id	sid	tid	token	lemma	pos
ap-7671	1	1	acta	acta	PROPN
ap-7671	1	2	polytechnica	polytechnica	PROPN
ap-7671	1	3	https://doi.org/10.14311/ap.2022.62.0208	https://doi.org/10.14311/ap.2022.62.0208	PUNCT
ap-7671	1	4	acta	acta	PROPN
ap-7671	1	5	polytechnica	polytechnica	NOUN
ap-7671	1	6	62(1):208–210	62(1):208–210	PROPN
ap-7671	1	7	,	,	PUNCT
ap-7671	1	8	2022	2022	NUM
ap-7671	1	9	©	©	ADP
ap-7671	1	10	2022	2022	NUM
ap-7671	1	11	the	the	DET
ap-7671	1	12	author(s	author(s	NOUN
ap-7671	1	13	)	)	PUNCT
ap-7671	1	14	.	.	PUNCT
ap-7671	2	1	licensed	license	VERB
ap-7671	2	2	under	under	ADP
ap-7671	2	3	a	a	DET
ap-7671	2	4	cc	cc	NOUN
ap-7671	2	5	-	-	PUNCT
ap-7671	2	6	by	by	ADP
ap-7671	2	7	4.0	4.0	NUM
ap-7671	2	8	licence	licence	NOUN
ap-7671	2	9	published	publish	VERB
ap-7671	2	10	by	by	ADP
ap-7671	2	11	the	the	DET
ap-7671	2	12	czech	czech	PROPN
ap-7671	2	13	technical	technical	PROPN
ap-7671	2	14	university	university	PROPN
ap-7671	2	15	in	in	ADP
ap-7671	2	16	prague	prague	PROPN
ap-7671	2	17	from	from	ADP
ap-7671	2	18	quartic	quartic	ADJ
ap-7671	2	19	anharmonic	anharmonic	ADJ
ap-7671	2	20	oscillator	oscillator	NOUN
ap-7671	2	21	to	to	PART
ap-7671	2	22	double	double	VERB
ap-7671	2	23	well	well	ADV
ap-7671	2	24	potential	potential	ADJ
ap-7671	2	25	alexander	alexander	NOUN
ap-7671	2	26	v.	v.	PROPN
ap-7671	2	27	turbiner∗	turbiner∗	PROPN
ap-7671	2	28	,	,	PUNCT
ap-7671	2	29	juan	juan	PROPN
ap-7671	2	30	carlos	carlos	PROPN
ap-7671	2	31	del	del	PROPN
ap-7671	2	32	valle	valle	PROPN
ap-7671	2	33	instituto	instituto	PROPN
ap-7671	2	34	de	de	PROPN
ap-7671	2	35	ciencias	ciencias	PROPN
ap-7671	2	36	nucleares	nucleare	NOUN
ap-7671	2	37	,	,	PUNCT
ap-7671	2	38	universidad	universidad	PROPN
ap-7671	2	39	nacional	nacional	PROPN
ap-7671	2	40	autónoma	autónoma	PROPN
ap-7671	2	41	de	de	PROPN
ap-7671	2	42	méxico	méxico	PROPN
ap-7671	2	43	,	,	PUNCT
ap-7671	2	44	apartado	apartado	X
ap-7671	2	45	postal	postal	ADJ
ap-7671	2	46	70	70	NUM
ap-7671	2	47	-	-	SYM
ap-7671	2	48	543	543	NUM
ap-7671	2	49	,	,	PUNCT
ap-7671	2	50	04510	04510	NUM
ap-7671	2	51	méxico	méxico	PROPN
ap-7671	2	52	-	-	PUNCT
ap-7671	2	53	city	city	PROPN
ap-7671	2	54	,	,	PUNCT
ap-7671	2	55	mexico	mexico	PROPN
ap-7671	2	56	∗	∗	VERB
ap-7671	2	57	corresponding	correspond	VERB
ap-7671	2	58	author	author	NOUN
ap-7671	2	59	:	:	PUNCT
ap-7671	2	60	turbiner@nucleares.unam.mx	turbiner@nucleares.unam.mx	DET
ap-7671	2	61	abstract	abstract	ADJ
ap-7671	2	62	.	.	PUNCT
ap-7671	3	1	quantum	quantum	PROPN
ap-7671	3	2	quartic	quartic	ADJ
ap-7671	3	3	single	single	ADJ
ap-7671	3	4	-	-	PUNCT
ap-7671	3	5	well	well	NOUN
ap-7671	3	6	anharmonic	anharmonic	ADJ
ap-7671	3	7	oscillator	oscillator	NOUN
ap-7671	3	8	vao(x	vao(x	PROPN
ap-7671	3	9	)	)	PUNCT
ap-7671	3	10	=	=	SYM
ap-7671	4	1	x2	x2	PROPN
ap-7671	4	2	+	+	CCONJ
ap-7671	4	3	g2x4	g2x4	NOUN
ap-7671	4	4	and	and	CCONJ
ap-7671	4	5	double	double	ADJ
ap-7671	4	6	-	-	PUNCT
ap-7671	4	7	well	well	NOUN
ap-7671	4	8	anharmonic	anharmonic	ADJ
ap-7671	4	9	oscillator	oscillator	NOUN
ap-7671	4	10	vdw(x	vdw(x	PROPN
ap-7671	4	11	)	)	PUNCT
ap-7671	4	12	=	=	PUNCT
ap-7671	4	13	x2(1−gx)2	x2(1−gx)2	PROPN
ap-7671	4	14	are	be	AUX
ap-7671	4	15	essentially	essentially	ADV
ap-7671	4	16	one	one	NUM
ap-7671	4	17	-	-	PUNCT
ap-7671	4	18	parametric	parametric	NOUN
ap-7671	4	19	,	,	PUNCT
ap-7671	4	20	they	they	PRON
ap-7671	4	21	depend	depend	VERB
ap-7671	4	22	on	on	ADP
ap-7671	4	23	a	a	DET
ap-7671	4	24	combination	combination	NOUN
ap-7671	4	25	(	(	PUNCT
ap-7671	4	26	g2ℏ	g2ℏ	PROPN
ap-7671	4	27	)	)	PUNCT
ap-7671	4	28	.	.	PUNCT
ap-7671	5	1	hence	hence	ADV
ap-7671	5	2	,	,	PUNCT
ap-7671	5	3	these	these	DET
ap-7671	5	4	problems	problem	NOUN
ap-7671	5	5	are	be	AUX
ap-7671	5	6	reduced	reduce	VERB
ap-7671	5	7	to	to	PART
ap-7671	5	8	study	study	VERB
ap-7671	5	9	the	the	DET
ap-7671	5	10	potentials	potential	NOUN
ap-7671	5	11	vao	vao	PROPN
ap-7671	5	12	=	=	SYM
ap-7671	5	13	u2	u2	PROPN
ap-7671	5	14	+	+	CCONJ
ap-7671	5	15	u4	u4	PROPN
ap-7671	5	16	and	and	CCONJ
ap-7671	5	17	vdw	vdw	PROPN
ap-7671	5	18	=	=	SYM
ap-7671	6	1	u2(1	u2(1	NOUN
ap-7671	6	2	−	−	PROPN
ap-7671	6	3	u)2	u)2	ADJ
ap-7671	6	4	,	,	PUNCT
ap-7671	6	5	respectively	respectively	ADV
ap-7671	6	6	.	.	PUNCT
ap-7671	7	1	it	it	PRON
ap-7671	7	2	is	be	AUX
ap-7671	7	3	shown	show	VERB
ap-7671	7	4	that	that	SCONJ
ap-7671	7	5	by	by	ADP
ap-7671	7	6	taking	take	VERB
ap-7671	7	7	uniformly	uniformly	ADV
ap-7671	7	8	-	-	PUNCT
ap-7671	7	9	accurate	accurate	ADJ
ap-7671	7	10	approximation	approximation	NOUN
ap-7671	7	11	for	for	ADP
ap-7671	7	12	anharmonic	anharmonic	ADJ
ap-7671	7	13	oscillator	oscillator	NOUN
ap-7671	7	14	eigenfunction	eigenfunction	NOUN
ap-7671	7	15	ψao(u	ψao(u	PROPN
ap-7671	7	16	)	)	PUNCT
ap-7671	7	17	,	,	PUNCT
ap-7671	7	18	obtained	obtain	VERB
ap-7671	7	19	recently	recently	ADV
ap-7671	7	20	,	,	PUNCT
ap-7671	7	21	see	see	VERB
ap-7671	7	22	jpa	jpa	PROPN
ap-7671	7	23	54	54	NUM
ap-7671	7	24	(	(	PUNCT
ap-7671	7	25	2021	2021	NUM
ap-7671	7	26	)	)	PUNCT
ap-7671	7	27	295204	295204	NUM
ap-7671	8	1	[	[	X
ap-7671	8	2	1	1	X
ap-7671	8	3	]	]	PUNCT
ap-7671	8	4	and	and	CCONJ
ap-7671	8	5	arxiv	arxiv	PROPN
ap-7671	9	1	2102.04623	2102.04623	NUM
ap-7671	10	1	[	[	X
ap-7671	10	2	2	2	NUM
ap-7671	10	3	]	]	PUNCT
ap-7671	10	4	,	,	PUNCT
ap-7671	10	5	and	and	CCONJ
ap-7671	10	6	then	then	ADV
ap-7671	10	7	forming	form	VERB
ap-7671	10	8	the	the	DET
ap-7671	10	9	function	function	NOUN
ap-7671	10	10	ψdw(u	ψdw(u	X
ap-7671	10	11	)	)	PUNCT
ap-7671	10	12	=	=	SYM
ap-7671	11	1	ψao(u)±ψao(u−1	ψao(u)±ψao(u−1	PROPN
ap-7671	11	2	)	)	PUNCT
ap-7671	11	3	allows	allow	VERB
ap-7671	11	4	to	to	PART
ap-7671	11	5	get	get	VERB
ap-7671	11	6	the	the	DET
ap-7671	11	7	highly	highly	ADV
ap-7671	11	8	accurate	accurate	ADJ
ap-7671	11	9	approximation	approximation	NOUN
ap-7671	11	10	for	for	ADP
ap-7671	11	11	both	both	CCONJ
ap-7671	11	12	the	the	DET
ap-7671	11	13	eigenfunctions	eigenfunction	NOUN
ap-7671	11	14	of	of	ADP
ap-7671	11	15	the	the	DET
ap-7671	11	16	double	double	ADJ
ap-7671	11	17	-	-	PUNCT
ap-7671	11	18	well	well	NOUN
ap-7671	11	19	potential	potential	NOUN
ap-7671	11	20	and	and	CCONJ
ap-7671	11	21	its	its	PRON
ap-7671	11	22	eigenvalues	eigenvalue	NOUN
ap-7671	11	23	.	.	PUNCT
ap-7671	12	1	keywords	keyword	NOUN
ap-7671	12	2	:	:	PUNCT
ap-7671	12	3	anharmonic	anharmonic	ADJ
ap-7671	12	4	oscillator	oscillator	NOUN
ap-7671	12	5	,	,	PUNCT
ap-7671	12	6	double	double	ADJ
ap-7671	12	7	-	-	PUNCT
ap-7671	12	8	well	well	NOUN
ap-7671	12	9	potential	potential	NOUN
ap-7671	12	10	,	,	PUNCT
ap-7671	12	11	perturbation	perturbation	NOUN
ap-7671	12	12	theory	theory	NOUN
ap-7671	12	13	,	,	PUNCT
ap-7671	12	14	semiclassical	semiclassical	ADJ
ap-7671	12	15	expansion	expansion	NOUN
ap-7671	12	16	.	.	PUNCT
ap-7671	13	1	1	1	X
ap-7671	13	2	.	.	X
ap-7671	13	3	introduction	introduction	NOUN
ap-7671	13	4	it	it	PRON
ap-7671	13	5	is	be	AUX
ap-7671	13	6	already	already	ADV
ap-7671	13	7	known	know	VERB
ap-7671	13	8	that	that	SCONJ
ap-7671	13	9	for	for	ADP
ap-7671	13	10	the	the	DET
ap-7671	13	11	one	one	NUM
ap-7671	13	12	-	-	PUNCT
ap-7671	13	13	dimensional	dimensional	ADJ
ap-7671	13	14	quantum	quantum	ADJ
ap-7671	13	15	quartic	quartic	ADJ
ap-7671	13	16	single	single	ADJ
ap-7671	13	17	-	-	PUNCT
ap-7671	13	18	well	well	NOUN
ap-7671	13	19	anharmonic	anharmonic	ADJ
ap-7671	13	20	oscillator	oscillator	NOUN
ap-7671	13	21	vao(x	vao(x	PROPN
ap-7671	13	22	)	)	PUNCT
ap-7671	13	23	=	=	SYM
ap-7671	14	1	x2	x2	PROPN
ap-7671	14	2	+	+	CCONJ
ap-7671	14	3	g2x4	g2x4	NOUN
ap-7671	14	4	and	and	CCONJ
ap-7671	14	5	double	double	ADJ
ap-7671	14	6	-	-	PUNCT
ap-7671	14	7	well	well	NOUN
ap-7671	14	8	anharmonic	anharmonic	ADJ
ap-7671	14	9	oscillator	oscillator	NOUN
ap-7671	14	10	with	with	ADP
ap-7671	14	11	potential	potential	ADJ
ap-7671	14	12	vdw(x	vdw(x	PROPN
ap-7671	14	13	)	)	PUNCT
ap-7671	14	14	=	=	SYM
ap-7671	15	1	x2(1	x2(1	NOUN
ap-7671	15	2	−	−	NOUN
ap-7671	16	1	gx)2	gx)2	VERB
ap-7671	16	2	the	the	DET
ap-7671	16	3	(	(	PUNCT
ap-7671	16	4	trans)series	trans)serie	NOUN
ap-7671	16	5	in	in	ADP
ap-7671	16	6	g	g	PROPN
ap-7671	16	7	(	(	PUNCT
ap-7671	16	8	which	which	PRON
ap-7671	16	9	is	be	AUX
ap-7671	16	10	the	the	DET
ap-7671	16	11	perturbation	perturbation	NOUN
ap-7671	16	12	theory	theory	NOUN
ap-7671	16	13	in	in	ADP
ap-7671	16	14	powers	power	NOUN
ap-7671	16	15	of	of	ADP
ap-7671	16	16	g	g	PROPN
ap-7671	16	17	(	(	PUNCT
ap-7671	16	18	the	the	DET
ap-7671	16	19	taylor	taylor	PROPN
ap-7671	16	20	expansion	expansion	NOUN
ap-7671	16	21	)	)	PUNCT
ap-7671	16	22	in	in	ADP
ap-7671	16	23	the	the	DET
ap-7671	16	24	former	former	ADJ
ap-7671	16	25	case	case	NOUN
ap-7671	16	26	vao(x	vao(x	NOUN
ap-7671	16	27	)	)	PUNCT
ap-7671	16	28	supplemented	supplement	VERB
ap-7671	16	29	by	by	ADP
ap-7671	16	30	exponentially	exponentially	ADV
ap-7671	16	31	-	-	PUNCT
ap-7671	16	32	small	small	ADJ
ap-7671	16	33	terms	term	NOUN
ap-7671	16	34	in	in	ADP
ap-7671	16	35	g	g	NOUN
ap-7671	16	36	in	in	ADP
ap-7671	16	37	the	the	DET
ap-7671	16	38	latter	latter	ADJ
ap-7671	16	39	case	case	NOUN
ap-7671	16	40	vdw(x	vdw(x	PROPN
ap-7671	16	41	)	)	PUNCT
ap-7671	16	42	)	)	PUNCT
ap-7671	16	43	and	and	CCONJ
ap-7671	16	44	the	the	DET
ap-7671	16	45	semiclassical	semiclassical	ADJ
ap-7671	16	46	expansion	expansion	NOUN
ap-7671	16	47	in	in	ADP
ap-7671	16	48	ℏ	ℏ	PROPN
ap-7671	16	49	(	(	PUNCT
ap-7671	16	50	the	the	DET
ap-7671	16	51	taylor	taylor	PROPN
ap-7671	16	52	expansion	expansion	NOUN
ap-7671	16	53	for	for	ADP
ap-7671	16	54	vao(x	vao(x	PROPN
ap-7671	16	55	)	)	PUNCT
ap-7671	16	56	supplemented	supplement	VERB
ap-7671	16	57	by	by	ADP
ap-7671	16	58	the	the	DET
ap-7671	16	59	exponentially	exponentially	ADV
ap-7671	16	60	small	small	ADJ
ap-7671	16	61	terms	term	NOUN
ap-7671	16	62	in	in	ADP
ap-7671	16	63	ℏ	ℏ	PROPN
ap-7671	16	64	for	for	ADP
ap-7671	16	65	vdw(x	vdw(x	PROPN
ap-7671	16	66	)	)	PUNCT
ap-7671	16	67	)	)	PUNCT
ap-7671	16	68	for	for	ADP
ap-7671	16	69	energies	energy	NOUN
ap-7671	16	70	coincide	coincide	VERB
ap-7671	16	71	[	[	X
ap-7671	16	72	3	3	NUM
ap-7671	16	73	]	]	PUNCT
ap-7671	16	74	.	.	PUNCT
ap-7671	17	1	this	this	DET
ap-7671	17	2	property	property	NOUN
ap-7671	17	3	plays	play	VERB
ap-7671	17	4	crucially	crucially	ADV
ap-7671	17	5	important	important	ADJ
ap-7671	17	6	role	role	NOUN
ap-7671	17	7	in	in	ADP
ap-7671	17	8	our	our	PRON
ap-7671	17	9	consideration	consideration	NOUN
ap-7671	17	10	.	.	PUNCT
ap-7671	18	1	both	both	CCONJ
ap-7671	18	2	the	the	DET
ap-7671	18	3	quartic	quartic	ADJ
ap-7671	18	4	anharmonic	anharmonic	ADJ
ap-7671	18	5	oscillator	oscillator	NOUN
ap-7671	18	6	v	v	NOUN
ap-7671	18	7	=	=	SYM
ap-7671	18	8	x2	x2	PROPN
ap-7671	19	1	+	+	CCONJ
ap-7671	19	2	g2x4	g2x4	NOUN
ap-7671	19	3	,	,	PUNCT
ap-7671	19	4	(	(	PUNCT
ap-7671	19	5	1	1	X
ap-7671	19	6	)	)	PUNCT
ap-7671	19	7	with	with	ADP
ap-7671	19	8	a	a	DET
ap-7671	19	9	single	single	ADJ
ap-7671	19	10	harmonic	harmonic	NOUN
ap-7671	19	11	well	well	ADV
ap-7671	19	12	at	at	ADP
ap-7671	19	13	x	x	X
ap-7671	19	14	=	=	SYM
ap-7671	19	15	0	0	NUM
ap-7671	19	16	and	and	CCONJ
ap-7671	19	17	the	the	DET
ap-7671	19	18	doublewell	doublewell	ADJ
ap-7671	19	19	potential	potential	NOUN
ap-7671	19	20	v	v	X
ap-7671	19	21	=	=	SYM
ap-7671	19	22	x2(1	x2(1	NOUN
ap-7671	19	23	−	−	NOUN
ap-7671	20	1	gx)2	gx)2	NOUN
ap-7671	20	2	,	,	PUNCT
ap-7671	20	3	(	(	PUNCT
ap-7671	20	4	2	2	NUM
ap-7671	20	5	)	)	PUNCT
ap-7671	20	6	with	with	ADP
ap-7671	20	7	two	two	NUM
ap-7671	20	8	symmetric	symmetric	ADJ
ap-7671	20	9	harmonic	harmonic	ADJ
ap-7671	20	10	wells	well	NOUN
ap-7671	20	11	at	at	ADP
ap-7671	20	12	x	x	X
ap-7671	20	13	=	=	SYM
ap-7671	20	14	0	0	NUM
ap-7671	20	15	and	and	CCONJ
ap-7671	20	16	x	x	SYM
ap-7671	20	17	=	=	SYM
ap-7671	20	18	1	1	NUM
ap-7671	20	19	/	/	SYM
ap-7671	20	20	g	g	NOUN
ap-7671	20	21	,	,	PUNCT
ap-7671	20	22	respectively	respectively	ADV
ap-7671	20	23	,	,	PUNCT
ap-7671	20	24	are	be	AUX
ap-7671	20	25	two	two	NUM
ap-7671	20	26	particular	particular	ADJ
ap-7671	20	27	cases	case	NOUN
ap-7671	20	28	of	of	ADP
ap-7671	20	29	the	the	DET
ap-7671	20	30	quartic	quartic	ADJ
ap-7671	20	31	polynomial	polynomial	ADJ
ap-7671	20	32	potential	potential	NOUN
ap-7671	20	33	v	v	X
ap-7671	20	34	=	=	SYM
ap-7671	20	35	x2	x2	PROPN
ap-7671	20	36	+	+	NUM
ap-7671	20	37	agx3	agx3	PROPN
ap-7671	20	38	+	+	CCONJ
ap-7671	20	39	g2x4	g2x4	NOUN
ap-7671	20	40	,	,	PUNCT
ap-7671	20	41	(	(	PUNCT
ap-7671	20	42	3	3	X
ap-7671	20	43	)	)	PUNCT
ap-7671	20	44	where	where	SCONJ
ap-7671	20	45	g	g	PROPN
ap-7671	20	46	is	be	AUX
ap-7671	20	47	the	the	DET
ap-7671	20	48	coupling	coupling	NOUN
ap-7671	20	49	constant	constant	ADJ
ap-7671	20	50	and	and	CCONJ
ap-7671	20	51	a	a	PRON
ap-7671	20	52	is	be	AUX
ap-7671	20	53	a	a	DET
ap-7671	20	54	parameter	parameter	NOUN
ap-7671	20	55	.	.	PUNCT
ap-7671	21	1	interestingly	interestingly	ADV
ap-7671	21	2	,	,	PUNCT
ap-7671	21	3	the	the	DET
ap-7671	21	4	potential	potential	ADJ
ap-7671	21	5	(	(	PUNCT
ap-7671	21	6	3	3	NUM
ap-7671	21	7	)	)	PUNCT
ap-7671	21	8	is	be	AUX
ap-7671	21	9	symmetric	symmetric	ADJ
ap-7671	21	10	for	for	ADP
ap-7671	21	11	three	three	NUM
ap-7671	21	12	particular	particular	ADJ
ap-7671	21	13	values	value	NOUN
ap-7671	21	14	of	of	ADP
ap-7671	21	15	the	the	DET
ap-7671	21	16	parameter	parameter	NOUN
ap-7671	21	17	a	a	PRON
ap-7671	21	18	:	:	PUNCT
ap-7671	21	19	a	a	DET
ap-7671	21	20	=	=	SYM
ap-7671	21	21	0	0	NUM
ap-7671	21	22	and	and	CCONJ
ap-7671	21	23	a	a	DET
ap-7671	21	24	=	=	NOUN
ap-7671	21	25	±2	±2	NOUN
ap-7671	21	26	.	.	PUNCT
ap-7671	22	1	all	all	DET
ap-7671	22	2	three	three	NUM
ap-7671	22	3	potentials	potential	NOUN
ap-7671	22	4	(	(	PUNCT
ap-7671	22	5	1	1	NUM
ap-7671	22	6	)	)	PUNCT
ap-7671	22	7	,	,	PUNCT
ap-7671	22	8	(	(	PUNCT
ap-7671	22	9	2	2	NUM
ap-7671	22	10	)	)	PUNCT
ap-7671	22	11	,	,	PUNCT
ap-7671	22	12	(	(	PUNCT
ap-7671	22	13	3	3	X
ap-7671	22	14	)	)	PUNCT
ap-7671	22	15	belong	belong	VERB
ap-7671	22	16	to	to	ADP
ap-7671	22	17	the	the	DET
ap-7671	22	18	family	family	NOUN
ap-7671	22	19	of	of	ADP
ap-7671	22	20	potentials	potential	NOUN
ap-7671	22	21	of	of	ADP
ap-7671	22	22	the	the	DET
ap-7671	22	23	form	form	NOUN
ap-7671	22	24	v	v	NOUN
ap-7671	22	25	=	=	SYM
ap-7671	22	26	1	1	NUM
ap-7671	22	27	g2	g2	PROPN
ap-7671	22	28	ṽ	ṽ	PROPN
ap-7671	22	29	(	(	PUNCT
ap-7671	22	30	gx	gx	PROPN
ap-7671	22	31	)	)	PUNCT
ap-7671	22	32	,	,	PUNCT
ap-7671	22	33	for	for	ADP
ap-7671	22	34	which	which	PRON
ap-7671	22	35	there	there	PRON
ap-7671	22	36	exists	exist	VERB
ap-7671	22	37	a	a	DET
ap-7671	22	38	remarkable	remarkable	ADJ
ap-7671	22	39	property	property	NOUN
ap-7671	22	40	:	:	PUNCT
ap-7671	22	41	the	the	DET
ap-7671	22	42	schrödinger	schrödinger	ADJ
ap-7671	22	43	equation	equation	NOUN
ap-7671	22	44	becomes	become	VERB
ap-7671	22	45	one	one	NUM
ap-7671	22	46	-	-	PUNCT
ap-7671	22	47	parametric	parametric	ADJ
ap-7671	22	48	,	,	PUNCT
ap-7671	22	49	both	both	CCONJ
ap-7671	22	50	the	the	DET
ap-7671	22	51	planck	planck	NOUN
ap-7671	22	52	constant	constant	ADJ
ap-7671	22	53	ℏ	ℏ	PROPN
ap-7671	22	54	and	and	CCONJ
ap-7671	22	55	the	the	DET
ap-7671	22	56	coupling	coupling	NOUN
ap-7671	22	57	constant	constant	ADJ
ap-7671	22	58	g	g	PROPN
ap-7671	22	59	appear	appear	VERB
ap-7671	22	60	in	in	ADP
ap-7671	22	61	the	the	DET
ap-7671	22	62	combination	combination	NOUN
ap-7671	22	63	(	(	PUNCT
ap-7671	22	64	ℏg2	ℏg2	NOUN
ap-7671	22	65	)	)	PUNCT
ap-7671	22	66	,	,	PUNCT
ap-7671	22	67	see	see	VERB
ap-7671	22	68	[	[	X
ap-7671	22	69	2	2	NUM
ap-7671	22	70	]	]	PUNCT
ap-7671	22	71	.	.	PUNCT
ap-7671	23	1	it	it	PRON
ap-7671	23	2	can	can	AUX
ap-7671	23	3	be	be	AUX
ap-7671	23	4	immediately	immediately	ADV
ap-7671	23	5	seen	see	VERB
ap-7671	23	6	if	if	SCONJ
ap-7671	23	7	instead	instead	ADV
ap-7671	23	8	of	of	ADP
ap-7671	23	9	the	the	DET
ap-7671	23	10	coordinate	coordinate	NOUN
ap-7671	23	11	x	x	PUNCT
ap-7671	23	12	the	the	DET
ap-7671	23	13	so	so	ADV
ap-7671	23	14	-	-	PUNCT
ap-7671	23	15	called	call	VERB
ap-7671	23	16	classical	classical	ADJ
ap-7671	23	17	coordinate	coordinate	NOUN
ap-7671	23	18	u	u	NOUN
ap-7671	23	19	=	=	PUNCT
ap-7671	23	20	(	(	PUNCT
ap-7671	23	21	g	g	NOUN
ap-7671	23	22	x	x	SYM
ap-7671	23	23	)	)	PUNCT
ap-7671	23	24	is	be	AUX
ap-7671	23	25	introduced	introduce	VERB
ap-7671	23	26	.	.	PUNCT
ap-7671	24	1	this	this	DET
ap-7671	24	2	property	property	NOUN
ap-7671	24	3	implies	imply	VERB
ap-7671	24	4	that	that	SCONJ
ap-7671	24	5	the	the	DET
ap-7671	24	6	action	action	NOUN
ap-7671	24	7	s	s	VERB
ap-7671	24	8	in	in	ADP
ap-7671	24	9	the	the	DET
ap-7671	24	10	path	path	NOUN
ap-7671	24	11	integral	integral	ADJ
ap-7671	24	12	formalism	formalism	NOUN
ap-7671	24	13	becomes	become	VERB
ap-7671	24	14	g	g	NOUN
ap-7671	24	15	-	-	PUNCT
ap-7671	24	16	independent	independent	ADJ
ap-7671	24	17	and	and	CCONJ
ap-7671	24	18	the	the	DET
ap-7671	24	19	factor	factor	NOUN
ap-7671	24	20	1	1	NUM
ap-7671	24	21	ℏ	ℏ	PROPN
ap-7671	24	22	in	in	ADP
ap-7671	24	23	the	the	DET
ap-7671	24	24	exponent	exponent	NOUN
ap-7671	24	25	becomes	become	VERB
ap-7671	24	26	1	1	NUM
ap-7671	24	27	ℏg2	ℏg2	NOUN
ap-7671	24	28	[	[	X
ap-7671	24	29	4	4	NUM
ap-7671	24	30	]	]	PUNCT
ap-7671	24	31	.	.	PUNCT
ap-7671	25	1	formally	formally	ADV
ap-7671	25	2	,	,	PUNCT
ap-7671	25	3	the	the	DET
ap-7671	25	4	potentials	potential	NOUN
ap-7671	25	5	(	(	PUNCT
ap-7671	25	6	1)-(2	1)-(2	NUM
ap-7671	25	7	)	)	PUNCT
ap-7671	25	8	,	,	PUNCT
ap-7671	25	9	which	which	PRON
ap-7671	25	10	enter	enter	VERB
ap-7671	25	11	to	to	ADP
ap-7671	25	12	the	the	DET
ap-7671	25	13	action	action	NOUN
ap-7671	25	14	,	,	PUNCT
ap-7671	25	15	appear	appear	VERB
ap-7671	25	16	at	at	ADP
ap-7671	25	17	g	g	NOUN
ap-7671	25	18	=	=	SYM
ap-7671	25	19	1	1	NUM
ap-7671	25	20	,	,	PUNCT
ap-7671	25	21	hence	hence	ADV
ap-7671	25	22	,	,	PUNCT
ap-7671	25	23	in	in	ADP
ap-7671	25	24	the	the	DET
ap-7671	25	25	form	form	NOUN
ap-7671	25	26	v	v	ADP
ap-7671	25	27	=	=	SYM
ap-7671	25	28	u2	u2	PROPN
ap-7671	25	29	+	+	CCONJ
ap-7671	25	30	u4	u4	PROPN
ap-7671	25	31	,	,	PUNCT
ap-7671	25	32	(	(	PUNCT
ap-7671	25	33	4	4	X
ap-7671	25	34	)	)	PUNCT
ap-7671	25	35	v	v	NOUN
ap-7671	25	36	=	=	SYM
ap-7671	25	37	u2(1	u2(1	NOUN
ap-7671	25	38	−	−	PROPN
ap-7671	25	39	u)2	u)2	ADV
ap-7671	25	40	,	,	PUNCT
ap-7671	25	41	(	(	PUNCT
ap-7671	25	42	5	5	X
ap-7671	25	43	)	)	PUNCT
ap-7671	25	44	respectively	respectively	ADV
ap-7671	25	45	.	.	PUNCT
ap-7671	26	1	both	both	DET
ap-7671	26	2	potentials	potential	NOUN
ap-7671	26	3	(	(	PUNCT
ap-7671	26	4	4	4	NUM
ap-7671	26	5	)	)	PUNCT
ap-7671	26	6	,	,	PUNCT
ap-7671	26	7	(	(	PUNCT
ap-7671	26	8	5	5	X
ap-7671	26	9	)	)	PUNCT
ap-7671	26	10	are	be	AUX
ap-7671	26	11	symmetric	symmetric	ADJ
ap-7671	26	12	with	with	ADP
ap-7671	26	13	respect	respect	NOUN
ap-7671	26	14	to	to	ADP
ap-7671	26	15	u	u	NOUN
ap-7671	26	16	=	=	NOUN
ap-7671	26	17	0	0	NUM
ap-7671	26	18	and	and	CCONJ
ap-7671	26	19	u	u	NOUN
ap-7671	26	20	=	=	PROPN
ap-7671	26	21	1/2	1/2	NUM
ap-7671	26	22	,	,	PUNCT
ap-7671	26	23	respectively	respectively	ADV
ap-7671	26	24	.	.	PUNCT
ap-7671	27	1	namely	namely	ADV
ap-7671	27	2	,	,	PUNCT
ap-7671	27	3	this	this	DET
ap-7671	27	4	form	form	NOUN
ap-7671	27	5	of	of	ADP
ap-7671	27	6	the	the	DET
ap-7671	27	7	potentials	potential	NOUN
ap-7671	27	8	will	will	AUX
ap-7671	27	9	be	be	AUX
ap-7671	27	10	used	use	VERB
ap-7671	27	11	in	in	ADP
ap-7671	27	12	this	this	DET
ap-7671	27	13	short	short	ADJ
ap-7671	27	14	note	note	NOUN
ap-7671	27	15	.	.	PUNCT
ap-7671	28	1	this	this	DET
ap-7671	28	2	note	note	NOUN
ap-7671	28	3	is	be	AUX
ap-7671	28	4	the	the	DET
ap-7671	28	5	extended	extended	ADJ
ap-7671	28	6	version	version	NOUN
ap-7671	28	7	of	of	ADP
ap-7671	28	8	a	a	DET
ap-7671	28	9	part	part	NOUN
ap-7671	28	10	of	of	ADP
ap-7671	28	11	presentation	presentation	NOUN
ap-7671	28	12	in	in	ADP
ap-7671	28	13	aamp-18	aamp-18	PROPN
ap-7671	28	14	given	give	VERB
ap-7671	28	15	by	by	ADP
ap-7671	28	16	the	the	DET
ap-7671	28	17	first	first	ADJ
ap-7671	28	18	author	author	NOUN
ap-7671	28	19	[	[	X
ap-7671	28	20	5	5	NUM
ap-7671	28	21	]	]	PUNCT
ap-7671	28	22	.	.	PUNCT
ap-7671	29	1	2	2	X
ap-7671	29	2	.	.	X
ap-7671	29	3	single	single	ADJ
ap-7671	29	4	-	-	PUNCT
ap-7671	29	5	well	well	NOUN
ap-7671	29	6	potential	potential	NOUN
ap-7671	29	7	in	in	ADP
ap-7671	29	8	[	[	X
ap-7671	29	9	1	1	NUM
ap-7671	29	10	]	]	PUNCT
ap-7671	29	11	for	for	ADP
ap-7671	29	12	the	the	DET
ap-7671	29	13	potential	potential	ADJ
ap-7671	29	14	(	(	PUNCT
ap-7671	29	15	4	4	X
ap-7671	29	16	)	)	PUNCT
ap-7671	29	17	matching	match	VERB
ap-7671	29	18	the	the	DET
ap-7671	29	19	small	small	ADJ
ap-7671	29	20	distances	distance	NOUN
ap-7671	29	21	u	u	PROPN
ap-7671	29	22	→	→	SYM
ap-7671	29	23	0	0	NUM
ap-7671	29	24	expansion	expansion	NOUN
ap-7671	29	25	and	and	CCONJ
ap-7671	29	26	the	the	DET
ap-7671	29	27	large	large	ADJ
ap-7671	29	28	distances	distance	NOUN
ap-7671	29	29	u	u	PROPN
ap-7671	29	30	→	→	SYM
ap-7671	29	31	∞	∞	NUM
ap-7671	29	32	expansion	expansion	NOUN
ap-7671	29	33	(	(	PUNCT
ap-7671	29	34	in	in	ADP
ap-7671	29	35	the	the	DET
ap-7671	29	36	form	form	NOUN
ap-7671	29	37	of	of	ADP
ap-7671	29	38	semiclassical	semiclassical	ADJ
ap-7671	29	39	expansion	expansion	NOUN
ap-7671	29	40	)	)	PUNCT
ap-7671	29	41	for	for	ADP
ap-7671	29	42	the	the	DET
ap-7671	29	43	phase	phase	NOUN
ap-7671	29	44	ϕ	ϕ	NOUN
ap-7671	29	45	in	in	ADP
ap-7671	29	46	the	the	DET
ap-7671	29	47	representation	representation	NOUN
ap-7671	29	48	ψ	ψ	X
ap-7671	29	49	=	=	X
ap-7671	29	50	p	p	X
ap-7671	29	51	(	(	PUNCT
ap-7671	29	52	u	u	NOUN
ap-7671	29	53	)	)	PUNCT
ap-7671	29	54	e−ϕ(u	e−ϕ(u	NOUN
ap-7671	29	55	)	)	PUNCT
ap-7671	29	56	,	,	PUNCT
ap-7671	29	57	of	of	ADP
ap-7671	29	58	the	the	DET
ap-7671	29	59	wave	wave	NOUN
ap-7671	29	60	function	function	NOUN
ap-7671	29	61	,	,	PUNCT
ap-7671	29	62	where	where	SCONJ
ap-7671	29	63	p	p	NOUN
ap-7671	29	64	is	be	AUX
ap-7671	29	65	a	a	DET
ap-7671	29	66	polynomial	polynomial	ADJ
ap-7671	29	67	,	,	PUNCT
ap-7671	29	68	it	it	PRON
ap-7671	29	69	was	be	AUX
ap-7671	29	70	constructed	construct	VERB
ap-7671	29	71	the	the	DET
ap-7671	29	72	following	follow	VERB
ap-7671	29	73	function	function	NOUN
ap-7671	29	74	for	for	ADP
ap-7671	29	75	the	the	DET
ap-7671	29	76	(	(	PUNCT
ap-7671	29	77	2n	2n	ADJ
ap-7671	29	78	+	+	CCONJ
ap-7671	29	79	p)-excited	p)-excited	ADJ
ap-7671	29	80	state	state	NOUN
ap-7671	29	81	with	with	ADP
ap-7671	29	82	quantum	quantum	ADJ
ap-7671	29	83	numbers	number	NOUN
ap-7671	29	84	(	(	PUNCT
ap-7671	29	85	n	n	X
ap-7671	29	86	,	,	PUNCT
ap-7671	29	87	p	p	NOUN
ap-7671	29	88	)	)	PUNCT
ap-7671	29	89	,	,	PUNCT
ap-7671	29	90	n	n	NOUN
ap-7671	29	91	=	=	SYM
ap-7671	29	92	0	0	NUM
ap-7671	29	93	,	,	PUNCT
ap-7671	29	94	1	1	NUM
ap-7671	29	95	,	,	PUNCT
ap-7671	29	96	2	2	NUM
ap-7671	29	97	,	,	PUNCT
ap-7671	29	98	.	.	PUNCT
ap-7671	29	99	.	.	PUNCT
ap-7671	30	1	.	.	PUNCT
ap-7671	31	1	,	,	PUNCT
ap-7671	31	2	p	p	X
ap-7671	31	3	=	=	NOUN
ap-7671	31	4	0	0	NUM
ap-7671	31	5	,	,	PUNCT
ap-7671	31	6	1	1	NUM
ap-7671	31	7	:	:	PUNCT
ap-7671	31	8	ψ(n	ψ(n	NUM
ap-7671	31	9	,	,	PUNCT
ap-7671	31	10	p	p	NOUN
ap-7671	31	11	)	)	PUNCT
ap-7671	31	12	(	(	PUNCT
ap-7671	31	13	approximation	approximation	NOUN
ap-7671	31	14	)	)	PUNCT
ap-7671	31	15	=	=	SYM
ap-7671	31	16	uppn	uppn	NOUN
ap-7671	31	17	,	,	PUNCT
ap-7671	31	18	p(u2	p(u2	NOUN
ap-7671	31	19	)	)	PUNCT
ap-7671	31	20	(	(	PUNCT
ap-7671	31	21	b2	b2	NOUN
ap-7671	31	22	+	+	CCONJ
ap-7671	31	23	u2	u2	NOUN
ap-7671	31	24	)	)	PUNCT
ap-7671	31	25	1	1	NUM
ap-7671	31	26	4	4	NUM
ap-7671	31	27	(	(	PUNCT
ap-7671	31	28	b	b	NOUN
ap-7671	31	29	+	+	CCONJ
ap-7671	31	30	√	√	NOUN
ap-7671	31	31	b2	b2	NOUN
ap-7671	31	32	+	+	CCONJ
ap-7671	31	33	u2	u2	NOUN
ap-7671	31	34	)	)	PUNCT
ap-7671	31	35	2n+p+	2n+p+	NUM
ap-7671	31	36	1	1	NUM
ap-7671	31	37	2	2	NUM
ap-7671	31	38	208	208	NUM
ap-7671	31	39	https://doi.org/10.14311/ap.2022.62.0208	https://doi.org/10.14311/ap.2022.62.0208	PUNCT
ap-7671	31	40	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7671	31	41	https://www.cvut.cz/en	https://www.cvut.cz/en	NOUN
ap-7671	31	42	vol	vol	NOUN
ap-7671	31	43	.	.	PROPN
ap-7671	32	1	62	62	NUM
ap-7671	32	2	no	no	INTJ
ap-7671	32	3	.	.	PUNCT
ap-7671	33	1	1/2022	1/2022	NUM
ap-7671	33	2	from	from	ADP
ap-7671	33	3	quartic	quartic	ADJ
ap-7671	33	4	anharmonic	anharmonic	ADJ
ap-7671	33	5	oscillator	oscillator	NOUN
ap-7671	33	6	to	to	PART
ap-7671	33	7	double	double	VERB
ap-7671	33	8	well	well	ADV
ap-7671	34	1	potential	potential	ADJ
ap-7671	34	2	-2	-2	INTJ
ap-7671	34	3	-1	-1	INTJ
ap-7671	34	4	1	1	NUM
ap-7671	34	5	2	2	NUM
ap-7671	34	6	u	u	NOUN
ap-7671	34	7	-1	-1	X
ap-7671	34	8	-0.5	-0.5	X
ap-7671	34	9	0.5	0.5	NUM
ap-7671	34	10	1	1	NUM
ap-7671	34	11	1.5	1.5	NUM
ap-7671	34	12	v	v	NOUN
ap-7671	34	13	(	(	PUNCT
ap-7671	34	14	u	u	NOUN
ap-7671	34	15	)	)	PUNCT
ap-7671	34	16	-2	-2	NOUN
ap-7671	35	1	-1	-1	NOUN
ap-7671	35	2	1	1	NUM
ap-7671	35	3	2	2	NUM
ap-7671	35	4	3	3	NUM
ap-7671	35	5	u	u	NOUN
ap-7671	35	6	-1	-1	X
ap-7671	35	7	-0.5	-0.5	X
ap-7671	35	8	0.5	0.5	NUM
ap-7671	35	9	1	1	NUM
ap-7671	35	10	1.5	1.5	NUM
ap-7671	35	11	v	v	NOUN
ap-7671	35	12	(	(	PUNCT
ap-7671	35	13	u	u	NOUN
ap-7671	35	14	)	)	PUNCT
ap-7671	35	15	figure	figure	NOUN
ap-7671	35	16	1	1	NUM
ap-7671	35	17	.	.	PUNCT
ap-7671	35	18	two	two	NUM
ap-7671	35	19	lowest	low	ADJ
ap-7671	35	20	,	,	PUNCT
ap-7671	35	21	normalized	normalize	VERB
ap-7671	35	22	to	to	ADP
ap-7671	35	23	one	one	NUM
ap-7671	35	24	eigenfunctions	eigenfunction	NOUN
ap-7671	35	25	of	of	ADP
ap-7671	35	26	positive	positive	ADJ
ap-7671	35	27	/	/	SYM
ap-7671	35	28	negative	negative	ADJ
ap-7671	35	29	parity	parity	NOUN
ap-7671	35	30	:	:	PUNCT
ap-7671	35	31	for	for	ADP
ap-7671	35	32	single	single	ADJ
ap-7671	35	33	-	-	PUNCT
ap-7671	35	34	well	well	NOUN
ap-7671	35	35	potential	potential	NOUN
ap-7671	35	36	(	(	PUNCT
ap-7671	35	37	4	4	NUM
ap-7671	35	38	)	)	PUNCT
ap-7671	35	39	,	,	PUNCT
ap-7671	35	40	see	see	VERB
ap-7671	35	41	(	(	PUNCT
ap-7671	35	42	6	6	NUM
ap-7671	35	43	)	)	PUNCT
ap-7671	35	44	(	(	PUNCT
ap-7671	35	45	top	top	NOUN
ap-7671	35	46	)	)	PUNCT
ap-7671	35	47	and	and	CCONJ
ap-7671	35	48	for	for	ADP
ap-7671	35	49	double	double	ADJ
ap-7671	35	50	-	-	PUNCT
ap-7671	35	51	well	well	NOUN
ap-7671	35	52	potential	potential	NOUN
ap-7671	35	53	(	(	PUNCT
ap-7671	35	54	5	5	NUM
ap-7671	35	55	)	)	PUNCT
ap-7671	35	56	,	,	PUNCT
ap-7671	35	57	see	see	VERB
ap-7671	35	58	(	(	PUNCT
ap-7671	35	59	9)(bottom	9)(bottom	NOUN
ap-7671	35	60	)	)	PUNCT
ap-7671	35	61	.	.	PUNCT
ap-7671	36	1	potentials	potential	NOUN
ap-7671	36	2	shown	show	VERB
ap-7671	36	3	by	by	ADP
ap-7671	36	4	black	black	ADJ
ap-7671	36	5	lines	line	NOUN
ap-7671	36	6	.	.	PUNCT
ap-7671	37	1	×	×	NOUN
ap-7671	37	2	exp	exp	NOUN
ap-7671	37	3	(	(	PUNCT
ap-7671	37	4	−	−	PROPN
ap-7671	37	5	a	a	DET
ap-7671	37	6	+	+	X
ap-7671	37	7	(	(	PUNCT
ap-7671	37	8	b2	b2	NOUN
ap-7671	37	9	+	+	CCONJ
ap-7671	37	10	3	3	X
ap-7671	37	11	)	)	PUNCT
ap-7671	37	12	u2/6	u2/6	NOUN
ap-7671	37	13	+	+	CCONJ
ap-7671	37	14	u4/3√	u4/3√	PROPN
ap-7671	37	15	b2	b2	NOUN
ap-7671	37	16	+	+	CCONJ
ap-7671	37	17	u2	u2	NOUN
ap-7671	37	18	+	+	CCONJ
ap-7671	37	19	a	a	DET
ap-7671	37	20	b	b	NOUN
ap-7671	37	21	)	)	PUNCT
ap-7671	37	22	,	,	PUNCT
ap-7671	37	23	(	(	PUNCT
ap-7671	37	24	6	6	NUM
ap-7671	37	25	)	)	PUNCT
ap-7671	37	26	where	where	SCONJ
ap-7671	37	27	pn	pn	PROPN
ap-7671	37	28	,	,	PUNCT
ap-7671	37	29	p	p	NOUN
ap-7671	37	30	is	be	AUX
ap-7671	37	31	some	some	DET
ap-7671	37	32	polynomial	polynomial	ADJ
ap-7671	37	33	of	of	ADP
ap-7671	37	34	degree	degree	NOUN
ap-7671	37	35	n	n	NOUN
ap-7671	37	36	in	in	ADP
ap-7671	37	37	u2	u2	NOUN
ap-7671	37	38	with	with	ADP
ap-7671	37	39	positive	positive	ADJ
ap-7671	37	40	roots	root	NOUN
ap-7671	37	41	.	.	PUNCT
ap-7671	38	1	here	here	ADV
ap-7671	38	2	a	a	DET
ap-7671	38	3	=	=	SYM
ap-7671	38	4	an	an	PROPN
ap-7671	38	5	,	,	PUNCT
ap-7671	38	6	p	p	X
ap-7671	38	7	,	,	PUNCT
ap-7671	38	8	b	b	NOUN
ap-7671	38	9	=	=	SYM
ap-7671	38	10	bn	bn	PROPN
ap-7671	38	11	,	,	PUNCT
ap-7671	38	12	p	p	NOUN
ap-7671	38	13	are	be	AUX
ap-7671	38	14	two	two	NUM
ap-7671	38	15	parameters	parameter	NOUN
ap-7671	38	16	of	of	ADP
ap-7671	38	17	interpolation	interpolation	NOUN
ap-7671	38	18	.	.	PUNCT
ap-7671	39	1	these	these	DET
ap-7671	39	2	parameters	parameter	NOUN
ap-7671	39	3	(	(	PUNCT
ap-7671	39	4	−a	−a	ADV
ap-7671	39	5	)	)	PUNCT
ap-7671	39	6	,	,	PUNCT
ap-7671	39	7	b	b	PROPN
ap-7671	39	8	are	be	AUX
ap-7671	39	9	slow	slow	ADV
ap-7671	39	10	-	-	PUNCT
ap-7671	39	11	growing	grow	VERB
ap-7671	39	12	with	with	ADP
ap-7671	39	13	quantum	quantum	ADJ
ap-7671	39	14	number	number	NOUN
ap-7671	39	15	n	n	CCONJ
ap-7671	39	16	at	at	ADP
ap-7671	39	17	fixed	fix	VERB
ap-7671	39	18	p	p	NOUN
ap-7671	39	19	taking	taking	NOUN
ap-7671	39	20	,	,	PUNCT
ap-7671	39	21	in	in	ADP
ap-7671	39	22	particular	particular	ADJ
ap-7671	39	23	,	,	PUNCT
ap-7671	39	24	the	the	DET
ap-7671	39	25	values	value	NOUN
ap-7671	39	26	a0,0	a0,0	NOUN
ap-7671	39	27	=	=	SYM
ap-7671	39	28	−0.6244	−0.6244	PROPN
ap-7671	39	29	,	,	PUNCT
ap-7671	39	30	b0,0	b0,0	PROPN
ap-7671	39	31	=	=	SYM
ap-7671	39	32	2.3667	2.3667	NUM
ap-7671	39	33	,	,	PUNCT
ap-7671	39	34	(	(	PUNCT
ap-7671	39	35	7	7	X
ap-7671	39	36	)	)	PUNCT
ap-7671	40	1	a0,1	a0,1	NOUN
ap-7671	40	2	=	=	PUNCT
ap-7671	40	3	−1.9289	−1.9289	X
ap-7671	40	4	,	,	PUNCT
ap-7671	40	5	b0,1	b0,1	NOUN
ap-7671	40	6	=	=	PROPN
ap-7671	40	7	2.5598	2.5598	NUM
ap-7671	40	8	,	,	PUNCT
ap-7671	40	9	(	(	PUNCT
ap-7671	40	10	8)	8)	NUM
ap-7671	40	11	for	for	ADP
ap-7671	40	12	the	the	DET
ap-7671	40	13	ground	ground	NOUN
ap-7671	40	14	state	state	NOUN
ap-7671	40	15	and	and	CCONJ
ap-7671	40	16	the	the	DET
ap-7671	40	17	first	first	ADJ
ap-7671	40	18	excited	excited	ADJ
ap-7671	40	19	state	state	NOUN
ap-7671	40	20	,	,	PUNCT
ap-7671	40	21	respectively	respectively	ADV
ap-7671	40	22	.	.	PUNCT
ap-7671	41	1	this	this	DET
ap-7671	41	2	remarkably	remarkably	ADV
ap-7671	41	3	simple	simple	ADJ
ap-7671	41	4	function	function	NOUN
ap-7671	41	5	(	(	PUNCT
ap-7671	41	6	6	6	NUM
ap-7671	41	7	)	)	PUNCT
ap-7671	41	8	,	,	PUNCT
ap-7671	41	9	see	see	VERB
ap-7671	41	10	figure	figure	NOUN
ap-7671	41	11	1	1	NUM
ap-7671	41	12	(	(	PUNCT
ap-7671	41	13	top	top	NOUN
ap-7671	41	14	)	)	PUNCT
ap-7671	41	15	,	,	PUNCT
ap-7671	41	16	provides	provide	VERB
ap-7671	41	17	10	10	NUM
ap-7671	41	18	-	-	SYM
ap-7671	41	19	11	11	NUM
ap-7671	41	20	exact	exact	ADJ
ap-7671	41	21	figures	figure	NOUN
ap-7671	41	22	in	in	ADP
ap-7671	41	23	energies	energy	NOUN
ap-7671	41	24	for	for	ADP
ap-7671	41	25	the	the	DET
ap-7671	41	26	first	first	ADJ
ap-7671	41	27	100	100	NUM
ap-7671	41	28	eigenstates	eigenstate	NOUN
ap-7671	41	29	.	.	PUNCT
ap-7671	42	1	furthermore	furthermore	ADV
ap-7671	42	2	,	,	PUNCT
ap-7671	42	3	the	the	DET
ap-7671	42	4	function	function	NOUN
ap-7671	42	5	(	(	PUNCT
ap-7671	42	6	6	6	NUM
ap-7671	42	7	)	)	PUNCT
ap-7671	42	8	deviates	deviate	VERB
ap-7671	42	9	uniformly	uniformly	ADV
ap-7671	42	10	for	for	ADP
ap-7671	42	11	u	u	PROPN
ap-7671	42	12	∈	∈	PROPN
ap-7671	42	13	(	(	PUNCT
ap-7671	42	14	−∞	−∞	NOUN
ap-7671	42	15	,	,	PUNCT
ap-7671	42	16	+	+	NOUN
ap-7671	42	17	∞	∞	NOUN
ap-7671	42	18	)	)	PUNCT
ap-7671	42	19	from	from	ADP
ap-7671	42	20	the	the	DET
ap-7671	42	21	exact	exact	ADJ
ap-7671	42	22	function	function	NOUN
ap-7671	42	23	in	in	ADP
ap-7671	42	24	∼	∼	NOUN
ap-7671	42	25	10−6	10−6	NUM
ap-7671	42	26	.	.	PUNCT
ap-7671	43	1	3	3	X
ap-7671	43	2	.	.	X
ap-7671	43	3	double	double	ADJ
ap-7671	43	4	-	-	PUNCT
ap-7671	43	5	well	well	NOUN
ap-7671	43	6	potential	potential	NOUN
ap-7671	43	7	:	:	PUNCT
ap-7671	43	8	wavefunctions	wavefunction	NOUN
ap-7671	43	9	following	follow	VERB
ap-7671	43	10	the	the	DET
ap-7671	43	11	prescription	prescription	NOUN
ap-7671	43	12	,	,	PUNCT
ap-7671	43	13	usually	usually	ADV
ap-7671	43	14	assigned	assign	VERB
ap-7671	43	15	in	in	ADP
ap-7671	43	16	folklore	folklore	NOUN
ap-7671	43	17	to	to	ADP
ap-7671	43	18	e.	e.	PROPN
ap-7671	43	19	m.	m.	PROPN
ap-7671	43	20	lifschitz	lifschitz	PROPN
ap-7671	43	21	–	–	PUNCT
ap-7671	43	22	one	one	NUM
ap-7671	43	23	of	of	ADP
ap-7671	43	24	the	the	DET
ap-7671	43	25	authors	author	NOUN
ap-7671	43	26	of	of	ADP
ap-7671	43	27	the	the	DET
ap-7671	43	28	famous	famous	ADJ
ap-7671	43	29	course	course	NOUN
ap-7671	43	30	on	on	ADP
ap-7671	43	31	theoretical	theoretical	ADJ
ap-7671	43	32	physics	physics	NOUN
ap-7671	43	33	by	by	ADP
ap-7671	43	34	l.	l.	PROPN
ap-7671	43	35	d.	d.	PROPN
ap-7671	43	36	landau	landau	NOUN
ap-7671	43	37	and	and	CCONJ
ap-7671	43	38	e.	e.	PROPN
ap-7671	43	39	m.	m.	PROPN
ap-7671	43	40	lifschitz	lifschitz	PROPN
ap-7671	43	41	–	–	PUNCT
ap-7671	43	42	when	when	SCONJ
ap-7671	43	43	a	a	DET
ap-7671	43	44	wavefunction	wavefunction	NOUN
ap-7671	43	45	for	for	ADP
ap-7671	43	46	single	single	ADJ
ap-7671	43	47	well	well	ADV
ap-7671	43	48	potential	potential	NOUN
ap-7671	43	49	with	with	ADP
ap-7671	43	50	minimum	minimum	NOUN
ap-7671	43	51	at	at	ADP
ap-7671	43	52	u	u	NOUN
ap-7671	43	53	=	=	SYM
ap-7671	43	54	0	0	NUM
ap-7671	43	55	is	be	AUX
ap-7671	43	56	known	know	VERB
ap-7671	43	57	,	,	PUNCT
ap-7671	43	58	ψ(u	ψ(u	PROPN
ap-7671	43	59	)	)	PUNCT
ap-7671	43	60	,	,	PUNCT
ap-7671	43	61	the	the	DET
ap-7671	43	62	wavefunction	wavefunction	NOUN
ap-7671	43	63	for	for	ADP
ap-7671	43	64	double	double	ADJ
ap-7671	43	65	well	well	ADV
ap-7671	43	66	potential	potential	NOUN
ap-7671	43	67	with	with	ADP
ap-7671	43	68	minima	minima	NOUN
ap-7671	43	69	at	at	ADP
ap-7671	43	70	u	u	NOUN
ap-7671	43	71	=	=	PROPN
ap-7671	43	72	0	0	NUM
ap-7671	43	73	,	,	PUNCT
ap-7671	43	74	1	1	NUM
ap-7671	43	75	can	can	AUX
ap-7671	43	76	be	be	AUX
ap-7671	43	77	written	write	VERB
ap-7671	43	78	as	as	ADP
ap-7671	43	79	ψ(u	ψ(u	PROPN
ap-7671	43	80	)	)	PUNCT
ap-7671	43	81	±	±	PROPN
ap-7671	43	82	ψ(u	ψ(u	PUNCT
ap-7671	43	83	−	−	NOUN
ap-7671	43	84	1	1	NUM
ap-7671	43	85	)	)	PUNCT
ap-7671	43	86	.	.	PUNCT
ap-7671	44	1	this	this	DET
ap-7671	44	2	prescription	prescription	NOUN
ap-7671	44	3	was	be	AUX
ap-7671	44	4	already	already	ADV
ap-7671	44	5	checked	check	VERB
ap-7671	44	6	successfully	successfully	ADV
ap-7671	44	7	for	for	ADP
ap-7671	44	8	the	the	DET
ap-7671	44	9	double	double	ADJ
ap-7671	44	10	-	-	PUNCT
ap-7671	44	11	well	well	NOUN
ap-7671	44	12	potential	potential	ADJ
ap-7671	44	13	(	(	PUNCT
ap-7671	44	14	2	2	NUM
ap-7671	44	15	)	)	PUNCT
ap-7671	44	16	in	in	ADP
ap-7671	44	17	[	[	X
ap-7671	44	18	6	6	NUM
ap-7671	44	19	]	]	PUNCT
ap-7671	44	20	for	for	ADP
ap-7671	44	21	somehow	somehow	ADV
ap-7671	44	22	simplified	simplify	VERB
ap-7671	44	23	version	version	NOUN
ap-7671	44	24	of	of	ADP
ap-7671	44	25	(	(	PUNCT
ap-7671	44	26	6	6	NUM
ap-7671	44	27	)	)	PUNCT
ap-7671	44	28	,	,	PUNCT
ap-7671	44	29	based	base	VERB
ap-7671	44	30	on	on	ADP
ap-7671	44	31	matching	match	VERB
ap-7671	44	32	the	the	DET
ap-7671	44	33	small	small	ADJ
ap-7671	44	34	distances	distance	NOUN
ap-7671	44	35	u	u	PROPN
ap-7671	44	36	→	→	SYM
ap-7671	44	37	0	0	NUM
ap-7671	44	38	expansion	expansion	NOUN
ap-7671	44	39	and	and	CCONJ
ap-7671	44	40	the	the	DET
ap-7671	44	41	large	large	ADJ
ap-7671	44	42	distances	distance	NOUN
ap-7671	44	43	u	u	PROPN
ap-7671	44	44	→	→	SYM
ap-7671	44	45	∞	∞	NUM
ap-7671	44	46	expansion	expansion	NOUN
ap-7671	44	47	for	for	ADP
ap-7671	44	48	the	the	DET
ap-7671	44	49	phase	phase	NOUN
ap-7671	44	50	ϕ	ϕ	NOUN
ap-7671	44	51	but	but	CCONJ
ap-7671	44	52	ignoring	ignore	VERB
ap-7671	44	53	subtleties	subtlety	NOUN
ap-7671	44	54	emerging	emerge	VERB
ap-7671	44	55	in	in	ADP
ap-7671	44	56	semiclassical	semiclassical	ADJ
ap-7671	44	57	expansion	expansion	NOUN
ap-7671	44	58	.	.	PUNCT
ap-7671	45	1	taking	take	VERB
ap-7671	45	2	the	the	DET
ap-7671	45	3	wavefunction	wavefunction	NOUN
ap-7671	45	4	(	(	PUNCT
ap-7671	45	5	6	6	NUM
ap-7671	45	6	)	)	PUNCT
ap-7671	45	7	one	one	NOUN
ap-7671	45	8	can	can	AUX
ap-7671	45	9	construct	construct	VERB
ap-7671	45	10	ψ(n	ψ(n	PROPN
ap-7671	45	11	,	,	PUNCT
ap-7671	45	12	p	p	NOUN
ap-7671	45	13	)	)	PUNCT
ap-7671	45	14	(	(	PUNCT
ap-7671	45	15	approximation	approximation	NOUN
ap-7671	45	16	)	)	PUNCT
ap-7671	45	17	=	=	SYM
ap-7671	45	18	pn	pn	PROPN
ap-7671	45	19	,	,	PUNCT
ap-7671	45	20	p(ũ2	p(ũ2	NOUN
ap-7671	45	21	)	)	PUNCT
ap-7671	45	22	(	(	PUNCT
ap-7671	45	23	b2	b2	NOUN
ap-7671	45	24	+	+	CCONJ
ap-7671	45	25	ũ2	ũ2	PROPN
ap-7671	45	26	)	)	PUNCT
ap-7671	45	27	1	1	NUM
ap-7671	45	28	4	4	NUM
ap-7671	45	29	(	(	PUNCT
ap-7671	45	30	αb	αb	NOUN
ap-7671	45	31	+	+	CCONJ
ap-7671	45	32	√	√	ADP
ap-7671	45	33	b2	b2	NOUN
ap-7671	45	34	+	+	CCONJ
ap-7671	45	35	ũ2	ũ2	PROPN
ap-7671	45	36	)	)	PUNCT
ap-7671	45	37	2n+	2n+	NUM
ap-7671	45	38	1	1	NUM
ap-7671	45	39	2	2	NUM
ap-7671	45	40	exp	exp	NOUN
ap-7671	45	41	(	(	PUNCT
ap-7671	45	42	−	−	PROPN
ap-7671	45	43	a	a	DET
ap-7671	45	44	+	+	X
ap-7671	45	45	(	(	PUNCT
ap-7671	45	46	b2	b2	NOUN
ap-7671	45	47	+	+	CCONJ
ap-7671	45	48	3	3	NUM
ap-7671	45	49	)	)	PUNCT
ap-7671	45	50	ũ2/6	ũ2/6	NOUN
ap-7671	46	1	+	+	CCONJ
ap-7671	46	2	ũ4/3√	ũ4/3√	ADJ
ap-7671	46	3	b2	b2	NOUN
ap-7671	46	4	+	+	CCONJ
ap-7671	46	5	ũ2	ũ2	PROPN
ap-7671	46	6	+	+	CCONJ
ap-7671	46	7	a	a	DET
ap-7671	46	8	b	b	NOUN
ap-7671	46	9	)	)	PUNCT
ap-7671	46	10	d(p	d(p	PROPN
ap-7671	46	11	)	)	PUNCT
ap-7671	46	12	,	,	PUNCT
ap-7671	46	13	(	(	PUNCT
ap-7671	46	14	9	9	X
ap-7671	46	15	)	)	PUNCT
ap-7671	46	16	where	where	SCONJ
ap-7671	46	17	p	p	NOUN
ap-7671	46	18	=	=	NOUN
ap-7671	46	19	0	0	NUM
ap-7671	46	20	,	,	PUNCT
ap-7671	46	21	1	1	NUM
ap-7671	46	22	and	and	CCONJ
ap-7671	46	23	d(0	d(0	NOUN
ap-7671	46	24	)	)	PUNCT
ap-7671	47	1	=	=	SYM
ap-7671	47	2	cosh	cosh	NOUN
ap-7671	47	3	(	(	PUNCT
ap-7671	47	4	a0ũ	a0ũ	ADJ
ap-7671	47	5	+	+	CCONJ
ap-7671	47	6	b0ũ3	b0ũ3	NOUN
ap-7671	47	7	√	√	ADP
ap-7671	47	8	b2	b2	NOUN
ap-7671	47	9	+	+	CCONJ
ap-7671	47	10	ũ2	ũ2	PROPN
ap-7671	47	11	)	)	PUNCT
ap-7671	47	12	,	,	PUNCT
ap-7671	47	13	d(1	d(1	PROPN
ap-7671	47	14	)	)	PUNCT
ap-7671	47	15	=	=	PUNCT
ap-7671	47	16	sinh	sinh	NOUN
ap-7671	47	17	(	(	PUNCT
ap-7671	47	18	a1ũ	a1ũ	NOUN
ap-7671	47	19	+	+	CCONJ
ap-7671	47	20	b1ũ3	b1ũ3	NOUN
ap-7671	47	21	√	√	ADP
ap-7671	47	22	b2	b2	NOUN
ap-7671	47	23	+	+	CCONJ
ap-7671	47	24	ũ2	ũ2	PROPN
ap-7671	47	25	)	)	PUNCT
ap-7671	47	26	.	.	PUNCT
ap-7671	48	1	here	here	ADV
ap-7671	48	2	ũ	ũ	PROPN
ap-7671	48	3	=	=	SYM
ap-7671	48	4	u	u	NOUN
ap-7671	48	5	−	−	PROPN
ap-7671	48	6	1	1	NUM
ap-7671	48	7	2	2	NUM
ap-7671	48	8	,	,	PUNCT
ap-7671	48	9	(	(	PUNCT
ap-7671	48	10	10	10	NUM
ap-7671	48	11	)	)	PUNCT
ap-7671	48	12	α	α	NOUN
ap-7671	48	13	=	=	SYM
ap-7671	48	14	1	1	NUM
ap-7671	48	15	and	and	CCONJ
ap-7671	48	16	a	a	DET
ap-7671	48	17	,	,	PUNCT
ap-7671	48	18	b	b	NOUN
ap-7671	48	19	,	,	PUNCT
ap-7671	48	20	a0,1	a0,1	NOUN
ap-7671	48	21	,	,	PUNCT
ap-7671	48	22	b0,1	b0,1	PRON
ap-7671	48	23	are	be	AUX
ap-7671	48	24	variational	variational	ADJ
ap-7671	48	25	parameters	parameter	NOUN
ap-7671	48	26	.	.	PUNCT
ap-7671	49	1	if	if	SCONJ
ap-7671	49	2	α	α	PRON
ap-7671	49	3	=	=	NOUN
ap-7671	49	4	0	0	PROPN
ap-7671	49	5	as	as	ADV
ap-7671	49	6	well	well	ADV
ap-7671	49	7	as	as	ADP
ap-7671	49	8	b0,1	b0,1	NOUN
ap-7671	49	9	=	=	NOUN
ap-7671	49	10	0	0	PROPN
ap-7671	50	1	the	the	DET
ap-7671	50	2	function	function	NOUN
ap-7671	50	3	(	(	PUNCT
ap-7671	50	4	9	9	NUM
ap-7671	50	5	)	)	PUNCT
ap-7671	50	6	is	be	AUX
ap-7671	50	7	reduced	reduce	VERB
ap-7671	50	8	to	to	ADP
ap-7671	50	9	ones	one	NOUN
ap-7671	50	10	which	which	PRON
ap-7671	50	11	were	be	AUX
ap-7671	50	12	explored	explore	VERB
ap-7671	50	13	in	in	ADP
ap-7671	50	14	[	[	X
ap-7671	50	15	6	6	NUM
ap-7671	50	16	]	]	PUNCT
ap-7671	50	17	,	,	PUNCT
ap-7671	50	18	see	see	VERB
ap-7671	50	19	eqs.(10)-(11	eqs.(10)-(11	NUM
ap-7671	50	20	)	)	PUNCT
ap-7671	50	21	therein	therein	ADV
ap-7671	50	22	.	.	PUNCT
ap-7671	51	1	the	the	DET
ap-7671	51	2	polynomial	polynomial	ADJ
ap-7671	51	3	pn	pn	PROPN
ap-7671	51	4	,	,	PUNCT
ap-7671	51	5	p	p	PROPN
ap-7671	51	6	is	be	AUX
ap-7671	51	7	found	find	VERB
ap-7671	51	8	unambiguously	unambiguously	ADV
ap-7671	51	9	after	after	ADP
ap-7671	51	10	imposing	impose	VERB
ap-7671	51	11	the	the	DET
ap-7671	51	12	orthogonality	orthogonality	NOUN
ap-7671	51	13	conditions	condition	NOUN
ap-7671	51	14	of	of	ADP
ap-7671	51	15	ψ(n	ψ(n	PROPN
ap-7671	51	16	,	,	PUNCT
ap-7671	51	17	p	p	NOUN
ap-7671	51	18	)	)	PUNCT
ap-7671	51	19	(	(	PUNCT
ap-7671	51	20	approximation	approximation	NOUN
ap-7671	51	21	)	)	PUNCT
ap-7671	51	22	to	to	ADP
ap-7671	51	23	ψ(k	ψ(k	PROPN
ap-7671	51	24	,	,	PUNCT
ap-7671	51	25	p	p	X
ap-7671	51	26	)	)	PUNCT
ap-7671	51	27	(	(	PUNCT
ap-7671	51	28	approximation	approximation	NOUN
ap-7671	51	29	)	)	PUNCT
ap-7671	51	30	at	at	ADP
ap-7671	51	31	k	k	PROPN
ap-7671	51	32	=	=	SYM
ap-7671	51	33	0	0	NUM
ap-7671	51	34	,	,	PUNCT
ap-7671	51	35	1	1	NUM
ap-7671	51	36	,	,	PUNCT
ap-7671	51	37	2	2	NUM
ap-7671	51	38	,	,	PUNCT
ap-7671	51	39	.	.	PUNCT
ap-7671	51	40	.	.	PUNCT
ap-7671	52	1	.	.	PUNCT
ap-7671	53	1	,	,	PUNCT
ap-7671	53	2	(	(	PUNCT
ap-7671	53	3	n	n	CCONJ
ap-7671	53	4	−	−	PROPN
ap-7671	53	5	1	1	NUM
ap-7671	53	6	)	)	PUNCT
ap-7671	53	7	,	,	PUNCT
ap-7671	53	8	here	here	ADV
ap-7671	53	9	it	it	PRON
ap-7671	53	10	is	be	AUX
ap-7671	53	11	assumed	assume	VERB
ap-7671	53	12	that	that	SCONJ
ap-7671	53	13	the	the	DET
ap-7671	53	14	polynomials	polynomial	NOUN
ap-7671	53	15	pk	pk	NOUN
ap-7671	53	16	,	,	PUNCT
ap-7671	53	17	p	p	NOUN
ap-7671	53	18	at	at	ADP
ap-7671	53	19	k	k	PROPN
ap-7671	53	20	=	=	SYM
ap-7671	53	21	0	0	NUM
ap-7671	53	22	,	,	PUNCT
ap-7671	53	23	1	1	NUM
ap-7671	53	24	,	,	PUNCT
ap-7671	53	25	2	2	NUM
ap-7671	53	26	,	,	PUNCT
ap-7671	53	27	.	.	PUNCT
ap-7671	53	28	.	.	PUNCT
ap-7671	54	1	.	.	PUNCT
ap-7671	55	1	,	,	PUNCT
ap-7671	55	2	(	(	PUNCT
ap-7671	55	3	n	n	CCONJ
ap-7671	55	4	−	−	PROPN
ap-7671	55	5	1	1	NUM
ap-7671	55	6	)	)	PUNCT
ap-7671	55	7	are	be	AUX
ap-7671	55	8	found	find	VERB
ap-7671	55	9	beforehand	beforehand	ADV
ap-7671	55	10	.	.	PUNCT
ap-7671	56	1	4	4	X
ap-7671	56	2	.	.	X
ap-7671	56	3	double	double	ADJ
ap-7671	56	4	-	-	PUNCT
ap-7671	56	5	well	well	NOUN
ap-7671	56	6	potential	potential	NOUN
ap-7671	56	7	:	:	PUNCT
ap-7671	56	8	results	result	NOUN
ap-7671	56	9	in	in	ADP
ap-7671	56	10	this	this	DET
ap-7671	56	11	section	section	NOUN
ap-7671	56	12	we	we	PRON
ap-7671	56	13	present	present	VERB
ap-7671	56	14	concrete	concrete	ADJ
ap-7671	56	15	results	result	NOUN
ap-7671	56	16	for	for	ADP
ap-7671	56	17	energies	energy	NOUN
ap-7671	56	18	of	of	ADP
ap-7671	56	19	the	the	DET
ap-7671	56	20	ground	ground	NOUN
ap-7671	56	21	state	state	NOUN
ap-7671	56	22	(	(	PUNCT
ap-7671	56	23	0	0	NUM
ap-7671	56	24	,	,	PUNCT
ap-7671	56	25	0	0	NUM
ap-7671	56	26	)	)	PUNCT
ap-7671	56	27	and	and	CCONJ
ap-7671	56	28	of	of	ADP
ap-7671	56	29	the	the	DET
ap-7671	56	30	first	first	ADJ
ap-7671	56	31	excited	excited	ADJ
ap-7671	56	32	state	state	NOUN
ap-7671	56	33	(	(	PUNCT
ap-7671	56	34	0	0	NUM
ap-7671	56	35	,	,	PUNCT
ap-7671	56	36	1	1	NUM
ap-7671	56	37	)	)	PUNCT
ap-7671	56	38	obtained	obtain	VERB
ap-7671	56	39	with	with	ADP
ap-7671	56	40	the	the	DET
ap-7671	56	41	function	function	NOUN
ap-7671	56	42	(	(	PUNCT
ap-7671	56	43	9	9	NUM
ap-7671	56	44	)	)	PUNCT
ap-7671	56	45	at	at	ADP
ap-7671	56	46	p	p	NOUN
ap-7671	56	47	=	=	PROPN
ap-7671	56	48	0	0	NUM
ap-7671	56	49	,	,	PUNCT
ap-7671	56	50	1	1	NUM
ap-7671	56	51	,	,	PUNCT
ap-7671	56	52	respectively	respectively	ADV
ap-7671	56	53	,	,	PUNCT
ap-7671	56	54	see	see	VERB
ap-7671	56	55	figure	figure	NOUN
ap-7671	56	56	1	1	NUM
ap-7671	56	57	(	(	PUNCT
ap-7671	56	58	bottom	bottom	NOUN
ap-7671	56	59	)	)	PUNCT
ap-7671	56	60	.	.	PUNCT
ap-7671	57	1	the	the	DET
ap-7671	57	2	results	result	NOUN
ap-7671	57	3	are	be	AUX
ap-7671	57	4	compared	compare	VERB
ap-7671	57	5	with	with	ADP
ap-7671	57	6	the	the	DET
ap-7671	57	7	lagrange	lagrange	ADJ
ap-7671	57	8	-	-	PUNCT
ap-7671	57	9	mesh	mesh	NOUN
ap-7671	57	10	method	method	NOUN
ap-7671	57	11	(	(	PUNCT
ap-7671	57	12	lmm	lmm	PROPN
ap-7671	57	13	)	)	PUNCT
ap-7671	58	1	[	[	X
ap-7671	58	2	7	7	NUM
ap-7671	58	3	]	]	PUNCT
ap-7671	58	4	.	.	PUNCT
ap-7671	59	1	4.1	4.1	NUM
ap-7671	59	2	.	.	PUNCT
ap-7671	59	3	ground	ground	NOUN
ap-7671	59	4	state	state	NOUN
ap-7671	59	5	(	(	PUNCT
ap-7671	59	6	0,0	0,0	NOUN
ap-7671	59	7	)	)	PUNCT
ap-7671	59	8	the	the	DET
ap-7671	59	9	ground	ground	NOUN
ap-7671	59	10	state	state	NOUN
ap-7671	59	11	energy	energy	NOUN
ap-7671	59	12	for	for	ADP
ap-7671	59	13	(	(	PUNCT
ap-7671	59	14	5	5	NUM
ap-7671	59	15	)	)	PUNCT
ap-7671	59	16	obtained	obtain	VERB
ap-7671	59	17	variationally	variationally	ADV
ap-7671	59	18	using	use	VERB
ap-7671	59	19	the	the	DET
ap-7671	59	20	function	function	NOUN
ap-7671	59	21	(	(	PUNCT
ap-7671	59	22	9	9	NUM
ap-7671	59	23	)	)	PUNCT
ap-7671	59	24	at	at	ADP
ap-7671	59	25	p	p	NOUN
ap-7671	59	26	=	=	PUNCT
ap-7671	59	27	0	0	PUNCT
ap-7671	59	28	and	and	CCONJ
ap-7671	59	29	compared	compare	VERB
ap-7671	59	30	with	with	ADP
ap-7671	59	31	lmm	lmm	PROPN
ap-7671	59	32	results	result	NOUN
ap-7671	59	33	[	[	X
ap-7671	59	34	7	7	NUM
ap-7671	59	35	]	]	PUNCT
ap-7671	59	36	,	,	PUNCT
ap-7671	59	37	where	where	SCONJ
ap-7671	59	38	all	all	DET
ap-7671	59	39	printed	print	VERB
ap-7671	59	40	digits	digit	NOUN
ap-7671	59	41	(	(	PUNCT
ap-7671	59	42	in	in	ADP
ap-7671	59	43	the	the	DET
ap-7671	59	44	second	second	ADJ
ap-7671	59	45	line	line	NOUN
ap-7671	59	46	)	)	PUNCT
ap-7671	59	47	are	be	AUX
ap-7671	59	48	correct	correct	ADJ
ap-7671	59	49	,	,	PUNCT
ap-7671	59	50	e(0,0	e(0,0	NOUN
ap-7671	59	51	)	)	PUNCT
ap-7671	59	52	var	var	NOUN
ap-7671	59	53	=	=	NOUN
ap-7671	59	54	0.932	0.932	NUM
ap-7671	59	55	517	517	NUM
ap-7671	59	56	518	518	NUM
ap-7671	59	57	401	401	NUM
ap-7671	59	58	,	,	PUNCT
ap-7671	59	59	e	e	X
ap-7671	59	60	(	(	PUNCT
ap-7671	59	61	0,0	0,0	NUM
ap-7671	59	62	)	)	PUNCT
ap-7671	59	63	mesh	mesh	NOUN
ap-7671	59	64	=	=	NOUN
ap-7671	59	65	0.932	0.932	NUM
ap-7671	59	66	517	517	NUM
ap-7671	59	67	518	518	NUM
ap-7671	59	68	372	372	NUM
ap-7671	59	69	.	.	PUNCT
ap-7671	60	1	note	note	VERB
ap-7671	60	2	that	that	SCONJ
ap-7671	60	3	ten	ten	NUM
ap-7671	60	4	decimal	decimal	ADJ
ap-7671	60	5	digits	digit	NOUN
ap-7671	60	6	in	in	ADP
ap-7671	60	7	e	e	PROPN
ap-7671	60	8	(	(	PUNCT
ap-7671	60	9	0,0	0,0	NOUN
ap-7671	60	10	)	)	PUNCT
ap-7671	60	11	var	var	NOUN
ap-7671	60	12	coincide	coincide	NOUN
ap-7671	60	13	with	with	ADP
ap-7671	60	14	ones	one	NOUN
ap-7671	60	15	in	in	ADP
ap-7671	60	16	e	e	PROPN
ap-7671	60	17	(	(	PUNCT
ap-7671	60	18	0,0	0,0	NOUN
ap-7671	60	19	)	)	PUNCT
ap-7671	60	20	mesh	mesh	NOUN
ap-7671	60	21	(	(	PUNCT
ap-7671	60	22	after	after	ADP
ap-7671	60	23	rounding	round	VERB
ap-7671	60	24	)	)	PUNCT
ap-7671	60	25	.	.	PUNCT
ap-7671	61	1	variational	variational	ADJ
ap-7671	61	2	parameters	parameter	NOUN
ap-7671	61	3	in	in	ADP
ap-7671	61	4	(	(	PUNCT
ap-7671	61	5	9	9	X
ap-7671	61	6	)	)	PUNCT
ap-7671	61	7	take	take	VERB
ap-7671	61	8	values	value	NOUN
ap-7671	61	9	,	,	PUNCT
ap-7671	61	10	a	a	DET
ap-7671	61	11	=	=	SYM
ap-7671	61	12	2.3237	2.3237	NUM
ap-7671	61	13	,	,	PUNCT
ap-7671	61	14	b	b	X
ap-7671	61	15	=	=	SYM
ap-7671	61	16	3.2734	3.2734	NUM
ap-7671	61	17	,	,	PUNCT
ap-7671	61	18	a0	a0	PROPN
ap-7671	61	19	=	=	SYM
ap-7671	61	20	2.3839	2.3839	NUM
ap-7671	61	21	,	,	PUNCT
ap-7671	61	22	b0	b0	NOUN
ap-7671	61	23	=	=	SYM
ap-7671	61	24	0.0605	0.0605	NUM
ap-7671	61	25	,	,	PUNCT
ap-7671	61	26	cf	cf	NOUN
ap-7671	61	27	.	.	PUNCT
ap-7671	62	1	(	(	PUNCT
ap-7671	62	2	7	7	NUM
ap-7671	62	3	)	)	PUNCT
ap-7671	62	4	.	.	PUNCT
ap-7671	63	1	note	note	VERB
ap-7671	63	2	that	that	SCONJ
ap-7671	63	3	b0	b0	NOUN
ap-7671	63	4	takes	take	VERB
ap-7671	63	5	a	a	DET
ap-7671	63	6	very	very	ADV
ap-7671	63	7	small	small	ADJ
ap-7671	63	8	value	value	NOUN
ap-7671	63	9	.	.	PUNCT
ap-7671	64	1	209	209	NUM
ap-7671	64	2	alexander	alexander	NOUN
ap-7671	64	3	v.	v.	ADP
ap-7671	64	4	turbiner	turbiner	PROPN
ap-7671	64	5	,	,	PUNCT
ap-7671	64	6	juan	juan	PROPN
ap-7671	64	7	carlos	carlos	PROPN
ap-7671	64	8	del	del	PROPN
ap-7671	64	9	valle	valle	PROPN
ap-7671	64	10	acta	acta	PROPN
ap-7671	64	11	polytechnica	polytechnica	PROPN
ap-7671	64	12	4.2	4.2	NUM
ap-7671	64	13	.	.	PUNCT
ap-7671	65	1	first	first	ADV
ap-7671	65	2	excited	excited	ADJ
ap-7671	65	3	state	state	NOUN
ap-7671	65	4	(	(	PUNCT
ap-7671	65	5	0,1	0,1	NUM
ap-7671	65	6	)	)	PUNCT
ap-7671	65	7	the	the	DET
ap-7671	65	8	first	first	ADJ
ap-7671	65	9	excited	excited	ADJ
ap-7671	65	10	state	state	NOUN
ap-7671	65	11	energy	energy	NOUN
ap-7671	65	12	for	for	ADP
ap-7671	65	13	(	(	PUNCT
ap-7671	65	14	5	5	NUM
ap-7671	65	15	)	)	PUNCT
ap-7671	65	16	obtained	obtain	VERB
ap-7671	65	17	variationally	variationally	ADV
ap-7671	65	18	using	use	VERB
ap-7671	65	19	the	the	DET
ap-7671	65	20	function	function	NOUN
ap-7671	65	21	(	(	PUNCT
ap-7671	65	22	9	9	NUM
ap-7671	65	23	)	)	PUNCT
ap-7671	65	24	at	at	ADP
ap-7671	65	25	p	p	NOUN
ap-7671	65	26	=	=	PROPN
ap-7671	65	27	1	1	NUM
ap-7671	65	28	and	and	CCONJ
ap-7671	65	29	compared	compare	VERB
ap-7671	65	30	with	with	ADP
ap-7671	65	31	lmm	lmm	PROPN
ap-7671	65	32	results	result	NOUN
ap-7671	65	33	[	[	X
ap-7671	65	34	7	7	NUM
ap-7671	65	35	]	]	PUNCT
ap-7671	65	36	,	,	PUNCT
ap-7671	65	37	where	where	SCONJ
ap-7671	65	38	all	all	DET
ap-7671	65	39	printed	print	VERB
ap-7671	65	40	digits	digit	NOUN
ap-7671	65	41	(	(	PUNCT
ap-7671	65	42	in	in	ADP
ap-7671	65	43	the	the	DET
ap-7671	65	44	second	second	ADJ
ap-7671	65	45	line	line	NOUN
ap-7671	65	46	)	)	PUNCT
ap-7671	65	47	are	be	AUX
ap-7671	65	48	correct	correct	ADJ
ap-7671	65	49	,	,	PUNCT
ap-7671	65	50	e(0,1	e(0,1	NOUN
ap-7671	65	51	)	)	PUNCT
ap-7671	65	52	var	var	NOUN
ap-7671	65	53	=	=	NOUN
ap-7671	65	54	3.396	3.396	NUM
ap-7671	65	55	279	279	NUM
ap-7671	65	56	329	329	NUM
ap-7671	65	57	936	936	NUM
ap-7671	65	58	,	,	PUNCT
ap-7671	65	59	e	e	X
ap-7671	65	60	(	(	PUNCT
ap-7671	65	61	0,1	0,1	NUM
ap-7671	65	62	)	)	PUNCT
ap-7671	65	63	mesh	mesh	NOUN
ap-7671	65	64	=	=	NOUN
ap-7671	65	65	3.396	3.396	NUM
ap-7671	65	66	279	279	NUM
ap-7671	65	67	329	329	NUM
ap-7671	65	68	887	887	NUM
ap-7671	65	69	.	.	PUNCT
ap-7671	66	1	note	note	VERB
ap-7671	66	2	that	that	SCONJ
ap-7671	66	3	ten	ten	NUM
ap-7671	66	4	decimal	decimal	ADJ
ap-7671	66	5	digits	digit	NOUN
ap-7671	66	6	in	in	ADP
ap-7671	66	7	e	e	PROPN
ap-7671	66	8	(	(	PUNCT
ap-7671	66	9	0,1	0,1	NUM
ap-7671	66	10	)	)	PUNCT
ap-7671	66	11	var	var	NOUN
ap-7671	66	12	coincide	coincide	NOUN
ap-7671	66	13	with	with	ADP
ap-7671	66	14	ones	one	NOUN
ap-7671	66	15	in	in	ADP
ap-7671	66	16	e	e	PROPN
ap-7671	66	17	(	(	PUNCT
ap-7671	66	18	0,1	0,1	NOUN
ap-7671	66	19	)	)	PUNCT
ap-7671	66	20	mesh	mesh	NOUN
ap-7671	66	21	.	.	PUNCT
ap-7671	67	1	variational	variational	ADJ
ap-7671	67	2	parameters	parameter	NOUN
ap-7671	67	3	in	in	ADP
ap-7671	67	4	(	(	PUNCT
ap-7671	67	5	9	9	X
ap-7671	67	6	)	)	PUNCT
ap-7671	67	7	take	take	VERB
ap-7671	67	8	values	value	NOUN
ap-7671	67	9	,	,	PUNCT
ap-7671	67	10	a	a	DET
ap-7671	67	11	=	=	SYM
ap-7671	67	12	−2.2957	−2.2957	NOUN
ap-7671	67	13	,	,	PUNCT
ap-7671	67	14	b	b	X
ap-7671	67	15	=	=	SYM
ap-7671	67	16	3.6991	3.6991	NUM
ap-7671	67	17	,	,	PUNCT
ap-7671	67	18	a1	a1	NOUN
ap-7671	67	19	=	=	SYM
ap-7671	67	20	4.7096	4.7096	NUM
ap-7671	67	21	,	,	PUNCT
ap-7671	67	22	b1	b1	NOUN
ap-7671	67	23	=	=	SYM
ap-7671	67	24	0.0590	0.0590	NUM
ap-7671	67	25	,	,	PUNCT
ap-7671	67	26	cf	cf	NOUN
ap-7671	67	27	.	.	PUNCT
ap-7671	68	1	(	(	PUNCT
ap-7671	68	2	8)	8)	NUM
ap-7671	68	3	.	.	PUNCT
ap-7671	68	4	note	note	NOUN
ap-7671	68	5	that	that	SCONJ
ap-7671	68	6	b1	b1	NOUN
ap-7671	68	7	takes	take	VERB
ap-7671	68	8	a	a	DET
ap-7671	68	9	very	very	ADV
ap-7671	68	10	small	small	ADJ
ap-7671	68	11	value	value	NOUN
ap-7671	68	12	similar	similar	ADJ
ap-7671	68	13	to	to	ADP
ap-7671	68	14	b0	b0	NOUN
ap-7671	68	15	.	.	PUNCT
ap-7671	69	1	5	5	NUM
ap-7671	69	2	.	.	X
ap-7671	69	3	conclusions	conclusion	NOUN
ap-7671	69	4	it	it	PRON
ap-7671	69	5	is	be	AUX
ap-7671	69	6	presented	present	VERB
ap-7671	69	7	the	the	DET
ap-7671	69	8	approximate	approximate	ADJ
ap-7671	69	9	expression	expression	NOUN
ap-7671	69	10	(	(	PUNCT
ap-7671	69	11	9	9	NUM
ap-7671	69	12	)	)	PUNCT
ap-7671	69	13	for	for	ADP
ap-7671	69	14	the	the	DET
ap-7671	69	15	eigenfunctions	eigenfunction	NOUN
ap-7671	69	16	in	in	ADP
ap-7671	69	17	the	the	DET
ap-7671	69	18	double	double	ADJ
ap-7671	69	19	-	-	PUNCT
ap-7671	69	20	well	well	NOUN
ap-7671	69	21	potential	potential	NOUN
ap-7671	69	22	(	(	PUNCT
ap-7671	69	23	5	5	NUM
ap-7671	69	24	)	)	PUNCT
ap-7671	69	25	.	.	PUNCT
ap-7671	70	1	in	in	ADP
ap-7671	70	2	nonlinearization	nonlinearization	NOUN
ap-7671	70	3	procedure	procedure	NOUN
ap-7671	70	4	[	[	X
ap-7671	70	5	8	8	NUM
ap-7671	70	6	]	]	PUNCT
ap-7671	70	7	it	it	PRON
ap-7671	70	8	can	can	AUX
ap-7671	70	9	be	be	AUX
ap-7671	70	10	calculated	calculate	VERB
ap-7671	70	11	the	the	DET
ap-7671	70	12	first	first	ADJ
ap-7671	70	13	correction	correction	NOUN
ap-7671	70	14	(	(	PUNCT
ap-7671	70	15	the	the	DET
ap-7671	70	16	first	first	ADJ
ap-7671	70	17	order	order	NOUN
ap-7671	70	18	deviation	deviation	NOUN
ap-7671	70	19	)	)	PUNCT
ap-7671	70	20	to	to	ADP
ap-7671	70	21	the	the	DET
ap-7671	70	22	function	function	NOUN
ap-7671	70	23	(	(	PUNCT
ap-7671	70	24	9	9	NUM
ap-7671	70	25	)	)	PUNCT
ap-7671	70	26	.	.	PUNCT
ap-7671	71	1	it	it	PRON
ap-7671	71	2	can	can	AUX
ap-7671	71	3	be	be	AUX
ap-7671	71	4	shown	show	VERB
ap-7671	71	5	that	that	SCONJ
ap-7671	71	6	for	for	ADP
ap-7671	71	7	any	any	DET
ap-7671	71	8	u	u	NOUN
ap-7671	71	9	∈	∈	PROPN
ap-7671	71	10	(	(	PUNCT
ap-7671	71	11	−∞	−∞	NOUN
ap-7671	71	12	,	,	PUNCT
ap-7671	71	13	+	+	NOUN
ap-7671	71	14	∞	∞	NOUN
ap-7671	71	15	)	)	PUNCT
ap-7671	71	16	the	the	DET
ap-7671	71	17	functions	function	NOUN
ap-7671	71	18	(	(	PUNCT
ap-7671	71	19	9	9	X
ap-7671	71	20	)	)	PUNCT
ap-7671	71	21	deviate	deviate	VERB
ap-7671	71	22	uniformly	uniformly	ADV
ap-7671	71	23	from	from	ADP
ap-7671	71	24	the	the	DET
ap-7671	71	25	exact	exact	ADJ
ap-7671	71	26	eigenfunctions	eigenfunction	NOUN
ap-7671	71	27	,	,	PUNCT
ap-7671	71	28	beyond	beyond	ADP
ap-7671	71	29	the	the	DET
ap-7671	71	30	sixth	sixth	ADJ
ap-7671	71	31	significant	significant	ADJ
ap-7671	71	32	figure	figure	NOUN
ap-7671	71	33	similarly	similarly	ADV
ap-7671	71	34	to	to	ADP
ap-7671	71	35	the	the	DET
ap-7671	71	36	function	function	NOUN
ap-7671	71	37	(	(	PUNCT
ap-7671	71	38	6	6	NUM
ap-7671	71	39	)	)	PUNCT
ap-7671	71	40	for	for	ADP
ap-7671	71	41	the	the	DET
ap-7671	71	42	single	single	ADJ
ap-7671	71	43	-	-	PUNCT
ap-7671	71	44	well	well	NOUN
ap-7671	71	45	case	case	NOUN
ap-7671	71	46	.	.	PUNCT
ap-7671	72	1	it	it	PRON
ap-7671	72	2	increases	increase	VERB
ap-7671	72	3	the	the	DET
ap-7671	72	4	accuracy	accuracy	NOUN
ap-7671	72	5	of	of	ADP
ap-7671	72	6	the	the	DET
ap-7671	72	7	simplified	simplified	ADJ
ap-7671	72	8	function	function	NOUN
ap-7671	72	9	,	,	PUNCT
ap-7671	72	10	proposed	propose	VERB
ap-7671	72	11	in	in	ADP
ap-7671	72	12	[	[	X
ap-7671	72	13	5	5	NUM
ap-7671	72	14	]	]	PUNCT
ap-7671	72	15	with	with	ADP
ap-7671	72	16	α	α	PROPN
ap-7671	72	17	=	=	SYM
ap-7671	72	18	0	0	NUM
ap-7671	72	19	and	and	CCONJ
ap-7671	72	20	b0,1	b0,1	NOUN
ap-7671	72	21	=	=	SYM
ap-7671	72	22	0	0	NUM
ap-7671	72	23	,	,	PUNCT
ap-7671	72	24	in	in	ADP
ap-7671	72	25	the	the	DET
ap-7671	72	26	domain	domain	NOUN
ap-7671	72	27	under	under	ADP
ap-7671	72	28	the	the	DET
ap-7671	72	29	barrier	barrier	NOUN
ap-7671	72	30	u	u	NOUN
ap-7671	72	31	∈	∈	PROPN
ap-7671	72	32	(	(	PUNCT
ap-7671	72	33	0.25	0.25	NUM
ap-7671	72	34	,	,	PUNCT
ap-7671	72	35	0.75	0.75	NUM
ap-7671	72	36	)	)	PUNCT
ap-7671	72	37	from	from	ADP
ap-7671	72	38	4	4	NUM
ap-7671	72	39	to	to	PART
ap-7671	72	40	6	6	NUM
ap-7671	72	41	significant	significant	ADJ
ap-7671	72	42	figures	figure	NOUN
ap-7671	72	43	leaving	leave	VERB
ap-7671	72	44	the	the	DET
ap-7671	72	45	accuracy	accuracy	NOUN
ap-7671	72	46	outside	outside	ADP
ap-7671	72	47	of	of	ADP
ap-7671	72	48	this	this	DET
ap-7671	72	49	domain	domain	NOUN
ap-7671	72	50	practically	practically	ADV
ap-7671	72	51	unchanged	unchanged	ADJ
ap-7671	72	52	.	.	PUNCT
ap-7671	73	1	acknowledgements	acknowledgement	NOUN
ap-7671	73	2	this	this	DET
ap-7671	73	3	work	work	NOUN
ap-7671	73	4	is	be	AUX
ap-7671	73	5	partially	partially	ADV
ap-7671	73	6	supported	support	VERB
ap-7671	73	7	by	by	ADP
ap-7671	73	8	conacyt	conacyt	ADJ
ap-7671	73	9	grant	grant	NOUN
ap-7671	73	10	a1s-17364	a1s-17364	PROPN
ap-7671	73	11	and	and	CCONJ
ap-7671	73	12	dgapa	dgapa	ADJ
ap-7671	73	13	grants	grant	NOUN
ap-7671	73	14	in113819	in113819	PROPN
ap-7671	73	15	,	,	PUNCT
ap-7671	73	16	in113022	in113022	PROPN
ap-7671	73	17	(	(	PUNCT
ap-7671	73	18	mexico	mexico	PROPN
ap-7671	73	19	)	)	PUNCT
ap-7671	73	20	.	.	PUNCT
ap-7671	74	1	avt	avt	PROPN
ap-7671	74	2	thanks	thank	NOUN
ap-7671	74	3	the	the	DET
ap-7671	74	4	paspa	paspa	NOUN
ap-7671	74	5	-	-	PUNCT
ap-7671	74	6	unam	unam	PROPN
ap-7671	74	7	program	program	NOUN
ap-7671	74	8	for	for	ADP
ap-7671	74	9	support	support	NOUN
ap-7671	74	10	during	during	ADP
ap-7671	74	11	his	his	PRON
ap-7671	74	12	sabbatical	sabbatical	ADJ
ap-7671	74	13	leave	leave	NOUN
ap-7671	74	14	.	.	PUNCT
ap-7671	75	1	references	reference	NOUN
ap-7671	75	2	[	[	X
ap-7671	75	3	1	1	NUM
ap-7671	75	4	]	]	PUNCT
ap-7671	75	5	a.	a.	NOUN
ap-7671	75	6	v.	v.	PROPN
ap-7671	75	7	turbiner	turbiner	PROPN
ap-7671	75	8	,	,	PUNCT
ap-7671	75	9	j.	j.	PROPN
ap-7671	75	10	c.	c.	PROPN
ap-7671	75	11	del	del	PROPN
ap-7671	75	12	valle	valle	PROPN
ap-7671	75	13	.	.	PUNCT
ap-7671	76	1	anharmonic	anharmonic	ADJ
ap-7671	76	2	oscillator	oscillator	NOUN
ap-7671	76	3	:	:	PUNCT
ap-7671	76	4	a	a	DET
ap-7671	76	5	solution	solution	NOUN
ap-7671	76	6	.	.	PUNCT
ap-7671	77	1	journal	journal	PROPN
ap-7671	77	2	of	of	ADP
ap-7671	77	3	physics	physics	PROPN
ap-7671	77	4	a	a	PRON
ap-7671	77	5	:	:	PUNCT
ap-7671	77	6	mathematical	mathematical	ADJ
ap-7671	77	7	and	and	CCONJ
ap-7671	77	8	theoretical	theoretical	ADJ
ap-7671	77	9	54(29):295204	54(29):295204	NUM
ap-7671	77	10	,	,	PUNCT
ap-7671	77	11	2021	2021	NUM
ap-7671	77	12	.	.	PUNCT
ap-7671	78	1	https://doi.org/10.1088/1751-8121/ac0733	https://doi.org/10.1088/1751-8121/ac0733	X
ap-7671	78	2	.	.	PUNCT
ap-7671	79	1	[	[	X
ap-7671	79	2	2	2	NUM
ap-7671	79	3	]	]	PUNCT
ap-7671	79	4	a.	a.	NOUN
ap-7671	79	5	v.	v.	PROPN
ap-7671	79	6	turbiner	turbiner	PROPN
ap-7671	79	7	,	,	PUNCT
ap-7671	79	8	e.	e.	PROPN
ap-7671	79	9	shuryak	shuryak	PROPN
ap-7671	79	10	.	.	PUNCT
ap-7671	80	1	on	on	ADP
ap-7671	80	2	connection	connection	NOUN
ap-7671	80	3	between	between	ADP
ap-7671	80	4	perturbation	perturbation	NOUN
ap-7671	80	5	theory	theory	NOUN
ap-7671	80	6	and	and	CCONJ
ap-7671	80	7	semiclassical	semiclassical	ADJ
ap-7671	80	8	expansion	expansion	NOUN
ap-7671	80	9	in	in	ADP
ap-7671	80	10	quantum	quantum	ADJ
ap-7671	80	11	mechanics	mechanic	NOUN
ap-7671	80	12	,	,	PUNCT
ap-7671	80	13	2021	2021	NUM
ap-7671	80	14	.	.	PUNCT
ap-7671	80	15	arxiv:2102.04623	arxiv:2102.04623	VERB
ap-7671	80	16	.	.	PUNCT
ap-7671	81	1	[	[	X
ap-7671	81	2	3	3	X
ap-7671	81	3	]	]	X
ap-7671	81	4	e.	e.	PROPN
ap-7671	81	5	shuryak	shuryak	PROPN
ap-7671	81	6	,	,	PUNCT
ap-7671	81	7	a.	a.	NOUN
ap-7671	81	8	v.	v.	PROPN
ap-7671	81	9	turbiner	turbiner	NOUN
ap-7671	81	10	.	.	PUNCT
ap-7671	82	1	transseries	transserie	NOUN
ap-7671	82	2	for	for	ADP
ap-7671	82	3	the	the	DET
ap-7671	82	4	ground	ground	NOUN
ap-7671	82	5	state	state	NOUN
ap-7671	82	6	density	density	NOUN
ap-7671	82	7	and	and	CCONJ
ap-7671	82	8	generalized	generalized	ADJ
ap-7671	82	9	bloch	bloch	NOUN
ap-7671	82	10	equation	equation	NOUN
ap-7671	82	11	:	:	PUNCT
ap-7671	82	12	doublewell	doublewell	VERB
ap-7671	82	13	potential	potential	ADJ
ap-7671	82	14	case	case	NOUN
ap-7671	82	15	.	.	PUNCT
ap-7671	83	1	physical	physical	ADJ
ap-7671	83	2	review	review	PROPN
ap-7671	83	3	d	d	PROPN
ap-7671	83	4	98:105007	98:105007	NOUN
ap-7671	83	5	,	,	PUNCT
ap-7671	83	6	2018	2018	NUM
ap-7671	83	7	.	.	PUNCT
ap-7671	84	1	https://doi.org/10.1103/physrevd.98.105007	https://doi.org/10.1103/physrevd.98.105007	NOUN
ap-7671	84	2	.	.	PUNCT
ap-7671	85	1	[	[	X
ap-7671	85	2	4	4	X
ap-7671	85	3	]	]	PUNCT
ap-7671	85	4	m.	m.	NOUN
ap-7671	85	5	a.	a.	PROPN
ap-7671	85	6	escobar	escobar	PROPN
ap-7671	85	7	-	-	PUNCT
ap-7671	85	8	ruiz	ruiz	PROPN
ap-7671	85	9	,	,	PUNCT
ap-7671	85	10	e.	e.	PROPN
ap-7671	85	11	shuryak	shuryak	PROPN
ap-7671	85	12	,	,	PUNCT
ap-7671	85	13	a.	a.	NOUN
ap-7671	85	14	v.	v.	PROPN
ap-7671	85	15	turbiner	turbiner	NOUN
ap-7671	85	16	.	.	PUNCT
ap-7671	86	1	quantum	quantum	NOUN
ap-7671	86	2	and	and	CCONJ
ap-7671	86	3	thermal	thermal	ADJ
ap-7671	86	4	fluctuations	fluctuation	NOUN
ap-7671	86	5	in	in	ADP
ap-7671	86	6	quantum	quantum	ADJ
ap-7671	86	7	mechanics	mechanic	NOUN
ap-7671	86	8	and	and	CCONJ
ap-7671	86	9	field	field	NOUN
ap-7671	86	10	theories	theory	NOUN
ap-7671	86	11	from	from	ADP
ap-7671	86	12	a	a	DET
ap-7671	86	13	new	new	ADJ
ap-7671	86	14	version	version	NOUN
ap-7671	86	15	of	of	ADP
ap-7671	86	16	semiclassical	semiclassical	ADJ
ap-7671	86	17	theory	theory	NOUN
ap-7671	86	18	.	.	PUNCT
ap-7671	87	1	physical	physical	ADJ
ap-7671	87	2	review	review	PROPN
ap-7671	87	3	d	d	PROPN
ap-7671	87	4	93:105039	93:105039	NOUN
ap-7671	87	5	,	,	PUNCT
ap-7671	87	6	2016	2016	NUM
ap-7671	87	7	.	.	PUNCT
ap-7671	88	1	https://doi.org/10.1103/physrevd.93.105039	https://doi.org/10.1103/physrevd.93.105039	NOUN
ap-7671	88	2	.	.	PUNCT
ap-7671	89	1	[	[	X
ap-7671	89	2	5	5	NUM
ap-7671	89	3	]	]	PUNCT
ap-7671	89	4	a.	a.	NOUN
ap-7671	89	5	v.	v.	PROPN
ap-7671	89	6	turbiner	turbiner	PROPN
ap-7671	89	7	,	,	PUNCT
ap-7671	89	8	j.	j.	PROPN
ap-7671	89	9	c.	c.	PROPN
ap-7671	89	10	del	del	PROPN
ap-7671	89	11	valle	valle	PROPN
ap-7671	89	12	.	.	PUNCT
ap-7671	90	1	anharmonic	anharmonic	ADJ
ap-7671	90	2	oscillator	oscillator	NOUN
ap-7671	90	3	:	:	PUNCT
ap-7671	90	4	almost	almost	ADV
ap-7671	90	5	analytic	analytic	ADJ
ap-7671	90	6	solution	solution	NOUN
ap-7671	90	7	,	,	PUNCT
ap-7671	90	8	2021	2021	NUM
ap-7671	90	9	.	.	PUNCT
ap-7671	91	1	talk	talk	NOUN
ap-7671	91	2	presented	present	VERB
ap-7671	91	3	by	by	ADP
ap-7671	91	4	avt	avt	PROPN
ap-7671	91	5	at	at	ADP
ap-7671	91	6	aamp-18	aamp-18	PROPN
ap-7671	91	7	(	(	PUNCT
ap-7671	91	8	sept.1	sept.1	PROPN
ap-7671	91	9	-	-	PUNCT
ap-7671	91	10	3	3	NUM
ap-7671	91	11	)	)	PUNCT
ap-7671	91	12	,	,	PUNCT
ap-7671	91	13	prague	prague	PROPN
ap-7671	91	14	,	,	PUNCT
ap-7671	91	15	czech	czech	PROPN
ap-7671	91	16	republic	republic	NOUN
ap-7671	91	17	(	(	PUNCT
ap-7671	91	18	september	september	PROPN
ap-7671	91	19	1	1	NUM
ap-7671	91	20	,	,	PUNCT
ap-7671	91	21	2021	2021	NUM
ap-7671	91	22	)	)	PUNCT
ap-7671	91	23	.	.	PUNCT
ap-7671	92	1	[	[	X
ap-7671	92	2	6	6	NUM
ap-7671	92	3	]	]	PUNCT
ap-7671	92	4	a.	a.	NOUN
ap-7671	92	5	v.	v.	PROPN
ap-7671	92	6	turbiner	turbiner	NOUN
ap-7671	92	7	.	.	PUNCT
ap-7671	93	1	double	double	ADJ
ap-7671	93	2	well	well	ADV
ap-7671	93	3	potential	potential	ADJ
ap-7671	93	4	:	:	PUNCT
ap-7671	93	5	perturbation	perturbation	NOUN
ap-7671	93	6	theory	theory	NOUN
ap-7671	93	7	,	,	PUNCT
ap-7671	93	8	tunneling	tunneling	NOUN
ap-7671	93	9	,	,	PUNCT
ap-7671	93	10	wkb	wkb	NOUN
ap-7671	93	11	(	(	PUNCT
ap-7671	93	12	beyond	beyond	ADP
ap-7671	93	13	instantons	instanton	NOUN
ap-7671	93	14	)	)	PUNCT
ap-7671	93	15	.	.	PUNCT
ap-7671	94	1	international	international	ADJ
ap-7671	94	2	journal	journal	PROPN
ap-7671	94	3	of	of	ADP
ap-7671	94	4	modern	modern	ADJ
ap-7671	94	5	physics	physic	NOUN
ap-7671	94	6	a	a	DET
ap-7671	94	7	25(02n03):647–658	25(02n03):647–658	NUM
ap-7671	94	8	,	,	PUNCT
ap-7671	94	9	2010	2010	NUM
ap-7671	94	10	.	.	PUNCT
ap-7671	95	1	https://doi.org/10.1142/s0217751x10048937	https://doi.org/10.1142/s0217751x10048937	X
ap-7671	95	2	.	.	PUNCT
ap-7671	96	1	[	[	X
ap-7671	96	2	7	7	NUM
ap-7671	96	3	]	]	X
ap-7671	96	4	a.	a.	NOUN
ap-7671	96	5	v.	v.	PROPN
ap-7671	96	6	turbiner	turbiner	PROPN
ap-7671	96	7	,	,	PUNCT
ap-7671	96	8	j.	j.	PROPN
ap-7671	96	9	c.	c.	PROPN
ap-7671	96	10	del	del	PROPN
ap-7671	96	11	valle	valle	PROPN
ap-7671	96	12	.	.	PUNCT
ap-7671	97	1	comment	comment	NOUN
ap-7671	97	2	on	on	ADP
ap-7671	97	3	:	:	PUNCT
ap-7671	97	4	uncommonly	uncommonly	ADV
ap-7671	97	5	accurate	accurate	ADJ
ap-7671	97	6	energies	energy	NOUN
ap-7671	97	7	for	for	ADP
ap-7671	97	8	the	the	DET
ap-7671	97	9	general	general	ADJ
ap-7671	97	10	quartic	quartic	ADJ
ap-7671	97	11	oscillator	oscillator	NOUN
ap-7671	97	12	.	.	PUNCT
ap-7671	98	1	international	international	ADJ
ap-7671	98	2	journal	journal	NOUN
ap-7671	98	3	of	of	ADP
ap-7671	98	4	quantum	quantum	ADJ
ap-7671	98	5	chemistry	chemistry	NOUN
ap-7671	98	6	121(19):e26766	121(19):e26766	NUM
ap-7671	98	7	,	,	PUNCT
ap-7671	98	8	2021	2021	NUM
ap-7671	98	9	.	.	PUNCT
ap-7671	99	1	https://doi.org/10.1002/qua.26766	https://doi.org/10.1002/qua.26766	PROPN
ap-7671	99	2	.	.	PUNCT
ap-7671	100	1	[	[	X
ap-7671	100	2	8	8	NUM
ap-7671	100	3	]	]	X
ap-7671	100	4	a.	a.	NOUN
ap-7671	100	5	v.	v.	PROPN
ap-7671	100	6	turbiner	turbiner	NOUN
ap-7671	100	7	.	.	PUNCT
ap-7671	101	1	the	the	DET
ap-7671	101	2	eigenvalue	eigenvalue	PROPN
ap-7671	101	3	spectrum	spectrum	NOUN
ap-7671	101	4	in	in	ADP
ap-7671	101	5	quantum	quantum	ADJ
ap-7671	101	6	mechanics	mechanic	NOUN
ap-7671	101	7	and	and	CCONJ
ap-7671	101	8	the	the	DET
ap-7671	101	9	nonlinearization	nonlinearization	NOUN
ap-7671	101	10	procedure	procedure	NOUN
ap-7671	101	11	.	.	PUNCT
ap-7671	102	1	soviet	soviet	ADJ
ap-7671	102	2	physics	physics	PROPN
ap-7671	102	3	uspekhi	uspekhi	VERB
ap-7671	102	4	27(9):668–694	27(9):668–694	PROPN
ap-7671	102	5	,	,	PUNCT
ap-7671	102	6	1984	1984	NUM
ap-7671	102	7	.	.	PUNCT
ap-7671	103	1	english	english	ADJ
ap-7671	103	2	translation	translation	NOUN
ap-7671	103	3	,	,	PUNCT
ap-7671	103	4	https://doi.org/10.1070/pu1984v027n09abeh004155	https://doi.org/10.1070/pu1984v027n09abeh004155	SYM
ap-7671	103	5	.	.	NOUN
ap-7671	103	6	210	210	NUM
ap-7671	103	7	https://doi.org/10.1088/1751-8121/ac0733	https://doi.org/10.1088/1751-8121/ac0733	NOUN
ap-7671	103	8	http://arxiv.org/abs/2102.04623	http://arxiv.org/abs/2102.04623	NOUN
ap-7671	103	9	https://doi.org/10.1103/physrevd.98.105007	https://doi.org/10.1103/physrevd.98.105007	NOUN
ap-7671	103	10	https://doi.org/10.1103/physrevd.93.105039	https://doi.org/10.1103/physrevd.93.105039	NOUN
ap-7671	103	11	https://doi.org/10.1142/s0217751x10048937	https://doi.org/10.1142/s0217751x10048937	X
ap-7671	103	12	https://doi.org/10.1002/qua.26766	https://doi.org/10.1002/qua.26766	PROPN
ap-7671	103	13	https://doi.org/10.1070/pu1984v027n09abeh004155	https://doi.org/10.1070/pu1984v027n09abeh004155	NUM
ap-7671	103	14	acta	acta	PROPN
ap-7671	103	15	polytechnica	polytechnica	PROPN
ap-7671	103	16	62(1):208–210	62(1):208–210	PROPN
ap-7671	103	17	,	,	PUNCT
ap-7671	103	18	2022	2022	NUM
ap-7671	103	19	1	1	NUM
ap-7671	103	20	introduction	introduction	NOUN
ap-7671	103	21	2	2	NUM
ap-7671	103	22	single	single	ADJ
ap-7671	103	23	-	-	PUNCT
ap-7671	103	24	well	well	NOUN
ap-7671	103	25	potential	potential	ADJ
ap-7671	103	26	3	3	NUM
ap-7671	103	27	double	double	ADJ
ap-7671	103	28	-	-	PUNCT
ap-7671	103	29	well	well	NOUN
ap-7671	103	30	potential	potential	NOUN
ap-7671	103	31	:	:	PUNCT
ap-7671	103	32	wavefunctions	wavefunction	NOUN
ap-7671	103	33	4	4	NUM
ap-7671	103	34	double	double	ADJ
ap-7671	103	35	-	-	PUNCT
ap-7671	103	36	well	well	NOUN
ap-7671	103	37	potential	potential	NOUN
ap-7671	103	38	:	:	PUNCT
ap-7671	103	39	results	result	VERB
ap-7671	103	40	4.1	4.1	NUM
ap-7671	103	41	ground	ground	NOUN
ap-7671	103	42	state	state	NOUN
ap-7671	103	43	(	(	PUNCT
ap-7671	103	44	0,0	0,0	NOUN
ap-7671	103	45	)	)	PUNCT
ap-7671	103	46	4.2	4.2	NUM
ap-7671	103	47	first	first	ADV
ap-7671	103	48	excited	excited	ADJ
ap-7671	103	49	state	state	NOUN
ap-7671	103	50	(	(	PUNCT
ap-7671	103	51	0,1	0,1	NUM
ap-7671	103	52	)	)	PUNCT
ap-7671	103	53	5	5	NUM
ap-7671	103	54	conclusions	conclusion	NOUN
ap-7671	103	55	acknowledgements	acknowledgement	NOUN
ap-7671	103	56	references	reference	NOUN