	361	10	.	.	PUNCT
ap-7659	362	1	spectral	spectral	ADJ
ap-7659	362	2	properties	property	NOUN
ap-7659	362	3	of	of	ADP
ap-7659	362	4	many	many	ADJ
ap-7659	362	5	-	-	PUNCT
ap-7659	362	6	body	body	NOUN
ap-7659	362	7	schrödinger	schrödinger	ADJ
ap-7659	362	8	operators	operator	NOUN
ap-7659	362	9	with	with	ADP
ap-7659	362	10	dilatation	dilatation	NOUN
ap-7659	362	11	-	-	PUNCT
ap-7659	362	12	analytic	analytic	ADJ
ap-7659	362	13	interactions	interaction	NOUN
ap-7659	362	14	.	.	PUNCT
ap-7659	363	1	communications	communication	NOUN
ap-7659	363	2	in	in	ADP
ap-7659	363	3	mathematical	mathematical	ADJ
ap-7659	363	4	physics	physics	NOUN
ap-7659	363	5	22:280–294	22:280–294	NUM
ap-7659	363	6	,	,	PUNCT
ap-7659	363	7	1971	1971	NUM
ap-7659	363	8	.	.	PUNCT
ap-7659	364	1	https://doi.org/10.1007/bf01877511	https://doi.org/10.1007/bf01877511	X
ap-7659	364	2	.	.	PUNCT
ap-7659	365	1	[	[	X
ap-7659	365	2	29	29	NUM
ap-7659	365	3	]	]	X
ap-7659	365	4	b.	b.	PROPN
ap-7659	365	5	simon	simon	PROPN
ap-7659	365	6	.	.	PUNCT
ap-7659	366	1	quadratic	quadratic	ADJ
ap-7659	366	2	form	form	NOUN
ap-7659	366	3	techniques	technique	NOUN
ap-7659	366	4	and	and	CCONJ
ap-7659	366	5	the	the	DET
ap-7659	366	6	balslev	balslev	NOUN
ap-7659	366	7	-	-	PUNCT
ap-7659	366	8	combes	combe	NOUN
ap-7659	366	9	theorem	theorem	PROPN
ap-7659	366	10	.	.	PUNCT
ap-7659	367	1	communications	communication	NOUN
ap-7659	367	2	in	in	ADP
ap-7659	367	3	mathematical	mathematical	ADJ
ap-7659	367	4	physics	physics	NOUN
ap-7659	367	5	27:1–9	27:1–9	NOUN
ap-7659	367	6	,	,	PUNCT
ap-7659	367	7	1972	1972	NUM
ap-7659	367	8	.	.	PUNCT
ap-7659	368	1	https://doi.org/10.1007/bf01649654	https://doi.org/10.1007/bf01649654	X
ap-7659	368	2	.	.	PUNCT
ap-7659	369	1	[	[	X
ap-7659	369	2	30	30	NUM
ap-7659	369	3	]	]	X
ap-7659	369	4	h.	h.	PROPN
ap-7659	369	5	feshbach	feshbach	PROPN
ap-7659	369	6	.	.	PUNCT
ap-7659	370	1	a	a	DET
ap-7659	370	2	unified	unified	ADJ
ap-7659	370	3	theory	theory	NOUN
ap-7659	370	4	of	of	ADP
ap-7659	370	5	nuclear	nuclear	ADJ
ap-7659	370	6	reactions	reaction	NOUN
ap-7659	370	7	.	.	PUNCT
ap-7659	371	1	ii	ii	PROPN
ap-7659	371	2	.	.	PROPN
ap-7659	371	3	annals	annal	NOUN
ap-7659	371	4	of	of	ADP
ap-7659	371	5	physics	physics	NOUN
ap-7659	371	6	19(2):287–313	19(2):287–313	PROPN
ap-7659	371	7	,	,	PUNCT
ap-7659	371	8	1962	1962	NUM
ap-7659	371	9	.	.	PUNCT
ap-7659	372	1	https://doi.org/10.1016/0003-4916(62)90221-x	https://doi.org/10.1016/0003-4916(62)90221-x	NOUN
ap-7659	372	2	.	.	PUNCT
ap-7659	373	1	[	[	X
ap-7659	373	2	31	31	NUM
ap-7659	373	3	]	]	X
ap-7659	373	4	y.	y.	PROPN
ap-7659	373	5	ho	ho	PROPN
ap-7659	373	6	.	.	PUNCT
ap-7659	374	1	the	the	DET
ap-7659	374	2	method	method	NOUN
ap-7659	374	3	of	of	ADP
ap-7659	374	4	complex	complex	ADJ
ap-7659	374	5	coordinate	coordinate	NOUN
ap-7659	374	6	rotation	rotation	NOUN
ap-7659	374	7	and	and	CCONJ
ap-7659	374	8	its	its	PRON
ap-7659	374	9	applications	application	NOUN
ap-7659	374	10	to	to	ADP
ap-7659	374	11	atomic	atomic	ADJ
ap-7659	374	12	collision	collision	NOUN
ap-7659	374	13	processes	process	NOUN
ap-7659	374	14	.	.	PUNCT
ap-7659	375	1	physics	physics	NOUN
ap-7659	375	2	reports	report	VERB
ap-7659	375	3	99(1):1–68	99(1):1–68	NUM
ap-7659	375	4	,	,	PUNCT
ap-7659	375	5	1983	1983	NUM
ap-7659	375	6	.	.	PUNCT
ap-7659	376	1	https://doi.org/10.1016/0370-1573(83)90112-6	https://doi.org/10.1016/0370-1573(83)90112-6	PROPN
ap-7659	376	2	.	.	PUNCT
ap-7659	377	1	[	[	X
ap-7659	377	2	32	32	NUM
ap-7659	377	3	]	]	PUNCT
ap-7659	377	4	t.	t.	PROPN
ap-7659	377	5	myo	myo	PROPN
ap-7659	377	6	,	,	PUNCT
ap-7659	377	7	k.	k.	PROPN
ap-7659	377	8	katõ	katõ	PROPN
ap-7659	377	9	.	.	PUNCT
ap-7659	378	1	complex	complex	ADJ
ap-7659	378	2	scaling	scaling	NOUN
ap-7659	378	3	:	:	PUNCT
ap-7659	378	4	physics	physics	NOUN
ap-7659	378	5	of	of	ADP
ap-7659	378	6	unbound	unbound	PROPN
ap-7659	378	7	light	light	NOUN
ap-7659	378	8	nuclei	nucleus	NOUN
ap-7659	378	9	and	and	CCONJ
ap-7659	378	10	perspective	perspective	NOUN
ap-7659	378	11	.	.	PUNCT
ap-7659	379	1	progress	progress	NOUN
ap-7659	379	2	of	of	ADP
ap-7659	379	3	theoretical	theoretical	ADJ
ap-7659	379	4	and	and	CCONJ
ap-7659	379	5	experimental	experimental	ADJ
ap-7659	379	6	physics	physics	NOUN
ap-7659	379	7	2020(12):12a101	2020(12):12a101	NUM
ap-7659	379	8	,	,	PUNCT
ap-7659	379	9	2020	2020	NUM
ap-7659	379	10	.	.	PUNCT
ap-7659	380	1	[	[	X
ap-7659	380	2	33	33	NUM
ap-7659	380	3	]	]	PUNCT
ap-7659	380	4	i.	i.	PROPN
ap-7659	380	5	m.	m.	PROPN
ap-7659	380	6	gel’fand	gel’fand	PROPN
ap-7659	380	7	,	,	PUNCT
ap-7659	380	8	g.	g.	PROPN
ap-7659	380	9	shilov	shilov	PROPN
ap-7659	380	10	.	.	PUNCT
ap-7659	381	1	generalized	generalized	ADJ
ap-7659	381	2	functions	function	NOUN
ap-7659	381	3	vol	vol	NOUN
ap-7659	381	4	.	.	PUNCT
ap-7659	381	5	i.	i.	PROPN
ap-7659	381	6	academic	academic	PROPN
ap-7659	381	7	press	press	PROPN
ap-7659	381	8	,	,	PUNCT
ap-7659	381	9	new	new	PROPN
ap-7659	381	10	york	york	PROPN
ap-7659	381	11	and	and	CCONJ
ap-7659	381	12	london	london	PROPN
ap-7659	381	13	,	,	PUNCT
ap-7659	381	14	1964	1964	NUM
ap-7659	381	15	.	.	PUNCT
ap-7659	382	1	[	[	X
ap-7659	382	2	34	34	NUM
ap-7659	382	3	]	]	X
ap-7659	382	4	a.	a.	PROPN
ap-7659	382	5	bohm	bohm	PROPN
ap-7659	382	6	,	,	PUNCT
ap-7659	382	7	j.	j.	PROPN
ap-7659	382	8	d.	d.	PROPN
ap-7659	382	9	dollard	dollard	PROPN
ap-7659	382	10	,	,	PUNCT
ap-7659	382	11	m.	m.	NOUN
ap-7659	382	12	gadella	gadella	PROPN
ap-7659	382	13	.	.	PUNCT
ap-7659	383	1	dirac	dirac	PROPN
ap-7659	383	2	kets	kets	PROPN
ap-7659	383	3	,	,	PUNCT
ap-7659	383	4	gamow	gamow	NOUN
ap-7659	383	5	vectors	vector	NOUN
ap-7659	383	6	and	and	CCONJ
ap-7659	383	7	gelfand	gelfand	ADJ
ap-7659	383	8	triplets	triplet	NOUN
ap-7659	383	9	.	.	PUNCT
ap-7659	384	1	lecture	lecture	NOUN
ap-7659	384	2	notes	note	NOUN
ap-7659	384	3	in	in	ADP
ap-7659	384	4	physics	physics	NOUN
ap-7659	384	5	vol	vol	NOUN
ap-7659	384	6	.	.	PUNCT
ap-7659	385	1	348	348	NUM
ap-7659	385	2	.	.	PUNCT
ap-7659	385	3	springer	springer	NOUN
ap-7659	385	4	,	,	PUNCT
ap-7659	385	5	1989	1989	NUM
ap-7659	385	6	.	.	PUNCT
ap-7659	386	1	[	[	X
ap-7659	386	2	35	35	NUM
ap-7659	386	3	]	]	PUNCT
ap-7659	386	4	a.	a.	NOUN
ap-7659	386	5	mostafazadeh	mostafazadeh	NOUN
ap-7659	386	6	.	.	PUNCT
ap-7659	387	1	pseudo	pseudo	NOUN
ap-7659	387	2	-	-	NOUN
ap-7659	387	3	hermiticity	hermiticity	NOUN
ap-7659	387	4	versus	versus	ADP
ap-7659	387	5	ptsymmetry	ptsymmetry	PROPN
ap-7659	387	6	.	.	PUNCT
ap-7659	388	1	ii	ii	PROPN
ap-7659	388	2	.	.	PUNCT
ap-7659	389	1	a	a	DET
ap-7659	389	2	complete	complete	ADJ
ap-7659	389	3	characterization	characterization	NOUN
ap-7659	389	4	of	of	ADP
ap-7659	389	5	non	non	ADJ
ap-7659	389	6	-	-	ADJ
ap-7659	389	7	hermitian	hermitian	ADJ
ap-7659	389	8	hamiltonians	hamiltonian	NOUN
ap-7659	389	9	with	with	ADP
ap-7659	389	10	a	a	DET
ap-7659	389	11	real	real	ADJ
ap-7659	389	12	spectrum	spectrum	NOUN
ap-7659	389	13	.	.	PUNCT
ap-7659	390	1	journal	journal	PROPN
ap-7659	390	2	of	of	ADP
ap-7659	390	3	mathematical	mathematical	ADJ
ap-7659	390	4	physics	physics	NOUN
ap-7659	390	5	43(5):2814–2816	43(5):2814–2816	PROPN
ap-7659	390	6	,	,	PUNCT
ap-7659	390	7	2002	2002	NUM
ap-7659	390	8	.	.	PUNCT
ap-7659	391	1	https://doi.org/10.1063/1.1461427	https://doi.org/10.1063/1.1461427	X
ap-7659	391	2	.	.	PUNCT
ap-7659	392	1	[	[	X
ap-7659	392	2	36	36	NUM
ap-7659	392	3	]	]	X
ap-7659	392	4	f.	f.	PROPN
ap-7659	392	5	bagarello	bagarello	PROPN
ap-7659	392	6	,	,	PUNCT
ap-7659	392	7	j.	j.	PROPN
ap-7659	392	8	p.	p.	PROPN
ap-7659	392	9	gazeau	gazeau	PROPN
ap-7659	392	10	,	,	PUNCT
ap-7659	392	11	f.	f.	PROPN
ap-7659	392	12	h.	h.	PROPN
ap-7659	392	13	szafraniec	szafraniec	PROPN
ap-7659	392	14	,	,	PUNCT
ap-7659	392	15	m.	m.	NOUN
ap-7659	392	16	znojil	znojil	PROPN
ap-7659	392	17	.	.	PUNCT
ap-7659	393	1	non	non	ADJ
ap-7659	393	2	-	-	ADJ
ap-7659	393	3	selfadjoint	selfadjoint	ADJ
ap-7659	393	4	operators	operator	NOUN
ap-7659	393	5	in	in	ADP
ap-7659	393	6	quantum	quantum	ADJ
ap-7659	393	7	physics	physics	NOUN
ap-7659	393	8	:	:	PUNCT
ap-7659	393	9	mathematical	mathematical	ADJ
ap-7659	393	10	aspects	aspect	NOUN
ap-7659	393	11	.	.	PUNCT
ap-7659	394	1	john	john	PROPN
ap-7659	394	2	wiley	wiley	PROPN
ap-7659	394	3	&	&	CCONJ
ap-7659	394	4	sons	sons	PROPN
ap-7659	394	5	,	,	PUNCT
ap-7659	394	6	usa	usa	PROPN
ap-7659	394	7	,	,	PUNCT
ap-7659	394	8	2015	2015	NUM
ap-7659	394	9	.	.	PUNCT
ap-7659	395	1	[	[	X
ap-7659	395	2	37	37	NUM
ap-7659	395	3	]	]	PUNCT
ap-7659	395	4	t.	t.	PROPN
ap-7659	395	5	y.	y.	PROPN
ap-7659	395	6	azizov	azizov	PROPN
ap-7659	395	7	,	,	PUNCT
ap-7659	395	8	i.	i.	PROPN
ap-7659	395	9	s.	s.	PROPN
ap-7659	395	10	iokhvidov	iokhvidov	PROPN
ap-7659	395	11	.	.	PUNCT
ap-7659	396	1	linear	linear	PROPN
ap-7659	396	2	operators	operator	NOUN
ap-7659	396	3	in	in	ADP
ap-7659	396	4	spaces	space	NOUN
ap-7659	396	5	with	with	ADP
ap-7659	396	6	an	an	DET
ap-7659	396	7	indefinite	indefinite	ADJ
ap-7659	396	8	metric	metric	NOUN
ap-7659	396	9	.	.	PUNCT
ap-7659	397	1	john	john	PROPN
ap-7659	397	2	wiley	wiley	PROPN
ap-7659	397	3	&	&	CCONJ
ap-7659	397	4	sons	sons	PROPN
ap-7659	397	5	,	,	PUNCT
ap-7659	397	6	usa	usa	PROPN
ap-7659	397	7	,	,	PUNCT
ap-7659	397	8	1989	1989	NUM
ap-7659	397	9	.	.	PUNCT
ap-7659	398	1	[	[	X
ap-7659	398	2	38	38	NUM
ap-7659	398	3	]	]	PUNCT
ap-7659	398	4	u.	u.	NOUN
ap-7659	398	5	günther	günther	PROPN
ap-7659	398	6	,	,	PUNCT
ap-7659	398	7	b.	b.	PROPN
ap-7659	398	8	f.	f.	PROPN
ap-7659	398	9	samsonov	samsonov	PROPN
ap-7659	398	10	.	.	PUNCT
ap-7659	399	1	naimark	naimark	PROPN
ap-7659	399	2	-	-	PUNCT
ap-7659	399	3	dilated	dilate	VERB
ap-7659	399	4	pt	pt	NOUN
ap-7659	399	5	-symmetric	-symmetric	ADJ
ap-7659	399	6	brachistochrone	brachistochrone	NOUN
ap-7659	399	7	.	.	PUNCT
ap-7659	400	1	physical	physical	ADJ
ap-7659	400	2	review	review	PROPN
ap-7659	400	3	letters	letter	NOUN
ap-7659	400	4	101:230404	101:230404	NUM
ap-7659	400	5	,	,	PUNCT
ap-7659	400	6	2008	2008	NUM
ap-7659	400	7	.	.	PUNCT
ap-7659	401	1	https://doi.org/10.1103/physrevlett.101.230404	https://doi.org/10.1103/physrevlett.101.230404	NOUN
ap-7659	401	2	.	.	PUNCT
ap-7659	402	1	[	[	X
ap-7659	402	2	39	39	NUM
ap-7659	402	3	]	]	PUNCT
ap-7659	402	4	u.	u.	NOUN
ap-7659	402	5	günther	günther	PROPN
ap-7659	402	6	,	,	PUNCT
ap-7659	402	7	s.	s.	PROPN
ap-7659	402	8	kuzhel	kuzhel	PROPN
ap-7659	402	9	.	.	PUNCT
ap-7659	403	1	pt	pt	PROPN
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ap-7659	403	3	,	,	PUNCT
ap-7659	403	4	cartan	cartan	ADJ
ap-7659	403	5	decompositions	decomposition	NOUN
ap-7659	403	6	,	,	PUNCT
ap-7659	403	7	lie	lie	VERB
ap-7659	403	8	triple	triple	ADJ
ap-7659	403	9	systems	system	NOUN
ap-7659	403	10	and	and	CCONJ
ap-7659	403	11	krein	krein	ADJ
ap-7659	403	12	space	space	NOUN
ap-7659	403	13	-	-	PUNCT
ap-7659	403	14	related	relate	VERB
ap-7659	403	15	clifford	clifford	PROPN
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ap-7659	404	1	a	a	PRON
ap-7659	404	2	:	:	PUNCT
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ap-7659	404	7	,	,	PUNCT
ap-7659	404	8	2010	2010	NUM
ap-7659	404	9	.	.	PUNCT
ap-7659	405	1	https://doi.org/10.1088/1751-8113/43/39/392002	https://doi.org/10.1088/1751-8113/43/39/392002	NOUN
ap-7659	405	2	.	.	PUNCT
ap-7659	406	1	[	[	X
ap-7659	406	2	40	40	NUM
ap-7659	406	3	]	]	PUNCT
ap-7659	406	4	a.	a.	NOUN
ap-7659	406	5	dijksma	dijksma	PROPN
ap-7659	406	6	,	,	PUNCT
ap-7659	406	7	h.	h.	PROPN
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ap-7659	406	9	.	.	PUNCT
ap-7659	407	1	operator	operator	NOUN
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ap-7659	407	4	ordinary	ordinary	ADJ
ap-7659	407	5	differential	differential	ADJ
ap-7659	407	6	operators	operator	NOUN
ap-7659	407	7	.	.	PUNCT
ap-7659	408	1	american	american	PROPN
ap-7659	408	2	mathematical	mathematical	PROPN
ap-7659	408	3	society	society	NOUN
ap-7659	408	4	,	,	PUNCT
ap-7659	408	5	providence	providence	NOUN
ap-7659	408	6	,	,	PUNCT
ap-7659	408	7	ri	ri	NOUN
ap-7659	408	8	,	,	PUNCT
ap-7659	408	9	1996	1996	NUM
ap-7659	408	10	.	.	PUNCT
ap-7659	409	1	[	[	X
ap-7659	409	2	41	41	NUM
ap-7659	409	3	]	]	X
ap-7659	409	4	f.	f.	PROPN
ap-7659	409	5	s.	s.	PROPN
ap-7659	409	6	u.	u.	PROPN
ap-7659	409	7	günther	günther	PROPN
ap-7659	409	8	.	.	PUNCT
ap-7659	410	1	ir	ir	ADJ
ap-7659	410	2	-	-	ADJ
ap-7659	410	3	truncated	truncate	VERB
ap-7659	410	4	pt	pt	NOUN
ap-7659	410	5	-symmetric	-symmetric	PROPN
ap-7659	410	6	ix3	ix3	PROPN
ap-7659	410	7	model	model	NOUN
ap-7659	410	8	and	and	CCONJ
ap-7659	410	9	its	its	PRON
ap-7659	410	10	asymptotic	asymptotic	ADJ
ap-7659	410	11	spectral	spectral	ADJ
ap-7659	410	12	scaling	scaling	NOUN
ap-7659	410	13	graph	graph	NOUN
ap-7659	410	14	.	.	PUNCT
ap-7659	411	1	arxiv:1901.08526	arxiv:1901.08526	PROPN
ap-7659	411	2	.	.	PUNCT
ap-7659	412	1	163	163	NUM
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ap-7659	412	5	https://doi.org/10.1088/1751-8113/41/24/244017	https://doi.org/10.1088/1751-8113/41/24/244017	CCONJ
ap-7659	412	6	https://doi.org/10.1142/s0219887810004816	https://doi.org/10.1142/s0219887810004816	NUM
ap-7659	412	7	https://doi.org/10.1063/1.3272002	https://doi.org/10.1063/1.3272002	INTJ
ap-7659	412	8	https://doi.org/10.1016/j.physleta.2009.09.054	https://doi.org/10.1016/j.physleta.2009.09.054	ADJ
ap-7659	412	9	https://doi.org/10.1142/9789814287333_0010	https://doi.org/10.1142/9789814287333_0010	VERB
ap-7659	413	1	https://doi.org/10.1016/j.physleta.2015.04.009	https://doi.org/10.1016/j.physleta.2015.04.009	PROPN
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ap-7659	414	1	https://doi.org/10.1007/bf01877510	https://doi.org/10.1007/bf01877510	VERB
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ap-7659	415	1	https://doi.org/10.1016/0003-4916(62)90221-x	https://doi.org/10.1016/0003-4916(62)90221-x	NOUN
ap-7659	415	2	https://doi.org/10.1016/0370-1573(83)90112-6	https://doi.org/10.1016/0370-1573(83)90112-6	PROPN
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ap-7659	415	5	https://doi.org/10.1088/1751-8113/43/39/392002	https://doi.org/10.1088/1751-8113/43/39/392002	NOUN
ap-7659	415	6	http://arxiv.org/abs/1901.08526	http://arxiv.org/abs/1901.08526	PROPN
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ap-7659	415	8	reboiro	reboiro	PROPN
ap-7659	415	9	,	,	PUNCT
ap-7659	415	10	r.	r.	PROPN
ap-7659	415	11	ramírez	ramírez	PROPN
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ap-7659	415	13	v.	v.	ADP
ap-7659	415	14	fernández	fernández	PROPN
ap-7659	415	15	acta	acta	PROPN
ap-7659	415	16	polytechnica	polytechnica	PROPN
ap-7659	416	1	[	[	X
ap-7659	416	2	42	42	NUM
ap-7659	416	3	]	]	X
ap-7659	416	4	d.	d.	PROPN
ap-7659	416	5	chruściński	chruściński	PROPN
ap-7659	416	6	.	.	PUNCT
ap-7659	417	1	quantum	quantum	ADJ
ap-7659	417	2	mechanics	mechanic	NOUN
ap-7659	417	3	of	of	ADP
ap-7659	417	4	damped	damped	NOUN
ap-7659	417	5	systems	system	NOUN
ap-7659	417	6	.	.	PUNCT
ap-7659	418	1	journal	journal	PROPN
ap-7659	418	2	of	of	ADP
ap-7659	418	3	mathematical	mathematical	ADJ
ap-7659	418	4	physics	physics	NOUN
ap-7659	418	5	44(9):3718	44(9):3718	NUM
ap-7659	418	6	–	–	PUNCT
ap-7659	418	7	3733	3733	NUM
ap-7659	418	8	,	,	PUNCT
ap-7659	418	9	2003	2003	NUM
ap-7659	418	10	.	.	PUNCT
ap-7659	419	1	https://doi.org/10.1063/1.1599074	https://doi.org/10.1063/1.1599074	PROPN
ap-7659	419	2	.	.	PUNCT
ap-7659	420	1	[	[	X
ap-7659	420	2	43	43	NUM
ap-7659	420	3	]	]	X
ap-7659	420	4	d.	d.	PROPN
ap-7659	420	5	chruściński	chruściński	PROPN
ap-7659	420	6	.	.	PUNCT
ap-7659	421	1	quantum	quantum	ADJ
ap-7659	421	2	mechanics	mechanic	NOUN
ap-7659	421	3	of	of	ADP
ap-7659	421	4	damped	damped	NOUN
ap-7659	421	5	systems	system	NOUN
ap-7659	421	6	.	.	PUNCT
ap-7659	422	1	ii	ii	PROPN
ap-7659	422	2	.	.	PUNCT
ap-7659	423	1	damping	damp	VERB
ap-7659	423	2	and	and	CCONJ
ap-7659	423	3	parabolic	parabolic	ADJ
ap-7659	423	4	potential	potential	ADJ
ap-7659	423	5	barrier	barrier	NOUN
ap-7659	423	6	.	.	PUNCT
ap-7659	424	1	journal	journal	NOUN
ap-7659	424	2	of	of	ADP
ap-7659	424	3	mathematical	mathematical	ADJ
ap-7659	424	4	physics	physics	NOUN
ap-7659	424	5	45(3):841–854	45(3):841–854	PROPN
ap-7659	424	6	,	,	PUNCT
ap-7659	424	7	2004	2004	NUM
ap-7659	424	8	.	.	PUNCT
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ap-7659	425	2	.	.	PUNCT
ap-7659	426	1	[	[	X
ap-7659	426	2	44	44	NUM
ap-7659	426	3	]	]	X
ap-7659	426	4	g.	g.	PROPN
ap-7659	426	5	marcucci	marcucci	PROPN
ap-7659	426	6	,	,	PUNCT
ap-7659	426	7	c.	c.	PROPN
ap-7659	426	8	conti	conti	PROPN
ap-7659	426	9	.	.	PROPN
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ap-7659	426	11	evolution	evolution	NOUN
ap-7659	426	12	of	of	ADP
ap-7659	426	13	a	a	DET
ap-7659	426	14	wave	wave	NOUN
ap-7659	426	15	packet	packet	NOUN
ap-7659	426	16	in	in	ADP
ap-7659	426	17	the	the	DET
ap-7659	426	18	rigged	rig	VERB
ap-7659	426	19	-	-	PUNCT
ap-7659	426	20	hilbert	hilbert	NOUN
ap-7659	426	21	-	-	PUNCT
ap-7659	426	22	space	space	NOUN
ap-7659	426	23	quantum	quantum	NOUN
ap-7659	426	24	mechanics	mechanic	NOUN
ap-7659	426	25	.	.	PUNCT
ap-7659	427	1	physical	physical	ADJ
ap-7659	427	2	review	review	NOUN
ap-7659	427	3	a	a	DET
ap-7659	427	4	94:052136	94:052136	NUM
ap-7659	427	5	,	,	PUNCT
ap-7659	427	6	2016	2016	NUM
ap-7659	427	7	.	.	PUNCT
ap-7659	428	1	https://doi.org/10.1103/physreva.94.052136	https://doi.org/10.1103/physreva.94.052136	NOUN
ap-7659	428	2	.	.	PUNCT
ap-7659	429	1	[	[	X
ap-7659	429	2	45	45	NUM
ap-7659	429	3	]	]	PUNCT
ap-7659	429	4	d.	d.	PROPN
ap-7659	429	5	bermudez	bermudez	PROPN
ap-7659	429	6	,	,	PUNCT
ap-7659	429	7	d.	d.	PROPN
ap-7659	429	8	j.	j.	PROPN
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ap-7659	429	10	c.	c.	PROPN
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ap-7659	429	12	method	method	NOUN
ap-7659	429	13	and	and	CCONJ
ap-7659	429	14	new	new	ADJ
ap-7659	429	15	potentials	potential	NOUN
ap-7659	429	16	from	from	ADP
ap-7659	429	17	the	the	DET
ap-7659	429	18	inverted	inverted	ADJ
ap-7659	429	19	oscillator	oscillator	NOUN
ap-7659	429	20	.	.	PUNCT
ap-7659	429	21	annals	annal	NOUN
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ap-7659	429	25	,	,	PUNCT
ap-7659	429	26	2013	2013	NUM
ap-7659	429	27	.	.	PUNCT
ap-7659	430	1	https://doi.org/10.1016/j.aop.2013.02.015	https://doi.org/10.1016/j.aop.2013.02.015	PROPN
ap-7659	430	2	.	.	PUNCT
ap-7659	431	1	[	[	X
ap-7659	431	2	46	46	NUM
ap-7659	431	3	]	]	PUNCT
ap-7659	431	4	s.	s.	PROPN
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ap-7659	431	8	fring	fring	NOUN
ap-7659	431	9	.	.	PUNCT
ap-7659	432	1	squeezed	squeeze	VERB
ap-7659	432	2	coherent	coherent	ADJ
ap-7659	432	3	states	state	NOUN
ap-7659	432	4	for	for	ADP
ap-7659	432	5	noncommutative	noncommutative	ADJ
ap-7659	432	6	spaces	space	NOUN
ap-7659	432	7	with	with	ADP
ap-7659	432	8	minimal	minimal	ADJ
ap-7659	432	9	length	length	NOUN
ap-7659	432	10	uncertainty	uncertainty	NOUN
ap-7659	432	11	relations	relation	NOUN
ap-7659	432	12	.	.	PUNCT
ap-7659	433	1	physical	physical	ADJ
ap-7659	433	2	review	review	PROPN
ap-7659	434	1	d	d	PROPN
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ap-7659	434	3	,	,	PUNCT
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ap-7659	434	5	.	.	PUNCT
ap-7659	435	1	https://doi.org/10.1103/physrevd.86.064038	https://doi.org/10.1103/physrevd.86.064038	NOUN
ap-7659	435	2	.	.	PUNCT
ap-7659	436	1	[	[	X
ap-7659	436	2	47	47	NUM
ap-7659	436	3	]	]	PUNCT
ap-7659	436	4	s.	s.	PROPN
ap-7659	436	5	dey	dey	PROPN
ap-7659	436	6	,	,	PUNCT
ap-7659	436	7	a.	a.	NOUN
ap-7659	436	8	fring	fring	PROPN
ap-7659	436	9	,	,	PUNCT
ap-7659	436	10	b.	b.	PROPN
ap-7659	436	11	khantoul	khantoul	PROPN
ap-7659	436	12	.	.	PUNCT
ap-7659	437	1	hermitian	hermitian	PROPN
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ap-7659	437	3	non	non	ADJ
ap-7659	437	4	-	-	ADJ
ap-7659	437	5	hermitian	hermitian	ADJ
ap-7659	437	6	representations	representation	NOUN
ap-7659	437	7	for	for	ADP
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ap-7659	437	10	uncertainty	uncertainty	NOUN
ap-7659	437	11	relations	relation	NOUN
ap-7659	437	12	.	.	PUNCT
ap-7659	438	1	journal	journal	PROPN
ap-7659	438	2	of	of	ADP
ap-7659	438	3	physics	physics	PROPN
ap-7659	438	4	a	a	PRON
ap-7659	438	5	:	:	PUNCT
ap-7659	438	6	mathematical	mathematical	ADJ
ap-7659	438	7	and	and	CCONJ
ap-7659	438	8	theoretical	theoretical	ADJ
ap-7659	438	9	46(33):335304	46(33):335304	NUM
ap-7659	438	10	,	,	PUNCT
ap-7659	438	11	2013	2013	NUM
ap-7659	438	12	.	.	PUNCT
ap-7659	439	1	https://doi.org/10.1088/1751-8113/46/33/335304	https://doi.org/10.1088/1751-8113/46/33/335304	PROPN
ap-7659	439	2	.	.	PUNCT
ap-7659	440	1	[	[	X
ap-7659	440	2	48	48	NUM
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ap-7659	440	10	.	.	PUNCT
ap-7659	441	1	on	on	ADP
ap-7659	441	2	the	the	DET
ap-7659	441	3	theory	theory	NOUN
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ap-7659	441	5	the	the	DET
ap-7659	441	6	optical	optical	ADJ
ap-7659	441	7	potential	potential	NOUN
ap-7659	441	8	.	.	PUNCT
ap-7659	442	1	annals	annal	NOUN
ap-7659	442	2	of	of	ADP
ap-7659	442	3	physics	physics	NOUN
ap-7659	442	4	54(2):403	54(2):403	NOUN
ap-7659	442	5	,	,	PUNCT
ap-7659	442	6	1969	1969	NUM
ap-7659	442	7	.	.	PUNCT
ap-7659	443	1	https://doi.org/10.1016/0003-4916(69)90161-4	https://doi.org/10.1016/0003-4916(69)90161-4	NOUN
ap-7659	443	2	.	.	PUNCT
ap-7659	444	1	[	[	X
ap-7659	444	2	49	49	NUM
ap-7659	444	3	]	]	PUNCT
ap-7659	444	4	j.	j.	PROPN
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ap-7659	444	10	g.	g.	PROPN
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ap-7659	444	13	et	et	PROPN
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ap-7659	444	15	.	.	PROPN
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ap-7659	444	17	potential	potential	NOUN
ap-7659	444	18	from	from	ADP
ap-7659	444	19	first	first	ADJ
ap-7659	444	20	principles	principle	NOUN
ap-7659	444	21	.	.	PUNCT
ap-7659	445	1	physical	physical	ADJ
ap-7659	445	2	review	review	PROPN
ap-7659	445	3	c	c	PROPN
ap-7659	445	4	95:024315	95:024315	PROPN
ap-7659	445	5	,	,	PUNCT
ap-7659	445	6	2017	2017	NUM
ap-7659	445	7	.	.	PUNCT
ap-7659	446	1	https://doi.org/10.1103/physrevc.95.024315	https://doi.org/10.1103/physrevc.95.024315	ADJ
ap-7659	446	2	.	.	PUNCT
ap-7659	447	1	[	[	X
ap-7659	447	2	50	50	NUM
ap-7659	447	3	]	]	PUNCT
ap-7659	447	4	r.	r.	PROPN
ap-7659	447	5	ramírez	ramírez	PROPN
ap-7659	447	6	,	,	PUNCT
ap-7659	447	7	m.	m.	NOUN
ap-7659	447	8	reboiro	reboiro	PROPN
ap-7659	447	9	.	.	PUNCT
ap-7659	448	1	squeezed	squeeze	VERB
ap-7659	448	2	states	state	NOUN
ap-7659	448	3	from	from	ADP
ap-7659	448	4	a	a	DET
ap-7659	448	5	quantum	quantum	NOUN
ap-7659	448	6	deformed	deform	VERB
ap-7659	448	7	oscillator	oscillator	NOUN
ap-7659	448	8	hamiltonian	hamiltonian	NOUN
ap-7659	448	9	.	.	PUNCT
ap-7659	449	1	physics	physics	NOUN
ap-7659	449	2	letters	letter	VERB
ap-7659	449	3	a	a	DET
ap-7659	449	4	380(11	380(11	NUM
ap-7659	449	5	-	-	PROPN
ap-7659	449	6	12):1117–1124	12):1117–1124	PROPN
ap-7659	449	7	,	,	PUNCT
ap-7659	449	8	2016	2016	NUM
ap-7659	449	9	.	.	PUNCT
ap-7659	450	1	https://doi.org/10.1016/j.physleta.2016.01.027	https://doi.org/10.1016/j.physleta.2016.01.027	PROPN
ap-7659	450	2	.	.	PUNCT
ap-7659	451	1	164	164	NUM
ap-7659	451	2	https://doi.org/10.1063/1.1599074	https://doi.org/10.1063/1.1599074	PROPN
ap-7659	451	3	https://doi.org/10.1063/1.1644751	https://doi.org/10.1063/1.1644751	PROPN
ap-7659	451	4	https://doi.org/10.1103/physreva.94.052136	https://doi.org/10.1103/physreva.94.052136	PROPN
ap-7659	451	5	https://doi.org/10.1016/j.aop.2013.02.015	https://doi.org/10.1016/j.aop.2013.02.015	PROPN
ap-7659	451	6	https://doi.org/10.1103/physrevd.86.064038	https://doi.org/10.1103/physrevd.86.064038	NOUN
ap-7659	451	7	https://doi.org/10.1088/1751-8113/46/33/335304	https://doi.org/10.1088/1751-8113/46/33/335304	PROPN
ap-7659	451	8	https://doi.org/10.1016/0003-4916(69)90161-4	https://doi.org/10.1016/0003-4916(69)90161-4	PROPN
ap-7659	451	9	https://doi.org/10.1103/physrevc.95.024315	https://doi.org/10.1103/physrevc.95.024315	NOUN
ap-7659	451	10	https://doi.org/10.1016/j.physleta.2016.01.027	https://doi.org/10.1016/j.physleta.2016.01.027	PROPN
ap-7659	451	11	acta	acta	PROPN
ap-7659	451	12	polytechnica	polytechnica	PROPN
ap-7659	451	13	62(1):157–164	62(1):157–164	NOUN
ap-7659	451	14	,	,	PUNCT
ap-7659	451	15	2022	2022	NUM
ap-7659	451	16	1	1	NUM
ap-7659	451	17	introduction	introduction	NOUN
ap-7659	451	18	2	2	NUM
ap-7659	451	19	formalism	formalism	NOUN
ap-7659	451	20	2.1	2.1	NUM
ap-7659	451	21	eigenfunctions	eigenfunction	NOUN
ap-7659	451	22	and	and	CCONJ
ap-7659	451	23	eigenvectors	eigenvector	NOUN
ap-7659	451	24	2.1.1	2.1.1	NUM
ap-7659	451	25	discrete	discrete	NOUN
ap-7659	451	26	spectrum	spectrum	NOUN
ap-7659	451	27	2.1.2	2.1.2	NUM
ap-7659	451	28	continuous	continuous	ADJ
ap-7659	451	29	spectrum	spectrum	NOUN
ap-7659	451	30	2.1.3	2.1.3	NUM
ap-7659	451	31	particular	particular	ADJ
ap-7659	451	32	cases	case	NOUN
ap-7659	451	33	2.2	2.2	NUM
ap-7659	451	34	mean	mean	ADJ
ap-7659	451	35	values	value	NOUN
ap-7659	451	36	of	of	ADP
ap-7659	451	37	observables	observable	NOUN
ap-7659	451	38	2.3	2.3	NUM
ap-7659	451	39	time	time	NOUN
ap-7659	451	40	dependent	dependent	ADJ
ap-7659	451	41	mean	mean	NOUN
ap-7659	451	42	values	value	NOUN
ap-7659	451	43	2.3.1	2.3.1	NUM
ap-7659	451	44	reigions	reigion	NOUN
ap-7659	452	1	i	i	PRON
ap-7659	452	2	and	and	CCONJ
ap-7659	452	3	iii	iii	NOUN
ap-7659	452	4	:	:	PUNCT
ap-7659	452	5	real	real	ADJ
ap-7659	452	6	spectrum	spectrum	NOUN
ap-7659	452	7	2.3.2	2.3.2	NUM
ap-7659	452	8	region	region	NOUN
ap-7659	452	9	ii	ii	PROPN
ap-7659	452	10	and	and	CCONJ
ap-7659	452	11	iv	iv	NUM
ap-7659	452	12	:	:	PUNCT
ap-7659	452	13	complex	complex	ADJ
ap-7659	452	14	spectrum	spectrum	NOUN
ap-7659	452	15	3	3	NUM
ap-7659	452	16	results	result	NOUN
ap-7659	452	17	and	and	CCONJ
ap-7659	452	18	discussion	discussion	NOUN
ap-7659	452	19	4	4	NUM
ap-7659	452	20	conclusions	conclusion	NOUN
ap-7659	452	21	acknowledgements	acknowledgement	NOUN
ap-7659	452	22	references	reference	NOUN