id	sid	tid	token	lemma	pos
ap-4603	1	1	acta	acta	PROPN
ap-4603	1	2	polytechnica	polytechnica	PROPN
ap-4603	1	3	doi:10.14311	doi:10.14311	PROPN
ap-4603	1	4	/	/	SYM
ap-4603	1	5	ap.2017.57.0385	ap.2017.57.0385	PROPN
ap-4603	1	6	acta	acta	PROPN
ap-4603	1	7	polytechnica	polytechnica	PROPN
ap-4603	1	8	57(6):385–390	57(6):385–390	PROPN
ap-4603	1	9	,	,	PUNCT
ap-4603	1	10	2017	2017	NUM
ap-4603	1	11	©	©	PROPN
ap-4603	1	12	czech	czech	PROPN
ap-4603	1	13	technical	technical	PROPN
ap-4603	1	14	university	university	PROPN
ap-4603	1	15	in	in	ADP
ap-4603	1	16	prague	prague	PROPN
ap-4603	1	17	,	,	PUNCT
ap-4603	1	18	2017	2017	NUM
ap-4603	1	19	available	available	ADJ
ap-4603	1	20	online	online	ADV
ap-4603	1	21	at	at	ADP
ap-4603	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4603	1	23	on	on	ADP
ap-4603	1	24	the	the	DET
ap-4603	1	25	spectrum	spectrum	NOUN
ap-4603	1	26	of	of	ADP
ap-4603	1	27	the	the	DET
ap-4603	1	28	one	one	NUM
ap-4603	1	29	-	-	PUNCT
ap-4603	1	30	dimensional	dimensional	ADJ
ap-4603	1	31	schrödinger	schrödinger	ADJ
ap-4603	1	32	hamiltonian	hamiltonian	NOUN
ap-4603	1	33	perturbed	perturb	VERB
ap-4603	1	34	by	by	ADP
ap-4603	1	35	an	an	DET
ap-4603	1	36	attractive	attractive	ADJ
ap-4603	1	37	gaussian	gaussian	ADJ
ap-4603	1	38	potential	potential	ADJ
ap-4603	1	39	silvestro	silvestro	PROPN
ap-4603	1	40	fassaria	fassaria	PROPN
ap-4603	1	41	,	,	PUNCT
ap-4603	1	42	b	b	NOUN
ap-4603	1	43	,	,	PUNCT
ap-4603	1	44	c,∗	c,∗	PROPN
ap-4603	1	45	,	,	PUNCT
ap-4603	1	46	manuel	manuel	PROPN
ap-4603	1	47	gadellaa	gadellaa	PROPN
ap-4603	1	48	,	,	PUNCT
ap-4603	1	49	luis	luis	PROPN
ap-4603	1	50	miguel	miguel	PROPN
ap-4603	1	51	nietoa	nietoa	PROPN
ap-4603	1	52	,	,	PUNCT
ap-4603	1	53	fabio	fabio	VERB
ap-4603	1	54	rinaldib	rinaldib	ADJ
ap-4603	1	55	,	,	PUNCT
ap-4603	1	56	c	c	PROPN
ap-4603	1	57	a	a	DET
ap-4603	1	58	departamento	departamento	PROPN
ap-4603	1	59	de	de	PROPN
ap-4603	1	60	física	física	PROPN
ap-4603	1	61	teórica	teórica	PROPN
ap-4603	1	62	,	,	PUNCT
ap-4603	1	63	atómica	atómica	PROPN
ap-4603	1	64	y	y	PROPN
ap-4603	1	65	óptica	óptica	PROPN
ap-4603	1	66	,	,	PUNCT
ap-4603	1	67	and	and	CCONJ
ap-4603	1	68	imuva	imuva	PROPN
ap-4603	1	69	,	,	PUNCT
ap-4603	1	70	universidad	universidad	PROPN
ap-4603	1	71	de	de	PROPN
ap-4603	1	72	valladolid	valladolid	PROPN
ap-4603	1	73	,	,	PUNCT
ap-4603	1	74	47011	47011	NUM
ap-4603	1	75	valladolid	valladolid	PROPN
ap-4603	1	76	,	,	PUNCT
ap-4603	1	77	spain	spain	PROPN
ap-4603	1	78	b	b	PROPN
ap-4603	1	79	cerfim	cerfim	PROPN
ap-4603	1	80	,	,	PUNCT
ap-4603	1	81	po	po	PROPN
ap-4603	1	82	box	box	PROPN
ap-4603	1	83	1132	1132	NUM
ap-4603	1	84	,	,	PUNCT
ap-4603	1	85	via	via	ADP
ap-4603	1	86	f.	f.	PROPN
ap-4603	1	87	rusca	rusca	PROPN
ap-4603	1	88	1	1	NUM
ap-4603	1	89	,	,	PUNCT
ap-4603	1	90	ch-6601	ch-6601	PROPN
ap-4603	1	91	locarno	locarno	PROPN
ap-4603	1	92	,	,	PUNCT
ap-4603	1	93	switzerland	switzerland	PROPN
ap-4603	1	94	c	c	SYM
ap-4603	1	95	dipartimento	dipartimento	PROPN
ap-4603	1	96	di	di	PROPN
ap-4603	1	97	fisica	fisica	PROPN
ap-4603	1	98	nucleare	nucleare	PROPN
ap-4603	1	99	,	,	PUNCT
ap-4603	1	100	subnucleare	subnucleare	PROPN
ap-4603	1	101	e	e	X
ap-4603	1	102	delle	delle	NOUN
ap-4603	1	103	radiazioni	radiazioni	PROPN
ap-4603	1	104	,	,	PUNCT
ap-4603	1	105	universitá	universitá	PROPN
ap-4603	1	106	degli	degli	NOUN
ap-4603	1	107	studi	studi	PROPN
ap-4603	1	108	guglielmo	guglielmo	PROPN
ap-4603	1	109	marconi	marconi	PROPN
ap-4603	1	110	,	,	PUNCT
ap-4603	1	111	via	via	ADP
ap-4603	1	112	plinio	plinio	NOUN
ap-4603	1	113	44	44	NUM
ap-4603	1	114	,	,	PUNCT
ap-4603	1	115	i-00193	i-00193	PROPN
ap-4603	1	116	rome	rome	PROPN
ap-4603	1	117	,	,	PUNCT
ap-4603	1	118	italy	italy	PROPN
ap-4603	1	119	∗	∗	VERB
ap-4603	1	120	corresponding	correspond	VERB
ap-4603	1	121	author	author	NOUN
ap-4603	1	122	:	:	PUNCT
ap-4603	1	123	silvestro.fassari@uva.es	silvestro.fassari@uva.es	NOUN
ap-4603	1	124	abstract	abstract	ADJ
ap-4603	1	125	.	.	PUNCT
ap-4603	2	1	we	we	PRON
ap-4603	2	2	propose	propose	VERB
ap-4603	2	3	a	a	DET
ap-4603	2	4	new	new	ADJ
ap-4603	2	5	approach	approach	NOUN
ap-4603	2	6	to	to	ADP
ap-4603	2	7	the	the	DET
ap-4603	2	8	problem	problem	NOUN
ap-4603	2	9	of	of	ADP
ap-4603	2	10	finding	find	VERB
ap-4603	2	11	the	the	DET
ap-4603	2	12	eigenvalues	eigenvalue	NOUN
ap-4603	2	13	(	(	PUNCT
ap-4603	2	14	energy	energy	NOUN
ap-4603	2	15	levels	level	NOUN
ap-4603	2	16	)	)	PUNCT
ap-4603	2	17	in	in	ADP
ap-4603	2	18	the	the	DET
ap-4603	2	19	discrete	discrete	ADJ
ap-4603	2	20	spectrum	spectrum	NOUN
ap-4603	2	21	of	of	ADP
ap-4603	2	22	the	the	DET
ap-4603	2	23	one	one	NUM
ap-4603	2	24	-	-	PUNCT
ap-4603	2	25	dimensional	dimensional	ADJ
ap-4603	2	26	hamiltonian	hamiltonian	ADJ
ap-4603	2	27	h	h	NOUN
ap-4603	2	28	=	=	PUNCT
ap-4603	2	29	−∂2	−∂2	PROPN
ap-4603	2	30	x	x	PUNCT
ap-4603	2	31	−	−	PUNCT
ap-4603	2	32	λe−x	λe−x	NOUN
ap-4603	2	33	2/2	2/2	NUM
ap-4603	2	34	,	,	PUNCT
ap-4603	2	35	by	by	ADP
ap-4603	2	36	using	use	VERB
ap-4603	2	37	essentially	essentially	ADV
ap-4603	2	38	the	the	DET
ap-4603	2	39	well	well	ADV
ap-4603	2	40	-	-	PUNCT
ap-4603	2	41	known	know	VERB
ap-4603	2	42	birman	birman	NOUN
ap-4603	2	43	-	-	PUNCT
ap-4603	2	44	schwinger	schwinger	NOUN
ap-4603	2	45	technique	technique	NOUN
ap-4603	2	46	.	.	PUNCT
ap-4603	3	1	however	however	ADV
ap-4603	3	2	,	,	PUNCT
ap-4603	3	3	in	in	ADP
ap-4603	3	4	place	place	NOUN
ap-4603	3	5	of	of	ADP
ap-4603	3	6	the	the	DET
ap-4603	3	7	birman	birman	NOUN
ap-4603	3	8	-	-	PUNCT
ap-4603	3	9	schwinger	schwinger	NOUN
ap-4603	3	10	integral	integral	ADJ
ap-4603	3	11	operator	operator	NOUN
ap-4603	3	12	we	we	PRON
ap-4603	3	13	consider	consider	VERB
ap-4603	3	14	an	an	DET
ap-4603	3	15	isospectral	isospectral	ADJ
ap-4603	3	16	operator	operator	NOUN
ap-4603	3	17	in	in	ADP
ap-4603	3	18	momentum	momentum	NOUN
ap-4603	3	19	space	space	NOUN
ap-4603	3	20	,	,	PUNCT
ap-4603	3	21	taking	take	VERB
ap-4603	3	22	advantage	advantage	NOUN
ap-4603	3	23	of	of	ADP
ap-4603	3	24	the	the	DET
ap-4603	3	25	unique	unique	ADJ
ap-4603	3	26	feature	feature	NOUN
ap-4603	3	27	of	of	ADP
ap-4603	3	28	this	this	DET
ap-4603	3	29	gaussian	gaussian	ADJ
ap-4603	3	30	potential	potential	NOUN
ap-4603	3	31	,	,	PUNCT
ap-4603	3	32	that	that	PRON
ap-4603	3	33	is	be	AUX
ap-4603	3	34	to	to	PART
ap-4603	3	35	say	say	VERB
ap-4603	3	36	its	its	PRON
ap-4603	3	37	invariance	invariance	NOUN
ap-4603	3	38	under	under	ADP
ap-4603	3	39	fourier	fourier	NOUN
ap-4603	3	40	transform	transform	NOUN
ap-4603	3	41	.	.	PUNCT
ap-4603	4	1	given	give	VERB
ap-4603	4	2	that	that	SCONJ
ap-4603	4	3	such	such	ADJ
ap-4603	4	4	integral	integral	ADJ
ap-4603	4	5	operators	operator	NOUN
ap-4603	4	6	are	be	AUX
ap-4603	4	7	trace	trace	NOUN
ap-4603	4	8	class	class	NOUN
ap-4603	4	9	,	,	PUNCT
ap-4603	4	10	it	it	PRON
ap-4603	4	11	is	be	AUX
ap-4603	4	12	possible	possible	ADJ
ap-4603	4	13	to	to	PART
ap-4603	4	14	determine	determine	VERB
ap-4603	4	15	the	the	DET
ap-4603	4	16	energy	energy	NOUN
ap-4603	4	17	levels	level	NOUN
ap-4603	4	18	in	in	ADP
ap-4603	4	19	the	the	DET
ap-4603	4	20	discrete	discrete	ADJ
ap-4603	4	21	spectrum	spectrum	NOUN
ap-4603	4	22	of	of	ADP
ap-4603	4	23	the	the	DET
ap-4603	4	24	hamiltonian	hamiltonian	NOUN
ap-4603	4	25	as	as	ADP
ap-4603	4	26	functions	function	NOUN
ap-4603	4	27	of	of	ADP
ap-4603	4	28	λ	λ	PROPN
ap-4603	4	29	with	with	ADP
ap-4603	4	30	great	great	ADJ
ap-4603	4	31	accuracy	accuracy	NOUN
ap-4603	4	32	by	by	ADP
ap-4603	4	33	solving	solve	VERB
ap-4603	4	34	a	a	DET
ap-4603	4	35	finite	finite	ADJ
ap-4603	4	36	number	number	NOUN
ap-4603	4	37	of	of	ADP
ap-4603	4	38	transcendental	transcendental	ADJ
ap-4603	4	39	equations	equation	NOUN
ap-4603	4	40	.	.	PUNCT
ap-4603	5	1	we	we	PRON
ap-4603	5	2	also	also	ADV
ap-4603	5	3	address	address	VERB
ap-4603	5	4	the	the	DET
ap-4603	5	5	important	important	ADJ
ap-4603	5	6	issue	issue	NOUN
ap-4603	5	7	of	of	ADP
ap-4603	5	8	the	the	DET
ap-4603	5	9	coupling	couple	VERB
ap-4603	5	10	constant	constant	ADJ
ap-4603	5	11	thresholds	threshold	NOUN
ap-4603	5	12	of	of	ADP
ap-4603	5	13	the	the	DET
ap-4603	5	14	hamiltonian	hamiltonian	NOUN
ap-4603	5	15	,	,	PUNCT
ap-4603	5	16	that	that	PRON
ap-4603	5	17	is	be	AUX
ap-4603	5	18	to	to	PART
ap-4603	5	19	say	say	VERB
ap-4603	5	20	the	the	DET
ap-4603	5	21	critical	critical	ADJ
ap-4603	5	22	values	value	NOUN
ap-4603	5	23	of	of	ADP
ap-4603	5	24	λ	λ	PROPN
ap-4603	5	25	for	for	ADP
ap-4603	5	26	which	which	PRON
ap-4603	5	27	we	we	PRON
ap-4603	5	28	have	have	VERB
ap-4603	5	29	the	the	DET
ap-4603	5	30	emergence	emergence	NOUN
ap-4603	5	31	of	of	ADP
ap-4603	5	32	an	an	DET
ap-4603	5	33	additional	additional	ADJ
ap-4603	5	34	bound	bind	VERB
ap-4603	5	35	state	state	NOUN
ap-4603	5	36	out	out	ADP
ap-4603	5	37	of	of	ADP
ap-4603	5	38	the	the	DET
ap-4603	5	39	absolutely	absolutely	ADV
ap-4603	5	40	continuous	continuous	ADJ
ap-4603	5	41	spectrum	spectrum	NOUN
ap-4603	5	42	.	.	PUNCT
ap-4603	6	1	keywords	keyword	NOUN
ap-4603	6	2	:	:	PUNCT
ap-4603	6	3	schrödinger	schrödinger	ADJ
ap-4603	6	4	equation	equation	NOUN
ap-4603	6	5	;	;	PUNCT
ap-4603	6	6	gaussian	gaussian	ADJ
ap-4603	6	7	potential	potential	NOUN
ap-4603	6	8	;	;	PUNCT
ap-4603	6	9	birman	birman	NOUN
ap-4603	6	10	-	-	PUNCT
ap-4603	6	11	schwinger	schwinger	NOUN
ap-4603	6	12	method	method	NOUN
ap-4603	6	13	;	;	PUNCT
ap-4603	6	14	trace	trace	NOUN
ap-4603	6	15	class	class	NOUN
ap-4603	6	16	operators	operator	NOUN
ap-4603	6	17	;	;	PUNCT
ap-4603	6	18	fredholm	fredholm	NOUN
ap-4603	6	19	determinant	determinant	ADJ
ap-4603	6	20	.	.	PUNCT
ap-4603	7	1	1	1	X
ap-4603	7	2	.	.	X
ap-4603	7	3	introduction	introduction	NOUN
ap-4603	7	4	given	give	VERB
ap-4603	7	5	its	its	PRON
ap-4603	7	6	increasing	increase	VERB
ap-4603	7	7	relevance	relevance	NOUN
ap-4603	7	8	in	in	ADP
ap-4603	7	9	the	the	DET
ap-4603	7	10	field	field	NOUN
ap-4603	7	11	of	of	ADP
ap-4603	7	12	nanophysics	nanophysic	NOUN
ap-4603	7	13	,	,	PUNCT
ap-4603	7	14	it	it	PRON
ap-4603	7	15	is	be	AUX
ap-4603	7	16	particularly	particularly	ADV
ap-4603	7	17	interesting	interesting	ADJ
ap-4603	7	18	to	to	PART
ap-4603	7	19	investigate	investigate	VERB
ap-4603	7	20	the	the	DET
ap-4603	7	21	schrödinger	schrödinger	ADJ
ap-4603	7	22	hamiltonian	hamiltonian	NOUN
ap-4603	7	23	with	with	ADP
ap-4603	7	24	an	an	DET
ap-4603	7	25	attractive	attractive	ADJ
ap-4603	7	26	gaussian	gaussian	ADJ
ap-4603	7	27	potential	potential	NOUN
ap-4603	7	28	v	v	X
ap-4603	7	29	=	=	SYM
ap-4603	7	30	−λe−x2/2	−λe−x2/2	PROPN
ap-4603	7	31	,	,	PUNCT
ap-4603	7	32	since	since	SCONJ
ap-4603	7	33	the	the	DET
ap-4603	7	34	latter	latter	NOUN
ap-4603	7	35	has	have	VERB
ap-4603	7	36	the	the	DET
ap-4603	7	37	typical	typical	ADJ
ap-4603	7	38	properties	property	NOUN
ap-4603	7	39	of	of	ADP
ap-4603	7	40	short	short	ADJ
ap-4603	7	41	-	-	PUNCT
ap-4603	7	42	range	range	NOUN
ap-4603	7	43	potentials	potential	NOUN
ap-4603	7	44	,	,	PUNCT
ap-4603	7	45	which	which	PRON
ap-4603	7	46	implies	imply	VERB
ap-4603	7	47	the	the	DET
ap-4603	7	48	existence	existence	NOUN
ap-4603	7	49	of	of	ADP
ap-4603	7	50	bound	bind	VERB
ap-4603	7	51	states	state	NOUN
ap-4603	7	52	with	with	ADP
ap-4603	7	53	negative	negative	ADJ
ap-4603	7	54	energies	energy	NOUN
ap-4603	7	55	below	below	ADP
ap-4603	7	56	the	the	DET
ap-4603	7	57	absolutely	absolutely	ADV
ap-4603	7	58	continuous	continuous	ADJ
ap-4603	7	59	spectrum	spectrum	NOUN
ap-4603	7	60	given	give	VERB
ap-4603	7	61	by	by	ADP
ap-4603	7	62	the	the	DET
ap-4603	7	63	semibounded	semibounde	VERB
ap-4603	7	64	interval	interval	NOUN
ap-4603	7	65	[	[	X
ap-4603	7	66	0,+∞	0,+∞	NUM
ap-4603	7	67	)	)	PUNCT
ap-4603	7	68	,	,	PUNCT
ap-4603	7	69	but	but	CCONJ
ap-4603	7	70	also	also	ADV
ap-4603	7	71	those	those	PRON
ap-4603	7	72	of	of	ADP
ap-4603	7	73	the	the	DET
ap-4603	7	74	harmonic	harmonic	ADJ
ap-4603	7	75	oscillator	oscillator	NOUN
ap-4603	7	76	near	near	ADP
ap-4603	7	77	the	the	DET
ap-4603	7	78	bottom	bottom	NOUN
ap-4603	7	79	of	of	ADP
ap-4603	7	80	the	the	DET
ap-4603	7	81	well	well	NOUN
ap-4603	7	82	.	.	PUNCT
ap-4603	8	1	hence	hence	ADV
ap-4603	8	2	,	,	PUNCT
ap-4603	8	3	the	the	DET
ap-4603	8	4	original	original	ADJ
ap-4603	8	5	schrödinger	schrödinger	ADJ
ap-4603	8	6	eigenvalue	eigenvalue	NOUN
ap-4603	8	7	problem	problem	NOUN
ap-4603	8	8	we	we	PRON
ap-4603	8	9	are	be	AUX
ap-4603	8	10	going	go	VERB
ap-4603	8	11	to	to	PART
ap-4603	8	12	consider	consider	VERB
ap-4603	8	13	is	be	AUX
ap-4603	8	14	(	(	PUNCT
ap-4603	8	15	−	−	PROPN
ap-4603	8	16	d2	d2	PROPN
ap-4603	8	17	dx2	dx2	PROPN
ap-4603	8	18	−	−	PROPN
ap-4603	8	19	λe	λe	ADP
ap-4603	8	20	−x2/2	−x2/2	ADJ
ap-4603	8	21	)	)	PUNCT
ap-4603	9	1	ψ	ψ	NOUN
ap-4603	9	2	=	=	SYM
ap-4603	9	3	−ε2ψ	−ε2ψ	PROPN
ap-4603	9	4	,	,	PUNCT
ap-4603	9	5	ε	ε	PROPN
ap-4603	9	6	>	>	X
ap-4603	9	7	0	0	PUNCT
ap-4603	10	1	(	(	PUNCT
ap-4603	10	2	1	1	NUM
ap-4603	10	3	)	)	PUNCT
ap-4603	10	4	although	although	SCONJ
ap-4603	10	5	there	there	PRON
ap-4603	10	6	have	have	AUX
ap-4603	10	7	been	be	AUX
ap-4603	10	8	quite	quite	DET
ap-4603	10	9	a	a	DET
ap-4603	10	10	few	few	ADJ
ap-4603	10	11	papers	paper	NOUN
ap-4603	10	12	on	on	ADP
ap-4603	10	13	this	this	DET
ap-4603	10	14	model	model	NOUN
ap-4603	10	15	,	,	PUNCT
ap-4603	10	16	the	the	DET
ap-4603	10	17	most	most	ADV
ap-4603	10	18	rigorous	rigorous	ADJ
ap-4603	10	19	of	of	ADP
ap-4603	10	20	which	which	PRON
ap-4603	10	21	being	be	AUX
ap-4603	10	22	[	[	X
ap-4603	10	23	1	1	NUM
ap-4603	10	24	]	]	PUNCT
ap-4603	10	25	by	by	ADP
ap-4603	10	26	f.	f.	PROPN
ap-4603	10	27	m.	m.	PROPN
ap-4603	10	28	fernández	fernández	PROPN
ap-4603	10	29	(	(	PUNCT
ap-4603	10	30	see	see	VERB
ap-4603	10	31	also	also	ADV
ap-4603	10	32	[	[	X
ap-4603	10	33	2	2	NUM
ap-4603	10	34	,	,	PUNCT
ap-4603	10	35	3	3	NUM
ap-4603	10	36	]	]	NUM
ap-4603	10	37	)	)	PUNCT
ap-4603	10	38	,	,	PUNCT
ap-4603	10	39	it	it	PRON
ap-4603	10	40	seems	seem	VERB
ap-4603	10	41	that	that	SCONJ
ap-4603	10	42	the	the	DET
ap-4603	10	43	implications	implication	NOUN
ap-4603	10	44	of	of	ADP
ap-4603	10	45	a	a	DET
ap-4603	10	46	remarkable	remarkable	ADJ
ap-4603	10	47	feature	feature	NOUN
ap-4603	10	48	of	of	ADP
ap-4603	10	49	this	this	DET
ap-4603	10	50	potential	potential	NOUN
ap-4603	10	51	,	,	PUNCT
ap-4603	10	52	namely	namely	ADV
ap-4603	10	53	its	its	PRON
ap-4603	10	54	invariance	invariance	NOUN
ap-4603	10	55	with	with	ADP
ap-4603	10	56	respect	respect	NOUN
ap-4603	10	57	to	to	ADP
ap-4603	10	58	the	the	DET
ap-4603	10	59	fourier	fourier	NOUN
ap-4603	10	60	transform	transform	NOUN
ap-4603	10	61	,	,	PUNCT
ap-4603	10	62	have	have	AUX
ap-4603	10	63	been	be	AUX
ap-4603	10	64	missed	miss	VERB
ap-4603	10	65	.	.	PUNCT
ap-4603	11	1	our	our	PRON
ap-4603	11	2	method	method	NOUN
ap-4603	11	3	,	,	PUNCT
ap-4603	11	4	whilst	whilst	SCONJ
ap-4603	11	5	being	be	AUX
ap-4603	11	6	essentially	essentially	ADV
ap-4603	11	7	based	base	VERB
ap-4603	11	8	on	on	ADP
ap-4603	11	9	the	the	PRON
ap-4603	11	10	(	(	PUNCT
ap-4603	11	11	by	by	ADP
ap-4603	11	12	now	now	ADV
ap-4603	11	13	)	)	PUNCT
ap-4603	11	14	classical	classical	ADJ
ap-4603	11	15	birman	birman	NOUN
ap-4603	11	16	-	-	PUNCT
ap-4603	11	17	schwinger	schwinger	NOUN
ap-4603	11	18	method	method	NOUN
ap-4603	11	19	(	(	PUNCT
ap-4603	11	20	see	see	VERB
ap-4603	11	21	,	,	PUNCT
ap-4603	11	22	e.g.	e.g.	ADV
ap-4603	11	23	,	,	PUNCT
ap-4603	11	24	[	[	X
ap-4603	11	25	4	4	NUM
ap-4603	11	26	,	,	PUNCT
ap-4603	11	27	5	5	NUM
ap-4603	11	28	]	]	NUM
ap-4603	11	29	)	)	PUNCT
ap-4603	11	30	,	,	PUNCT
ap-4603	11	31	considers	consider	VERB
ap-4603	11	32	instead	instead	ADV
ap-4603	11	33	of	of	ADP
ap-4603	11	34	the	the	DET
ap-4603	11	35	integral	integral	ADJ
ap-4603	11	36	operator	operator	NOUN
ap-4603	11	37	associated	associate	VERB
ap-4603	11	38	to	to	ADP
ap-4603	11	39	(	(	PUNCT
ap-4603	11	40	1	1	X
ap-4603	11	41	)	)	PUNCT
ap-4603	11	42	λe−x	λe−x	NOUN
ap-4603	11	43	2/4	2/4	NUM
ap-4603	11	44	(	(	PUNCT
ap-4603	11	45	−	−	PROPN
ap-4603	11	46	d2	d2	PROPN
ap-4603	11	47	dx2	dx2	PROPN
ap-4603	11	48	+	+	CCONJ
ap-4603	11	49	ε2	ε2	ADJ
ap-4603	11	50	)	)	PUNCT
ap-4603	11	51	−1	−1	NOUN
ap-4603	11	52	e−x	e−x	PROPN
ap-4603	11	53	2/4	2/4	NUM
ap-4603	11	54	,	,	PUNCT
ap-4603	11	55	(	(	PUNCT
ap-4603	11	56	2	2	X
ap-4603	11	57	)	)	PUNCT
ap-4603	11	58	another	another	DET
ap-4603	11	59	integral	integral	ADJ
ap-4603	11	60	operator	operator	NOUN
ap-4603	11	61	which	which	PRON
ap-4603	11	62	is	be	AUX
ap-4603	11	63	isospectral	isospectral	ADJ
ap-4603	11	64	to	to	ADP
ap-4603	11	65	the	the	DET
ap-4603	11	66	birman	birman	NOUN
ap-4603	11	67	-	-	PUNCT
ap-4603	11	68	schwinger	schwinger	NOUN
ap-4603	11	69	one	one	NOUN
ap-4603	11	70	given	give	VERB
ap-4603	11	71	in	in	ADP
ap-4603	11	72	(	(	PUNCT
ap-4603	11	73	2	2	NUM
ap-4603	11	74	)	)	PUNCT
ap-4603	11	75	(	(	PUNCT
ap-4603	11	76	see	see	VERB
ap-4603	11	77	[	[	X
ap-4603	11	78	6–8	6–8	NOUN
ap-4603	11	79	]	]	X
ap-4603	11	80	):	):	PUNCT
ap-4603	12	1	λbε	λbε	PROPN
ap-4603	12	2	=	=	SYM
ap-4603	12	3	λ	λ	PROPN
ap-4603	12	4	(	(	PUNCT
ap-4603	12	5	−	−	PROPN
ap-4603	12	6	d2	d2	PROPN
ap-4603	12	7	dx2	dx2	PROPN
ap-4603	12	8	+	+	CCONJ
ap-4603	12	9	ε2	ε2	ADJ
ap-4603	12	10	)	)	PUNCT
ap-4603	12	11	−1/2	−1/2	VERB
ap-4603	12	12	e−x	e−x	PROPN
ap-4603	12	13	2/2	2/2	NUM
ap-4603	12	14	(	(	PUNCT
ap-4603	12	15	−	−	PROPN
ap-4603	12	16	d2	d2	PROPN
ap-4603	12	17	dx2	dx2	PROPN
ap-4603	12	18	+	+	CCONJ
ap-4603	12	19	ε2	ε2	ADJ
ap-4603	12	20	)	)	PUNCT
ap-4603	12	21	−1/2	−1/2	ADJ
ap-4603	12	22	.	.	PUNCT
ap-4603	13	1	(	(	PUNCT
ap-4603	13	2	3	3	X
ap-4603	13	3	)	)	PUNCT
ap-4603	13	4	given	give	VERB
ap-4603	13	5	that	that	SCONJ
ap-4603	13	6	the	the	DET
ap-4603	13	7	function	function	NOUN
ap-4603	13	8	e−x2/2	e−x2/2	PROPN
ap-4603	13	9	is	be	AUX
ap-4603	13	10	invariant	invariant	ADJ
ap-4603	13	11	under	under	ADP
ap-4603	13	12	the	the	DET
ap-4603	13	13	fourier	fourier	NOUN
ap-4603	13	14	transform	transform	NOUN
ap-4603	13	15	,	,	PUNCT
ap-4603	13	16	the	the	DET
ap-4603	13	17	unitary	unitary	ADJ
ap-4603	13	18	equivalent	equivalent	NOUN
ap-4603	13	19	of	of	ADP
ap-4603	13	20	the	the	DET
ap-4603	13	21	above	above	ADJ
ap-4603	13	22	integral	integral	ADJ
ap-4603	13	23	operator	operator	NOUN
ap-4603	13	24	,	,	PUNCT
ap-4603	13	25	still	still	ADV
ap-4603	13	26	denoted	denote	VERB
ap-4603	13	27	by	by	ADP
ap-4603	13	28	bε	bε	NOUN
ap-4603	13	29	,	,	PUNCT
ap-4603	13	30	is	be	AUX
ap-4603	13	31	bε	bε	ADJ
ap-4603	13	32	=	=	SYM
ap-4603	13	33	1√	1√	NUM
ap-4603	13	34	2π	2π	NOUN
ap-4603	13	35	(	(	PUNCT
ap-4603	13	36	p2	p2	X
ap-4603	13	37	+	+	CCONJ
ap-4603	13	38	ε2	ε2	ADJ
ap-4603	13	39	)	)	PUNCT
ap-4603	13	40	−1/2	−1/2	PROPN
ap-4603	13	41	e−p	e−p	NOUN
ap-4603	13	42	2/2	2/2	NUM
ap-4603	13	43	∗	∗	NOUN
ap-4603	13	44	(	(	PUNCT
ap-4603	13	45	p2	p2	X
ap-4603	13	46	+	+	CCONJ
ap-4603	13	47	ε2	ε2	ADJ
ap-4603	13	48	)	)	PUNCT
ap-4603	13	49	−1/2	−1/2	ADJ
ap-4603	13	50	,	,	PUNCT
ap-4603	13	51	(	(	PUNCT
ap-4603	13	52	4	4	NUM
ap-4603	13	53	)	)	PUNCT
ap-4603	13	54	385	385	NUM
ap-4603	13	55	http://dx.doi.org/10.14311/ap.2017.57.0385	http://dx.doi.org/10.14311/ap.2017.57.0385	NOUN
ap-4603	14	1	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-4603	14	2	s.	s.	PROPN
ap-4603	14	3	fassari	fassari	PROPN
ap-4603	14	4	,	,	PUNCT
ap-4603	14	5	m.	m.	NOUN
ap-4603	14	6	gadella	gadella	PROPN
ap-4603	14	7	,	,	PUNCT
ap-4603	14	8	l.	l.	PROPN
ap-4603	14	9	m.	m.	PROPN
ap-4603	14	10	nieto	nieto	PROPN
ap-4603	14	11	,	,	PUNCT
ap-4603	14	12	f.	f.	PROPN
ap-4603	14	13	rinaldi	rinaldi	PROPN
ap-4603	14	14	acta	acta	PROPN
ap-4603	14	15	polytechnica	polytechnica	PROPN
ap-4603	14	16	where	where	SCONJ
ap-4603	14	17	the	the	DET
ap-4603	14	18	star	star	NOUN
ap-4603	14	19	denotes	denote	VERB
ap-4603	14	20	the	the	DET
ap-4603	14	21	convolution	convolution	NOUN
ap-4603	14	22	.	.	PUNCT
ap-4603	15	1	therefore	therefore	ADV
ap-4603	15	2	,	,	PUNCT
ap-4603	15	3	the	the	DET
ap-4603	15	4	schrödinger	schrödinger	ADJ
ap-4603	15	5	equation	equation	NOUN
ap-4603	15	6	(	(	PUNCT
ap-4603	15	7	1	1	X
ap-4603	15	8	)	)	PUNCT
ap-4603	15	9	can	can	AUX
ap-4603	15	10	be	be	AUX
ap-4603	15	11	reformulated	reformulate	VERB
ap-4603	15	12	in	in	ADP
ap-4603	15	13	terms	term	NOUN
ap-4603	15	14	of	of	ADP
ap-4603	15	15	the	the	DET
ap-4603	15	16	following	follow	VERB
ap-4603	15	17	integral	integral	ADJ
ap-4603	15	18	equation	equation	NOUN
ap-4603	15	19	:	:	PUNCT
ap-4603	15	20	χ(p	χ(p	X
ap-4603	15	21	)	)	PUNCT
ap-4603	16	1	=	=	SYM
ap-4603	16	2	1√	1√	NUM
ap-4603	16	3	2π	2π	NOUN
ap-4603	16	4	(	(	PUNCT
ap-4603	16	5	p2	p2	X
ap-4603	16	6	+	+	CCONJ
ap-4603	16	7	ε2	ε2	ADJ
ap-4603	16	8	)	)	PUNCT
ap-4603	16	9	−1/2	−1/2	ADJ
ap-4603	16	10	∫	∫	PROPN
ap-4603	17	1	+	+	X
ap-4603	17	2	∞	∞	PROPN
ap-4603	17	3	−∞	−∞	ADP
ap-4603	17	4	e−(p−q)2/2(q2	e−(p−q)2/2(q2	PROPN
ap-4603	17	5	+	+	CCONJ
ap-4603	17	6	ε2	ε2	ADJ
ap-4603	17	7	)	)	PUNCT
ap-4603	17	8	−1/2	−1/2	PROPN
ap-4603	17	9	χ(q	χ(q	PROPN
ap-4603	17	10	)	)	PUNCT
ap-4603	17	11	dq	dq	PROPN
ap-4603	17	12	,	,	PUNCT
ap-4603	17	13	(	(	PUNCT
ap-4603	17	14	5	5	NUM
ap-4603	17	15	)	)	PUNCT
ap-4603	17	16	with	with	ADP
ap-4603	17	17	ψ̂(p	ψ̂(p	NOUN
ap-4603	17	18	)	)	PUNCT
ap-4603	17	19	=	=	PUNCT
ap-4603	17	20	(	(	PUNCT
ap-4603	17	21	p2	p2	PROPN
ap-4603	17	22	+	+	CCONJ
ap-4603	17	23	ε2)−1/2χ(p	ε2)−1/2χ(p	NUM
ap-4603	17	24	)	)	PUNCT
ap-4603	17	25	,	,	PUNCT
ap-4603	17	26	in	in	ADP
ap-4603	17	27	the	the	DET
ap-4603	17	28	sense	sense	NOUN
ap-4603	17	29	that	that	SCONJ
ap-4603	17	30	if	if	SCONJ
ap-4603	17	31	ε	ε	PROPN
ap-4603	17	32	is	be	AUX
ap-4603	17	33	a	a	DET
ap-4603	17	34	value	value	NOUN
ap-4603	17	35	for	for	ADP
ap-4603	17	36	which	which	PRON
ap-4603	17	37	the	the	DET
ap-4603	17	38	above	above	ADJ
ap-4603	17	39	integral	integral	ADJ
ap-4603	17	40	operator	operator	NOUN
ap-4603	17	41	has	have	VERB
ap-4603	17	42	an	an	DET
ap-4603	17	43	eigenvalue	eigenvalue	NOUN
ap-4603	17	44	equal	equal	ADJ
ap-4603	17	45	to	to	ADP
ap-4603	17	46	one	one	NUM
ap-4603	17	47	,	,	PUNCT
ap-4603	17	48	then	then	ADV
ap-4603	17	49	−ε2	−ε2	PROPN
ap-4603	17	50	is	be	AUX
ap-4603	17	51	an	an	DET
ap-4603	17	52	eigenvalue	eigenvalue	NOUN
ap-4603	17	53	of	of	ADP
ap-4603	17	54	the	the	DET
ap-4603	17	55	original	original	ADJ
ap-4603	17	56	schrödinger	schrödinger	ADJ
ap-4603	17	57	equation	equation	NOUN
ap-4603	17	58	.	.	PUNCT
ap-4603	18	1	as	as	ADP
ap-4603	18	2	a	a	DET
ap-4603	18	3	consequence	consequence	NOUN
ap-4603	18	4	,	,	PUNCT
ap-4603	18	5	understanding	understanding	NOUN
ap-4603	18	6	in	in	ADP
ap-4603	18	7	depth	depth	NOUN
ap-4603	18	8	the	the	DET
ap-4603	18	9	properties	property	NOUN
ap-4603	18	10	of	of	ADP
ap-4603	18	11	the	the	DET
ap-4603	18	12	integral	integral	ADJ
ap-4603	18	13	operator	operator	NOUN
ap-4603	18	14	is	be	AUX
ap-4603	18	15	crucial	crucial	ADJ
ap-4603	18	16	in	in	ADP
ap-4603	18	17	order	order	NOUN
ap-4603	18	18	to	to	PART
ap-4603	18	19	get	get	VERB
ap-4603	18	20	a	a	DET
ap-4603	18	21	detailed	detailed	ADJ
ap-4603	18	22	description	description	NOUN
ap-4603	18	23	of	of	ADP
ap-4603	18	24	the	the	DET
ap-4603	18	25	discrete	discrete	ADJ
ap-4603	18	26	spectrum	spectrum	NOUN
ap-4603	18	27	of	of	ADP
ap-4603	18	28	the	the	DET
ap-4603	18	29	original	original	ADJ
ap-4603	18	30	hamiltonian	hamiltonian	NOUN
ap-4603	18	31	.	.	PUNCT
ap-4603	19	1	2	2	X
ap-4603	19	2	.	.	X
ap-4603	19	3	the	the	DET
ap-4603	19	4	integral	integral	ADJ
ap-4603	19	5	operator	operator	NOUN
ap-4603	19	6	bε	bε	NOUN
ap-4603	19	7	we	we	PRON
ap-4603	19	8	wish	wish	VERB
ap-4603	19	9	to	to	PART
ap-4603	19	10	open	open	VERB
ap-4603	19	11	this	this	DET
ap-4603	19	12	section	section	NOUN
ap-4603	19	13	by	by	ADP
ap-4603	19	14	stating	state	VERB
ap-4603	19	15	and	and	CCONJ
ap-4603	19	16	proving	prove	VERB
ap-4603	19	17	the	the	DET
ap-4603	19	18	key	key	ADJ
ap-4603	19	19	property	property	NOUN
ap-4603	19	20	of	of	ADP
ap-4603	19	21	the	the	DET
ap-4603	19	22	integral	integral	ADJ
ap-4603	19	23	operator	operator	NOUN
ap-4603	19	24	bε	bε	NOUN
ap-4603	19	25	.	.	PUNCT
ap-4603	20	1	theorem	theorem	VERB
ap-4603	20	2	2.1	2.1	NUM
ap-4603	20	3	.	.	PUNCT
ap-4603	21	1	the	the	DET
ap-4603	21	2	integral	integral	ADJ
ap-4603	21	3	operator	operator	NOUN
ap-4603	21	4	bε	bε	NOUN
ap-4603	21	5	is	be	AUX
ap-4603	21	6	trace	trace	NOUN
ap-4603	21	7	class	class	NOUN
ap-4603	21	8	.	.	PUNCT
ap-4603	22	1	proof	proof	NOUN
ap-4603	22	2	.	.	PUNCT
ap-4603	23	1	as	as	ADP
ap-4603	23	2	a	a	DET
ap-4603	23	3	consequence	consequence	NOUN
ap-4603	23	4	of	of	ADP
ap-4603	23	5	a	a	DET
ap-4603	23	6	well	well	ADV
ap-4603	23	7	-	-	PUNCT
ap-4603	23	8	known	know	VERB
ap-4603	23	9	theorem	theorem	NOUN
ap-4603	23	10	(	(	PUNCT
ap-4603	23	11	see	see	VERB
ap-4603	23	12	[	[	X
ap-4603	23	13	9	9	NUM
ap-4603	23	14	]	]	NUM
ap-4603	23	15	)	)	PUNCT
ap-4603	23	16	,	,	PUNCT
ap-4603	23	17	given	give	VERB
ap-4603	23	18	the	the	DET
ap-4603	23	19	positivity	positivity	NOUN
ap-4603	23	20	of	of	ADP
ap-4603	23	21	the	the	DET
ap-4603	23	22	integral	integral	ADJ
ap-4603	23	23	kernel	kernel	NOUN
ap-4603	23	24	and	and	CCONJ
ap-4603	23	25	its	its	PRON
ap-4603	23	26	smoothness	smoothness	NOUN
ap-4603	23	27	,	,	PUNCT
ap-4603	23	28	the	the	DET
ap-4603	23	29	trace	trace	NOUN
ap-4603	23	30	is	be	AUX
ap-4603	23	31	simply	simply	ADV
ap-4603	23	32	given	give	VERB
ap-4603	23	33	by	by	ADP
ap-4603	23	34	the	the	DET
ap-4603	23	35	integral	integral	NOUN
ap-4603	23	36	of	of	ADP
ap-4603	23	37	the	the	DET
ap-4603	23	38	kernel	kernel	NOUN
ap-4603	23	39	evaluated	evaluate	VERB
ap-4603	23	40	along	along	ADP
ap-4603	23	41	the	the	DET
ap-4603	23	42	diagonal	diagonal	ADJ
ap-4603	23	43	p	p	NOUN
ap-4603	23	44	=	=	ADJ
ap-4603	23	45	q	q	NOUN
ap-4603	23	46	,	,	PUNCT
ap-4603	23	47	that	that	PRON
ap-4603	23	48	is	be	AUX
ap-4603	23	49	to	to	PART
ap-4603	23	50	say	say	VERB
ap-4603	23	51	:	:	PUNCT
ap-4603	23	52	1√	1√	ADJ
ap-4603	23	53	2π	2π	NUM
ap-4603	23	54	∫	∫	PROPN
ap-4603	24	1	+	+	X
ap-4603	24	2	∞	∞	PROPN
ap-4603	24	3	−∞	−∞	ADP
ap-4603	24	4	dp	dp	NOUN
ap-4603	24	5	p2	p2	NOUN
ap-4603	24	6	+	+	CCONJ
ap-4603	24	7	ε2	ε2	ADJ
ap-4603	24	8	=	=	PUNCT
ap-4603	24	9	√	√	NUM
ap-4603	24	10	π	π	SYM
ap-4603	24	11	2	2	NUM
ap-4603	24	12	1	1	NUM
ap-4603	24	13	ε	ε	NOUN
ap-4603	24	14	.	.	PUNCT
ap-4603	25	1	(	(	PUNCT
ap-4603	25	2	6	6	X
ap-4603	25	3	)	)	PUNCT
ap-4603	25	4	the	the	DET
ap-4603	25	5	fact	fact	NOUN
ap-4603	25	6	that	that	SCONJ
ap-4603	25	7	the	the	DET
ap-4603	25	8	trace	trace	NOUN
ap-4603	25	9	diverges	diverge	VERB
ap-4603	25	10	as	as	ADP
ap-4603	25	11	ε→	ε→	NUM
ap-4603	25	12	0	0	NUM
ap-4603	25	13	+	+	ADJ
ap-4603	25	14	,	,	PUNCT
ap-4603	25	15	guarantees	guarantee	VERB
ap-4603	25	16	that	that	SCONJ
ap-4603	25	17	there	there	PRON
ap-4603	25	18	is	be	VERB
ap-4603	25	19	always	always	ADV
ap-4603	25	20	at	at	ADV
ap-4603	25	21	least	least	ADJ
ap-4603	25	22	one	one	NUM
ap-4603	25	23	bound	bind	VERB
ap-4603	25	24	state	state	NOUN
ap-4603	25	25	even	even	ADV
ap-4603	25	26	for	for	ADP
ap-4603	25	27	very	very	ADV
ap-4603	25	28	small	small	ADJ
ap-4603	25	29	values	value	NOUN
ap-4603	25	30	of	of	ADP
ap-4603	25	31	the	the	DET
ap-4603	25	32	coupling	coupling	NOUN
ap-4603	25	33	constant	constant	ADJ
ap-4603	25	34	(	(	PUNCT
ap-4603	25	35	shallow	shallow	ADJ
ap-4603	25	36	wells	well	NOUN
ap-4603	25	37	)	)	PUNCT
ap-4603	25	38	.	.	PUNCT
ap-4603	26	1	we	we	PRON
ap-4603	26	2	take	take	VERB
ap-4603	26	3	this	this	DET
ap-4603	26	4	opportunity	opportunity	NOUN
ap-4603	26	5	to	to	PART
ap-4603	26	6	remind	remind	VERB
ap-4603	26	7	the	the	DET
ap-4603	26	8	reader	reader	NOUN
ap-4603	26	9	that	that	SCONJ
ap-4603	26	10	the	the	DET
ap-4603	26	11	latter	latter	ADJ
ap-4603	26	12	property	property	NOUN
ap-4603	26	13	is	be	AUX
ap-4603	26	14	typical	typical	ADJ
ap-4603	26	15	of	of	ADP
ap-4603	26	16	one	one	NUM
ap-4603	26	17	-	-	PUNCT
ap-4603	26	18	dimensional	dimensional	ADJ
ap-4603	26	19	quantum	quantum	ADJ
ap-4603	26	20	hamiltonians	hamiltonian	NOUN
ap-4603	26	21	,	,	PUNCT
ap-4603	26	22	as	as	SCONJ
ap-4603	26	23	shown	show	VERB
ap-4603	26	24	in	in	ADP
ap-4603	26	25	[	[	X
ap-4603	26	26	5	5	NUM
ap-4603	26	27	,	,	PUNCT
ap-4603	26	28	10	10	NUM
ap-4603	26	29	]	]	PUNCT
ap-4603	26	30	.	.	PUNCT
ap-4603	27	1	we	we	PRON
ap-4603	27	2	also	also	ADV
ap-4603	27	3	notice	notice	VERB
ap-4603	27	4	that	that	SCONJ
ap-4603	27	5	,	,	PUNCT
ap-4603	27	6	by	by	ADP
ap-4603	27	7	expanding	expand	VERB
ap-4603	27	8	the	the	DET
ap-4603	27	9	square	square	NOUN
ap-4603	27	10	in	in	ADP
ap-4603	27	11	the	the	DET
ap-4603	27	12	exponent	exponent	NOUN
ap-4603	27	13	of	of	ADP
ap-4603	27	14	the	the	DET
ap-4603	27	15	gaussian	gaussian	NOUN
ap-4603	27	16	in	in	ADP
ap-4603	27	17	(	(	PUNCT
ap-4603	27	18	5	5	NUM
ap-4603	27	19	)	)	PUNCT
ap-4603	27	20	,	,	PUNCT
ap-4603	27	21	the	the	DET
ap-4603	27	22	integral	integral	ADJ
ap-4603	27	23	kernel	kernel	NOUN
ap-4603	27	24	bε(p	bε(p	NUM
ap-4603	27	25	,	,	PUNCT
ap-4603	27	26	q	q	NOUN
ap-4603	27	27	)	)	PUNCT
ap-4603	27	28	of	of	ADP
ap-4603	27	29	the	the	DET
ap-4603	27	30	operator	operator	NOUN
ap-4603	27	31	can	can	AUX
ap-4603	27	32	be	be	AUX
ap-4603	27	33	recast	recast	VERB
ap-4603	27	34	as	as	ADP
ap-4603	27	35	:	:	PUNCT
ap-4603	27	36	bε(p	bε(p	NUM
ap-4603	27	37	,	,	PUNCT
ap-4603	27	38	q	q	X
ap-4603	27	39	)	)	PUNCT
ap-4603	27	40	=	=	SYM
ap-4603	27	41	1√	1√	NUM
ap-4603	27	42	2π	2π	NOUN
ap-4603	27	43	e−p	e−p	NOUN
ap-4603	27	44	2/2	2/2	NUM
ap-4603	27	45	(	(	PUNCT
ap-4603	27	46	p2	p2	PROPN
ap-4603	27	47	+	+	CCONJ
ap-4603	27	48	ε2)1/2	ε2)1/2	PROPN
ap-4603	27	49	e	e	PROPN
ap-4603	27	50	pq	pq	PROPN
ap-4603	27	51	e−q	e−q	PROPN
ap-4603	27	52	2/2	2/2	NUM
ap-4603	27	53	(	(	PUNCT
ap-4603	27	54	q2	q2	NOUN
ap-4603	27	55	+	+	CCONJ
ap-4603	27	56	ε2)1/2	ε2)1/2	ADJ
ap-4603	27	57	,	,	PUNCT
ap-4603	27	58	(	(	PUNCT
ap-4603	27	59	7	7	X
ap-4603	27	60	)	)	PUNCT
ap-4603	27	61	as	as	ADP
ap-4603	27	62	an	an	DET
ap-4603	27	63	immediate	immediate	ADJ
ap-4603	27	64	consequence	consequence	NOUN
ap-4603	27	65	of	of	ADP
ap-4603	27	66	(	(	PUNCT
ap-4603	27	67	7	7	NUM
ap-4603	27	68	)	)	PUNCT
ap-4603	27	69	,	,	PUNCT
ap-4603	27	70	the	the	DET
ap-4603	27	71	operator	operator	NOUN
ap-4603	27	72	bε	bε	NOUN
ap-4603	27	73	can	can	AUX
ap-4603	27	74	be	be	AUX
ap-4603	27	75	written	write	VERB
ap-4603	27	76	as	as	ADP
ap-4603	27	77	a	a	DET
ap-4603	27	78	direct	direct	ADJ
ap-4603	27	79	sum	sum	NOUN
ap-4603	27	80	of	of	ADP
ap-4603	27	81	two	two	NUM
ap-4603	27	82	operators	operator	NOUN
ap-4603	27	83	,	,	PUNCT
ap-4603	27	84	one	one	NUM
ap-4603	27	85	acting	act	VERB
ap-4603	27	86	onto	onto	ADP
ap-4603	27	87	the	the	DET
ap-4603	27	88	symmetric	symmetric	ADJ
ap-4603	27	89	subspace	subspace	NOUN
ap-4603	27	90	(	(	PUNCT
ap-4603	27	91	s	s	X
ap-4603	27	92	)	)	PUNCT
ap-4603	27	93	the	the	DET
ap-4603	27	94	other	other	ADJ
ap-4603	27	95	onto	onto	ADP
ap-4603	27	96	the	the	DET
ap-4603	27	97	antisymmetric	antisymmetric	ADJ
ap-4603	27	98	one	one	NOUN
ap-4603	27	99	(	(	PUNCT
ap-4603	27	100	a	a	NOUN
ap-4603	27	101	)	)	PUNCT
ap-4603	27	102	,	,	PUNCT
ap-4603	27	103	whose	whose	DET
ap-4603	27	104	kernels	kernel	NOUN
ap-4603	27	105	are	be	AUX
ap-4603	27	106	:	:	PUNCT
ap-4603	27	107	bsε	bsε	NOUN
ap-4603	27	108	(	(	PUNCT
ap-4603	27	109	p	p	X
ap-4603	27	110	,	,	PUNCT
ap-4603	27	111	q	q	NOUN
ap-4603	27	112	)	)	PUNCT
ap-4603	27	113	=	=	SYM
ap-4603	27	114	1√	1√	NUM
ap-4603	27	115	2π	2π	NOUN
ap-4603	27	116	e−p	e−p	NOUN
ap-4603	27	117	2/2	2/2	NUM
ap-4603	27	118	(	(	PUNCT
ap-4603	27	119	p2	p2	PROPN
ap-4603	27	120	+	+	CCONJ
ap-4603	27	121	ε2)1/2	ε2)1/2	ADJ
ap-4603	27	122	cosh(pq	cosh(pq	NOUN
ap-4603	27	123	)	)	PUNCT
ap-4603	27	124	e−q	e−q	NOUN
ap-4603	27	125	2/2	2/2	NUM
ap-4603	27	126	(	(	PUNCT
ap-4603	27	127	q2	q2	NOUN
ap-4603	27	128	+	+	CCONJ
ap-4603	27	129	ε2)1/2	ε2)1/2	ADJ
ap-4603	27	130	,	,	PUNCT
ap-4603	27	131	(	(	PUNCT
ap-4603	27	132	8)	8)	NUM
ap-4603	27	133	baε	baε	NOUN
ap-4603	27	134	(	(	PUNCT
ap-4603	27	135	p	p	X
ap-4603	27	136	,	,	PUNCT
ap-4603	27	137	q	q	NOUN
ap-4603	27	138	)	)	PUNCT
ap-4603	27	139	=	=	SYM
ap-4603	27	140	1√	1√	NUM
ap-4603	27	141	2π	2π	NOUN
ap-4603	27	142	e−p	e−p	NOUN
ap-4603	27	143	2/2	2/2	NUM
ap-4603	27	144	(	(	PUNCT
ap-4603	27	145	p2	p2	PROPN
ap-4603	27	146	+	+	CCONJ
ap-4603	27	147	ε2)1/2	ε2)1/2	ADJ
ap-4603	27	148	sinh(pq	sinh(pq	NOUN
ap-4603	27	149	)	)	PUNCT
ap-4603	27	150	e−q	e−q	NOUN
ap-4603	27	151	2/2	2/2	NUM
ap-4603	27	152	(	(	PUNCT
ap-4603	27	153	q2	q2	NOUN
ap-4603	27	154	+	+	CCONJ
ap-4603	27	155	ε2)1/2	ε2)1/2	ADJ
ap-4603	27	156	.	.	PUNCT
ap-4603	28	1	(	(	PUNCT
ap-4603	28	2	9	9	NUM
ap-4603	28	3	)	)	PUNCT
ap-4603	28	4	by	by	ADP
ap-4603	28	5	using	use	VERB
ap-4603	28	6	the	the	DET
ap-4603	28	7	taylor	taylor	PROPN
ap-4603	28	8	expansion	expansion	NOUN
ap-4603	28	9	for	for	ADP
ap-4603	28	10	each	each	DET
ap-4603	28	11	hyperbolic	hyperbolic	ADJ
ap-4603	28	12	function	function	NOUN
ap-4603	28	13	,	,	PUNCT
ap-4603	28	14	the	the	DET
ap-4603	28	15	two	two	NUM
ap-4603	28	16	integral	integral	ADJ
ap-4603	28	17	operators	operator	NOUN
ap-4603	28	18	can	can	AUX
ap-4603	28	19	be	be	AUX
ap-4603	28	20	written	write	VERB
ap-4603	28	21	as	as	ADP
ap-4603	28	22	infinite	infinite	ADJ
ap-4603	28	23	sums	sum	NOUN
ap-4603	28	24	of	of	ADP
ap-4603	28	25	rank	rank	NOUN
ap-4603	28	26	one	one	NUM
ap-4603	28	27	operators	operator	NOUN
ap-4603	28	28	,	,	PUNCT
ap-4603	28	29	namely	namely	ADV
ap-4603	28	30	:	:	PUNCT
ap-4603	28	31	bsε	bsε	NOUN
ap-4603	28	32	=	=	SYM
ap-4603	28	33	1√	1√	NUM
ap-4603	28	34	2π	2π	NOUN
ap-4603	28	35	∞∑	∞∑	NUM
ap-4603	28	36	n=0	n=0	SYM
ap-4603	28	37	1	1	NUM
ap-4603	28	38	(	(	PUNCT
ap-4603	28	39	2n	2n	NUM
ap-4603	28	40	)	)	PUNCT
ap-4603	28	41	!	!	PUNCT
ap-4603	29	1	∣∣∣∣	∣∣∣∣	PROPN
ap-4603	29	2	p2ne−p	p2ne−p	PROPN
ap-4603	29	3	2/2	2/2	NUM
ap-4603	29	4	(	(	PUNCT
ap-4603	29	5	p2	p2	X
ap-4603	29	6	+	+	CCONJ
ap-4603	29	7	ε2)1/2	ε2)1/2	ADJ
ap-4603	29	8	〉	〉	NOUN
ap-4603	29	9	〈	〈	PROPN
ap-4603	29	10	p2ne−p	p2ne−p	NOUN
ap-4603	29	11	2/2	2/2	NUM
ap-4603	29	12	(	(	PUNCT
ap-4603	29	13	p2	p2	X
ap-4603	29	14	+	+	CCONJ
ap-4603	29	15	ε2)1/2	ε2)1/2	PROPN
ap-4603	29	16	∣∣∣∣	∣∣∣∣	PROPN
ap-4603	29	17	,	,	PUNCT
ap-4603	29	18	(	(	PUNCT
ap-4603	29	19	10	10	NUM
ap-4603	29	20	)	)	PUNCT
ap-4603	29	21	baε	baε	NOUN
ap-4603	29	22	=	=	SYM
ap-4603	29	23	1√	1√	PROPN
ap-4603	29	24	2π	2π	NOUN
ap-4603	29	25	∞∑	∞∑	NUM
ap-4603	29	26	n=0	n=0	SYM
ap-4603	29	27	1	1	NUM
ap-4603	29	28	(	(	PUNCT
ap-4603	29	29	2n+	2n+	NUM
ap-4603	29	30	1	1	NUM
ap-4603	29	31	)	)	PUNCT
ap-4603	29	32	!	!	PUNCT
ap-4603	29	33	∣∣∣∣p2n+1e−p	∣∣∣∣p2n+1e−p	NOUN
ap-4603	30	1	2/2	2/2	NUM
ap-4603	30	2	(	(	PUNCT
ap-4603	30	3	p2	p2	X
ap-4603	30	4	+	+	CCONJ
ap-4603	30	5	ε2)1/2	ε2)1/2	ADJ
ap-4603	30	6	〉	〉	NOUN
ap-4603	30	7	〈	〈	PROPN
ap-4603	30	8	p2n+1e−p	p2n+1e−p	NOUN
ap-4603	30	9	2/2	2/2	NUM
ap-4603	30	10	(	(	PUNCT
ap-4603	30	11	p2	p2	PROPN
ap-4603	30	12	+	+	CCONJ
ap-4603	30	13	ε2)1/2	ε2)1/2	ADJ
ap-4603	30	14	∣∣∣∣.	∣∣∣∣.	NOUN
ap-4603	30	15	(	(	PUNCT
ap-4603	30	16	11	11	NUM
ap-4603	30	17	)	)	PUNCT
ap-4603	30	18	obviously	obviously	ADV
ap-4603	30	19	,	,	PUNCT
ap-4603	30	20	as	as	ADP
ap-4603	30	21	a	a	DET
ap-4603	30	22	consequence	consequence	NOUN
ap-4603	30	23	of	of	ADP
ap-4603	30	24	(	(	PUNCT
ap-4603	30	25	6	6	NUM
ap-4603	30	26	)	)	PUNCT
ap-4603	30	27	,	,	PUNCT
ap-4603	30	28	both	both	DET
ap-4603	30	29	operators	operator	NOUN
ap-4603	30	30	are	be	AUX
ap-4603	30	31	trace	trace	NOUN
ap-4603	30	32	class	class	NOUN
ap-4603	30	33	,	,	PUNCT
ap-4603	30	34	which	which	PRON
ap-4603	30	35	implies	imply	VERB
ap-4603	30	36	that	that	SCONJ
ap-4603	30	37	both	both	DET
ap-4603	30	38	series	serie	NOUN
ap-4603	30	39	are	be	AUX
ap-4603	30	40	convergent	convergent	ADJ
ap-4603	30	41	in	in	ADP
ap-4603	30	42	the	the	DET
ap-4603	30	43	trace	trace	NOUN
ap-4603	30	44	class	class	NOUN
ap-4603	30	45	norm	norm	NOUN
ap-4603	30	46	.	.	PUNCT
ap-4603	31	1	furthermore	furthermore	ADV
ap-4603	31	2	,	,	PUNCT
ap-4603	31	3	although	although	SCONJ
ap-4603	31	4	either	either	DET
ap-4603	31	5	operator	operator	NOUN
ap-4603	31	6	has	have	AUX
ap-4603	31	7	not	not	PART
ap-4603	31	8	yet	yet	ADV
ap-4603	31	9	been	be	AUX
ap-4603	31	10	diagonalised	diagonalise	VERB
ap-4603	31	11	at	at	ADP
ap-4603	31	12	this	this	DET
ap-4603	31	13	stage	stage	NOUN
ap-4603	31	14	(	(	PUNCT
ap-4603	31	15	because	because	SCONJ
ap-4603	31	16	the	the	DET
ap-4603	31	17	rank	rank	NOUN
ap-4603	31	18	one	one	NUM
ap-4603	31	19	operators	operator	NOUN
ap-4603	31	20	are	be	AUX
ap-4603	31	21	not	not	PART
ap-4603	31	22	mutually	mutually	ADV
ap-4603	31	23	orthogonal	orthogonal	ADJ
ap-4603	31	24	)	)	PUNCT
ap-4603	31	25	,	,	PUNCT
ap-4603	31	26	their	their	PRON
ap-4603	31	27	diagonalisation	diagonalisation	NOUN
ap-4603	31	28	can	can	AUX
ap-4603	31	29	be	be	AUX
ap-4603	31	30	achieved	achieve	VERB
ap-4603	31	31	starting	start	VERB
ap-4603	31	32	from	from	ADP
ap-4603	31	33	the	the	DET
ap-4603	31	34	first	first	ADJ
ap-4603	31	35	rank	rank	NOUN
ap-4603	31	36	one	one	NUM
ap-4603	31	37	operator	operator	NOUN
ap-4603	31	38	in	in	ADP
ap-4603	31	39	each	each	DET
ap-4603	31	40	expansion	expansion	NOUN
ap-4603	31	41	(	(	PUNCT
ap-4603	31	42	n	n	NOUN
ap-4603	31	43	=	=	SYM
ap-4603	31	44	0	0	NUM
ap-4603	31	45	)	)	PUNCT
ap-4603	31	46	,	,	PUNCT
ap-4603	31	47	that	that	PRON
ap-4603	31	48	is	be	AUX
ap-4603	31	49	to	to	PART
ap-4603	31	50	say	say	VERB
ap-4603	31	51	:	:	PUNCT
ap-4603	31	52	bs,0ε	bs,0ε	X
ap-4603	31	53	=	=	SYM
ap-4603	31	54	1√	1√	PROPN
ap-4603	31	55	2π	2π	PROPN
ap-4603	31	56	∣∣∣∣	∣∣∣∣	PROPN
ap-4603	31	57	e−p	e−p	PROPN
ap-4603	31	58	2/2	2/2	NUM
ap-4603	31	59	(	(	PUNCT
ap-4603	31	60	p2	p2	X
ap-4603	31	61	+	+	CCONJ
ap-4603	31	62	ε2)1/2	ε2)1/2	PROPN
ap-4603	31	63	〉	〉	NOUN
ap-4603	31	64	〈	〈	PROPN
ap-4603	31	65	e−p	e−p	PROPN
ap-4603	31	66	2/2	2/2	NUM
ap-4603	31	67	(	(	PUNCT
ap-4603	31	68	p2	p2	X
ap-4603	31	69	+	+	CCONJ
ap-4603	31	70	ε2)1/2	ε2)1/2	PROPN
ap-4603	31	71	∣∣∣∣	∣∣∣∣	PROPN
ap-4603	31	72	,	,	PUNCT
ap-4603	31	73	(	(	PUNCT
ap-4603	31	74	12	12	NUM
ap-4603	31	75	)	)	PUNCT
ap-4603	31	76	ba,0ε	ba,0ε	NOUN
ap-4603	31	77	=	=	SYM
ap-4603	31	78	1√	1√	PROPN
ap-4603	31	79	2π	2π	PROPN
ap-4603	31	80	∣∣∣∣	∣∣∣∣	NOUN
ap-4603	31	81	pe−p	pe−p	NOUN
ap-4603	31	82	2/2	2/2	NUM
ap-4603	31	83	(	(	PUNCT
ap-4603	31	84	p2	p2	X
ap-4603	31	85	+	+	CCONJ
ap-4603	31	86	ε2)1/2	ε2)1/2	ADJ
ap-4603	31	87	〉	〉	NOUN
ap-4603	31	88	〈	〈	PROPN
ap-4603	31	89	pe−p	pe−p	NOUN
ap-4603	31	90	2/2	2/2	NUM
ap-4603	31	91	(	(	PUNCT
ap-4603	31	92	p2	p2	X
ap-4603	31	93	+	+	CCONJ
ap-4603	31	94	ε2)1/2	ε2)1/2	ADJ
ap-4603	31	95	∣∣∣∣.	∣∣∣∣.	X
ap-4603	31	96	(	(	PUNCT
ap-4603	31	97	13	13	NUM
ap-4603	31	98	)	)	PUNCT
ap-4603	31	99	their	their	PRON
ap-4603	31	100	norms	norm	NOUN
ap-4603	31	101	can	can	AUX
ap-4603	31	102	be	be	AUX
ap-4603	31	103	easily	easily	ADV
ap-4603	31	104	computed	compute	VERB
ap-4603	31	105	as	as	SCONJ
ap-4603	31	106	the	the	DET
ap-4603	31	107	required	require	VERB
ap-4603	31	108	improper	improper	ADJ
ap-4603	31	109	integrals	integral	NOUN
ap-4603	31	110	are	be	AUX
ap-4603	31	111	well	well	ADV
ap-4603	31	112	known	known	ADJ
ap-4603	31	113	:	:	PUNCT
ap-4603	31	114	‖bs,0ε	‖bs,0ε	NUM
ap-4603	31	115	‖	‖	PROPN
ap-4603	31	116	=	=	SYM
ap-4603	31	117	1√	1√	ADJ
ap-4603	31	118	2π	2π	NUM
ap-4603	31	119	∫	∫	PROPN
ap-4603	32	1	+	+	NUM
ap-4603	32	2	∞	∞	PROPN
ap-4603	32	3	−∞	−∞	X
ap-4603	32	4	e−p	e−p	PROPN
ap-4603	32	5	2	2	NUM
ap-4603	32	6	p2	p2	NOUN
ap-4603	32	7	+	+	CCONJ
ap-4603	32	8	ε2	ε2	ADJ
ap-4603	32	9	dp	dp	NOUN
ap-4603	32	10	=	=	PUNCT
ap-4603	32	11	√	√	PROPN
ap-4603	32	12	π	π	PROPN
ap-4603	32	13	2ε2	2ε2	NUM
ap-4603	32	14	e	e	NOUN
ap-4603	32	15	ε2	ε2	PROPN
ap-4603	32	16	erfc(ε	erfc(ε	PROPN
ap-4603	32	17	)	)	PUNCT
ap-4603	32	18	,	,	PUNCT
ap-4603	32	19	(	(	PUNCT
ap-4603	32	20	14	14	NUM
ap-4603	32	21	)	)	PUNCT
ap-4603	32	22	‖ba,0ε	‖ba,0ε	NOUN
ap-4603	33	1	‖	‖	ADJ
ap-4603	33	2	=	=	SYM
ap-4603	33	3	1√	1√	ADJ
ap-4603	33	4	2π	2π	NUM
ap-4603	33	5	∫	∫	PROPN
ap-4603	34	1	+	+	X
ap-4603	34	2	∞	∞	PROPN
ap-4603	34	3	−∞	−∞	ADP
ap-4603	34	4	p2e−p	p2e−p	ADJ
ap-4603	34	5	2	2	NUM
ap-4603	34	6	p2	p2	NOUN
ap-4603	34	7	+	+	CCONJ
ap-4603	34	8	ε2	ε2	ADJ
ap-4603	34	9	dp	dp	NOUN
ap-4603	34	10	=	=	SYM
ap-4603	34	11	1√	1√	PROPN
ap-4603	34	12	2	2	NUM
ap-4603	34	13	(	(	PUNCT
ap-4603	34	14	1−	1−	NUM
ap-4603	34	15	√	√	PROPN
ap-4603	34	16	πεeε	πεeε	NOUN
ap-4603	34	17	2	2	NUM
ap-4603	34	18	erfc(ε	erfc(ε	NOUN
ap-4603	34	19	)	)	PUNCT
ap-4603	34	20	)	)	PUNCT
ap-4603	34	21	.	.	PUNCT
ap-4603	35	1	(	(	PUNCT
ap-4603	35	2	15	15	NUM
ap-4603	35	3	)	)	PUNCT
ap-4603	35	4	386	386	NUM
ap-4603	35	5	vol	vol	NOUN
ap-4603	35	6	.	.	PUNCT
ap-4603	36	1	57	57	NUM
ap-4603	36	2	no	no	NOUN
ap-4603	36	3	.	.	PUNCT
ap-4603	37	1	6/2017	6/2017	NUM
ap-4603	37	2	on	on	ADP
ap-4603	37	3	the	the	DET
ap-4603	37	4	spectrum	spectrum	NOUN
ap-4603	37	5	of	of	ADP
ap-4603	37	6	the	the	DET
ap-4603	37	7	one	one	NUM
ap-4603	37	8	-	-	PUNCT
ap-4603	37	9	dimensional	dimensional	ADJ
ap-4603	37	10	schrödinger	schrödinger	ADJ
ap-4603	37	11	hamiltonian	hamiltonian	NOUN
ap-4603	37	12	as	as	SCONJ
ap-4603	37	13	can	can	AUX
ap-4603	37	14	be	be	AUX
ap-4603	37	15	understood	understand	VERB
ap-4603	37	16	from	from	ADP
ap-4603	37	17	(	(	PUNCT
ap-4603	37	18	14	14	NUM
ap-4603	37	19	)	)	PUNCT
ap-4603	37	20	,	,	PUNCT
ap-4603	37	21	the	the	DET
ap-4603	37	22	divergence	divergence	NOUN
ap-4603	37	23	of	of	ADP
ap-4603	37	24	the	the	DET
ap-4603	37	25	trace	trace	NOUN
ap-4603	37	26	of	of	ADP
ap-4603	37	27	the	the	DET
ap-4603	37	28	entire	entire	ADJ
ap-4603	37	29	operator	operator	NOUN
ap-4603	37	30	as	as	ADP
ap-4603	37	31	ε→	ε→	X
ap-4603	37	32	0	0	NUM
ap-4603	38	1	+	+	CCONJ
ap-4603	38	2	is	be	AUX
ap-4603	38	3	only	only	ADV
ap-4603	38	4	due	due	ADJ
ap-4603	38	5	to	to	ADP
ap-4603	38	6	the	the	DET
ap-4603	38	7	the	the	DET
ap-4603	38	8	divergence	divergence	NOUN
ap-4603	38	9	of	of	ADP
ap-4603	38	10	bs,0ε	bs,0ε	PROPN
ap-4603	38	11	.	.	PUNCT
ap-4603	39	1	in	in	ADP
ap-4603	39	2	fact	fact	NOUN
ap-4603	39	3	,	,	PUNCT
ap-4603	39	4	the	the	DET
ap-4603	39	5	trace	trace	NOUN
ap-4603	39	6	class	class	NOUN
ap-4603	39	7	norm	norm	NOUN
ap-4603	39	8	of	of	ADP
ap-4603	39	9	the	the	DET
ap-4603	39	10	positive	positive	ADJ
ap-4603	39	11	operator	operator	NOUN
ap-4603	39	12	bs,1ε	bs,1ε	AUX
ap-4603	39	13	=	=	SYM
ap-4603	39	14	bsε	bsε	NOUN
ap-4603	39	15	−	−	PROPN
ap-4603	39	16	bs,0ε	bs,0ε	PROPN
ap-4603	39	17	can	can	AUX
ap-4603	39	18	be	be	AUX
ap-4603	39	19	calculated	calculate	VERB
ap-4603	39	20	as	as	SCONJ
ap-4603	39	21	follows	follow	VERB
ap-4603	39	22	:	:	PUNCT
ap-4603	39	23	‖bs,1ε	‖bs,1ε	X
ap-4603	39	24	‖1	‖1	X
ap-4603	39	25	=	=	SYM
ap-4603	39	26	1√	1√	PROPN
ap-4603	39	27	2π	2π	NUM
ap-4603	39	28	∫	∫	PROPN
ap-4603	40	1	+	+	NUM
ap-4603	40	2	∞	∞	PROPN
ap-4603	40	3	−∞	−∞	AUX
ap-4603	40	4	e−p	e−p	PROPN
ap-4603	40	5	2(cosh	2(cosh	PROPN
ap-4603	40	6	p2	p2	VERB
ap-4603	40	7	−	−	PROPN
ap-4603	40	8	1	1	NUM
ap-4603	40	9	)	)	PUNCT
ap-4603	40	10	p2	p2	PROPN
ap-4603	40	11	+	+	CCONJ
ap-4603	40	12	ε2	ε2	ADJ
ap-4603	40	13	dp	dp	NOUN
ap-4603	40	14	.	.	PUNCT
ap-4603	41	1	(	(	PUNCT
ap-4603	41	2	16	16	NUM
ap-4603	41	3	)	)	PUNCT
ap-4603	41	4	by	by	ADP
ap-4603	41	5	writing	write	VERB
ap-4603	41	6	the	the	DET
ap-4603	41	7	hyperbolic	hyperbolic	ADJ
ap-4603	41	8	cosine	cosine	NOUN
ap-4603	41	9	as	as	ADP
ap-4603	41	10	a	a	DET
ap-4603	41	11	combination	combination	NOUN
ap-4603	41	12	of	of	ADP
ap-4603	41	13	two	two	NUM
ap-4603	41	14	exponentials	exponential	NOUN
ap-4603	41	15	,	,	PUNCT
ap-4603	41	16	the	the	DET
ap-4603	41	17	right	right	ADJ
ap-4603	41	18	hand	hand	NOUN
ap-4603	41	19	side	side	NOUN
ap-4603	41	20	of	of	ADP
ap-4603	41	21	(	(	PUNCT
ap-4603	41	22	16	16	NUM
ap-4603	41	23	)	)	PUNCT
ap-4603	41	24	is	be	AUX
ap-4603	41	25	easily	easily	ADV
ap-4603	41	26	seen	see	VERB
ap-4603	41	27	to	to	PART
ap-4603	41	28	be	be	AUX
ap-4603	41	29	equal	equal	ADJ
ap-4603	41	30	to	to	ADP
ap-4603	41	31	‖bs,1ε	‖bs,1ε	X
ap-4603	41	32	‖1	‖1	PROPN
ap-4603	41	33	=	=	PUNCT
ap-4603	42	1	√	√	PROPN
ap-4603	42	2	π	π	SYM
ap-4603	42	3	23ε2	23ε2	NUM
ap-4603	42	4	(	(	PUNCT
ap-4603	42	5	1	1	NUM
ap-4603	42	6	+	+	CCONJ
ap-4603	42	7	e2ε2	e2ε2	X
ap-4603	42	8	erfc(21/2ε)−	erfc(21/2ε)−	ADJ
ap-4603	42	9	2eε	2eε	ADJ
ap-4603	42	10	2	2	NUM
ap-4603	42	11	erfc(ε	erfc(ε	NOUN
ap-4603	42	12	)	)	PUNCT
ap-4603	42	13	)	)	PUNCT
ap-4603	43	1	,	,	PUNCT
ap-4603	43	2	(	(	PUNCT
ap-4603	43	3	17	17	NUM
ap-4603	43	4	)	)	PUNCT
ap-4603	43	5	which	which	PRON
ap-4603	43	6	,	,	PUNCT
ap-4603	43	7	given	give	VERB
ap-4603	43	8	its	its	PRON
ap-4603	43	9	removable	removable	ADJ
ap-4603	43	10	singularity	singularity	NOUN
ap-4603	43	11	at	at	ADP
ap-4603	43	12	the	the	DET
ap-4603	43	13	origin	origin	NOUN
ap-4603	43	14	,	,	PUNCT
ap-4603	43	15	is	be	AUX
ap-4603	43	16	almost	almost	ADV
ap-4603	43	17	immediately	immediately	ADV
ap-4603	43	18	seen	see	VERB
ap-4603	43	19	to	to	PART
ap-4603	43	20	converge	converge	VERB
ap-4603	43	21	to	to	ADP
ap-4603	43	22	√	√	PROPN
ap-4603	43	23	2−	2−	NUM
ap-4603	43	24	1	1	NUM
ap-4603	43	25	as	as	ADP
ap-4603	43	26	ε→	ε→	NUM
ap-4603	43	27	0	0	NUM
ap-4603	44	1	+	+	NOUN
ap-4603	44	2	.	.	PUNCT
ap-4603	44	3	before	before	ADP
ap-4603	44	4	determining	determine	VERB
ap-4603	44	5	the	the	DET
ap-4603	44	6	equation	equation	NOUN
ap-4603	44	7	that	that	PRON
ap-4603	44	8	will	will	AUX
ap-4603	44	9	enable	enable	VERB
ap-4603	44	10	us	we	PRON
ap-4603	44	11	to	to	PART
ap-4603	44	12	compute	compute	VERB
ap-4603	44	13	the	the	DET
ap-4603	44	14	ground	ground	NOUN
ap-4603	44	15	state	state	NOUN
ap-4603	44	16	energy	energy	NOUN
ap-4603	44	17	as	as	ADP
ap-4603	44	18	a	a	DET
ap-4603	44	19	function	function	NOUN
ap-4603	44	20	of	of	ADP
ap-4603	44	21	the	the	DET
ap-4603	44	22	coupling	coupling	NOUN
ap-4603	44	23	parameter	parameter	NOUN
ap-4603	44	24	λ	λ	PROPN
ap-4603	44	25	,	,	PUNCT
ap-4603	44	26	let	let	VERB
ap-4603	44	27	us	we	PRON
ap-4603	44	28	consider	consider	VERB
ap-4603	44	29	also	also	ADV
ap-4603	44	30	the	the	DET
ap-4603	44	31	antisymmetric	antisymmetric	ADJ
ap-4603	44	32	component	component	NOUN
ap-4603	44	33	baε	baε	NOUN
ap-4603	44	34	.	.	PUNCT
ap-4603	45	1	as	as	ADP
ap-4603	45	2	a	a	DET
ap-4603	45	3	result	result	NOUN
ap-4603	45	4	of	of	ADP
ap-4603	45	5	the	the	DET
ap-4603	45	6	explicit	explicit	ADJ
ap-4603	45	7	expression	expression	NOUN
ap-4603	45	8	of	of	ADP
ap-4603	45	9	the	the	DET
ap-4603	45	10	integral	integral	ADJ
ap-4603	45	11	kernel	kernel	NOUN
ap-4603	45	12	of	of	ADP
ap-4603	45	13	baε	baε	PROPN
ap-4603	45	14	,	,	PUNCT
ap-4603	45	15	it	it	PRON
ap-4603	45	16	is	be	AUX
ap-4603	45	17	not	not	PART
ap-4603	45	18	difficult	difficult	ADJ
ap-4603	45	19	to	to	PART
ap-4603	45	20	show	show	VERB
ap-4603	45	21	that	that	SCONJ
ap-4603	45	22	the	the	DET
ap-4603	45	23	latter	latter	ADJ
ap-4603	45	24	operator	operator	NOUN
ap-4603	45	25	converges	converge	VERB
ap-4603	45	26	weakly	weakly	ADV
ap-4603	45	27	to	to	ADP
ap-4603	45	28	ba0	ba0	NOUN
ap-4603	45	29	,	,	PUNCT
ap-4603	45	30	where	where	SCONJ
ap-4603	45	31	ba0	ba0	PROPN
ap-4603	45	32	(	(	PUNCT
ap-4603	45	33	p	p	X
ap-4603	45	34	,	,	PUNCT
ap-4603	45	35	q	q	NOUN
ap-4603	45	36	)	)	PUNCT
ap-4603	45	37	=	=	SYM
ap-4603	45	38	1√	1√	NUM
ap-4603	45	39	2π	2π	PROPN
ap-4603	45	40	e−p	e−p	NOUN
ap-4603	45	41	2/2	2/2	NUM
ap-4603	45	42	|p|	|p|	PRON
ap-4603	45	43	sinh(pq)e	sinh(pq)e	NOUN
ap-4603	45	44	−q2/2	−q2/2	VERB
ap-4603	45	45	|q|	|q|	PRON
ap-4603	45	46	.	.	PUNCT
ap-4603	46	1	(	(	PUNCT
ap-4603	46	2	18	18	NUM
ap-4603	46	3	)	)	PUNCT
ap-4603	46	4	the	the	DET
ap-4603	46	5	latter	latter	ADJ
ap-4603	46	6	is	be	AUX
ap-4603	46	7	a	a	DET
ap-4603	46	8	positive	positive	ADJ
ap-4603	46	9	trace	trace	NOUN
ap-4603	46	10	class	class	NOUN
ap-4603	46	11	operator	operator	NOUN
ap-4603	46	12	with	with	ADP
ap-4603	46	13	trace	trace	NOUN
ap-4603	46	14	equal	equal	ADJ
ap-4603	46	15	to	to	ADP
ap-4603	46	16	‖ba0‖1	‖ba0‖1	VERB
ap-4603	46	17	=	=	SYM
ap-4603	46	18	1√	1√	PROPN
ap-4603	46	19	2π	2π	NUM
ap-4603	46	20	∫	∫	PROPN
ap-4603	47	1	+	+	NUM
ap-4603	47	2	∞	∞	PROPN
ap-4603	47	3	−∞	−∞	X
ap-4603	47	4	e−p	e−p	PROPN
ap-4603	47	5	2	2	NUM
ap-4603	47	6	p2	p2	NOUN
ap-4603	47	7	sinh	sinh	NOUN
ap-4603	47	8	p2	p2	NOUN
ap-4603	47	9	dp	dp	NOUN
ap-4603	47	10	=	=	SYM
ap-4603	47	11	1	1	NUM
ap-4603	47	12	,	,	PUNCT
ap-4603	47	13	(	(	PUNCT
ap-4603	47	14	19	19	NUM
ap-4603	47	15	)	)	PUNCT
ap-4603	47	16	as	as	SCONJ
ap-4603	47	17	follows	follow	VERB
ap-4603	47	18	easily	easily	ADV
ap-4603	47	19	by	by	ADP
ap-4603	47	20	writing	write	VERB
ap-4603	47	21	the	the	DET
ap-4603	47	22	hyperbolic	hyperbolic	ADJ
ap-4603	47	23	sine	sine	NOUN
ap-4603	47	24	as	as	ADP
ap-4603	47	25	a	a	DET
ap-4603	47	26	combination	combination	NOUN
ap-4603	47	27	of	of	ADP
ap-4603	47	28	two	two	NUM
ap-4603	47	29	exponentials	exponential	NOUN
ap-4603	47	30	and	and	CCONJ
ap-4603	47	31	using	use	VERB
ap-4603	47	32	integration	integration	NOUN
ap-4603	47	33	by	by	ADP
ap-4603	47	34	parts	part	NOUN
ap-4603	47	35	.	.	PUNCT
ap-4603	48	1	it	it	PRON
ap-4603	48	2	is	be	AUX
ap-4603	48	3	worth	worth	ADJ
ap-4603	48	4	pointing	point	VERB
ap-4603	48	5	out	out	ADP
ap-4603	48	6	that	that	SCONJ
ap-4603	48	7	the	the	DET
ap-4603	48	8	latter	latter	ADJ
ap-4603	48	9	quantity	quantity	NOUN
ap-4603	48	10	is	be	AUX
ap-4603	48	11	nothing	nothing	PRON
ap-4603	48	12	else	else	ADV
ap-4603	48	13	but	but	CCONJ
ap-4603	48	14	the	the	DET
ap-4603	48	15	limit	limit	NOUN
ap-4603	48	16	,	,	PUNCT
ap-4603	48	17	as	as	ADP
ap-4603	48	18	ε→	ε→	X
ap-4603	48	19	0	0	NUM
ap-4603	48	20	+	+	NUM
ap-4603	48	21	of	of	ADP
ap-4603	48	22	the	the	DET
ap-4603	48	23	trace	trace	NOUN
ap-4603	48	24	class	class	NOUN
ap-4603	48	25	norm	norm	NOUN
ap-4603	48	26	of	of	ADP
ap-4603	48	27	baε	baε	NOUN
ap-4603	48	28	,	,	PUNCT
ap-4603	48	29	since	since	SCONJ
ap-4603	48	30	‖baε	‖baε	NOUN
ap-4603	48	31	‖1	‖1	NOUN
ap-4603	48	32	=	=	SYM
ap-4603	48	33	1√	1√	ADJ
ap-4603	48	34	2π	2π	NUM
ap-4603	48	35	∫	∫	PROPN
ap-4603	49	1	+	+	NUM
ap-4603	49	2	∞	∞	PROPN
ap-4603	49	3	−∞	−∞	X
ap-4603	49	4	e−p	e−p	PROPN
ap-4603	49	5	2	2	NUM
ap-4603	49	6	sinh	sinh	NOUN
ap-4603	49	7	p2	p2	NOUN
ap-4603	49	8	p2	p2	NOUN
ap-4603	49	9	+	+	CCONJ
ap-4603	49	10	ε2	ε2	ADJ
ap-4603	49	11	dp	dp	NOUN
ap-4603	49	12	=	=	PUNCT
ap-4603	49	13	√	√	PROPN
ap-4603	49	14	π	π	SYM
ap-4603	49	15	23ε2	23ε2	NUM
ap-4603	49	16	(	(	PUNCT
ap-4603	49	17	1−	1−	NUM
ap-4603	49	18	e2ε2	e2ε2	X
ap-4603	49	19	erfc	erfc	PROPN
ap-4603	49	20	(	(	PUNCT
ap-4603	49	21	√	√	NUM
ap-4603	49	22	2ε	2ε	NUM
ap-4603	49	23	)	)	PUNCT
ap-4603	49	24	)	)	PUNCT
ap-4603	50	1	,	,	PUNCT
ap-4603	50	2	(	(	PUNCT
ap-4603	50	3	20	20	NUM
ap-4603	50	4	)	)	PUNCT
ap-4603	50	5	which	which	PRON
ap-4603	50	6	ensures	ensure	VERB
ap-4603	50	7	the	the	DET
ap-4603	50	8	convergence	convergence	NOUN
ap-4603	50	9	in	in	ADP
ap-4603	50	10	the	the	DET
ap-4603	50	11	norm	norm	NOUN
ap-4603	50	12	topology	topology	NOUN
ap-4603	50	13	of	of	ADP
ap-4603	50	14	trace	trace	NOUN
ap-4603	50	15	class	class	NOUN
ap-4603	50	16	operators	operator	NOUN
ap-4603	50	17	,	,	PUNCT
ap-4603	50	18	as	as	ADP
ap-4603	50	19	a	a	DET
ap-4603	50	20	consequence	consequence	NOUN
ap-4603	50	21	of	of	ADP
ap-4603	50	22	a	a	DET
ap-4603	50	23	well	well	ADV
ap-4603	50	24	-	-	PUNCT
ap-4603	50	25	known	know	VERB
ap-4603	50	26	theorem	theorem	NOUN
ap-4603	50	27	on	on	ADP
ap-4603	50	28	operators	operator	NOUN
ap-4603	50	29	belonging	belong	VERB
ap-4603	50	30	not	not	PART
ap-4603	50	31	only	only	ADV
ap-4603	50	32	to	to	ADP
ap-4603	50	33	the	the	DET
ap-4603	50	34	trace	trace	NOUN
ap-4603	50	35	class	class	NOUN
ap-4603	50	36	t1	t1	NOUN
ap-4603	50	37	but	but	CCONJ
ap-4603	50	38	to	to	ADP
ap-4603	50	39	any	any	DET
ap-4603	50	40	ideal	ideal	NOUN
ap-4603	50	41	tp	tp	X
ap-4603	50	42	(	(	PUNCT
ap-4603	50	43	see	see	VERB
ap-4603	50	44	[	[	X
ap-4603	50	45	11	11	NUM
ap-4603	50	46	]	]	NUM
ap-4603	50	47	)	)	PUNCT
ap-4603	50	48	.	.	PUNCT
ap-4603	51	1	this	this	DET
ap-4603	51	2	result	result	NOUN
ap-4603	51	3	can	can	AUX
ap-4603	51	4	be	be	AUX
ap-4603	51	5	summarised	summarise	VERB
ap-4603	51	6	in	in	ADP
ap-4603	51	7	the	the	DET
ap-4603	51	8	following	follow	VERB
ap-4603	51	9	statement	statement	NOUN
ap-4603	51	10	.	.	PUNCT
ap-4603	52	1	theorem	theorem	VERB
ap-4603	52	2	2.2	2.2	NUM
ap-4603	52	3	.	.	PUNCT
ap-4603	53	1	the	the	DET
ap-4603	53	2	positive	positive	ADJ
ap-4603	53	3	trace	trace	NOUN
ap-4603	53	4	class	class	NOUN
ap-4603	53	5	operator	operator	NOUN
ap-4603	53	6	baε	baε	NOUN
ap-4603	53	7	converges	converge	VERB
ap-4603	53	8	,	,	PUNCT
ap-4603	53	9	as	as	ADP
ap-4603	53	10	ε	ε	PROPN
ap-4603	53	11	→	→	SYM
ap-4603	53	12	0	0	NUM
ap-4603	54	1	+	+	ADJ
ap-4603	54	2	,	,	PUNCT
ap-4603	54	3	to	to	ADP
ap-4603	54	4	ba0	ba0	NOUN
ap-4603	54	5	,	,	PUNCT
ap-4603	54	6	the	the	DET
ap-4603	54	7	positive	positive	ADJ
ap-4603	54	8	trace	trace	NOUN
ap-4603	54	9	class	class	NOUN
ap-4603	54	10	operator	operator	NOUN
ap-4603	54	11	defined	define	VERB
ap-4603	54	12	by	by	ADP
ap-4603	54	13	its	its	PRON
ap-4603	54	14	kernel	kernel	NOUN
ap-4603	54	15	in	in	ADP
ap-4603	54	16	(	(	PUNCT
ap-4603	54	17	18	18	NUM
ap-4603	54	18	)	)	PUNCT
ap-4603	54	19	,	,	PUNCT
ap-4603	54	20	in	in	ADP
ap-4603	54	21	the	the	DET
ap-4603	54	22	norm	norm	NOUN
ap-4603	54	23	topology	topology	NOUN
ap-4603	54	24	of	of	ADP
ap-4603	54	25	trace	trace	NOUN
ap-4603	54	26	class	class	NOUN
ap-4603	54	27	operators	operator	NOUN
ap-4603	54	28	.	.	PUNCT
ap-4603	55	1	it	it	PRON
ap-4603	55	2	is	be	AUX
ap-4603	55	3	crucial	crucial	ADJ
ap-4603	55	4	to	to	PART
ap-4603	55	5	point	point	VERB
ap-4603	55	6	out	out	ADP
ap-4603	55	7	that	that	SCONJ
ap-4603	55	8	,	,	PUNCT
ap-4603	55	9	whilst	whilst	SCONJ
ap-4603	55	10	bs,0ε	bs,0ε	PROPN
ap-4603	55	11	,	,	PUNCT
ap-4603	55	12	the	the	DET
ap-4603	55	13	first	first	ADJ
ap-4603	55	14	rank	rank	NOUN
ap-4603	55	15	one	one	NUM
ap-4603	55	16	summand	summand	NOUN
ap-4603	55	17	in	in	ADP
ap-4603	55	18	the	the	DET
ap-4603	55	19	expansion	expansion	NOUN
ap-4603	55	20	of	of	ADP
ap-4603	55	21	the	the	DET
ap-4603	55	22	symmetric	symmetric	ADJ
ap-4603	55	23	component	component	NOUN
ap-4603	55	24	of	of	ADP
ap-4603	55	25	our	our	PRON
ap-4603	55	26	integral	integral	ADJ
ap-4603	55	27	operator	operator	NOUN
ap-4603	55	28	,	,	PUNCT
ap-4603	55	29	diverges	diverge	VERB
ap-4603	55	30	as	as	ADP
ap-4603	55	31	ε	ε	PROPN
ap-4603	55	32	→	→	SYM
ap-4603	55	33	0	0	NUM
ap-4603	55	34	+	+	PROPN
ap-4603	55	35	,	,	PUNCT
ap-4603	55	36	ba,0ε	ba,0ε	PROPN
ap-4603	55	37	obviously	obviously	ADV
ap-4603	55	38	converges	converge	VERB
ap-4603	55	39	to	to	ADP
ap-4603	55	40	the	the	DET
ap-4603	55	41	following	follow	VERB
ap-4603	55	42	rank	rank	NOUN
ap-4603	55	43	one	one	NUM
ap-4603	55	44	operator	operator	NOUN
ap-4603	55	45	:	:	PUNCT
ap-4603	55	46	ba0	ba0	NOUN
ap-4603	55	47	0	0	X
ap-4603	56	1	=	=	SYM
ap-4603	56	2	1√	1√	NUM
ap-4603	56	3	2π	2π	NOUN
ap-4603	56	4	∣∣∣∣pe−p2/2	∣∣∣∣pe−p2/2	VERB
ap-4603	56	5	|p|	|p|	PRON
ap-4603	56	6	〉	〉	NOUN
ap-4603	56	7	〈	〈	NOUN
ap-4603	56	8	pe−p	pe−p	NOUN
ap-4603	56	9	2/2	2/2	NUM
ap-4603	56	10	|p|	|p|	PRON
ap-4603	56	11	∣∣∣∣	∣∣∣∣	NOUN
ap-4603	56	12	=	=	SYM
ap-4603	56	13	1√	1√	NUM
ap-4603	56	14	2π	2π	NOUN
ap-4603	56	15	∣∣sgn(p)e−p	∣∣sgn(p)e−p	NOUN
ap-4603	56	16	2/2〉〈sgn(p)e−p	2/2〉〈sgn(p)e−p	NUM
ap-4603	56	17	2/2∣∣.	2/2∣∣.	PROPN
ap-4603	56	18	(	(	PUNCT
ap-4603	56	19	21	21	NUM
ap-4603	56	20	)	)	PUNCT
ap-4603	56	21	although	although	SCONJ
ap-4603	56	22	the	the	DET
ap-4603	56	23	antisymmetric	antisymmetric	ADJ
ap-4603	56	24	function	function	NOUN
ap-4603	56	25	sgn(p)e−p2/2	sgn(p)e−p2/2	NUM
ap-4603	56	26	has	have	VERB
ap-4603	56	27	a	a	DET
ap-4603	56	28	jump	jump	NOUN
ap-4603	56	29	discontinuity	discontinuity	NOUN
ap-4603	56	30	at	at	ADP
ap-4603	56	31	the	the	DET
ap-4603	56	32	origin	origin	NOUN
ap-4603	56	33	,	,	PUNCT
ap-4603	56	34	its	its	PRON
ap-4603	56	35	square	square	NOUN
ap-4603	56	36	coincides	coincide	VERB
ap-4603	56	37	with	with	ADP
ap-4603	56	38	the	the	DET
ap-4603	56	39	one	one	NUM
ap-4603	56	40	of	of	ADP
ap-4603	56	41	the	the	DET
ap-4603	56	42	unnormalised	unnormalised	ADJ
ap-4603	56	43	ground	ground	NOUN
ap-4603	56	44	state	state	NOUN
ap-4603	56	45	eigenfunction	eigenfunction	NOUN
ap-4603	56	46	of	of	ADP
ap-4603	56	47	the	the	DET
ap-4603	56	48	harmonic	harmonic	ADJ
ap-4603	56	49	oscillator	oscillator	NOUN
ap-4603	56	50	in	in	ADP
ap-4603	56	51	momentum	momentum	NOUN
ap-4603	56	52	space	space	NOUN
ap-4603	56	53	.	.	PUNCT
ap-4603	57	1	3	3	X
ap-4603	57	2	.	.	X
ap-4603	57	3	the	the	DET
ap-4603	57	4	two	two	NUM
ap-4603	57	5	lowest	low	ADJ
ap-4603	57	6	eigenvalues	eigenvalue	NOUN
ap-4603	57	7	of	of	ADP
ap-4603	57	8	−∂2	−∂2	PROPN
ap-4603	57	9	x	x	PROPN
ap-4603	57	10	−	−	PROPN
ap-4603	57	11	λe−x2/2	λe−x2/2	PUNCT
ap-4603	57	12	3.1	3.1	NUM
ap-4603	57	13	.	.	PUNCT
ap-4603	58	1	the	the	DET
ap-4603	58	2	ground	ground	NOUN
ap-4603	58	3	state	state	NOUN
ap-4603	58	4	as	as	SCONJ
ap-4603	58	5	pointed	point	VERB
ap-4603	58	6	out	out	ADP
ap-4603	58	7	earlier	early	ADV
ap-4603	58	8	,	,	PUNCT
ap-4603	58	9	the	the	DET
ap-4603	58	10	divergent	divergent	ADJ
ap-4603	58	11	behaviour	behaviour	NOUN
ap-4603	58	12	of	of	ADP
ap-4603	58	13	the	the	DET
ap-4603	58	14	first	first	ADJ
ap-4603	58	15	term	term	NOUN
ap-4603	58	16	(	(	PUNCT
ap-4603	58	17	n	n	NOUN
ap-4603	58	18	=	=	SYM
ap-4603	58	19	0	0	NUM
ap-4603	58	20	)	)	PUNCT
ap-4603	58	21	of	of	ADP
ap-4603	58	22	the	the	DET
ap-4603	58	23	expansion	expansion	NOUN
ap-4603	58	24	of	of	ADP
ap-4603	58	25	the	the	DET
ap-4603	58	26	symmetric	symmetric	ADJ
ap-4603	58	27	part	part	NOUN
ap-4603	58	28	(	(	PUNCT
ap-4603	58	29	12	12	NUM
ap-4603	58	30	)	)	PUNCT
ap-4603	58	31	implies	imply	VERB
ap-4603	58	32	that	that	SCONJ
ap-4603	58	33	,	,	PUNCT
ap-4603	58	34	no	no	ADV
ap-4603	58	35	matter	matter	ADV
ap-4603	58	36	how	how	SCONJ
ap-4603	58	37	shallow	shallow	ADJ
ap-4603	58	38	the	the	DET
ap-4603	58	39	gaussian	gaussian	NOUN
ap-4603	58	40	well	well	ADV
ap-4603	58	41	may	may	AUX
ap-4603	58	42	be	be	AUX
ap-4603	58	43	(	(	PUNCT
ap-4603	58	44	small	small	ADJ
ap-4603	58	45	values	value	NOUN
ap-4603	58	46	of	of	ADP
ap-4603	58	47	the	the	DET
ap-4603	58	48	coupling	couple	VERB
ap-4603	58	49	constant	constant	ADJ
ap-4603	58	50	λ	λ	NOUN
ap-4603	58	51	)	)	PUNCT
ap-4603	58	52	,	,	PUNCT
ap-4603	58	53	there	there	PRON
ap-4603	58	54	will	will	AUX
ap-4603	58	55	always	always	ADV
ap-4603	58	56	exist	exist	VERB
ap-4603	58	57	at	at	ADV
ap-4603	58	58	least	least	ADV
ap-4603	58	59	one	one	NUM
ap-4603	58	60	bound	bind	VERB
ap-4603	58	61	state	state	NOUN
ap-4603	58	62	,	,	PUNCT
ap-4603	58	63	the	the	DET
ap-4603	58	64	ground	ground	NOUN
ap-4603	58	65	state	state	NOUN
ap-4603	58	66	,	,	PUNCT
ap-4603	58	67	whose	whose	DET
ap-4603	58	68	energy	energy	NOUN
ap-4603	58	69	is	be	AUX
ap-4603	58	70	−ε0(λ)2	−ε0(λ)2	ADJ
ap-4603	58	71	with	with	ADP
ap-4603	58	72	ε0(λ	ε0(λ	PROPN
ap-4603	58	73	)	)	PUNCT
ap-4603	58	74	given	give	VERB
ap-4603	58	75	by	by	ADP
ap-4603	58	76	the	the	DET
ap-4603	58	77	solution	solution	NOUN
ap-4603	58	78	of	of	ADP
ap-4603	58	79	a	a	DET
ap-4603	58	80	transcendental	transcendental	ADJ
ap-4603	58	81	equation	equation	NOUN
ap-4603	58	82	that	that	PRON
ap-4603	58	83	can	can	AUX
ap-4603	58	84	be	be	AUX
ap-4603	58	85	derived	derive	VERB
ap-4603	58	86	from	from	ADP
ap-4603	58	87	the	the	DET
ap-4603	58	88	application	application	NOUN
ap-4603	58	89	of	of	ADP
ap-4603	58	90	well	well	ADV
ap-4603	58	91	-	-	PUNCT
ap-4603	58	92	known	know	VERB
ap-4603	58	93	facts	fact	NOUN
ap-4603	58	94	regarding	regard	VERB
ap-4603	58	95	the	the	DET
ap-4603	58	96	fredholm	fredholm	NOUN
ap-4603	58	97	determinant	determinant	ADJ
ap-4603	58	98	of	of	ADP
ap-4603	58	99	a	a	DET
ap-4603	58	100	trace	trace	NOUN
ap-4603	58	101	class	class	NOUN
ap-4603	58	102	operator	operator	NOUN
ap-4603	58	103	(	(	PUNCT
ap-4603	58	104	see	see	VERB
ap-4603	58	105	,	,	PUNCT
ap-4603	58	106	e.g.	e.g.	ADV
ap-4603	58	107	,	,	PUNCT
ap-4603	58	108	[	[	X
ap-4603	58	109	12	12	NUM
ap-4603	58	110	]	]	NUM
ap-4603	58	111	)	)	PUNCT
ap-4603	58	112	,	,	PUNCT
ap-4603	58	113	namely	namely	ADV
ap-4603	58	114	:	:	PUNCT
ap-4603	58	115	det	det	X
ap-4603	58	116	(	(	PUNCT
ap-4603	58	117	1−	1−	NUM
ap-4603	58	118	λbsε	λbsε	NOUN
ap-4603	58	119	)	)	PUNCT
ap-4603	59	1	=	=	PUNCT
ap-4603	59	2	0	0	X
ap-4603	59	3	.	.	PUNCT
ap-4603	60	1	(	(	PUNCT
ap-4603	60	2	22	22	NUM
ap-4603	60	3	)	)	PUNCT
ap-4603	60	4	by	by	ADP
ap-4603	60	5	isolating	isolate	VERB
ap-4603	60	6	the	the	DET
ap-4603	60	7	first	first	ADJ
ap-4603	60	8	divergent	divergent	ADJ
ap-4603	60	9	rank	rank	NOUN
ap-4603	60	10	one	one	NUM
ap-4603	60	11	operator	operator	NOUN
ap-4603	60	12	in	in	ADP
ap-4603	60	13	the	the	DET
ap-4603	60	14	expansion	expansion	NOUN
ap-4603	60	15	of	of	ADP
ap-4603	60	16	λbsε	λbsε	NOUN
ap-4603	60	17	and	and	CCONJ
ap-4603	60	18	taking	take	VERB
ap-4603	60	19	advantage	advantage	NOUN
ap-4603	60	20	of	of	ADP
ap-4603	60	21	the	the	DET
ap-4603	60	22	boundedness	boundedness	NOUN
ap-4603	60	23	of	of	ADP
ap-4603	60	24	λbs,1ε	λbs,1ε	NOUN
ap-4603	60	25	,	,	PUNCT
ap-4603	60	26	the	the	DET
ap-4603	60	27	left	left	ADJ
ap-4603	60	28	hand	hand	NOUN
ap-4603	60	29	side	side	NOUN
ap-4603	60	30	of	of	ADP
ap-4603	60	31	(	(	PUNCT
ap-4603	60	32	22	22	NUM
ap-4603	60	33	)	)	PUNCT
ap-4603	60	34	can	can	AUX
ap-4603	60	35	be	be	AUX
ap-4603	60	36	rewritten	rewrite	VERB
ap-4603	60	37	as	as	ADP
ap-4603	60	38	det	det	X
ap-4603	60	39	(	(	PUNCT
ap-4603	60	40	1−	1−	NUM
ap-4603	60	41	λbs,0ε	λbs,0ε	NOUN
ap-4603	60	42	(	(	PUNCT
ap-4603	60	43	1−	1−	NUM
ap-4603	60	44	λbs,1ε	λbs,1ε	NOUN
ap-4603	60	45	)	)	PUNCT
ap-4603	60	46	−1	−1	NOUN
ap-4603	60	47	)	)	PUNCT
ap-4603	60	48	det	det	NOUN
ap-4603	60	49	(	(	PUNCT
ap-4603	60	50	1−	1−	NUM
ap-4603	60	51	λbs,1ε	λbs,1ε	NOUN
ap-4603	60	52	)	)	PUNCT
ap-4603	60	53	.	.	PUNCT
ap-4603	61	1	(	(	PUNCT
ap-4603	61	2	23	23	NUM
ap-4603	61	3	)	)	PUNCT
ap-4603	61	4	387	387	NUM
ap-4603	61	5	s.	s.	PROPN
ap-4603	61	6	fassari	fassari	PROPN
ap-4603	61	7	,	,	PUNCT
ap-4603	61	8	m.	m.	NOUN
ap-4603	61	9	gadella	gadella	PROPN
ap-4603	61	10	,	,	PUNCT
ap-4603	61	11	l.	l.	PROPN
ap-4603	61	12	m.	m.	PROPN
ap-4603	61	13	nieto	nieto	PROPN
ap-4603	61	14	,	,	PUNCT
ap-4603	61	15	f.	f.	PROPN
ap-4603	61	16	rinaldi	rinaldi	PROPN
ap-4603	61	17	acta	acta	PROPN
ap-4603	61	18	polytechnica	polytechnica	PROPN
ap-4603	61	19	0	0	NUM
ap-4603	61	20	1	1	NUM
ap-4603	61	21	2	2	NUM
ap-4603	61	22	3	3	NUM
ap-4603	61	23	4	4	NUM
ap-4603	61	24	-3.0	-3.0	NOUN
ap-4603	61	25	-2.5	-2.5	ADJ
ap-4603	61	26	-2.0	-2.0	ADJ
ap-4603	61	27	-1.5	-1.5	ADJ
ap-4603	61	28	-1.0	-1.0	PROPN
ap-4603	61	29	-0.5	-0.5	NUM
ap-4603	61	30	0.0	0.0	NUM
ap-4603	61	31	λ	λ	PROPN
ap-4603	61	32	e0	e0	NOUN
ap-4603	61	33	figure	figure	NOUN
ap-4603	61	34	1	1	NUM
ap-4603	61	35	.	.	PUNCT
ap-4603	62	1	the	the	DET
ap-4603	62	2	ground	ground	NOUN
ap-4603	62	3	state	state	NOUN
ap-4603	62	4	energy	energy	NOUN
ap-4603	62	5	e0(λ	e0(λ	PROPN
ap-4603	62	6	)	)	PUNCT
ap-4603	62	7	=	=	SYM
ap-4603	62	8	−ε0(λ)2	−ε0(λ)2	NOUN
ap-4603	62	9	,	,	PUNCT
ap-4603	62	10	as	as	ADP
ap-4603	62	11	a	a	DET
ap-4603	62	12	function	function	NOUN
ap-4603	62	13	of	of	ADP
ap-4603	62	14	the	the	DET
ap-4603	62	15	coupling	coupling	NOUN
ap-4603	62	16	parameter	parameter	PROPN
ap-4603	62	17	λ	λ	PROPN
ap-4603	62	18	.	.	PROPN
ap-4603	63	1	as	as	SCONJ
ap-4603	63	2	the	the	DET
ap-4603	63	3	first	first	ADJ
ap-4603	63	4	factor	factor	NOUN
ap-4603	63	5	is	be	AUX
ap-4603	63	6	the	the	DET
ap-4603	63	7	only	only	ADJ
ap-4603	63	8	one	one	NUM
ap-4603	63	9	involving	involve	VERB
ap-4603	63	10	the	the	DET
ap-4603	63	11	divergent	divergent	ADJ
ap-4603	63	12	rank	rank	NOUN
ap-4603	63	13	one	one	NUM
ap-4603	63	14	operator	operator	NOUN
ap-4603	63	15	bs,0ε	bs,0ε	NOUN
ap-4603	63	16	,	,	PUNCT
ap-4603	63	17	the	the	DET
ap-4603	63	18	equation	equation	NOUN
ap-4603	63	19	leading	lead	VERB
ap-4603	63	20	to	to	ADP
ap-4603	63	21	the	the	DET
ap-4603	63	22	determination	determination	NOUN
ap-4603	63	23	of	of	ADP
ap-4603	63	24	the	the	DET
ap-4603	63	25	ground	ground	NOUN
ap-4603	63	26	state	state	NOUN
ap-4603	63	27	energy	energy	NOUN
ap-4603	63	28	reduces	reduce	VERB
ap-4603	63	29	to	to	ADP
ap-4603	63	30	det	det	PROPN
ap-4603	63	31	(	(	PUNCT
ap-4603	63	32	1−	1−	NUM
ap-4603	63	33	λbs,0ε	λbs,0ε	NOUN
ap-4603	63	34	(	(	PUNCT
ap-4603	63	35	1−	1−	NUM
ap-4603	63	36	λbs,1ε	λbs,1ε	NOUN
ap-4603	63	37	)	)	PUNCT
ap-4603	63	38	−1	−1	NOUN
ap-4603	63	39	)	)	PUNCT
ap-4603	63	40	=	=	SYM
ap-4603	64	1	1−	1−	NUM
ap-4603	64	2	tr	tr	NOUN
ap-4603	64	3	(	(	PUNCT
ap-4603	64	4	λbs,0ε	λbs,0ε	PROPN
ap-4603	64	5	(	(	PUNCT
ap-4603	64	6	1−	1−	NUM
ap-4603	64	7	λbs,1ε	λbs,1ε	NOUN
ap-4603	64	8	)	)	PUNCT
ap-4603	64	9	−1	−1	NOUN
ap-4603	64	10	)	)	PUNCT
ap-4603	64	11	=	=	SYM
ap-4603	65	1	0	0	NUM
ap-4603	65	2	,	,	PUNCT
ap-4603	65	3	(	(	PUNCT
ap-4603	65	4	24	24	NUM
ap-4603	65	5	)	)	PUNCT
ap-4603	65	6	given	give	VERB
ap-4603	65	7	that	that	SCONJ
ap-4603	65	8	the	the	DET
ap-4603	65	9	second	second	ADJ
ap-4603	65	10	term	term	NOUN
ap-4603	65	11	inside	inside	ADP
ap-4603	65	12	the	the	DET
ap-4603	65	13	deteminant	deteminant	NOUN
ap-4603	65	14	is	be	AUX
ap-4603	65	15	a	a	DET
ap-4603	65	16	rank	rank	NOUN
ap-4603	65	17	one	one	NUM
ap-4603	65	18	operator	operator	NOUN
ap-4603	65	19	.	.	PUNCT
ap-4603	66	1	by	by	ADP
ap-4603	66	2	taking	take	VERB
ap-4603	66	3	only	only	ADV
ap-4603	66	4	the	the	DET
ap-4603	66	5	terms	term	NOUN
ap-4603	66	6	up	up	ADP
ap-4603	66	7	to	to	ADP
ap-4603	66	8	λ	λ	PROPN
ap-4603	66	9	in	in	ADP
ap-4603	66	10	the	the	DET
ap-4603	66	11	expansion	expansion	NOUN
ap-4603	66	12	of	of	ADP
ap-4603	66	13	the	the	DET
ap-4603	66	14	inverse	inverse	NOUN
ap-4603	66	15	inside	inside	ADP
ap-4603	66	16	the	the	DET
ap-4603	66	17	trace	trace	NOUN
ap-4603	66	18	in	in	ADP
ap-4603	66	19	(	(	PUNCT
ap-4603	66	20	24	24	NUM
ap-4603	66	21	)	)	PUNCT
ap-4603	66	22	,	,	PUNCT
ap-4603	66	23	we	we	PRON
ap-4603	66	24	get	get	VERB
ap-4603	66	25	the	the	DET
ap-4603	66	26	following	follow	VERB
ap-4603	66	27	quadratic	quadratic	ADJ
ap-4603	66	28	equation	equation	NOUN
ap-4603	66	29	in	in	ADP
ap-4603	66	30	λ	λ	NOUN
ap-4603	66	31	:	:	PUNCT
ap-4603	66	32	g0(ε	g0(ε	NOUN
ap-4603	66	33	)	)	PUNCT
ap-4603	66	34	2π	2π	PROPN
ap-4603	66	35	λ2	λ2	NOUN
ap-4603	66	36	+	+	CCONJ
ap-4603	66	37	f0(ε)√	f0(ε)√	ADJ
ap-4603	66	38	2π	2π	NOUN
ap-4603	66	39	λ−	λ−	PROPN
ap-4603	66	40	1	1	NUM
ap-4603	66	41	=	=	SYM
ap-4603	66	42	0	0	NUM
ap-4603	66	43	,	,	PUNCT
ap-4603	66	44	(	(	PUNCT
ap-4603	66	45	25	25	NUM
ap-4603	66	46	)	)	PUNCT
ap-4603	66	47	with	with	ADP
ap-4603	66	48	f0(ε	f0(ε	PRON
ap-4603	66	49	)	)	PUNCT
ap-4603	66	50	=	=	SYM
ap-4603	67	1	∫	∫	PROPN
ap-4603	68	1	+	+	NUM
ap-4603	68	2	∞	∞	PROPN
ap-4603	68	3	−∞	−∞	X
ap-4603	68	4	e−p	e−p	PROPN
ap-4603	68	5	2	2	NUM
ap-4603	68	6	p2	p2	NOUN
ap-4603	68	7	+	+	CCONJ
ap-4603	68	8	ε2	ε2	ADJ
ap-4603	68	9	dp	dp	NOUN
ap-4603	69	1	=	=	NOUN
ap-4603	69	2	π	π	X
ap-4603	69	3	ε	ε	PROPN
ap-4603	69	4	eε	eε	PROPN
ap-4603	69	5	2	2	NUM
ap-4603	69	6	erfc(ε	erfc(ε	NOUN
ap-4603	69	7	)	)	PUNCT
ap-4603	69	8	,	,	PUNCT
ap-4603	69	9	(	(	PUNCT
ap-4603	69	10	26	26	NUM
ap-4603	69	11	)	)	PUNCT
ap-4603	69	12	g0(ε	g0(ε	NOUN
ap-4603	69	13	)	)	PUNCT
ap-4603	69	14	=	=	SYM
ap-4603	70	1	∫	∫	PROPN
ap-4603	71	1	+	+	NUM
ap-4603	71	2	∞	∞	PROPN
ap-4603	71	3	−∞	−∞	ADP
ap-4603	71	4	dp	dp	NOUN
ap-4603	71	5	∫	∫	PROPN
ap-4603	72	1	+	+	PROPN
ap-4603	72	2	∞	∞	PROPN
ap-4603	72	3	−∞	−∞	X
ap-4603	72	4	e−p	e−p	PROPN
ap-4603	72	5	2	2	NUM
ap-4603	72	6	p2	p2	NOUN
ap-4603	72	7	+	+	CCONJ
ap-4603	72	8	ε2	ε2	ADJ
ap-4603	72	9	(	(	PUNCT
ap-4603	72	10	cosh(pq)−	cosh(pq)−	NOUN
ap-4603	72	11	1	1	NUM
ap-4603	72	12	)	)	PUNCT
ap-4603	72	13	e−q	e−q	NOUN
ap-4603	72	14	2	2	NUM
ap-4603	72	15	q2	q2	NOUN
ap-4603	72	16	+	+	CCONJ
ap-4603	72	17	ε2	ε2	PROPN
ap-4603	72	18	dq	dq	PROPN
ap-4603	72	19	.	.	PUNCT
ap-4603	73	1	(	(	PUNCT
ap-4603	73	2	27	27	NUM
ap-4603	73	3	)	)	PUNCT
ap-4603	73	4	by	by	ADP
ap-4603	73	5	using	use	VERB
ap-4603	73	6	the	the	DET
ap-4603	73	7	standard	standard	ADJ
ap-4603	73	8	taylor	taylor	PROPN
ap-4603	73	9	expansion	expansion	NOUN
ap-4603	73	10	of	of	ADP
ap-4603	73	11	the	the	DET
ap-4603	73	12	hyperbolic	hyperbolic	ADJ
ap-4603	73	13	cosine	cosine	NOUN
ap-4603	73	14	,	,	PUNCT
ap-4603	73	15	the	the	DET
ap-4603	73	16	latter	latter	ADJ
ap-4603	73	17	double	double	ADJ
ap-4603	73	18	integral	integral	NOUN
ap-4603	73	19	can	can	AUX
ap-4603	73	20	be	be	AUX
ap-4603	73	21	recast	recast	VERB
ap-4603	73	22	as	as	ADP
ap-4603	73	23	the	the	DET
ap-4603	73	24	following	follow	VERB
ap-4603	73	25	convergent	convergent	NOUN
ap-4603	73	26	series	serie	NOUN
ap-4603	73	27	whose	whose	DET
ap-4603	73	28	coefficients	coefficient	NOUN
ap-4603	73	29	are	be	AUX
ap-4603	73	30	expressed	express	VERB
ap-4603	73	31	in	in	ADP
ap-4603	73	32	terms	term	NOUN
ap-4603	73	33	of	of	ADP
ap-4603	73	34	the	the	DET
ap-4603	73	35	gamma	gamma	NOUN
ap-4603	73	36	and	and	CCONJ
ap-4603	73	37	the	the	DET
ap-4603	73	38	incomplete	incomplete	ADJ
ap-4603	73	39	gamma	gamma	NOUN
ap-4603	73	40	functions	function	NOUN
ap-4603	73	41	:	:	PUNCT
ap-4603	73	42	g0(ε	g0(ε	X
ap-4603	73	43	)	)	PUNCT
ap-4603	73	44	=	=	NOUN
ap-4603	74	1	∞∑	∞∑	NUM
ap-4603	74	2	n=1	n=1	PROPN
ap-4603	74	3	1	1	NUM
ap-4603	74	4	(	(	PUNCT
ap-4603	74	5	2n	2n	NUM
ap-4603	74	6	)	)	PUNCT
ap-4603	74	7	!	!	PUNCT
ap-4603	75	1	(	(	PUNCT
ap-4603	75	2	∫	∫	PROPN
ap-4603	75	3	+	+	ADJ
ap-4603	75	4	∞	∞	PROPN
ap-4603	75	5	−∞	−∞	X
ap-4603	75	6	p2ne−p	p2ne−p	NOUN
ap-4603	75	7	2	2	NUM
ap-4603	75	8	p2	p2	NOUN
ap-4603	75	9	+	+	CCONJ
ap-4603	75	10	ε2	ε2	ADJ
ap-4603	75	11	dp	dp	NOUN
ap-4603	75	12	)	)	PUNCT
ap-4603	75	13	2	2	NUM
ap-4603	75	14	=	=	SYM
ap-4603	75	15	e2ε2	e2ε2	X
ap-4603	75	16	∞∑	∞∑	NUM
ap-4603	75	17	n=1	n=1	PROPN
ap-4603	75	18	ε2(2n−1	ε2(2n−1	PROPN
ap-4603	75	19	)	)	PUNCT
ap-4603	75	20	(	(	PUNCT
ap-4603	75	21	γ(n+	γ(n+	NOUN
ap-4603	75	22	1/2)γ(−n+	1/2)γ(−n+	NUM
ap-4603	75	23	1/2	1/2	NUM
ap-4603	75	24	,	,	PUNCT
ap-4603	75	25	ε2))2	ε2))2	NOUN
ap-4603	75	26	γ(2n+	γ(2n+	PROPN
ap-4603	75	27	1	1	NUM
ap-4603	75	28	)	)	PUNCT
ap-4603	75	29	.	.	PUNCT
ap-4603	76	1	(	(	PUNCT
ap-4603	76	2	28	28	NUM
ap-4603	76	3	)	)	PUNCT
ap-4603	76	4	hence	hence	ADV
ap-4603	76	5	,	,	PUNCT
ap-4603	76	6	the	the	DET
ap-4603	76	7	positive	positive	ADJ
ap-4603	76	8	solution	solution	NOUN
ap-4603	76	9	of	of	ADP
ap-4603	76	10	(	(	PUNCT
ap-4603	76	11	25	25	NUM
ap-4603	76	12	)	)	PUNCT
ap-4603	76	13	is	be	AUX
ap-4603	76	14	given	give	VERB
ap-4603	76	15	by	by	ADP
ap-4603	76	16	the	the	DET
ap-4603	76	17	function	function	NOUN
ap-4603	76	18	from	from	ADP
ap-4603	76	19	[	[	X
ap-4603	76	20	0,+∞	0,+∞	NUM
ap-4603	76	21	)	)	PUNCT
ap-4603	76	22	to	to	ADP
ap-4603	76	23	[	[	X
ap-4603	76	24	0,+∞	0,+∞	NUM
ap-4603	76	25	):	):	PUNCT
ap-4603	76	26	λ(ε	λ(ε	X
ap-4603	76	27	)	)	PUNCT
ap-4603	77	1	=	=	SYM
ap-4603	77	2	2	2	NUM
ap-4603	77	3	√	√	NUM
ap-4603	77	4	2π	2π	NOUN
ap-4603	77	5	(	(	PUNCT
ap-4603	77	6	f2	f2	PROPN
ap-4603	77	7	0	0	NUM
ap-4603	77	8	(	(	PUNCT
ap-4603	77	9	ε	ε	PROPN
ap-4603	77	10	)	)	PUNCT
ap-4603	77	11	+	+	NOUN
ap-4603	77	12	4g0(ε))1/2	4g0(ε))1/2	NUM
ap-4603	77	13	+	+	CCONJ
ap-4603	77	14	f0(ε	f0(ε	NOUN
ap-4603	77	15	)	)	PUNCT
ap-4603	77	16	,	,	PUNCT
ap-4603	77	17	(	(	PUNCT
ap-4603	77	18	29	29	NUM
ap-4603	77	19	)	)	PUNCT
ap-4603	77	20	which	which	PRON
ap-4603	77	21	can	can	AUX
ap-4603	77	22	be	be	AUX
ap-4603	77	23	inverted	invert	VERB
ap-4603	77	24	to	to	PART
ap-4603	77	25	get	get	VERB
ap-4603	77	26	the	the	DET
ap-4603	77	27	required	required	ADJ
ap-4603	77	28	ε0(λ	ε0(λ	PROPN
ap-4603	77	29	)	)	PUNCT
ap-4603	77	30	,	,	PUNCT
ap-4603	77	31	leading	lead	VERB
ap-4603	77	32	to	to	ADP
ap-4603	77	33	the	the	DET
ap-4603	77	34	ground	ground	NOUN
ap-4603	77	35	state	state	NOUN
ap-4603	77	36	energy	energy	NOUN
ap-4603	77	37	e0(λ	e0(λ	PROPN
ap-4603	77	38	)	)	PUNCT
ap-4603	77	39	=	=	SYM
ap-4603	77	40	−ε0(λ)2	−ε0(λ)2	NOUN
ap-4603	77	41	,	,	PUNCT
ap-4603	77	42	the	the	DET
ap-4603	77	43	plot	plot	NOUN
ap-4603	77	44	of	of	ADP
ap-4603	77	45	which	which	PRON
ap-4603	77	46	is	be	AUX
ap-4603	77	47	shown	show	VERB
ap-4603	77	48	in	in	ADP
ap-4603	77	49	figure	figure	NOUN
ap-4603	77	50	1	1	NUM
ap-4603	77	51	.	.	NOUN
ap-4603	77	52	3.2	3.2	NUM
ap-4603	77	53	.	.	PUNCT
ap-4603	78	1	the	the	DET
ap-4603	78	2	first	first	ADJ
ap-4603	78	3	excited	excited	ADJ
ap-4603	78	4	state	state	NOUN
ap-4603	78	5	let	let	VERB
ap-4603	78	6	us	we	PRON
ap-4603	78	7	now	now	ADV
ap-4603	78	8	consider	consider	VERB
ap-4603	78	9	the	the	DET
ap-4603	78	10	antisymmetric	antisymmetric	ADJ
ap-4603	78	11	component	component	NOUN
ap-4603	78	12	given	give	VERB
ap-4603	78	13	by	by	ADP
ap-4603	78	14	(	(	PUNCT
ap-4603	78	15	9	9	NUM
ap-4603	78	16	)	)	PUNCT
ap-4603	78	17	or	or	CCONJ
ap-4603	78	18	(	(	PUNCT
ap-4603	78	19	11	11	NUM
ap-4603	78	20	)	)	PUNCT
ap-4603	78	21	,	,	PUNCT
ap-4603	78	22	so	so	SCONJ
ap-4603	78	23	that	that	SCONJ
ap-4603	78	24	we	we	PRON
ap-4603	78	25	have	have	VERB
ap-4603	78	26	to	to	PART
ap-4603	78	27	study	study	VERB
ap-4603	78	28	the	the	DET
ap-4603	78	29	equation	equation	NOUN
ap-4603	78	30	det	det	X
ap-4603	78	31	(	(	PUNCT
ap-4603	78	32	1−	1−	NUM
ap-4603	78	33	λbaε	λbaε	NOUN
ap-4603	78	34	)	)	PUNCT
ap-4603	79	1	=	=	PUNCT
ap-4603	79	2	0	0	X
ap-4603	79	3	.	.	PUNCT
ap-4603	80	1	as	as	ADP
ap-4603	80	2	a	a	DET
ap-4603	80	3	result	result	NOUN
ap-4603	80	4	of	of	ADP
ap-4603	80	5	the	the	DET
ap-4603	80	6	explicit	explicit	ADJ
ap-4603	80	7	expression	expression	NOUN
ap-4603	80	8	of	of	ADP
ap-4603	80	9	the	the	DET
ap-4603	80	10	integral	integral	ADJ
ap-4603	80	11	kernel	kernel	NOUN
ap-4603	80	12	of	of	ADP
ap-4603	80	13	baε	baε	PROPN
ap-4603	80	14	,	,	PUNCT
ap-4603	80	15	it	it	PRON
ap-4603	80	16	is	be	AUX
ap-4603	80	17	not	not	PART
ap-4603	80	18	difficult	difficult	ADJ
ap-4603	80	19	to	to	PART
ap-4603	80	20	show	show	VERB
ap-4603	80	21	that	that	SCONJ
ap-4603	80	22	λbaε	λbaε	PROPN
ap-4603	80	23	converges	converge	VERB
ap-4603	80	24	weakly	weakly	ADJ
ap-4603	80	25	to	to	ADP
ap-4603	80	26	λba0	λba0	NOUN
ap-4603	80	27	,	,	PUNCT
ap-4603	80	28	where	where	SCONJ
ap-4603	80	29	the	the	DET
ap-4603	80	30	trace	trace	NOUN
ap-4603	80	31	class	class	NOUN
ap-4603	80	32	operator	operator	NOUN
ap-4603	80	33	ba0	ba0	NOUN
ap-4603	80	34	is	be	AUX
ap-4603	80	35	given	give	VERB
ap-4603	80	36	by	by	ADP
ap-4603	80	37	(	(	PUNCT
ap-4603	80	38	18	18	NUM
ap-4603	80	39	)	)	PUNCT
ap-4603	80	40	.	.	PUNCT
ap-4603	81	1	as	as	ADP
ap-4603	81	2	a	a	DET
ap-4603	81	3	consequence	consequence	NOUN
ap-4603	81	4	of	of	ADP
ap-4603	81	5	theorem	theorem	NOUN
ap-4603	81	6	2.2	2.2	NUM
ap-4603	81	7	,	,	PUNCT
ap-4603	81	8	and	and	CCONJ
ap-4603	81	9	in	in	ADP
ap-4603	81	10	analogy	analogy	NOUN
ap-4603	81	11	to	to	ADP
ap-4603	81	12	what	what	PRON
ap-4603	81	13	has	have	AUX
ap-4603	81	14	been	be	AUX
ap-4603	81	15	done	do	VERB
ap-4603	81	16	for	for	ADP
ap-4603	81	17	the	the	DET
ap-4603	81	18	determination	determination	NOUN
ap-4603	81	19	of	of	ADP
ap-4603	81	20	the	the	DET
ap-4603	81	21	ground	ground	NOUN
ap-4603	81	22	state	state	NOUN
ap-4603	81	23	energy	energy	NOUN
ap-4603	81	24	,	,	PUNCT
ap-4603	81	25	e1(λ	e1(λ	PROPN
ap-4603	81	26	)	)	PUNCT
ap-4603	81	27	=	=	SYM
ap-4603	81	28	−ε1(λ)2	−ε1(λ)2	ADJ
ap-4603	81	29	,	,	PUNCT
ap-4603	81	30	the	the	DET
ap-4603	81	31	energy	energy	NOUN
ap-4603	81	32	of	of	ADP
ap-4603	81	33	the	the	DET
ap-4603	81	34	first	first	ADJ
ap-4603	81	35	antisymmetric	antisymmetric	ADJ
ap-4603	81	36	bound	bind	VERB
ap-4603	81	37	state	state	NOUN
ap-4603	81	38	,	,	PUNCT
ap-4603	81	39	can	can	AUX
ap-4603	81	40	be	be	AUX
ap-4603	81	41	determined	determine	VERB
ap-4603	81	42	by	by	ADP
ap-4603	81	43	means	mean	NOUN
ap-4603	81	44	of	of	ADP
ap-4603	81	45	the	the	DET
ap-4603	81	46	following	follow	VERB
ap-4603	81	47	equation	equation	NOUN
ap-4603	81	48	:	:	PUNCT
ap-4603	81	49	det	det	PROPN
ap-4603	81	50	(	(	PUNCT
ap-4603	81	51	1−	1−	NUM
ap-4603	81	52	λba,0ε	λba,0ε	NOUN
ap-4603	81	53	(	(	PUNCT
ap-4603	81	54	i	i	PRON
ap-4603	81	55	−	−	VERB
ap-4603	81	56	λba,1ε	λba,1ε	NOUN
ap-4603	81	57	)	)	PUNCT
ap-4603	81	58	−1	−1	NOUN
ap-4603	81	59	)	)	PUNCT
ap-4603	82	1	=	=	SYM
ap-4603	82	2	0	0	NUM
ap-4603	82	3	,	,	PUNCT
ap-4603	82	4	(	(	PUNCT
ap-4603	82	5	30	30	NUM
ap-4603	82	6	)	)	PUNCT
ap-4603	82	7	with	with	ADP
ap-4603	82	8	ba,1ε	ba,1ε	NOUN
ap-4603	82	9	=	=	SYM
ap-4603	82	10	baε	baε	PROPN
ap-4603	82	11	−	−	PROPN
ap-4603	82	12	ba,0ε	ba,0ε	PROPN
ap-4603	82	13	,	,	PUNCT
ap-4603	82	14	which	which	PRON
ap-4603	82	15	is	be	AUX
ap-4603	82	16	obviously	obviously	ADV
ap-4603	82	17	trace	trace	NOUN
ap-4603	82	18	class	class	NOUN
ap-4603	82	19	.	.	PUNCT
ap-4603	83	1	taking	take	VERB
ap-4603	83	2	account	account	NOUN
ap-4603	83	3	of	of	ADP
ap-4603	83	4	the	the	DET
ap-4603	83	5	fact	fact	NOUN
ap-4603	83	6	that	that	SCONJ
ap-4603	83	7	ba,0ε	ba,0ε	PROPN
ap-4603	83	8	is	be	AUX
ap-4603	83	9	a	a	DET
ap-4603	83	10	rank	rank	NOUN
ap-4603	83	11	one	one	NUM
ap-4603	83	12	operator	operator	NOUN
ap-4603	83	13	,	,	PUNCT
ap-4603	83	14	the	the	DET
ap-4603	83	15	latter	latter	ADJ
ap-4603	83	16	equation	equation	NOUN
ap-4603	83	17	becomes	become	VERB
ap-4603	83	18	1−	1−	NUM
ap-4603	83	19	λ	λ	NOUN
ap-4603	83	20	tr	tr	PUNCT
ap-4603	83	21	(	(	PUNCT
ap-4603	83	22	ba,0ε	ba,0ε	PROPN
ap-4603	83	23	(	(	PUNCT
ap-4603	83	24	i	i	PRON
ap-4603	83	25	−	−	VERB
ap-4603	83	26	λba,1ε	λba,1ε	NOUN
ap-4603	83	27	)	)	PUNCT
ap-4603	83	28	−1	−1	NOUN
ap-4603	83	29	)	)	PUNCT
ap-4603	83	30	=	=	SYM
ap-4603	84	1	0	0	PUNCT
ap-4603	85	1	(	(	PUNCT
ap-4603	85	2	31	31	NUM
ap-4603	85	3	)	)	PUNCT
ap-4603	85	4	388	388	NUM
ap-4603	85	5	vol	vol	NOUN
ap-4603	85	6	.	.	PUNCT
ap-4603	86	1	57	57	NUM
ap-4603	86	2	no	no	NOUN
ap-4603	86	3	.	.	PUNCT
ap-4603	87	1	6/2017	6/2017	NUM
ap-4603	87	2	on	on	ADP
ap-4603	87	3	the	the	DET
ap-4603	87	4	spectrum	spectrum	NOUN
ap-4603	87	5	of	of	ADP
ap-4603	87	6	the	the	DET
ap-4603	87	7	one	one	NUM
ap-4603	87	8	-	-	PUNCT
ap-4603	87	9	dimensional	dimensional	ADJ
ap-4603	87	10	schrödinger	schrödinger	ADJ
ap-4603	87	11	hamiltonian	hamiltonian	ADJ
ap-4603	87	12	1.5	1.5	NUM
ap-4603	87	13	2.0	2.0	NUM
ap-4603	87	14	2.5	2.5	NUM
ap-4603	87	15	3.0	3.0	NUM
ap-4603	87	16	3.5	3.5	NUM
ap-4603	87	17	4.0	4.0	NUM
ap-4603	87	18	-0.7	-0.7	PROPN
ap-4603	87	19	-0.6	-0.6	X
ap-4603	87	20	-0.5	-0.5	PROPN
ap-4603	87	21	-0.4	-0.4	PROPN
ap-4603	87	22	-0.3	-0.3	PROPN
ap-4603	87	23	-0.2	-0.2	PROPN
ap-4603	87	24	-0.1	-0.1	PROPN
ap-4603	87	25	0.0	0.0	NUM
ap-4603	87	26	λ	λ	NOUN
ap-4603	87	27	e1	e1	NOUN
ap-4603	87	28	figure	figure	NOUN
ap-4603	87	29	2	2	NUM
ap-4603	87	30	.	.	PUNCT
ap-4603	88	1	the	the	DET
ap-4603	88	2	energy	energy	NOUN
ap-4603	88	3	of	of	ADP
ap-4603	88	4	the	the	DET
ap-4603	88	5	first	first	ADJ
ap-4603	88	6	excited	excited	ADJ
ap-4603	88	7	state	state	NOUN
ap-4603	88	8	e1(λ	e1(λ	PROPN
ap-4603	88	9	)	)	PUNCT
ap-4603	88	10	=	=	SYM
ap-4603	88	11	−ε1(λ)2	−ε1(λ)2	ADJ
ap-4603	88	12	,	,	PUNCT
ap-4603	88	13	as	as	ADP
ap-4603	88	14	a	a	DET
ap-4603	88	15	function	function	NOUN
ap-4603	88	16	of	of	ADP
ap-4603	88	17	the	the	DET
ap-4603	88	18	coupling	coupling	NOUN
ap-4603	88	19	parameter	parameter	PROPN
ap-4603	88	20	λ	λ	PROPN
ap-4603	88	21	.	.	PUNCT
ap-4603	88	22	by	by	ADP
ap-4603	88	23	taking	take	VERB
ap-4603	88	24	only	only	ADV
ap-4603	88	25	the	the	DET
ap-4603	88	26	terms	term	NOUN
ap-4603	88	27	up	up	ADP
ap-4603	88	28	to	to	ADP
ap-4603	88	29	λ	λ	PROPN
ap-4603	88	30	in	in	ADP
ap-4603	88	31	the	the	DET
ap-4603	88	32	expansion	expansion	NOUN
ap-4603	88	33	of	of	ADP
ap-4603	88	34	the	the	DET
ap-4603	88	35	inverse	inverse	NOUN
ap-4603	88	36	,	,	PUNCT
ap-4603	88	37	we	we	PRON
ap-4603	88	38	get	get	VERB
ap-4603	88	39	the	the	DET
ap-4603	88	40	equation	equation	NOUN
ap-4603	88	41	:	:	PUNCT
ap-4603	88	42	g1(ε	g1(ε	SYM
ap-4603	88	43	)	)	PUNCT
ap-4603	88	44	2π	2π	PROPN
ap-4603	88	45	λ2	λ2	NOUN
ap-4603	88	46	+	+	CCONJ
ap-4603	88	47	f1(ε)√	f1(ε)√	ADJ
ap-4603	88	48	2π	2π	NOUN
ap-4603	88	49	λ−	λ−	PROPN
ap-4603	88	50	1	1	NUM
ap-4603	88	51	=	=	SYM
ap-4603	88	52	0	0	NUM
ap-4603	88	53	,	,	PUNCT
ap-4603	88	54	(	(	PUNCT
ap-4603	88	55	32	32	NUM
ap-4603	88	56	)	)	PUNCT
ap-4603	88	57	with	with	ADP
ap-4603	88	58	f1(ε	f1(ε	NOUN
ap-4603	88	59	)	)	PUNCT
ap-4603	88	60	=	=	SYM
ap-4603	88	61	∫	∫	PROPN
ap-4603	89	1	+	+	NUM
ap-4603	89	2	∞	∞	PROPN
ap-4603	89	3	−∞	−∞	ADP
ap-4603	89	4	p2e−p	p2e−p	ADJ
ap-4603	89	5	2	2	NUM
ap-4603	89	6	p2	p2	NOUN
ap-4603	89	7	+	+	CCONJ
ap-4603	89	8	ε2	ε2	ADJ
ap-4603	89	9	dp	dp	NOUN
ap-4603	89	10	=	=	PUNCT
ap-4603	89	11	√	√	NUM
ap-4603	89	12	π	π	PROPN
ap-4603	89	13	−	−	PROPN
ap-4603	89	14	πεeε	πεeε	NOUN
ap-4603	89	15	2	2	NUM
ap-4603	89	16	erfc(ε	erfc(ε	NOUN
ap-4603	89	17	)	)	PUNCT
ap-4603	89	18	,	,	PUNCT
ap-4603	89	19	(	(	PUNCT
ap-4603	89	20	33	33	NUM
ap-4603	89	21	)	)	PUNCT
ap-4603	89	22	g1(ε	g1(ε	PROPN
ap-4603	89	23	)	)	PUNCT
ap-4603	89	24	=	=	SYM
ap-4603	90	1	∫	∫	PROPN
ap-4603	91	1	+	+	NUM
ap-4603	91	2	∞	∞	PROPN
ap-4603	91	3	−∞	−∞	ADP
ap-4603	91	4	dp	dp	NOUN
ap-4603	91	5	pe−p	pe−p	NOUN
ap-4603	91	6	2	2	NUM
ap-4603	91	7	p2	p2	NOUN
ap-4603	91	8	+	+	CCONJ
ap-4603	91	9	ε2	ε2	ADJ
ap-4603	91	10	∫	∫	PROPN
ap-4603	92	1	+	+	X
ap-4603	92	2	∞	∞	PROPN
ap-4603	92	3	−∞	−∞	ADP
ap-4603	92	4	dq	dq	PROPN
ap-4603	92	5	(	(	PUNCT
ap-4603	92	6	sinh(pq)−	sinh(pq)−	PROPN
ap-4603	92	7	pq	pq	NOUN
ap-4603	92	8	)	)	PUNCT
ap-4603	92	9	qe−q2	qe−q2	PROPN
ap-4603	92	10	q2	q2	NOUN
ap-4603	92	11	+	+	CCONJ
ap-4603	92	12	ε2	ε2	ADJ
ap-4603	92	13	.	.	PUNCT
ap-4603	93	1	(	(	PUNCT
ap-4603	93	2	34	34	NUM
ap-4603	93	3	)	)	PUNCT
ap-4603	93	4	by	by	ADP
ap-4603	93	5	using	use	VERB
ap-4603	93	6	now	now	ADV
ap-4603	93	7	the	the	DET
ap-4603	93	8	standard	standard	ADJ
ap-4603	93	9	taylor	taylor	PROPN
ap-4603	93	10	expansion	expansion	NOUN
ap-4603	93	11	of	of	ADP
ap-4603	93	12	the	the	DET
ap-4603	93	13	hyperbolic	hyperbolic	ADJ
ap-4603	93	14	sine	sine	NOUN
ap-4603	93	15	,	,	PUNCT
ap-4603	93	16	the	the	DET
ap-4603	93	17	latter	latter	ADJ
ap-4603	93	18	double	double	ADJ
ap-4603	93	19	integral	integral	NOUN
ap-4603	93	20	can	can	AUX
ap-4603	93	21	be	be	AUX
ap-4603	93	22	recast	recast	VERB
ap-4603	93	23	as	as	ADP
ap-4603	93	24	the	the	DET
ap-4603	93	25	following	follow	VERB
ap-4603	93	26	convergent	convergent	NOUN
ap-4603	93	27	series	serie	NOUN
ap-4603	93	28	whose	whose	DET
ap-4603	93	29	coefficients	coefficient	NOUN
ap-4603	93	30	are	be	AUX
ap-4603	93	31	expressed	express	VERB
ap-4603	93	32	in	in	ADP
ap-4603	93	33	terms	term	NOUN
ap-4603	93	34	of	of	ADP
ap-4603	93	35	the	the	DET
ap-4603	93	36	gamma	gamma	NOUN
ap-4603	93	37	and	and	CCONJ
ap-4603	93	38	the	the	DET
ap-4603	93	39	incomplete	incomplete	ADJ
ap-4603	93	40	gamma	gamma	NOUN
ap-4603	93	41	function	function	NOUN
ap-4603	93	42	:	:	PUNCT
ap-4603	94	1	g1(ε	g1(ε	X
ap-4603	94	2	)	)	PUNCT
ap-4603	94	3	=	=	PUNCT
ap-4603	95	1	∞∑	∞∑	NUM
ap-4603	95	2	n=1	n=1	PROPN
ap-4603	95	3	1	1	NUM
ap-4603	95	4	(	(	PUNCT
ap-4603	95	5	2n+	2n+	NUM
ap-4603	95	6	1	1	NUM
ap-4603	95	7	)	)	PUNCT
ap-4603	95	8	!	!	PUNCT
ap-4603	96	1	(	(	PUNCT
ap-4603	96	2	∫	∫	PROPN
ap-4603	96	3	∞	∞	PROPN
ap-4603	96	4	−∞	−∞	X
ap-4603	96	5	p2n+2e−p	p2n+2e−p	NOUN
ap-4603	96	6	2	2	NUM
ap-4603	96	7	p2	p2	NOUN
ap-4603	96	8	+	+	CCONJ
ap-4603	96	9	ε2	ε2	ADJ
ap-4603	96	10	dp	dp	NOUN
ap-4603	96	11	)	)	PUNCT
ap-4603	96	12	2	2	NUM
ap-4603	96	13	=	=	SYM
ap-4603	96	14	e2ε2	e2ε2	X
ap-4603	96	15	∞∑	∞∑	NUM
ap-4603	96	16	n=1	n=1	PROPN
ap-4603	96	17	ε2(2n+1	ε2(2n+1	PROPN
ap-4603	96	18	)	)	PUNCT
ap-4603	96	19	(	(	PUNCT
ap-4603	96	20	γ(n+	γ(n+	NUM
ap-4603	96	21	3/2)γ(−n−	3/2)γ(−n−	NUM
ap-4603	96	22	1/2	1/2	NUM
ap-4603	96	23	,	,	PUNCT
ap-4603	96	24	ε2))2	ε2))2	NOUN
ap-4603	96	25	γ(2n+	γ(2n+	PROPN
ap-4603	96	26	2	2	NUM
ap-4603	96	27	)	)	PUNCT
ap-4603	96	28	.	.	PUNCT
ap-4603	97	1	(	(	PUNCT
ap-4603	97	2	35	35	NUM
ap-4603	97	3	)	)	PUNCT
ap-4603	97	4	hence	hence	ADV
ap-4603	97	5	,	,	PUNCT
ap-4603	97	6	the	the	DET
ap-4603	97	7	positive	positive	ADJ
ap-4603	97	8	solution	solution	NOUN
ap-4603	97	9	of	of	ADP
ap-4603	97	10	(	(	PUNCT
ap-4603	97	11	32	32	NUM
ap-4603	97	12	)	)	PUNCT
ap-4603	97	13	is	be	AUX
ap-4603	97	14	given	give	VERB
ap-4603	97	15	by	by	ADP
ap-4603	97	16	λ1(ε	λ1(ε	NOUN
ap-4603	97	17	)	)	PUNCT
ap-4603	97	18	=	=	SYM
ap-4603	98	1	2	2	NUM
ap-4603	98	2	√	√	NUM
ap-4603	98	3	2π	2π	NOUN
ap-4603	98	4	(	(	PUNCT
ap-4603	98	5	f2	f2	PROPN
ap-4603	98	6	1	1	NUM
ap-4603	98	7	(	(	PUNCT
ap-4603	98	8	ε	ε	PROPN
ap-4603	98	9	)	)	PUNCT
ap-4603	98	10	+	+	CCONJ
ap-4603	98	11	4g1(ε))1/2	4g1(ε))1/2	NUM
ap-4603	98	12	+	+	ADJ
ap-4603	98	13	f1(ε	f1(ε	NOUN
ap-4603	98	14	)	)	PUNCT
ap-4603	98	15	,	,	PUNCT
ap-4603	98	16	(	(	PUNCT
ap-4603	98	17	36	36	NUM
ap-4603	98	18	)	)	PUNCT
ap-4603	98	19	with	with	ADP
ap-4603	98	20	domain	domain	NOUN
ap-4603	98	21	[	[	X
ap-4603	98	22	0,+∞	0,+∞	NUM
ap-4603	98	23	)	)	PUNCT
ap-4603	98	24	and	and	CCONJ
ap-4603	98	25	codomain	codomain	ADV
ap-4603	98	26	given	give	VERB
ap-4603	98	27	by	by	ADP
ap-4603	98	28	[	[	X
ap-4603	98	29	λ1(0),+∞	λ1(0),+∞	X
ap-4603	98	30	)	)	PUNCT
ap-4603	98	31	,	,	PUNCT
ap-4603	98	32	λ1(0	λ1(0	PROPN
ap-4603	98	33	)	)	PUNCT
ap-4603	98	34	being	be	AUX
ap-4603	98	35	λ1(0	λ1(0	PRON
ap-4603	98	36	)	)	PUNCT
ap-4603	98	37	=	=	SYM
ap-4603	99	1	2	2	NUM
ap-4603	99	2	√	√	NUM
ap-4603	99	3	6	6	NUM
ap-4603	99	4	√	√	NOUN
ap-4603	99	5	4π	4π	NUM
ap-4603	99	6	−	−	NUM
ap-4603	99	7	9	9	NUM
ap-4603	99	8	+	+	CCONJ
ap-4603	99	9	√	√	NUM
ap-4603	99	10	3	3	NUM
ap-4603	99	11	≈	≈	PROPN
ap-4603	99	12	1.35311	1.35311	NUM
ap-4603	99	13	.	.	PUNCT
ap-4603	100	1	(	(	PUNCT
ap-4603	100	2	37	37	NUM
ap-4603	100	3	)	)	PUNCT
ap-4603	100	4	hence	hence	ADV
ap-4603	100	5	,	,	PUNCT
ap-4603	100	6	the	the	DET
ap-4603	100	7	latter	latter	ADJ
ap-4603	100	8	function	function	NOUN
ap-4603	100	9	can	can	AUX
ap-4603	100	10	be	be	AUX
ap-4603	100	11	inverted	invert	VERB
ap-4603	100	12	to	to	PART
ap-4603	100	13	get	get	VERB
ap-4603	100	14	ε1(λ	ε1(λ	NOUN
ap-4603	100	15	)	)	PUNCT
ap-4603	100	16	,	,	PUNCT
ap-4603	100	17	as	as	ADV
ap-4603	100	18	well	well	ADV
ap-4603	100	19	as	as	ADP
ap-4603	100	20	e1(λ	e1(λ	NOUN
ap-4603	100	21	)	)	PUNCT
ap-4603	100	22	=	=	SYM
ap-4603	101	1	−ε1(λ)2	−ε1(λ)2	ADJ
ap-4603	101	2	whose	whose	DET
ap-4603	101	3	plot	plot	NOUN
ap-4603	101	4	is	be	AUX
ap-4603	101	5	given	give	VERB
ap-4603	101	6	in	in	ADP
ap-4603	101	7	figure	figure	NOUN
ap-4603	101	8	2	2	NUM
ap-4603	101	9	.	.	PUNCT
ap-4603	102	1	the	the	DET
ap-4603	102	2	plot	plot	NOUN
ap-4603	102	3	of	of	ADP
ap-4603	102	4	both	both	PRON
ap-4603	102	5	eigenvalues	eigenvalue	VERB
ap-4603	102	6	e0	e0	PROPN
ap-4603	102	7	and	and	CCONJ
ap-4603	102	8	e1	e1	PROPN
ap-4603	102	9	as	as	ADP
ap-4603	102	10	functions	function	NOUN
ap-4603	102	11	of	of	ADP
ap-4603	102	12	the	the	DET
ap-4603	102	13	coupling	coupling	NOUN
ap-4603	102	14	parameter	parameter	NOUN
ap-4603	102	15	λ	λ	PROPN
ap-4603	102	16	is	be	AUX
ap-4603	102	17	shown	show	VERB
ap-4603	102	18	in	in	ADP
ap-4603	102	19	figure	figure	NOUN
ap-4603	102	20	3	3	NUM
ap-4603	102	21	.	.	PUNCT
ap-4603	103	1	the	the	DET
ap-4603	103	2	isolated	isolated	ADJ
ap-4603	103	3	points	point	NOUN
ap-4603	103	4	are	be	AUX
ap-4603	103	5	those	those	PRON
ap-4603	103	6	resulting	result	VERB
ap-4603	103	7	from	from	ADP
ap-4603	103	8	table	table	NOUN
ap-4603	103	9	1	1	NUM
ap-4603	103	10	in	in	ADP
ap-4603	103	11	the	the	DET
ap-4603	103	12	aforementioned	aforementioned	ADJ
ap-4603	103	13	paper	paper	NOUN
ap-4603	103	14	by	by	ADP
ap-4603	103	15	fernández	fernández	PROPN
ap-4603	104	1	[	[	X
ap-4603	104	2	1	1	NUM
ap-4603	104	3	]	]	PUNCT
ap-4603	104	4	.	.	PUNCT
ap-4603	105	1	4	4	X
ap-4603	105	2	.	.	X
ap-4603	105	3	conclusions	conclusion	NOUN
ap-4603	105	4	by	by	ADP
ap-4603	105	5	combining	combine	VERB
ap-4603	105	6	a	a	DET
ap-4603	105	7	variation	variation	NOUN
ap-4603	105	8	of	of	ADP
ap-4603	105	9	the	the	DET
ap-4603	105	10	renowned	renowned	ADJ
ap-4603	105	11	birman	birman	NOUN
ap-4603	105	12	-	-	PUNCT
ap-4603	105	13	schwinger	schwinger	NOUN
ap-4603	105	14	principle	principle	NOUN
ap-4603	105	15	and	and	CCONJ
ap-4603	105	16	the	the	DET
ap-4603	105	17	use	use	NOUN
ap-4603	105	18	of	of	ADP
ap-4603	105	19	fredholm	fredholm	ADJ
ap-4603	105	20	determinants	determinant	NOUN
ap-4603	105	21	,	,	PUNCT
ap-4603	105	22	given	give	VERB
ap-4603	105	23	that	that	SCONJ
ap-4603	105	24	all	all	DET
ap-4603	105	25	the	the	DET
ap-4603	105	26	integral	integral	ADJ
ap-4603	105	27	operators	operator	NOUN
ap-4603	105	28	involved	involve	VERB
ap-4603	105	29	are	be	AUX
ap-4603	105	30	positive	positive	ADJ
ap-4603	105	31	trace	trace	NOUN
ap-4603	105	32	class	class	NOUN
ap-4603	105	33	operators	operator	NOUN
ap-4603	105	34	,	,	PUNCT
ap-4603	105	35	we	we	PRON
ap-4603	105	36	have	have	AUX
ap-4603	105	37	been	be	AUX
ap-4603	105	38	able	able	ADJ
ap-4603	105	39	to	to	PART
ap-4603	105	40	determine	determine	VERB
ap-4603	105	41	the	the	DET
ap-4603	105	42	two	two	NUM
ap-4603	105	43	lowest	low	ADJ
ap-4603	105	44	eigenenergies	eigenenergie	NOUN
ap-4603	105	45	,	,	PUNCT
ap-4603	105	46	the	the	DET
ap-4603	105	47	one	one	NUM
ap-4603	105	48	of	of	ADP
ap-4603	105	49	the	the	DET
ap-4603	105	50	ground	ground	NOUN
ap-4603	105	51	state	state	NOUN
ap-4603	105	52	and	and	CCONJ
ap-4603	105	53	that	that	PRON
ap-4603	105	54	of	of	ADP
ap-4603	105	55	the	the	DET
ap-4603	105	56	lowest	low	ADJ
ap-4603	105	57	antisymmetric	antisymmetric	ADJ
ap-4603	105	58	bound	bind	VERB
ap-4603	105	59	state	state	NOUN
ap-4603	105	60	,	,	PUNCT
ap-4603	105	61	of	of	ADP
ap-4603	105	62	the	the	DET
ap-4603	105	63	one	one	NUM
ap-4603	105	64	-	-	PUNCT
ap-4603	105	65	dimensional	dimensional	ADJ
ap-4603	105	66	hamiltonian	hamiltonian	ADJ
ap-4603	105	67	−∂2	−∂2	PROPN
ap-4603	105	68	x−λe−x	x−λe−x	PROPN
ap-4603	105	69	2/2	2/2	NUM
ap-4603	105	70	as	as	ADP
ap-4603	105	71	functions	function	NOUN
ap-4603	105	72	of	of	ADP
ap-4603	105	73	the	the	DET
ap-4603	105	74	coupling	coupling	NOUN
ap-4603	105	75	parameter	parameter	NOUN
ap-4603	105	76	.	.	PUNCT
ap-4603	106	1	whilst	whilst	SCONJ
ap-4603	106	2	the	the	DET
ap-4603	106	3	ground	ground	NOUN
ap-4603	106	4	state	state	NOUN
ap-4603	106	5	energy	energy	NOUN
ap-4603	106	6	emerges	emerge	VERB
ap-4603	106	7	out	out	ADP
ap-4603	106	8	of	of	ADP
ap-4603	106	9	the	the	DET
ap-4603	106	10	absolutely	absolutely	ADV
ap-4603	106	11	continuous	continuous	ADJ
ap-4603	106	12	spectrum	spectrum	NOUN
ap-4603	106	13	at	at	ADP
ap-4603	106	14	λ	λ	X
ap-4603	106	15	=	=	SYM
ap-4603	106	16	λ0(0	λ0(0	PROPN
ap-4603	106	17	)	)	PUNCT
ap-4603	107	1	=	=	SYM
ap-4603	107	2	0	0	NUM
ap-4603	107	3	,	,	PUNCT
ap-4603	107	4	the	the	DET
ap-4603	107	5	latter	latter	ADJ
ap-4603	107	6	emerges	emerge	VERB
ap-4603	107	7	at	at	ADP
ap-4603	107	8	λ	λ	PROPN
ap-4603	107	9	=	=	PUNCT
ap-4603	107	10	λ1(0	λ1(0	PROPN
ap-4603	107	11	)	)	PUNCT
ap-4603	107	12	,	,	PUNCT
ap-4603	107	13	approximately	approximately	ADV
ap-4603	107	14	equal	equal	ADJ
ap-4603	107	15	to	to	ADP
ap-4603	107	16	1.35311	1.35311	NUM
ap-4603	107	17	.	.	PUNCT
ap-4603	108	1	the	the	DET
ap-4603	108	2	method	method	NOUN
ap-4603	108	3	can	can	AUX
ap-4603	108	4	be	be	AUX
ap-4603	108	5	further	far	ADV
ap-4603	108	6	exploited	exploit	VERB
ap-4603	108	7	to	to	PART
ap-4603	108	8	determine	determine	VERB
ap-4603	108	9	other	other	ADJ
ap-4603	108	10	eigenvalues	eigenvalue	NOUN
ap-4603	108	11	of	of	ADP
ap-4603	108	12	the	the	DET
ap-4603	108	13	hamiltonian	hamiltonian	NOUN
ap-4603	108	14	.	.	PUNCT
ap-4603	109	1	for	for	ADP
ap-4603	109	2	example	example	NOUN
ap-4603	109	3	,	,	PUNCT
ap-4603	109	4	by	by	ADP
ap-4603	109	5	starting	start	VERB
ap-4603	109	6	with	with	ADP
ap-4603	109	7	the	the	DET
ap-4603	109	8	function	function	NOUN
ap-4603	109	9	ψ̂2(p	ψ̂2(p	NOUN
ap-4603	109	10	)	)	PUNCT
ap-4603	109	11	=	=	SYM
ap-4603	109	12	(	(	PUNCT
ap-4603	109	13	p2	p2	PROPN
ap-4603	109	14	−	−	PROPN
ap-4603	109	15	ε(1−	ε(1−	PROPN
ap-4603	109	16	ε)√	ε)√	PROPN
ap-4603	109	17	πeε2	πeε2	PROPN
ap-4603	109	18	erfc(ε	erfc(ε	PROPN
ap-4603	109	19	)	)	PUNCT
ap-4603	109	20	)	)	PUNCT
ap-4603	110	1	e−p	e−p	PROPN
ap-4603	110	2	2/2	2/2	NUM
ap-4603	110	3	(	(	PUNCT
ap-4603	110	4	p2	p2	PROPN
ap-4603	110	5	+	+	CCONJ
ap-4603	110	6	ε2)1/2	ε2)1/2	ADJ
ap-4603	110	7	,	,	PUNCT
ap-4603	110	8	(	(	PUNCT
ap-4603	110	9	38	38	NUM
ap-4603	110	10	)	)	PUNCT
ap-4603	110	11	389	389	NUM
ap-4603	110	12	s.	s.	PROPN
ap-4603	110	13	fassari	fassari	PROPN
ap-4603	110	14	,	,	PUNCT
ap-4603	110	15	m.	m.	NOUN
ap-4603	110	16	gadella	gadella	PROPN
ap-4603	110	17	,	,	PUNCT
ap-4603	110	18	l.	l.	PROPN
ap-4603	110	19	m.	m.	PROPN
ap-4603	110	20	nieto	nieto	PROPN
ap-4603	110	21	,	,	PUNCT
ap-4603	110	22	f.	f.	PROPN
ap-4603	110	23	rinaldi	rinaldi	PROPN
ap-4603	110	24	acta	acta	PROPN
ap-4603	110	25	polytechnica	polytechnica	PROPN
ap-4603	110	26	0	0	NUM
ap-4603	110	27	1	1	NUM
ap-4603	110	28	2	2	NUM
ap-4603	110	29	3	3	NUM
ap-4603	110	30	4	4	NUM
ap-4603	110	31	-3.0	-3.0	NOUN
ap-4603	110	32	-2.5	-2.5	ADJ
ap-4603	110	33	-2.0	-2.0	ADJ
ap-4603	110	34	-1.5	-1.5	ADJ
ap-4603	110	35	-1.0	-1.0	PROPN
ap-4603	110	36	-0.5	-0.5	PROPN
ap-4603	110	37	0.0	0.0	NUM
ap-4603	110	38	λ	λ	NOUN
ap-4603	110	39	e	e	NOUN
ap-4603	110	40	figure	figure	NOUN
ap-4603	110	41	3	3	NUM
ap-4603	110	42	.	.	PUNCT
ap-4603	111	1	the	the	DET
ap-4603	111	2	curves	curve	NOUN
ap-4603	111	3	of	of	ADP
ap-4603	111	4	both	both	DET
ap-4603	111	5	energies	energy	NOUN
ap-4603	111	6	,	,	PUNCT
ap-4603	111	7	e0	e0	PROPN
ap-4603	111	8	(	(	PUNCT
ap-4603	111	9	blue	blue	ADJ
ap-4603	111	10	)	)	PUNCT
ap-4603	111	11	and	and	CCONJ
ap-4603	111	12	e1	e1	PROPN
ap-4603	111	13	(	(	PUNCT
ap-4603	111	14	yellow	yellow	ADJ
ap-4603	111	15	)	)	PUNCT
ap-4603	111	16	,	,	PUNCT
ap-4603	111	17	as	as	ADP
ap-4603	111	18	functions	function	NOUN
ap-4603	111	19	of	of	ADP
ap-4603	111	20	the	the	DET
ap-4603	111	21	coupling	coupling	NOUN
ap-4603	111	22	parameter	parameter	NOUN
ap-4603	111	23	λ	λ	PROPN
ap-4603	111	24	,	,	PUNCT
ap-4603	111	25	and	and	CCONJ
ap-4603	111	26	the	the	DET
ap-4603	111	27	points	point	NOUN
ap-4603	111	28	resulting	result	VERB
ap-4603	111	29	from	from	ADP
ap-4603	111	30	the	the	DET
ap-4603	111	31	table	table	NOUN
ap-4603	111	32	provided	provide	VERB
ap-4603	111	33	by	by	ADP
ap-4603	111	34	fernández	fernández	PROPN
ap-4603	111	35	in	in	ADP
ap-4603	111	36	[	[	X
ap-4603	111	37	1	1	NUM
ap-4603	111	38	]	]	PUNCT
ap-4603	111	39	.	.	PUNCT
ap-4603	112	1	orthogonal	orthogonal	ADJ
ap-4603	112	2	to	to	ADP
ap-4603	112	3	the	the	DET
ap-4603	112	4	ground	ground	NOUN
ap-4603	112	5	state	state	NOUN
ap-4603	112	6	eigenfunction	eigenfunction	NOUN
ap-4603	112	7	ψ̂0(p	ψ̂0(p	NOUN
ap-4603	112	8	)	)	PUNCT
ap-4603	112	9	=	=	SYM
ap-4603	112	10	e−p	e−p	NOUN
ap-4603	112	11	2/2/(p2	2/2/(p2	NUM
ap-4603	113	1	+	+	CCONJ
ap-4603	113	2	ε2)1/2	ε2)1/2	ADJ
ap-4603	113	3	(	(	PUNCT
ap-4603	113	4	by	by	ADP
ap-4603	113	5	using	use	VERB
ap-4603	113	6	the	the	DET
ap-4603	113	7	gram	gram	NOUN
ap-4603	113	8	-	-	PUNCT
ap-4603	113	9	schmidt	schmidt	NOUN
ap-4603	113	10	procedure	procedure	NOUN
ap-4603	113	11	)	)	PUNCT
ap-4603	113	12	,	,	PUNCT
ap-4603	113	13	and	and	CCONJ
ap-4603	113	14	the	the	DET
ap-4603	113	15	fredholm	fredholm	NOUN
ap-4603	113	16	determinant	determinant	ADJ
ap-4603	113	17	det(1	det(1	NOUN
ap-4603	113	18	−	−	PROPN
ap-4603	113	19	λbs,1ε	λbs,1ε	NOUN
ap-4603	113	20	)	)	PUNCT
ap-4603	113	21	,	,	PUNCT
ap-4603	113	22	one	one	PRON
ap-4603	113	23	can	can	AUX
ap-4603	113	24	determine	determine	VERB
ap-4603	113	25	the	the	DET
ap-4603	113	26	energy	energy	NOUN
ap-4603	113	27	of	of	ADP
ap-4603	113	28	the	the	DET
ap-4603	113	29	first	first	ADJ
ap-4603	113	30	excited	excited	ADJ
ap-4603	113	31	symmetric	symmetric	ADJ
ap-4603	113	32	bound	bind	VERB
ap-4603	113	33	state	state	NOUN
ap-4603	113	34	as	as	ADP
ap-4603	113	35	a	a	DET
ap-4603	113	36	function	function	NOUN
ap-4603	113	37	of	of	ADP
ap-4603	113	38	the	the	DET
ap-4603	113	39	coupling	coupling	NOUN
ap-4603	113	40	parameter	parameter	NOUN
ap-4603	113	41	emerging	emerge	VERB
ap-4603	113	42	out	out	ADP
ap-4603	113	43	of	of	ADP
ap-4603	113	44	the	the	DET
ap-4603	113	45	absolutely	absolutely	ADV
ap-4603	113	46	continuous	continuous	ADJ
ap-4603	113	47	spectrum	spectrum	NOUN
ap-4603	113	48	at	at	ADP
ap-4603	113	49	the	the	DET
ap-4603	113	50	next	next	ADJ
ap-4603	113	51	coupling	couple	VERB
ap-4603	113	52	constant	constant	ADJ
ap-4603	113	53	threshold	threshold	NOUN
ap-4603	113	54	.	.	PUNCT
ap-4603	114	1	work	work	NOUN
ap-4603	114	2	in	in	ADP
ap-4603	114	3	this	this	DET
ap-4603	114	4	direction	direction	NOUN
ap-4603	114	5	is	be	AUX
ap-4603	114	6	in	in	ADP
ap-4603	114	7	progress	progress	NOUN
ap-4603	114	8	.	.	PUNCT
ap-4603	115	1	5	5	X
ap-4603	115	2	.	.	X
ap-4603	115	3	acknowledgements	acknowledgement	NOUN
ap-4603	115	4	fabio	fabio	VERB
ap-4603	115	5	rinaldi	rinaldi	PROPN
ap-4603	115	6	would	would	AUX
ap-4603	115	7	like	like	VERB
ap-4603	115	8	to	to	PART
ap-4603	115	9	thank	thank	VERB
ap-4603	115	10	prof	prof	PROPN
ap-4603	115	11	.	.	PUNCT
ap-4603	116	1	m.	m.	NOUN
ap-4603	116	2	znojil	znojil	PROPN
ap-4603	116	3	for	for	ADP
ap-4603	116	4	kindly	kindly	ADV
ap-4603	116	5	inviting	invite	VERB
ap-4603	116	6	him	he	PRON
ap-4603	116	7	to	to	PART
ap-4603	116	8	present	present	VERB
ap-4603	116	9	the	the	DET
ap-4603	116	10	main	main	ADJ
ap-4603	116	11	points	point	NOUN
ap-4603	116	12	of	of	ADP
ap-4603	116	13	this	this	DET
ap-4603	116	14	article	article	NOUN
ap-4603	116	15	in	in	ADP
ap-4603	116	16	the	the	DET
ap-4603	116	17	final	final	ADJ
ap-4603	116	18	session	session	NOUN
ap-4603	116	19	of	of	ADP
ap-4603	116	20	the	the	DET
ap-4603	116	21	conference	conference	NOUN
ap-4603	116	22	“	"	PUNCT
ap-4603	116	23	analytic	analytic	ADJ
ap-4603	116	24	and	and	CCONJ
ap-4603	116	25	algebraic	algebraic	ADJ
ap-4603	116	26	methods	method	NOUN
ap-4603	116	27	in	in	ADP
ap-4603	116	28	physics	physics	NOUN
ap-4603	116	29	”	"	PUNCT
ap-4603	116	30	held	hold	VERB
ap-4603	116	31	in	in	ADP
ap-4603	116	32	prague	prague	PROPN
ap-4603	116	33	,	,	PUNCT
ap-4603	116	34	11–14	11–14	NUM
ap-4603	116	35	september	september	PROPN
ap-4603	116	36	2017	2017	NUM
ap-4603	116	37	.	.	PUNCT
ap-4603	117	1	partial	partial	ADJ
ap-4603	117	2	financial	financial	ADJ
ap-4603	117	3	support	support	NOUN
ap-4603	117	4	is	be	AUX
ap-4603	117	5	acknowledged	acknowledge	VERB
ap-4603	117	6	to	to	ADP
ap-4603	117	7	the	the	DET
ap-4603	117	8	spanish	spanish	ADJ
ap-4603	117	9	junta	junta	PROPN
ap-4603	117	10	de	de	PROPN
ap-4603	117	11	castilla	castilla	PROPN
ap-4603	117	12	y	y	PROPN
ap-4603	117	13	león	león	PROPN
ap-4603	117	14	and	and	CCONJ
ap-4603	117	15	feder	feder	PROPN
ap-4603	117	16	(	(	PUNCT
ap-4603	117	17	project	project	NOUN
ap-4603	117	18	va057u16	va057u16	PROPN
ap-4603	117	19	)	)	PUNCT
ap-4603	117	20	,	,	PUNCT
ap-4603	117	21	and	and	CCONJ
ap-4603	117	22	mineco	mineco	PROPN
ap-4603	117	23	(	(	PUNCT
ap-4603	117	24	project	project	NOUN
ap-4603	117	25	mtm2014	mtm2014	NOUN
ap-4603	117	26	-	-	PUNCT
ap-4603	117	27	57129	57129	NUM
ap-4603	117	28	-	-	PUNCT
ap-4603	117	29	c2	c2	PROPN
ap-4603	117	30	-	-	PUNCT
ap-4603	117	31	1	1	NUM
ap-4603	117	32	-	-	PUNCT
ap-4603	117	33	p	p	NOUN
ap-4603	117	34	)	)	PUNCT
ap-4603	117	35	.	.	PUNCT
ap-4603	118	1	s.	s.	PROPN
ap-4603	118	2	fassari	fassari	PROPN
ap-4603	118	3	also	also	ADV
ap-4603	118	4	wishes	wish	VERB
ap-4603	118	5	to	to	PART
ap-4603	118	6	thank	thank	VERB
ap-4603	118	7	the	the	DET
ap-4603	118	8	entire	entire	ADJ
ap-4603	118	9	staff	staff	NOUN
ap-4603	118	10	at	at	ADP
ap-4603	118	11	departamento	departamento	PROPN
ap-4603	118	12	de	de	PROPN
ap-4603	118	13	física	física	PROPN
ap-4603	118	14	teórica	teórica	PROPN
ap-4603	118	15	,	,	PUNCT
ap-4603	118	16	atómica	atómica	PROPN
ap-4603	118	17	y	y	PROPN
ap-4603	118	18	óptica	óptica	PROPN
ap-4603	118	19	,	,	PUNCT
ap-4603	118	20	universidad	universidad	PROPN
ap-4603	118	21	de	de	PROPN
ap-4603	118	22	valladolid	valladolid	PROPN
ap-4603	118	23	,	,	PUNCT
ap-4603	118	24	for	for	ADP
ap-4603	118	25	their	their	PRON
ap-4603	118	26	warm	warm	ADJ
ap-4603	118	27	hospitality	hospitality	NOUN
ap-4603	118	28	throughout	throughout	ADP
ap-4603	118	29	his	his	PRON
ap-4603	118	30	stay	stay	NOUN
ap-4603	118	31	.	.	PUNCT
ap-4603	119	1	references	reference	NOUN
ap-4603	119	2	[	[	X
ap-4603	119	3	1	1	NUM
ap-4603	119	4	]	]	X
ap-4603	119	5	fernández	fernández	PROPN
ap-4603	119	6	f.m	f.m	PROPN
ap-4603	119	7	.	.	PROPN
ap-4603	119	8	:	:	PUNCT
ap-4603	119	9	quantum	quantum	PROPN
ap-4603	119	10	gaussian	gaussian	ADJ
ap-4603	119	11	wells	well	NOUN
ap-4603	119	12	and	and	CCONJ
ap-4603	119	13	barriers	barrier	NOUN
ap-4603	119	14	,	,	PUNCT
ap-4603	119	15	am	be	AUX
ap-4603	119	16	.	.	PUNCT
ap-4603	120	1	j.	j.	PROPN
ap-4603	120	2	physics	physics	PROPN
ap-4603	120	3	,	,	PUNCT
ap-4603	120	4	79	79	NUM
ap-4603	120	5	(	(	PUNCT
ap-4603	120	6	7	7	NUM
ap-4603	120	7	)	)	PUNCT
ap-4603	120	8	,	,	PUNCT
ap-4603	120	9	2011	2011	NUM
ap-4603	120	10	,	,	PUNCT
ap-4603	120	11	752	752	NUM
ap-4603	120	12	-	-	SYM
ap-4603	120	13	754	754	NUM
ap-4603	120	14	.	.	PUNCT
ap-4603	121	1	[	[	X
ap-4603	121	2	2	2	X
ap-4603	121	3	]	]	PUNCT
ap-4603	121	4	muchatibaya	muchatibaya	PROPN
ap-4603	121	5	g.	g.	PROPN
ap-4603	121	6	,	,	PUNCT
ap-4603	121	7	fassari	fassari	PROPN
ap-4603	121	8	s.	s.	PROPN
ap-4603	121	9	,	,	PUNCT
ap-4603	121	10	rinaldi	rinaldi	PROPN
ap-4603	121	11	f.	f.	PROPN
ap-4603	121	12	,	,	PUNCT
ap-4603	121	13	mushanyu	mushanyu	PROPN
ap-4603	121	14	j.	j.	PROPN
ap-4603	121	15	:	:	PUNCT
ap-4603	121	16	a	a	DET
ap-4603	121	17	note	note	NOUN
ap-4603	121	18	on	on	ADP
ap-4603	121	19	the	the	DET
ap-4603	121	20	discrete	discrete	ADJ
ap-4603	121	21	spectrum	spectrum	NOUN
ap-4603	121	22	of	of	ADP
ap-4603	121	23	gaussian	gaussian	ADJ
ap-4603	121	24	wells	well	NOUN
ap-4603	121	25	(	(	PUNCT
ap-4603	121	26	i	i	NOUN
ap-4603	121	27	):	):	PUNCT
ap-4603	121	28	the	the	DET
ap-4603	121	29	ground	ground	NOUN
ap-4603	121	30	state	state	NOUN
ap-4603	121	31	energy	energy	NOUN
ap-4603	121	32	in	in	ADP
ap-4603	121	33	one	one	NUM
ap-4603	121	34	dimension	dimension	NOUN
ap-4603	121	35	,	,	PUNCT
ap-4603	121	36	advances	advance	NOUN
ap-4603	121	37	in	in	ADP
ap-4603	121	38	mathematical	mathematical	ADJ
ap-4603	121	39	physics	physics	NOUN
ap-4603	121	40	,	,	PUNCT
ap-4603	121	41	2016	2016	NUM
ap-4603	121	42	.	.	PUNCT
ap-4603	122	1	[	[	X
ap-4603	122	2	3	3	X
ap-4603	122	3	]	]	X
ap-4603	122	4	nandi	nandi	PROPN
ap-4603	122	5	s.	s.	PROPN
ap-4603	122	6	:	:	PUNCT
ap-4603	122	7	the	the	DET
ap-4603	122	8	quantum	quantum	PROPN
ap-4603	122	9	gaussian	gaussian	NOUN
ap-4603	122	10	well	well	ADV
ap-4603	122	11	,	,	PUNCT
ap-4603	122	12	am	be	AUX
ap-4603	122	13	.	.	PUNCT
ap-4603	123	1	j.	j.	PROPN
ap-4603	123	2	physics	physics	PROPN
ap-4603	123	3	,	,	PUNCT
ap-4603	123	4	78	78	NUM
ap-4603	123	5	,	,	PUNCT
ap-4603	123	6	2010	2010	NUM
ap-4603	123	7	,	,	PUNCT
ap-4603	123	8	1341	1341	NUM
ap-4603	123	9	-	-	SYM
ap-4603	123	10	1345	1345	NUM
ap-4603	123	11	.	.	PUNCT
ap-4603	124	1	[	[	X
ap-4603	124	2	4	4	NUM
ap-4603	124	3	]	]	X
ap-4603	124	4	klaus	klaus	PROPN
ap-4603	124	5	m.	m.	NOUN
ap-4603	124	6	:	:	PUNCT
ap-4603	124	7	some	some	DET
ap-4603	124	8	applications	application	NOUN
ap-4603	124	9	of	of	ADP
ap-4603	124	10	the	the	DET
ap-4603	124	11	birman	birman	NOUN
ap-4603	124	12	-	-	PUNCT
ap-4603	124	13	schwinger	schwinger	NOUN
ap-4603	124	14	principle	principle	NOUN
ap-4603	124	15	,	,	PUNCT
ap-4603	124	16	helv	helv	PROPN
ap-4603	124	17	.	.	PUNCT
ap-4603	125	1	physics	physics	PROPN
ap-4603	125	2	acta	acta	PROPN
ap-4603	125	3	55	55	NUM
ap-4603	125	4	,	,	PUNCT
ap-4603	125	5	1982	1982	NUM
ap-4603	125	6	,	,	PUNCT
ap-4603	125	7	413	413	NUM
ap-4603	125	8	-	-	SYM
ap-4603	125	9	419	419	NUM
ap-4603	125	10	.	.	PUNCT
ap-4603	126	1	[	[	X
ap-4603	126	2	5	5	NUM
ap-4603	126	3	]	]	X
ap-4603	126	4	klaus	klaus	NOUN
ap-4603	126	5	m.	m.	NOUN
ap-4603	126	6	:	:	PUNCT
ap-4603	126	7	on	on	ADP
ap-4603	126	8	the	the	DET
ap-4603	126	9	bound	bind	VERB
ap-4603	126	10	state	state	NOUN
ap-4603	126	11	of	of	ADP
ap-4603	126	12	schrödinger	schrödinger	NOUN
ap-4603	126	13	operators	operator	NOUN
ap-4603	126	14	in	in	ADP
ap-4603	126	15	one	one	NUM
ap-4603	126	16	dimension	dimension	NOUN
ap-4603	126	17	,	,	PUNCT
ap-4603	126	18	annals	annal	NOUN
ap-4603	126	19	of	of	ADP
ap-4603	126	20	physics	physics	NOUN
ap-4603	126	21	108	108	NUM
ap-4603	126	22	,	,	PUNCT
ap-4603	126	23	1977	1977	NUM
ap-4603	126	24	,	,	PUNCT
ap-4603	126	25	288	288	NUM
ap-4603	126	26	-	-	SYM
ap-4603	126	27	300	300	NUM
ap-4603	126	28	.	.	PUNCT
ap-4603	127	1	[	[	X
ap-4603	127	2	6	6	NUM
ap-4603	127	3	]	]	X
ap-4603	127	4	klaus	klaus	PROPN
ap-4603	127	5	m.	m.	NOUN
ap-4603	127	6	:	:	PUNCT
ap-4603	127	7	a	a	DET
ap-4603	127	8	remark	remark	NOUN
ap-4603	127	9	about	about	ADP
ap-4603	127	10	weakly	weakly	ADV
ap-4603	127	11	coupled	couple	VERB
ap-4603	127	12	one	one	NUM
ap-4603	127	13	-	-	PUNCT
ap-4603	127	14	dimensional	dimensional	ADJ
ap-4603	127	15	schrödinger	schrödinger	ADJ
ap-4603	127	16	operators	operator	NOUN
ap-4603	127	17	helv	helv	VERB
ap-4603	127	18	.	.	PUNCT
ap-4603	128	1	phys	phy	NOUN
ap-4603	128	2	.	.	PUNCT
ap-4603	129	1	acta	acta	PROPN
ap-4603	129	2	52	52	NUM
ap-4603	129	3	,	,	PUNCT
ap-4603	129	4	1979	1979	NUM
ap-4603	129	5	,	,	PUNCT
ap-4603	129	6	223	223	NUM
ap-4603	129	7	.	.	PUNCT
ap-4603	130	1	[	[	X
ap-4603	130	2	7	7	X
ap-4603	130	3	]	]	X
ap-4603	130	4	fassari	fassari	PROPN
ap-4603	130	5	s.	s.	PROPN
ap-4603	130	6	:	:	PUNCT
ap-4603	130	7	an	an	DET
ap-4603	130	8	estimate	estimate	NOUN
ap-4603	130	9	regarding	regard	VERB
ap-4603	130	10	one	one	NUM
ap-4603	130	11	-	-	PUNCT
ap-4603	130	12	dimensional	dimensional	ADJ
ap-4603	130	13	point	point	NOUN
ap-4603	130	14	interactions	interaction	NOUN
ap-4603	130	15	helv	helv	ADJ
ap-4603	130	16	.	.	PUNCT
ap-4603	131	1	phys	phy	NOUN
ap-4603	131	2	.	.	PUNCT
ap-4603	132	1	acta	acta	PROPN
ap-4603	132	2	68	68	NUM
ap-4603	132	3	,	,	PUNCT
ap-4603	132	4	1995	1995	NUM
ap-4603	132	5	,	,	PUNCT
ap-4603	132	6	121	121	NUM
ap-4603	132	7	-	-	SYM
ap-4603	132	8	125	125	NUM
ap-4603	132	9	.	.	PUNCT
ap-4603	133	1	[	[	X
ap-4603	133	2	8	8	X
ap-4603	133	3	]	]	X
ap-4603	133	4	fassari	fassari	PROPN
ap-4603	133	5	s.	s.	PROPN
ap-4603	133	6	,	,	PUNCT
ap-4603	133	7	rinaldi	rinaldi	PROPN
ap-4603	133	8	f.	f.	PROPN
ap-4603	133	9	:	:	PUNCT
ap-4603	133	10	on	on	ADP
ap-4603	133	11	the	the	DET
ap-4603	133	12	spectrum	spectrum	NOUN
ap-4603	133	13	of	of	ADP
ap-4603	133	14	the	the	DET
ap-4603	133	15	schrödinger	schrödinger	ADJ
ap-4603	133	16	hamiltonian	hamiltonian	NOUN
ap-4603	133	17	with	with	ADP
ap-4603	133	18	a	a	DET
ap-4603	133	19	particular	particular	ADJ
ap-4603	133	20	configuration	configuration	NOUN
ap-4603	133	21	of	of	ADP
ap-4603	133	22	three	three	NUM
ap-4603	133	23	point	point	NOUN
ap-4603	133	24	interactions	interaction	NOUN
ap-4603	133	25	,	,	PUNCT
ap-4603	133	26	reports	report	NOUN
ap-4603	133	27	on	on	ADP
ap-4603	133	28	mathematical	mathematical	ADJ
ap-4603	133	29	physics	physics	NOUN
ap-4603	133	30	,	,	PUNCT
ap-4603	133	31	64	64	NUM
ap-4603	133	32	(	(	PUNCT
ap-4603	133	33	3	3	NUM
ap-4603	133	34	)	)	PUNCT
ap-4603	133	35	2009	2009	NUM
ap-4603	133	36	,	,	PUNCT
ap-4603	133	37	367	367	NUM
ap-4603	133	38	-	-	SYM
ap-4603	133	39	393	393	NUM
ap-4603	133	40	.	.	PUNCT
ap-4603	134	1	[	[	X
ap-4603	134	2	9	9	NUM
ap-4603	134	3	]	]	X
ap-4603	134	4	reed	reed	NOUN
ap-4603	134	5	m	m	PROPN
ap-4603	134	6	,	,	PUNCT
ap-4603	134	7	simon	simon	PROPN
ap-4603	134	8	b.	b.	PROPN
ap-4603	134	9	:	:	PUNCT
ap-4603	134	10	methods	method	NOUN
ap-4603	134	11	in	in	ADP
ap-4603	134	12	modern	modern	ADJ
ap-4603	134	13	mathematical	mathematical	ADJ
ap-4603	134	14	physics	physics	NOUN
ap-4603	134	15	iii	iii	NOUN
ap-4603	134	16	scattering	scatter	VERB
ap-4603	134	17	theory	theory	NOUN
ap-4603	134	18	,	,	PUNCT
ap-4603	134	19	academic	academic	ADJ
ap-4603	134	20	press	press	NOUN
ap-4603	134	21	,	,	PUNCT
ap-4603	134	22	ny	ny	PROPN
ap-4603	134	23	1979	1979	NUM
ap-4603	134	24	[	[	X
ap-4603	134	25	10	10	NUM
ap-4603	134	26	]	]	X
ap-4603	134	27	simon	simon	PROPN
ap-4603	134	28	b.	b.	PROPN
ap-4603	134	29	:	:	PUNCT
ap-4603	135	1	the	the	DET
ap-4603	135	2	bound	bound	ADJ
ap-4603	135	3	state	state	NOUN
ap-4603	135	4	of	of	ADP
ap-4603	135	5	weakly	weakly	ADV
ap-4603	135	6	coupled	couple	VERB
ap-4603	135	7	schrödinger	schrödinger	NOUN
ap-4603	135	8	operators	operator	NOUN
ap-4603	135	9	in	in	ADP
ap-4603	135	10	one	one	NUM
ap-4603	135	11	and	and	CCONJ
ap-4603	135	12	two	two	NUM
ap-4603	135	13	dimensions	dimension	NOUN
ap-4603	135	14	,	,	PUNCT
ap-4603	135	15	annals	annal	NOUN
ap-4603	135	16	of	of	ADP
ap-4603	135	17	physics	physics	NOUN
ap-4603	135	18	,	,	PUNCT
ap-4603	135	19	97	97	NUM
ap-4603	135	20	,	,	PUNCT
ap-4603	135	21	1976	1976	NUM
ap-4603	135	22	,	,	PUNCT
ap-4603	135	23	279	279	NUM
ap-4603	135	24	-	-	SYM
ap-4603	135	25	288	288	NUM
ap-4603	135	26	.	.	PUNCT
ap-4603	136	1	[	[	X
ap-4603	136	2	11	11	NUM
ap-4603	136	3	]	]	X
ap-4603	136	4	simon	simon	PROPN
ap-4603	136	5	b.	b.	PROPN
ap-4603	136	6	:	:	PUNCT
ap-4603	136	7	trace	trace	NOUN
ap-4603	136	8	ideals	ideal	NOUN
ap-4603	136	9	and	and	CCONJ
ap-4603	136	10	their	their	PRON
ap-4603	136	11	applications	application	NOUN
ap-4603	136	12	,	,	PUNCT
ap-4603	136	13	cambridge	cambridge	PROPN
ap-4603	136	14	university	university	PROPN
ap-4603	136	15	press	press	NOUN
ap-4603	136	16	,	,	PUNCT
ap-4603	136	17	cambridge	cambridge	NOUN
ap-4603	136	18	1979	1979	NUM
ap-4603	136	19	[	[	X
ap-4603	136	20	12	12	NUM
ap-4603	136	21	]	]	X
ap-4603	136	22	reed	reed	PROPN
ap-4603	136	23	m	m	PROPN
ap-4603	136	24	,	,	PUNCT
ap-4603	136	25	simon	simon	PROPN
ap-4603	136	26	b.	b.	PROPN
ap-4603	136	27	:	:	PUNCT
ap-4603	136	28	methods	method	NOUN
ap-4603	136	29	in	in	ADP
ap-4603	136	30	modern	modern	ADJ
ap-4603	136	31	mathematical	mathematical	ADJ
ap-4603	136	32	physics	physics	NOUN
ap-4603	136	33	iv	iv	ADP
ap-4603	137	1	analysis	analysis	NOUN
ap-4603	137	2	of	of	ADP
ap-4603	137	3	operators	operator	NOUN
ap-4603	137	4	,	,	PUNCT
ap-4603	137	5	academic	academic	ADJ
ap-4603	137	6	press	press	NOUN
ap-4603	137	7	,	,	PUNCT
ap-4603	137	8	ny	ny	PROPN
ap-4603	137	9	1978	1978	NUM
ap-4603	137	10	390	390	NUM
ap-4603	137	11	acta	acta	PROPN
ap-4603	137	12	polytechnica	polytechnica	PROPN
ap-4603	137	13	57(6):385–390	57(6):385–390	PROPN
ap-4603	137	14	,	,	PUNCT
ap-4603	137	15	2017	2017	NUM
ap-4603	137	16	1	1	NUM
ap-4603	137	17	introduction	introduction	NOUN
ap-4603	137	18	2	2	NUM
ap-4603	137	19	the	the	DET
ap-4603	137	20	integral	integral	ADJ
ap-4603	137	21	operator	operator	NOUN
ap-4603	137	22	b	b	PROPN
ap-4603	137	23	3	3	NUM
ap-4603	137	24	the	the	DET
ap-4603	137	25	two	two	NUM
ap-4603	137	26	lowest	low	ADJ
ap-4603	137	27	eigenvalues	eigenvalue	NOUN
ap-4603	137	28	of	of	ADP
ap-4603	137	29	-x2	-x2	X
ap-4603	137	30	-e	-e	X
ap-4603	137	31	-	-	PUNCT
ap-4603	137	32	x2/2	x2/2	NOUN
ap-4603	137	33	3.1	3.1	NUM
ap-4603	137	34	the	the	DET
ap-4603	137	35	ground	ground	NOUN
ap-4603	137	36	state	state	NOUN
ap-4603	137	37	3.2	3.2	NUM
ap-4603	137	38	the	the	DET
ap-4603	137	39	first	first	ADJ
ap-4603	137	40	excited	excited	ADJ
ap-4603	137	41	state	state	NOUN
ap-4603	137	42	4	4	NUM
ap-4603	137	43	conclusions	conclusion	NOUN
ap-4603	137	44	5	5	NUM
ap-4603	137	45	acknowledgements	acknowledgement	NOUN
ap-4603	137	46	references	reference	NOUN