id	sid	tid	token	lemma	pos
ap-1257	1	1	ap-5-10.dvi	ap-5-10.dvi	PROPN
ap-1257	1	2	acta	acta	PROPN
ap-1257	1	3	polytechnica	polytechnica	PROPN
ap-1257	1	4	vol	vol	NOUN
ap-1257	1	5	.	.	PROPN
ap-1257	2	1	50	50	NUM
ap-1257	2	2	no	no	NOUN
ap-1257	2	3	.	.	PUNCT
ap-1257	3	1	5/2010	5/2010	NUM
ap-1257	3	2	two	two	NUM
ap-1257	3	3	-	-	PUNCT
ap-1257	3	4	particle	particle	NOUN
ap-1257	3	5	harmonic	harmonic	ADJ
ap-1257	3	6	oscillator	oscillator	NOUN
ap-1257	3	7	in	in	ADP
ap-1257	3	8	a	a	DET
ap-1257	3	9	one	one	NUM
ap-1257	3	10	-	-	PUNCT
ap-1257	3	11	dimensional	dimensional	ADJ
ap-1257	3	12	box	box	NOUN
ap-1257	3	13	p.	p.	PROPN
ap-1257	3	14	amore	amore	PROPN
ap-1257	3	15	,	,	PUNCT
ap-1257	4	1	f.	f.	PROPN
ap-1257	4	2	m.	m.	PROPN
ap-1257	4	3	fernández	fernández	PROPN
ap-1257	4	4	abstract	abstract	ADV
ap-1257	4	5	we	we	PRON
ap-1257	4	6	study	study	VERB
ap-1257	4	7	a	a	DET
ap-1257	4	8	harmonic	harmonic	ADJ
ap-1257	4	9	molecule	molecule	NOUN
ap-1257	4	10	confined	confine	VERB
ap-1257	4	11	to	to	ADP
ap-1257	4	12	a	a	DET
ap-1257	4	13	one	one	NUM
ap-1257	4	14	-	-	PUNCT
ap-1257	4	15	dimensional	dimensional	ADJ
ap-1257	4	16	box	box	NOUN
ap-1257	4	17	with	with	ADP
ap-1257	4	18	impenetrable	impenetrable	ADJ
ap-1257	4	19	walls	wall	NOUN
ap-1257	4	20	.	.	PUNCT
ap-1257	5	1	we	we	PRON
ap-1257	5	2	explicitly	explicitly	ADV
ap-1257	5	3	consider	consider	VERB
ap-1257	5	4	the	the	DET
ap-1257	5	5	symmetry	symmetry	NOUN
ap-1257	5	6	of	of	ADP
ap-1257	5	7	the	the	DET
ap-1257	5	8	problem	problem	NOUN
ap-1257	5	9	for	for	ADP
ap-1257	5	10	the	the	DET
ap-1257	5	11	cases	case	NOUN
ap-1257	5	12	of	of	ADP
ap-1257	5	13	different	different	ADJ
ap-1257	5	14	and	and	CCONJ
ap-1257	5	15	equal	equal	ADJ
ap-1257	5	16	masses	masse	NOUN
ap-1257	5	17	.	.	PUNCT
ap-1257	6	1	we	we	PRON
ap-1257	6	2	propose	propose	VERB
ap-1257	6	3	suitable	suitable	ADJ
ap-1257	6	4	variational	variational	ADJ
ap-1257	6	5	functions	function	NOUN
ap-1257	6	6	and	and	CCONJ
ap-1257	6	7	compare	compare	VERB
ap-1257	6	8	the	the	DET
ap-1257	6	9	approximate	approximate	ADJ
ap-1257	6	10	energies	energy	NOUN
ap-1257	6	11	given	give	VERB
ap-1257	6	12	by	by	ADP
ap-1257	6	13	the	the	DET
ap-1257	6	14	variation	variation	NOUN
ap-1257	6	15	method	method	NOUN
ap-1257	6	16	and	and	CCONJ
ap-1257	6	17	perturbation	perturbation	NOUN
ap-1257	6	18	theory	theory	NOUN
ap-1257	6	19	with	with	ADP
ap-1257	6	20	accurate	accurate	ADJ
ap-1257	6	21	numerical	numerical	ADJ
ap-1257	6	22	ones	one	NOUN
ap-1257	6	23	for	for	ADP
ap-1257	6	24	a	a	DET
ap-1257	6	25	wide	wide	ADJ
ap-1257	6	26	range	range	NOUN
ap-1257	6	27	of	of	ADP
ap-1257	6	28	values	value	NOUN
ap-1257	6	29	of	of	ADP
ap-1257	6	30	the	the	DET
ap-1257	6	31	box	box	NOUN
ap-1257	6	32	length	length	NOUN
ap-1257	6	33	.	.	PUNCT
ap-1257	7	1	we	we	PRON
ap-1257	7	2	analyze	analyze	VERB
ap-1257	7	3	the	the	DET
ap-1257	7	4	limits	limit	NOUN
ap-1257	7	5	of	of	ADP
ap-1257	7	6	small	small	ADJ
ap-1257	7	7	and	and	CCONJ
ap-1257	7	8	large	large	ADJ
ap-1257	7	9	box	box	NOUN
ap-1257	7	10	size	size	NOUN
ap-1257	7	11	.	.	PUNCT
ap-1257	8	1	keywords	keyword	NOUN
ap-1257	8	2	:	:	PUNCT
ap-1257	8	3	harmonic	harmonic	ADJ
ap-1257	8	4	oscillator	oscillator	NOUN
ap-1257	8	5	,	,	PUNCT
ap-1257	8	6	diatomic	diatomic	ADJ
ap-1257	8	7	molecule	molecule	NOUN
ap-1257	8	8	,	,	PUNCT
ap-1257	8	9	confined	confine	VERB
ap-1257	8	10	system	system	NOUN
ap-1257	8	11	,	,	PUNCT
ap-1257	8	12	one	one	NUM
ap-1257	8	13	-	-	PUNCT
ap-1257	8	14	dimensional	dimensional	ADJ
ap-1257	8	15	box	box	NOUN
ap-1257	8	16	,	,	PUNCT
ap-1257	8	17	point	point	NOUN
ap-1257	8	18	symmetry	symmetry	NOUN
ap-1257	8	19	,	,	PUNCT
ap-1257	8	20	avoided	avoid	VERB
ap-1257	8	21	crossings	crossing	NOUN
ap-1257	8	22	,	,	PUNCT
ap-1257	8	23	perturbation	perturbation	NOUN
ap-1257	8	24	theory	theory	NOUN
ap-1257	8	25	,	,	PUNCT
ap-1257	8	26	variational	variational	ADJ
ap-1257	8	27	method	method	NOUN
ap-1257	8	28	.	.	PUNCT
ap-1257	9	1	1	1	NUM
ap-1257	9	2	introduction	introduction	NOUN
ap-1257	9	3	during	during	ADP
ap-1257	9	4	the	the	DET
ap-1257	9	5	last	last	ADJ
ap-1257	9	6	decades	decade	NOUN
ap-1257	9	7	,	,	PUNCT
ap-1257	9	8	there	there	PRON
ap-1257	9	9	has	have	AUX
ap-1257	9	10	been	be	AUX
ap-1257	9	11	great	great	ADJ
ap-1257	9	12	interest	interest	NOUN
ap-1257	9	13	in	in	ADP
ap-1257	9	14	the	the	DET
ap-1257	9	15	model	model	NOUN
ap-1257	9	16	of	of	ADP
ap-1257	9	17	a	a	DET
ap-1257	9	18	harmonic	harmonic	ADJ
ap-1257	9	19	oscillator	oscillator	NOUN
ap-1257	9	20	confined	confine	VERB
ap-1257	9	21	to	to	ADP
ap-1257	9	22	boxes	box	NOUN
ap-1257	9	23	of	of	ADP
ap-1257	9	24	different	different	ADJ
ap-1257	9	25	shapes	shape	NOUN
ap-1257	9	26	and	and	CCONJ
ap-1257	9	27	sizes	size	NOUN
ap-1257	9	28	[	[	X
ap-1257	9	29	1	1	NUM
ap-1257	9	30	,	,	PUNCT
ap-1257	9	31	2	2	NUM
ap-1257	9	32	,	,	PUNCT
ap-1257	9	33	3	3	NUM
ap-1257	9	34	,	,	PUNCT
ap-1257	9	35	4	4	NUM
ap-1257	9	36	,	,	PUNCT
ap-1257	9	37	5	5	NUM
ap-1257	9	38	,	,	PUNCT
ap-1257	9	39	6	6	NUM
ap-1257	9	40	,	,	PUNCT
ap-1257	9	41	7	7	NUM
ap-1257	9	42	,	,	PUNCT
ap-1257	9	43	8	8	NUM
ap-1257	9	44	,	,	PUNCT
ap-1257	9	45	9	9	NUM
ap-1257	9	46	,	,	PUNCT
ap-1257	9	47	10	10	NUM
ap-1257	9	48	,	,	PUNCT
ap-1257	9	49	11	11	NUM
ap-1257	9	50	,	,	PUNCT
ap-1257	9	51	12	12	NUM
ap-1257	9	52	,	,	PUNCT
ap-1257	9	53	13	13	NUM
ap-1257	9	54	,	,	PUNCT
ap-1257	9	55	14	14	NUM
ap-1257	9	56	,	,	PUNCT
ap-1257	9	57	15	15	NUM
ap-1257	9	58	,	,	PUNCT
ap-1257	9	59	16	16	NUM
ap-1257	9	60	,	,	PUNCT
ap-1257	9	61	17	17	NUM
ap-1257	9	62	,	,	PUNCT
ap-1257	9	63	18	18	NUM
ap-1257	9	64	,	,	PUNCT
ap-1257	9	65	19	19	NUM
ap-1257	9	66	,	,	PUNCT
ap-1257	9	67	20	20	NUM
ap-1257	9	68	,	,	PUNCT
ap-1257	9	69	21	21	NUM
ap-1257	9	70	,	,	PUNCT
ap-1257	9	71	22	22	NUM
ap-1257	9	72	,	,	PUNCT
ap-1257	9	73	23	23	NUM
ap-1257	9	74	]	]	PUNCT
ap-1257	9	75	.	.	PUNCT
ap-1257	10	1	such	such	DET
ap-1257	10	2	a	a	DET
ap-1257	10	3	model	model	NOUN
ap-1257	10	4	has	have	AUX
ap-1257	10	5	been	be	AUX
ap-1257	10	6	suitable	suitable	ADJ
ap-1257	10	7	for	for	ADP
ap-1257	10	8	the	the	DET
ap-1257	10	9	study	study	NOUN
ap-1257	10	10	of	of	ADP
ap-1257	10	11	several	several	ADJ
ap-1257	10	12	physical	physical	ADJ
ap-1257	10	13	problems	problem	NOUN
ap-1257	10	14	,	,	PUNCT
ap-1257	10	15	ranging	range	VERB
ap-1257	10	16	from	from	ADP
ap-1257	10	17	dynamical	dynamical	ADJ
ap-1257	10	18	friction	friction	NOUN
ap-1257	10	19	in	in	ADP
ap-1257	10	20	star	star	NOUN
ap-1257	10	21	clusters	cluster	NOUN
ap-1257	10	22	[	[	X
ap-1257	10	23	4	4	X
ap-1257	10	24	]	]	PUNCT
ap-1257	10	25	to	to	ADP
ap-1257	10	26	magnetic	magnetic	ADJ
ap-1257	10	27	properties	property	NOUN
ap-1257	10	28	of	of	ADP
ap-1257	10	29	solids	solid	NOUN
ap-1257	10	30	[	[	X
ap-1257	10	31	6	6	NUM
ap-1257	10	32	]	]	PUNCT
ap-1257	10	33	and	and	CCONJ
ap-1257	10	34	impurities	impurity	NOUN
ap-1257	10	35	in	in	ADP
ap-1257	10	36	quantum	quantum	ADJ
ap-1257	10	37	dots	dot	NOUN
ap-1257	10	38	[	[	X
ap-1257	10	39	23	23	NUM
ap-1257	10	40	]	]	PUNCT
ap-1257	10	41	.	.	PUNCT
ap-1257	11	1	one	one	NUM
ap-1257	11	2	of	of	ADP
ap-1257	11	3	the	the	DET
ap-1257	11	4	most	most	ADV
ap-1257	11	5	widely	widely	ADV
ap-1257	11	6	studied	study	VERB
ap-1257	11	7	models	model	NOUN
ap-1257	11	8	is	be	AUX
ap-1257	11	9	given	give	VERB
ap-1257	11	10	by	by	ADP
ap-1257	11	11	a	a	DET
ap-1257	11	12	particle	particle	NOUN
ap-1257	11	13	confined	confine	VERB
ap-1257	11	14	to	to	ADP
ap-1257	11	15	a	a	DET
ap-1257	11	16	box	box	NOUN
ap-1257	11	17	with	with	ADP
ap-1257	11	18	impenetrable	impenetrable	ADJ
ap-1257	11	19	walls	wall	NOUN
ap-1257	11	20	at	at	ADP
ap-1257	11	21	−l/2	−l/2	PROPN
ap-1257	11	22	and	and	CCONJ
ap-1257	11	23	l/2	l/2	PROPN
ap-1257	11	24	bound	bind	VERB
ap-1257	11	25	by	by	ADP
ap-1257	11	26	a	a	DET
ap-1257	11	27	linear	linear	ADJ
ap-1257	11	28	force	force	NOUN
ap-1257	11	29	that	that	PRON
ap-1257	11	30	produces	produce	VERB
ap-1257	11	31	a	a	DET
ap-1257	11	32	parabolic	parabolic	ADJ
ap-1257	11	33	potential	potential	NOUN
ap-1257	11	34	–	–	PUNCT
ap-1257	11	35	energy	energy	NOUN
ap-1257	11	36	function	function	NOUN
ap-1257	11	37	v	v	NOUN
ap-1257	11	38	(	(	PUNCT
ap-1257	11	39	x	x	NOUN
ap-1257	11	40	)	)	PUNCT
ap-1257	11	41	=	=	SYM
ap-1257	11	42	k(x−x0)2/2	k(x−x0)2/2	PROPN
ap-1257	11	43	,	,	PUNCT
ap-1257	11	44	where	where	SCONJ
ap-1257	11	45	|x0|	|x0|	PROPN
ap-1257	11	46	<	<	X
ap-1257	11	47	l/2	l/2	PROPN
ap-1257	11	48	.	.	PUNCT
ap-1257	12	1	when	when	SCONJ
ap-1257	12	2	x0	x0	PROPN
ap-1257	13	1	=	=	NOUN
ap-1257	13	2	0	0	PUNCT
ap-1257	14	1	the	the	DET
ap-1257	14	2	problem	problem	NOUN
ap-1257	14	3	is	be	AUX
ap-1257	14	4	symmetric	symmetric	ADJ
ap-1257	14	5	and	and	CCONJ
ap-1257	14	6	the	the	DET
ap-1257	14	7	eigenfunctions	eigenfunction	NOUN
ap-1257	14	8	are	be	AUX
ap-1257	14	9	either	either	CCONJ
ap-1257	14	10	even	even	ADV
ap-1257	14	11	or	or	CCONJ
ap-1257	14	12	odd	odd	ADJ
ap-1257	14	13	;	;	PUNCT
ap-1257	14	14	such	such	ADJ
ap-1257	14	15	symmetry	symmetry	NOUN
ap-1257	14	16	is	be	AUX
ap-1257	14	17	broken	break	VERB
ap-1257	15	1	when	when	SCONJ
ap-1257	15	2	x0	x0	PROPN
ap-1257	15	3	=	=	PUNCT
ap-1257	15	4	0	0	X
ap-1257	15	5	.	.	PUNCT
ap-1257	16	1	although	although	SCONJ
ap-1257	16	2	interesting	interesting	ADJ
ap-1257	16	3	in	in	ADP
ap-1257	16	4	itself	itself	PRON
ap-1257	16	5	,	,	PUNCT
ap-1257	16	6	this	this	DET
ap-1257	16	7	model	model	NOUN
ap-1257	16	8	is	be	AUX
ap-1257	16	9	rather	rather	ADV
ap-1257	16	10	artificial	artificial	ADJ
ap-1257	16	11	because	because	SCONJ
ap-1257	16	12	the	the	DET
ap-1257	16	13	cause	cause	NOUN
ap-1257	16	14	of	of	ADP
ap-1257	16	15	the	the	DET
ap-1257	16	16	force	force	NOUN
ap-1257	16	17	is	be	AUX
ap-1257	16	18	not	not	PART
ap-1257	16	19	specified	specify	VERB
ap-1257	16	20	.	.	PUNCT
ap-1257	17	1	it	it	PRON
ap-1257	17	2	may	may	AUX
ap-1257	17	3	,	,	PUNCT
ap-1257	17	4	for	for	ADP
ap-1257	17	5	example	example	NOUN
ap-1257	17	6	,	,	PUNCT
ap-1257	17	7	arise	arise	VERB
ap-1257	17	8	from	from	ADP
ap-1257	17	9	an	an	DET
ap-1257	17	10	infinitely	infinitely	ADV
ap-1257	17	11	heavy	heavy	ADJ
ap-1257	17	12	particle	particle	NOUN
ap-1257	17	13	clamped	clamp	VERB
ap-1257	17	14	at	at	ADP
ap-1257	17	15	x0	x0	PROPN
ap-1257	17	16	.	.	PUNCT
ap-1257	18	1	in	in	ADP
ap-1257	18	2	such	such	DET
ap-1257	18	3	a	a	DET
ap-1257	18	4	case	case	NOUN
ap-1257	18	5	we	we	PRON
ap-1257	18	6	think	think	VERB
ap-1257	18	7	that	that	SCONJ
ap-1257	18	8	it	it	PRON
ap-1257	18	9	is	be	AUX
ap-1257	18	10	more	more	ADV
ap-1257	18	11	interesting	interesting	ADJ
ap-1257	18	12	to	to	PART
ap-1257	18	13	consider	consider	VERB
ap-1257	18	14	that	that	SCONJ
ap-1257	18	15	the	the	DET
ap-1257	18	16	other	other	ADJ
ap-1257	18	17	particle	particle	NOUN
ap-1257	18	18	also	also	ADV
ap-1257	18	19	moves	move	VERB
ap-1257	18	20	within	within	ADP
ap-1257	18	21	the	the	DET
ap-1257	18	22	box	box	NOUN
ap-1257	18	23	.	.	PUNCT
ap-1257	19	1	the	the	DET
ap-1257	19	2	purpose	purpose	NOUN
ap-1257	19	3	of	of	ADP
ap-1257	19	4	this	this	DET
ap-1257	19	5	paper	paper	NOUN
ap-1257	19	6	is	be	AUX
ap-1257	19	7	to	to	PART
ap-1257	19	8	discuss	discuss	VERB
ap-1257	19	9	the	the	DET
ap-1257	19	10	model	model	NOUN
ap-1257	19	11	of	of	ADP
ap-1257	19	12	two	two	NUM
ap-1257	19	13	particles	particle	NOUN
ap-1257	19	14	confined	confine	VERB
ap-1257	19	15	to	to	ADP
ap-1257	19	16	a	a	DET
ap-1257	19	17	one	one	NUM
ap-1257	19	18	-	-	PUNCT
ap-1257	19	19	dimensional	dimensional	ADJ
ap-1257	19	20	box	box	NOUN
ap-1257	19	21	with	with	ADP
ap-1257	19	22	impenetrable	impenetrable	ADJ
ap-1257	19	23	walls	wall	NOUN
ap-1257	19	24	.	.	PUNCT
ap-1257	20	1	for	for	ADP
ap-1257	20	2	simplicity	simplicity	NOUN
ap-1257	20	3	we	we	PRON
ap-1257	20	4	assume	assume	VERB
ap-1257	20	5	that	that	SCONJ
ap-1257	20	6	the	the	DET
ap-1257	20	7	force	force	NOUN
ap-1257	20	8	between	between	ADP
ap-1257	20	9	them	they	PRON
ap-1257	20	10	is	be	AUX
ap-1257	20	11	linear	linear	ADJ
ap-1257	20	12	.	.	PUNCT
ap-1257	21	1	in	in	ADP
ap-1257	21	2	sec	sec	PROPN
ap-1257	21	3	.	.	PROPN
ap-1257	21	4	2	2	NUM
ap-1257	21	5	we	we	PRON
ap-1257	21	6	introduce	introduce	VERB
ap-1257	21	7	the	the	DET
ap-1257	21	8	model	model	NOUN
ap-1257	21	9	and	and	CCONJ
ap-1257	21	10	discuss	discuss	VERB
ap-1257	21	11	some	some	PRON
ap-1257	21	12	of	of	ADP
ap-1257	21	13	its	its	PRON
ap-1257	21	14	general	general	ADJ
ap-1257	21	15	mathematical	mathematical	ADJ
ap-1257	21	16	properties	property	NOUN
ap-1257	21	17	.	.	PUNCT
ap-1257	22	1	in	in	ADP
ap-1257	22	2	sec	sec	PROPN
ap-1257	22	3	.	.	PROPN
ap-1257	22	4	3	3	NUM
ap-1257	22	5	we	we	PRON
ap-1257	22	6	discuss	discuss	VERB
ap-1257	22	7	the	the	DET
ap-1257	22	8	solutions	solution	NOUN
ap-1257	22	9	of	of	ADP
ap-1257	22	10	the	the	DET
ap-1257	22	11	schrödinger	schrödinger	NOUN
ap-1257	22	12	equation	equation	NOUN
ap-1257	22	13	for	for	ADP
ap-1257	22	14	small	small	ADJ
ap-1257	22	15	box	box	NOUN
ap-1257	22	16	lengths	length	NOUN
ap-1257	22	17	by	by	ADP
ap-1257	22	18	means	mean	NOUN
ap-1257	22	19	of	of	ADP
ap-1257	22	20	perturbation	perturbation	NOUN
ap-1257	22	21	theory	theory	NOUN
ap-1257	22	22	.	.	PUNCT
ap-1257	23	1	in	in	ADP
ap-1257	23	2	sec	sec	PROPN
ap-1257	23	3	.	.	PROPN
ap-1257	23	4	4	4	NUM
ap-1257	23	5	we	we	PRON
ap-1257	23	6	consider	consider	VERB
ap-1257	23	7	the	the	DET
ap-1257	23	8	regime	regime	NOUN
ap-1257	23	9	of	of	ADP
ap-1257	23	10	large	large	ADJ
ap-1257	23	11	boxes	box	NOUN
ap-1257	23	12	and	and	CCONJ
ap-1257	23	13	propose	propose	VERB
ap-1257	23	14	suitable	suitable	ADJ
ap-1257	23	15	variational	variational	ADJ
ap-1257	23	16	functions	function	NOUN
ap-1257	23	17	.	.	PUNCT
ap-1257	24	1	in	in	ADP
ap-1257	24	2	sec	sec	PROPN
ap-1257	24	3	.	.	PROPN
ap-1257	24	4	5	5	NUM
ap-1257	24	5	we	we	PRON
ap-1257	24	6	compare	compare	VERB
ap-1257	24	7	the	the	DET
ap-1257	24	8	approximate	approximate	ADJ
ap-1257	24	9	energies	energy	NOUN
ap-1257	24	10	provided	provide	VERB
ap-1257	24	11	by	by	ADP
ap-1257	24	12	perturbation	perturbation	NOUN
ap-1257	24	13	theory	theory	NOUN
ap-1257	24	14	and	and	CCONJ
ap-1257	24	15	the	the	DET
ap-1257	24	16	variational	variational	ADJ
ap-1257	24	17	method	method	NOUN
ap-1257	24	18	with	with	ADP
ap-1257	24	19	accurate	accurate	ADJ
ap-1257	24	20	numerical	numerical	ADJ
ap-1257	24	21	methods	method	NOUN
ap-1257	24	22	.	.	PUNCT
ap-1257	25	1	finally	finally	ADV
ap-1257	25	2	,	,	PUNCT
ap-1257	25	3	in	in	ADP
ap-1257	25	4	sec	sec	PROPN
ap-1257	25	5	.	.	PROPN
ap-1257	25	6	6	6	NUM
ap-1257	25	7	we	we	PRON
ap-1257	25	8	summarize	summarize	VERB
ap-1257	25	9	the	the	DET
ap-1257	25	10	main	main	ADJ
ap-1257	25	11	results	result	NOUN
ap-1257	25	12	and	and	CCONJ
ap-1257	25	13	draw	draw	VERB
ap-1257	25	14	additional	additional	ADJ
ap-1257	25	15	conclusions	conclusion	NOUN
ap-1257	25	16	.	.	PUNCT
ap-1257	26	1	2	2	NUM
ap-1257	26	2	the	the	DET
ap-1257	26	3	model	model	NOUN
ap-1257	26	4	as	as	SCONJ
ap-1257	26	5	mentioned	mention	VERB
ap-1257	26	6	above	above	ADV
ap-1257	26	7	,	,	PUNCT
ap-1257	26	8	we	we	PRON
ap-1257	26	9	are	be	AUX
ap-1257	26	10	interested	interested	ADJ
ap-1257	26	11	in	in	ADP
ap-1257	26	12	a	a	DET
ap-1257	26	13	system	system	NOUN
ap-1257	26	14	of	of	ADP
ap-1257	26	15	two	two	NUM
ap-1257	26	16	particles	particle	NOUN
ap-1257	26	17	of	of	ADP
ap-1257	26	18	masses	masse	NOUN
ap-1257	26	19	m1	m1	PROPN
ap-1257	26	20	and	and	CCONJ
ap-1257	26	21	m2	m2	PROPN
ap-1257	26	22	confined	confine	VERB
ap-1257	26	23	to	to	ADP
ap-1257	26	24	a	a	DET
ap-1257	26	25	onedimensional	onedimensional	ADJ
ap-1257	26	26	box	box	NOUN
ap-1257	26	27	with	with	ADP
ap-1257	26	28	impenetrable	impenetrable	ADJ
ap-1257	26	29	walls	wall	NOUN
ap-1257	26	30	located	locate	VERB
ap-1257	26	31	at	at	ADP
ap-1257	26	32	x	x	X
ap-1257	27	1	=	=	PUNCT
ap-1257	27	2	−l/2	−l/2	PROPN
ap-1257	27	3	and	and	CCONJ
ap-1257	27	4	x	x	X
ap-1257	27	5	=	=	PUNCT
ap-1257	27	6	l/2	l/2	PROPN
ap-1257	27	7	.	.	PUNCT
ap-1257	28	1	if	if	SCONJ
ap-1257	28	2	we	we	PRON
ap-1257	28	3	assume	assume	VERB
ap-1257	28	4	a	a	DET
ap-1257	28	5	linear	linear	ADJ
ap-1257	28	6	force	force	NOUN
ap-1257	28	7	between	between	ADP
ap-1257	28	8	the	the	DET
ap-1257	28	9	particles	particle	NOUN
ap-1257	28	10	then	then	ADV
ap-1257	28	11	the	the	DET
ap-1257	28	12	hamiltonian	hamiltonian	ADJ
ap-1257	28	13	operator	operator	NOUN
ap-1257	28	14	reads	read	VERB
ap-1257	28	15	ĥ	ĥ	X
ap-1257	28	16	=	=	SYM
ap-1257	28	17	−	−	PROPN
ap-1257	28	18	h̄2	h̄2	X
ap-1257	28	19	2	2	NUM
ap-1257	28	20	(	(	PUNCT
ap-1257	28	21	1	1	NUM
ap-1257	28	22	m1	m1	PROPN
ap-1257	28	23	∂2	∂2	PROPN
ap-1257	28	24	∂x21	∂x21	PROPN
ap-1257	28	25	+	+	CCONJ
ap-1257	28	26	1	1	NUM
ap-1257	28	27	m2	m2	PROPN
ap-1257	28	28	∂2	∂2	PROPN
ap-1257	28	29	∂x22	∂x22	PROPN
ap-1257	28	30	)	)	PUNCT
ap-1257	29	1	+	+	CCONJ
ap-1257	29	2	k	k	SYM
ap-1257	29	3	2	2	NUM
ap-1257	29	4	(	(	PUNCT
ap-1257	29	5	x1	x1	PROPN
ap-1257	29	6	−	−	PROPN
ap-1257	29	7	x2)2	x2)2	X
ap-1257	29	8	(	(	PUNCT
ap-1257	29	9	1	1	NUM
ap-1257	29	10	)	)	PUNCT
ap-1257	29	11	and	and	CCONJ
ap-1257	29	12	the	the	DET
ap-1257	29	13	boundary	boundary	ADJ
ap-1257	29	14	conditions	condition	NOUN
ap-1257	29	15	are	be	AUX
ap-1257	29	16	ψ	ψ	X
ap-1257	29	17	=	=	X
ap-1257	29	18	0	0	PROPN
ap-1257	29	19	when	when	SCONJ
ap-1257	29	20	xi	xi	X
ap-1257	29	21	=	=	SYM
ap-1257	29	22	±l/2	±l/2	PROPN
ap-1257	29	23	.	.	PUNCT
ap-1257	30	1	it	it	PRON
ap-1257	30	2	is	be	AUX
ap-1257	30	3	convenient	convenient	ADJ
ap-1257	30	4	to	to	PART
ap-1257	30	5	convert	convert	VERB
ap-1257	30	6	it	it	PRON
ap-1257	30	7	to	to	ADP
ap-1257	30	8	a	a	DET
ap-1257	30	9	dimensionless	dimensionless	NOUN
ap-1257	30	10	form	form	NOUN
ap-1257	30	11	by	by	ADP
ap-1257	30	12	means	mean	NOUN
ap-1257	30	13	of	of	ADP
ap-1257	30	14	the	the	DET
ap-1257	30	15	variable	variable	ADJ
ap-1257	30	16	transformation	transformation	NOUN
ap-1257	30	17	qi	qi	PROPN
ap-1257	30	18	=	=	SYM
ap-1257	30	19	xi	xi	PROPN
ap-1257	30	20	/	/	SYM
ap-1257	30	21	l	l	NOUN
ap-1257	30	22	that	that	PRON
ap-1257	30	23	leads	lead	VERB
ap-1257	30	24	to	to	ADP
ap-1257	30	25	:	:	PUNCT
ap-1257	30	26	ĥd	ĥd	X
ap-1257	30	27	=	=	PUNCT
ap-1257	30	28	m1l	m1l	ADJ
ap-1257	30	29	2	2	NUM
ap-1257	30	30	h̄2	h̄2	NOUN
ap-1257	30	31	ĥ	ĥ	X
ap-1257	30	32	=	=	SYM
ap-1257	30	33	−1	−1	NOUN
ap-1257	30	34	2	2	NUM
ap-1257	30	35	(	(	PUNCT
ap-1257	30	36	∂2	∂2	PROPN
ap-1257	30	37	∂q21	∂q21	NOUN
ap-1257	30	38	+	+	CCONJ
ap-1257	30	39	β	β	X
ap-1257	30	40	∂2	∂2	PROPN
ap-1257	30	41	∂q22	∂q22	NOUN
ap-1257	30	42	)	)	PUNCT
ap-1257	31	1	+	+	CCONJ
ap-1257	31	2	λ	λ	X
ap-1257	31	3	2	2	NUM
ap-1257	31	4	(	(	PUNCT
ap-1257	31	5	q1	q1	NOUN
ap-1257	31	6	−	−	PROPN
ap-1257	31	7	q2	q2	NOUN
ap-1257	31	8	)	)	PUNCT
ap-1257	31	9	2	2	NUM
ap-1257	31	10	(	(	PUNCT
ap-1257	31	11	2	2	NUM
ap-1257	31	12	)	)	PUNCT
ap-1257	31	13	where	where	SCONJ
ap-1257	31	14	β	β	X
ap-1257	31	15	=	=	SYM
ap-1257	31	16	m1	m1	PROPN
ap-1257	31	17	/	/	SYM
ap-1257	31	18	m2	m2	PROPN
ap-1257	31	19	,	,	PUNCT
ap-1257	31	20	λ	λ	X
ap-1257	31	21	=	=	SYM
ap-1257	31	22	km1l	km1l	PROPN
ap-1257	31	23	4	4	NUM
ap-1257	31	24	/	/	SYM
ap-1257	31	25	h̄2	h̄2	NOUN
ap-1257	31	26	and	and	CCONJ
ap-1257	31	27	the	the	DET
ap-1257	31	28	boundary	boundary	ADJ
ap-1257	31	29	conditions	condition	NOUN
ap-1257	31	30	become	become	VERB
ap-1257	31	31	ψ	ψ	NOUN
ap-1257	31	32	=	=	SYM
ap-1257	31	33	0	0	PUNCT
ap-1257	31	34	if	if	SCONJ
ap-1257	31	35	qi	qi	NOUN
ap-1257	31	36	=	=	NOUN
ap-1257	31	37	±1/2	±1/2	PROPN
ap-1257	31	38	.	.	PUNCT
ap-1257	32	1	without	without	ADP
ap-1257	32	2	loss	loss	NOUN
ap-1257	32	3	of	of	ADP
ap-1257	32	4	generality	generality	NOUN
ap-1257	32	5	we	we	PRON
ap-1257	32	6	assume	assume	VERB
ap-1257	32	7	that	that	SCONJ
ap-1257	32	8	0	0	PUNCT
ap-1257	32	9	<	<	X
ap-1257	32	10	β	β	X
ap-1257	32	11	≤	≤	NUM
ap-1257	32	12	1	1	NUM
ap-1257	32	13	.	.	PUNCT
ap-1257	33	1	the	the	DET
ap-1257	33	2	free	free	ADJ
ap-1257	33	3	problem	problem	NOUN
ap-1257	33	4	(	(	PUNCT
ap-1257	33	5	−∞	−∞	X
ap-1257	33	6	<	<	X
ap-1257	33	7	xi	xi	ADP
ap-1257	33	8	<	<	X
ap-1257	33	9	∞	∞	PROPN
ap-1257	33	10	)	)	PUNCT
ap-1257	33	11	is	be	AUX
ap-1257	33	12	separable	separable	ADJ
ap-1257	33	13	in	in	ADP
ap-1257	33	14	terms	term	NOUN
ap-1257	33	15	of	of	ADP
ap-1257	33	16	relative	relative	ADJ
ap-1257	33	17	and	and	CCONJ
ap-1257	33	18	center	center	NOUN
ap-1257	33	19	-	-	PUNCT
ap-1257	33	20	of	of	ADP
ap-1257	33	21	-	-	PUNCT
ap-1257	33	22	mass	mass	NOUN
ap-1257	33	23	variables	variable	NOUN
ap-1257	33	24	x	x	PUNCT
ap-1257	34	1	=	=	SYM
ap-1257	34	2	x1	x1	NUM
ap-1257	34	3	−	−	NUM
ap-1257	35	1	x2	x2	NOUN
ap-1257	35	2	x	x	SYM
ap-1257	35	3	=	=	SYM
ap-1257	35	4	1	1	NUM
ap-1257	35	5	m	m	VERB
ap-1257	35	6	(	(	PUNCT
ap-1257	35	7	m1x1	m1x1	X
ap-1257	35	8	+	+	ADJ
ap-1257	35	9	m2x2	m2x2	NOUN
ap-1257	35	10	)	)	PUNCT
ap-1257	35	11	,	,	PUNCT
ap-1257	35	12	m	m	VERB
ap-1257	35	13	=	=	PUNCT
ap-1257	35	14	m1	m1	PROPN
ap-1257	36	1	+	+	PROPN
ap-1257	36	2	m2	m2	PROPN
ap-1257	36	3	(	(	PUNCT
ap-1257	36	4	3	3	NUM
ap-1257	36	5	)	)	PUNCT
ap-1257	36	6	17	17	NUM
ap-1257	36	7	acta	acta	PROPN
ap-1257	36	8	polytechnica	polytechnica	PROPN
ap-1257	36	9	vol	vol	NOUN
ap-1257	36	10	.	.	PROPN
ap-1257	37	1	50	50	NUM
ap-1257	37	2	no	no	NOUN
ap-1257	37	3	.	.	PUNCT
ap-1257	38	1	5/2010	5/2010	NUM
ap-1257	38	2	respectively	respectively	ADV
ap-1257	38	3	,	,	PUNCT
ap-1257	38	4	that	that	PRON
ap-1257	38	5	lead	lead	VERB
ap-1257	38	6	to	to	ADP
ap-1257	38	7	ĥ	ĥ	PROPN
ap-1257	38	8	=	=	SYM
ap-1257	38	9	−	−	PROPN
ap-1257	38	10	h̄2	h̄2	X
ap-1257	38	11	2	2	NUM
ap-1257	38	12	(	(	PUNCT
ap-1257	38	13	1	1	NUM
ap-1257	38	14	m	m	PROPN
ap-1257	38	15	∂2	∂2	NOUN
ap-1257	38	16	∂x2	∂x2	NOUN
ap-1257	38	17	+	+	NOUN
ap-1257	38	18	1	1	NUM
ap-1257	38	19	m	m	NOUN
ap-1257	38	20	∂2	∂2	ADJ
ap-1257	38	21	∂x2	∂x2	NOUN
ap-1257	38	22	)	)	PUNCT
ap-1257	39	1	+	+	CCONJ
ap-1257	39	2	v	v	X
ap-1257	39	3	(	(	PUNCT
ap-1257	39	4	x	x	NOUN
ap-1257	39	5	)	)	PUNCT
ap-1257	39	6	,	,	PUNCT
ap-1257	39	7	m	m	VERB
ap-1257	39	8	=	=	SYM
ap-1257	39	9	m1m2	m1m2	X
ap-1257	39	10	m	m	NOUN
ap-1257	39	11	.	.	PUNCT
ap-1257	40	1	(	(	PUNCT
ap-1257	40	2	4	4	X
ap-1257	40	3	)	)	PUNCT
ap-1257	40	4	in	in	ADP
ap-1257	40	5	this	this	DET
ap-1257	40	6	case	case	NOUN
ap-1257	40	7	we	we	PRON
ap-1257	40	8	can	can	AUX
ap-1257	40	9	factor	factor	VERB
ap-1257	40	10	the	the	DET
ap-1257	40	11	eigenfunctions	eigenfunction	NOUN
ap-1257	40	12	as	as	ADP
ap-1257	40	13	ψkv(x1	ψkv(x1	PROPN
ap-1257	40	14	,	,	PUNCT
ap-1257	40	15	x2	x2	PROPN
ap-1257	40	16	)	)	PUNCT
ap-1257	40	17	=	=	SYM
ap-1257	40	18	eikxφv(x	eikxφv(x	X
ap-1257	40	19	)	)	PUNCT
ap-1257	41	1	−∞	−∞	ADP
ap-1257	41	2	<	<	X
ap-1257	41	3	k	k	X
ap-1257	41	4	<	<	X
ap-1257	41	5	∞	∞	PROPN
ap-1257	41	6	,	,	PUNCT
ap-1257	41	7	v	v	NOUN
ap-1257	41	8	=	=	SYM
ap-1257	41	9	0	0	NUM
ap-1257	41	10	,	,	PUNCT
ap-1257	41	11	1	1	NUM
ap-1257	41	12	,	,	PUNCT
ap-1257	41	13	.	.	PUNCT
ap-1257	41	14	.	.	PUNCT
ap-1257	41	15	.	.	PUNCT
ap-1257	42	1	(	(	PUNCT
ap-1257	42	2	5	5	X
ap-1257	42	3	)	)	PUNCT
ap-1257	42	4	where	where	SCONJ
ap-1257	42	5	φv(x	φv(x	NUM
ap-1257	42	6	)	)	PUNCT
ap-1257	42	7	are	be	AUX
ap-1257	42	8	the	the	DET
ap-1257	42	9	well	well	ADV
ap-1257	42	10	–	–	PUNCT
ap-1257	42	11	known	know	VERB
ap-1257	42	12	eigenfunctions	eigenfunction	NOUN
ap-1257	42	13	of	of	ADP
ap-1257	42	14	the	the	DET
ap-1257	42	15	harmonic	harmonic	ADJ
ap-1257	42	16	oscillator	oscillator	NOUN
ap-1257	42	17	,	,	PUNCT
ap-1257	42	18	and	and	CCONJ
ap-1257	42	19	the	the	DET
ap-1257	42	20	eigenvalues	eigenvalue	NOUN
ap-1257	42	21	read	read	VERB
ap-1257	42	22	ekv	ekv	PROPN
ap-1257	42	23	=	=	PROPN
ap-1257	42	24	h̄2k2	h̄2k2	PROPN
ap-1257	42	25	2	2	NUM
ap-1257	42	26	m	m	NOUN
ap-1257	42	27	+	+	NUM
ap-1257	42	28	h̄	h̄	NUM
ap-1257	43	1	√	√	INTJ
ap-1257	43	2	k	k	NOUN
ap-1257	43	3	m	m	VERB
ap-1257	43	4	(	(	PUNCT
ap-1257	43	5	v	v	X
ap-1257	43	6	+	+	CCONJ
ap-1257	43	7	1	1	NUM
ap-1257	43	8	2	2	NUM
ap-1257	43	9	)	)	PUNCT
ap-1257	43	10	.	.	PUNCT
ap-1257	44	1	(	(	PUNCT
ap-1257	44	2	6	6	NUM
ap-1257	44	3	)	)	PUNCT
ap-1257	44	4	however	however	ADV
ap-1257	44	5	,	,	PUNCT
ap-1257	44	6	because	because	SCONJ
ap-1257	44	7	of	of	ADP
ap-1257	44	8	the	the	DET
ap-1257	44	9	boundary	boundary	ADJ
ap-1257	44	10	conditions	condition	NOUN
ap-1257	44	11	,	,	PUNCT
ap-1257	44	12	any	any	DET
ap-1257	44	13	eigenfunction	eigenfunction	NOUN
ap-1257	44	14	is	be	AUX
ap-1257	44	15	of	of	ADP
ap-1257	44	16	the	the	DET
ap-1257	44	17	form	form	NOUN
ap-1257	44	18	ψ(x1	ψ(x1	NOUN
ap-1257	44	19	,	,	PUNCT
ap-1257	44	20	x2	x2	PROPN
ap-1257	44	21	)	)	PUNCT
ap-1257	44	22	=	=	SYM
ap-1257	45	1	(	(	PUNCT
ap-1257	45	2	l	l	NOUN
ap-1257	45	3	2/4	2/4	NUM
ap-1257	45	4	−	−	PROPN
ap-1257	45	5	x21	x21	PROPN
ap-1257	45	6	)	)	PUNCT
ap-1257	45	7	(	(	PUNCT
ap-1257	45	8	l2/4	l2/4	X
ap-1257	45	9	−	−	PROPN
ap-1257	45	10	x22)φ(x1	x22)φ(x1	PROPN
ap-1257	45	11	,	,	PUNCT
ap-1257	45	12	x2	x2	PROPN
ap-1257	45	13	)	)	PUNCT
ap-1257	45	14	,	,	PUNCT
ap-1257	45	15	where	where	SCONJ
ap-1257	45	16	φ(x1	φ(x1	NOUN
ap-1257	45	17	,	,	PUNCT
ap-1257	45	18	x2	x2	PROPN
ap-1257	45	19	)	)	PUNCT
ap-1257	45	20	does	do	AUX
ap-1257	45	21	not	not	PART
ap-1257	45	22	vanish	vanish	VERB
ap-1257	45	23	at	at	ADP
ap-1257	45	24	the	the	DET
ap-1257	45	25	walls	wall	NOUN
ap-1257	45	26	.	.	PUNCT
ap-1257	46	1	we	we	PRON
ap-1257	46	2	clearly	clearly	ADV
ap-1257	46	3	appreciate	appreciate	VERB
ap-1257	46	4	that	that	SCONJ
ap-1257	46	5	the	the	DET
ap-1257	46	6	separation	separation	NOUN
ap-1257	46	7	just	just	ADV
ap-1257	46	8	outlined	outline	VERB
ap-1257	46	9	is	be	AUX
ap-1257	46	10	not	not	PART
ap-1257	46	11	possible	possible	ADJ
ap-1257	46	12	in	in	ADP
ap-1257	46	13	the	the	DET
ap-1257	46	14	confined	confine	VERB
ap-1257	46	15	model	model	NOUN
ap-1257	46	16	.	.	PUNCT
ap-1257	47	1	when	when	SCONJ
ap-1257	47	2	β	β	X
ap-1257	47	3	<	<	X
ap-1257	47	4	1	1	NUM
ap-1257	47	5	the	the	DET
ap-1257	47	6	transformations	transformation	NOUN
ap-1257	47	7	that	that	PRON
ap-1257	47	8	leave	leave	VERB
ap-1257	47	9	the	the	DET
ap-1257	47	10	hamiltonian	hamiltonian	ADJ
ap-1257	47	11	operator	operator	NOUN
ap-1257	47	12	(	(	PUNCT
ap-1257	47	13	including	include	VERB
ap-1257	47	14	the	the	DET
ap-1257	47	15	boundary	boundary	ADJ
ap-1257	47	16	conditions	condition	NOUN
ap-1257	47	17	)	)	PUNCT
ap-1257	47	18	invariant	invariant	PROPN
ap-1257	47	19	are	be	AUX
ap-1257	47	20	:	:	PUNCT
ap-1257	47	21	identity	identity	NOUN
ap-1257	47	22	ê	ê	PROPN
ap-1257	47	23	:	:	PUNCT
ap-1257	47	24	(	(	PUNCT
ap-1257	47	25	q1	q1	X
ap-1257	47	26	,	,	PUNCT
ap-1257	47	27	q2	q2	NOUN
ap-1257	47	28	)	)	PUNCT
ap-1257	47	29	→	→	SYM
ap-1257	47	30	(	(	PUNCT
ap-1257	47	31	q1	q1	PROPN
ap-1257	47	32	,	,	PUNCT
ap-1257	47	33	q2	q2	NOUN
ap-1257	47	34	)	)	PUNCT
ap-1257	47	35	and	and	CCONJ
ap-1257	47	36	inversion	inversion	NOUN
ap-1257	47	37	ı̂	ı̂	PUNCT
ap-1257	47	38	:	:	PUNCT
ap-1257	47	39	(	(	PUNCT
ap-1257	47	40	q1	q1	X
ap-1257	47	41	,	,	PUNCT
ap-1257	47	42	q2	q2	NOUN
ap-1257	47	43	)	)	PUNCT
ap-1257	47	44	→	→	SYM
ap-1257	47	45	(	(	PUNCT
ap-1257	47	46	−q1	−q1	PROPN
ap-1257	47	47	,	,	PUNCT
ap-1257	47	48	−q2	−q2	PROPN
ap-1257	47	49	)	)	PUNCT
ap-1257	47	50	.	.	PUNCT
ap-1257	48	1	therefore	therefore	ADV
ap-1257	48	2	,	,	PUNCT
ap-1257	48	3	the	the	DET
ap-1257	48	4	eigenfunctions	eigenfunction	NOUN
ap-1257	48	5	of	of	ADP
ap-1257	48	6	ĥd	ĥd	X
ap-1257	48	7	are	be	AUX
ap-1257	48	8	the	the	DET
ap-1257	48	9	basis	basis	NOUN
ap-1257	48	10	for	for	ADP
ap-1257	48	11	the	the	DET
ap-1257	48	12	irreducible	irreducible	ADJ
ap-1257	48	13	representations	representation	NOUN
ap-1257	48	14	ag	ag	PROPN
ap-1257	48	15	and	and	CCONJ
ap-1257	48	16	au	au	ADV
ap-1257	48	17	of	of	ADP
ap-1257	48	18	the	the	DET
ap-1257	48	19	point	point	NOUN
ap-1257	48	20	group	group	NOUN
ap-1257	48	21	s2	s2	NOUN
ap-1257	48	22	[	[	X
ap-1257	48	23	24	24	NUM
ap-1257	48	24	]	]	PUNCT
ap-1257	48	25	(	(	PUNCT
ap-1257	48	26	also	also	ADV
ap-1257	48	27	called	call	VERB
ap-1257	48	28	ci	ci	NOUN
ap-1257	48	29	by	by	ADP
ap-1257	48	30	other	other	ADJ
ap-1257	48	31	authors	author	NOUN
ap-1257	48	32	)	)	PUNCT
ap-1257	48	33	.	.	PUNCT
ap-1257	49	1	on	on	ADP
ap-1257	49	2	the	the	DET
ap-1257	49	3	other	other	ADJ
ap-1257	49	4	hand	hand	NOUN
ap-1257	49	5	,	,	PUNCT
ap-1257	49	6	when	when	SCONJ
ap-1257	49	7	β	β	X
ap-1257	49	8	=	=	SYM
ap-1257	49	9	1	1	NUM
ap-1257	49	10	(	(	PUNCT
ap-1257	49	11	equal	equal	ADJ
ap-1257	49	12	masses	masse	NOUN
ap-1257	49	13	)	)	PUNCT
ap-1257	49	14	the	the	DET
ap-1257	49	15	problem	problem	NOUN
ap-1257	49	16	exhibits	exhibit	VERB
ap-1257	49	17	the	the	DET
ap-1257	49	18	highest	high	ADJ
ap-1257	49	19	possible	possible	ADJ
ap-1257	49	20	symmetry	symmetry	NOUN
ap-1257	49	21	.	.	PUNCT
ap-1257	50	1	the	the	DET
ap-1257	50	2	transformations	transformation	NOUN
ap-1257	50	3	that	that	PRON
ap-1257	50	4	leave	leave	VERB
ap-1257	50	5	the	the	DET
ap-1257	50	6	hamiltonian	hamiltonian	ADJ
ap-1257	50	7	operator	operator	NOUN
ap-1257	50	8	(	(	PUNCT
ap-1257	50	9	including	include	VERB
ap-1257	50	10	the	the	DET
ap-1257	50	11	boundary	boundary	ADJ
ap-1257	50	12	conditions	condition	NOUN
ap-1257	50	13	)	)	PUNCT
ap-1257	50	14	invariant	invariant	PROPN
ap-1257	50	15	are	be	AUX
ap-1257	50	16	:	:	PUNCT
ap-1257	50	17	identity	identity	NOUN
ap-1257	50	18	ê	ê	PROPN
ap-1257	50	19	:	:	PUNCT
ap-1257	50	20	(	(	PUNCT
ap-1257	50	21	q1	q1	PROPN
ap-1257	50	22	,	,	PUNCT
ap-1257	50	23	q2)→	q2)→	PART
ap-1257	50	24	(	(	PUNCT
ap-1257	50	25	q1	q1	PROPN
ap-1257	50	26	,	,	PUNCT
ap-1257	50	27	q2	q2	NOUN
ap-1257	50	28	)	)	PUNCT
ap-1257	50	29	,	,	PUNCT
ap-1257	50	30	rotation	rotation	NOUN
ap-1257	50	31	by	by	ADP
ap-1257	50	32	π	π	PROPN
ap-1257	50	33	c2	c2	PROPN
ap-1257	50	34	:	:	PUNCT
ap-1257	50	35	(	(	PUNCT
ap-1257	50	36	q1	q1	PROPN
ap-1257	50	37	,	,	PUNCT
ap-1257	50	38	q2)→	q2)→	PART
ap-1257	50	39	(	(	PUNCT
ap-1257	50	40	q2	q2	NOUN
ap-1257	50	41	,	,	PUNCT
ap-1257	50	42	q1	q1	PROPN
ap-1257	50	43	)	)	PUNCT
ap-1257	50	44	,	,	PUNCT
ap-1257	50	45	inversion	inversion	NOUN
ap-1257	50	46	ı̂	ı̂	PUNCT
ap-1257	50	47	:	:	PUNCT
ap-1257	50	48	(	(	PUNCT
ap-1257	50	49	q1	q1	PROPN
ap-1257	50	50	,	,	PUNCT
ap-1257	50	51	q2)→	q2)→	PROPN
ap-1257	50	52	(	(	PUNCT
ap-1257	50	53	−q1	−q1	PROPN
ap-1257	50	54	,	,	PUNCT
ap-1257	50	55	−q2	−q2	PROPN
ap-1257	50	56	)	)	PUNCT
ap-1257	50	57	,	,	PUNCT
ap-1257	50	58	and	and	CCONJ
ap-1257	50	59	reflection	reflection	NOUN
ap-1257	50	60	in	in	ADP
ap-1257	50	61	a	a	DET
ap-1257	50	62	plane	plane	NOUN
ap-1257	50	63	perpendicular	perpendicular	NOUN
ap-1257	50	64	to	to	ADP
ap-1257	50	65	the	the	DET
ap-1257	50	66	rotation	rotation	NOUN
ap-1257	50	67	axis	axis	NOUN
ap-1257	50	68	σh	σh	PROPN
ap-1257	50	69	:	:	PUNCT
ap-1257	50	70	(	(	PUNCT
ap-1257	50	71	q1	q1	PROPN
ap-1257	50	72	,	,	PUNCT
ap-1257	50	73	q2)→	q2)→	PART
ap-1257	50	74	(	(	PUNCT
ap-1257	50	75	−q2	−q2	PROPN
ap-1257	50	76	,	,	PUNCT
ap-1257	50	77	−q1	−q1	PROPN
ap-1257	50	78	)	)	PUNCT
ap-1257	50	79	.	.	PUNCT
ap-1257	51	1	in	in	ADP
ap-1257	51	2	this	this	DET
ap-1257	51	3	case	case	NOUN
ap-1257	51	4	,	,	PUNCT
ap-1257	51	5	the	the	DET
ap-1257	51	6	states	state	NOUN
ap-1257	51	7	are	be	AUX
ap-1257	51	8	basis	basis	NOUN
ap-1257	51	9	functions	function	NOUN
ap-1257	51	10	for	for	ADP
ap-1257	51	11	the	the	DET
ap-1257	51	12	irreducible	irreducible	ADJ
ap-1257	51	13	representations	representation	NOUN
ap-1257	51	14	ag	ag	PROPN
ap-1257	51	15	,	,	PUNCT
ap-1257	51	16	au	au	ADP
ap-1257	51	17	,	,	PUNCT
ap-1257	51	18	bg	bg	PROPN
ap-1257	51	19	,	,	PUNCT
ap-1257	51	20	and	and	CCONJ
ap-1257	51	21	bu	bu	ADP
ap-1257	51	22	of	of	ADP
ap-1257	51	23	the	the	DET
ap-1257	51	24	point	point	NOUN
ap-1257	51	25	group	group	NOUN
ap-1257	51	26	c2h	c2h	PROPN
ap-1257	52	1	[	[	X
ap-1257	52	2	24	24	NUM
ap-1257	52	3	]	]	PUNCT
ap-1257	52	4	.	.	PUNCT
ap-1257	53	1	3	3	NUM
ap-1257	53	2	small	small	PROPN
ap-1257	53	3	box	box	NOUN
ap-1257	53	4	when	when	SCONJ
ap-1257	53	5	λ	λ	X
ap-1257	53	6	�	�	PROPN
ap-1257	53	7	1	1	NUM
ap-1257	53	8	we	we	PRON
ap-1257	53	9	can	can	AUX
ap-1257	53	10	apply	apply	VERB
ap-1257	53	11	perturbation	perturbation	NOUN
ap-1257	53	12	theory	theory	NOUN
ap-1257	53	13	choosing	choose	VERB
ap-1257	53	14	the	the	DET
ap-1257	53	15	unperturbed	unperturbed	ADJ
ap-1257	53	16	or	or	CCONJ
ap-1257	53	17	reference	reference	NOUN
ap-1257	53	18	hamiltonian	hamiltonian	ADJ
ap-1257	53	19	operator	operator	NOUN
ap-1257	53	20	to	to	PART
ap-1257	53	21	be	be	AUX
ap-1257	53	22	ĥ0d	ĥ0d	NOUN
ap-1257	53	23	=	=	PUNCT
ap-1257	53	24	ĥd(λ	ĥd(λ	NOUN
ap-1257	53	25	=	=	SYM
ap-1257	53	26	0	0	NUM
ap-1257	53	27	)	)	PUNCT
ap-1257	53	28	.	.	PUNCT
ap-1257	54	1	its	its	PRON
ap-1257	54	2	eigenfunctions	eigenfunction	NOUN
ap-1257	54	3	and	and	CCONJ
ap-1257	54	4	eigenvalues	eigenvalue	NOUN
ap-1257	54	5	are	be	AUX
ap-1257	54	6	given	give	VERB
ap-1257	54	7	by	by	ADP
ap-1257	54	8	ϕ(0)n1,n2(q1	ϕ(0)n1,n2(q1	PROPN
ap-1257	54	9	,	,	PUNCT
ap-1257	54	10	q2	q2	NOUN
ap-1257	54	11	)	)	PUNCT
ap-1257	55	1	=	=	SYM
ap-1257	55	2	⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩	⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩	NUM
ap-1257	55	3	2	2	NUM
ap-1257	55	4	cos[(2i	cos[(2i	NOUN
ap-1257	55	5	−	−	ADP
ap-1257	55	6	1)πq1	1)πq1	PRON
ap-1257	55	7	]	]	PUNCT
ap-1257	55	8	cos[(2j	cos[(2j	PROPN
ap-1257	55	9	−	−	PROPN
ap-1257	55	10	1)πq2	1)πq2	NUM
ap-1257	55	11	]	]	SYM
ap-1257	55	12	ag	ag	PROPN
ap-1257	55	13	2	2	NUM
ap-1257	55	14	sin(2iπq1	sin(2iπq1	NOUN
ap-1257	55	15	)	)	PUNCT
ap-1257	55	16	sin(2jπq2	sin(2jπq2	NOUN
ap-1257	55	17	)	)	PUNCT
ap-1257	55	18	ag	ag	PROPN
ap-1257	55	19	2	2	NUM
ap-1257	55	20	cos[(2i	cos[(2i	NOUN
ap-1257	55	21	−	−	ADP
ap-1257	55	22	1)πq1	1)πq1	PRON
ap-1257	55	23	]	]	X
ap-1257	55	24	sin(2jπq2	sin(2jπq2	NOUN
ap-1257	55	25	)	)	PUNCT
ap-1257	55	26	au	au	ADV
ap-1257	55	27	2	2	NUM
ap-1257	55	28	sin(2iπq1	sin(2iπq1	NOUN
ap-1257	55	29	)	)	PUNCT
ap-1257	55	30	cos[(2j	cos[(2j	PROPN
ap-1257	55	31	−	−	PROPN
ap-1257	55	32	1)πq2	1)πq2	NUM
ap-1257	55	33	]	]	PUNCT
ap-1257	55	34	au	au	X
ap-1257	55	35	,	,	PUNCT
ap-1257	55	36	i	i	PRON
ap-1257	55	37	,	,	PUNCT
ap-1257	55	38	j	j	PROPN
ap-1257	55	39	=	=	SYM
ap-1257	55	40	1	1	NUM
ap-1257	55	41	,	,	PUNCT
ap-1257	55	42	2	2	NUM
ap-1257	55	43	,	,	PUNCT
ap-1257	55	44	.	.	PUNCT
ap-1257	55	45	.	.	PUNCT
ap-1257	55	46	.	.	PUNCT
ap-1257	56	1	ε(0)n1,n2	ε(0)n1,n2	X
ap-1257	57	1	=	=	X
ap-1257	57	2	π2	π2	X
ap-1257	57	3	2	2	NUM
ap-1257	57	4	(	(	PUNCT
ap-1257	57	5	n21	n21	NOUN
ap-1257	57	6	+	+	CCONJ
ap-1257	57	7	βn22	βn22	PROPN
ap-1257	57	8	)	)	PUNCT
ap-1257	57	9	,	,	PUNCT
ap-1257	57	10	n1	n1	NOUN
ap-1257	57	11	,	,	PUNCT
ap-1257	57	12	n2	n2	NOUN
ap-1257	57	13	=	=	SYM
ap-1257	57	14	1	1	NUM
ap-1257	57	15	,	,	PUNCT
ap-1257	57	16	2	2	NUM
ap-1257	57	17	,	,	PUNCT
ap-1257	57	18	.	.	PUNCT
ap-1257	57	19	.	.	PUNCT
ap-1257	57	20	.	.	PUNCT
ap-1257	58	1	(	(	PUNCT
ap-1257	58	2	7	7	X
ap-1257	58	3	)	)	PUNCT
ap-1257	58	4	there	there	PRON
ap-1257	58	5	is	be	VERB
ap-1257	58	6	no	no	DET
ap-1257	58	7	degeneracy	degeneracy	NOUN
ap-1257	58	8	when	when	SCONJ
ap-1257	58	9	β	β	X
ap-1257	58	10	<	<	X
ap-1257	58	11	1	1	NUM
ap-1257	58	12	,	,	PUNCT
ap-1257	58	13	except	except	SCONJ
ap-1257	58	14	for	for	ADP
ap-1257	58	15	the	the	DET
ap-1257	58	16	accidental	accidental	ADJ
ap-1257	58	17	one	one	NOUN
ap-1257	58	18	that	that	PRON
ap-1257	58	19	takes	take	VERB
ap-1257	58	20	place	place	NOUN
ap-1257	58	21	for	for	ADP
ap-1257	58	22	particular	particular	ADJ
ap-1257	58	23	values	value	NOUN
ap-1257	58	24	of	of	ADP
ap-1257	58	25	β	β	PRON
ap-1257	58	26	which	which	PRON
ap-1257	58	27	we	we	PRON
ap-1257	58	28	will	will	AUX
ap-1257	58	29	not	not	PART
ap-1257	58	30	discuss	discuss	VERB
ap-1257	58	31	in	in	ADP
ap-1257	58	32	this	this	DET
ap-1257	58	33	paper	paper	NOUN
ap-1257	58	34	.	.	PUNCT
ap-1257	59	1	the	the	DET
ap-1257	59	2	energies	energy	NOUN
ap-1257	59	3	corrected	correct	VERB
ap-1257	59	4	to	to	ADP
ap-1257	59	5	first	first	ADJ
ap-1257	59	6	order	order	NOUN
ap-1257	59	7	read	read	VERB
ap-1257	59	8	ε[1]n1,n2	ε[1]n1,n2	X
ap-1257	59	9	=	=	SYM
ap-1257	59	10	π2	π2	ADV
ap-1257	59	11	2	2	NUM
ap-1257	59	12	(	(	PUNCT
ap-1257	59	13	n21	n21	NOUN
ap-1257	59	14	+	+	CCONJ
ap-1257	59	15	βn22	βn22	PROPN
ap-1257	59	16	)	)	PUNCT
ap-1257	60	1	+	+	PUNCT
ap-1257	61	1	λ	λ	X
ap-1257	61	2	π2n21n	π2n21n	PROPN
ap-1257	61	3	2	2	NUM
ap-1257	61	4	2	2	NUM
ap-1257	61	5	−	−	NOUN
ap-1257	61	6	3	3	NUM
ap-1257	61	7	(	(	PUNCT
ap-1257	61	8	n21	n21	PROPN
ap-1257	61	9	+	+	CCONJ
ap-1257	61	10	n22	n22	PROPN
ap-1257	61	11	)	)	PUNCT
ap-1257	61	12	12π2n21n	12π2n21n	NUM
ap-1257	61	13	2	2	NUM
ap-1257	61	14	2	2	NUM
ap-1257	61	15	.	.	PUNCT
ap-1257	62	1	(	(	PUNCT
ap-1257	62	2	8)	8)	NUM
ap-1257	62	3	when	when	SCONJ
ap-1257	62	4	β	β	X
ap-1257	62	5	=	=	VERB
ap-1257	62	6	1	1	NUM
ap-1257	62	7	the	the	DET
ap-1257	62	8	zeroth	zeroth	ADJ
ap-1257	62	9	–	–	PUNCT
ap-1257	62	10	order	order	NOUN
ap-1257	62	11	states	state	VERB
ap-1257	62	12	ϕ(0)n1,n2	ϕ(0)n1,n2	PRON
ap-1257	62	13	and	and	CCONJ
ap-1257	62	14	ϕ(0)n2,n1	ϕ(0)n2,n1	NUM
ap-1257	62	15	(	(	PUNCT
ap-1257	62	16	n1	n1	PROPN
ap-1257	62	17	=	=	SYM
ap-1257	62	18	n2	n2	NOUN
ap-1257	62	19	)	)	PUNCT
ap-1257	62	20	are	be	AUX
ap-1257	62	21	degenerate	degenerate	ADJ
ap-1257	62	22	,	,	PUNCT
ap-1257	62	23	but	but	CCONJ
ap-1257	62	24	it	it	PRON
ap-1257	62	25	is	be	AUX
ap-1257	62	26	not	not	PART
ap-1257	62	27	necessary	necessary	ADJ
ap-1257	62	28	to	to	PART
ap-1257	62	29	resort	resort	VERB
ap-1257	62	30	to	to	ADP
ap-1257	62	31	perturbation	perturbation	NOUN
ap-1257	62	32	theory	theory	NOUN
ap-1257	62	33	for	for	ADP
ap-1257	62	34	degenerate	degenerate	ADJ
ap-1257	62	35	states	state	NOUN
ap-1257	62	36	in	in	ADP
ap-1257	62	37	order	order	NOUN
ap-1257	62	38	to	to	PART
ap-1257	62	39	obtain	obtain	VERB
ap-1257	62	40	the	the	DET
ap-1257	62	41	first	first	ADJ
ap-1257	62	42	-	-	PUNCT
ap-1257	62	43	order	order	NOUN
ap-1257	62	44	energies	energy	NOUN
ap-1257	62	45	.	.	PUNCT
ap-1257	63	1	we	we	PRON
ap-1257	63	2	simply	simply	ADV
ap-1257	63	3	take	take	VERB
ap-1257	63	4	into	into	ADP
ap-1257	63	5	account	account	NOUN
ap-1257	63	6	that	that	SCONJ
ap-1257	63	7	the	the	DET
ap-1257	63	8	eigenfunctions	eigenfunction	NOUN
ap-1257	63	9	of	of	ADP
ap-1257	63	10	ĥ0d	ĥ0d	NOUN
ap-1257	63	11	adapted	adapt	VERB
ap-1257	63	12	to	to	ADP
ap-1257	63	13	the	the	DET
ap-1257	63	14	symmetry	symmetry	NOUN
ap-1257	63	15	of	of	ADP
ap-1257	63	16	the	the	DET
ap-1257	63	17	problem	problem	NOUN
ap-1257	63	18	are	be	AUX
ap-1257	63	19	18	18	NUM
ap-1257	63	20	acta	acta	PROPN
ap-1257	63	21	polytechnica	polytechnica	PROPN
ap-1257	63	22	vol	vol	NOUN
ap-1257	63	23	.	.	PROPN
ap-1257	64	1	50	50	NUM
ap-1257	64	2	no	no	NOUN
ap-1257	64	3	.	.	PUNCT
ap-1257	65	1	5/2010	5/2010	NUM
ap-1257	65	2	ϕ(0)n1,n2(q1	ϕ(0)n1,n2(q1	NOUN
ap-1257	65	3	,	,	PUNCT
ap-1257	65	4	q2	q2	NOUN
ap-1257	65	5	)	)	PUNCT
ap-1257	66	1	=	=	SYM
ap-1257	66	2	⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩	⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩	PROPN
ap-1257	66	3	√	√	NUM
ap-1257	66	4	2−	2−	NUM
ap-1257	66	5	δij	δij	NOUN
ap-1257	66	6	{	{	PUNCT
ap-1257	66	7	cos[(2i	cos[(2i	X
ap-1257	66	8	−	−	VERB
ap-1257	66	9	1)πq1	1)πq1	X
ap-1257	66	10	]	]	PUNCT
ap-1257	66	11	cos[(2j	cos[(2j	PROPN
ap-1257	66	12	−	−	NOUN
ap-1257	66	13	1)πq2	1)πq2	NUM
ap-1257	66	14	]	]	PUNCT
ap-1257	67	1	+	+	CCONJ
ap-1257	67	2	cos[(2j	cos[(2j	PROPN
ap-1257	67	3	−	−	PROPN
ap-1257	67	4	1)πq1	1)πq1	PRON
ap-1257	67	5	]	]	X
ap-1257	67	6	cos[(2i	cos[(2i	PROPN
ap-1257	67	7	−	−	NOUN
ap-1257	67	8	1)πq2	1)πq2	NUM
ap-1257	67	9	]	]	PUNCT
ap-1257	67	10	}	}	PUNCT
ap-1257	67	11	ag	ag	NOUN
ap-1257	67	12	√	√	ADV
ap-1257	67	13	2	2	NUM
ap-1257	67	14	{	{	PUNCT
ap-1257	67	15	cos[(2i	cos[(2i	X
ap-1257	67	16	−	−	ADP
ap-1257	67	17	1)πq1	1)πq1	PRON
ap-1257	67	18	]	]	PUNCT
ap-1257	67	19	cos[(2j	cos[(2j	PROPN
ap-1257	67	20	−	−	NOUN
ap-1257	67	21	1)πq2	1)πq2	NUM
ap-1257	67	22	]	]	PUNCT
ap-1257	67	23	−	−	PROPN
ap-1257	67	24	cos[(2j	cos[(2j	PROPN
ap-1257	67	25	−	−	PROPN
ap-1257	67	26	1)πq1	1)πq1	PRON
ap-1257	67	27	]	]	X
ap-1257	67	28	cos[(2i	cos[(2i	PROPN
ap-1257	67	29	−	−	NOUN
ap-1257	67	30	1)πq2	1)πq2	NUM
ap-1257	67	31	]	]	PUNCT
ap-1257	67	32	}	}	PUNCT
ap-1257	67	33	bg	bg	NOUN
ap-1257	67	34	√	√	ADJ
ap-1257	67	35	2	2	NUM
ap-1257	67	36	{	{	PUNCT
ap-1257	67	37	cos[(2i	cos[(2i	X
ap-1257	67	38	−	−	PROPN
ap-1257	68	1	1)πq1	1)πq1	PRON
ap-1257	68	2	]	]	X
ap-1257	68	3	sin[2jπq2	sin[2jπq2	NOUN
ap-1257	68	4	]	]	X
ap-1257	68	5	+	+	CCONJ
ap-1257	68	6	sin[2jπq1	sin[2jπq1	NOUN
ap-1257	68	7	]	]	X
ap-1257	68	8	cos[(2i	cos[(2i	NOUN
ap-1257	68	9	−	−	NOUN
ap-1257	68	10	1)πq2	1)πq2	NUM
ap-1257	68	11	]	]	PUNCT
ap-1257	68	12	}	}	PUNCT
ap-1257	68	13	au	au	ADV
ap-1257	68	14	√	√	ADP
ap-1257	68	15	2	2	NUM
ap-1257	68	16	{	{	PUNCT
ap-1257	68	17	cos[(2i	cos[(2i	X
ap-1257	68	18	−	−	ADP
ap-1257	68	19	1)πq1	1)πq1	DET
ap-1257	68	20	]	]	X
ap-1257	68	21	sin[2jπq2]−	sin[2jπq2]−	NOUN
ap-1257	68	22	sin[2jπq1	sin[2jπq1	NOUN
ap-1257	68	23	]	]	X
ap-1257	68	24	cos[(2i	cos[(2i	PROPN
ap-1257	68	25	−	−	NOUN
ap-1257	68	26	1)πq2	1)πq2	NUM
ap-1257	68	27	]	]	PUNCT
ap-1257	68	28	}	}	PUNCT
ap-1257	68	29	bu	bu	ADP
ap-1257	68	30	√	√	PROPN
ap-1257	68	31	2−	2−	NUM
ap-1257	68	32	δij	δij	NOUN
ap-1257	68	33	{	{	PUNCT
ap-1257	68	34	sin[2iπq1	sin[2iπq1	X
ap-1257	68	35	]	]	X
ap-1257	68	36	sin[2jπq2	sin[2jπq2	NOUN
ap-1257	68	37	]	]	X
ap-1257	68	38	+	+	CCONJ
ap-1257	68	39	sin[2jπq1	sin[2jπq1	NOUN
ap-1257	68	40	]	]	X
ap-1257	68	41	sin[2iπq2	sin[2iπq2	NOUN
ap-1257	68	42	]	]	X
ap-1257	68	43	}	}	PUNCT
ap-1257	68	44	ag	ag	NOUN
ap-1257	68	45	√	√	ADV
ap-1257	68	46	2	2	NUM
ap-1257	68	47	{	{	PUNCT
ap-1257	68	48	sin[2iπq1	sin[2iπq1	NOUN
ap-1257	68	49	]	]	X
ap-1257	68	50	sin[2jπq2]−	sin[2jπq2]−	NOUN
ap-1257	68	51	sin[2jπq1	sin[2jπq1	NOUN
ap-1257	68	52	]	]	X
ap-1257	68	53	sin[2iπq2	sin[2iπq2	PROPN
ap-1257	68	54	]	]	X
ap-1257	68	55	}	}	PUNCT
ap-1257	68	56	bg	bg	NOUN
ap-1257	68	57	(	(	PUNCT
ap-1257	68	58	9	9	NUM
ap-1257	68	59	)	)	PUNCT
ap-1257	68	60	where	where	SCONJ
ap-1257	68	61	i	i	PRON
ap-1257	68	62	,	,	PUNCT
ap-1257	68	63	j	j	PROPN
ap-1257	68	64	=	=	SYM
ap-1257	68	65	1	1	NUM
ap-1257	68	66	,	,	PUNCT
ap-1257	68	67	2	2	NUM
ap-1257	68	68	,	,	PUNCT
ap-1257	68	69	.	.	PUNCT
ap-1257	68	70	.	.	PUNCT
ap-1257	69	1	.	.	PUNCT
ap-1257	70	1	they	they	PRON
ap-1257	70	2	give	give	VERB
ap-1257	70	3	us	we	PRON
ap-1257	70	4	the	the	DET
ap-1257	70	5	energies	energy	NOUN
ap-1257	70	6	corrected	correct	VERB
ap-1257	70	7	to	to	ADP
ap-1257	70	8	first	first	ADJ
ap-1257	70	9	order	order	NOUN
ap-1257	70	10	as	as	ADP
ap-1257	70	11	ε[1]n	ε[1]n	NOUN
ap-1257	70	12	(	(	PUNCT
ap-1257	70	13	s	s	NOUN
ap-1257	70	14	)	)	PUNCT
ap-1257	70	15	=	=	PUNCT
ap-1257	70	16	〈	〈	PROPN
ap-1257	70	17	ϕ	ϕ	NOUN
ap-1257	70	18	(	(	PUNCT
ap-1257	70	19	0	0	NUM
ap-1257	70	20	)	)	PUNCT
ap-1257	70	21	ij	ij	NOUN
ap-1257	70	22	(	(	PUNCT
ap-1257	70	23	s	s	NOUN
ap-1257	70	24	)	)	PUNCT
ap-1257	70	25	∣∣∣	∣∣∣	NOUN
ap-1257	70	26	ĥd	ĥd	X
ap-1257	70	27	∣∣∣ϕ(0)ij	∣∣∣ϕ(0)ij	NOUN
ap-1257	70	28	(	(	PUNCT
ap-1257	70	29	s	s	NOUN
ap-1257	70	30	)	)	PUNCT
ap-1257	70	31	〉	〉	NOUN
ap-1257	70	32	where	where	SCONJ
ap-1257	70	33	s	s	VERB
ap-1257	70	34	denotes	denote	VERB
ap-1257	70	35	the	the	DET
ap-1257	70	36	irreducible	irreducible	ADJ
ap-1257	70	37	representation	representation	NOUN
ap-1257	70	38	.	.	PUNCT
ap-1257	71	1	since	since	SCONJ
ap-1257	71	2	some	some	PRON
ap-1257	71	3	of	of	ADP
ap-1257	71	4	these	these	DET
ap-1257	71	5	analytical	analytical	ADJ
ap-1257	71	6	expressions	expression	NOUN
ap-1257	71	7	are	be	AUX
ap-1257	71	8	rather	rather	ADV
ap-1257	71	9	cumbersome	cumbersome	ADJ
ap-1257	71	10	for	for	ADP
ap-1257	71	11	arbitrary	arbitrary	ADJ
ap-1257	71	12	quantum	quantum	ADJ
ap-1257	71	13	numbers	number	NOUN
ap-1257	71	14	,	,	PUNCT
ap-1257	71	15	we	we	PRON
ap-1257	71	16	simply	simply	ADV
ap-1257	71	17	show	show	VERB
ap-1257	71	18	the	the	DET
ap-1257	71	19	first	first	ADJ
ap-1257	71	20	six	six	NUM
ap-1257	71	21	energy	energy	NOUN
ap-1257	71	22	levels	level	NOUN
ap-1257	71	23	for	for	ADP
ap-1257	71	24	future	future	ADJ
ap-1257	71	25	reference	reference	NOUN
ap-1257	71	26	:	:	PUNCT
ap-1257	71	27	ε	ε	PROPN
ap-1257	72	1	[	[	X
ap-1257	72	2	1	1	NUM
ap-1257	72	3	]	]	SYM
ap-1257	72	4	1	1	NUM
ap-1257	72	5	(	(	PUNCT
ap-1257	72	6	ag	ag	PROPN
ap-1257	72	7	)	)	PUNCT
ap-1257	72	8	=	=	PUNCT
ap-1257	72	9	π2	π2	ADJ
ap-1257	72	10	+	+	CCONJ
ap-1257	72	11	λ(π2	λ(π2	NOUN
ap-1257	72	12	−	−	PROPN
ap-1257	72	13	6	6	NUM
ap-1257	72	14	)	)	PUNCT
ap-1257	72	15	12π2	12π2	NUM
ap-1257	72	16	ε	ε	PROPN
ap-1257	73	1	[	[	X
ap-1257	73	2	1	1	NUM
ap-1257	73	3	]	]	SYM
ap-1257	73	4	1	1	NUM
ap-1257	73	5	(	(	PUNCT
ap-1257	73	6	au	au	PROPN
ap-1257	73	7	)	)	PUNCT
ap-1257	73	8	=	=	SYM
ap-1257	73	9	5π2	5π2	NUM
ap-1257	73	10	2	2	NUM
ap-1257	74	1	+	+	CCONJ
ap-1257	74	2	λ(108π4	λ(108π4	PUNCT
ap-1257	74	3	−	−	PROPN
ap-1257	74	4	405π2	405π2	NUM
ap-1257	74	5	−	−	NUM
ap-1257	74	6	4	4	NUM
ap-1257	74	7	096	096	NUM
ap-1257	74	8	)	)	PUNCT
ap-1257	74	9	1	1	NUM
ap-1257	74	10	296π4	296π4	NUM
ap-1257	74	11	ε	ε	X
ap-1257	75	1	[	[	X
ap-1257	75	2	1	1	NUM
ap-1257	75	3	]	]	SYM
ap-1257	75	4	1	1	NUM
ap-1257	75	5	(	(	PUNCT
ap-1257	75	6	bu	bu	NOUN
ap-1257	75	7	)	)	PUNCT
ap-1257	75	8	=	=	SYM
ap-1257	75	9	5π2	5π2	NUM
ap-1257	75	10	2	2	NUM
ap-1257	75	11	+	+	CCONJ
ap-1257	75	12	λ(108π4	λ(108π4	PUNCT
ap-1257	75	13	−	−	PROPN
ap-1257	75	14	405π2	405π2	NUM
ap-1257	76	1	+	+	CCONJ
ap-1257	76	2	4	4	NUM
ap-1257	76	3	096	096	NUM
ap-1257	76	4	)	)	PUNCT
ap-1257	76	5	1	1	NUM
ap-1257	76	6	296π4	296π4	NUM
ap-1257	76	7	ε	ε	X
ap-1257	77	1	[	[	X
ap-1257	77	2	1	1	NUM
ap-1257	77	3	]	]	SYM
ap-1257	77	4	2	2	NUM
ap-1257	77	5	(	(	PUNCT
ap-1257	77	6	ag	ag	PROPN
ap-1257	77	7	)	)	PUNCT
ap-1257	77	8	=	=	SYM
ap-1257	77	9	4π	4π	NUM
ap-1257	77	10	2	2	NUM
ap-1257	78	1	+	+	CCONJ
ap-1257	78	2	λ(2π2	λ(2π2	NUM
ap-1257	79	1	−	−	NOUN
ap-1257	79	2	3	3	NUM
ap-1257	79	3	)	)	PUNCT
ap-1257	79	4	24π2	24π2	NUM
ap-1257	79	5	ε	ε	PROPN
ap-1257	80	1	[	[	X
ap-1257	80	2	1	1	NUM
ap-1257	80	3	]	]	SYM
ap-1257	80	4	3	3	NUM
ap-1257	80	5	(	(	PUNCT
ap-1257	80	6	ag	ag	PROPN
ap-1257	80	7	)	)	PUNCT
ap-1257	80	8	=	=	PUNCT
ap-1257	80	9	ε	ε	PROPN
ap-1257	81	1	[	[	X
ap-1257	81	2	1	1	NUM
ap-1257	81	3	]	]	SYM
ap-1257	81	4	1	1	NUM
ap-1257	81	5	(	(	PUNCT
ap-1257	81	6	bg	bg	NOUN
ap-1257	81	7	)	)	PUNCT
ap-1257	81	8	=	=	PUNCT
ap-1257	82	1	5π2	5π2	NUM
ap-1257	82	2	+	+	CCONJ
ap-1257	82	3	λ(3π2	λ(3π2	NUM
ap-1257	82	4	−	−	NUM
ap-1257	82	5	10	10	NUM
ap-1257	82	6	)	)	PUNCT
ap-1257	82	7	36π2	36π2	NUM
ap-1257	82	8	.	.	PUNCT
ap-1257	83	1	(	(	PUNCT
ap-1257	83	2	10	10	NUM
ap-1257	83	3	)	)	PUNCT
ap-1257	83	4	the	the	DET
ap-1257	83	5	degeneracy	degeneracy	NOUN
ap-1257	83	6	of	of	ADP
ap-1257	83	7	the	the	DET
ap-1257	83	8	approximate	approximate	ADJ
ap-1257	83	9	energies	energy	NOUN
ap-1257	83	10	denoted	denote	VERB
ap-1257	83	11	ε	ε	PROPN
ap-1257	84	1	[	[	X
ap-1257	84	2	1	1	NUM
ap-1257	84	3	]	]	SYM
ap-1257	84	4	3	3	NUM
ap-1257	84	5	(	(	PUNCT
ap-1257	84	6	ag	ag	PROPN
ap-1257	84	7	)	)	PUNCT
ap-1257	84	8	and	and	CCONJ
ap-1257	84	9	ε	ε	PROPN
ap-1257	85	1	[	[	X
ap-1257	85	2	1	1	NUM
ap-1257	85	3	]	]	SYM
ap-1257	85	4	1	1	NUM
ap-1257	85	5	(	(	PUNCT
ap-1257	85	6	bg	bg	NOUN
ap-1257	85	7	)	)	PUNCT
ap-1257	85	8	is	be	AUX
ap-1257	85	9	broken	break	VERB
ap-1257	85	10	at	at	ADP
ap-1257	85	11	higher	high	ADJ
ap-1257	85	12	perturbation	perturbation	NOUN
ap-1257	85	13	orders	order	NOUN
ap-1257	85	14	as	as	SCONJ
ap-1257	85	15	shown	show	VERB
ap-1257	85	16	by	by	ADP
ap-1257	85	17	the	the	DET
ap-1257	85	18	numerical	numerical	ADJ
ap-1257	85	19	results	result	NOUN
ap-1257	85	20	in	in	ADP
ap-1257	85	21	sec	sec	PROPN
ap-1257	85	22	.	.	PROPN
ap-1257	86	1	5	5	NUM
ap-1257	86	2	.	.	NOUN
ap-1257	86	3	4	4	NUM
ap-1257	86	4	large	large	ADJ
ap-1257	86	5	box	box	NOUN
ap-1257	86	6	when	when	SCONJ
ap-1257	86	7	l	l	PROPN
ap-1257	86	8	→	→	SYM
ap-1257	86	9	∞	∞	PROPN
ap-1257	86	10	the	the	DET
ap-1257	86	11	energy	energy	NOUN
ap-1257	86	12	eigenvalues	eigenvalue	VERB
ap-1257	86	13	tend	tend	VERB
ap-1257	86	14	to	to	ADP
ap-1257	86	15	those	those	PRON
ap-1257	86	16	of	of	ADP
ap-1257	86	17	the	the	DET
ap-1257	86	18	free	free	ADJ
ap-1257	86	19	system	system	NOUN
ap-1257	86	20	(	(	PUNCT
ap-1257	86	21	6	6	NUM
ap-1257	86	22	)	)	PUNCT
ap-1257	86	23	.	.	PUNCT
ap-1257	87	1	more	more	ADV
ap-1257	87	2	precisely	precisely	ADV
ap-1257	87	3	,	,	PUNCT
ap-1257	87	4	we	we	PRON
ap-1257	87	5	expect	expect	VERB
ap-1257	87	6	that	that	SCONJ
ap-1257	87	7	the	the	DET
ap-1257	87	8	states	state	NOUN
ap-1257	87	9	with	with	ADP
ap-1257	87	10	finite	finite	ADJ
ap-1257	87	11	quantum	quantum	ADJ
ap-1257	87	12	numbers	number	NOUN
ap-1257	87	13	n1	n1	NOUN
ap-1257	87	14	,	,	PUNCT
ap-1257	87	15	n2	n2	NOUN
ap-1257	87	16	at	at	ADP
ap-1257	87	17	l	l	NOUN
ap-1257	87	18	=	=	SYM
ap-1257	87	19	0	0	NUM
ap-1257	87	20	correlate	correlate	VERB
ap-1257	87	21	with	with	ADP
ap-1257	87	22	those	those	PRON
ap-1257	87	23	with	with	ADP
ap-1257	87	24	k	k	PROPN
ap-1257	87	25	=	=	PUNCT
ap-1257	87	26	0	0	PUNCT
ap-1257	87	27	when	when	SCONJ
ap-1257	87	28	l	l	NOUN
ap-1257	87	29	→	→	SYM
ap-1257	87	30	∞	∞	PROPN
ap-1257	87	31	:	:	PUNCT
ap-1257	87	32	lim	lim	PROPN
ap-1257	87	33	λ→∞	λ→∞	PRON
ap-1257	87	34	ε(β	ε(β	PROPN
ap-1257	87	35	,	,	PUNCT
ap-1257	87	36	λ)√	λ)√	PROPN
ap-1257	87	37	λ	λ	X
ap-1257	87	38	=	=	NOUN
ap-1257	87	39	√	√	ADP
ap-1257	87	40	1	1	NUM
ap-1257	87	41	+	+	CCONJ
ap-1257	87	42	β	β	X
ap-1257	87	43	(	(	PUNCT
ap-1257	87	44	v	v	X
ap-1257	87	45	+	+	CCONJ
ap-1257	87	46	1	1	NUM
ap-1257	87	47	2	2	NUM
ap-1257	87	48	)	)	PUNCT
ap-1257	87	49	,	,	PUNCT
ap-1257	87	50	v	v	NOUN
ap-1257	87	51	=	=	SYM
ap-1257	87	52	0	0	NUM
ap-1257	87	53	,	,	PUNCT
ap-1257	87	54	1	1	NUM
ap-1257	87	55	,	,	PUNCT
ap-1257	87	56	.	.	PUNCT
ap-1257	87	57	.	.	PUNCT
ap-1257	87	58	.	.	PUNCT
ap-1257	88	1	(	(	PUNCT
ap-1257	88	2	11	11	NUM
ap-1257	88	3	)	)	PUNCT
ap-1257	88	4	besides	besides	SCONJ
ap-1257	88	5	,	,	PUNCT
ap-1257	88	6	we	we	PRON
ap-1257	88	7	should	should	AUX
ap-1257	88	8	take	take	VERB
ap-1257	88	9	into	into	ADP
ap-1257	88	10	account	account	NOUN
ap-1257	88	11	that	that	SCONJ
ap-1257	88	12	the	the	DET
ap-1257	88	13	symmetry	symmetry	NOUN
ap-1257	88	14	of	of	ADP
ap-1257	88	15	a	a	DET
ap-1257	88	16	given	give	VERB
ap-1257	88	17	state	state	NOUN
ap-1257	88	18	is	be	AUX
ap-1257	88	19	conserved	conserve	VERB
ap-1257	88	20	as	as	ADP
ap-1257	88	21	l	l	NOUN
ap-1257	88	22	increases	increase	NOUN
ap-1257	88	23	from	from	ADP
ap-1257	88	24	0	0	NUM
ap-1257	88	25	to	to	ADP
ap-1257	88	26	∞.	∞.	PROPN
ap-1257	88	27	when	when	SCONJ
ap-1257	88	28	β	β	X
ap-1257	88	29	<	<	X
ap-1257	88	30	1	1	NUM
ap-1257	88	31	we	we	PRON
ap-1257	88	32	expect	expect	VERB
ap-1257	88	33	that	that	SCONJ
ap-1257	88	34	the	the	DET
ap-1257	88	35	states	state	NOUN
ap-1257	88	36	approach	approach	VERB
ap-1257	88	37	ψkv(x	ψkv(x	PROPN
ap-1257	88	38	,	,	PUNCT
ap-1257	88	39	x	x	X
ap-1257	88	40	)	)	PUNCT
ap-1257	89	1	=	=	SYM
ap-1257	89	2	⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩	⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩	PROPN
ap-1257	89	3	cos(kx)φ2v(x	cos(kx)φ2v(x	PROPN
ap-1257	89	4	)	)	PUNCT
ap-1257	89	5	ag	ag	PROPN
ap-1257	89	6	sin(kx)φ2v+1(x	sin(kx)φ2v+1(x	NOUN
ap-1257	89	7	)	)	PUNCT
ap-1257	89	8	ag	ag	PROPN
ap-1257	89	9	sin(kx)φ2v(x	sin(kx)φ2v(x	PROPN
ap-1257	89	10	)	)	PUNCT
ap-1257	89	11	au	au	ADP
ap-1257	89	12	cos(kx)φ2v+1(x	cos(kx)φ2v+1(x	NOUN
ap-1257	89	13	)	)	PUNCT
ap-1257	89	14	au	au	PUNCT
ap-1257	89	15	(	(	PUNCT
ap-1257	89	16	12	12	NUM
ap-1257	89	17	)	)	PUNCT
ap-1257	89	18	as	as	ADP
ap-1257	89	19	l	l	PROPN
ap-1257	89	20	→	→	SYM
ap-1257	89	21	∞.	∞.	PROPN
ap-1257	89	22	19	19	NUM
ap-1257	89	23	acta	acta	PROPN
ap-1257	89	24	polytechnica	polytechnica	PROPN
ap-1257	89	25	vol	vol	NOUN
ap-1257	89	26	.	.	PROPN
ap-1257	90	1	50	50	NUM
ap-1257	90	2	no	no	NOUN
ap-1257	90	3	.	.	PUNCT
ap-1257	91	1	5/2010	5/2010	NUM
ap-1257	91	2	for	for	ADP
ap-1257	91	3	the	the	DET
ap-1257	91	4	more	more	ADV
ap-1257	91	5	symmetric	symmetric	ADJ
ap-1257	91	6	case	case	NOUN
ap-1257	91	7	β	β	X
ap-1257	91	8	=	=	SYM
ap-1257	91	9	1	1	NUM
ap-1257	91	10	the	the	DET
ap-1257	91	11	states	state	NOUN
ap-1257	91	12	should	should	AUX
ap-1257	91	13	be	be	AUX
ap-1257	91	14	ψkv(x	ψkv(x	PROPN
ap-1257	91	15	,	,	PUNCT
ap-1257	91	16	x	x	NOUN
ap-1257	91	17	)	)	PUNCT
ap-1257	92	1	=	=	SYM
ap-1257	92	2	⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩	⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩	PROPN
ap-1257	92	3	cos(kx)φ2v(x	cos(kx)φ2v(x	PROPN
ap-1257	92	4	)	)	PUNCT
ap-1257	92	5	ag	ag	PROPN
ap-1257	92	6	sin(kx)φ2v(x	sin(kx)φ2v(x	PROPN
ap-1257	92	7	)	)	PUNCT
ap-1257	92	8	au	au	ADP
ap-1257	92	9	cos(kx)φ2v+1(x	cos(kx)φ2v+1(x	NOUN
ap-1257	92	10	)	)	PUNCT
ap-1257	92	11	bu	bu	ADP
ap-1257	92	12	sin(kx)φ2v+1(x	sin(kx)φ2v+1(x	NOUN
ap-1257	92	13	)	)	PUNCT
ap-1257	92	14	bg	bg	PROPN
ap-1257	92	15	.	.	PUNCT
ap-1257	93	1	(	(	PUNCT
ap-1257	93	2	13	13	NUM
ap-1257	93	3	)	)	PUNCT
ap-1257	93	4	obviously	obviously	ADV
ap-1257	93	5	,	,	PUNCT
ap-1257	93	6	perturbation	perturbation	NOUN
ap-1257	93	7	expressions	expression	NOUN
ap-1257	93	8	(	(	PUNCT
ap-1257	93	9	8)	8)	NUM
ap-1257	93	10	or	or	CCONJ
ap-1257	93	11	(	(	PUNCT
ap-1257	93	12	10	10	NUM
ap-1257	93	13	)	)	PUNCT
ap-1257	93	14	are	be	AUX
ap-1257	93	15	unsuitable	unsuitable	ADJ
ap-1257	93	16	for	for	ADP
ap-1257	93	17	this	this	DET
ap-1257	93	18	analysis	analysis	NOUN
ap-1257	93	19	and	and	CCONJ
ap-1257	93	20	we	we	PRON
ap-1257	93	21	have	have	VERB
ap-1257	93	22	to	to	PART
ap-1257	93	23	resort	resort	VERB
ap-1257	93	24	to	to	ADP
ap-1257	93	25	other	other	ADJ
ap-1257	93	26	approaches	approach	NOUN
ap-1257	93	27	.	.	PUNCT
ap-1257	94	1	in	in	ADP
ap-1257	94	2	order	order	NOUN
ap-1257	94	3	to	to	PART
ap-1257	94	4	obtain	obtain	VERB
ap-1257	94	5	accurate	accurate	ADJ
ap-1257	94	6	eigenvalues	eigenvalue	NOUN
ap-1257	94	7	and	and	CCONJ
ap-1257	94	8	eigenfunctions	eigenfunction	NOUN
ap-1257	94	9	for	for	ADP
ap-1257	94	10	the	the	DET
ap-1257	94	11	present	present	ADJ
ap-1257	94	12	model	model	NOUN
ap-1257	94	13	we	we	PRON
ap-1257	94	14	may	may	AUX
ap-1257	94	15	resort	resort	VERB
ap-1257	94	16	to	to	ADP
ap-1257	94	17	the	the	DET
ap-1257	94	18	rayleigh	rayleigh	PROPN
ap-1257	94	19	-	-	PUNCT
ap-1257	94	20	ritz	ritz	PROPN
ap-1257	94	21	variational	variational	ADJ
ap-1257	94	22	method	method	NOUN
ap-1257	94	23	and	and	CCONJ
ap-1257	94	24	the	the	DET
ap-1257	94	25	basis	basis	NOUN
ap-1257	94	26	set	set	NOUN
ap-1257	94	27	of	of	ADP
ap-1257	94	28	eigenfunctions	eigenfunction	NOUN
ap-1257	94	29	of	of	ADP
ap-1257	94	30	ĥ0d	ĥ0d	NOUN
ap-1257	94	31	given	give	VERB
ap-1257	94	32	in	in	ADP
ap-1257	94	33	equations	equation	NOUN
ap-1257	94	34	(	(	PUNCT
ap-1257	94	35	7	7	NUM
ap-1257	94	36	)	)	PUNCT
ap-1257	94	37	and	and	CCONJ
ap-1257	94	38	(	(	PUNCT
ap-1257	94	39	9	9	NUM
ap-1257	94	40	)	)	PUNCT
ap-1257	94	41	.	.	PUNCT
ap-1257	95	1	alternatively	alternatively	ADV
ap-1257	95	2	,	,	PUNCT
ap-1257	95	3	we	we	PRON
ap-1257	95	4	can	can	AUX
ap-1257	95	5	also	also	ADV
ap-1257	95	6	make	make	VERB
ap-1257	95	7	use	use	NOUN
ap-1257	95	8	of	of	ADP
ap-1257	95	9	the	the	DET
ap-1257	95	10	collocation	collocation	NOUN
ap-1257	95	11	method	method	NOUN
ap-1257	95	12	with	with	ADP
ap-1257	95	13	the	the	DET
ap-1257	95	14	so	so	ADV
ap-1257	95	15	-	-	PUNCT
ap-1257	95	16	called	call	VERB
ap-1257	95	17	little	little	ADJ
ap-1257	95	18	sinc	sinc	NOUN
ap-1257	95	19	functions	function	NOUN
ap-1257	95	20	(	(	PUNCT
ap-1257	95	21	lsf	lsf	NOUN
ap-1257	95	22	)	)	PUNCT
ap-1257	95	23	that	that	PRON
ap-1257	95	24	proved	prove	VERB
ap-1257	95	25	useful	useful	ADJ
ap-1257	95	26	for	for	ADP
ap-1257	95	27	the	the	DET
ap-1257	95	28	treatment	treatment	NOUN
ap-1257	95	29	of	of	ADP
ap-1257	95	30	coupled	couple	VERB
ap-1257	95	31	anharmonic	anharmonic	ADJ
ap-1257	95	32	oscillators	oscillator	NOUN
ap-1257	95	33	[	[	X
ap-1257	95	34	25	25	NUM
ap-1257	95	35	]	]	PUNCT
ap-1257	95	36	.	.	PUNCT
ap-1257	96	1	in	in	ADP
ap-1257	96	2	this	this	DET
ap-1257	96	3	paper	paper	NOUN
ap-1257	96	4	we	we	PRON
ap-1257	96	5	choose	choose	VERB
ap-1257	96	6	the	the	DET
ap-1257	96	7	latter	latter	ADJ
ap-1257	96	8	approach	approach	NOUN
ap-1257	96	9	.	.	PUNCT
ap-1257	97	1	another	another	DET
ap-1257	97	2	way	way	NOUN
ap-1257	97	3	of	of	ADP
ap-1257	97	4	obtaining	obtain	VERB
ap-1257	97	5	approximate	approximate	ADJ
ap-1257	97	6	eigenvalues	eigenvalue	NOUN
ap-1257	97	7	and	and	CCONJ
ap-1257	97	8	eigenfunctions	eigenfunction	NOUN
ap-1257	97	9	is	be	AUX
ap-1257	97	10	provided	provide	VERB
ap-1257	97	11	by	by	ADP
ap-1257	97	12	a	a	DET
ap-1257	97	13	straightforward	straightforward	ADJ
ap-1257	97	14	variational	variational	ADJ
ap-1257	97	15	method	method	NOUN
ap-1257	97	16	proposed	propose	VERB
ap-1257	97	17	some	some	DET
ap-1257	97	18	time	time	NOUN
ap-1257	97	19	ago	ago	ADV
ap-1257	97	20	[	[	X
ap-1257	97	21	26	26	NUM
ap-1257	97	22	]	]	PUNCT
ap-1257	97	23	.	.	PUNCT
ap-1257	98	1	the	the	DET
ap-1257	98	2	trial	trial	NOUN
ap-1257	98	3	functions	function	NOUN
ap-1257	98	4	suitable	suitable	ADJ
ap-1257	98	5	for	for	ADP
ap-1257	98	6	the	the	DET
ap-1257	98	7	present	present	ADJ
ap-1257	98	8	model	model	NOUN
ap-1257	98	9	are	be	AUX
ap-1257	98	10	of	of	ADP
ap-1257	98	11	the	the	DET
ap-1257	98	12	form	form	NOUN
ap-1257	98	13	ϕ(q1	ϕ(q1	NOUN
ap-1257	98	14	,	,	PUNCT
ap-1257	98	15	q2	q2	NOUN
ap-1257	98	16	)	)	PUNCT
ap-1257	98	17	=	=	PUNCT
ap-1257	99	1	(	(	PUNCT
ap-1257	99	2	1	1	NUM
ap-1257	99	3	4	4	NUM
ap-1257	99	4	−	−	NOUN
ap-1257	99	5	q21	q21	NOUN
ap-1257	99	6	)	)	PUNCT
ap-1257	99	7	(	(	PUNCT
ap-1257	99	8	1	1	NUM
ap-1257	99	9	4	4	NUM
ap-1257	99	10	−	−	NOUN
ap-1257	99	11	q22	q22	NOUN
ap-1257	99	12	)	)	PUNCT
ap-1257	99	13	f(c	f(c	PROPN
ap-1257	99	14	,	,	PUNCT
ap-1257	99	15	q1	q1	PROPN
ap-1257	99	16	,	,	PUNCT
ap-1257	99	17	q2)e−a(q1−q2	q2)e−a(q1−q2	PROPN
ap-1257	99	18	)	)	PUNCT
ap-1257	99	19	2	2	NUM
ap-1257	99	20	(	(	PUNCT
ap-1257	99	21	14	14	NUM
ap-1257	99	22	)	)	PUNCT
ap-1257	99	23	where	where	SCONJ
ap-1257	99	24	c	c	NOUN
ap-1257	99	25	=	=	SYM
ap-1257	99	26	{	{	PUNCT
ap-1257	99	27	c1	c1	PROPN
ap-1257	99	28	,	,	PUNCT
ap-1257	99	29	c2	c2	PROPN
ap-1257	99	30	,	,	PUNCT
ap-1257	99	31	.	.	PUNCT
ap-1257	99	32	.	.	PUNCT
ap-1257	99	33	.	.	PUNCT
ap-1257	100	1	,	,	PUNCT
ap-1257	100	2	cn	cn	X
ap-1257	100	3	}	}	PUNCT
ap-1257	100	4	are	be	AUX
ap-1257	100	5	linear	linear	ADJ
ap-1257	100	6	variational	variational	ADJ
ap-1257	100	7	parameters	parameter	NOUN
ap-1257	100	8	,	,	PUNCT
ap-1257	100	9	which	which	PRON
ap-1257	100	10	would	would	AUX
ap-1257	100	11	give	give	VERB
ap-1257	100	12	rise	rise	NOUN
ap-1257	100	13	to	to	ADP
ap-1257	100	14	the	the	DET
ap-1257	100	15	well	well	ADV
ap-1257	100	16	known	know	VERB
ap-1257	100	17	rayleighritz	rayleighritz	NOUN
ap-1257	100	18	secular	secular	ADJ
ap-1257	100	19	equations	equation	NOUN
ap-1257	100	20	,	,	PUNCT
ap-1257	100	21	and	and	CCONJ
ap-1257	100	22	a	a	PRON
ap-1257	100	23	is	be	AUX
ap-1257	100	24	a	a	DET
ap-1257	100	25	nonlinear	nonlinear	ADJ
ap-1257	100	26	variational	variational	ADJ
ap-1257	100	27	parameter	parameter	NOUN
ap-1257	100	28	.	.	PUNCT
ap-1257	101	1	even	even	ADV
ap-1257	101	2	the	the	DET
ap-1257	101	3	simplest	simple	ADJ
ap-1257	101	4	and	and	CCONJ
ap-1257	101	5	crudest	crudest	ADJ
ap-1257	101	6	variational	variational	ADJ
ap-1257	101	7	functions	function	NOUN
ap-1257	101	8	provide	provide	VERB
ap-1257	101	9	reasonable	reasonable	ADJ
ap-1257	101	10	results	result	NOUN
ap-1257	101	11	for	for	ADP
ap-1257	101	12	all	all	DET
ap-1257	101	13	values	value	NOUN
ap-1257	101	14	of	of	ADP
ap-1257	101	15	λ	λ	NOUN
ap-1257	101	16	,	,	PUNCT
ap-1257	101	17	as	as	SCONJ
ap-1257	101	18	shown	show	VERB
ap-1257	101	19	in	in	ADP
ap-1257	101	20	sec	sec	PROPN
ap-1257	101	21	.	.	PROPN
ap-1257	101	22	5	5	NUM
ap-1257	101	23	.	.	PUNCT
ap-1257	101	24	the	the	DET
ap-1257	101	25	simplest	simple	ADJ
ap-1257	101	26	trial	trial	NOUN
ap-1257	101	27	function	function	NOUN
ap-1257	101	28	for	for	ADP
ap-1257	101	29	the	the	DET
ap-1257	101	30	ground	ground	NOUN
ap-1257	101	31	state	state	NOUN
ap-1257	101	32	of	of	ADP
ap-1257	101	33	the	the	DET
ap-1257	101	34	model	model	NOUN
ap-1257	101	35	with	with	ADP
ap-1257	101	36	β	β	X
ap-1257	101	37	<	<	X
ap-1257	101	38	1	1	NUM
ap-1257	101	39	is	be	AUX
ap-1257	101	40	ϕ(q1	ϕ(q1	NOUN
ap-1257	101	41	,	,	PUNCT
ap-1257	101	42	q2	q2	NOUN
ap-1257	101	43	)	)	PUNCT
ap-1257	102	1	=	=	PUNCT
ap-1257	102	2	(	(	PUNCT
ap-1257	102	3	1	1	NUM
ap-1257	102	4	4	4	NUM
ap-1257	102	5	−	−	NOUN
ap-1257	102	6	q21	q21	NOUN
ap-1257	102	7	)	)	PUNCT
ap-1257	102	8	(	(	PUNCT
ap-1257	102	9	1	1	NUM
ap-1257	102	10	4	4	NUM
ap-1257	102	11	−	−	NOUN
ap-1257	102	12	q22	q22	NOUN
ap-1257	102	13	)	)	PUNCT
ap-1257	102	14	e−a(q1−q2	e−a(q1−q2	NOUN
ap-1257	102	15	)	)	PUNCT
ap-1257	102	16	2	2	NUM
ap-1257	102	17	.	.	PUNCT
ap-1257	103	1	(	(	PUNCT
ap-1257	103	2	15	15	NUM
ap-1257	103	3	)	)	PUNCT
ap-1257	103	4	note	note	NOUN
ap-1257	103	5	that	that	SCONJ
ap-1257	103	6	this	this	DET
ap-1257	103	7	function	function	NOUN
ap-1257	103	8	is	be	AUX
ap-1257	103	9	the	the	DET
ap-1257	103	10	basis	basis	NOUN
ap-1257	103	11	for	for	ADP
ap-1257	103	12	the	the	DET
ap-1257	103	13	irreducible	irreducible	ADJ
ap-1257	103	14	representation	representation	NOUN
ap-1257	103	15	ag	ag	PROPN
ap-1257	103	16	.	.	PUNCT
ap-1257	104	1	we	we	PRON
ap-1257	104	2	calculate	calculate	VERB
ap-1257	104	3	w(a	w(a	PROPN
ap-1257	104	4	,	,	PUNCT
ap-1257	104	5	λ	λ	X
ap-1257	104	6	)	)	PUNCT
ap-1257	104	7	=	=	SYM
ap-1257	104	8	〈	〈	PROPN
ap-1257	104	9	ϕ	ϕ	X
ap-1257	104	10	∣∣∣ĥd	∣∣∣ĥd	NUM
ap-1257	104	11	∣∣∣ϕ	∣∣∣ϕ	NOUN
ap-1257	104	12	〉	〉	NOUN
ap-1257	104	13	/	/	SYM
ap-1257	104	14	〈	〈	PROPN
ap-1257	104	15	ϕ|ϕ	ϕ|ϕ	NOUN
ap-1257	104	16	〉	〉	PROPN
ap-1257	104	17	and	and	CCONJ
ap-1257	104	18	obtain	obtain	VERB
ap-1257	104	19	λ(a	λ(a	NOUN
ap-1257	104	20	)	)	PUNCT
ap-1257	104	21	from	from	ADP
ap-1257	104	22	the	the	DET
ap-1257	104	23	variational	variational	ADJ
ap-1257	104	24	condition	condition	NOUN
ap-1257	104	25	∂w/∂a	∂w/∂a	PUNCT
ap-1257	104	26	=	=	SYM
ap-1257	104	27	0	0	PUNCT
ap-1257	105	1	so	so	SCONJ
ap-1257	105	2	that	that	SCONJ
ap-1257	105	3	[	[	X
ap-1257	105	4	w(a	w(a	VERB
ap-1257	105	5	,	,	PUNCT
ap-1257	105	6	λ(a	λ(a	NOUN
ap-1257	105	7	)	)	PUNCT
ap-1257	105	8	)	)	PUNCT
ap-1257	105	9	,	,	PUNCT
ap-1257	105	10	λ(a	λ(a	PROPN
ap-1257	105	11	)	)	PUNCT
ap-1257	105	12	]	]	PUNCT
ap-1257	105	13	is	be	AUX
ap-1257	105	14	a	a	DET
ap-1257	105	15	suitable	suitable	ADJ
ap-1257	105	16	parametric	parametric	ADJ
ap-1257	105	17	representation	representation	NOUN
ap-1257	105	18	of	of	ADP
ap-1257	105	19	the	the	DET
ap-1257	105	20	approximate	approximate	ADJ
ap-1257	105	21	energy	energy	NOUN
ap-1257	105	22	.	.	PUNCT
ap-1257	106	1	in	in	ADP
ap-1257	106	2	this	this	DET
ap-1257	106	3	way	way	NOUN
ap-1257	106	4	we	we	PRON
ap-1257	106	5	avoid	avoid	VERB
ap-1257	106	6	the	the	DET
ap-1257	106	7	tedious	tedious	ADJ
ap-1257	106	8	numerical	numerical	ADJ
ap-1257	106	9	calculation	calculation	NOUN
ap-1257	106	10	of	of	ADP
ap-1257	106	11	a	a	PRON
ap-1257	106	12	for	for	ADP
ap-1257	106	13	each	each	DET
ap-1257	106	14	given	give	VERB
ap-1257	106	15	value	value	NOUN
ap-1257	106	16	of	of	ADP
ap-1257	106	17	λ	λ	PROPN
ap-1257	106	18	and	and	CCONJ
ap-1257	106	19	obtain	obtain	VERB
ap-1257	106	20	an	an	DET
ap-1257	106	21	analytical	analytical	ADJ
ap-1257	106	22	parametric	parametric	ADJ
ap-1257	106	23	expression	expression	NOUN
ap-1257	106	24	for	for	ADP
ap-1257	106	25	the	the	DET
ap-1257	106	26	energy	energy	NOUN
ap-1257	106	27	,	,	PUNCT
ap-1257	106	28	which	which	PRON
ap-1257	106	29	we	we	PRON
ap-1257	106	30	do	do	AUX
ap-1257	106	31	not	not	PART
ap-1257	106	32	show	show	VERB
ap-1257	106	33	here	here	ADV
ap-1257	106	34	because	because	SCONJ
ap-1257	106	35	it	it	PRON
ap-1257	106	36	is	be	AUX
ap-1257	106	37	rather	rather	ADV
ap-1257	106	38	cumbersome	cumbersome	ADJ
ap-1257	106	39	.	.	PUNCT
ap-1257	107	1	we	we	PRON
ap-1257	107	2	just	just	ADV
ap-1257	107	3	mention	mention	VERB
ap-1257	107	4	that	that	SCONJ
ap-1257	107	5	the	the	DET
ap-1257	107	6	parametric	parametric	ADJ
ap-1257	107	7	expression	expression	NOUN
ap-1257	107	8	is	be	AUX
ap-1257	107	9	valid	valid	ADJ
ap-1257	107	10	for	for	ADP
ap-1257	107	11	a	a	DET
ap-1257	107	12	>	>	X
ap-1257	107	13	a0	a0	NOUN
ap-1257	107	14	where	where	SCONJ
ap-1257	107	15	a0	a0	PROPN
ap-1257	107	16	is	be	AUX
ap-1257	107	17	the	the	DET
ap-1257	107	18	greatest	great	ADJ
ap-1257	107	19	positive	positive	ADJ
ap-1257	107	20	root	root	NOUN
ap-1257	107	21	of	of	ADP
ap-1257	107	22	λ(a	λ(a	NOUN
ap-1257	107	23	)	)	PUNCT
ap-1257	107	24	=	=	PUNCT
ap-1257	108	1	0	0	X
ap-1257	108	2	.	.	PUNCT
ap-1257	109	1	when	when	SCONJ
ap-1257	109	2	β	β	X
ap-1257	109	3	=	=	NOUN
ap-1257	109	4	1	1	NUM
ap-1257	109	5	we	we	PRON
ap-1257	109	6	choose	choose	VERB
ap-1257	109	7	the	the	DET
ap-1257	109	8	following	follow	VERB
ap-1257	109	9	trial	trial	NOUN
ap-1257	109	10	functions	function	NOUN
ap-1257	109	11	for	for	ADP
ap-1257	109	12	the	the	DET
ap-1257	109	13	lowest	low	ADJ
ap-1257	109	14	states	state	NOUN
ap-1257	109	15	of	of	ADP
ap-1257	109	16	each	each	DET
ap-1257	109	17	symmetry	symmetry	NOUN
ap-1257	109	18	type	type	NOUN
ap-1257	109	19	ϕag	ϕag	NOUN
ap-1257	109	20	(	(	PUNCT
ap-1257	109	21	q1	q1	PROPN
ap-1257	109	22	,	,	PUNCT
ap-1257	109	23	q2	q2	NOUN
ap-1257	109	24	)	)	PUNCT
ap-1257	109	25	=	=	PUNCT
ap-1257	110	1	(	(	PUNCT
ap-1257	110	2	1	1	NUM
ap-1257	110	3	4	4	NUM
ap-1257	110	4	−	−	NOUN
ap-1257	110	5	q21	q21	NOUN
ap-1257	110	6	)	)	PUNCT
ap-1257	110	7	(	(	PUNCT
ap-1257	110	8	1	1	NUM
ap-1257	110	9	4	4	NUM
ap-1257	110	10	−	−	NOUN
ap-1257	110	11	q22	q22	NOUN
ap-1257	110	12	)	)	PUNCT
ap-1257	110	13	e−a(q1−q2	e−a(q1−q2	NOUN
ap-1257	110	14	)	)	PUNCT
ap-1257	110	15	2	2	NUM
ap-1257	110	16	ϕau(q1	ϕau(q1	PROPN
ap-1257	110	17	,	,	PUNCT
ap-1257	110	18	q2	q2	NOUN
ap-1257	110	19	)	)	PUNCT
ap-1257	110	20	=	=	PUNCT
ap-1257	111	1	(	(	PUNCT
ap-1257	111	2	1	1	NUM
ap-1257	111	3	4	4	NUM
ap-1257	111	4	−	−	NOUN
ap-1257	111	5	q21	q21	NOUN
ap-1257	111	6	)	)	PUNCT
ap-1257	111	7	(	(	PUNCT
ap-1257	111	8	1	1	NUM
ap-1257	111	9	4	4	NUM
ap-1257	111	10	−	−	NOUN
ap-1257	111	11	q22	q22	NOUN
ap-1257	111	12	)	)	PUNCT
ap-1257	111	13	(	(	PUNCT
ap-1257	111	14	q1	q1	NOUN
ap-1257	111	15	+	+	CCONJ
ap-1257	111	16	q2)e−a(q1−q2	q2)e−a(q1−q2	PROPN
ap-1257	111	17	)	)	PUNCT
ap-1257	111	18	2	2	NUM
ap-1257	111	19	ϕbu(q1	ϕbu(q1	PROPN
ap-1257	111	20	,	,	PUNCT
ap-1257	111	21	q2	q2	NOUN
ap-1257	111	22	)	)	PUNCT
ap-1257	111	23	=	=	PUNCT
ap-1257	112	1	(	(	PUNCT
ap-1257	112	2	1	1	NUM
ap-1257	112	3	4	4	NUM
ap-1257	112	4	−	−	NOUN
ap-1257	112	5	q21	q21	NOUN
ap-1257	112	6	)	)	PUNCT
ap-1257	112	7	(	(	PUNCT
ap-1257	112	8	1	1	NUM
ap-1257	112	9	4	4	NUM
ap-1257	112	10	−	−	NOUN
ap-1257	112	11	q22	q22	NOUN
ap-1257	112	12	)	)	PUNCT
ap-1257	112	13	(	(	PUNCT
ap-1257	112	14	q1	q1	NOUN
ap-1257	112	15	−	−	PROPN
ap-1257	112	16	q2)e−a(q1−q2	q2)e−a(q1−q2	PROPN
ap-1257	112	17	)	)	PUNCT
ap-1257	112	18	2	2	NUM
ap-1257	112	19	ϕbg	ϕbg	NOUN
ap-1257	112	20	(	(	PUNCT
ap-1257	112	21	q1	q1	PROPN
ap-1257	112	22	,	,	PUNCT
ap-1257	112	23	q2	q2	NOUN
ap-1257	112	24	)	)	PUNCT
ap-1257	112	25	=	=	PUNCT
ap-1257	113	1	(	(	PUNCT
ap-1257	113	2	1	1	NUM
ap-1257	113	3	4	4	NUM
ap-1257	113	4	−	−	NOUN
ap-1257	113	5	q21	q21	NOUN
ap-1257	113	6	)	)	PUNCT
ap-1257	113	7	(	(	PUNCT
ap-1257	113	8	1	1	NUM
ap-1257	113	9	4	4	NUM
ap-1257	113	10	−	−	NOUN
ap-1257	113	11	q22	q22	NOUN
ap-1257	113	12	)	)	PUNCT
ap-1257	113	13	(	(	PUNCT
ap-1257	113	14	q21	q21	NOUN
ap-1257	113	15	−	−	PROPN
ap-1257	113	16	q22	q22	NOUN
ap-1257	113	17	)	)	PUNCT
ap-1257	113	18	e−a(q1−q2	e−a(q1−q2	NOUN
ap-1257	113	19	)	)	PUNCT
ap-1257	113	20	2	2	NUM
ap-1257	113	21	.	.	PUNCT
ap-1257	114	1	(	(	PUNCT
ap-1257	114	2	16	16	NUM
ap-1257	114	3	)	)	SYM
ap-1257	114	4	5	5	NUM
ap-1257	114	5	results	result	VERB
ap-1257	114	6	fig	fig	NOUN
ap-1257	114	7	.	.	PUNCT
ap-1257	115	1	1	1	NUM
ap-1257	115	2	shows	show	VERB
ap-1257	115	3	the	the	DET
ap-1257	115	4	ground	ground	NOUN
ap-1257	115	5	-	-	PUNCT
ap-1257	115	6	state	state	NOUN
ap-1257	115	7	energy	energy	NOUN
ap-1257	115	8	for	for	ADP
ap-1257	115	9	β	β	X
ap-1257	115	10	=	=	SYM
ap-1257	115	11	1/2	1/2	NUM
ap-1257	115	12	calculated	calculate	VERB
ap-1257	115	13	by	by	ADP
ap-1257	115	14	means	mean	NOUN
ap-1257	115	15	of	of	ADP
ap-1257	115	16	perturbation	perturbation	NOUN
ap-1257	115	17	theory	theory	NOUN
ap-1257	115	18	,	,	PUNCT
ap-1257	115	19	the	the	DET
ap-1257	115	20	lsf	lsf	PROPN
ap-1257	115	21	method	method	NOUN
ap-1257	115	22	and	and	CCONJ
ap-1257	115	23	the	the	DET
ap-1257	115	24	variational	variational	ADJ
ap-1257	115	25	function	function	NOUN
ap-1257	115	26	(	(	PUNCT
ap-1257	115	27	15	15	NUM
ap-1257	115	28	)	)	PUNCT
ap-1257	115	29	for	for	ADP
ap-1257	115	30	small	small	ADJ
ap-1257	115	31	and	and	CCONJ
ap-1257	115	32	moderate	moderate	ADJ
ap-1257	115	33	values	value	NOUN
ap-1257	115	34	of	of	ADP
ap-1257	115	35	λ	λ	PROPN
ap-1257	115	36	.	.	PROPN
ap-1257	115	37	fig	fig	NOUN
ap-1257	115	38	.	.	PUNCT
ap-1257	116	1	2	2	NUM
ap-1257	116	2	shows	show	VERB
ap-1257	116	3	the	the	DET
ap-1257	116	4	results	result	NOUN
ap-1257	116	5	of	of	ADP
ap-1257	116	6	the	the	DET
ap-1257	116	7	latter	latter	ADJ
ap-1257	116	8	two	two	NUM
ap-1257	116	9	approaches	approach	NOUN
ap-1257	116	10	for	for	ADP
ap-1257	116	11	a	a	DET
ap-1257	116	12	wider	wide	ADJ
ap-1257	116	13	range	range	NOUN
ap-1257	116	14	of	of	ADP
ap-1257	116	15	values	value	NOUN
ap-1257	116	16	of	of	ADP
ap-1257	116	17	λ	λ	NOUN
ap-1257	116	18	.	.	PUNCT
ap-1257	117	1	we	we	PRON
ap-1257	117	2	appreciate	appreciate	VERB
ap-1257	117	3	the	the	DET
ap-1257	117	4	accuracy	accuracy	NOUN
ap-1257	117	5	of	of	ADP
ap-1257	117	6	the	the	DET
ap-1257	117	7	energy	energy	NOUN
ap-1257	117	8	provided	provide	VERB
ap-1257	117	9	by	by	ADP
ap-1257	117	10	the	the	DET
ap-1257	117	11	simple	simple	ADJ
ap-1257	117	12	variational	variational	ADJ
ap-1257	117	13	function	function	NOUN
ap-1257	117	14	(	(	PUNCT
ap-1257	117	15	15	15	NUM
ap-1257	117	16	)	)	PUNCT
ap-1257	117	17	for	for	ADP
ap-1257	117	18	all	all	DET
ap-1257	117	19	values	value	NOUN
ap-1257	117	20	of	of	ADP
ap-1257	117	21	λ	λ	PROPN
ap-1257	117	22	.	.	PUNCT
ap-1257	118	1	the	the	DET
ap-1257	118	2	reader	reader	NOUN
ap-1257	118	3	will	will	AUX
ap-1257	118	4	find	find	VERB
ap-1257	118	5	all	all	DET
ap-1257	118	6	the	the	DET
ap-1257	118	7	necessary	necessary	ADJ
ap-1257	118	8	details	detail	NOUN
ap-1257	118	9	about	about	ADP
ap-1257	118	10	the	the	DET
ap-1257	118	11	lsf	lsf	PROPN
ap-1257	118	12	collocation	collocation	NOUN
ap-1257	118	13	method	method	NOUN
ap-1257	118	14	elsewhere	elsewhere	ADV
ap-1257	118	15	[	[	X
ap-1257	118	16	25	25	NUM
ap-1257	118	17	]	]	PUNCT
ap-1257	118	18	.	.	PUNCT
ap-1257	119	1	here	here	ADV
ap-1257	119	2	we	we	PRON
ap-1257	119	3	just	just	ADV
ap-1257	119	4	mention	mention	VERB
ap-1257	119	5	that	that	SCONJ
ap-1257	119	6	a	a	DET
ap-1257	119	7	grid	grid	NOUN
ap-1257	119	8	with	with	ADP
ap-1257	119	9	n	n	NOUN
ap-1257	119	10	=	=	SYM
ap-1257	119	11	60	60	NUM
ap-1257	119	12	was	be	AUX
ap-1257	119	13	sufficient	sufficient	ADJ
ap-1257	119	14	for	for	ADP
ap-1257	119	15	the	the	DET
ap-1257	119	16	calculations	calculation	NOUN
ap-1257	119	17	carried	carry	VERB
ap-1257	119	18	out	out	ADP
ap-1257	119	19	in	in	ADP
ap-1257	119	20	this	this	DET
ap-1257	119	21	paper	paper	NOUN
ap-1257	119	22	.	.	PUNCT
ap-1257	120	1	fig	fig	NOUN
ap-1257	120	2	.	.	PUNCT
ap-1257	121	1	3	3	NUM
ap-1257	121	2	shows	show	VERB
ap-1257	121	3	that	that	SCONJ
ap-1257	121	4	ε(λ)/	ε(λ)/	NOUN
ap-1257	121	5	√	√	ADP
ap-1257	121	6	λ	λ	NOUN
ap-1257	121	7	calculated	calculate	VERB
ap-1257	121	8	by	by	ADP
ap-1257	121	9	the	the	DET
ap-1257	121	10	same	same	ADJ
ap-1257	121	11	two	two	NUM
ap-1257	121	12	methods	method	NOUN
ap-1257	121	13	for	for	ADP
ap-1257	121	14	β	β	X
ap-1257	121	15	=	=	SYM
ap-1257	121	16	1/2	1/2	NUM
ap-1257	121	17	approaches	approach	NOUN
ap-1257	121	18	√	√	NOUN
ap-1257	121	19	3/8	3/8	NUM
ap-1257	121	20	as	as	SCONJ
ap-1257	121	21	suggested	suggest	VERB
ap-1257	121	22	by	by	ADP
ap-1257	121	23	equation	equation	NOUN
ap-1257	121	24	(	(	PUNCT
ap-1257	121	25	11	11	NUM
ap-1257	121	26	)	)	PUNCT
ap-1257	121	27	.	.	PUNCT
ap-1257	122	1	fig	fig	NOUN
ap-1257	122	2	.	.	PUNCT
ap-1257	123	1	4	4	NUM
ap-1257	123	2	shows	show	VERB
ap-1257	123	3	the	the	DET
ap-1257	123	4	first	first	ADJ
ap-1257	123	5	six	six	NUM
ap-1257	123	6	eigenvalues	eigenvalue	NOUN
ap-1257	123	7	ε(λ	ε(λ	NOUN
ap-1257	123	8	)	)	PUNCT
ap-1257	123	9	for	for	ADP
ap-1257	123	10	β	β	X
ap-1257	123	11	=	=	SYM
ap-1257	123	12	1/2	1/2	NUM
ap-1257	123	13	calculated	calculate	VERB
ap-1257	123	14	by	by	ADP
ap-1257	123	15	means	mean	NOUN
ap-1257	123	16	of	of	ADP
ap-1257	123	17	the	the	DET
ap-1257	123	18	lsf	lsf	PROPN
ap-1257	123	19	collocation	collocation	NOUN
ap-1257	123	20	method	method	NOUN
ap-1257	123	21	.	.	PUNCT
ap-1257	124	1	the	the	DET
ap-1257	124	2	level	level	NOUN
ap-1257	124	3	order	order	NOUN
ap-1257	124	4	to	to	ADP
ap-1257	124	5	the	the	DET
ap-1257	124	6	left	left	NOUN
ap-1257	124	7	of	of	ADP
ap-1257	124	8	the	the	DET
ap-1257	124	9	crossings	crossing	NOUN
ap-1257	124	10	20	20	NUM
ap-1257	124	11	acta	acta	PROPN
ap-1257	124	12	polytechnica	polytechnica	PROPN
ap-1257	124	13	vol	vol	NOUN
ap-1257	124	14	.	.	PROPN
ap-1257	125	1	50	50	NUM
ap-1257	125	2	no	no	NOUN
ap-1257	125	3	.	.	PUNCT
ap-1257	126	1	5/2010	5/2010	NUM
ap-1257	126	2	0	0	NUM
ap-1257	126	3	50	50	NUM
ap-1257	126	4	100	100	NUM
ap-1257	126	5	150	150	NUM
ap-1257	126	6	200	200	NUM
ap-1257	126	7	λ	λ	NOUN
ap-1257	126	8	8	8	NUM
ap-1257	126	9	10	10	NUM
ap-1257	126	10	12	12	NUM
ap-1257	126	11	14	14	NUM
ap-1257	126	12	ε	ε	PROPN
ap-1257	126	13	fig	fig	NOUN
ap-1257	126	14	.	.	PUNCT
ap-1257	127	1	1	1	NUM
ap-1257	127	2	:	:	PUNCT
ap-1257	127	3	perturbation	perturbation	NOUN
ap-1257	127	4	theory	theory	NOUN
ap-1257	127	5	(	(	PUNCT
ap-1257	127	6	dotted	dotted	ADJ
ap-1257	127	7	line	line	NOUN
ap-1257	127	8	)	)	PUNCT
ap-1257	127	9	,	,	PUNCT
ap-1257	127	10	lsf	lsf	X
ap-1257	127	11	(	(	PUNCT
ap-1257	127	12	points	point	NOUN
ap-1257	127	13	)	)	PUNCT
ap-1257	127	14	and	and	CCONJ
ap-1257	127	15	variational	variational	ADJ
ap-1257	127	16	(	(	PUNCT
ap-1257	127	17	solid	solid	ADJ
ap-1257	127	18	line	line	NOUN
ap-1257	127	19	)	)	PUNCT
ap-1257	127	20	calculation	calculation	NOUN
ap-1257	127	21	of	of	ADP
ap-1257	127	22	the	the	DET
ap-1257	127	23	ground	ground	NOUN
ap-1257	127	24	-	-	PUNCT
ap-1257	127	25	state	state	NOUN
ap-1257	127	26	energy	energy	NOUN
ap-1257	127	27	ε(λ	ε(λ	NOUN
ap-1257	127	28	)	)	PUNCT
ap-1257	127	29	for	for	ADP
ap-1257	127	30	β	β	X
ap-1257	127	31	=	=	SYM
ap-1257	127	32	1/2	1/2	NUM
ap-1257	127	33	0	0	NUM
ap-1257	127	34	500	500	NUM
ap-1257	127	35	1000	1000	NUM
ap-1257	127	36	1500	1500	NUM
ap-1257	127	37	2000	2000	NUM
ap-1257	127	38	λ	λ	NOUN
ap-1257	127	39	10	10	NUM
ap-1257	127	40	15	15	NUM
ap-1257	127	41	20	20	NUM
ap-1257	127	42	25	25	NUM
ap-1257	127	43	30	30	NUM
ap-1257	127	44	ε	ε	PROPN
ap-1257	127	45	fig	fig	NOUN
ap-1257	127	46	.	.	PUNCT
ap-1257	128	1	2	2	NUM
ap-1257	128	2	:	:	PUNCT
ap-1257	128	3	variational	variational	ADJ
ap-1257	128	4	(	(	PUNCT
ap-1257	128	5	line	line	NOUN
ap-1257	128	6	)	)	PUNCT
ap-1257	128	7	and	and	CCONJ
ap-1257	128	8	lsf	lsf	PROPN
ap-1257	128	9	(	(	PUNCT
ap-1257	128	10	points	point	NOUN
ap-1257	128	11	)	)	PUNCT
ap-1257	128	12	calculation	calculation	NOUN
ap-1257	128	13	of	of	ADP
ap-1257	128	14	the	the	DET
ap-1257	128	15	ground	ground	NOUN
ap-1257	128	16	-	-	PUNCT
ap-1257	128	17	state	state	NOUN
ap-1257	128	18	ε(λ	ε(λ	NOUN
ap-1257	128	19	)	)	PUNCT
ap-1257	128	20	for	for	ADP
ap-1257	128	21	β	β	X
ap-1257	128	22	=	=	SYM
ap-1257	128	23	1/2	1/2	NUM
ap-1257	128	24	10	10	NUM
ap-1257	128	25	-1	-1	SYM
ap-1257	129	1	10	10	NUM
ap-1257	129	2	0	0	NUM
ap-1257	129	3	10	10	NUM
ap-1257	129	4	1	1	NUM
ap-1257	129	5	10	10	NUM
ap-1257	129	6	2	2	NUM
ap-1257	129	7	10	10	NUM
ap-1257	129	8	3	3	NUM
ap-1257	129	9	10	10	NUM
ap-1257	129	10	4	4	NUM
ap-1257	129	11	10	10	NUM
ap-1257	129	12	5	5	NUM
ap-1257	129	13	10	10	NUM
ap-1257	129	14	6	6	NUM
ap-1257	129	15	λ	λ	NOUN
ap-1257	129	16	0	0	NUM
ap-1257	129	17	1	1	NUM
ap-1257	129	18	2	2	NUM
ap-1257	129	19	3	3	NUM
ap-1257	129	20	4	4	NUM
ap-1257	129	21	5	5	NUM
ap-1257	129	22	6	6	NUM
ap-1257	129	23	7	7	NUM
ap-1257	129	24	8	8	NUM
ap-1257	129	25	9	9	NUM
ap-1257	129	26	10	10	NUM
ap-1257	129	27	ε	ε	PROPN
ap-1257	129	28	/λ	/λ	VERB
ap-1257	129	29	1/	1/	NUM
ap-1257	129	30	2	2	NUM
ap-1257	129	31	fig	fig	NOUN
ap-1257	129	32	.	.	PUNCT
ap-1257	130	1	3	3	NUM
ap-1257	130	2	:	:	PUNCT
ap-1257	130	3	variational	variational	ADJ
ap-1257	130	4	(	(	PUNCT
ap-1257	130	5	line	line	NOUN
ap-1257	130	6	)	)	PUNCT
ap-1257	130	7	and	and	CCONJ
ap-1257	130	8	lsf	lsf	PROPN
ap-1257	130	9	(	(	PUNCT
ap-1257	130	10	points	point	NOUN
ap-1257	130	11	)	)	PUNCT
ap-1257	130	12	calculation	calculation	NOUN
ap-1257	130	13	of	of	ADP
ap-1257	130	14	the	the	DET
ap-1257	130	15	ground	ground	NOUN
ap-1257	130	16	-	-	PUNCT
ap-1257	130	17	state	state	NOUN
ap-1257	130	18	ε(λ)/	ε(λ)/	NOUN
ap-1257	130	19	√	√	ADP
ap-1257	130	20	λ	λ	NOUN
ap-1257	130	21	for	for	ADP
ap-1257	130	22	β	β	X
ap-1257	130	23	=	=	SYM
ap-1257	130	24	1/2	1/2	NUM
ap-1257	130	25	.	.	PUNCT
ap-1257	131	1	the	the	DET
ap-1257	131	2	horizontal	horizontal	ADJ
ap-1257	131	3	line	line	NOUN
ap-1257	131	4	marks	mark	VERB
ap-1257	131	5	the	the	DET
ap-1257	131	6	limit	limit	NOUN
ap-1257	131	7	√	√	NOUN
ap-1257	131	8	3/8	3/8	NUM
ap-1257	131	9	21	21	NUM
ap-1257	131	10	acta	acta	PROPN
ap-1257	131	11	polytechnica	polytechnica	PROPN
ap-1257	131	12	vol	vol	NOUN
ap-1257	131	13	.	.	PROPN
ap-1257	132	1	50	50	NUM
ap-1257	132	2	no	no	NOUN
ap-1257	132	3	.	.	PUNCT
ap-1257	133	1	5/2010	5/2010	NUM
ap-1257	133	2	0	0	NUM
ap-1257	134	1	200	200	NUM
ap-1257	134	2	400	400	NUM
ap-1257	134	3	600	600	NUM
ap-1257	134	4	800	800	NUM
ap-1257	134	5	1000	1000	NUM
ap-1257	134	6	λ	λ	NOUN
ap-1257	134	7	0	0	NUM
ap-1257	134	8	10	10	NUM
ap-1257	134	9	20	20	NUM
ap-1257	134	10	30	30	NUM
ap-1257	134	11	40	40	NUM
ap-1257	134	12	50	50	NUM
ap-1257	134	13	60	60	NUM
ap-1257	134	14	70	70	NUM
ap-1257	134	15	80	80	NUM
ap-1257	134	16	ε	ε	PROPN
ap-1257	134	17	fig	fig	NOUN
ap-1257	134	18	.	.	PUNCT
ap-1257	135	1	4	4	NUM
ap-1257	135	2	:	:	PUNCT
ap-1257	135	3	first	first	ADJ
ap-1257	135	4	six	six	NUM
ap-1257	135	5	eigenvalues	eigenvalue	NOUN
ap-1257	135	6	for	for	ADP
ap-1257	135	7	β	β	X
ap-1257	135	8	=	=	SYM
ap-1257	135	9	1/2	1/2	NUM
ap-1257	135	10	calculated	calculate	VERB
ap-1257	135	11	by	by	ADP
ap-1257	135	12	means	mean	NOUN
ap-1257	135	13	of	of	ADP
ap-1257	135	14	the	the	DET
ap-1257	135	15	lsf	lsf	PROPN
ap-1257	135	16	method	method	PROPN
ap-1257	135	17	0	0	NUM
ap-1257	135	18	50	50	NUM
ap-1257	135	19	100	100	NUM
ap-1257	135	20	150	150	NUM
ap-1257	135	21	200	200	NUM
ap-1257	135	22	λ	λ	NOUN
ap-1257	135	23	0	0	NUM
ap-1257	135	24	10	10	NUM
ap-1257	135	25	20	20	NUM
ap-1257	135	26	30	30	NUM
ap-1257	135	27	40	40	NUM
ap-1257	135	28	50	50	NUM
ap-1257	135	29	60	60	NUM
ap-1257	135	30	70	70	NUM
ap-1257	135	31	ε	ε	PROPN
ap-1257	135	32	fig	fig	NOUN
ap-1257	135	33	.	.	PUNCT
ap-1257	136	1	5	5	NUM
ap-1257	136	2	:	:	PUNCT
ap-1257	136	3	first	first	ADJ
ap-1257	136	4	six	six	NUM
ap-1257	136	5	eigenvalues	eigenvalue	NOUN
ap-1257	136	6	for	for	ADP
ap-1257	136	7	β	β	NOUN
ap-1257	136	8	=	=	SYM
ap-1257	136	9	1	1	X
ap-1257	136	10	.	.	PUNCT
ap-1257	136	11	circles	circle	NOUN
ap-1257	136	12	,	,	PUNCT
ap-1257	136	13	dotted	dotted	ADJ
ap-1257	136	14	line	line	NOUN
ap-1257	136	15	and	and	CCONJ
ap-1257	136	16	solid	solid	ADJ
ap-1257	136	17	line	line	NOUN
ap-1257	136	18	correspond	correspond	NOUN
ap-1257	136	19	to	to	ADP
ap-1257	136	20	the	the	DET
ap-1257	136	21	lsf	lsf	PROPN
ap-1257	136	22	collocation	collocation	NOUN
ap-1257	136	23	approach	approach	NOUN
ap-1257	136	24	,	,	PUNCT
ap-1257	136	25	perturbation	perturbation	NOUN
ap-1257	136	26	theory	theory	NOUN
ap-1257	136	27	and	and	CCONJ
ap-1257	136	28	variation	variation	NOUN
ap-1257	136	29	method	method	NOUN
ap-1257	136	30	,	,	PUNCT
ap-1257	136	31	respectively	respectively	ADV
ap-1257	136	32	.	.	PUNCT
ap-1257	137	1	the	the	DET
ap-1257	137	2	level	level	NOUN
ap-1257	137	3	order	order	NOUN
ap-1257	137	4	is	be	AUX
ap-1257	137	5	ag	ag	PROPN
ap-1257	137	6	<	<	X
ap-1257	137	7	au	au	X
ap-1257	137	8	<	<	X
ap-1257	137	9	bu	bu	X
ap-1257	137	10	<	<	X
ap-1257	137	11	2ag	2ag	NOUN
ap-1257	137	12	<	<	X
ap-1257	137	13	3ag	3ag	ADJ
ap-1257	137	14	<	<	X
ap-1257	137	15	bg	bg	PROPN
ap-1257	137	16	10	10	NUM
ap-1257	137	17	0	0	NUM
ap-1257	137	18	10	10	NUM
ap-1257	137	19	1	1	NUM
ap-1257	137	20	10	10	NUM
ap-1257	137	21	2	2	NUM
ap-1257	137	22	10	10	NUM
ap-1257	137	23	3	3	NUM
ap-1257	137	24	10	10	NUM
ap-1257	137	25	4	4	NUM
ap-1257	137	26	10	10	NUM
ap-1257	137	27	5	5	NUM
ap-1257	137	28	10	10	NUM
ap-1257	137	29	6	6	NUM
ap-1257	137	30	λ	λ	NOUN
ap-1257	137	31	1	1	NUM
ap-1257	137	32	10	10	NUM
ap-1257	137	33	100	100	NUM
ap-1257	137	34	ε	ε	PROPN
ap-1257	137	35	/	/	SYM
ap-1257	137	36	λ	λ	PROPN
ap-1257	137	37	1/	1/	NUM
ap-1257	137	38	2	2	NUM
ap-1257	137	39	a	a	DET
ap-1257	137	40	g	g	NOUN
ap-1257	137	41	a	a	DET
ap-1257	137	42	u	u	NOUN
ap-1257	137	43	b	b	PROPN
ap-1257	137	44	u	u	PROPN
ap-1257	137	45	b	b	PROPN
ap-1257	137	46	g	g	PROPN
ap-1257	137	47	fig	fig	NOUN
ap-1257	137	48	.	.	PUNCT
ap-1257	138	1	6	6	NUM
ap-1257	138	2	:	:	PUNCT
ap-1257	138	3	variational	variational	ADJ
ap-1257	138	4	(	(	PUNCT
ap-1257	138	5	solid	solid	ADJ
ap-1257	138	6	line	line	NOUN
ap-1257	138	7	)	)	PUNCT
ap-1257	138	8	and	and	CCONJ
ap-1257	138	9	lsf	lsf	PROPN
ap-1257	138	10	(	(	PUNCT
ap-1257	138	11	symbols	symbol	NOUN
ap-1257	138	12	)	)	PUNCT
ap-1257	138	13	calculation	calculation	NOUN
ap-1257	138	14	of	of	ADP
ap-1257	138	15	ε(λ)/	ε(λ)/	X
ap-1257	138	16	√	√	ADP
ap-1257	138	17	λ	λ	NOUN
ap-1257	138	18	for	for	ADP
ap-1257	138	19	β	β	X
ap-1257	138	20	=	=	SYM
ap-1257	138	21	1	1	X
ap-1257	138	22	.	.	PUNCT
ap-1257	139	1	the	the	DET
ap-1257	139	2	horizontal	horizontal	ADJ
ap-1257	139	3	lines	line	NOUN
ap-1257	139	4	mark	mark	VERB
ap-1257	139	5	the	the	DET
ap-1257	139	6	limits	limit	NOUN
ap-1257	139	7	1/	1/	NUM
ap-1257	139	8	√	√	NUM
ap-1257	139	9	2	2	NUM
ap-1257	139	10	and	and	CCONJ
ap-1257	139	11	3/	3/	NUM
ap-1257	139	12	√	√	NUM
ap-1257	139	13	2	2	NUM
ap-1257	139	14	22	22	NUM
ap-1257	139	15	acta	acta	PROPN
ap-1257	139	16	polytechnica	polytechnica	PROPN
ap-1257	139	17	vol	vol	NOUN
ap-1257	139	18	.	.	PROPN
ap-1257	140	1	50	50	NUM
ap-1257	140	2	no	no	NOUN
ap-1257	140	3	.	.	PUNCT
ap-1257	141	1	5/2010	5/2010	PROPN
ap-1257	141	2	is	be	AUX
ap-1257	141	3	ε1(ag	ε1(ag	NUM
ap-1257	141	4	)	)	PUNCT
ap-1257	141	5	<	<	X
ap-1257	141	6	ε1(au	ε1(au	PROPN
ap-1257	141	7	)	)	PUNCT
ap-1257	141	8	<	<	X
ap-1257	141	9	ε2(au	ε2(au	PROPN
ap-1257	141	10	)	)	PUNCT
ap-1257	141	11	<	<	X
ap-1257	141	12	ε2(ag	ε2(ag	NUM
ap-1257	141	13	)	)	PUNCT
ap-1257	141	14	<	<	X
ap-1257	141	15	ε3(ag	ε3(ag	PROPN
ap-1257	141	16	)	)	PUNCT
ap-1257	141	17	<	<	X
ap-1257	141	18	ε3(au	ε3(au	PROPN
ap-1257	141	19	)	)	PUNCT
ap-1257	141	20	.	.	PUNCT
ap-1257	142	1	note	note	VERB
ap-1257	142	2	the	the	DET
ap-1257	142	3	crossings	crossing	NOUN
ap-1257	142	4	between	between	ADP
ap-1257	142	5	states	state	NOUN
ap-1257	142	6	of	of	ADP
ap-1257	142	7	different	different	ADJ
ap-1257	142	8	symmetry	symmetry	NOUN
ap-1257	142	9	and	and	CCONJ
ap-1257	142	10	the	the	DET
ap-1257	142	11	avoided	avoid	VERB
ap-1257	142	12	crossing	crossing	NOUN
ap-1257	142	13	between	between	ADP
ap-1257	142	14	the	the	DET
ap-1257	142	15	states	state	NOUN
ap-1257	142	16	2au	2au	ADJ
ap-1257	142	17	and	and	CCONJ
ap-1257	142	18	3au	3au	ADJ
ap-1257	142	19	.	.	PUNCT
ap-1257	143	1	fig	fig	NOUN
ap-1257	143	2	.	.	PUNCT
ap-1257	144	1	5	5	NUM
ap-1257	144	2	shows	show	VERB
ap-1257	144	3	the	the	DET
ap-1257	144	4	first	first	ADJ
ap-1257	144	5	six	six	NUM
ap-1257	144	6	eigenvalues	eigenvalue	NOUN
ap-1257	144	7	for	for	ADP
ap-1257	144	8	β	β	NOUN
ap-1257	144	9	=	=	SYM
ap-1257	144	10	1	1	NUM
ap-1257	144	11	calculated	calculate	VERB
ap-1257	144	12	by	by	ADP
ap-1257	144	13	means	mean	NOUN
ap-1257	144	14	of	of	ADP
ap-1257	144	15	perturbation	perturbation	NOUN
ap-1257	144	16	theory	theory	NOUN
ap-1257	144	17	,	,	PUNCT
ap-1257	144	18	the	the	DET
ap-1257	144	19	lsf	lsf	PROPN
ap-1257	144	20	method	method	NOUN
ap-1257	144	21	and	and	CCONJ
ap-1257	144	22	the	the	DET
ap-1257	144	23	variational	variational	ADJ
ap-1257	144	24	functions	function	NOUN
ap-1257	144	25	(	(	PUNCT
ap-1257	144	26	16	16	NUM
ap-1257	144	27	)	)	PUNCT
ap-1257	144	28	for	for	ADP
ap-1257	144	29	small	small	ADJ
ap-1257	144	30	values	value	NOUN
ap-1257	144	31	of	of	ADP
ap-1257	144	32	λ	λ	PROPN
ap-1257	144	33	.	.	PUNCT
ap-1257	145	1	the	the	DET
ap-1257	145	2	energy	energy	NOUN
ap-1257	145	3	order	order	NOUN
ap-1257	145	4	is	be	AUX
ap-1257	145	5	ε1(ag	ε1(ag	NUM
ap-1257	145	6	)	)	PUNCT
ap-1257	145	7	<	<	X
ap-1257	145	8	ε1(au	ε1(au	PROPN
ap-1257	145	9	)	)	PUNCT
ap-1257	145	10	<	<	X
ap-1257	145	11	ε1(bu	ε1(bu	PROPN
ap-1257	145	12	)	)	PUNCT
ap-1257	145	13	<	<	X
ap-1257	145	14	ε2(ag	ε2(ag	NUM
ap-1257	145	15	)	)	PUNCT
ap-1257	145	16	<	<	X
ap-1257	145	17	ε3(ag	ε3(ag	PROPN
ap-1257	145	18	)	)	PUNCT
ap-1257	145	19	<	<	X
ap-1257	145	20	ε1(bg	ε1(bg	NOUN
ap-1257	145	21	)	)	PUNCT
ap-1257	145	22	and	and	CCONJ
ap-1257	145	23	we	we	PRON
ap-1257	145	24	appreciate	appreciate	VERB
ap-1257	145	25	the	the	DET
ap-1257	145	26	splitting	splitting	NOUN
ap-1257	145	27	of	of	ADP
ap-1257	145	28	the	the	DET
ap-1257	145	29	energy	energy	NOUN
ap-1257	145	30	levels	level	NOUN
ap-1257	145	31	ε3(ag	ε3(ag	NOUN
ap-1257	145	32	)	)	PUNCT
ap-1257	145	33	and	and	CCONJ
ap-1257	145	34	ε1(bg	ε1(bg	NOUN
ap-1257	145	35	)	)	PUNCT
ap-1257	145	36	that	that	PRON
ap-1257	145	37	does	do	AUX
ap-1257	145	38	not	not	PART
ap-1257	145	39	take	take	VERB
ap-1257	145	40	place	place	NOUN
ap-1257	145	41	at	at	ADP
ap-1257	145	42	the	the	DET
ap-1257	145	43	first	first	ADJ
ap-1257	145	44	order	order	NOUN
ap-1257	145	45	of	of	ADP
ap-1257	145	46	perturbation	perturbation	NOUN
ap-1257	145	47	theory	theory	NOUN
ap-1257	145	48	,	,	PUNCT
ap-1257	145	49	as	as	SCONJ
ap-1257	145	50	discussed	discuss	VERB
ap-1257	145	51	in	in	ADP
ap-1257	145	52	sec	sec	PROPN
ap-1257	145	53	.	.	PROPN
ap-1257	146	1	3	3	X
ap-1257	146	2	.	.	X
ap-1257	146	3	finally	finally	ADV
ap-1257	146	4	,	,	PUNCT
ap-1257	146	5	fig	fig	NOUN
ap-1257	146	6	.	.	PUNCT
ap-1257	146	7	6	6	NUM
ap-1257	146	8	shows	show	VERB
ap-1257	146	9	ε(λ)/	ε(λ)/	NOUN
ap-1257	146	10	√	√	ADP
ap-1257	146	11	λ	λ	NOUN
ap-1257	146	12	for	for	ADP
ap-1257	146	13	sufficiently	sufficiently	ADV
ap-1257	146	14	large	large	ADJ
ap-1257	146	15	values	value	NOUN
ap-1257	146	16	of	of	ADP
ap-1257	146	17	λ	λ	PROPN
ap-1257	146	18	.	.	PUNCT
ap-1257	147	1	we	we	PRON
ap-1257	147	2	appreciate	appreciate	VERB
ap-1257	147	3	that	that	SCONJ
ap-1257	147	4	the	the	DET
ap-1257	147	5	four	four	NUM
ap-1257	147	6	simple	simple	ADJ
ap-1257	147	7	variational	variational	ADJ
ap-1257	147	8	functions	function	NOUN
ap-1257	147	9	(	(	PUNCT
ap-1257	147	10	16	16	NUM
ap-1257	147	11	)	)	PUNCT
ap-1257	147	12	are	be	AUX
ap-1257	147	13	remarkably	remarkably	ADV
ap-1257	147	14	accurate	accurate	ADJ
ap-1257	147	15	and	and	CCONJ
ap-1257	147	16	that	that	SCONJ
ap-1257	147	17	ε(λ)/	ε(λ)/	X
ap-1257	147	18	√	√	ADP
ap-1257	147	19	λ	λ	X
ap-1257	147	20	→	→	SYM
ap-1257	147	21	1/	1/	NUM
ap-1257	147	22	√	√	NUM
ap-1257	147	23	2	2	NUM
ap-1257	147	24	for	for	ADP
ap-1257	147	25	the	the	DET
ap-1257	147	26	first	first	ADJ
ap-1257	147	27	two	two	NUM
ap-1257	147	28	states	state	NOUN
ap-1257	147	29	of	of	ADP
ap-1257	147	30	symmetry	symmetry	NOUN
ap-1257	147	31	ag	ag	PROPN
ap-1257	147	32	and	and	CCONJ
ap-1257	147	33	au	au	ADJ
ap-1257	147	34	and	and	CCONJ
ap-1257	147	35	ε(λ)/	ε(λ)/	NOUN
ap-1257	147	36	√	√	ADP
ap-1257	147	37	λ	λ	X
ap-1257	147	38	→	→	SYM
ap-1257	147	39	3/	3/	NUM
ap-1257	147	40	√	√	NUM
ap-1257	147	41	2	2	NUM
ap-1257	147	42	for	for	ADP
ap-1257	147	43	the	the	DET
ap-1257	147	44	next	next	ADJ
ap-1257	147	45	two	two	NUM
ap-1257	147	46	ones	one	NOUN
ap-1257	147	47	of	of	ADP
ap-1257	147	48	symmetry	symmetry	NOUN
ap-1257	147	49	bu	bu	PROPN
ap-1257	147	50	and	and	CCONJ
ap-1257	147	51	bg	bg	PROPN
ap-1257	147	52	.	.	PUNCT
ap-1257	148	1	these	these	DET
ap-1257	148	2	results	result	NOUN
ap-1257	148	3	are	be	AUX
ap-1257	148	4	consistent	consistent	ADJ
ap-1257	148	5	with	with	ADP
ap-1257	148	6	equation	equation	NOUN
ap-1257	148	7	(	(	PUNCT
ap-1257	148	8	13	13	NUM
ap-1257	148	9	)	)	PUNCT
ap-1257	148	10	,	,	PUNCT
ap-1257	148	11	which	which	PRON
ap-1257	148	12	suggests	suggest	VERB
ap-1257	148	13	that	that	SCONJ
ap-1257	148	14	the	the	DET
ap-1257	148	15	energies	energy	NOUN
ap-1257	148	16	of	of	ADP
ap-1257	148	17	the	the	DET
ap-1257	148	18	states	state	NOUN
ap-1257	148	19	with	with	ADP
ap-1257	148	20	symmetry	symmetry	NOUN
ap-1257	148	21	a	a	PRON
ap-1257	148	22	and	and	CCONJ
ap-1257	148	23	b	b	NOUN
ap-1257	148	24	approach	approach	NOUN
ap-1257	148	25	√	√	ADP
ap-1257	148	26	2(2v	2(2v	NUM
ap-1257	148	27	+	+	NOUN
ap-1257	148	28	1/2	1/2	NUM
ap-1257	148	29	)	)	PUNCT
ap-1257	148	30	and	and	CCONJ
ap-1257	148	31	√	√	ADP
ap-1257	148	32	2(2v	2(2v	NUM
ap-1257	148	33	+	+	SYM
ap-1257	148	34	3/2	3/2	NUM
ap-1257	148	35	)	)	PUNCT
ap-1257	148	36	,	,	PUNCT
ap-1257	148	37	respectively	respectively	ADV
ap-1257	148	38	.	.	PUNCT
ap-1257	149	1	in	in	ADP
ap-1257	149	2	fact	fact	NOUN
ap-1257	149	3	,	,	PUNCT
ap-1257	149	4	fig	fig	NOUN
ap-1257	149	5	.	.	PUNCT
ap-1257	150	1	6	6	NUM
ap-1257	150	2	shows	show	VERB
ap-1257	150	3	four	four	NUM
ap-1257	150	4	particular	particular	ADJ
ap-1257	150	5	examples	example	NOUN
ap-1257	150	6	with	with	ADP
ap-1257	150	7	v	v	NOUN
ap-1257	150	8	=	=	SYM
ap-1257	150	9	0	0	NUM
ap-1257	150	10	.	.	NOUN
ap-1257	150	11	6	6	NUM
ap-1257	150	12	conclusions	conclusion	NOUN
ap-1257	150	13	the	the	DET
ap-1257	150	14	model	model	NOUN
ap-1257	150	15	discussed	discuss	VERB
ap-1257	150	16	in	in	ADP
ap-1257	150	17	this	this	DET
ap-1257	150	18	paper	paper	NOUN
ap-1257	150	19	is	be	AUX
ap-1257	150	20	different	different	ADJ
ap-1257	150	21	from	from	ADP
ap-1257	150	22	those	those	PRON
ap-1257	150	23	considered	consider	VERB
ap-1257	150	24	before	before	ADP
ap-1257	150	25	[	[	X
ap-1257	150	26	1	1	NUM
ap-1257	150	27	,	,	PUNCT
ap-1257	150	28	2	2	NUM
ap-1257	150	29	,	,	PUNCT
ap-1257	150	30	3	3	NUM
ap-1257	150	31	,	,	PUNCT
ap-1257	150	32	4	4	NUM
ap-1257	150	33	,	,	PUNCT
ap-1257	150	34	5	5	NUM
ap-1257	150	35	,	,	PUNCT
ap-1257	150	36	6	6	NUM
ap-1257	150	37	,	,	PUNCT
ap-1257	150	38	7	7	NUM
ap-1257	150	39	,	,	PUNCT
ap-1257	150	40	8	8	NUM
ap-1257	150	41	,	,	PUNCT
ap-1257	150	42	9	9	NUM
ap-1257	150	43	,	,	PUNCT
ap-1257	150	44	10	10	NUM
ap-1257	150	45	,	,	PUNCT
ap-1257	150	46	11	11	NUM
ap-1257	150	47	,	,	PUNCT
ap-1257	150	48	12	12	NUM
ap-1257	150	49	,	,	PUNCT
ap-1257	150	50	13	13	NUM
ap-1257	150	51	,	,	PUNCT
ap-1257	150	52	14	14	NUM
ap-1257	150	53	,	,	PUNCT
ap-1257	150	54	15	15	NUM
ap-1257	150	55	,	,	PUNCT
ap-1257	150	56	16	16	NUM
ap-1257	150	57	,	,	PUNCT
ap-1257	150	58	17	17	NUM
ap-1257	150	59	,	,	PUNCT
ap-1257	150	60	18	18	NUM
ap-1257	150	61	,	,	PUNCT
ap-1257	150	62	19	19	NUM
ap-1257	150	63	,	,	PUNCT
ap-1257	150	64	20	20	NUM
ap-1257	150	65	,	,	PUNCT
ap-1257	150	66	21	21	NUM
ap-1257	150	67	,	,	PUNCT
ap-1257	150	68	22	22	NUM
ap-1257	150	69	,	,	PUNCT
ap-1257	150	70	23	23	NUM
ap-1257	150	71	]	]	PUNCT
ap-1257	150	72	,	,	PUNCT
ap-1257	150	73	because	because	SCONJ
ap-1257	150	74	in	in	ADP
ap-1257	150	75	the	the	DET
ap-1257	150	76	present	present	ADJ
ap-1257	150	77	case	case	NOUN
ap-1257	150	78	the	the	DET
ap-1257	150	79	linear	linear	ADJ
ap-1257	150	80	force	force	NOUN
ap-1257	150	81	is	be	AUX
ap-1257	150	82	due	due	ADJ
ap-1257	150	83	to	to	ADP
ap-1257	150	84	the	the	DET
ap-1257	150	85	interaction	interaction	NOUN
ap-1257	150	86	between	between	ADP
ap-1257	150	87	two	two	NUM
ap-1257	150	88	particles	particle	NOUN
ap-1257	150	89	.	.	PUNCT
ap-1257	151	1	although	although	SCONJ
ap-1257	151	2	the	the	DET
ap-1257	151	3	interaction	interaction	NOUN
ap-1257	151	4	potential	potential	NOUN
ap-1257	151	5	depends	depend	VERB
ap-1257	151	6	on	on	ADP
ap-1257	151	7	the	the	DET
ap-1257	151	8	distance	distance	NOUN
ap-1257	151	9	between	between	ADP
ap-1257	151	10	the	the	DET
ap-1257	151	11	particles	particle	NOUN
ap-1257	151	12	the	the	DET
ap-1257	151	13	problem	problem	NOUN
ap-1257	151	14	is	be	AUX
ap-1257	151	15	not	not	PART
ap-1257	151	16	separable	separable	ADJ
ap-1257	151	17	and	and	CCONJ
ap-1257	151	18	should	should	AUX
ap-1257	151	19	be	be	AUX
ap-1257	151	20	treated	treat	VERB
ap-1257	151	21	as	as	ADP
ap-1257	151	22	a	a	DET
ap-1257	151	23	two	two	NUM
ap-1257	151	24	-	-	PUNCT
ap-1257	151	25	dimensional	dimensional	ADJ
ap-1257	151	26	eigenvalue	eigenvalue	NOUN
ap-1257	151	27	equation	equation	NOUN
ap-1257	151	28	.	.	PUNCT
ap-1257	152	1	it	it	PRON
ap-1257	152	2	is	be	AUX
ap-1257	152	3	almost	almost	ADV
ap-1257	152	4	separable	separable	ADJ
ap-1257	152	5	for	for	ADP
ap-1257	152	6	a	a	DET
ap-1257	152	7	sufficiently	sufficiently	ADV
ap-1257	152	8	small	small	ADJ
ap-1257	152	9	box	box	NOUN
ap-1257	152	10	because	because	SCONJ
ap-1257	152	11	the	the	DET
ap-1257	152	12	interaction	interaction	NOUN
ap-1257	152	13	potential	potential	NOUN
ap-1257	152	14	is	be	AUX
ap-1257	152	15	negligible	negligible	ADJ
ap-1257	152	16	in	in	ADP
ap-1257	152	17	such	such	DET
ap-1257	152	18	a	a	DET
ap-1257	152	19	limit	limit	NOUN
ap-1257	152	20	,	,	PUNCT
ap-1257	152	21	and	and	CCONJ
ap-1257	152	22	also	also	ADV
ap-1257	152	23	for	for	ADP
ap-1257	152	24	a	a	DET
ap-1257	152	25	sufficiently	sufficiently	ADV
ap-1257	152	26	large	large	ADJ
ap-1257	152	27	box	box	NOUN
ap-1257	152	28	where	where	SCONJ
ap-1257	152	29	the	the	DET
ap-1257	152	30	boundary	boundary	ADJ
ap-1257	152	31	conditions	condition	NOUN
ap-1257	152	32	have	have	VERB
ap-1257	152	33	no	no	DET
ap-1257	152	34	effect	effect	NOUN
ap-1257	152	35	.	.	PUNCT
ap-1257	153	1	it	it	PRON
ap-1257	153	2	is	be	AUX
ap-1257	153	3	convenient	convenient	ADJ
ap-1257	153	4	to	to	PART
ap-1257	153	5	take	take	VERB
ap-1257	153	6	into	into	ADP
ap-1257	153	7	account	account	NOUN
ap-1257	153	8	the	the	DET
ap-1257	153	9	symmetry	symmetry	NOUN
ap-1257	153	10	of	of	ADP
ap-1257	153	11	the	the	DET
ap-1257	153	12	problem	problem	NOUN
ap-1257	153	13	and	and	CCONJ
ap-1257	153	14	classify	classify	VERB
ap-1257	153	15	the	the	DET
ap-1257	153	16	states	state	NOUN
ap-1257	153	17	in	in	ADP
ap-1257	153	18	terms	term	NOUN
ap-1257	153	19	of	of	ADP
ap-1257	153	20	the	the	DET
ap-1257	153	21	irreducible	irreducible	ADJ
ap-1257	153	22	representations	representation	NOUN
ap-1257	153	23	because	because	SCONJ
ap-1257	153	24	it	it	PRON
ap-1257	153	25	facilitates	facilitate	VERB
ap-1257	153	26	the	the	DET
ap-1257	153	27	discussion	discussion	NOUN
ap-1257	153	28	of	of	ADP
ap-1257	153	29	the	the	DET
ap-1257	153	30	connection	connection	NOUN
ap-1257	153	31	between	between	ADP
ap-1257	153	32	both	both	DET
ap-1257	153	33	regimes	regime	NOUN
ap-1257	153	34	.	.	PUNCT
ap-1257	154	1	the	the	DET
ap-1257	154	2	model	model	NOUN
ap-1257	154	3	may	may	AUX
ap-1257	154	4	be	be	AUX
ap-1257	154	5	suitable	suitable	ADJ
ap-1257	154	6	for	for	ADP
ap-1257	154	7	investigating	investigate	VERB
ap-1257	154	8	the	the	DET
ap-1257	154	9	effect	effect	NOUN
ap-1257	154	10	of	of	ADP
ap-1257	154	11	pressure	pressure	NOUN
ap-1257	154	12	on	on	ADP
ap-1257	154	13	the	the	DET
ap-1257	154	14	vibrational	vibrational	ADJ
ap-1257	154	15	spectrum	spectrum	NOUN
ap-1257	154	16	of	of	ADP
ap-1257	154	17	a	a	DET
ap-1257	154	18	diatomic	diatomic	ADJ
ap-1257	154	19	molecule	molecule	NOUN
ap-1257	154	20	,	,	PUNCT
ap-1257	154	21	and	and	CCONJ
ap-1257	154	22	in	in	ADP
ap-1257	154	23	principle	principle	NOUN
ap-1257	154	24	one	one	NUM
ap-1257	154	25	can	can	AUX
ap-1257	154	26	calculate	calculate	VERB
ap-1257	154	27	the	the	DET
ap-1257	154	28	spectral	spectral	ADJ
ap-1257	154	29	lines	line	NOUN
ap-1257	154	30	by	by	ADP
ap-1257	154	31	means	mean	NOUN
ap-1257	154	32	of	of	ADP
ap-1257	154	33	the	the	DET
ap-1257	154	34	rayleigh	rayleigh	PROPN
ap-1257	154	35	-	-	PUNCT
ap-1257	154	36	ritz	ritz	PROPN
ap-1257	154	37	or	or	CCONJ
ap-1257	154	38	the	the	DET
ap-1257	154	39	lsf	lsf	PROPN
ap-1257	154	40	collocation	collocation	NOUN
ap-1257	154	41	method	method	NOUN
ap-1257	154	42	[	[	X
ap-1257	154	43	25	25	NUM
ap-1257	154	44	]	]	PUNCT
ap-1257	154	45	.	.	PUNCT
ap-1257	155	1	the	the	DET
ap-1257	155	2	simple	simple	ADJ
ap-1257	155	3	variational	variational	ADJ
ap-1257	155	4	functions	function	NOUN
ap-1257	155	5	developed	develop	VERB
ap-1257	155	6	some	some	DET
ap-1257	155	7	time	time	NOUN
ap-1257	155	8	ago	ago	ADV
ap-1257	155	9	[	[	X
ap-1257	155	10	26	26	NUM
ap-1257	155	11	]	]	PUNCT
ap-1257	155	12	and	and	CCONJ
ap-1257	155	13	adapted	adapt	VERB
ap-1257	155	14	to	to	PART
ap-1257	155	15	present	present	ADJ
ap-1257	155	16	problem	problem	NOUN
ap-1257	155	17	in	in	ADP
ap-1257	155	18	sec	sec	PROPN
ap-1257	155	19	.	.	PROPN
ap-1257	155	20	4	4	NUM
ap-1257	155	21	provide	provide	VERB
ap-1257	155	22	remarkably	remarkably	ADV
ap-1257	155	23	accurate	accurate	ADJ
ap-1257	155	24	energies	energy	NOUN
ap-1257	155	25	for	for	ADP
ap-1257	155	26	all	all	DET
ap-1257	155	27	box	box	NOUN
ap-1257	155	28	size	size	NOUN
ap-1257	155	29	values	value	NOUN
ap-1257	155	30	,	,	PUNCT
ap-1257	155	31	and	and	CCONJ
ap-1257	155	32	are	be	AUX
ap-1257	155	33	,	,	PUNCT
ap-1257	155	34	for	for	ADP
ap-1257	155	35	that	that	DET
ap-1257	155	36	reason	reason	NOUN
ap-1257	155	37	,	,	PUNCT
ap-1257	155	38	most	most	ADV
ap-1257	155	39	useful	useful	ADJ
ap-1257	155	40	for	for	ADP
ap-1257	155	41	showing	show	VERB
ap-1257	155	42	the	the	DET
ap-1257	155	43	connection	connection	NOUN
ap-1257	155	44	between	between	ADP
ap-1257	155	45	the	the	DET
ap-1257	155	46	two	two	NUM
ap-1257	155	47	regimes	regime	NOUN
ap-1257	155	48	and	and	CCONJ
ap-1257	155	49	for	for	ADP
ap-1257	155	50	verifying	verify	VERB
ap-1257	155	51	the	the	DET
ap-1257	155	52	accuracy	accuracy	NOUN
ap-1257	155	53	of	of	ADP
ap-1257	155	54	more	more	ADV
ap-1257	155	55	elaborate	elaborate	ADJ
ap-1257	155	56	numerical	numerical	ADJ
ap-1257	155	57	calculations	calculation	NOUN
ap-1257	155	58	.	.	PUNCT
ap-1257	156	1	references	reference	NOUN
ap-1257	156	2	[	[	X
ap-1257	156	3	1	1	NUM
ap-1257	156	4	]	]	PUNCT
ap-1257	156	5	auluck	auluck	PROPN
ap-1257	156	6	,	,	PUNCT
ap-1257	156	7	f.	f.	PROPN
ap-1257	156	8	c.	c.	PROPN
ap-1257	156	9	,	,	PUNCT
ap-1257	156	10	kothari	kothari	PROPN
ap-1257	156	11	,	,	PUNCT
ap-1257	156	12	d.	d.	PROPN
ap-1257	156	13	s.	s.	PROPN
ap-1257	156	14	:	:	PUNCT
ap-1257	157	1	energy	energy	NOUN
ap-1257	157	2	-	-	PUNCT
ap-1257	157	3	levels	level	NOUN
ap-1257	157	4	of	of	ADP
ap-1257	157	5	an	an	DET
ap-1257	157	6	artificially	artificially	ADV
ap-1257	157	7	bounded	bound	VERB
ap-1257	157	8	linear	linear	PROPN
ap-1257	157	9	oscillator	oscillator	PROPN
ap-1257	157	10	.	.	PUNCT
ap-1257	158	1	science	science	NOUN
ap-1257	158	2	and	and	CCONJ
ap-1257	158	3	culture	culture	NOUN
ap-1257	158	4	,	,	PUNCT
ap-1257	158	5	7	7	NUM
ap-1257	158	6	(	(	PUNCT
ap-1257	158	7	6	6	NUM
ap-1257	158	8	)	)	PUNCT
ap-1257	158	9	,	,	PUNCT
ap-1257	158	10	1940	1940	NUM
ap-1257	158	11	,	,	PUNCT
ap-1257	158	12	p.	p.	NOUN
ap-1257	158	13	370–371	370–371	NUM
ap-1257	158	14	.	.	PUNCT
ap-1257	159	1	[	[	X
ap-1257	159	2	2	2	NUM
ap-1257	159	3	]	]	PUNCT
ap-1257	159	4	auluck	auluck	PROPN
ap-1257	159	5	,	,	PUNCT
ap-1257	159	6	f.	f.	PROPN
ap-1257	159	7	c.	c.	PROPN
ap-1257	159	8	:	:	PUNCT
ap-1257	159	9	energy	energy	NOUN
ap-1257	159	10	levels	level	NOUN
ap-1257	159	11	of	of	ADP
ap-1257	159	12	an	an	DET
ap-1257	159	13	artificially	artificially	ADV
ap-1257	159	14	bounded	bound	VERB
ap-1257	159	15	linear	linear	PROPN
ap-1257	159	16	oscillator	oscillator	PROPN
ap-1257	159	17	.	.	PUNCT
ap-1257	160	1	proc	proc	PROPN
ap-1257	160	2	.	.	PUNCT
ap-1257	161	1	nat	nat	PROPN
ap-1257	161	2	.	.	PUNCT
ap-1257	161	3	inst	inst	PROPN
ap-1257	161	4	.	.	PUNCT
ap-1257	162	1	india	india	PROPN
ap-1257	162	2	,	,	PUNCT
ap-1257	162	3	7	7	NUM
ap-1257	162	4	(	(	PUNCT
ap-1257	162	5	2	2	NUM
ap-1257	162	6	)	)	PUNCT
ap-1257	162	7	,	,	PUNCT
ap-1257	162	8	1941	1941	NUM
ap-1257	162	9	,	,	PUNCT
ap-1257	162	10	p.	p.	NOUN
ap-1257	162	11	133–140	133–140	NUM
ap-1257	162	12	.	.	PUNCT
ap-1257	163	1	[	[	X
ap-1257	163	2	3	3	NUM
ap-1257	163	3	]	]	PUNCT
ap-1257	163	4	auluck	auluck	PROPN
ap-1257	163	5	,	,	PUNCT
ap-1257	163	6	f.	f.	PROPN
ap-1257	163	7	c.	c.	PROPN
ap-1257	163	8	:	:	PUNCT
ap-1257	163	9	white	white	ADJ
ap-1257	163	10	dwarf	dwarf	NOUN
ap-1257	163	11	and	and	CCONJ
ap-1257	163	12	harmonic	harmonic	ADJ
ap-1257	163	13	oscillator	oscillator	NOUN
ap-1257	163	14	.	.	PUNCT
ap-1257	164	1	proc	proc	NOUN
ap-1257	164	2	.	.	PUNCT
ap-1257	165	1	nat	nat	PROPN
ap-1257	165	2	.	.	PUNCT
ap-1257	165	3	inst	inst	PROPN
ap-1257	165	4	.	.	PUNCT
ap-1257	166	1	india	india	PROPN
ap-1257	166	2	,	,	PUNCT
ap-1257	166	3	8	8	NUM
ap-1257	166	4	(	(	PUNCT
ap-1257	166	5	2	2	NUM
ap-1257	166	6	)	)	PUNCT
ap-1257	166	7	,	,	PUNCT
ap-1257	166	8	1942	1942	NUM
ap-1257	166	9	,	,	PUNCT
ap-1257	166	10	p.	p.	NOUN
ap-1257	166	11	147–156	147–156	NUM
ap-1257	166	12	.	.	PUNCT
ap-1257	167	1	[	[	X
ap-1257	167	2	4	4	NUM
ap-1257	167	3	]	]	X
ap-1257	167	4	chandrasekhar	chandrasekhar	PROPN
ap-1257	167	5	,	,	PUNCT
ap-1257	167	6	s.	s.	PROPN
ap-1257	167	7	:	:	PUNCT
ap-1257	167	8	dynamical	dynamical	ADJ
ap-1257	167	9	friction	friction	PROPN
ap-1257	167	10	ii	ii	PROPN
ap-1257	167	11	.	.	PUNCT
ap-1257	168	1	the	the	DET
ap-1257	168	2	rate	rate	NOUN
ap-1257	168	3	of	of	ADP
ap-1257	168	4	escape	escape	NOUN
ap-1257	168	5	of	of	ADP
ap-1257	168	6	stars	star	NOUN
ap-1257	168	7	from	from	ADP
ap-1257	168	8	clusters	cluster	NOUN
ap-1257	168	9	and	and	CCONJ
ap-1257	168	10	the	the	DET
ap-1257	168	11	evidence	evidence	NOUN
ap-1257	168	12	for	for	ADP
ap-1257	168	13	the	the	DET
ap-1257	168	14	operation	operation	NOUN
ap-1257	168	15	of	of	ADP
ap-1257	168	16	dynamical	dynamical	ADJ
ap-1257	168	17	friction	friction	NOUN
ap-1257	168	18	.	.	PUNCT
ap-1257	169	1	astrophys	astrophy	NOUN
ap-1257	169	2	.	.	PUNCT
ap-1257	170	1	j.	j.	PROPN
ap-1257	170	2	,	,	PUNCT
ap-1257	170	3	97	97	NUM
ap-1257	170	4	(	(	PUNCT
ap-1257	170	5	2	2	NUM
ap-1257	170	6	)	)	PUNCT
ap-1257	170	7	,	,	PUNCT
ap-1257	170	8	1943	1943	NUM
ap-1257	170	9	,	,	PUNCT
ap-1257	170	10	p.	p.	NOUN
ap-1257	170	11	263–273	263–273	NUM
ap-1257	170	12	.	.	PUNCT
ap-1257	171	1	[	[	X
ap-1257	171	2	5	5	NUM
ap-1257	171	3	]	]	PUNCT
ap-1257	171	4	auluck	auluck	PROPN
ap-1257	171	5	,	,	PUNCT
ap-1257	171	6	f.	f.	PROPN
ap-1257	171	7	c.	c.	PROPN
ap-1257	171	8	,	,	PUNCT
ap-1257	171	9	kothari	kothari	PROPN
ap-1257	171	10	,	,	PUNCT
ap-1257	171	11	d.	d.	PROPN
ap-1257	171	12	s.	s.	PROPN
ap-1257	171	13	:	:	PUNCT
ap-1257	171	14	the	the	DET
ap-1257	171	15	quantum	quantum	ADJ
ap-1257	171	16	mechanics	mechanic	NOUN
ap-1257	171	17	of	of	ADP
ap-1257	171	18	a	a	DET
ap-1257	171	19	bounded	bounded	ADJ
ap-1257	171	20	linear	linear	PROPN
ap-1257	171	21	harmonic	harmonic	ADJ
ap-1257	171	22	oscillator	oscillator	NOUN
ap-1257	171	23	.	.	PUNCT
ap-1257	172	1	proc	proc	PROPN
ap-1257	172	2	.	.	PUNCT
ap-1257	173	1	camb	camb	PROPN
ap-1257	173	2	.	.	PUNCT
ap-1257	174	1	phil	phil	PROPN
ap-1257	174	2	.	.	PUNCT
ap-1257	175	1	soc	soc	PROPN
ap-1257	175	2	.	.	PUNCT
ap-1257	175	3	,	,	PUNCT
ap-1257	175	4	41	41	NUM
ap-1257	175	5	(	(	PUNCT
ap-1257	175	6	2	2	NUM
ap-1257	175	7	)	)	PUNCT
ap-1257	175	8	,	,	PUNCT
ap-1257	175	9	1945	1945	NUM
ap-1257	175	10	,	,	PUNCT
ap-1257	175	11	p.	p.	NOUN
ap-1257	175	12	175–179	175–179	NUM
ap-1257	175	13	.	.	PUNCT
ap-1257	176	1	[	[	X
ap-1257	176	2	6	6	NUM
ap-1257	176	3	]	]	X
ap-1257	176	4	dingle	dingle	NOUN
ap-1257	176	5	,	,	PUNCT
ap-1257	176	6	r.	r.	PROPN
ap-1257	176	7	b.	b.	PROPN
ap-1257	176	8	:	:	PUNCT
ap-1257	176	9	some	some	DET
ap-1257	176	10	magnetic	magnetic	ADJ
ap-1257	176	11	properties	property	NOUN
ap-1257	176	12	of	of	ADP
ap-1257	176	13	metals	metal	NOUN
ap-1257	176	14	iv	iv	NOUN
ap-1257	176	15	.	.	PUNCT
ap-1257	176	16	properties	property	NOUN
ap-1257	176	17	of	of	ADP
ap-1257	176	18	small	small	ADJ
ap-1257	176	19	systems	system	NOUN
ap-1257	176	20	of	of	ADP
ap-1257	176	21	electrons	electron	NOUN
ap-1257	176	22	.	.	PUNCT
ap-1257	177	1	proc	proc	NOUN
ap-1257	177	2	.	.	PUNCT
ap-1257	178	1	roy	roy	PROPN
ap-1257	178	2	.	.	PROPN
ap-1257	178	3	soc	soc	PROPN
ap-1257	178	4	.	.	PUNCT
ap-1257	179	1	london	london	PROPN
ap-1257	179	2	ser	ser	PROPN
ap-1257	179	3	.	.	PUNCT
ap-1257	180	1	a	a	PRON
ap-1257	180	2	,	,	PUNCT
ap-1257	180	3	212	212	NUM
ap-1257	180	4	(	(	PUNCT
ap-1257	180	5	1108	1108	NUM
ap-1257	180	6	)	)	PUNCT
ap-1257	180	7	,	,	PUNCT
ap-1257	180	8	1952	1952	NUM
ap-1257	180	9	,	,	PUNCT
ap-1257	180	10	p.	p.	NOUN
ap-1257	180	11	47–65	47–65	NUM
ap-1257	180	12	.	.	PUNCT
ap-1257	181	1	[	[	X
ap-1257	181	2	7	7	NUM
ap-1257	181	3	]	]	PUNCT
ap-1257	181	4	baijal	baijal	ADV
ap-1257	181	5	,	,	PUNCT
ap-1257	181	6	j.	j.	PROPN
ap-1257	181	7	s.	s.	PROPN
ap-1257	181	8	,	,	PUNCT
ap-1257	181	9	singh	singh	PROPN
ap-1257	181	10	,	,	PUNCT
ap-1257	181	11	k.	k.	PROPN
ap-1257	181	12	k.	k.	PROPN
ap-1257	181	13	:	:	PUNCT
ap-1257	181	14	the	the	DET
ap-1257	181	15	energy	energy	NOUN
ap-1257	181	16	-	-	PUNCT
ap-1257	181	17	levels	level	NOUN
ap-1257	181	18	and	and	CCONJ
ap-1257	181	19	transition	transition	NOUN
ap-1257	181	20	probabilities	probability	NOUN
ap-1257	181	21	for	for	ADP
ap-1257	181	22	a	a	DET
ap-1257	181	23	bounded	bounded	ADJ
ap-1257	181	24	linear	linear	PROPN
ap-1257	181	25	harmonic	harmonic	PROPN
ap-1257	181	26	oscillator	oscillator	NOUN
ap-1257	181	27	.	.	PUNCT
ap-1257	182	1	prog	prog	NOUN
ap-1257	182	2	.	.	PUNCT
ap-1257	183	1	theor	theor	PROPN
ap-1257	183	2	.	.	PUNCT
ap-1257	184	1	phys	phy	NOUN
ap-1257	184	2	.	.	PUNCT
ap-1257	184	3	,	,	PUNCT
ap-1257	184	4	14	14	NUM
ap-1257	184	5	(	(	PUNCT
ap-1257	184	6	3	3	NUM
ap-1257	184	7	)	)	PUNCT
ap-1257	184	8	,	,	PUNCT
ap-1257	184	9	1955	1955	NUM
ap-1257	184	10	,	,	PUNCT
ap-1257	184	11	p.	p.	NOUN
ap-1257	184	12	214–224	214–224	NUM
ap-1257	184	13	.	.	PUNCT
ap-1257	185	1	[	[	X
ap-1257	185	2	8	8	NUM
ap-1257	185	3	]	]	X
ap-1257	185	4	dean	dean	NOUN
ap-1257	185	5	,	,	PUNCT
ap-1257	185	6	p.	p.	NOUN
ap-1257	185	7	:	:	PUNCT
ap-1257	185	8	the	the	DET
ap-1257	185	9	constrained	constrain	VERB
ap-1257	185	10	quantum	quantum	ADJ
ap-1257	185	11	mechanical	mechanical	ADJ
ap-1257	185	12	harmonic	harmonic	ADJ
ap-1257	185	13	oscillator	oscillator	NOUN
ap-1257	185	14	.	.	PUNCT
ap-1257	186	1	proc	proc	PROPN
ap-1257	186	2	.	.	PUNCT
ap-1257	187	1	camb	camb	PROPN
ap-1257	187	2	.	.	PUNCT
ap-1257	188	1	phil	phil	PROPN
ap-1257	188	2	.	.	PUNCT
ap-1257	189	1	soc	soc	PROPN
ap-1257	189	2	.	.	PUNCT
ap-1257	190	1	,	,	PUNCT
ap-1257	190	2	62	62	NUM
ap-1257	190	3	(	(	PUNCT
ap-1257	190	4	2	2	NUM
ap-1257	190	5	)	)	PUNCT
ap-1257	190	6	,	,	PUNCT
ap-1257	190	7	1966	1966	NUM
ap-1257	190	8	,	,	PUNCT
ap-1257	190	9	p.	p.	NOUN
ap-1257	190	10	277–286	277–286	NUM
ap-1257	190	11	.	.	PUNCT
ap-1257	191	1	[	[	X
ap-1257	191	2	9	9	NUM
ap-1257	191	3	]	]	SYM
ap-1257	191	4	vawter	vawter	NOUN
ap-1257	191	5	,	,	PUNCT
ap-1257	191	6	r.	r.	PROPN
ap-1257	191	7	:	:	PUNCT
ap-1257	191	8	effects	effect	NOUN
ap-1257	191	9	of	of	ADP
ap-1257	191	10	finite	finite	ADJ
ap-1257	191	11	boundaries	boundary	NOUN
ap-1257	191	12	on	on	ADP
ap-1257	191	13	a	a	DET
ap-1257	191	14	one	one	NUM
ap-1257	191	15	-	-	PUNCT
ap-1257	191	16	dimensional	dimensional	ADJ
ap-1257	191	17	harmonic	harmonic	ADJ
ap-1257	191	18	oscillator	oscillator	NOUN
ap-1257	191	19	.	.	PUNCT
ap-1257	192	1	phys	phy	NOUN
ap-1257	192	2	.	.	PUNCT
ap-1257	193	1	rev	rev	PROPN
ap-1257	193	2	.	.	PROPN
ap-1257	193	3	,	,	PUNCT
ap-1257	193	4	174	174	NUM
ap-1257	193	5	(	(	PUNCT
ap-1257	193	6	3	3	NUM
ap-1257	193	7	)	)	PUNCT
ap-1257	193	8	,	,	PUNCT
ap-1257	193	9	1968	1968	NUM
ap-1257	193	10	,	,	PUNCT
ap-1257	193	11	p.	p.	NOUN
ap-1257	193	12	749–757	749–757	NUM
ap-1257	193	13	.	.	PUNCT
ap-1257	194	1	[	[	X
ap-1257	194	2	10	10	NUM
ap-1257	194	3	]	]	X
ap-1257	194	4	vawter	vawter	NOUN
ap-1257	194	5	,	,	PUNCT
ap-1257	194	6	r.	r.	PROPN
ap-1257	194	7	:	:	PUNCT
ap-1257	194	8	energy	energy	NOUN
ap-1257	194	9	eigenvalues	eigenvalue	NOUN
ap-1257	194	10	of	of	ADP
ap-1257	194	11	a	a	DET
ap-1257	194	12	bounded	bound	VERB
ap-1257	194	13	centrally	centrally	ADV
ap-1257	194	14	located	locate	VERB
ap-1257	194	15	harmonic	harmonic	ADJ
ap-1257	194	16	oscillator	oscillator	NOUN
ap-1257	194	17	.	.	PUNCT
ap-1257	195	1	j.	j.	PROPN
ap-1257	195	2	math	math	PROPN
ap-1257	195	3	.	.	PUNCT
ap-1257	196	1	phys	phy	NOUN
ap-1257	196	2	.	.	PUNCT
ap-1257	196	3	,	,	PUNCT
ap-1257	196	4	14	14	NUM
ap-1257	196	5	(	(	PUNCT
ap-1257	196	6	12	12	NUM
ap-1257	196	7	)	)	PUNCT
ap-1257	196	8	,	,	PUNCT
ap-1257	196	9	1973	1973	NUM
ap-1257	196	10	,	,	PUNCT
ap-1257	196	11	p.	p.	NOUN
ap-1257	196	12	1	1	NUM
ap-1257	196	13	864–1	864–1	NUM
ap-1257	196	14	870	870	NUM
ap-1257	196	15	.	.	PUNCT
ap-1257	197	1	23	23	NUM
ap-1257	197	2	acta	acta	PROPN
ap-1257	197	3	polytechnica	polytechnica	PROPN
ap-1257	197	4	vol	vol	NOUN
ap-1257	197	5	.	.	PROPN
ap-1257	198	1	50	50	NUM
ap-1257	198	2	no	no	NOUN
ap-1257	198	3	.	.	PUNCT
ap-1257	199	1	5/2010	5/2010	NUM
ap-1257	200	1	[	[	X
ap-1257	200	2	11	11	NUM
ap-1257	200	3	]	]	PUNCT
ap-1257	200	4	consortini	consortini	PROPN
ap-1257	200	5	,	,	PUNCT
ap-1257	200	6	a.	a.	PROPN
ap-1257	200	7	,	,	PUNCT
ap-1257	200	8	frieden	frieden	PROPN
ap-1257	200	9	,	,	PUNCT
ap-1257	200	10	b.	b.	PROPN
ap-1257	200	11	r.	r.	PROPN
ap-1257	200	12	:	:	PUNCT
ap-1257	200	13	quantum	quantum	ADJ
ap-1257	200	14	-	-	ADJ
ap-1257	200	15	mechanical	mechanical	ADJ
ap-1257	200	16	solution	solution	NOUN
ap-1257	200	17	for	for	ADP
ap-1257	200	18	the	the	DET
ap-1257	200	19	simple	simple	ADJ
ap-1257	200	20	harmonic	harmonic	ADJ
ap-1257	200	21	oscillator	oscillator	NOUN
ap-1257	200	22	in	in	ADP
ap-1257	200	23	a	a	DET
ap-1257	200	24	box	box	NOUN
ap-1257	200	25	.	.	PUNCT
ap-1257	201	1	nuovo	nuovo	PROPN
ap-1257	201	2	cim	cim	PROPN
ap-1257	201	3	.	.	PUNCT
ap-1257	202	1	b	b	X
ap-1257	202	2	,	,	PUNCT
ap-1257	202	3	35	35	NUM
ap-1257	202	4	(	(	PUNCT
ap-1257	202	5	2	2	NUM
ap-1257	202	6	)	)	PUNCT
ap-1257	202	7	,	,	PUNCT
ap-1257	202	8	1976	1976	NUM
ap-1257	202	9	,	,	PUNCT
ap-1257	202	10	p.	p.	NOUN
ap-1257	202	11	153–163	153–163	NUM
ap-1257	202	12	.	.	PUNCT
ap-1257	203	1	[	[	X
ap-1257	203	2	12	12	NUM
ap-1257	203	3	]	]	X
ap-1257	203	4	adams	adams	PROPN
ap-1257	203	5	,	,	PUNCT
ap-1257	203	6	j.	j.	PROPN
ap-1257	203	7	e.	e.	PROPN
ap-1257	203	8	,	,	PUNCT
ap-1257	203	9	miller	miller	PROPN
ap-1257	203	10	,	,	PUNCT
ap-1257	203	11	w.	w.	PROPN
ap-1257	203	12	h.	h.	PROPN
ap-1257	203	13	:	:	PUNCT
ap-1257	203	14	semiclassical	semiclassical	ADJ
ap-1257	203	15	eigenvalues	eigenvalue	VERB
ap-1257	203	16	for	for	ADP
ap-1257	203	17	potential	potential	ADJ
ap-1257	203	18	functions	function	NOUN
ap-1257	203	19	defined	define	VERB
ap-1257	203	20	on	on	ADP
ap-1257	203	21	a	a	DET
ap-1257	203	22	finite	finite	ADJ
ap-1257	203	23	interval	interval	NOUN
ap-1257	203	24	.	.	PUNCT
ap-1257	204	1	j.	j.	PROPN
ap-1257	204	2	chem	chem	PROPN
ap-1257	204	3	.	.	PUNCT
ap-1257	205	1	phys	phy	NOUN
ap-1257	205	2	.	.	PUNCT
ap-1257	205	3	,	,	PUNCT
ap-1257	205	4	67	67	NUM
ap-1257	205	5	(	(	PUNCT
ap-1257	205	6	12	12	NUM
ap-1257	205	7	)	)	PUNCT
ap-1257	205	8	,	,	PUNCT
ap-1257	205	9	1977	1977	NUM
ap-1257	205	10	,	,	PUNCT
ap-1257	205	11	p.	p.	NOUN
ap-1257	205	12	5	5	NUM
ap-1257	205	13	775–5	775–5	NUM
ap-1257	205	14	778	778	NUM
ap-1257	205	15	.	.	PUNCT
ap-1257	206	1	[	[	X
ap-1257	206	2	13	13	NUM
ap-1257	206	3	]	]	SYM
ap-1257	206	4	rotbar	rotbar	NOUN
ap-1257	206	5	,	,	PUNCT
ap-1257	206	6	f.	f.	PROPN
ap-1257	206	7	c.	c.	PROPN
ap-1257	206	8	:	:	PUNCT
ap-1257	206	9	quantum	quantum	ADJ
ap-1257	206	10	symmetrical	symmetrical	ADJ
ap-1257	206	11	quadratic	quadratic	ADJ
ap-1257	206	12	potential	potential	NOUN
ap-1257	206	13	in	in	ADP
ap-1257	206	14	a	a	DET
ap-1257	206	15	box	box	NOUN
ap-1257	206	16	.	.	PUNCT
ap-1257	207	1	j.	j.	PROPN
ap-1257	207	2	phys	phys	PROPN
ap-1257	207	3	.	.	PUNCT
ap-1257	208	1	a	a	DET
ap-1257	208	2	,	,	PUNCT
ap-1257	208	3	11	11	NUM
ap-1257	208	4	(	(	PUNCT
ap-1257	208	5	12	12	NUM
ap-1257	208	6	)	)	PUNCT
ap-1257	208	7	,	,	PUNCT
ap-1257	208	8	1978	1978	NUM
ap-1257	208	9	,	,	PUNCT
ap-1257	208	10	p.	p.	NOUN
ap-1257	208	11	2	2	NUM
ap-1257	208	12	363–2368	363–2368	NUM
ap-1257	208	13	.	.	PUNCT
ap-1257	209	1	[	[	X
ap-1257	209	2	14	14	NUM
ap-1257	209	3	]	]	X
ap-1257	209	4	aguilera	aguilera	NOUN
ap-1257	209	5	-	-	PUNCT
ap-1257	209	6	navarro	navarro	PROPN
ap-1257	209	7	,	,	PUNCT
ap-1257	209	8	v.	v.	PROPN
ap-1257	209	9	c.	c.	PROPN
ap-1257	209	10	,	,	PUNCT
ap-1257	209	11	ley	ley	PROPN
ap-1257	209	12	koo	koo	PROPN
ap-1257	209	13	,	,	PUNCT
ap-1257	209	14	e.	e.	PROPN
ap-1257	209	15	,	,	PUNCT
ap-1257	209	16	zimerman	zimerman	NOUN
ap-1257	209	17	,	,	PUNCT
ap-1257	209	18	a.	a.	PROPN
ap-1257	209	19	h.	h.	PROPN
ap-1257	209	20	:	:	PUNCT
ap-1257	209	21	perturbative	perturbative	ADJ
ap-1257	209	22	,	,	PUNCT
ap-1257	209	23	asymptotic	asymptotic	ADJ
ap-1257	209	24	and	and	CCONJ
ap-1257	209	25	pade	pade	NOUN
ap-1257	209	26	-	-	PUNCT
ap-1257	209	27	approximant	approximant	ADJ
ap-1257	209	28	solutions	solution	NOUN
ap-1257	209	29	for	for	ADP
ap-1257	209	30	harmonic	harmonic	ADJ
ap-1257	209	31	and	and	CCONJ
ap-1257	209	32	inverted	inverted	ADJ
ap-1257	209	33	oscillators	oscillator	NOUN
ap-1257	209	34	in	in	ADP
ap-1257	209	35	a	a	DET
ap-1257	209	36	box	box	NOUN
ap-1257	209	37	.	.	PUNCT
ap-1257	210	1	j.	j.	PROPN
ap-1257	210	2	phys	phys	PROPN
ap-1257	210	3	.	.	PUNCT
ap-1257	211	1	a	a	DET
ap-1257	211	2	,	,	PUNCT
ap-1257	211	3	13	13	NUM
ap-1257	211	4	(	(	PUNCT
ap-1257	211	5	12	12	NUM
ap-1257	211	6	)	)	PUNCT
ap-1257	211	7	,	,	PUNCT
ap-1257	211	8	1980	1980	NUM
ap-1257	211	9	,	,	PUNCT
ap-1257	211	10	p.	p.	NOUN
ap-1257	211	11	3	3	NUM
ap-1257	212	1	585–3	585–3	NUM
ap-1257	212	2	598	598	NUM
ap-1257	212	3	.	.	PUNCT
ap-1257	213	1	[	[	X
ap-1257	213	2	15	15	NUM
ap-1257	213	3	]	]	X
ap-1257	213	4	aguilera	aguilera	NOUN
ap-1257	213	5	-	-	PUNCT
ap-1257	213	6	navarro	navarro	PROPN
ap-1257	213	7	,	,	PUNCT
ap-1257	213	8	v.	v.	PROPN
ap-1257	213	9	c.	c.	PROPN
ap-1257	213	10	,	,	PUNCT
ap-1257	213	11	iwamoto	iwamoto	PROPN
ap-1257	213	12	,	,	PUNCT
ap-1257	213	13	h.	h.	PROPN
ap-1257	213	14	,	,	PUNCT
ap-1257	213	15	ley	ley	PROPN
ap-1257	213	16	koo	koo	PROPN
ap-1257	213	17	,	,	PUNCT
ap-1257	213	18	e.	e.	PROPN
ap-1257	213	19	,	,	PUNCT
ap-1257	213	20	zimerman	zimerman	NOUN
ap-1257	213	21	,	,	PUNCT
ap-1257	213	22	a.	a.	PROPN
ap-1257	213	23	h.	h.	PROPN
ap-1257	213	24	:	:	PUNCT
ap-1257	213	25	quantum	quantum	ADJ
ap-1257	213	26	-	-	ADJ
ap-1257	213	27	mechanical	mechanical	ADJ
ap-1257	213	28	solution	solution	NOUN
ap-1257	213	29	of	of	ADP
ap-1257	213	30	the	the	DET
ap-1257	213	31	double	double	ADJ
ap-1257	213	32	oscillator	oscillator	NOUN
ap-1257	213	33	in	in	ADP
ap-1257	213	34	a	a	DET
ap-1257	213	35	box	box	NOUN
ap-1257	213	36	.	.	PUNCT
ap-1257	214	1	nuovo	nuovo	PROPN
ap-1257	214	2	cim	cim	PROPN
ap-1257	214	3	.	.	PUNCT
ap-1257	215	1	b	b	X
ap-1257	215	2	,	,	PUNCT
ap-1257	215	3	62	62	NUM
ap-1257	215	4	(	(	PUNCT
ap-1257	215	5	1	1	NUM
ap-1257	215	6	)	)	PUNCT
ap-1257	215	7	,	,	PUNCT
ap-1257	215	8	1981	1981	NUM
ap-1257	215	9	,	,	PUNCT
ap-1257	215	10	p.	p.	NOUN
ap-1257	215	11	91–128	91–128	NUM
ap-1257	215	12	.	.	PUNCT
ap-1257	216	1	[	[	X
ap-1257	216	2	16	16	NUM
ap-1257	216	3	]	]	X
ap-1257	216	4	barakat	barakat	PROPN
ap-1257	216	5	,	,	PUNCT
ap-1257	216	6	r.	r.	PROPN
ap-1257	216	7	,	,	PUNCT
ap-1257	216	8	rosner	rosner	PROPN
ap-1257	216	9	,	,	PUNCT
ap-1257	216	10	r.	r.	PROPN
ap-1257	216	11	:	:	PUNCT
ap-1257	216	12	the	the	DET
ap-1257	216	13	bounded	bounded	ADJ
ap-1257	216	14	quartic	quartic	ADJ
ap-1257	216	15	oscillator	oscillator	NOUN
ap-1257	216	16	.	.	PUNCT
ap-1257	217	1	phys	phy	NOUN
ap-1257	217	2	.	.	PUNCT
ap-1257	218	1	lett	lett	PROPN
ap-1257	218	2	.	.	PUNCT
ap-1257	219	1	a	a	DET
ap-1257	219	2	,	,	PUNCT
ap-1257	219	3	83	83	NUM
ap-1257	219	4	(	(	PUNCT
ap-1257	219	5	4	4	NUM
ap-1257	219	6	)	)	PUNCT
ap-1257	219	7	,	,	PUNCT
ap-1257	219	8	1981	1981	NUM
ap-1257	219	9	,	,	PUNCT
ap-1257	219	10	p.	p.	NOUN
ap-1257	219	11	149–150	149–150	NUM
ap-1257	219	12	.	.	PUNCT
ap-1257	220	1	[	[	X
ap-1257	220	2	17	17	NUM
ap-1257	220	3	]	]	X
ap-1257	220	4	fernández	fernández	PROPN
ap-1257	220	5	,	,	PUNCT
ap-1257	220	6	f.	f.	PROPN
ap-1257	220	7	m.	m.	PROPN
ap-1257	220	8	,	,	PUNCT
ap-1257	220	9	castro	castro	PROPN
ap-1257	220	10	,	,	PUNCT
ap-1257	220	11	e.	e.	PROPN
ap-1257	220	12	a.	a.	PROPN
ap-1257	220	13	:	:	PUNCT
ap-1257	220	14	hypervirial	hypervirial	ADJ
ap-1257	220	15	treatment	treatment	NOUN
ap-1257	220	16	of	of	ADP
ap-1257	220	17	multidimensional	multidimensional	ADJ
ap-1257	220	18	isotropic	isotropic	NOUN
ap-1257	220	19	bounded	bound	VERB
ap-1257	220	20	oscillators	oscillator	NOUN
ap-1257	220	21	.	.	PUNCT
ap-1257	221	1	phys	phy	NOUN
ap-1257	221	2	.	.	PUNCT
ap-1257	222	1	rev	rev	PROPN
ap-1257	222	2	.	.	PROPN
ap-1257	223	1	a	a	DET
ap-1257	223	2	,	,	PUNCT
ap-1257	223	3	24	24	NUM
ap-1257	223	4	(	(	PUNCT
ap-1257	223	5	5	5	NUM
ap-1257	223	6	)	)	PUNCT
ap-1257	223	7	,	,	PUNCT
ap-1257	223	8	1981	1981	NUM
ap-1257	223	9	,	,	PUNCT
ap-1257	223	10	p.	p.	NOUN
ap-1257	223	11	2	2	NUM
ap-1257	223	12	883–2	883–2	NUM
ap-1257	223	13	888	888	NUM
ap-1257	223	14	.	.	PUNCT
ap-1257	224	1	[	[	X
ap-1257	224	2	18	18	NUM
ap-1257	224	3	]	]	SYM
ap-1257	224	4	fernández	fernández	PROPN
ap-1257	224	5	,	,	PUNCT
ap-1257	224	6	f.	f.	PROPN
ap-1257	224	7	m.	m.	PROPN
ap-1257	224	8	,	,	PUNCT
ap-1257	224	9	castro	castro	PROPN
ap-1257	224	10	,	,	PUNCT
ap-1257	224	11	e.	e.	PROPN
ap-1257	224	12	a.	a.	PROPN
ap-1257	224	13	:	:	PUNCT
ap-1257	224	14	hypervirial	hypervirial	ADJ
ap-1257	224	15	calculation	calculation	NOUN
ap-1257	224	16	of	of	ADP
ap-1257	224	17	energy	energy	NOUN
ap-1257	224	18	eigenvalues	eigenvalue	NOUN
ap-1257	224	19	of	of	ADP
ap-1257	224	20	a	a	DET
ap-1257	224	21	bounded	bound	VERB
ap-1257	224	22	centrally	centrally	ADV
ap-1257	224	23	located	locate	VERB
ap-1257	224	24	harmonic	harmonic	ADJ
ap-1257	224	25	oscillator	oscillator	NOUN
ap-1257	224	26	.	.	PUNCT
ap-1257	225	1	j.	j.	PROPN
ap-1257	225	2	math	math	PROPN
ap-1257	225	3	.	.	PUNCT
ap-1257	226	1	phys	phy	NOUN
ap-1257	226	2	.	.	PUNCT
ap-1257	226	3	,	,	PUNCT
ap-1257	226	4	22	22	NUM
ap-1257	226	5	(	(	PUNCT
ap-1257	226	6	8)	8)	NUM
ap-1257	226	7	,	,	PUNCT
ap-1257	226	8	1981	1981	NUM
ap-1257	226	9	,	,	PUNCT
ap-1257	226	10	p.	p.	NOUN
ap-1257	226	11	1	1	NUM
ap-1257	226	12	669–1671	669–1671	NUM
ap-1257	226	13	.	.	PUNCT
ap-1257	227	1	[	[	X
ap-1257	227	2	19	19	NUM
ap-1257	227	3	]	]	X
ap-1257	227	4	aguilera	aguilera	NOUN
ap-1257	227	5	-	-	PUNCT
ap-1257	227	6	navarro	navarro	PROPN
ap-1257	227	7	,	,	PUNCT
ap-1257	227	8	v.	v.	PROPN
ap-1257	227	9	c.	c.	PROPN
ap-1257	227	10	,	,	PUNCT
ap-1257	227	11	gomes	gomes	PROPN
ap-1257	227	12	,	,	PUNCT
ap-1257	227	13	j.	j.	PROPN
ap-1257	227	14	f.	f.	PROPN
ap-1257	227	15	,	,	PUNCT
ap-1257	227	16	zimerman	zimerman	NOUN
ap-1257	227	17	,	,	PUNCT
ap-1257	227	18	a.	a.	PROPN
ap-1257	227	19	h.	h.	PROPN
ap-1257	227	20	,	,	PUNCT
ap-1257	227	21	ley	ley	PROPN
ap-1257	227	22	koo	koo	PROPN
ap-1257	227	23	,	,	PUNCT
ap-1257	227	24	e.	e.	PROPN
ap-1257	227	25	:	:	PUNCT
ap-1257	227	26	on	on	ADP
ap-1257	227	27	the	the	DET
ap-1257	227	28	radius	radius	NOUN
ap-1257	227	29	of	of	ADP
ap-1257	227	30	convergence	convergence	NOUN
ap-1257	227	31	of	of	ADP
ap-1257	227	32	rayleigh	rayleigh	PROPN
ap-1257	227	33	-	-	PUNCT
ap-1257	227	34	schroedinger	schroedinger	PROPN
ap-1257	227	35	perturbative	perturbative	ADJ
ap-1257	227	36	solutions	solution	NOUN
ap-1257	227	37	for	for	ADP
ap-1257	227	38	quantum	quantum	NOUN
ap-1257	227	39	oscillators	oscillator	NOUN
ap-1257	227	40	in	in	ADP
ap-1257	227	41	circular	circular	ADJ
ap-1257	227	42	and	and	CCONJ
ap-1257	227	43	spherical	spherical	ADJ
ap-1257	227	44	boxes	box	NOUN
ap-1257	227	45	.	.	PUNCT
ap-1257	228	1	j.	j.	PROPN
ap-1257	228	2	phys	phys	PROPN
ap-1257	228	3	.	.	PUNCT
ap-1257	229	1	a	a	DET
ap-1257	229	2	,	,	PUNCT
ap-1257	229	3	16	16	NUM
ap-1257	229	4	(	(	PUNCT
ap-1257	229	5	13	13	NUM
ap-1257	229	6	)	)	PUNCT
ap-1257	229	7	,	,	PUNCT
ap-1257	229	8	1983	1983	NUM
ap-1257	229	9	,	,	PUNCT
ap-1257	230	1	p.	p.	NOUN
ap-1257	230	2	2	2	NUM
ap-1257	230	3	943–2952	943–2952	NUM
ap-1257	230	4	.	.	PUNCT
ap-1257	231	1	[	[	X
ap-1257	231	2	20	20	NUM
ap-1257	231	3	]	]	SYM
ap-1257	231	4	chaudhuri	chaudhuri	PROPN
ap-1257	231	5	,	,	PUNCT
ap-1257	231	6	r.	r.	PROPN
ap-1257	231	7	n.	n.	PROPN
ap-1257	231	8	,	,	PUNCT
ap-1257	231	9	mukherjee	mukherjee	PROPN
ap-1257	231	10	,	,	PUNCT
ap-1257	231	11	b.	b.	PROPN
ap-1257	231	12	:	:	PUNCT
ap-1257	231	13	the	the	DET
ap-1257	231	14	eigenvalues	eigenvalue	NOUN
ap-1257	231	15	of	of	ADP
ap-1257	231	16	the	the	DET
ap-1257	231	17	bounded	bounded	ADJ
ap-1257	231	18	lx2	lx2	PROPN
ap-1257	231	19	m	m	PROPN
ap-1257	231	20	oscillators	oscillator	NOUN
ap-1257	231	21	.	.	PUNCT
ap-1257	232	1	j.	j.	PROPN
ap-1257	232	2	phys	phys	PROPN
ap-1257	232	3	.	.	PUNCT
ap-1257	233	1	a	a	DET
ap-1257	233	2	,	,	PUNCT
ap-1257	233	3	16	16	NUM
ap-1257	233	4	(	(	PUNCT
ap-1257	233	5	14	14	NUM
ap-1257	233	6	)	)	PUNCT
ap-1257	233	7	,	,	PUNCT
ap-1257	233	8	1983	1983	NUM
ap-1257	233	9	,	,	PUNCT
ap-1257	233	10	p.	p.	NOUN
ap-1257	233	11	3	3	NUM
ap-1257	233	12	193–3196	193–3196	NUM
ap-1257	233	13	.	.	PUNCT
ap-1257	234	1	[	[	X
ap-1257	234	2	21	21	NUM
ap-1257	234	3	]	]	SYM
ap-1257	234	4	mei	mei	PROPN
ap-1257	234	5	,	,	PUNCT
ap-1257	234	6	w.	w.	PROPN
ap-1257	234	7	n.	n.	PROPN
ap-1257	234	8	,	,	PUNCT
ap-1257	234	9	lee	lee	PROPN
ap-1257	234	10	,	,	PUNCT
ap-1257	234	11	y.	y.	PROPN
ap-1257	234	12	c.	c.	PROPN
ap-1257	234	13	:	:	PUNCT
ap-1257	234	14	harmonic	harmonic	ADJ
ap-1257	234	15	oscillator	oscillator	NOUN
ap-1257	234	16	with	with	ADP
ap-1257	234	17	potential	potential	ADJ
ap-1257	234	18	barriers	barrier	NOUN
ap-1257	234	19	—	—	PUNCT
ap-1257	234	20	exact	exact	ADJ
ap-1257	234	21	solutions	solution	NOUN
ap-1257	234	22	and	and	CCONJ
ap-1257	234	23	perturbative	perturbative	ADJ
ap-1257	234	24	treatments	treatment	NOUN
ap-1257	234	25	.	.	PUNCT
ap-1257	235	1	j.	j.	PROPN
ap-1257	235	2	phys	phys	PROPN
ap-1257	235	3	.	.	PUNCT
ap-1257	236	1	a	a	PRON
ap-1257	236	2	,	,	PUNCT
ap-1257	236	3	16	16	NUM
ap-1257	236	4	(	(	PUNCT
ap-1257	236	5	8)	8)	NUM
ap-1257	236	6	,	,	PUNCT
ap-1257	236	7	1983	1983	NUM
ap-1257	236	8	,	,	PUNCT
ap-1257	236	9	p.	p.	NOUN
ap-1257	236	10	1	1	NUM
ap-1257	236	11	623–1	623–1	NUM
ap-1257	236	12	632	632	NUM
ap-1257	236	13	.	.	PUNCT
ap-1257	237	1	[	[	X
ap-1257	237	2	22	22	NUM
ap-1257	237	3	]	]	X
ap-1257	237	4	aquino	aquino	NOUN
ap-1257	237	5	,	,	PUNCT
ap-1257	237	6	n.	n.	NOUN
ap-1257	237	7	:	:	PUNCT
ap-1257	237	8	the	the	DET
ap-1257	237	9	isotropic	isotropic	NOUN
ap-1257	237	10	bounded	bound	VERB
ap-1257	237	11	oscillators	oscillator	NOUN
ap-1257	237	12	.	.	PUNCT
ap-1257	238	1	j.	j.	PROPN
ap-1257	238	2	phys	phys	PROPN
ap-1257	238	3	.	.	PUNCT
ap-1257	239	1	a	a	PRON
ap-1257	239	2	,	,	PUNCT
ap-1257	239	3	30	30	NUM
ap-1257	239	4	(	(	PUNCT
ap-1257	239	5	7	7	NUM
ap-1257	239	6	)	)	PUNCT
ap-1257	239	7	,	,	PUNCT
ap-1257	239	8	1997	1997	NUM
ap-1257	239	9	,	,	PUNCT
ap-1257	239	10	p.	p.	NOUN
ap-1257	239	11	2	2	NUM
ap-1257	239	12	403–2415	403–2415	NUM
ap-1257	239	13	.	.	PUNCT
ap-1257	240	1	[	[	X
ap-1257	240	2	23	23	NUM
ap-1257	240	3	]	]	PUNCT
ap-1257	240	4	varshni	varshni	NOUN
ap-1257	240	5	,	,	PUNCT
ap-1257	240	6	y.	y.	PROPN
ap-1257	240	7	p.	p.	PROPN
ap-1257	240	8	:	:	PUNCT
ap-1257	240	9	simple	simple	ADJ
ap-1257	240	10	wavefunction	wavefunction	NOUN
ap-1257	240	11	for	for	ADP
ap-1257	240	12	an	an	DET
ap-1257	240	13	impurity	impurity	NOUN
ap-1257	240	14	in	in	ADP
ap-1257	240	15	a	a	DET
ap-1257	240	16	parabolic	parabolic	ADJ
ap-1257	240	17	quantum	quantum	NOUN
ap-1257	240	18	dot	dot	NOUN
ap-1257	240	19	.	.	PUNCT
ap-1257	240	20	superlattice	superlattice	NOUN
ap-1257	240	21	microst	microst	ADJ
ap-1257	240	22	,	,	PUNCT
ap-1257	240	23	23	23	NUM
ap-1257	240	24	(	(	PUNCT
ap-1257	240	25	1	1	NUM
ap-1257	240	26	)	)	PUNCT
ap-1257	240	27	,	,	PUNCT
ap-1257	240	28	1998	1998	NUM
ap-1257	240	29	,	,	PUNCT
ap-1257	240	30	p.	p.	NOUN
ap-1257	240	31	145–149	145–149	NUM
ap-1257	240	32	.	.	PUNCT
ap-1257	241	1	[	[	X
ap-1257	241	2	24	24	NUM
ap-1257	241	3	]	]	SYM
ap-1257	241	4	tinkham	tinkham	NOUN
ap-1257	241	5	,	,	PUNCT
ap-1257	241	6	m.	m.	NOUN
ap-1257	241	7	:	:	PUNCT
ap-1257	241	8	group	group	NOUN
ap-1257	241	9	theory	theory	NOUN
ap-1257	241	10	and	and	CCONJ
ap-1257	241	11	quantum	quantum	NOUN
ap-1257	241	12	mechanics	mechanic	NOUN
ap-1257	241	13	,	,	PUNCT
ap-1257	241	14	new	new	PROPN
ap-1257	241	15	york	york	PROPN
ap-1257	241	16	,	,	PUNCT
ap-1257	241	17	mcgraw	mcgraw	PROPN
ap-1257	241	18	-	-	PUNCT
ap-1257	241	19	hill	hill	NOUN
ap-1257	241	20	,	,	PUNCT
ap-1257	241	21	1964	1964	NUM
ap-1257	241	22	.	.	PUNCT
ap-1257	242	1	[	[	X
ap-1257	242	2	25	25	NUM
ap-1257	242	3	]	]	X
ap-1257	242	4	amore	amore	NOUN
ap-1257	242	5	,	,	PUNCT
ap-1257	242	6	p.	p.	PROPN
ap-1257	242	7	,	,	PUNCT
ap-1257	242	8	fernández	fernández	PROPN
ap-1257	242	9	,	,	PUNCT
ap-1257	242	10	f.	f.	PROPN
ap-1257	242	11	m.	m.	PROPN
ap-1257	242	12	:	:	PUNCT
ap-1257	242	13	variational	variational	ADJ
ap-1257	242	14	collocation	collocation	NOUN
ap-1257	242	15	for	for	ADP
ap-1257	242	16	systems	system	NOUN
ap-1257	242	17	of	of	ADP
ap-1257	242	18	coupled	couple	VERB
ap-1257	242	19	anharmonic	anharmonic	ADJ
ap-1257	242	20	oscillators	oscillator	NOUN
ap-1257	242	21	.	.	PUNCT
ap-1257	243	1	arxiv	arxiv	NOUN
ap-1257	243	2	:	:	PUNCT
ap-1257	243	3	0905.1038v1	0905.1038v1	PUNCT
ap-1257	244	1	[	[	X
ap-1257	244	2	quant	quant	NOUN
ap-1257	244	3	-	-	PUNCT
ap-1257	244	4	ph	ph	ADJ
ap-1257	244	5	]	]	X
ap-1257	244	6	.	.	PUNCT
ap-1257	245	1	[	[	X
ap-1257	245	2	26	26	NUM
ap-1257	245	3	]	]	X
ap-1257	245	4	arteca	arteca	NOUN
ap-1257	245	5	,	,	PUNCT
ap-1257	245	6	g.	g.	PROPN
ap-1257	245	7	a.	a.	PROPN
ap-1257	245	8	,	,	PUNCT
ap-1257	245	9	fernández	fernández	PROPN
ap-1257	245	10	,	,	PUNCT
ap-1257	245	11	f.	f.	PROPN
ap-1257	245	12	m.	m.	PROPN
ap-1257	245	13	,	,	PUNCT
ap-1257	245	14	castro	castro	PROPN
ap-1257	245	15	,	,	PUNCT
ap-1257	245	16	e.	e.	PROPN
ap-1257	245	17	a.	a.	PROPN
ap-1257	245	18	:	:	PUNCT
ap-1257	245	19	approximate	approximate	ADJ
ap-1257	245	20	calculation	calculation	NOUN
ap-1257	245	21	of	of	ADP
ap-1257	245	22	physical	physical	ADJ
ap-1257	245	23	properties	property	NOUN
ap-1257	245	24	of	of	ADP
ap-1257	245	25	enclosed	enclose	VERB
ap-1257	245	26	central	central	ADJ
ap-1257	245	27	field	field	NOUN
ap-1257	245	28	quantum	quantum	NOUN
ap-1257	245	29	systems	system	NOUN
ap-1257	245	30	.	.	PUNCT
ap-1257	246	1	j.	j.	PROPN
ap-1257	246	2	chem	chem	PROPN
ap-1257	246	3	.	.	PUNCT
ap-1257	247	1	phys	phy	NOUN
ap-1257	247	2	.	.	PUNCT
ap-1257	247	3	,	,	PUNCT
ap-1257	247	4	80	80	NUM
ap-1257	247	5	(	(	PUNCT
ap-1257	247	6	4	4	NUM
ap-1257	247	7	)	)	PUNCT
ap-1257	247	8	,	,	PUNCT
ap-1257	247	9	1984	1984	NUM
ap-1257	247	10	,	,	PUNCT
ap-1257	247	11	p.	p.	NOUN
ap-1257	247	12	1	1	NUM
ap-1257	247	13	569–1	569–1	NUM
ap-1257	247	14	575	575	NUM
ap-1257	247	15	.	.	PUNCT
ap-1257	248	1	dr	dr	PROPN
ap-1257	248	2	.	.	PROPN
ap-1257	248	3	paolo	paolo	PROPN
ap-1257	248	4	amore	amore	PROPN
ap-1257	248	5	e	e	PROPN
ap-1257	248	6	-	-	NOUN
ap-1257	248	7	mail	mail	NOUN
ap-1257	248	8	:	:	PUNCT
ap-1257	248	9	paolo.amore@gmail.com	paolo.amore@gmail.com	X
ap-1257	248	10	facultad	facultad	PROPN
ap-1257	248	11	de	de	PROPN
ap-1257	248	12	ciencias	ciencias	PROPN
ap-1257	248	13	,	,	PUNCT
ap-1257	248	14	cuicbas	cuicbas	PROPN
ap-1257	248	15	universidad	universidad	PROPN
ap-1257	248	16	de	de	PROPN
ap-1257	248	17	colima	colima	PROPN
ap-1257	248	18	bernal	bernal	PROPN
ap-1257	248	19	dı́az	dı́az	PROPN
ap-1257	248	20	del	del	PROPN
ap-1257	248	21	castillo	castillo	PROPN
ap-1257	248	22	340	340	NUM
ap-1257	248	23	,	,	PUNCT
ap-1257	248	24	colima	colima	PROPN
ap-1257	248	25	,	,	PUNCT
ap-1257	248	26	colima	colima	PROPN
ap-1257	248	27	,	,	PUNCT
ap-1257	249	1	mexico	mexico	PROPN
ap-1257	249	2	dr	dr	PROPN
ap-1257	249	3	.	.	PROPN
ap-1257	249	4	francisco	francisco	PROPN
ap-1257	249	5	m.	m.	NOUN
ap-1257	249	6	fernández	fernández	PROPN
ap-1257	249	7	e	e	NOUN
ap-1257	249	8	-	-	NOUN
ap-1257	249	9	mail	mail	NOUN
ap-1257	249	10	:	:	PUNCT
ap-1257	249	11	fernande@quimica.unlp.edu.ar	fernande@quimica.unlp.edu.ar	VERB
ap-1257	249	12	inifta	inifta	PROPN
ap-1257	249	13	(	(	PUNCT
ap-1257	249	14	conicet	conicet	PROPN
ap-1257	249	15	,	,	PUNCT
ap-1257	249	16	unlp	unlp	ADJ
ap-1257	249	17	)	)	PUNCT
ap-1257	249	18	division	division	NOUN
ap-1257	249	19	quimica	quimica	PROPN
ap-1257	249	20	teorica	teorica	PROPN
ap-1257	249	21	diagonal	diagonal	ADJ
ap-1257	249	22	113	113	NUM
ap-1257	249	23	y	y	PROPN
ap-1257	249	24	64	64	NUM
ap-1257	249	25	s	s	NOUN
ap-1257	249	26	/	/	SYM
ap-1257	249	27	n	n	X
ap-1257	249	28	sucursal	sucursal	ADJ
ap-1257	249	29	4	4	NUM
ap-1257	249	30	,	,	PUNCT
ap-1257	249	31	casilla	casilla	X
ap-1257	249	32	de	de	X
ap-1257	249	33	correo	correo	PROPN
ap-1257	249	34	16	16	NUM
ap-1257	249	35	,	,	PUNCT
ap-1257	249	36	1900	1900	NUM
ap-1257	249	37	la	la	PROPN
ap-1257	249	38	plata	plata	PROPN
ap-1257	249	39	,	,	PUNCT
ap-1257	249	40	argentina	argentina	PROPN
ap-1257	249	41	24	24	NUM