id	sid	tid	token	lemma	pos
ap-7668	1	1	acta	acta	PROPN
ap-7668	1	2	polytechnica	polytechnica	PROPN
ap-7668	1	3	https://doi.org/10.14311/ap.2022.62.0050	https://doi.org/10.14311/ap.2022.62.0050	PROPN
ap-7668	1	4	acta	acta	PROPN
ap-7668	1	5	polytechnica	polytechnica	PROPN
ap-7668	1	6	62(1):50–55	62(1):50–55	ADP
ap-7668	1	7	,	,	PUNCT
ap-7668	1	8	2022	2022	NUM
ap-7668	1	9	©	©	ADP
ap-7668	1	10	2022	2022	NUM
ap-7668	1	11	the	the	DET
ap-7668	1	12	author(s	author(s	NOUN
ap-7668	1	13	)	)	PUNCT
ap-7668	1	14	.	.	PUNCT
ap-7668	2	1	licensed	license	VERB
ap-7668	2	2	under	under	ADP
ap-7668	2	3	a	a	DET
ap-7668	2	4	cc	cc	NOUN
ap-7668	2	5	-	-	PUNCT
ap-7668	2	6	by	by	ADP
ap-7668	2	7	4.0	4.0	NUM
ap-7668	2	8	licence	licence	NOUN
ap-7668	2	9	published	publish	VERB
ap-7668	2	10	by	by	ADP
ap-7668	2	11	the	the	DET
ap-7668	2	12	czech	czech	PROPN
ap-7668	2	13	technical	technical	PROPN
ap-7668	2	14	university	university	PROPN
ap-7668	2	15	in	in	ADP
ap-7668	2	16	prague	prague	PROPN
ap-7668	2	17	generalized	generalize	VERB
ap-7668	2	18	three	three	NUM
ap-7668	2	19	-	-	PUNCT
ap-7668	2	20	body	body	NOUN
ap-7668	2	21	harmonic	harmonic	ADJ
ap-7668	2	22	oscillator	oscillator	NOUN
ap-7668	2	23	system	system	NOUN
ap-7668	2	24	:	:	PUNCT
ap-7668	2	25	ground	ground	NOUN
ap-7668	2	26	state	state	PROPN
ap-7668	2	27	adrian	adrian	PROPN
ap-7668	2	28	m.	m.	NOUN
ap-7668	2	29	escobar	escobar	PROPN
ap-7668	2	30	-	-	PUNCT
ap-7668	2	31	ruiz∗	ruiz∗	NOUN
ap-7668	2	32	,	,	PUNCT
ap-7668	2	33	fidel	fidel	PROPN
ap-7668	2	34	montoya	montoya	PROPN
ap-7668	2	35	universidad	universidad	PROPN
ap-7668	2	36	autónoma	autónoma	PROPN
ap-7668	2	37	metropolitana	metropolitana	PROPN
ap-7668	2	38	,	,	PUNCT
ap-7668	2	39	departamento	departamento	PROPN
ap-7668	2	40	de	de	PROPN
ap-7668	2	41	física	física	PROPN
ap-7668	2	42	,	,	PUNCT
ap-7668	2	43	av	av	PROPN
ap-7668	2	44	.	.	PUNCT
ap-7668	3	1	san	san	PROPN
ap-7668	3	2	rafael	rafael	PROPN
ap-7668	3	3	atlixco	atlixco	PROPN
ap-7668	3	4	186	186	NUM
ap-7668	3	5	,	,	PUNCT
ap-7668	3	6	09340	09340	NUM
ap-7668	3	7	ciudad	ciudad	PROPN
ap-7668	3	8	de	de	PROPN
ap-7668	3	9	méxico	méxico	PROPN
ap-7668	3	10	,	,	PUNCT
ap-7668	3	11	cdmx	cdmx	PROPN
ap-7668	3	12	,	,	PUNCT
ap-7668	3	13	méxico	méxico	PROPN
ap-7668	3	14	∗	∗	NOUN
ap-7668	3	15	corresponding	correspond	VERB
ap-7668	3	16	author	author	NOUN
ap-7668	3	17	:	:	PUNCT
ap-7668	3	18	admau@xanum.uam.mx	admau@xanum.uam.mx	ADJ
ap-7668	3	19	abstract	abstract	NOUN
ap-7668	3	20	.	.	PUNCT
ap-7668	4	1	in	in	ADP
ap-7668	4	2	this	this	DET
ap-7668	4	3	work	work	NOUN
ap-7668	4	4	we	we	PRON
ap-7668	4	5	report	report	VERB
ap-7668	4	6	on	on	ADP
ap-7668	4	7	a	a	DET
ap-7668	4	8	3	3	NUM
ap-7668	4	9	-	-	PUNCT
ap-7668	4	10	body	body	NOUN
ap-7668	4	11	system	system	NOUN
ap-7668	4	12	in	in	ADP
ap-7668	4	13	a	a	DET
ap-7668	4	14	d−dimensional	d−dimensional	ADJ
ap-7668	4	15	space	space	NOUN
ap-7668	4	16	rd	rd	NOUN
ap-7668	4	17	with	with	ADP
ap-7668	4	18	a	a	DET
ap-7668	4	19	quadratic	quadratic	ADJ
ap-7668	4	20	harmonic	harmonic	ADJ
ap-7668	4	21	potential	potential	NOUN
ap-7668	4	22	in	in	ADP
ap-7668	4	23	the	the	DET
ap-7668	4	24	relative	relative	ADJ
ap-7668	4	25	distances	distance	NOUN
ap-7668	4	26	rij	rij	PROPN
ap-7668	5	1	=	=	PUNCT
ap-7668	5	2	|ri	|ri	PROPN
ap-7668	5	3	−	−	X
ap-7668	5	4	rj	rj	PROPN
ap-7668	5	5	|	|	ADV
ap-7668	5	6	between	between	ADP
ap-7668	5	7	particles	particle	NOUN
ap-7668	5	8	.	.	PUNCT
ap-7668	6	1	our	our	PRON
ap-7668	6	2	study	study	NOUN
ap-7668	6	3	considers	consider	VERB
ap-7668	6	4	unequal	unequal	ADJ
ap-7668	6	5	masses	masse	NOUN
ap-7668	6	6	,	,	PUNCT
ap-7668	6	7	different	different	ADJ
ap-7668	6	8	spring	spring	NOUN
ap-7668	6	9	constants	constant	NOUN
ap-7668	7	1	and	and	CCONJ
ap-7668	7	2	it	it	PRON
ap-7668	7	3	is	be	AUX
ap-7668	7	4	defined	define	VERB
ap-7668	7	5	in	in	ADP
ap-7668	7	6	the	the	DET
ap-7668	7	7	three	three	NUM
ap-7668	7	8	-	-	PUNCT
ap-7668	7	9	dimensional	dimensional	ADJ
ap-7668	7	10	(	(	PUNCT
ap-7668	7	11	sub)space	sub)space	NOUN
ap-7668	7	12	of	of	ADP
ap-7668	7	13	solutions	solution	NOUN
ap-7668	7	14	characterized	characterize	VERB
ap-7668	7	15	(	(	PUNCT
ap-7668	7	16	globally	globally	ADV
ap-7668	7	17	)	)	PUNCT
ap-7668	7	18	by	by	ADP
ap-7668	7	19	zero	zero	NUM
ap-7668	7	20	total	total	ADJ
ap-7668	7	21	angular	angular	ADJ
ap-7668	7	22	momentum	momentum	NOUN
ap-7668	7	23	.	.	PUNCT
ap-7668	8	1	this	this	DET
ap-7668	8	2	system	system	NOUN
ap-7668	8	3	is	be	AUX
ap-7668	8	4	exactly	exactly	ADV
ap-7668	8	5	-	-	PUNCT
ap-7668	8	6	solvable	solvable	ADJ
ap-7668	8	7	with	with	ADP
ap-7668	8	8	hidden	hidden	ADJ
ap-7668	8	9	algebra	algebra	NOUN
ap-7668	8	10	sℓ4(r	sℓ4(r	PROPN
ap-7668	8	11	)	)	PUNCT
ap-7668	8	12	.	.	PUNCT
ap-7668	9	1	it	it	PRON
ap-7668	9	2	is	be	AUX
ap-7668	9	3	shown	show	VERB
ap-7668	9	4	that	that	SCONJ
ap-7668	9	5	in	in	ADP
ap-7668	9	6	some	some	DET
ap-7668	9	7	particular	particular	ADJ
ap-7668	9	8	cases	case	NOUN
ap-7668	9	9	the	the	DET
ap-7668	9	10	system	system	NOUN
ap-7668	9	11	becomes	become	VERB
ap-7668	9	12	maximally	maximally	ADV
ap-7668	9	13	(	(	PUNCT
ap-7668	9	14	minimally	minimally	ADV
ap-7668	9	15	)	)	PUNCT
ap-7668	9	16	superintegrable	superintegrable	ADJ
ap-7668	9	17	.	.	PUNCT
ap-7668	10	1	we	we	PRON
ap-7668	10	2	pay	pay	VERB
ap-7668	10	3	special	special	ADJ
ap-7668	10	4	attention	attention	NOUN
ap-7668	10	5	to	to	ADP
ap-7668	10	6	a	a	DET
ap-7668	10	7	physically	physically	ADV
ap-7668	10	8	relevant	relevant	ADJ
ap-7668	10	9	generalization	generalization	NOUN
ap-7668	10	10	of	of	ADP
ap-7668	10	11	the	the	DET
ap-7668	10	12	model	model	NOUN
ap-7668	10	13	where	where	SCONJ
ap-7668	10	14	eventually	eventually	ADV
ap-7668	10	15	the	the	DET
ap-7668	10	16	integrability	integrability	NOUN
ap-7668	10	17	is	be	AUX
ap-7668	10	18	lost	lose	VERB
ap-7668	10	19	.	.	PUNCT
ap-7668	11	1	in	in	ADP
ap-7668	11	2	particular	particular	ADJ
ap-7668	11	3	,	,	PUNCT
ap-7668	11	4	the	the	DET
ap-7668	11	5	ground	ground	NOUN
ap-7668	11	6	state	state	NOUN
ap-7668	11	7	and	and	CCONJ
ap-7668	11	8	the	the	DET
ap-7668	11	9	first	first	ADJ
ap-7668	11	10	excited	excited	ADJ
ap-7668	11	11	state	state	NOUN
ap-7668	11	12	are	be	AUX
ap-7668	11	13	determined	determine	VERB
ap-7668	11	14	within	within	ADP
ap-7668	11	15	a	a	DET
ap-7668	11	16	perturbative	perturbative	ADJ
ap-7668	11	17	framework	framework	NOUN
ap-7668	11	18	.	.	PUNCT
ap-7668	12	1	keywords	keyword	NOUN
ap-7668	12	2	:	:	PUNCT
ap-7668	12	3	three	three	NUM
ap-7668	12	4	-	-	PUNCT
ap-7668	12	5	body	body	NOUN
ap-7668	12	6	system	system	NOUN
ap-7668	12	7	,	,	PUNCT
ap-7668	12	8	exact	exact	ADJ
ap-7668	12	9	-	-	PUNCT
ap-7668	12	10	solvability	solvability	NOUN
ap-7668	12	11	,	,	PUNCT
ap-7668	12	12	hidden	hidden	ADJ
ap-7668	12	13	algebra	algebra	NOUN
ap-7668	12	14	,	,	PUNCT
ap-7668	12	15	integrability	integrability	NOUN
ap-7668	12	16	.	.	PUNCT
ap-7668	13	1	1	1	X
ap-7668	13	2	.	.	X
ap-7668	13	3	introduction	introduction	NOUN
ap-7668	13	4	the	the	DET
ap-7668	13	5	two	two	NUM
ap-7668	13	6	-	-	PUNCT
ap-7668	13	7	body	body	NOUN
ap-7668	13	8	harmonic	harmonic	ADJ
ap-7668	13	9	oscillator	oscillator	NOUN
ap-7668	13	10	,	,	PUNCT
ap-7668	13	11	i.e.	i.e.	X
ap-7668	13	12	two	two	NUM
ap-7668	13	13	particles	particle	NOUN
ap-7668	13	14	with	with	ADP
ap-7668	13	15	masses	masse	NOUN
ap-7668	13	16	m1	m1	PROPN
ap-7668	13	17	and	and	CCONJ
ap-7668	13	18	m2	m2	PROPN
ap-7668	13	19	interacting	interact	VERB
ap-7668	13	20	via	via	ADP
ap-7668	13	21	the	the	DET
ap-7668	13	22	translational	translational	ADJ
ap-7668	13	23	invariant	invariant	ADJ
ap-7668	13	24	potential	potential	NOUN
ap-7668	13	25	v	v	ADP
ap-7668	13	26	∝	∝	PROPN
ap-7668	13	27	|ri	|ri	X
ap-7668	13	28	−	−	PROPN
ap-7668	13	29	rj	rj	PROPN
ap-7668	13	30	|2	|2	NUM
ap-7668	13	31	,	,	PUNCT
ap-7668	13	32	appears	appear	VERB
ap-7668	13	33	in	in	ADP
ap-7668	13	34	all	all	DET
ap-7668	13	35	textbook	textbook	NOUN
ap-7668	13	36	in	in	ADP
ap-7668	13	37	classical	classical	ADJ
ap-7668	13	38	mechanics	mechanic	NOUN
ap-7668	13	39	.	.	PUNCT
ap-7668	14	1	in	in	ADP
ap-7668	14	2	an	an	DET
ap-7668	14	3	arbitrary	arbitrary	ADJ
ap-7668	14	4	d−dimensional	d−dimensional	ADJ
ap-7668	14	5	euclidean	euclidean	ADJ
ap-7668	14	6	space	space	NOUN
ap-7668	14	7	rd	rd	PROPN
ap-7668	14	8	this	this	DET
ap-7668	14	9	system	system	NOUN
ap-7668	14	10	admits	admit	VERB
ap-7668	14	11	separation	separation	NOUN
ap-7668	14	12	of	of	ADP
ap-7668	14	13	variables	variable	NOUN
ap-7668	14	14	in	in	ADP
ap-7668	14	15	the	the	DET
ap-7668	14	16	center	center	NOUN
ap-7668	14	17	-	-	PUNCT
ap-7668	14	18	of	of	ADP
ap-7668	14	19	-	-	PUNCT
ap-7668	14	20	mass	mass	ADJ
ap-7668	14	21	and	and	CCONJ
ap-7668	14	22	relative	relative	ADJ
ap-7668	14	23	coordinates	coordinate	NOUN
ap-7668	14	24	as	as	ADV
ap-7668	14	25	well	well	ADV
ap-7668	14	26	as	as	ADP
ap-7668	14	27	exact	exact	ADJ
ap-7668	14	28	solvability	solvability	NOUN
ap-7668	14	29	.	.	PUNCT
ap-7668	15	1	the	the	DET
ap-7668	15	2	relevance	relevance	NOUN
ap-7668	15	3	of	of	ADP
ap-7668	15	4	such	such	DET
ap-7668	15	5	a	a	DET
ap-7668	15	6	system	system	NOUN
ap-7668	15	7	is	be	AUX
ap-7668	15	8	obvious	obvious	ADJ
ap-7668	15	9	:	:	PUNCT
ap-7668	15	10	any	any	DET
ap-7668	15	11	scalar	scalar	ADJ
ap-7668	15	12	potential	potential	ADJ
ap-7668	15	13	u	u	NOUN
ap-7668	15	14	=	=	SYM
ap-7668	15	15	u(|ri	u(|ri	PROPN
ap-7668	15	16	−	−	PROPN
ap-7668	15	17	rj	rj	PROPN
ap-7668	15	18	|	|	NOUN
ap-7668	15	19	)	)	PUNCT
ap-7668	15	20	can	can	AUX
ap-7668	15	21	be	be	AUX
ap-7668	15	22	approximated	approximate	VERB
ap-7668	15	23	by	by	ADP
ap-7668	15	24	the	the	DET
ap-7668	15	25	two	two	NUM
ap-7668	15	26	-	-	PUNCT
ap-7668	15	27	body	body	NOUN
ap-7668	15	28	harmonic	harmonic	ADJ
ap-7668	15	29	oscillator	oscillator	NOUN
ap-7668	15	30	.	.	PUNCT
ap-7668	16	1	in	in	ADP
ap-7668	16	2	this	this	DET
ap-7668	16	3	case	case	NOUN
ap-7668	16	4	,	,	PUNCT
ap-7668	16	5	the	the	DET
ap-7668	16	6	centerof	centerof	NOUN
ap-7668	16	7	-	-	PUNCT
ap-7668	16	8	mass	mass	ADJ
ap-7668	16	9	and	and	CCONJ
ap-7668	16	10	relative	relative	ADJ
ap-7668	16	11	coordinates	coordinate	NOUN
ap-7668	16	12	are	be	AUX
ap-7668	16	13	nothing	nothing	PRON
ap-7668	16	14	but	but	SCONJ
ap-7668	16	15	the	the	DET
ap-7668	16	16	normal	normal	ADJ
ap-7668	16	17	coordinates	coordinate	NOUN
ap-7668	16	18	.	.	PUNCT
ap-7668	17	1	therefore	therefore	ADV
ap-7668	17	2	,	,	PUNCT
ap-7668	17	3	in	in	ADP
ap-7668	17	4	the	the	DET
ap-7668	17	5	n	n	CCONJ
ap-7668	17	6	-	-	PUNCT
ap-7668	17	7	body	body	NOUN
ap-7668	17	8	case	case	NOUN
ap-7668	17	9	of	of	ADP
ap-7668	17	10	n	n	PROPN
ap-7668	17	11	>	>	SYM
ap-7668	17	12	2	2	NUM
ap-7668	17	13	particles	particle	NOUN
ap-7668	17	14	interacting	interact	VERB
ap-7668	17	15	by	by	ADP
ap-7668	17	16	a	a	DET
ap-7668	17	17	quadratic	quadratic	ADJ
ap-7668	17	18	pairwise	pairwise	NOUN
ap-7668	17	19	potential	potential	NOUN
ap-7668	17	20	it	it	PRON
ap-7668	17	21	is	be	AUX
ap-7668	17	22	natural	natural	ADJ
ap-7668	17	23	to	to	PART
ap-7668	17	24	ask	ask	VERB
ap-7668	17	25	the	the	DET
ap-7668	17	26	question	question	NOUN
ap-7668	17	27	about	about	ADP
ap-7668	17	28	the	the	DET
ap-7668	17	29	existence	existence	NOUN
ap-7668	17	30	of	of	ADP
ap-7668	17	31	normal	normal	ADJ
ap-7668	17	32	coordinates	coordinate	NOUN
ap-7668	17	33	and	and	CCONJ
ap-7668	17	34	the	the	DET
ap-7668	17	35	corresponding	corresponding	ADJ
ap-7668	17	36	explicit	explicit	ADJ
ap-7668	17	37	exact	exact	ADJ
ap-7668	17	38	solutions	solution	NOUN
ap-7668	17	39	.	.	PUNCT
ap-7668	18	1	interestingly	interestingly	ADV
ap-7668	18	2	,	,	PUNCT
ap-7668	18	3	even	even	ADV
ap-7668	18	4	for	for	ADP
ap-7668	18	5	the	the	DET
ap-7668	18	6	three	three	NUM
ap-7668	18	7	-	-	PUNCT
ap-7668	18	8	body	body	NOUN
ap-7668	18	9	case	case	NOUN
ap-7668	18	10	n	n	NOUN
ap-7668	18	11	=	=	SYM
ap-7668	18	12	3	3	NUM
ap-7668	18	13	a	a	DET
ap-7668	18	14	complete	complete	ADJ
ap-7668	18	15	separation	separation	NOUN
ap-7668	18	16	of	of	ADP
ap-7668	18	17	variables	variable	NOUN
ap-7668	18	18	can	can	AUX
ap-7668	18	19	not	not	PART
ap-7668	18	20	be	be	AUX
ap-7668	18	21	achieved	achieve	VERB
ap-7668	18	22	in	in	ADP
ap-7668	18	23	full	full	ADJ
ap-7668	18	24	generality	generality	NOUN
ap-7668	18	25	.	.	PUNCT
ap-7668	19	1	starting	start	VERB
ap-7668	19	2	in	in	ADP
ap-7668	19	3	1935	1935	NUM
ap-7668	19	4	,	,	PUNCT
ap-7668	19	5	the	the	DET
ap-7668	19	6	quantum	quantum	NOUN
ap-7668	19	7	n−body	n−body	PROPN
ap-7668	19	8	problem	problem	NOUN
ap-7668	19	9	in	in	ADP
ap-7668	19	10	r3	r3	PROPN
ap-7668	19	11	was	be	AUX
ap-7668	19	12	studied	study	VERB
ap-7668	19	13	by	by	ADP
ap-7668	19	14	zernike	zernike	NOUN
ap-7668	19	15	and	and	CCONJ
ap-7668	19	16	brinkman	brinkman	NOUN
ap-7668	20	1	[	[	X
ap-7668	20	2	1	1	NUM
ap-7668	20	3	]	]	PUNCT
ap-7668	20	4	using	use	VERB
ap-7668	20	5	the	the	DET
ap-7668	20	6	so	so	ADV
ap-7668	20	7	-	-	PUNCT
ap-7668	20	8	called	call	VERB
ap-7668	20	9	hyperspherical	hyperspherical	ADJ
ap-7668	20	10	-	-	PUNCT
ap-7668	20	11	harmonic	harmonic	ADJ
ap-7668	20	12	expansion	expansion	NOUN
ap-7668	20	13	.	.	PUNCT
ap-7668	21	1	two	two	NUM
ap-7668	21	2	decades	decade	NOUN
ap-7668	21	3	later	later	ADV
ap-7668	21	4	,	,	PUNCT
ap-7668	21	5	this	this	DET
ap-7668	21	6	method	method	NOUN
ap-7668	21	7	possessing	possess	VERB
ap-7668	21	8	an	an	DET
ap-7668	21	9	underlying	underlie	VERB
ap-7668	21	10	group	group	NOUN
ap-7668	21	11	-	-	PUNCT
ap-7668	21	12	theoretical	theoretical	ADJ
ap-7668	21	13	nature	nature	NOUN
ap-7668	21	14	was	be	AUX
ap-7668	21	15	then	then	ADV
ap-7668	21	16	reacquainted	reacquaint	VERB
ap-7668	21	17	and	and	CCONJ
ap-7668	21	18	refined	refine	VERB
ap-7668	21	19	in	in	ADP
ap-7668	21	20	the	the	DET
ap-7668	21	21	papers	paper	NOUN
ap-7668	21	22	by	by	ADP
ap-7668	21	23	delves	delf	NOUN
ap-7668	21	24	[	[	X
ap-7668	21	25	2	2	NUM
ap-7668	21	26	]	]	PUNCT
ap-7668	21	27	and	and	CCONJ
ap-7668	21	28	smith	smith	NOUN
ap-7668	22	1	[	[	X
ap-7668	22	2	3	3	NUM
ap-7668	22	3	]	]	PUNCT
ap-7668	22	4	.	.	PUNCT
ap-7668	23	1	nevertheless	nevertheless	ADV
ap-7668	23	2	,	,	PUNCT
ap-7668	23	3	in	in	ADP
ap-7668	23	4	practice	practice	NOUN
ap-7668	23	5	the	the	DET
ap-7668	23	6	success	success	NOUN
ap-7668	23	7	of	of	ADP
ap-7668	23	8	the	the	DET
ap-7668	23	9	method	method	NOUN
ap-7668	23	10	is	be	AUX
ap-7668	23	11	limited	limit	VERB
ap-7668	23	12	to	to	ADP
ap-7668	23	13	the	the	DET
ap-7668	23	14	case	case	NOUN
ap-7668	23	15	of	of	ADP
ap-7668	23	16	highly	highly	ADV
ap-7668	23	17	symmetric	symmetric	ADJ
ap-7668	23	18	systems	system	NOUN
ap-7668	23	19	,	,	PUNCT
ap-7668	23	20	namely	namely	ADV
ap-7668	23	21	identical	identical	ADJ
ap-7668	23	22	particles	particle	NOUN
ap-7668	23	23	with	with	ADP
ap-7668	23	24	equal	equal	ADJ
ap-7668	23	25	masses	masse	NOUN
ap-7668	23	26	and	and	CCONJ
ap-7668	23	27	equal	equal	ADJ
ap-7668	23	28	spring	spring	NOUN
ap-7668	23	29	constants	constant	NOUN
ap-7668	23	30	.	.	PUNCT
ap-7668	24	1	in	in	ADP
ap-7668	24	2	a	a	DET
ap-7668	24	3	previous	previous	ADJ
ap-7668	24	4	work	work	NOUN
ap-7668	24	5	[	[	X
ap-7668	24	6	4	4	NUM
ap-7668	24	7	]	]	PUNCT
ap-7668	24	8	,	,	PUNCT
ap-7668	24	9	the	the	DET
ap-7668	24	10	most	most	ADV
ap-7668	24	11	general	general	ADJ
ap-7668	24	12	quantum	quantum	ADJ
ap-7668	24	13	system	system	NOUN
ap-7668	24	14	of	of	ADP
ap-7668	24	15	a	a	DET
ap-7668	24	16	three	three	NUM
ap-7668	24	17	-	-	PUNCT
ap-7668	24	18	body	body	NOUN
ap-7668	24	19	chain	chain	NOUN
ap-7668	24	20	of	of	ADP
ap-7668	24	21	harmonic	harmonic	ADJ
ap-7668	24	22	oscillators	oscillator	NOUN
ap-7668	24	23	,	,	PUNCT
ap-7668	24	24	in	in	ADP
ap-7668	24	25	rd	rd	PROPN
ap-7668	24	26	,	,	PUNCT
ap-7668	24	27	was	be	AUX
ap-7668	24	28	explored	explore	VERB
ap-7668	24	29	exhaustively	exhaustively	ADV
ap-7668	24	30	.	.	PUNCT
ap-7668	25	1	for	for	ADP
ap-7668	25	2	arbitrary	arbitrary	ADJ
ap-7668	25	3	masses	masse	NOUN
ap-7668	25	4	and	and	CCONJ
ap-7668	25	5	spring	spring	NOUN
ap-7668	25	6	constants	constant	NOUN
ap-7668	25	7	this	this	DET
ap-7668	25	8	problem	problem	NOUN
ap-7668	25	9	possesses	possess	VERB
ap-7668	25	10	spherical	spherical	ADJ
ap-7668	25	11	symmetry	symmetry	NOUN
ap-7668	25	12	.	.	PUNCT
ap-7668	26	1	it	it	PRON
ap-7668	26	2	implies	imply	VERB
ap-7668	26	3	that	that	SCONJ
ap-7668	26	4	the	the	DET
ap-7668	26	5	total	total	ADJ
ap-7668	26	6	angular	angular	ADJ
ap-7668	26	7	momentum	momentum	NOUN
ap-7668	26	8	is	be	AUX
ap-7668	26	9	a	a	DET
ap-7668	26	10	well	well	ADV
ap-7668	26	11	-	-	PUNCT
ap-7668	26	12	defined	define	VERB
ap-7668	26	13	observable	observable	ADJ
ap-7668	26	14	which	which	PRON
ap-7668	26	15	allows	allow	VERB
ap-7668	26	16	to	to	PART
ap-7668	26	17	reduce	reduce	VERB
ap-7668	26	18	effectively	effectively	ADV
ap-7668	26	19	the	the	DET
ap-7668	26	20	number	number	NOUN
ap-7668	26	21	of	of	ADP
ap-7668	26	22	degrees	degree	NOUN
ap-7668	26	23	of	of	ADP
ap-7668	26	24	freedom	freedom	NOUN
ap-7668	26	25	in	in	ADP
ap-7668	26	26	the	the	DET
ap-7668	26	27	corresponding	correspond	VERB
ap-7668	26	28	schrödinger	schrödinger	ADJ
ap-7668	26	29	equation	equation	NOUN
ap-7668	26	30	governing	govern	VERB
ap-7668	26	31	the	the	DET
ap-7668	26	32	states	state	NOUN
ap-7668	26	33	with	with	ADP
ap-7668	26	34	zero	zero	NUM
ap-7668	26	35	angular	angular	ADJ
ap-7668	26	36	momentum	momentum	NOUN
ap-7668	26	37	.	.	PUNCT
ap-7668	27	1	in	in	ADP
ap-7668	27	2	the	the	DET
ap-7668	27	3	sector	sector	NOUN
ap-7668	27	4	of	of	ADP
ap-7668	27	5	vanishing	vanish	VERB
ap-7668	27	6	angular	angular	ADJ
ap-7668	27	7	momentum	momentum	NOUN
ap-7668	27	8	,	,	PUNCT
ap-7668	27	9	it	it	PRON
ap-7668	27	10	turns	turn	VERB
ap-7668	27	11	out	out	ADP
ap-7668	27	12	that	that	SCONJ
ap-7668	27	13	this	this	DET
ap-7668	27	14	three	three	NUM
ap-7668	27	15	-	-	PUNCT
ap-7668	27	16	body	body	NOUN
ap-7668	27	17	quantum	quantum	NOUN
ap-7668	27	18	system	system	NOUN
ap-7668	27	19	is	be	AUX
ap-7668	27	20	exactly	exactly	ADV
ap-7668	27	21	solvable	solvable	ADJ
ap-7668	27	22	.	.	PUNCT
ap-7668	28	1	the	the	DET
ap-7668	28	2	hidden	hide	VERB
ap-7668	28	3	algebra	algebra	NOUN
ap-7668	28	4	sℓ(4,r	sℓ(4,r	ADJ
ap-7668	28	5	)	)	PUNCT
ap-7668	28	6	responsible	responsible	ADJ
ap-7668	28	7	of	of	ADP
ap-7668	28	8	the	the	DET
ap-7668	28	9	exact	exact	ADJ
ap-7668	28	10	solvability	solvability	NOUN
ap-7668	28	11	was	be	AUX
ap-7668	28	12	exhibited	exhibit	VERB
ap-7668	28	13	in	in	ADP
ap-7668	28	14	[	[	X
ap-7668	28	15	4	4	X
ap-7668	28	16	]	]	PUNCT
ap-7668	28	17	using	use	VERB
ap-7668	28	18	the	the	DET
ap-7668	28	19	ρ	ρ	NOUN
ap-7668	28	20	-	-	PUNCT
ap-7668	28	21	representation	representation	NOUN
ap-7668	28	22	.	.	PUNCT
ap-7668	29	1	in	in	ADP
ap-7668	29	2	the	the	DET
ap-7668	29	3	present	present	ADJ
ap-7668	29	4	work	work	NOUN
ap-7668	29	5	we	we	PRON
ap-7668	29	6	consider	consider	VERB
ap-7668	29	7	a	a	DET
ap-7668	29	8	physically	physically	ADV
ap-7668	29	9	relevant	relevant	ADJ
ap-7668	29	10	generalization	generalization	NOUN
ap-7668	29	11	of	of	ADP
ap-7668	29	12	the	the	DET
ap-7668	29	13	model	model	NOUN
ap-7668	29	14	where	where	SCONJ
ap-7668	29	15	eventually	eventually	ADV
ap-7668	29	16	the	the	DET
ap-7668	29	17	integrability	integrability	NOUN
ap-7668	29	18	properties	property	NOUN
ap-7668	29	19	are	be	AUX
ap-7668	29	20	lost	lose	VERB
ap-7668	29	21	.	.	PUNCT
ap-7668	30	1	again	again	ADV
ap-7668	30	2	,	,	PUNCT
ap-7668	30	3	in	in	ADP
ap-7668	30	4	our	our	PRON
ap-7668	30	5	analysis	analysis	NOUN
ap-7668	30	6	we	we	PRON
ap-7668	30	7	assume	assume	VERB
ap-7668	30	8	a	a	DET
ap-7668	30	9	system	system	NOUN
ap-7668	30	10	of	of	ADP
ap-7668	30	11	arbitrary	arbitrary	ADJ
ap-7668	30	12	masses	masse	NOUN
ap-7668	30	13	and	and	CCONJ
ap-7668	30	14	spring	spring	NOUN
ap-7668	30	15	constants	constant	NOUN
ap-7668	30	16	with	with	ADP
ap-7668	30	17	the	the	DET
ap-7668	30	18	total	total	ADJ
ap-7668	30	19	angular	angular	ADJ
ap-7668	30	20	momentum	momentum	NOUN
ap-7668	30	21	identically	identically	ADV
ap-7668	30	22	zero	zero	NUM
ap-7668	30	23	.	.	PUNCT
ap-7668	31	1	in	in	ADP
ap-7668	31	2	the	the	DET
ap-7668	31	3	current	current	ADJ
ap-7668	31	4	study	study	NOUN
ap-7668	31	5	we	we	PRON
ap-7668	31	6	revisited	revisit	VERB
ap-7668	31	7	the	the	DET
ap-7668	31	8	algebraic	algebraic	ADJ
ap-7668	31	9	structure	structure	NOUN
ap-7668	31	10	and	and	CCONJ
ap-7668	31	11	solvability	solvability	NOUN
ap-7668	31	12	of	of	ADP
ap-7668	31	13	the	the	DET
ap-7668	31	14	quantum	quantum	ADJ
ap-7668	31	15	3	3	NUM
ap-7668	31	16	-	-	PUNCT
ap-7668	31	17	body	body	NOUN
ap-7668	31	18	quantum	quantum	NOUN
ap-7668	31	19	oscillator	oscillator	NOUN
ap-7668	31	20	system	system	NOUN
ap-7668	31	21	in	in	ADP
ap-7668	31	22	the	the	DET
ap-7668	31	23	special	special	ADJ
ap-7668	31	24	set	set	NOUN
ap-7668	31	25	of	of	ADP
ap-7668	31	26	coordinates	coordinate	NOUN
ap-7668	31	27	appearing	appear	VERB
ap-7668	31	28	in	in	ADP
ap-7668	31	29	[	[	X
ap-7668	31	30	5	5	NUM
ap-7668	31	31	]	]	PUNCT
ap-7668	31	32	,	,	PUNCT
ap-7668	31	33	[	[	X
ap-7668	31	34	6	6	NUM
ap-7668	31	35	]	]	PUNCT
ap-7668	31	36	.	.	PUNCT
ap-7668	32	1	afterwards	afterwards	ADV
ap-7668	32	2	,	,	PUNCT
ap-7668	32	3	a	a	DET
ap-7668	32	4	physically	physically	ADV
ap-7668	32	5	motivated	motivated	ADJ
ap-7668	32	6	generalization	generalization	NOUN
ap-7668	32	7	of	of	ADP
ap-7668	32	8	the	the	DET
ap-7668	32	9	model	model	NOUN
ap-7668	32	10	is	be	AUX
ap-7668	32	11	considered	consider	VERB
ap-7668	32	12	.	.	PUNCT
ap-7668	33	1	the	the	DET
ap-7668	33	2	goal	goal	NOUN
ap-7668	33	3	of	of	ADP
ap-7668	33	4	the	the	DET
ap-7668	33	5	paper	paper	NOUN
ap-7668	33	6	is	be	AUX
ap-7668	33	7	two	two	NUM
ap-7668	33	8	-	-	NUM
ap-7668	33	9	fold	fold	ADV
ap-7668	33	10	.	.	PUNCT
ap-7668	34	1	firstly	firstly	ADV
ap-7668	34	2	,	,	PUNCT
ap-7668	34	3	in	in	ADP
ap-7668	34	4	the	the	DET
ap-7668	34	5	(	(	PUNCT
ap-7668	34	6	sub)-space	sub)-space	NOUN
ap-7668	34	7	of	of	ADP
ap-7668	34	8	zero	zero	NUM
ap-7668	34	9	total	total	ADJ
ap-7668	34	10	angular	angular	ADJ
ap-7668	34	11	momentum	momentum	NOUN
ap-7668	34	12	we	we	PRON
ap-7668	34	13	will	will	AUX
ap-7668	34	14	describe	describe	VERB
ap-7668	34	15	the	the	DET
ap-7668	34	16	reduced	reduce	VERB
ap-7668	34	17	hamiltonian	hamiltonian	ADJ
ap-7668	34	18	operator	operator	NOUN
ap-7668	34	19	which	which	PRON
ap-7668	34	20	admits	admit	VERB
ap-7668	34	21	a	a	DET
ap-7668	34	22	hidden	hidden	ADJ
ap-7668	34	23	sℓ(4;r	sℓ(4;r	NUM
ap-7668	34	24	)	)	PUNCT
ap-7668	34	25	algebraic	algebraic	ADJ
ap-7668	34	26	structure	structure	NOUN
ap-7668	34	27	,	,	PUNCT
ap-7668	34	28	hence	hence	ADV
ap-7668	34	29	,	,	PUNCT
ap-7668	34	30	allowing	allow	VERB
ap-7668	34	31	exactanalytical	exactanalytical	ADJ
ap-7668	34	32	eigenfunctions	eigenfunction	NOUN
ap-7668	34	33	.	.	PUNCT
ap-7668	35	1	especially	especially	ADV
ap-7668	35	2	,	,	PUNCT
ap-7668	35	3	at	at	ADP
ap-7668	35	4	any	any	DET
ap-7668	35	5	d	d	X
ap-7668	35	6	≥	≥	NUM
ap-7668	35	7	1	1	NUM
ap-7668	35	8	it	it	PRON
ap-7668	35	9	is	be	AUX
ap-7668	35	10	demonstrated	demonstrate	VERB
ap-7668	35	11	the	the	DET
ap-7668	35	12	existence	existence	NOUN
ap-7668	35	13	of	of	ADP
ap-7668	35	14	an	an	DET
ap-7668	35	15	exactly	exactly	ADV
ap-7668	35	16	-	-	PUNCT
ap-7668	35	17	solvable	solvable	ADJ
ap-7668	35	18	model	model	NOUN
ap-7668	35	19	that	that	PRON
ap-7668	35	20	solely	solely	ADV
ap-7668	35	21	depends	depend	VERB
ap-7668	35	22	on	on	ADP
ap-7668	35	23	the	the	DET
ap-7668	35	24	moment	moment	NOUN
ap-7668	35	25	of	of	ADP
ap-7668	35	26	inertia	inertia	NOUN
ap-7668	35	27	of	of	ADP
ap-7668	35	28	the	the	DET
ap-7668	35	29	system	system	NOUN
ap-7668	35	30	.	.	PUNCT
ap-7668	36	1	this	this	DET
ap-7668	36	2	model	model	NOUN
ap-7668	36	3	,	,	PUNCT
ap-7668	36	4	admits	admit	VERB
ap-7668	36	5	a	a	DET
ap-7668	36	6	quasi	quasi	ADJ
ap-7668	36	7	-	-	ADJ
ap-7668	36	8	exactlysolvable	exactlysolvable	ADJ
ap-7668	36	9	extension	extension	NOUN
ap-7668	36	10	as	as	ADV
ap-7668	36	11	well	well	ADV
ap-7668	36	12	.	.	PUNCT
ap-7668	37	1	secondly	secondly	ADV
ap-7668	37	2	,	,	PUNCT
ap-7668	37	3	we	we	PRON
ap-7668	37	4	explore	explore	VERB
ap-7668	37	5	a	a	DET
ap-7668	37	6	physically	physically	ADV
ap-7668	37	7	relevant	relevant	ADJ
ap-7668	37	8	generalization	generalization	NOUN
ap-7668	37	9	of	of	ADP
ap-7668	37	10	the	the	DET
ap-7668	37	11	model	model	NOUN
ap-7668	37	12	.	.	PUNCT
ap-7668	38	1	approximate	approximate	ADJ
ap-7668	38	2	solutions	solution	NOUN
ap-7668	38	3	of	of	ADP
ap-7668	38	4	the	the	DET
ap-7668	38	5	problem	problem	NOUN
ap-7668	38	6	are	be	AUX
ap-7668	38	7	presented	present	VERB
ap-7668	38	8	just	just	ADV
ap-7668	38	9	for	for	ADP
ap-7668	38	10	the	the	DET
ap-7668	38	11	case	case	NOUN
ap-7668	38	12	of	of	ADP
ap-7668	38	13	equal	equal	ADJ
ap-7668	38	14	masses	masse	NOUN
ap-7668	38	15	in	in	ADP
ap-7668	38	16	the	the	DET
ap-7668	38	17	framework	framework	NOUN
ap-7668	38	18	of	of	ADP
ap-7668	38	19	standard	standard	ADJ
ap-7668	38	20	perturbation	perturbation	NOUN
ap-7668	38	21	theory	theory	NOUN
ap-7668	38	22	and	and	CCONJ
ap-7668	38	23	complemented	complement	VERB
ap-7668	38	24	by	by	ADP
ap-7668	38	25	the	the	DET
ap-7668	38	26	variational	variational	ADJ
ap-7668	38	27	method	method	NOUN
ap-7668	38	28	.	.	PUNCT
ap-7668	39	1	the	the	DET
ap-7668	39	2	first	first	ADJ
ap-7668	39	3	excited	excited	ADJ
ap-7668	39	4	state	state	NOUN
ap-7668	39	5	,	,	PUNCT
ap-7668	39	6	thus	thus	ADV
ap-7668	39	7	the	the	DET
ap-7668	39	8	energy	energy	NOUN
ap-7668	39	9	gap	gap	NOUN
ap-7668	39	10	of	of	ADP
ap-7668	39	11	the	the	DET
ap-7668	39	12	system	system	NOUN
ap-7668	39	13	,	,	PUNCT
ap-7668	39	14	is	be	AUX
ap-7668	39	15	briefly	briefly	ADV
ap-7668	39	16	discussed	discuss	VERB
ap-7668	39	17	.	.	PUNCT
ap-7668	40	1	50	50	NUM
ap-7668	40	2	https://doi.org/10.14311/ap.2022.62.0050	https://doi.org/10.14311/ap.2022.62.0050	PROPN
ap-7668	40	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7668	40	4	https://www.cvut.cz/en	https://www.cvut.cz/en	NOUN
ap-7668	40	5	vol	vol	NOUN
ap-7668	40	6	.	.	PROPN
ap-7668	41	1	62	62	NUM
ap-7668	41	2	no	no	INTJ
ap-7668	41	3	.	.	PUNCT
ap-7668	42	1	1/2022	1/2022	NUM
ap-7668	42	2	generalized	generalized	ADJ
ap-7668	42	3	three	three	NUM
ap-7668	42	4	-	-	PUNCT
ap-7668	42	5	body	body	NOUN
ap-7668	42	6	harmonic	harmonic	ADJ
ap-7668	42	7	oscillator	oscillator	NOUN
ap-7668	42	8	system	system	NOUN
ap-7668	42	9	:	:	PUNCT
ap-7668	42	10	ground	ground	NOUN
ap-7668	42	11	state	state	NOUN
ap-7668	42	12	2	2	NUM
ap-7668	42	13	.	.	PUNCT
ap-7668	43	1	generalities	generality	NOUN
ap-7668	43	2	the	the	DET
ap-7668	43	3	quantum	quantum	NOUN
ap-7668	43	4	hamiltonian	hamiltonian	NOUN
ap-7668	43	5	in	in	ADP
ap-7668	43	6	rd	rd	PROPN
ap-7668	43	7	(	(	PUNCT
ap-7668	43	8	d	d	X
ap-7668	43	9	>	>	X
ap-7668	43	10	1	1	NUM
ap-7668	43	11	)	)	PUNCT
ap-7668	43	12	for	for	ADP
ap-7668	43	13	three	three	NUM
ap-7668	43	14	nonrelativistic	nonrelativistic	ADJ
ap-7668	43	15	spinless	spinless	ADJ
ap-7668	43	16	particles	particle	NOUN
ap-7668	43	17	with	with	ADP
ap-7668	43	18	masses	masse	NOUN
ap-7668	43	19	m1,m2,m3	m1,m2,m3	ADJ
ap-7668	43	20	and	and	CCONJ
ap-7668	43	21	translationally	translationally	ADV
ap-7668	43	22	invariant	invariant	ADJ
ap-7668	43	23	potential	potential	NOUN
ap-7668	43	24	is	be	AUX
ap-7668	43	25	given	give	VERB
ap-7668	43	26	by	by	ADP
ap-7668	43	27	h	h	NOUN
ap-7668	43	28	=	=	SYM
ap-7668	44	1	−	−	PROPN
ap-7668	45	1	3∑	3∑	NUM
ap-7668	45	2	i=1	i=1	NUM
ap-7668	45	3	1	1	NUM
ap-7668	45	4	2mi	2mi	ADJ
ap-7668	45	5	∆(d	∆(d	PROPN
ap-7668	45	6	)	)	PUNCT
ap-7668	45	7	i	i	PRON
ap-7668	45	8	+	+	CCONJ
ap-7668	45	9	v	v	X
ap-7668	45	10	(	(	PUNCT
ap-7668	45	11	r12	r12	NOUN
ap-7668	45	12	,	,	PUNCT
ap-7668	45	13	r13	r13	NOUN
ap-7668	45	14	,	,	PUNCT
ap-7668	45	15	r23	r23	NOUN
ap-7668	45	16	)	)	PUNCT
ap-7668	45	17	,	,	PUNCT
ap-7668	45	18	(	(	PUNCT
ap-7668	45	19	1	1	X
ap-7668	45	20	)	)	PUNCT
ap-7668	45	21	(	(	PUNCT
ap-7668	45	22	ℏ	ℏ	NOUN
ap-7668	45	23	=	=	SYM
ap-7668	45	24	1	1	X
ap-7668	45	25	)	)	PUNCT
ap-7668	45	26	see	see	VERB
ap-7668	45	27	e.g.	e.g.	ADV
ap-7668	45	28	[	[	X
ap-7668	45	29	4	4	NUM
ap-7668	45	30	,	,	PUNCT
ap-7668	45	31	5	5	NUM
ap-7668	45	32	]	]	PUNCT
ap-7668	45	33	,	,	PUNCT
ap-7668	45	34	where	where	SCONJ
ap-7668	45	35	∆(d	∆(d	PROPN
ap-7668	45	36	)	)	PUNCT
ap-7668	45	37	i	i	PRON
ap-7668	45	38	stands	stand	VERB
ap-7668	45	39	for	for	ADP
ap-7668	45	40	the	the	DET
ap-7668	45	41	individual	individual	ADJ
ap-7668	45	42	laplace	laplace	NOUN
ap-7668	45	43	operator	operator	NOUN
ap-7668	45	44	of	of	ADP
ap-7668	45	45	the	the	DET
ap-7668	45	46	ith	ith	PROPN
ap-7668	45	47	mass	mass	PROPN
ap-7668	45	48	with	with	ADP
ap-7668	45	49	d−dimensional	d−dimensional	ADJ
ap-7668	45	50	position	position	NOUN
ap-7668	45	51	vector	vector	NOUN
ap-7668	45	52	ri	ri	PROPN
ap-7668	45	53	,	,	PUNCT
ap-7668	45	54	and	and	CCONJ
ap-7668	45	55	rij	rij	X
ap-7668	45	56	=	=	PUNCT
ap-7668	46	1	|ri	|ri	X
ap-7668	46	2	−	−	PROPN
ap-7668	46	3	rj	rj	PROPN
ap-7668	46	4	|	|	ADV
ap-7668	46	5	,	,	PUNCT
ap-7668	46	6	(	(	PUNCT
ap-7668	46	7	2	2	X
ap-7668	46	8	)	)	PUNCT
ap-7668	46	9	(	(	PUNCT
ap-7668	46	10	j	j	NOUN
ap-7668	46	11	=	=	SYM
ap-7668	46	12	1	1	NUM
ap-7668	46	13	,	,	PUNCT
ap-7668	46	14	2	2	NUM
ap-7668	46	15	,	,	PUNCT
ap-7668	46	16	3	3	NUM
ap-7668	46	17	)	)	PUNCT
ap-7668	46	18	is	be	AUX
ap-7668	46	19	the	the	DET
ap-7668	46	20	relative	relative	ADJ
ap-7668	46	21	mutual	mutual	ADJ
ap-7668	46	22	distance	distance	NOUN
ap-7668	46	23	between	between	ADP
ap-7668	46	24	the	the	DET
ap-7668	46	25	bodies	body	NOUN
ap-7668	46	26	i	i	PRON
ap-7668	46	27	and	and	CCONJ
ap-7668	46	28	j.	j.	PROPN
ap-7668	46	29	the	the	DET
ap-7668	46	30	eigenfunctions	eigenfunction	NOUN
ap-7668	46	31	of	of	ADP
ap-7668	46	32	(	(	PUNCT
ap-7668	46	33	1	1	NUM
ap-7668	46	34	)	)	PUNCT
ap-7668	46	35	which	which	PRON
ap-7668	46	36	solely	solely	ADV
ap-7668	46	37	depend	depend	VERB
ap-7668	46	38	on	on	ADP
ap-7668	46	39	the	the	DET
ap-7668	46	40	ρ	ρ	NOUN
ap-7668	46	41	-	-	PUNCT
ap-7668	46	42	variables	variable	NOUN
ap-7668	46	43	,	,	PUNCT
ap-7668	46	44	ρij	ρij	NOUN
ap-7668	46	45	=	=	SYM
ap-7668	46	46	r2	r2	PROPN
ap-7668	46	47	ij	ij	INTJ
ap-7668	46	48	,	,	PUNCT
ap-7668	46	49	are	be	AUX
ap-7668	46	50	governed	govern	VERB
ap-7668	46	51	by	by	ADP
ap-7668	46	52	a	a	DET
ap-7668	46	53	three	three	NUM
ap-7668	46	54	-	-	PUNCT
ap-7668	46	55	dimensional	dimensional	ADJ
ap-7668	46	56	reduced	reduce	VERB
ap-7668	46	57	hamiltonian	hamiltonian	NOUN
ap-7668	47	1	[	[	X
ap-7668	47	2	4	4	NUM
ap-7668	47	3	]	]	PUNCT
ap-7668	47	4	hrad	hrad	PROPN
ap-7668	47	5	≡	≡	PROPN
ap-7668	47	6	−∆rad	−∆rad	PROPN
ap-7668	47	7	+	+	CCONJ
ap-7668	47	8	v	v	PROPN
ap-7668	47	9	(	(	PUNCT
ap-7668	47	10	ρ	ρ	NOUN
ap-7668	47	11	)	)	PUNCT
ap-7668	47	12	,	,	PUNCT
ap-7668	47	13	(	(	PUNCT
ap-7668	47	14	3	3	X
ap-7668	47	15	)	)	PUNCT
ap-7668	47	16	where	where	SCONJ
ap-7668	47	17	∆rad	∆rad	PRON
ap-7668	47	18	=	=	SYM
ap-7668	47	19	2	2	NUM
ap-7668	47	20	µ12	µ12	NOUN
ap-7668	47	21	ρ12	ρ12	VERB
ap-7668	47	22	∂2	∂2	PROPN
ap-7668	47	23	ρ12	ρ12	NOUN
ap-7668	47	24	+	+	CCONJ
ap-7668	47	25	2	2	NUM
ap-7668	47	26	µ13	µ13	NOUN
ap-7668	47	27	ρ13	ρ13	NOUN
ap-7668	47	28	∂2	∂2	NOUN
ap-7668	48	1	ρ13	ρ13	NOUN
ap-7668	48	2	+	+	CCONJ
ap-7668	48	3	2	2	NUM
ap-7668	48	4	µ23	µ23	NOUN
ap-7668	48	5	ρ23	ρ23	NOUN
ap-7668	48	6	∂2	∂2	NOUN
ap-7668	48	7	ρ23	ρ23	NOUN
ap-7668	48	8	+	+	CCONJ
ap-7668	48	9	2(ρ13	2(ρ13	NUM
ap-7668	49	1	+	+	CCONJ
ap-7668	49	2	ρ12	ρ12	VERB
ap-7668	49	3	−	−	PROPN
ap-7668	49	4	ρ23	ρ23	NOUN
ap-7668	49	5	)	)	PUNCT
ap-7668	49	6	m1	m1	NOUN
ap-7668	49	7	∂ρ13	∂ρ13	NOUN
ap-7668	49	8	,	,	PUNCT
ap-7668	49	9	ρ12	ρ12	VERB
ap-7668	49	10	+2(ρ13	+2(ρ13	PRON
ap-7668	49	11	+	+	NUM
ap-7668	49	12	ρ23	ρ23	NOUN
ap-7668	49	13	−	−	PROPN
ap-7668	49	14	ρ12	ρ12	PROPN
ap-7668	49	15	)	)	PUNCT
ap-7668	49	16	m3	m3	PROPN
ap-7668	49	17	∂ρ13	∂ρ13	NOUN
ap-7668	49	18	,	,	PUNCT
ap-7668	49	19	ρ23	ρ23	NOUN
ap-7668	49	20	+	+	CCONJ
ap-7668	49	21	2(ρ23	2(ρ23	NUM
ap-7668	50	1	+	+	NUM
ap-7668	50	2	ρ12	ρ12	NOUN
ap-7668	50	3	−	−	PROPN
ap-7668	50	4	ρ13	ρ13	NOUN
ap-7668	50	5	)	)	PUNCT
ap-7668	50	6	m2	m2	PROPN
ap-7668	50	7	∂ρ23	∂ρ23	PROPN
ap-7668	50	8	,	,	PUNCT
ap-7668	50	9	ρ12	ρ12	VERB
ap-7668	50	10	+	+	CCONJ
ap-7668	50	11	d	d	PROPN
ap-7668	50	12	µ12	µ12	NOUN
ap-7668	50	13	∂ρ12	∂ρ12	NOUN
ap-7668	50	14	+	+	CCONJ
ap-7668	50	15	d	d	SYM
ap-7668	50	16	µ13	µ13	NOUN
ap-7668	50	17	∂ρ13	∂ρ13	NOUN
ap-7668	51	1	+	+	CCONJ
ap-7668	51	2	d	d	NOUN
ap-7668	51	3	µ23	µ23	NOUN
ap-7668	51	4	∂ρ23	∂ρ23	NOUN
ap-7668	51	5	,	,	PUNCT
ap-7668	51	6	(	(	PUNCT
ap-7668	51	7	4	4	X
ap-7668	51	8	)	)	PUNCT
ap-7668	51	9	c.f	c.f	PROPN
ap-7668	51	10	.	.	PUNCT
ap-7668	52	1	[	[	X
ap-7668	52	2	5	5	NUM
ap-7668	52	3	]	]	PUNCT
ap-7668	52	4	,	,	PUNCT
ap-7668	52	5	and	and	CCONJ
ap-7668	52	6	µij	µij	ADV
ap-7668	52	7	=	=	PROPN
ap-7668	52	8	mi	mi	PROPN
ap-7668	52	9	mj	mj	PROPN
ap-7668	52	10	mi	mi	PROPN
ap-7668	53	1	+	+	PROPN
ap-7668	53	2	mj	mj	PROPN
ap-7668	53	3	,	,	PUNCT
ap-7668	53	4	denotes	denote	VERB
ap-7668	53	5	a	a	DET
ap-7668	53	6	reduced	reduced	ADJ
ap-7668	53	7	mass	mass	NOUN
ap-7668	53	8	.	.	PUNCT
ap-7668	54	1	the	the	DET
ap-7668	54	2	operator	operator	NOUN
ap-7668	54	3	(	(	PUNCT
ap-7668	54	4	3	3	X
ap-7668	54	5	)	)	PUNCT
ap-7668	54	6	describes	describe	VERB
ap-7668	54	7	three	three	NUM
ap-7668	54	8	-	-	PUNCT
ap-7668	54	9	dimensional	dimensional	ADJ
ap-7668	54	10	(	(	PUNCT
ap-7668	54	11	radial	radial	ADJ
ap-7668	54	12	)	)	PUNCT
ap-7668	54	13	dynamics	dynamic	NOUN
ap-7668	54	14	in	in	ADP
ap-7668	54	15	variables	variable	NOUN
ap-7668	54	16	ρ12	ρ12	PROPN
ap-7668	54	17	,	,	PUNCT
ap-7668	54	18	ρ13	ρ13	NUM
ap-7668	54	19	,	,	PUNCT
ap-7668	54	20	ρ23	ρ23	NOUN
ap-7668	54	21	.	.	PUNCT
ap-7668	55	1	this	this	DET
ap-7668	55	2	operator	operator	NOUN
ap-7668	55	3	hrad	hrad	NOUN
ap-7668	55	4	is	be	AUX
ap-7668	55	5	,	,	PUNCT
ap-7668	55	6	in	in	ADP
ap-7668	55	7	fact	fact	NOUN
ap-7668	55	8	,	,	PUNCT
ap-7668	55	9	equivalent	equivalent	ADJ
ap-7668	55	10	to	to	ADP
ap-7668	55	11	a	a	DET
ap-7668	55	12	schrödinger	schrödinger	ADJ
ap-7668	55	13	operator	operator	NOUN
ap-7668	55	14	,	,	PUNCT
ap-7668	55	15	see	see	VERB
ap-7668	55	16	[	[	X
ap-7668	55	17	4	4	NUM
ap-7668	55	18	]	]	PUNCT
ap-7668	55	19	.	.	PUNCT
ap-7668	56	1	we	we	PRON
ap-7668	56	2	call	call	VERB
ap-7668	56	3	it	it	PRON
ap-7668	56	4	three	three	NUM
ap-7668	56	5	-	-	PUNCT
ap-7668	56	6	dimensional	dimensional	ADJ
ap-7668	56	7	(	(	PUNCT
ap-7668	56	8	radial	radial	ADJ
ap-7668	56	9	)	)	PUNCT
ap-7668	56	10	hamiltonian	hamiltonian	NOUN
ap-7668	56	11	.	.	PUNCT
ap-7668	57	1	all	all	DET
ap-7668	57	2	the	the	DET
ap-7668	57	3	d−dependence	d−dependence	NOUN
ap-7668	57	4	in	in	ADP
ap-7668	57	5	(	(	PUNCT
ap-7668	57	6	3	3	X
ap-7668	57	7	)	)	PUNCT
ap-7668	57	8	occurs	occur	VERB
ap-7668	57	9	in	in	ADP
ap-7668	57	10	the	the	DET
ap-7668	57	11	coefficients	coefficient	NOUN
ap-7668	57	12	in	in	ADP
ap-7668	57	13	front	front	NOUN
ap-7668	57	14	of	of	ADP
ap-7668	57	15	the	the	DET
ap-7668	57	16	first	first	ADJ
ap-7668	57	17	derivatives	derivative	NOUN
ap-7668	57	18	.	.	PUNCT
ap-7668	58	1	2.1	2.1	NUM
ap-7668	58	2	.	.	PUNCT
ap-7668	58	3	case	case	NOUN
ap-7668	58	4	of	of	ADP
ap-7668	58	5	identical	identical	ADJ
ap-7668	58	6	particles	particle	NOUN
ap-7668	58	7	:	:	PUNCT
ap-7668	58	8	τ	τ	NOUN
ap-7668	58	9	-	-	PUNCT
ap-7668	58	10	representation	representation	NOUN
ap-7668	58	11	now	now	ADV
ap-7668	58	12	,	,	PUNCT
ap-7668	58	13	let	let	VERB
ap-7668	58	14	us	we	PRON
ap-7668	58	15	consider	consider	VERB
ap-7668	58	16	the	the	DET
ap-7668	58	17	case	case	NOUN
ap-7668	58	18	of	of	ADP
ap-7668	58	19	identical	identical	ADJ
ap-7668	58	20	masses	masse	NOUN
ap-7668	58	21	m1	m1	NOUN
ap-7668	58	22	=	=	SYM
ap-7668	58	23	1	1	NUM
ap-7668	58	24	;	;	PUNCT
ap-7668	58	25	m2	m2	PROPN
ap-7668	58	26	=	=	PROPN
ap-7668	58	27	1	1	NUM
ap-7668	58	28	;	;	PUNCT
ap-7668	58	29	m3	m3	PROPN
ap-7668	58	30	=	=	SYM
ap-7668	58	31	1	1	NUM
ap-7668	58	32	,	,	PUNCT
ap-7668	58	33	thus	thus	ADV
ap-7668	58	34	,	,	PUNCT
ap-7668	58	35	µij	µij	ADV
ap-7668	58	36	=	=	SYM
ap-7668	58	37	1	1	NUM
ap-7668	58	38	2	2	NUM
ap-7668	58	39	,	,	PUNCT
ap-7668	58	40	and	and	CCONJ
ap-7668	58	41	the	the	DET
ap-7668	58	42	operator	operator	NOUN
ap-7668	58	43	(	(	PUNCT
ap-7668	58	44	4	4	X
ap-7668	58	45	)	)	PUNCT
ap-7668	58	46	is	be	AUX
ap-7668	58	47	s3	s3	PROPN
ap-7668	58	48	permutationally	permutationally	ADV
ap-7668	58	49	-	-	PUNCT
ap-7668	58	50	invariant	invariant	ADJ
ap-7668	58	51	in	in	ADP
ap-7668	58	52	the	the	DET
ap-7668	58	53	ρ	ρ	NOUN
ap-7668	58	54	-	-	PUNCT
ap-7668	58	55	variables	variable	NOUN
ap-7668	58	56	.	.	PUNCT
ap-7668	59	1	it	it	PRON
ap-7668	59	2	suggests	suggest	VERB
ap-7668	59	3	the	the	DET
ap-7668	59	4	change	change	NOUN
ap-7668	59	5	of	of	ADP
ap-7668	59	6	variables	variable	NOUN
ap-7668	59	7	ρ	ρ	PROPN
ap-7668	59	8	↔	↔	PROPN
ap-7668	59	9	τ	τ	X
ap-7668	59	10	where	where	SCONJ
ap-7668	59	11	τ1	τ1	NOUN
ap-7668	59	12	=	=	SYM
ap-7668	59	13	ρ12	ρ12	NOUN
ap-7668	60	1	+	+	NOUN
ap-7668	61	1	ρ13	ρ13	NOUN
ap-7668	61	2	+	+	CCONJ
ap-7668	61	3	ρ23	ρ23	NOUN
ap-7668	61	4	,	,	PUNCT
ap-7668	61	5	τ2	τ2	NOUN
ap-7668	61	6	=	=	SYM
ap-7668	61	7	ρ12	ρ12	VERB
ap-7668	61	8	ρ13	ρ13	NOUN
ap-7668	62	1	+	+	NOUN
ap-7668	62	2	ρ12	ρ12	NOUN
ap-7668	62	3	ρ23	ρ23	NOUN
ap-7668	62	4	+	+	CCONJ
ap-7668	62	5	ρ13	ρ13	NOUN
ap-7668	62	6	ρ23	ρ23	NOUN
ap-7668	62	7	,	,	PUNCT
ap-7668	62	8	τ3	τ3	NOUN
ap-7668	62	9	=	=	SYM
ap-7668	62	10	ρ12	ρ12	VERB
ap-7668	62	11	ρ13	ρ13	NOUN
ap-7668	62	12	ρ23	ρ23	NOUN
ap-7668	62	13	,	,	PUNCT
ap-7668	62	14	(	(	PUNCT
ap-7668	62	15	5	5	X
ap-7668	62	16	)	)	PUNCT
ap-7668	62	17	are	be	AUX
ap-7668	62	18	nothing	nothing	PRON
ap-7668	62	19	but	but	SCONJ
ap-7668	62	20	the	the	DET
ap-7668	62	21	lowest	low	ADJ
ap-7668	62	22	elementary	elementary	ADJ
ap-7668	62	23	symmetric	symmetric	ADJ
ap-7668	62	24	polynomials	polynomial	NOUN
ap-7668	62	25	in	in	ADP
ap-7668	62	26	ρ	ρ	NOUN
ap-7668	62	27	-	-	PUNCT
ap-7668	62	28	coordinates	coordinate	NOUN
ap-7668	62	29	.	.	PUNCT
ap-7668	63	1	in	in	ADP
ap-7668	63	2	these	these	DET
ap-7668	63	3	variables	variable	NOUN
ap-7668	63	4	(	(	PUNCT
ap-7668	63	5	5	5	NUM
ap-7668	63	6	)	)	PUNCT
ap-7668	63	7	,	,	PUNCT
ap-7668	63	8	the	the	DET
ap-7668	63	9	coefficients	coefficient	NOUN
ap-7668	63	10	of	of	ADP
ap-7668	63	11	the	the	DET
ap-7668	63	12	operator	operator	NOUN
ap-7668	63	13	∆rad	∆rad	NOUN
ap-7668	63	14	are	be	AUX
ap-7668	63	15	also	also	ADV
ap-7668	63	16	polynomials	polynomial	NOUN
ap-7668	63	17	,	,	PUNCT
ap-7668	63	18	hence	hence	ADV
ap-7668	63	19	,	,	PUNCT
ap-7668	63	20	this	this	DET
ap-7668	63	21	operator	operator	NOUN
ap-7668	63	22	is	be	AUX
ap-7668	63	23	algebraic	algebraic	ADJ
ap-7668	63	24	in	in	ADP
ap-7668	63	25	both	both	DET
ap-7668	63	26	representations	representation	NOUN
ap-7668	63	27	.	.	PUNCT
ap-7668	64	1	explicitly	explicitly	ADV
ap-7668	64	2	,	,	PUNCT
ap-7668	64	3	∆rad	∆rad	PROPN
ap-7668	64	4	=	=	PUNCT
ap-7668	64	5	6	6	NUM
ap-7668	64	6	τ1∂	τ1∂	SYM
ap-7668	64	7	2	2	NUM
ap-7668	64	8	1	1	NUM
ap-7668	64	9	+	+	NUM
ap-7668	64	10	2τ1(7τ2	2τ1(7τ2	NUM
ap-7668	64	11	−	−	NOUN
ap-7668	64	12	τ2	τ2	NOUN
ap-7668	64	13	1	1	NUM
ap-7668	64	14	)	)	PUNCT
ap-7668	64	15	∂2	∂2	NOUN
ap-7668	64	16	2	2	NUM
ap-7668	65	1	+	+	NUM
ap-7668	65	2	2τ3(6τ2	2τ3(6τ2	NUM
ap-7668	65	3	−	−	ADP
ap-7668	65	4	τ2	τ2	NOUN
ap-7668	65	5	1	1	NUM
ap-7668	65	6	)	)	PUNCT
ap-7668	65	7	∂2	∂2	NOUN
ap-7668	65	8	3	3	NUM
ap-7668	65	9	+	+	CCONJ
ap-7668	65	10	24	24	NUM
ap-7668	65	11	τ2∂	τ2∂	NUM
ap-7668	65	12	2	2	NUM
ap-7668	65	13	1,2	1,2	NUM
ap-7668	65	14	+	+	CCONJ
ap-7668	65	15	36τ3∂	36τ3∂	NUM
ap-7668	65	16	2	2	NUM
ap-7668	65	17	1,3	1,3	NUM
ap-7668	65	18	+	+	CCONJ
ap-7668	65	19	2	2	NUM
ap-7668	66	1	[	[	X
ap-7668	66	2	9τ3τ1	9τ3τ1	NOUN
ap-7668	66	3	+	+	CCONJ
ap-7668	66	4	4τ2(τ2	4τ2(τ2	NUM
ap-7668	66	5	−	−	NOUN
ap-7668	66	6	τ2	τ2	NOUN
ap-7668	66	7	1	1	NUM
ap-7668	66	8	)	)	PUNCT
ap-7668	66	9	]	]	PUNCT
ap-7668	66	10	∂2	∂2	NOUN
ap-7668	66	11	2,3	2,3	NUM
ap-7668	67	1	+	+	CCONJ
ap-7668	68	1	6	6	NUM
ap-7668	68	2	d	d	NOUN
ap-7668	68	3	∂1	∂1	ADJ
ap-7668	68	4	+	+	CCONJ
ap-7668	68	5	2	2	NUM
ap-7668	68	6	(	(	PUNCT
ap-7668	68	7	2d+	2d+	NUM
ap-7668	68	8	1)τ1	1)τ1	NUM
ap-7668	68	9	∂2	∂2	NOUN
ap-7668	68	10	+	+	CCONJ
ap-7668	68	11	2	2	NUM
ap-7668	68	12	[	[	X
ap-7668	68	13	(	(	PUNCT
ap-7668	68	14	d+	d+	X
ap-7668	68	15	4)τ2	4)τ2	NOUN
ap-7668	68	16	−	−	NOUN
ap-7668	68	17	τ2	τ2	NOUN
ap-7668	68	18	1	1	NUM
ap-7668	68	19	]	]	PUNCT
ap-7668	68	20	∂3	∂3	NOUN
ap-7668	68	21	(	(	PUNCT
ap-7668	68	22	6	6	NUM
ap-7668	68	23	)	)	PUNCT
ap-7668	68	24	∂i	∂i	PROPN
ap-7668	68	25	≡	≡	PROPN
ap-7668	69	1	∂τi	∂τi	PROPN
ap-7668	69	2	,	,	PUNCT
ap-7668	69	3	i	i	PRON
ap-7668	69	4	=	=	NOUN
ap-7668	69	5	1	1	NUM
ap-7668	69	6	,	,	PUNCT
ap-7668	69	7	2	2	NUM
ap-7668	69	8	,	,	PUNCT
ap-7668	69	9	3	3	NUM
ap-7668	69	10	.	.	NOUN
ap-7668	69	11	3	3	NUM
ap-7668	69	12	.	.	PUNCT
ap-7668	69	13	laplace	laplace	NOUN
ap-7668	69	14	-	-	PUNCT
ap-7668	69	15	beltrami	beltrami	ADJ
ap-7668	69	16	operator	operator	NOUN
ap-7668	69	17	now	now	ADV
ap-7668	69	18	,	,	PUNCT
ap-7668	69	19	as	as	ADP
ap-7668	69	20	a	a	DET
ap-7668	69	21	result	result	NOUN
ap-7668	69	22	of	of	ADP
ap-7668	69	23	calculations	calculation	NOUN
ap-7668	69	24	it	it	PRON
ap-7668	69	25	is	be	AUX
ap-7668	69	26	convenient	convenient	ADJ
ap-7668	69	27	to	to	PART
ap-7668	69	28	consider	consider	VERB
ap-7668	69	29	the	the	DET
ap-7668	69	30	following	follow	VERB
ap-7668	69	31	gauge	gauge	NOUN
ap-7668	69	32	factor	factor	NOUN
ap-7668	69	33	γ4	γ4	NOUN
ap-7668	69	34	=	=	SYM
ap-7668	69	35	(	(	PUNCT
ap-7668	69	36	s2	s2	PROPN
ap-7668	69	37	△	△	X
ap-7668	69	38	)	)	PUNCT
ap-7668	69	39	2−d	2−d	NUM
ap-7668	69	40	m	m	VERB
ap-7668	69	41	i	i	PRON
ap-7668	69	42	,	,	PUNCT
ap-7668	69	43	(	(	PUNCT
ap-7668	69	44	7	7	X
ap-7668	69	45	)	)	PUNCT
ap-7668	69	46	m	m	PROPN
ap-7668	70	1	=	=	PUNCT
ap-7668	70	2	m1	m1	PROPN
ap-7668	70	3	+	+	PROPN
ap-7668	70	4	m2	m2	PROPN
ap-7668	70	5	+	+	PROPN
ap-7668	70	6	m3	m3	PROPN
ap-7668	70	7	,	,	PUNCT
ap-7668	70	8	where	where	SCONJ
ap-7668	70	9	s2	s2	X
ap-7668	70	10	△	△	X
ap-7668	70	11	=	=	SYM
ap-7668	71	1	2ρ12	2ρ12	NUM
ap-7668	72	1	ρ13	ρ13	NOUN
ap-7668	72	2	+	+	SYM
ap-7668	72	3	2ρ12	2ρ12	NUM
ap-7668	72	4	ρ23	ρ23	NOUN
ap-7668	72	5	+	+	CCONJ
ap-7668	72	6	2ρ23	2ρ23	NOUN
ap-7668	72	7	ρ13	ρ13	NOUN
ap-7668	72	8	−	−	PROPN
ap-7668	72	9	ρ2	ρ2	NOUN
ap-7668	72	10	12	12	NUM
ap-7668	72	11	−	−	NOUN
ap-7668	72	12	ρ2	ρ2	NOUN
ap-7668	72	13	13	13	NUM
ap-7668	72	14	−	−	NOUN
ap-7668	72	15	ρ2	ρ2	NOUN
ap-7668	72	16	23	23	NUM
ap-7668	72	17	16	16	NUM
ap-7668	72	18	,	,	PUNCT
ap-7668	72	19	and	and	CCONJ
ap-7668	72	20	i	i	PRON
ap-7668	72	21	=	=	SYM
ap-7668	73	1	m1m2	m1m2	X
ap-7668	73	2	ρ12	ρ12	X
ap-7668	73	3	+	+	CCONJ
ap-7668	73	4	m1m3	m1m3	PROPN
ap-7668	73	5	ρ13	ρ13	PROPN
ap-7668	73	6	+	+	CCONJ
ap-7668	73	7	m2m3	m2m3	ADP
ap-7668	73	8	ρ23	ρ23	NOUN
ap-7668	73	9	m	m	PROPN
ap-7668	73	10	,	,	PUNCT
ap-7668	73	11	possess	possess	VERB
ap-7668	73	12	a	a	DET
ap-7668	73	13	geometrical	geometrical	ADJ
ap-7668	73	14	meaning	meaning	NOUN
ap-7668	73	15	.	.	PUNCT
ap-7668	74	1	the	the	DET
ap-7668	74	2	term	term	NOUN
ap-7668	74	3	s2	s2	PROPN
ap-7668	74	4	△	△	PROPN
ap-7668	74	5	is	be	AUX
ap-7668	74	6	the	the	DET
ap-7668	74	7	area	area	NOUN
ap-7668	74	8	(	(	PUNCT
ap-7668	74	9	squared	square	VERB
ap-7668	74	10	)	)	PUNCT
ap-7668	74	11	of	of	ADP
ap-7668	74	12	the	the	DET
ap-7668	74	13	triangle	triangle	NOUN
ap-7668	74	14	formed	form	VERB
ap-7668	74	15	by	by	ADP
ap-7668	74	16	the	the	DET
ap-7668	74	17	position	position	NOUN
ap-7668	74	18	vectors	vector	NOUN
ap-7668	74	19	of	of	ADP
ap-7668	74	20	the	the	DET
ap-7668	74	21	three	three	NUM
ap-7668	74	22	bodies	body	NOUN
ap-7668	74	23	whilst	whilst	SCONJ
ap-7668	74	24	the	the	DET
ap-7668	74	25	term	term	NOUN
ap-7668	74	26	i	i	PRON
ap-7668	74	27	is	be	AUX
ap-7668	74	28	the	the	DET
ap-7668	74	29	moment	moment	NOUN
ap-7668	74	30	of	of	ADP
ap-7668	74	31	inertia	inertia	NOUN
ap-7668	74	32	of	of	ADP
ap-7668	74	33	the	the	DET
ap-7668	74	34	system	system	NOUN
ap-7668	74	35	with	with	ADP
ap-7668	74	36	respect	respect	NOUN
ap-7668	74	37	to	to	ADP
ap-7668	74	38	its	its	PRON
ap-7668	74	39	center	center	NOUN
ap-7668	74	40	of	of	ADP
ap-7668	74	41	mass	mass	PROPN
ap-7668	74	42	.	.	PUNCT
ap-7668	75	1	the	the	DET
ap-7668	75	2	radial	radial	ADJ
ap-7668	75	3	operator	operator	NOUN
ap-7668	75	4	hrad	hrad	NOUN
ap-7668	75	5	(	(	PUNCT
ap-7668	75	6	3	3	NUM
ap-7668	75	7	)	)	PUNCT
ap-7668	75	8	is	be	AUX
ap-7668	75	9	gaugetransformed	gaugetransforme	VERB
ap-7668	75	10	to	to	ADP
ap-7668	75	11	a	a	DET
ap-7668	75	12	truly	truly	ADV
ap-7668	75	13	schrödinger	schrödinger	ADJ
ap-7668	75	14	operator	operator	NOUN
ap-7668	75	15	[	[	X
ap-7668	75	16	4	4	NUM
ap-7668	75	17	]	]	PUNCT
ap-7668	75	18	,	,	PUNCT
ap-7668	75	19	hlb	hlb	PROPN
ap-7668	75	20	≡	≡	PROPN
ap-7668	75	21	γ−1	γ−1	PROPN
ap-7668	75	22	hrad	hrad	PROPN
ap-7668	75	23	γ	γ	X
ap-7668	75	24	=	=	SYM
ap-7668	75	25	−∆lb	−∆lb	PROPN
ap-7668	76	1	+	+	CCONJ
ap-7668	76	2	v	v	NOUN
ap-7668	76	3	+	+	CCONJ
ap-7668	76	4	v	v	PROPN
ap-7668	76	5	(	(	PUNCT
ap-7668	76	6	eff	eff	PROPN
ap-7668	76	7	)	)	PUNCT
ap-7668	76	8	,	,	PUNCT
ap-7668	76	9	(	(	PUNCT
ap-7668	76	10	8)	8)	X
ap-7668	76	11	here	here	ADV
ap-7668	76	12	∆lb	∆lb	PROPN
ap-7668	76	13	stands	stand	VERB
ap-7668	76	14	for	for	ADP
ap-7668	76	15	the	the	DET
ap-7668	76	16	laplace	laplace	NOUN
ap-7668	76	17	-	-	PUNCT
ap-7668	76	18	beltrami	beltrami	ADJ
ap-7668	76	19	operator	operator	NOUN
ap-7668	76	20	∆lb(ρ	∆lb(ρ	NOUN
ap-7668	76	21	)	)	PUNCT
ap-7668	76	22	=	=	SYM
ap-7668	77	1	√	√	NUM
ap-7668	78	1	|	|	ADV
ap-7668	78	2	g	g	PROPN
ap-7668	78	3	|	|	PROPN
ap-7668	78	4	∂µ	∂µ	PROPN
ap-7668	78	5	1√	1√	PROPN
ap-7668	78	6	|	|	ADV
ap-7668	78	7	g	g	NOUN
ap-7668	78	8	|	|	ADV
ap-7668	78	9	gµν∂ν	gµν∂ν	NOUN
ap-7668	78	10	,	,	PUNCT
ap-7668	78	11	(	(	PUNCT
ap-7668	78	12	ν	ν	X
ap-7668	78	13	,	,	PUNCT
ap-7668	78	14	µ	µ	X
ap-7668	78	15	=	=	SYM
ap-7668	78	16	1	1	NUM
ap-7668	78	17	,	,	PUNCT
ap-7668	78	18	2	2	NUM
ap-7668	78	19	,	,	PUNCT
ap-7668	78	20	3	3	NUM
ap-7668	78	21	)	)	PUNCT
ap-7668	78	22	and	and	CCONJ
ap-7668	78	23	∂1	∂1	ADJ
ap-7668	78	24	=	=	SYM
ap-7668	78	25	∂	∂	NUM
ap-7668	78	26	∂ρ12	∂ρ12	NOUN
ap-7668	78	27	,	,	PUNCT
ap-7668	78	28	∂2	∂2	NUM
ap-7668	78	29	=	=	SYM
ap-7668	78	30	∂	∂	NOUN
ap-7668	78	31	∂ρ13	∂ρ13	NOUN
ap-7668	78	32	,	,	PUNCT
ap-7668	78	33	∂3	∂3	NUM
ap-7668	78	34	=	=	SYM
ap-7668	78	35	∂	∂	NUM
ap-7668	78	36	∂ρ23	∂ρ23	NOUN
ap-7668	78	37	.	.	PUNCT
ap-7668	79	1	the	the	DET
ap-7668	79	2	corresponding	corresponding	ADJ
ap-7668	79	3	co	co	NOUN
ap-7668	79	4	-	-	NOUN
ap-7668	79	5	metric	metric	ADJ
ap-7668	79	6	in	in	ADP
ap-7668	79	7	∆lb(ρ	∆lb(ρ	NOUN
ap-7668	79	8	)	)	PUNCT
ap-7668	79	9	reads	read	VERB
ap-7668	79	10	gµν	gµν	NOUN
ap-7668	79	11	=	=	SYM
ap-7668	79	12			NOUN
ap-7668	79	13	2	2	NUM
ap-7668	79	14	µ12	µ12	NOUN
ap-7668	79	15	ρ12	ρ12	NUM
ap-7668	79	16	(	(	PUNCT
ap-7668	79	17	ρ13+ρ12−ρ23	ρ13+ρ12−ρ23	NOUN
ap-7668	79	18	)	)	PUNCT
ap-7668	79	19	m1	m1	NOUN
ap-7668	79	20	(	(	PUNCT
ap-7668	79	21	ρ23+ρ12−ρ13	ρ23+ρ12−ρ13	PROPN
ap-7668	79	22	)	)	PUNCT
ap-7668	79	23	m2	m2	PROPN
ap-7668	79	24	(	(	PUNCT
ap-7668	79	25	ρ13+ρ12−ρ23	ρ13+ρ12−ρ23	NOUN
ap-7668	79	26	)	)	PUNCT
ap-7668	79	27	m1	m1	NOUN
ap-7668	79	28	2	2	NUM
ap-7668	79	29	µ13	µ13	NOUN
ap-7668	79	30	ρ13	ρ13	PROPN
ap-7668	79	31	(	(	PUNCT
ap-7668	79	32	ρ13+ρ23−ρ12	ρ13+ρ23−ρ12	PROPN
ap-7668	79	33	)	)	PUNCT
ap-7668	79	34	m3	m3	PROPN
ap-7668	79	35	(	(	PUNCT
ap-7668	79	36	ρ23+ρ12−ρ13	ρ23+ρ12−ρ13	PROPN
ap-7668	79	37	)	)	PUNCT
ap-7668	80	1	m2	m2	PROPN
ap-7668	80	2	(	(	PUNCT
ap-7668	80	3	ρ13+ρ23−ρ12	ρ13+ρ23−ρ12	PROPN
ap-7668	80	4	)	)	PUNCT
ap-7668	80	5	m3	m3	PROPN
ap-7668	80	6	2	2	NUM
ap-7668	80	7	µ23	µ23	NOUN
ap-7668	80	8	ρ23	ρ23	NOUN
ap-7668	80	9			NOUN
ap-7668	80	10	.	.	PUNCT
ap-7668	81	1	its	its	PRON
ap-7668	81	2	determinant	determinant	ADJ
ap-7668	81	3	|	|	ADV
ap-7668	81	4	g	g	PROPN
ap-7668	81	5	|	|	ADV
ap-7668	81	6	≡	≡	PROPN
ap-7668	81	7	detgµν	detgµν	VERB
ap-7668	81	8	=	=	SYM
ap-7668	81	9	32	32	NUM
ap-7668	81	10	m2	m2	PROPN
ap-7668	81	11	m2	m2	PROPN
ap-7668	81	12	1	1	NUM
ap-7668	81	13	m	m	PROPN
ap-7668	81	14	2	2	NUM
ap-7668	81	15	2	2	NUM
ap-7668	81	16	m	m	NUM
ap-7668	81	17	2	2	NUM
ap-7668	81	18	3	3	NUM
ap-7668	81	19	i	i	PRON
ap-7668	81	20	s2	s2	VERB
ap-7668	81	21	△	△	X
ap-7668	81	22	,	,	PUNCT
ap-7668	81	23	(	(	PUNCT
ap-7668	81	24	9	9	X
ap-7668	81	25	)	)	PUNCT
ap-7668	81	26	admits	admit	VERB
ap-7668	81	27	factorization	factorization	NOUN
ap-7668	81	28	and	and	CCONJ
ap-7668	81	29	is	be	AUX
ap-7668	81	30	positive	positive	ADJ
ap-7668	81	31	definite	definite	ADJ
ap-7668	81	32	.	.	PUNCT
ap-7668	82	1	the	the	DET
ap-7668	82	2	term	term	NOUN
ap-7668	82	3	v	v	PROPN
ap-7668	82	4	(	(	PUNCT
ap-7668	82	5	eff	eff	PROPN
ap-7668	82	6	)	)	PUNCT
ap-7668	82	7	denotes	denote	VERB
ap-7668	82	8	an	an	DET
ap-7668	82	9	effective	effective	ADJ
ap-7668	82	10	potential	potential	ADJ
ap-7668	82	11	v	v	NOUN
ap-7668	82	12	(	(	PUNCT
ap-7668	82	13	eff	eff	PROPN
ap-7668	82	14	)	)	PUNCT
ap-7668	82	15	=	=	NOUN
ap-7668	82	16	3	3	NUM
ap-7668	82	17	8	8	NUM
ap-7668	82	18	1	1	NUM
ap-7668	82	19	i	i	PRON
ap-7668	82	20	+	+	CCONJ
ap-7668	82	21	(	(	PUNCT
ap-7668	82	22	d−	d−	PROPN
ap-7668	82	23	2)(d−	2)(d−	NUM
ap-7668	82	24	4	4	NUM
ap-7668	82	25	)	)	PUNCT
ap-7668	82	26	32	32	NUM
ap-7668	82	27	m	m	NOUN
ap-7668	83	1	i	i	NOUN
ap-7668	83	2	m1	m1	PROPN
ap-7668	83	3	m2	m2	PROPN
ap-7668	83	4	m3	m3	PROPN
ap-7668	83	5	s2	s2	PROPN
ap-7668	83	6	△	△	PROPN
ap-7668	83	7	,	,	PUNCT
ap-7668	83	8	which	which	PRON
ap-7668	83	9	depends	depend	VERB
ap-7668	83	10	on	on	ADP
ap-7668	83	11	the	the	DET
ap-7668	83	12	two	two	NUM
ap-7668	83	13	variables	variable	NOUN
ap-7668	83	14	i	i	PRON
ap-7668	83	15	and	and	CCONJ
ap-7668	83	16	s2	s2	VERB
ap-7668	83	17	△	△	X
ap-7668	83	18	alone	alone	ADV
ap-7668	83	19	.	.	PUNCT
ap-7668	84	1	thus	thus	ADV
ap-7668	84	2	,	,	PUNCT
ap-7668	84	3	the	the	DET
ap-7668	84	4	underlying	underlie	VERB
ap-7668	84	5	geometry	geometry	NOUN
ap-7668	84	6	of	of	ADP
ap-7668	84	7	the	the	DET
ap-7668	84	8	system	system	NOUN
ap-7668	84	9	emerges	emerge	VERB
ap-7668	84	10	.	.	PUNCT
ap-7668	85	1	the	the	DET
ap-7668	85	2	classical	classical	ADJ
ap-7668	85	3	analogue	analogue	NOUN
ap-7668	85	4	of	of	ADP
ap-7668	85	5	the	the	DET
ap-7668	85	6	quantum	quantum	ADJ
ap-7668	85	7	hamiltonian	hamiltonian	ADJ
ap-7668	85	8	operator	operator	NOUN
ap-7668	85	9	(	(	PUNCT
ap-7668	85	10	8)	8)	NUM
ap-7668	85	11	describes	describe	VERB
ap-7668	85	12	an	an	DET
ap-7668	85	13	effective	effective	ADJ
ap-7668	85	14	non	non	ADJ
ap-7668	85	15	-	-	ADJ
ap-7668	85	16	relativistic	relativistic	ADJ
ap-7668	85	17	51	51	NUM
ap-7668	85	18	adrian	adrian	PROPN
ap-7668	85	19	m.	m.	NOUN
ap-7668	85	20	escobar	escobar	PROPN
ap-7668	85	21	-	-	PUNCT
ap-7668	85	22	ruiz	ruiz	NOUN
ap-7668	85	23	,	,	PUNCT
ap-7668	85	24	fidel	fidel	PROPN
ap-7668	85	25	montoya	montoya	PROPN
ap-7668	85	26	acta	acta	PROPN
ap-7668	85	27	polytechnica	polytechnica	PROPN
ap-7668	85	28	figure	figure	NOUN
ap-7668	85	29	1	1	NUM
ap-7668	85	30	.	.	NOUN
ap-7668	85	31	3	3	NUM
ap-7668	85	32	-	-	PUNCT
ap-7668	85	33	body	body	NOUN
ap-7668	85	34	chain	chain	NOUN
ap-7668	85	35	of	of	ADP
ap-7668	85	36	harmonic	harmonic	ADJ
ap-7668	85	37	oscillators	oscillator	NOUN
ap-7668	85	38	.	.	PUNCT
ap-7668	86	1	classical	classical	ADJ
ap-7668	86	2	particle	particle	NOUN
ap-7668	86	3	in	in	ADP
ap-7668	86	4	a	a	DET
ap-7668	86	5	three	three	NUM
ap-7668	86	6	-	-	PUNCT
ap-7668	86	7	dimensional	dimensional	ADJ
ap-7668	86	8	curved	curved	ADJ
ap-7668	86	9	space	space	NOUN
ap-7668	86	10	.	.	PUNCT
ap-7668	87	1	explicitly	explicitly	ADV
ap-7668	87	2	,	,	PUNCT
ap-7668	87	3	the	the	DET
ap-7668	87	4	hamiltonian	hamiltonian	ADJ
ap-7668	87	5	function	function	NOUN
ap-7668	87	6	takes	take	VERB
ap-7668	87	7	the	the	DET
ap-7668	87	8	form	form	NOUN
ap-7668	87	9	h(classical	h(classical	ADJ
ap-7668	87	10	)	)	PUNCT
ap-7668	87	11	lb	lb	NOUN
ap-7668	87	12	=	=	NOUN
ap-7668	87	13	gµν	gµν	NOUN
ap-7668	87	14	πµ	πµ	PROPN
ap-7668	87	15	πν	πν	PROPN
ap-7668	88	1	+	+	PROPN
ap-7668	88	2	v	v	NOUN
ap-7668	88	3	,	,	PUNCT
ap-7668	88	4	(	(	PUNCT
ap-7668	88	5	10	10	NUM
ap-7668	88	6	)	)	PUNCT
ap-7668	88	7	where	where	SCONJ
ap-7668	88	8	πµ	πµ	PROPN
ap-7668	88	9	,	,	PUNCT
ap-7668	88	10	µ	µ	X
ap-7668	88	11	=	=	SYM
ap-7668	88	12	12	12	NUM
ap-7668	88	13	,	,	PUNCT
ap-7668	88	14	23	23	NUM
ap-7668	88	15	,	,	PUNCT
ap-7668	88	16	13	13	NUM
ap-7668	88	17	are	be	AUX
ap-7668	88	18	the	the	DET
ap-7668	88	19	associated	associated	ADJ
ap-7668	88	20	canonical	canonical	ADJ
ap-7668	88	21	conjugate	conjugate	ADJ
ap-7668	88	22	momenta	momenta	NOUN
ap-7668	88	23	to	to	ADP
ap-7668	88	24	the	the	DET
ap-7668	88	25	ρ	ρ	NOUN
ap-7668	88	26	-	-	PUNCT
ap-7668	88	27	coordinates	coordinate	NOUN
ap-7668	88	28	.	.	PUNCT
ap-7668	89	1	the	the	DET
ap-7668	89	2	hamilton	hamilton	PROPN
ap-7668	89	3	-	-	PUNCT
ap-7668	89	4	jacobi	jacobi	PROPN
ap-7668	89	5	equation	equation	NOUN
ap-7668	89	6	,	,	PUNCT
ap-7668	89	7	at	at	ADP
ap-7668	89	8	vanishing	vanish	VERB
ap-7668	89	9	potential	potential	ADJ
ap-7668	89	10	v	v	NOUN
ap-7668	89	11	=	=	SYM
ap-7668	89	12	0	0	PUNCT
ap-7668	89	13	(	(	PUNCT
ap-7668	89	14	free	free	ADJ
ap-7668	89	15	motion	motion	NOUN
ap-7668	89	16	)	)	PUNCT
ap-7668	89	17	,	,	PUNCT
ap-7668	89	18	is	be	AUX
ap-7668	89	19	clearly	clearly	ADV
ap-7668	89	20	integrable	integrable	ADJ
ap-7668	89	21	.	.	PUNCT
ap-7668	90	1	however	however	ADV
ap-7668	90	2	,	,	PUNCT
ap-7668	90	3	a	a	DET
ap-7668	90	4	complete	complete	ADJ
ap-7668	90	5	separation	separation	NOUN
ap-7668	90	6	of	of	ADP
ap-7668	90	7	variables	variable	NOUN
ap-7668	90	8	is	be	AUX
ap-7668	90	9	absent	absent	ADJ
ap-7668	90	10	in	in	ADP
ap-7668	90	11	the	the	DET
ap-7668	90	12	ρ	ρ	NOUN
ap-7668	90	13	-	-	PUNCT
ap-7668	90	14	representation	representation	NOUN
ap-7668	90	15	.	.	PUNCT
ap-7668	91	1	the	the	DET
ap-7668	91	2	poisson	poisson	PROPN
ap-7668	91	3	bracket	bracket	NOUN
ap-7668	91	4	between	between	ADP
ap-7668	91	5	the	the	DET
ap-7668	91	6	kinetic	kinetic	ADJ
ap-7668	91	7	energy	energy	NOUN
ap-7668	91	8	t	t	NOUN
ap-7668	91	9	=	=	NOUN
ap-7668	91	10	gµν	gµν	NOUN
ap-7668	91	11	πµ	πµ	PROPN
ap-7668	91	12	πν	πν	PROPN
ap-7668	91	13	and	and	CCONJ
ap-7668	91	14	the	the	DET
ap-7668	91	15	linear	linear	ADJ
ap-7668	91	16	function	function	NOUN
ap-7668	91	17	in	in	ADP
ap-7668	91	18	momentum	momentum	NOUN
ap-7668	91	19	variables	variable	NOUN
ap-7668	91	20	l	l	NOUN
ap-7668	91	21	(	(	PUNCT
ap-7668	91	22	c	c	NOUN
ap-7668	91	23	)	)	PUNCT
ap-7668	91	24	1	1	NUM
ap-7668	91	25	=	=	SYM
ap-7668	91	26	(	(	PUNCT
ap-7668	91	27	ρ13−ρ23)π12+(ρ23−ρ12)π13+(ρ12−ρ13)π23	ρ13−ρ23)π12+(ρ23−ρ12)π13+(ρ12−ρ13)π23	NOUN
ap-7668	91	28	,	,	PUNCT
ap-7668	91	29	is	be	AUX
ap-7668	91	30	zero	zero	NUM
ap-7668	91	31	.	.	PUNCT
ap-7668	92	1	4	4	NUM
ap-7668	92	2	.	.	X
ap-7668	92	3	three	three	NUM
ap-7668	92	4	body	body	NOUN
ap-7668	92	5	harmonic	harmonic	ADJ
ap-7668	92	6	oscillator	oscillator	NOUN
ap-7668	92	7	system	system	NOUN
ap-7668	92	8	in	in	ADP
ap-7668	92	9	the	the	DET
ap-7668	92	10	spectral	spectral	ADJ
ap-7668	92	11	problem	problem	NOUN
ap-7668	92	12	with	with	ADP
ap-7668	92	13	hamiltonian	hamiltonian	ADJ
ap-7668	92	14	(	(	PUNCT
ap-7668	92	15	3	3	X
ap-7668	92	16	)	)	PUNCT
ap-7668	92	17	we	we	PRON
ap-7668	92	18	take	take	VERB
ap-7668	92	19	the	the	DET
ap-7668	92	20	harmonic	harmonic	ADJ
ap-7668	92	21	potential	potential	NOUN
ap-7668	92	22	v	v	NOUN
ap-7668	92	23	(	(	PUNCT
ap-7668	92	24	ho)(ρ	ho)(ρ	X
ap-7668	92	25	)	)	PUNCT
ap-7668	93	1	=	=	SYM
ap-7668	93	2	2ω2	2ω2	NUM
ap-7668	93	3	[	[	PUNCT
ap-7668	93	4	ν12	ν12	NOUN
ap-7668	93	5	ρ12	ρ12	VERB
ap-7668	93	6	+	+	CCONJ
ap-7668	93	7	ν13	ν13	NOUN
ap-7668	93	8	ρ13	ρ13	PROPN
ap-7668	93	9	+	+	CCONJ
ap-7668	93	10	ν23	ν23	ADJ
ap-7668	93	11	ρ23	ρ23	NOUN
ap-7668	93	12	]	]	PUNCT
ap-7668	93	13	,	,	PUNCT
ap-7668	93	14	(	(	PUNCT
ap-7668	93	15	11	11	NUM
ap-7668	93	16	)	)	PUNCT
ap-7668	93	17	ω	ω	NOUN
ap-7668	93	18	>	>	X
ap-7668	93	19	0	0	PUNCT
ap-7668	93	20	is	be	AUX
ap-7668	93	21	frequency	frequency	NOUN
ap-7668	93	22	and	and	CCONJ
ap-7668	93	23	ν12	ν12	NOUN
ap-7668	93	24	,	,	PUNCT
ap-7668	93	25	ν13	ν13	PROPN
ap-7668	93	26	,	,	PUNCT
ap-7668	93	27	ν23	ν23	PROPN
ap-7668	93	28	>	>	X
ap-7668	93	29	0	0	NUM
ap-7668	93	30	are	be	AUX
ap-7668	93	31	constants	constant	NOUN
ap-7668	93	32	with	with	ADP
ap-7668	93	33	dimension	dimension	NOUN
ap-7668	93	34	of	of	ADP
ap-7668	93	35	mass	mass	PROPN
ap-7668	93	36	.	.	PUNCT
ap-7668	94	1	this	this	DET
ap-7668	94	2	problem	problem	NOUN
ap-7668	94	3	can	can	AUX
ap-7668	94	4	be	be	AUX
ap-7668	94	5	solved	solve	VERB
ap-7668	94	6	exactly	exactly	ADV
ap-7668	94	7	[	[	X
ap-7668	94	8	4	4	NUM
ap-7668	94	9	]	]	PUNCT
ap-7668	94	10	.	.	PUNCT
ap-7668	95	1	in	in	ADP
ap-7668	95	2	particular	particular	ADJ
ap-7668	95	3	,	,	PUNCT
ap-7668	95	4	in	in	ADP
ap-7668	95	5	ρ	ρ	NOUN
ap-7668	95	6	-	-	PUNCT
ap-7668	95	7	space	space	NOUN
ap-7668	95	8	the	the	DET
ap-7668	95	9	reduced	reduce	VERB
ap-7668	95	10	operator	operator	NOUN
ap-7668	95	11	(	(	PUNCT
ap-7668	95	12	3	3	X
ap-7668	95	13	)	)	PUNCT
ap-7668	95	14	possesses	possess	VERB
ap-7668	95	15	multivariate	multivariate	VERB
ap-7668	95	16	polynomial	polynomial	ADJ
ap-7668	95	17	eigenfunctions	eigenfunction	NOUN
ap-7668	95	18	,	,	PUNCT
ap-7668	95	19	see	see	VERB
ap-7668	95	20	below	below	ADV
ap-7668	95	21	.	.	PUNCT
ap-7668	96	1	we	we	PRON
ap-7668	96	2	call	call	VERB
ap-7668	96	3	the	the	DET
ap-7668	96	4	above	above	ADJ
ap-7668	96	5	potential	potential	ADJ
ap-7668	96	6	v	v	NOUN
ap-7668	96	7	(	(	PUNCT
ap-7668	96	8	ho)(ρ	ho)(ρ	PROPN
ap-7668	96	9	)	)	PUNCT
ap-7668	96	10	the	the	DET
ap-7668	96	11	3	3	NUM
ap-7668	96	12	-	-	PUNCT
ap-7668	96	13	body	body	NOUN
ap-7668	96	14	oscillator	oscillator	NOUN
ap-7668	96	15	system	system	NOUN
ap-7668	96	16	.	.	PUNCT
ap-7668	97	1	we	we	PRON
ap-7668	97	2	mention	mention	VERB
ap-7668	97	3	that	that	SCONJ
ap-7668	97	4	in	in	ADP
ap-7668	97	5	the	the	DET
ap-7668	97	6	case	case	NOUN
ap-7668	97	7	d	d	NOUN
ap-7668	97	8	=	=	SYM
ap-7668	97	9	1	1	NUM
ap-7668	97	10	(	(	PUNCT
ap-7668	97	11	3	3	NUM
ap-7668	97	12	particles	particle	NOUN
ap-7668	97	13	on	on	ADP
ap-7668	97	14	a	a	DET
ap-7668	97	15	line	line	NOUN
ap-7668	97	16	)	)	PUNCT
ap-7668	97	17	,	,	PUNCT
ap-7668	97	18	the	the	DET
ap-7668	97	19	corresponding	corresponding	ADJ
ap-7668	97	20	spectral	spectral	ADJ
ap-7668	97	21	problem	problem	NOUN
ap-7668	97	22	was	be	AUX
ap-7668	97	23	studied	study	VERB
ap-7668	97	24	in	in	ADP
ap-7668	97	25	the	the	DET
ap-7668	97	26	paper	paper	NOUN
ap-7668	98	1	[	[	X
ap-7668	98	2	7	7	NUM
ap-7668	98	3	]	]	PUNCT
ap-7668	98	4	.	.	PUNCT
ap-7668	99	1	in	in	ADP
ap-7668	99	2	the	the	DET
ap-7668	99	3	current	current	ADJ
ap-7668	99	4	report	report	NOUN
ap-7668	99	5	,	,	PUNCT
ap-7668	99	6	we	we	PRON
ap-7668	99	7	analyze	analyze	VERB
ap-7668	99	8	the	the	DET
ap-7668	99	9	d−dimensional	d−dimensional	ADJ
ap-7668	99	10	case	case	NOUN
ap-7668	99	11	with	with	ADP
ap-7668	99	12	d	d	PROPN
ap-7668	99	13	>	>	X
ap-7668	99	14	1	1	NUM
ap-7668	99	15	.	.	PUNCT
ap-7668	100	1	in	in	ADP
ap-7668	100	2	r	r	NOUN
ap-7668	100	3	-	-	PUNCT
ap-7668	100	4	variables	variable	NOUN
ap-7668	100	5	,	,	PUNCT
ap-7668	100	6	ρ	ρ	NOUN
ap-7668	100	7	=	=	SYM
ap-7668	100	8	r2	r2	PROPN
ap-7668	100	9	,	,	PUNCT
ap-7668	100	10	the	the	DET
ap-7668	100	11	potential	potential	ADJ
ap-7668	100	12	(	(	PUNCT
ap-7668	100	13	11	11	NUM
ap-7668	100	14	)	)	PUNCT
ap-7668	100	15	can	can	AUX
ap-7668	100	16	be	be	AUX
ap-7668	100	17	interpreted	interpret	VERB
ap-7668	100	18	as	as	ADP
ap-7668	100	19	a	a	DET
ap-7668	100	20	three	three	NUM
ap-7668	100	21	-	-	PUNCT
ap-7668	100	22	dimensional	dimensional	ADJ
ap-7668	100	23	(	(	PUNCT
ap-7668	100	24	an)isotropic	an)isotropic	ADJ
ap-7668	100	25	onebody	onebody	ADJ
ap-7668	100	26	oscillator	oscillator	NOUN
ap-7668	100	27	.	.	PUNCT
ap-7668	101	1	it	it	PRON
ap-7668	101	2	is	be	AUX
ap-7668	101	3	displayed	display	VERB
ap-7668	101	4	in	in	ADP
ap-7668	101	5	figure	figure	NOUN
ap-7668	101	6	1	1	NUM
ap-7668	101	7	.	.	PUNCT
ap-7668	102	1	the	the	DET
ap-7668	102	2	configuration	configuration	NOUN
ap-7668	102	3	space	space	NOUN
ap-7668	102	4	is	be	AUX
ap-7668	102	5	a	a	DET
ap-7668	102	6	subspace	subspace	NOUN
ap-7668	102	7	of	of	ADP
ap-7668	102	8	the	the	DET
ap-7668	102	9	cube	cube	NOUN
ap-7668	102	10	r3	r3	PROPN
ap-7668	102	11	+	+	PROPN
ap-7668	102	12	(	(	PUNCT
ap-7668	102	13	ρ	ρ	NOUN
ap-7668	102	14	)	)	PUNCT
ap-7668	102	15	in	in	ADP
ap-7668	102	16	e3	e3	NOUN
ap-7668	102	17	ρ	ρ	NOUN
ap-7668	102	18	-	-	NOUN
ap-7668	102	19	space	space	NOUN
ap-7668	102	20	.	.	PUNCT
ap-7668	103	1	the	the	DET
ap-7668	103	2	ρ	ρ	PROPN
ap-7668	103	3	-	-	PUNCT
ap-7668	103	4	variables	variable	NOUN
ap-7668	103	5	must	must	AUX
ap-7668	103	6	obey	obey	VERB
ap-7668	103	7	the	the	DET
ap-7668	103	8	“	"	PUNCT
ap-7668	103	9	triangle	triangle	NOUN
ap-7668	103	10	condition	condition	NOUN
ap-7668	103	11	”	"	PUNCT
ap-7668	103	12	s2	s2	PROPN
ap-7668	103	13	△	△	X
ap-7668	103	14	⩾	⩾	NOUN
ap-7668	103	15	0	0	NUM
ap-7668	103	16	,	,	PUNCT
ap-7668	103	17	namely	namely	ADV
ap-7668	103	18	the	the	DET
ap-7668	103	19	area	area	NOUN
ap-7668	103	20	of	of	ADP
ap-7668	103	21	the	the	DET
ap-7668	103	22	triangle	triangle	NOUN
ap-7668	103	23	formed	form	VERB
ap-7668	103	24	by	by	ADP
ap-7668	103	25	the	the	DET
ap-7668	103	26	position	position	NOUN
ap-7668	103	27	vectors	vector	NOUN
ap-7668	103	28	of	of	ADP
ap-7668	103	29	the	the	DET
ap-7668	103	30	bodies	body	NOUN
ap-7668	103	31	is	be	AUX
ap-7668	103	32	always	always	ADV
ap-7668	103	33	positive	positive	ADJ
ap-7668	103	34	.	.	PUNCT
ap-7668	104	1	4.1	4.1	NUM
ap-7668	104	2	.	.	PUNCT
ap-7668	104	3	solution	solution	NOUN
ap-7668	104	4	for	for	ADP
ap-7668	104	5	the	the	DET
ap-7668	104	6	ground	ground	NOUN
ap-7668	104	7	state	state	NOUN
ap-7668	104	8	in	in	ADP
ap-7668	104	9	the	the	DET
ap-7668	104	10	harmonic	harmonic	ADJ
ap-7668	104	11	potential	potential	NOUN
ap-7668	104	12	(	(	PUNCT
ap-7668	104	13	11	11	NUM
ap-7668	104	14	)	)	PUNCT
ap-7668	104	15	,	,	PUNCT
ap-7668	104	16	the	the	DET
ap-7668	104	17	ground	ground	NOUN
ap-7668	104	18	state	state	NOUN
ap-7668	104	19	eigenfunction	eigenfunction	NOUN
ap-7668	104	20	reads	read	VERB
ap-7668	104	21	ψ(ho	ψ(ho	NOUN
ap-7668	104	22	)	)	PUNCT
ap-7668	104	23	0	0	NUM
ap-7668	105	1	=	=	PUNCT
ap-7668	105	2	e−ω	e−ω	NOUN
ap-7668	105	3	(	(	PUNCT
ap-7668	105	4	a1	a1	PROPN
ap-7668	105	5	µ12	µ12	NOUN
ap-7668	105	6	ρ12	ρ12	NOUN
ap-7668	105	7	+	+	NUM
ap-7668	105	8	a2	a2	PROPN
ap-7668	105	9	µ13	µ13	PROPN
ap-7668	105	10	ρ13	ρ13	PROPN
ap-7668	105	11	+	+	NUM
ap-7668	105	12	a3	a3	NOUN
ap-7668	105	13	µ23	µ23	NOUN
ap-7668	105	14	ρ23	ρ23	NOUN
ap-7668	105	15	)	)	PUNCT
ap-7668	105	16	,	,	PUNCT
ap-7668	105	17	(	(	PUNCT
ap-7668	105	18	12	12	NUM
ap-7668	105	19	)	)	PUNCT
ap-7668	105	20	where	where	SCONJ
ap-7668	105	21	the	the	DET
ap-7668	105	22	parameters	parameter	NOUN
ap-7668	105	23	a1	a1	VERB
ap-7668	105	24	,	,	PUNCT
ap-7668	105	25	a2	a2	PROPN
ap-7668	105	26	,	,	PUNCT
ap-7668	105	27	a3	a3	VERB
ap-7668	105	28	≥	≥	NOUN
ap-7668	105	29	0	0	NUM
ap-7668	105	30	are	be	AUX
ap-7668	105	31	introduced	introduce	VERB
ap-7668	105	32	for	for	ADP
ap-7668	105	33	convenience	convenience	NOUN
ap-7668	105	34	.	.	PUNCT
ap-7668	106	1	they	they	PRON
ap-7668	106	2	define	define	VERB
ap-7668	106	3	the	the	DET
ap-7668	106	4	spring	spring	NOUN
ap-7668	106	5	constants	constant	NOUN
ap-7668	106	6	,	,	PUNCT
ap-7668	106	7	see	see	VERB
ap-7668	106	8	below	below	ADV
ap-7668	106	9	.	.	PUNCT
ap-7668	107	1	the	the	DET
ap-7668	107	2	associated	associated	ADJ
ap-7668	107	3	ground	ground	NOUN
ap-7668	107	4	state	state	NOUN
ap-7668	107	5	energy	energy	NOUN
ap-7668	107	6	e0	e0	PROPN
ap-7668	107	7	=	=	PUNCT
ap-7668	108	1	ω	ω	PROPN
ap-7668	108	2	d	d	X
ap-7668	108	3	(	(	PUNCT
ap-7668	108	4	a1	a1	NOUN
ap-7668	108	5	+	+	CCONJ
ap-7668	108	6	a2	a2	PROPN
ap-7668	108	7	+	+	NUM
ap-7668	108	8	a3	a3	NOUN
ap-7668	108	9	)	)	PUNCT
ap-7668	108	10	,	,	PUNCT
ap-7668	108	11	(	(	PUNCT
ap-7668	108	12	13	13	NUM
ap-7668	108	13	)	)	PUNCT
ap-7668	108	14	is	be	AUX
ap-7668	108	15	mass	mass	ADJ
ap-7668	108	16	-	-	PUNCT
ap-7668	108	17	independent	independent	ADJ
ap-7668	108	18	.	.	PUNCT
ap-7668	109	1	there	there	PRON
ap-7668	109	2	exists	exist	VERB
ap-7668	109	3	the	the	DET
ap-7668	109	4	following	follow	VERB
ap-7668	109	5	algebraic	algebraic	ADJ
ap-7668	109	6	relations	relation	NOUN
ap-7668	109	7	ν12	ν12	NOUN
ap-7668	109	8	=	=	SYM
ap-7668	109	9	a2	a2	PROPN
ap-7668	109	10	1	1	NUM
ap-7668	109	11	µ12	µ12	NOUN
ap-7668	109	12	+	+	CCONJ
ap-7668	109	13	a1	a1	NOUN
ap-7668	109	14	a2	a2	PROPN
ap-7668	109	15	µ12	µ12	PROPN
ap-7668	110	1	µ13	µ13	PROPN
ap-7668	110	2	m1	m1	PROPN
ap-7668	110	3	+	+	CCONJ
ap-7668	110	4	a1	a1	NOUN
ap-7668	110	5	a3	a3	NOUN
ap-7668	110	6	µ12	µ12	PROPN
ap-7668	110	7	µ23	µ23	NUM
ap-7668	110	8	m2	m2	PROPN
ap-7668	110	9	−	−	PROPN
ap-7668	110	10	a2	a2	PROPN
ap-7668	110	11	a3	a3	PROPN
ap-7668	110	12	µ13	µ13	PROPN
ap-7668	110	13	µ23	µ23	NOUN
ap-7668	110	14	m3	m3	PROPN
ap-7668	110	15	,	,	PUNCT
ap-7668	110	16	ν13	ν13	NOUN
ap-7668	110	17	=	=	SYM
ap-7668	110	18	a2	a2	PROPN
ap-7668	110	19	2	2	NUM
ap-7668	110	20	µ13	µ13	NOUN
ap-7668	110	21	+	+	CCONJ
ap-7668	110	22	a1	a1	NOUN
ap-7668	110	23	a2	a2	PROPN
ap-7668	110	24	µ12	µ12	PROPN
ap-7668	110	25	µ13	µ13	PROPN
ap-7668	110	26	m1	m1	PROPN
ap-7668	110	27	+	+	CCONJ
ap-7668	110	28	a2	a2	PROPN
ap-7668	110	29	a3	a3	NOUN
ap-7668	110	30	µ13	µ13	PROPN
ap-7668	110	31	µ23	µ23	AUX
ap-7668	110	32	m3	m3	PROPN
ap-7668	110	33	−	−	NOUN
ap-7668	110	34	a1	a1	NOUN
ap-7668	110	35	a3	a3	NOUN
ap-7668	110	36	µ12	µ12	PROPN
ap-7668	110	37	µ23	µ23	NOUN
ap-7668	110	38	m2	m2	PROPN
ap-7668	110	39	,	,	PUNCT
ap-7668	110	40	ν23	ν23	PROPN
ap-7668	110	41	=	=	SYM
ap-7668	110	42	a2	a2	PROPN
ap-7668	110	43	3	3	NUM
ap-7668	110	44	µ23	µ23	NOUN
ap-7668	110	45	+	+	CCONJ
ap-7668	110	46	a1	a1	NOUN
ap-7668	110	47	a3	a3	NOUN
ap-7668	110	48	µ12	µ12	PROPN
ap-7668	110	49	µ23	µ23	NUM
ap-7668	110	50	m2	m2	PROPN
ap-7668	110	51	+	+	PROPN
ap-7668	110	52	a2	a2	PROPN
ap-7668	110	53	a3	a3	NOUN
ap-7668	110	54	µ13	µ13	PROPN
ap-7668	110	55	µ23	µ23	AUX
ap-7668	110	56	m3	m3	PROPN
ap-7668	110	57	−	−	NOUN
ap-7668	110	58	a1	a1	NOUN
ap-7668	110	59	a2	a2	PROPN
ap-7668	110	60	µ12	µ12	PROPN
ap-7668	110	61	µ13	µ13	PROPN
ap-7668	110	62	m1	m1	PROPN
ap-7668	110	63	.	.	PUNCT
ap-7668	111	1	5	5	X
ap-7668	111	2	.	.	X
ap-7668	111	3	lie	lie	VERB
ap-7668	111	4	algebraic	algebraic	ADJ
ap-7668	111	5	structure	structure	NOUN
ap-7668	111	6	using	use	VERB
ap-7668	111	7	the	the	DET
ap-7668	111	8	previous	previous	ADJ
ap-7668	111	9	function	function	NOUN
ap-7668	111	10	ψ(ho	ψ(ho	NOUN
ap-7668	111	11	)	)	PUNCT
ap-7668	111	12	0	0	NUM
ap-7668	112	1	(	(	PUNCT
ap-7668	112	2	12	12	NUM
ap-7668	112	3	)	)	PUNCT
ap-7668	112	4	as	as	ADP
ap-7668	112	5	a	a	DET
ap-7668	112	6	gauge	gauge	NOUN
ap-7668	112	7	factor	factor	NOUN
ap-7668	112	8	,	,	PUNCT
ap-7668	112	9	the	the	DET
ap-7668	112	10	transformed	transform	VERB
ap-7668	112	11	hamiltonian	hamiltonian	ADJ
ap-7668	112	12	hrad	hrad	PROPN
ap-7668	112	13	(	(	PUNCT
ap-7668	112	14	3	3	NUM
ap-7668	112	15	)	)	PUNCT
ap-7668	112	16	h(algebraic	h(algebraic	PROPN
ap-7668	112	17	)	)	PUNCT
ap-7668	112	18	≡	≡	PROPN
ap-7668	112	19	(	(	PUNCT
ap-7668	112	20	ψ(ho	ψ(ho	PROPN
ap-7668	112	21	)	)	PUNCT
ap-7668	112	22	0	0	NUM
ap-7668	112	23	)	)	PUNCT
ap-7668	112	24	−1	−1	NOUN
ap-7668	113	1	[	[	X
ap-7668	113	2	−∆rad	−∆rad	X
ap-7668	113	3	+	+	CCONJ
ap-7668	113	4	v	v	ADP
ap-7668	113	5	−	−	PROPN
ap-7668	113	6	e0	e0	PROPN
ap-7668	113	7	]	]	PUNCT
ap-7668	113	8	ψ(ho	ψ(ho	PROPN
ap-7668	113	9	)	)	PUNCT
ap-7668	113	10	0	0	NUM
ap-7668	114	1	(	(	PUNCT
ap-7668	114	2	14	14	NUM
ap-7668	114	3	)	)	PUNCT
ap-7668	114	4	is	be	AUX
ap-7668	114	5	an	an	DET
ap-7668	114	6	algebraic	algebraic	ADJ
ap-7668	114	7	operator	operator	NOUN
ap-7668	114	8	,	,	PUNCT
ap-7668	114	9	i.e.	i.e.	X
ap-7668	114	10	the	the	DET
ap-7668	114	11	coefficient	coefficient	NOUN
ap-7668	114	12	are	be	AUX
ap-7668	114	13	polynomials	polynomial	NOUN
ap-7668	114	14	in	in	ADP
ap-7668	114	15	the	the	DET
ap-7668	114	16	ρ	ρ	NOUN
ap-7668	114	17	-	-	PUNCT
ap-7668	114	18	variables	variable	NOUN
ap-7668	114	19	.	.	PUNCT
ap-7668	115	1	the	the	DET
ap-7668	115	2	e0	e0	PROPN
ap-7668	115	3	is	be	AUX
ap-7668	115	4	taken	take	VERB
ap-7668	115	5	from	from	ADP
ap-7668	115	6	(	(	PUNCT
ap-7668	115	7	13	13	NUM
ap-7668	115	8	)	)	PUNCT
ap-7668	115	9	.	.	PUNCT
ap-7668	116	1	in	in	ADP
ap-7668	116	2	addition	addition	NOUN
ap-7668	116	3	,	,	PUNCT
ap-7668	116	4	this	this	DET
ap-7668	116	5	algebraic	algebraic	ADJ
ap-7668	116	6	operator	operator	NOUN
ap-7668	116	7	(	(	PUNCT
ap-7668	116	8	14	14	NUM
ap-7668	116	9	)	)	PUNCT
ap-7668	116	10	is	be	AUX
ap-7668	116	11	of	of	ADP
ap-7668	116	12	liealgebraic	liealgebraic	ADJ
ap-7668	116	13	nature	nature	NOUN
ap-7668	116	14	.	.	PUNCT
ap-7668	117	1	it	it	PRON
ap-7668	117	2	admits	admit	VERB
ap-7668	117	3	a	a	DET
ap-7668	117	4	representation	representation	NOUN
ap-7668	117	5	in	in	ADP
ap-7668	117	6	terms	term	NOUN
ap-7668	117	7	of	of	ADP
ap-7668	117	8	the	the	DET
ap-7668	117	9	generators	generator	NOUN
ap-7668	118	1	j	j	PROPN
ap-7668	118	2	−	−	VERB
ap-7668	119	1	i	i	NOUN
ap-7668	119	2	=	=	SYM
ap-7668	119	3	∂	∂	NUM
ap-7668	119	4	∂yi	∂yi	PROPN
ap-7668	119	5	,	,	PUNCT
ap-7668	119	6	j	j	PROPN
ap-7668	119	7	0	0	NUM
ap-7668	119	8	ij	ij	NOUN
ap-7668	119	9	=	=	PROPN
ap-7668	119	10	yi	yi	PROPN
ap-7668	119	11	∂	∂	NUM
ap-7668	119	12	∂yj	∂yj	PROPN
ap-7668	119	13	,	,	PUNCT
ap-7668	119	14	j	j	NOUN
ap-7668	119	15	0(n	0(n	NUM
ap-7668	119	16	)	)	PUNCT
ap-7668	120	1	=	=	SYM
ap-7668	120	2	3∑	3∑	NUM
ap-7668	120	3	i=1	i=1	PROPN
ap-7668	120	4	yi	yi	PROPN
ap-7668	120	5	∂	∂	NOUN
ap-7668	120	6	∂yi	∂yi	PROPN
ap-7668	120	7	−n	−n	PROPN
ap-7668	120	8	,	,	PUNCT
ap-7668	120	9	j	j	PROPN
ap-7668	121	1	+	+	CCONJ
ap-7668	121	2	i	i	PROPN
ap-7668	121	3	(	(	PUNCT
ap-7668	121	4	n	n	CCONJ
ap-7668	121	5	)	)	PUNCT
ap-7668	121	6	=	=	SYM
ap-7668	121	7	yi	yi	PROPN
ap-7668	121	8	j	j	NOUN
ap-7668	121	9	0(n	0(n	NUM
ap-7668	121	10	)	)	PUNCT
ap-7668	122	1	=	=	SYM
ap-7668	122	2	yi	yi	NOUN
ap-7668	122	3			PROPN
ap-7668	122	4	3∑	3∑	PROPN
ap-7668	122	5	j=1	j=1	PROPN
ap-7668	122	6	yj	yj	PROPN
ap-7668	122	7	∂	∂	PROPN
ap-7668	122	8	∂yj	∂yj	PROPN
ap-7668	122	9	−n	−n	ADP
ap-7668	122	10			PROPN
ap-7668	122	11	,	,	PUNCT
ap-7668	122	12	(	(	PUNCT
ap-7668	122	13	i	i	PRON
ap-7668	122	14	,	,	PUNCT
ap-7668	122	15	j	j	PROPN
ap-7668	122	16	=	=	SYM
ap-7668	122	17	1	1	NUM
ap-7668	122	18	,	,	PUNCT
ap-7668	122	19	2	2	NUM
ap-7668	122	20	,	,	PUNCT
ap-7668	122	21	3	3	NUM
ap-7668	122	22	)	)	PUNCT
ap-7668	122	23	of	of	ADP
ap-7668	122	24	the	the	DET
ap-7668	122	25	algebra	algebra	NOUN
ap-7668	122	26	sℓ(4,r	sℓ(4,r	ADJ
ap-7668	122	27	)	)	PUNCT
ap-7668	122	28	,	,	PUNCT
ap-7668	122	29	see	see	VERB
ap-7668	122	30	[	[	X
ap-7668	122	31	8	8	NUM
ap-7668	122	32	,	,	PUNCT
ap-7668	122	33	9	9	NUM
ap-7668	122	34	]	]	PUNCT
ap-7668	122	35	here	here	ADV
ap-7668	122	36	n	n	PRON
ap-7668	122	37	is	be	AUX
ap-7668	122	38	a	a	DET
ap-7668	122	39	constant	constant	ADJ
ap-7668	122	40	.	.	PUNCT
ap-7668	123	1	the	the	DET
ap-7668	123	2	notation	notation	NOUN
ap-7668	123	3	y1	y1	NOUN
ap-7668	123	4	=	=	PUNCT
ap-7668	123	5	ρ12	ρ12	NOUN
ap-7668	123	6	,	,	PUNCT
ap-7668	123	7	y2	y2	NOUN
ap-7668	123	8	=	=	NOUN
ap-7668	124	1	ρ13	ρ13	NOUN
ap-7668	124	2	,	,	PUNCT
ap-7668	124	3	y3	y3	NOUN
ap-7668	124	4	=	=	PUNCT
ap-7668	124	5	ρ23	ρ23	NOUN
ap-7668	124	6	,	,	PUNCT
ap-7668	124	7	was	be	AUX
ap-7668	124	8	employed	employ	VERB
ap-7668	124	9	for	for	ADP
ap-7668	124	10	simplicity	simplicity	NOUN
ap-7668	124	11	.	.	PUNCT
ap-7668	125	1	if	if	SCONJ
ap-7668	125	2	n	n	PRON
ap-7668	125	3	is	be	AUX
ap-7668	125	4	a	a	DET
ap-7668	125	5	non	non	ADJ
ap-7668	125	6	-	-	ADJ
ap-7668	125	7	negative	negative	ADJ
ap-7668	125	8	integer	integer	NOUN
ap-7668	125	9	,	,	PUNCT
ap-7668	125	10	a	a	DET
ap-7668	125	11	finite	finite	ADJ
ap-7668	125	12	-	-	ADJ
ap-7668	125	13	dimensional	dimensional	ADJ
ap-7668	125	14	representation	representation	NOUN
ap-7668	125	15	space	space	NOUN
ap-7668	125	16	takes	take	VERB
ap-7668	125	17	place	place	NOUN
ap-7668	125	18	,	,	PUNCT
ap-7668	125	19	vn	vn	NOUN
ap-7668	125	20	=	=	SYM
ap-7668	125	21	⟨yn1	⟨yn1	NOUN
ap-7668	125	22	1	1	NUM
ap-7668	125	23	yn2	yn2	NOUN
ap-7668	125	24	2	2	NUM
ap-7668	125	25	yn3	yn3	NOUN
ap-7668	125	26	3	3	NUM
ap-7668	125	27	|	|	CCONJ
ap-7668	125	28	0	0	NUM
ap-7668	125	29	≤	≤	NOUN
ap-7668	125	30	n1	n1	NOUN
ap-7668	125	31	+	+	CCONJ
ap-7668	125	32	n2	n2	ADJ
ap-7668	125	33	+	+	CCONJ
ap-7668	125	34	n3	n3	ADJ
ap-7668	125	35	≤	≤	PROPN
ap-7668	125	36	n⟩	n⟩	PROPN
ap-7668	125	37	.	.	PUNCT
ap-7668	126	1	(	(	PUNCT
ap-7668	126	2	15	15	NUM
ap-7668	126	3	)	)	PUNCT
ap-7668	126	4	52	52	NUM
ap-7668	126	5	vol	vol	NOUN
ap-7668	126	6	.	.	PUNCT
ap-7668	127	1	62	62	NUM
ap-7668	127	2	no	no	INTJ
ap-7668	127	3	.	.	PUNCT
ap-7668	128	1	1/2022	1/2022	NUM
ap-7668	128	2	generalized	generalized	ADJ
ap-7668	128	3	three	three	NUM
ap-7668	128	4	-	-	PUNCT
ap-7668	128	5	body	body	NOUN
ap-7668	128	6	harmonic	harmonic	ADJ
ap-7668	128	7	oscillator	oscillator	NOUN
ap-7668	128	8	system	system	NOUN
ap-7668	128	9	:	:	PUNCT
ap-7668	128	10	ground	ground	NOUN
ap-7668	128	11	state	state	NOUN
ap-7668	128	12	6	6	NUM
ap-7668	128	13	.	.	PUNCT
ap-7668	128	14	relation	relation	NOUN
ap-7668	128	15	with	with	ADP
ap-7668	128	16	the	the	DET
ap-7668	128	17	jacobi	jacobi	PROPN
ap-7668	128	18	oscillator	oscillator	NOUN
ap-7668	128	19	now	now	ADV
ap-7668	128	20	,	,	PUNCT
ap-7668	128	21	we	we	PRON
ap-7668	128	22	can	can	AUX
ap-7668	128	23	indicate	indicate	VERB
ap-7668	128	24	an	an	DET
ap-7668	128	25	emergent	emergent	ADJ
ap-7668	128	26	relation	relation	NOUN
ap-7668	128	27	between	between	ADP
ap-7668	128	28	the	the	DET
ap-7668	128	29	harmonic	harmonic	ADJ
ap-7668	128	30	potential	potential	NOUN
ap-7668	128	31	(	(	PUNCT
ap-7668	128	32	11	11	NUM
ap-7668	128	33	)	)	PUNCT
ap-7668	128	34	and	and	CCONJ
ap-7668	128	35	the	the	DET
ap-7668	128	36	jacobi	jacobi	PROPN
ap-7668	128	37	oscillator	oscillator	NOUN
ap-7668	128	38	system	system	NOUN
ap-7668	128	39	h(jacobi	h(jacobi	NOUN
ap-7668	128	40	)	)	PUNCT
ap-7668	128	41	≡	≡	PROPN
ap-7668	129	1	2∑	2∑	X
ap-7668	129	2	i=1	i=1	X
ap-7668	130	1	[	[	PUNCT
ap-7668	130	2	−	−	PROPN
ap-7668	130	3	∂2	∂2	PROPN
ap-7668	130	4	∂zi∂zi	∂zi∂zi	NOUN
ap-7668	130	5	+	+	CCONJ
ap-7668	130	6	4	4	NUM
ap-7668	130	7	λi	λi	NOUN
ap-7668	130	8	ω	ω	NUM
ap-7668	130	9	2	2	NUM
ap-7668	130	10	zi	zi	NOUN
ap-7668	130	11	·	·	PUNCT
ap-7668	130	12	zi	zi	NOUN
ap-7668	130	13	]	]	PUNCT
ap-7668	130	14	,	,	PUNCT
ap-7668	130	15	(	(	PUNCT
ap-7668	130	16	16	16	NUM
ap-7668	130	17	)	)	PUNCT
ap-7668	131	1	where	where	SCONJ
ap-7668	131	2	ω	ω	X
ap-7668	131	3	>	>	X
ap-7668	131	4	0	0	PROPN
ap-7668	131	5	,	,	PUNCT
ap-7668	131	6	λ1	λ1	ADJ
ap-7668	131	7	,	,	PUNCT
ap-7668	131	8	λ2	λ2	PROPN
ap-7668	131	9	≥	≥	NOUN
ap-7668	131	10	0	0	NUM
ap-7668	131	11	,	,	PUNCT
ap-7668	131	12	and	and	CCONJ
ap-7668	131	13	z1	z1	PROPN
ap-7668	131	14	=	=	SYM
ap-7668	131	15	√	√	PROPN
ap-7668	131	16	m1	m1	PROPN
ap-7668	131	17	m2	m2	PROPN
ap-7668	131	18	m1	m1	PROPN
ap-7668	131	19	+	+	PROPN
ap-7668	131	20	m2	m2	PROPN
ap-7668	131	21	(	(	PUNCT
ap-7668	131	22	r1	r1	PROPN
ap-7668	131	23	−	−	PROPN
ap-7668	131	24	r2	r2	PROPN
ap-7668	131	25	)	)	PUNCT
ap-7668	131	26	z2	z2	PROPN
ap-7668	131	27	=	=	SYM
ap-7668	131	28	√	√	PROPN
ap-7668	131	29	(	(	PUNCT
ap-7668	131	30	m1	m1	PROPN
ap-7668	131	31	+	+	PROPN
ap-7668	131	32	m2)m3	m2)m3	ADJ
ap-7668	131	33	m1	m1	PROPN
ap-7668	131	34	+	+	PROPN
ap-7668	131	35	m2	m2	PROPN
ap-7668	131	36	+	+	PROPN
ap-7668	131	37	m3	m3	PROPN
ap-7668	131	38	(	(	PUNCT
ap-7668	131	39	r3	r3	PROPN
ap-7668	131	40	−	−	PROPN
ap-7668	131	41	m1	m1	PROPN
ap-7668	131	42	r1	r1	PROPN
ap-7668	131	43	+	+	PROPN
ap-7668	131	44	m2	m2	PROPN
ap-7668	131	45	r2	r2	PROPN
ap-7668	131	46	m1	m1	PROPN
ap-7668	131	47	+	+	PROPN
ap-7668	131	48	m2	m2	PROPN
ap-7668	131	49	)	)	PUNCT
ap-7668	131	50	are	be	AUX
ap-7668	131	51	standard	standard	ADJ
ap-7668	131	52	jacobi	jacobi	PROPN
ap-7668	131	53	variables	variable	NOUN
ap-7668	131	54	,	,	PUNCT
ap-7668	131	55	see	see	VERB
ap-7668	132	1	e.g.	e.g.	ADV
ap-7668	132	2	[	[	X
ap-7668	132	3	10	10	NUM
ap-7668	132	4	]	]	PUNCT
ap-7668	132	5	.	.	PUNCT
ap-7668	133	1	this	this	DET
ap-7668	133	2	hamiltonian	hamiltonian	NOUN
ap-7668	133	3	describes	describe	VERB
ap-7668	133	4	two	two	NUM
ap-7668	133	5	decoupled	decouple	VERB
ap-7668	133	6	harmonic	harmonic	ADJ
ap-7668	133	7	oscillators	oscillator	NOUN
ap-7668	133	8	in	in	ADP
ap-7668	133	9	flat	flat	ADJ
ap-7668	133	10	space	space	NOUN
ap-7668	133	11	,	,	PUNCT
ap-7668	133	12	see	see	VERB
ap-7668	133	13	[	[	X
ap-7668	133	14	6	6	NUM
ap-7668	133	15	]	]	PUNCT
ap-7668	133	16	.	.	PUNCT
ap-7668	134	1	consequently	consequently	ADV
ap-7668	134	2	,	,	PUNCT
ap-7668	134	3	it	it	PRON
ap-7668	134	4	is	be	AUX
ap-7668	134	5	an	an	DET
ap-7668	134	6	exactly	exactly	ADV
ap-7668	134	7	-	-	PUNCT
ap-7668	134	8	solvable	solvable	ADJ
ap-7668	134	9	problem	problem	NOUN
ap-7668	134	10	.	.	PUNCT
ap-7668	135	1	the	the	DET
ap-7668	135	2	complete	complete	ADJ
ap-7668	135	3	spectra	spectra	NOUN
ap-7668	135	4	and	and	CCONJ
ap-7668	135	5	eigenfunctions	eigenfunction	NOUN
ap-7668	135	6	can	can	AUX
ap-7668	135	7	be	be	AUX
ap-7668	135	8	calculated	calculate	VERB
ap-7668	135	9	by	by	ADP
ap-7668	135	10	pure	pure	ADJ
ap-7668	135	11	algebraic	algebraic	ADJ
ap-7668	135	12	means	mean	NOUN
ap-7668	135	13	.	.	PUNCT
ap-7668	136	1	the	the	DET
ap-7668	136	2	solutions	solution	NOUN
ap-7668	136	3	of	of	ADP
ap-7668	136	4	the	the	DET
ap-7668	136	5	jacobi	jacobi	PROPN
ap-7668	136	6	oscillator	oscillator	NOUN
ap-7668	136	7	that	that	PRON
ap-7668	136	8	solely	solely	ADV
ap-7668	136	9	depend	depend	VERB
ap-7668	136	10	on	on	ADP
ap-7668	136	11	the	the	DET
ap-7668	136	12	jacoby	jacoby	PROPN
ap-7668	136	13	distances	distance	NOUN
ap-7668	136	14	zi	zi	NOUN
ap-7668	136	15	=	=	SYM
ap-7668	136	16	|zi|	|zi|	NUM
ap-7668	136	17	are	be	AUX
ap-7668	136	18	governed	govern	VERB
ap-7668	136	19	by	by	ADP
ap-7668	136	20	the	the	DET
ap-7668	136	21	operator	operator	NOUN
ap-7668	136	22	,	,	PUNCT
ap-7668	136	23	h(jacobi	h(jacobi	NOUN
ap-7668	136	24	)	)	PUNCT
ap-7668	136	25	rad	rad	NOUN
ap-7668	137	1	=	=	SYM
ap-7668	137	2	2∑	2∑	NUM
ap-7668	137	3	i=1	i=1	X
ap-7668	138	1	[	[	PUNCT
ap-7668	138	2	−	−	PROPN
ap-7668	138	3	∂2	∂2	PROPN
ap-7668	138	4	∂zi∂zi	∂zi∂zi	NOUN
ap-7668	138	5	−	−	PROPN
ap-7668	138	6	(	(	PUNCT
ap-7668	138	7	d−	d−	PROPN
ap-7668	138	8	1	1	NUM
ap-7668	138	9	)	)	PUNCT
ap-7668	138	10	zi	zi	NOUN
ap-7668	138	11	∂	∂	NUM
ap-7668	138	12	∂zi	∂zi	NOUN
ap-7668	138	13	]	]	PUNCT
ap-7668	139	1	+	+	CCONJ
ap-7668	139	2	4	4	NUM
ap-7668	139	3	λ1	λ1	ADJ
ap-7668	139	4	ω	ω	NUM
ap-7668	139	5	2	2	NUM
ap-7668	139	6	z2	z2	PROPN
ap-7668	139	7	1	1	NUM
ap-7668	139	8	+	+	CCONJ
ap-7668	139	9	4	4	NUM
ap-7668	139	10	λ2	λ2	NOUN
ap-7668	139	11	ω	ω	NUM
ap-7668	139	12	2	2	NUM
ap-7668	139	13	z2	z2	PROPN
ap-7668	139	14	2	2	NUM
ap-7668	139	15	.	.	PUNCT
ap-7668	140	1	(	(	PUNCT
ap-7668	140	2	17	17	NUM
ap-7668	140	3	)	)	PUNCT
ap-7668	140	4	in	in	ADP
ap-7668	140	5	this	this	DET
ap-7668	140	6	case	case	NOUN
ap-7668	140	7	,	,	PUNCT
ap-7668	140	8	the	the	DET
ap-7668	140	9	associated	associated	ADJ
ap-7668	140	10	hidden	hide	VERB
ap-7668	140	11	algebra	algebra	NOUN
ap-7668	140	12	is	be	AUX
ap-7668	140	13	given	give	VERB
ap-7668	140	14	by	by	ADP
ap-7668	140	15	sl	sl	PROPN
ap-7668	140	16	⊗	⊗	PROPN
ap-7668	140	17	(	(	PUNCT
ap-7668	140	18	2	2	NUM
ap-7668	140	19	)	)	PUNCT
ap-7668	140	20	2	2	NUM
ap-7668	140	21	which	which	PRON
ap-7668	140	22	acts	act	VERB
ap-7668	140	23	on	on	ADP
ap-7668	140	24	the	the	DET
ap-7668	140	25	two	two	NUM
ap-7668	140	26	-	-	PUNCT
ap-7668	140	27	dimensional	dimensional	ADJ
ap-7668	140	28	space	space	NOUN
ap-7668	140	29	(	(	PUNCT
ap-7668	140	30	z1	z1	NOUN
ap-7668	140	31	,	,	PUNCT
ap-7668	140	32	z2	z2	PROPN
ap-7668	140	33	)	)	PUNCT
ap-7668	140	34	.	.	PUNCT
ap-7668	141	1	in	in	ADP
ap-7668	141	2	particular	particular	ADJ
ap-7668	141	3	,	,	PUNCT
ap-7668	141	4	the	the	DET
ap-7668	141	5	eigenfunctions	eigenfunction	NOUN
ap-7668	141	6	of	of	ADP
ap-7668	141	7	h(jacobi	h(jacobi	NOUN
ap-7668	141	8	)	)	PUNCT
ap-7668	141	9	(	(	PUNCT
ap-7668	141	10	16	16	NUM
ap-7668	141	11	)	)	PUNCT
ap-7668	141	12	can	can	AUX
ap-7668	141	13	be	be	AUX
ap-7668	141	14	employed	employ	VERB
ap-7668	141	15	to	to	PART
ap-7668	141	16	construct	construct	VERB
ap-7668	141	17	approximate	approximate	ADJ
ap-7668	141	18	solutions	solution	NOUN
ap-7668	141	19	for	for	ADP
ap-7668	141	20	the	the	DET
ap-7668	141	21	n	n	CCONJ
ap-7668	141	22	-	-	PUNCT
ap-7668	141	23	body	body	NOUN
ap-7668	141	24	problem	problem	NOUN
ap-7668	141	25	,	,	PUNCT
ap-7668	141	26	for	for	ADP
ap-7668	141	27	this	this	DET
ap-7668	141	28	discussion	discussion	NOUN
ap-7668	141	29	see	see	VERB
ap-7668	141	30	[	[	X
ap-7668	141	31	10	10	NUM
ap-7668	141	32	]	]	PUNCT
ap-7668	141	33	.	.	PUNCT
ap-7668	142	1	assuming	assume	VERB
ap-7668	142	2	any	any	PRON
ap-7668	142	3	of	of	ADP
ap-7668	142	4	the	the	DET
ap-7668	142	5	two	two	NUM
ap-7668	142	6	conditions	condition	NOUN
ap-7668	142	7	m2	m2	PROPN
ap-7668	142	8	m3	m3	PROPN
ap-7668	142	9	=	=	PROPN
ap-7668	142	10	ν12	ν12	PROPN
ap-7668	142	11	ν13	ν13	NOUN
ap-7668	142	12	;	;	PUNCT
ap-7668	142	13	m1	m1	PROPN
ap-7668	142	14	m2	m2	PROPN
ap-7668	142	15	=	=	PROPN
ap-7668	142	16	ν13	ν13	PROPN
ap-7668	142	17	ν23	ν23	PROPN
ap-7668	142	18	,	,	PUNCT
ap-7668	142	19	in	in	ADP
ap-7668	142	20	the	the	DET
ap-7668	142	21	harmonic	harmonic	ADJ
ap-7668	142	22	oscillator	oscillator	NOUN
ap-7668	142	23	potential	potential	NOUN
ap-7668	142	24	v	v	X
ap-7668	142	25	(	(	PUNCT
ap-7668	142	26	ho	ho	PROPN
ap-7668	142	27	)	)	PUNCT
ap-7668	142	28	(	(	PUNCT
ap-7668	142	29	11	11	NUM
ap-7668	142	30	)	)	PUNCT
ap-7668	142	31	,	,	PUNCT
ap-7668	142	32	we	we	PRON
ap-7668	142	33	obtain	obtain	VERB
ap-7668	142	34	u	u	NOUN
ap-7668	142	35	(	(	PUNCT
ap-7668	142	36	ho	ho	PROPN
ap-7668	142	37	)	)	PUNCT
ap-7668	142	38	j	j	PROPN
ap-7668	142	39	≡	≡	PROPN
ap-7668	142	40	4	4	NUM
ap-7668	142	41	λ1	λ1	PROPN
ap-7668	142	42	ω	ω	NUM
ap-7668	142	43	2	2	NUM
ap-7668	142	44	z2	z2	PROPN
ap-7668	142	45	1	1	NUM
ap-7668	142	46	+	+	CCONJ
ap-7668	142	47	4	4	NUM
ap-7668	142	48	λ2	λ2	NOUN
ap-7668	142	49	ω	ω	NUM
ap-7668	142	50	2	2	NUM
ap-7668	142	51	z2	z2	NUM
ap-7668	142	52	2	2	NUM
ap-7668	142	53	=	=	SYM
ap-7668	142	54	2ω2	2ω2	NUM
ap-7668	142	55	[	[	PUNCT
ap-7668	142	56	ν12	ν12	NOUN
ap-7668	142	57	ρ12	ρ12	VERB
ap-7668	142	58	+	+	CCONJ
ap-7668	142	59	ν13	ν13	NOUN
ap-7668	142	60	ρ13	ρ13	PROPN
ap-7668	142	61	+	+	CCONJ
ap-7668	142	62	ν23	ν23	ADJ
ap-7668	142	63	ρ23	ρ23	NOUN
ap-7668	142	64	]	]	PUNCT
ap-7668	143	1	=	=	SYM
ap-7668	143	2	v	v	X
ap-7668	143	3	(	(	PUNCT
ap-7668	143	4	ho	ho	PROPN
ap-7668	143	5	)	)	PUNCT
ap-7668	143	6	(	(	PUNCT
ap-7668	143	7	18	18	NUM
ap-7668	143	8	)	)	PUNCT
ap-7668	143	9	with	with	ADP
ap-7668	143	10	λ1	λ1	ADJ
ap-7668	143	11	=	=	SYM
ap-7668	143	12	λ2	λ2	PROPN
ap-7668	143	13	=	=	SYM
ap-7668	143	14	m1	m1	PROPN
ap-7668	143	15	+	+	PROPN
ap-7668	143	16	m2	m2	PROPN
ap-7668	143	17	+	+	PROPN
ap-7668	143	18	m3	m3	PROPN
ap-7668	143	19	2m1	2m1	NUM
ap-7668	143	20	m3	m3	PROPN
ap-7668	143	21	ν13	ν13	PROPN
ap-7668	143	22	,	,	PUNCT
ap-7668	143	23	hence	hence	ADV
ap-7668	143	24	,	,	PUNCT
ap-7668	143	25	in	in	ADP
ap-7668	143	26	this	this	DET
ap-7668	143	27	case	case	NOUN
ap-7668	143	28	the	the	DET
ap-7668	143	29	three	three	NUM
ap-7668	143	30	-	-	PUNCT
ap-7668	143	31	body	body	NOUN
ap-7668	143	32	oscillator	oscillator	NOUN
ap-7668	143	33	potential	potential	NOUN
ap-7668	143	34	coincides	coincide	VERB
ap-7668	143	35	with	with	ADP
ap-7668	143	36	the	the	DET
ap-7668	143	37	two	two	NUM
ap-7668	143	38	-	-	PUNCT
ap-7668	143	39	body	body	NOUN
ap-7668	143	40	jacobi	jacobi	PROPN
ap-7668	143	41	oscillator	oscillator	NOUN
ap-7668	143	42	potential	potential	NOUN
ap-7668	143	43	.	.	PUNCT
ap-7668	144	1	in	in	ADP
ap-7668	144	2	fact	fact	NOUN
ap-7668	144	3	,	,	PUNCT
ap-7668	144	4	imposing	impose	VERB
ap-7668	144	5	the	the	DET
ap-7668	144	6	singly	singly	ADV
ap-7668	144	7	condition	condition	NOUN
ap-7668	144	8	m2	m2	PROPN
ap-7668	144	9	ν13	ν13	PROPN
ap-7668	144	10	=	=	PROPN
ap-7668	144	11	m3	m3	PROPN
ap-7668	144	12	ν12	ν12	VERB
ap-7668	144	13	the	the	DET
ap-7668	144	14	equality	equality	NOUN
ap-7668	144	15	(	(	PUNCT
ap-7668	144	16	18	18	NUM
ap-7668	144	17	)	)	PUNCT
ap-7668	144	18	is	be	AUX
ap-7668	144	19	still	still	ADV
ap-7668	144	20	valid	valid	ADJ
ap-7668	144	21	but	but	CCONJ
ap-7668	144	22	λ1	λ1	ADJ
ap-7668	144	23	̸=	̸=	PROPN
ap-7668	144	24	λ2	λ2	PROPN
ap-7668	144	25	and	and	CCONJ
ap-7668	144	26	the	the	DET
ap-7668	144	27	system	system	NOUN
ap-7668	144	28	is	be	AUX
ap-7668	144	29	not	not	PART
ap-7668	144	30	maximally	maximally	ADV
ap-7668	144	31	superintegrable	superintegrable	ADJ
ap-7668	144	32	any	any	PRON
ap-7668	144	33	more	more	ADJ
ap-7668	144	34	.	.	PUNCT
ap-7668	145	1	6.1	6.1	NUM
ap-7668	145	2	.	.	PUNCT
ap-7668	145	3	identical	identical	ADJ
ap-7668	145	4	particles	particle	NOUN
ap-7668	145	5	:	:	PUNCT
ap-7668	145	6	hyperradious	hyperradious	ADJ
ap-7668	145	7	a	a	DET
ap-7668	145	8	remarkable	remarkable	ADJ
ap-7668	145	9	simplification	simplification	NOUN
ap-7668	145	10	occurs	occur	VERB
ap-7668	145	11	in	in	ADP
ap-7668	145	12	the	the	DET
ap-7668	145	13	case	case	NOUN
ap-7668	145	14	of	of	ADP
ap-7668	145	15	three	three	NUM
ap-7668	145	16	identical	identical	ADJ
ap-7668	145	17	particles	particle	NOUN
ap-7668	145	18	with	with	ADP
ap-7668	145	19	the	the	DET
ap-7668	145	20	same	same	ADJ
ap-7668	145	21	common	common	ADJ
ap-7668	145	22	spring	spring	NOUN
ap-7668	145	23	constant	constant	ADJ
ap-7668	145	24	,	,	PUNCT
ap-7668	145	25	namely	namely	ADV
ap-7668	145	26	m1	m1	NOUN
ap-7668	145	27	=	=	SYM
ap-7668	145	28	m2	m2	PROPN
ap-7668	145	29	=	=	PROPN
ap-7668	145	30	m3	m3	PROPN
ap-7668	145	31	=	=	SYM
ap-7668	145	32	1	1	NUM
ap-7668	145	33	,	,	PUNCT
ap-7668	145	34	a1	a1	NOUN
ap-7668	145	35	=	=	SYM
ap-7668	145	36	a2	a2	PROPN
ap-7668	145	37	=	=	PUNCT
ap-7668	145	38	a3	a3	PROPN
ap-7668	145	39	≡	≡	PROPN
ap-7668	145	40	a	a	PRON
ap-7668	145	41	.	.	PUNCT
ap-7668	146	1	(	(	PUNCT
ap-7668	146	2	19	19	NUM
ap-7668	146	3	)	)	PUNCT
ap-7668	146	4	thus	thus	ADV
ap-7668	146	5	,	,	PUNCT
ap-7668	146	6	the	the	DET
ap-7668	146	7	potential	potential	ADJ
ap-7668	146	8	(	(	PUNCT
ap-7668	146	9	11	11	NUM
ap-7668	146	10	)	)	PUNCT
ap-7668	146	11	reduces	reduce	VERB
ap-7668	146	12	to	to	ADP
ap-7668	146	13	v	v	NOUN
ap-7668	146	14	(	(	PUNCT
ap-7668	146	15	ho	ho	PROPN
ap-7668	146	16	)	)	PUNCT
ap-7668	146	17	=	=	SYM
ap-7668	146	18	3	3	NUM
ap-7668	146	19	2	2	NUM
ap-7668	146	20	a	a	DET
ap-7668	146	21	2	2	NUM
ap-7668	146	22	ω2	ω2	NOUN
ap-7668	146	23	(	(	PUNCT
ap-7668	146	24	ρ12	ρ12	NOUN
ap-7668	146	25	+	+	X
ap-7668	146	26	ρ13	ρ13	NOUN
ap-7668	146	27	+	+	CCONJ
ap-7668	146	28	ρ23	ρ23	NOUN
ap-7668	146	29	)	)	PUNCT
ap-7668	146	30	=	=	SYM
ap-7668	146	31	3	3	NUM
ap-7668	146	32	2	2	NUM
ap-7668	146	33	a	a	DET
ap-7668	146	34	2	2	NUM
ap-7668	146	35	ω2	ω2	NOUN
ap-7668	146	36	τ1	τ1	NOUN
ap-7668	146	37	.	.	PUNCT
ap-7668	147	1	consequently	consequently	ADV
ap-7668	147	2	,	,	PUNCT
ap-7668	147	3	the	the	DET
ap-7668	147	4	ground	ground	NOUN
ap-7668	147	5	state	state	NOUN
ap-7668	147	6	solutions	solution	NOUN
ap-7668	147	7	(	(	PUNCT
ap-7668	147	8	12	12	NUM
ap-7668	147	9	)	)	PUNCT
ap-7668	147	10	and	and	CCONJ
ap-7668	147	11	(	(	PUNCT
ap-7668	147	12	13	13	NUM
ap-7668	147	13	)	)	PUNCT
ap-7668	147	14	read	read	VERB
ap-7668	147	15	ψ(3a	ψ(3a	NOUN
ap-7668	147	16	)	)	PUNCT
ap-7668	147	17	0	0	NUM
ap-7668	148	1	=	=	SYM
ap-7668	148	2	e−	e−	PROPN
ap-7668	148	3	ω	ω	NUM
ap-7668	148	4	2	2	NUM
ap-7668	148	5	a	a	PRON
ap-7668	148	6	(	(	PUNCT
ap-7668	148	7	ρ12	ρ12	NOUN
ap-7668	148	8	+	+	NOUN
ap-7668	148	9	ρ13	ρ13	NOUN
ap-7668	148	10	+	+	CCONJ
ap-7668	148	11	ρ23	ρ23	NOUN
ap-7668	148	12	)	)	PUNCT
ap-7668	148	13	=	=	PUNCT
ap-7668	149	1	e−	e−	PROPN
ap-7668	149	2	ω	ω	NUM
ap-7668	149	3	2	2	NUM
ap-7668	149	4	a	a	DET
ap-7668	149	5	τ1	τ1	NOUN
ap-7668	149	6	,	,	PUNCT
ap-7668	149	7	(	(	PUNCT
ap-7668	149	8	20	20	NUM
ap-7668	149	9	)	)	PUNCT
ap-7668	149	10	e0	e0	NOUN
ap-7668	150	1	=	=	PUNCT
ap-7668	151	1	3ω	3ω	PROPN
ap-7668	152	1	d	d	X
ap-7668	152	2	a	a	PRON
ap-7668	152	3	,	,	PUNCT
ap-7668	152	4	(	(	PUNCT
ap-7668	152	5	21	21	NUM
ap-7668	152	6	)	)	PUNCT
ap-7668	152	7	respectively	respectively	ADV
ap-7668	152	8	.	.	PUNCT
ap-7668	153	1	moreover	moreover	ADV
ap-7668	153	2	,	,	PUNCT
ap-7668	153	3	from	from	ADP
ap-7668	153	4	(	(	PUNCT
ap-7668	153	5	6	6	NUM
ap-7668	153	6	)	)	PUNCT
ap-7668	153	7	it	it	PRON
ap-7668	153	8	follows	follow	VERB
ap-7668	153	9	that	that	SCONJ
ap-7668	153	10	in	in	ADP
ap-7668	153	11	this	this	DET
ap-7668	153	12	case	case	NOUN
ap-7668	153	13	there	there	PRON
ap-7668	153	14	exists	exist	VERB
ap-7668	153	15	an	an	DET
ap-7668	153	16	infinite	infinite	ADJ
ap-7668	153	17	family	family	NOUN
ap-7668	153	18	of	of	ADP
ap-7668	153	19	eigenfunctions	eigenfunction	NOUN
ap-7668	153	20	ψn	ψn	X
ap-7668	153	21	(	(	PUNCT
ap-7668	153	22	τ1	τ1	NOUN
ap-7668	153	23	)	)	PUNCT
ap-7668	153	24	=	=	PUNCT
ap-7668	154	1	e−	e−	VERB
ap-7668	154	2	1	1	NUM
ap-7668	154	3	2	2	NUM
ap-7668	154	4	a	a	DET
ap-7668	154	5	ω	ω	NUM
ap-7668	154	6	τ1	τ1	NOUN
ap-7668	154	7	l	l	NOUN
ap-7668	154	8	(	(	PUNCT
ap-7668	154	9	d−1	d−1	PROPN
ap-7668	154	10	)	)	PUNCT
ap-7668	154	11	n	n	CCONJ
ap-7668	154	12	(	(	PUNCT
ap-7668	154	13	aω	aω	PROPN
ap-7668	154	14	τ1	τ1	NOUN
ap-7668	154	15	)	)	PUNCT
ap-7668	154	16	,	,	PUNCT
ap-7668	154	17	with	with	ADP
ap-7668	154	18	energy	energy	NOUN
ap-7668	154	19	en	en	X
ap-7668	154	20	=	=	SYM
ap-7668	154	21	3	3	NUM
ap-7668	154	22	aω	aω	X
ap-7668	154	23	(	(	PUNCT
ap-7668	154	24	d	d	NOUN
ap-7668	154	25	+	+	X
ap-7668	154	26	2n	2n	NUM
ap-7668	154	27	)	)	PUNCT
ap-7668	154	28	,	,	PUNCT
ap-7668	154	29	n	n	NOUN
ap-7668	154	30	=	=	SYM
ap-7668	154	31	0	0	NUM
ap-7668	154	32	,	,	PUNCT
ap-7668	154	33	1	1	NUM
ap-7668	154	34	,	,	PUNCT
ap-7668	154	35	2	2	NUM
ap-7668	154	36	,	,	PUNCT
ap-7668	154	37	3	3	NUM
ap-7668	154	38	,	,	PUNCT
ap-7668	154	39	.	.	PUNCT
ap-7668	154	40	.	.	PUNCT
ap-7668	155	1	.	.	PUNCT
ap-7668	155	2	,	,	PUNCT
ap-7668	155	3	that	that	PRON
ap-7668	155	4	solely	solely	ADV
ap-7668	155	5	depend	depend	VERB
ap-7668	155	6	on	on	ADP
ap-7668	155	7	the	the	DET
ap-7668	155	8	variable	variable	ADJ
ap-7668	155	9	τ1	τ1	NOUN
ap-7668	155	10	,	,	PUNCT
ap-7668	155	11	the	the	DET
ap-7668	155	12	so	so	ADV
ap-7668	155	13	called	call	VERB
ap-7668	155	14	hyperradious	hyperradious	ADJ
ap-7668	155	15	,	,	PUNCT
ap-7668	155	16	here	here	ADV
ap-7668	155	17	l(d−1	l(d−1	NOUN
ap-7668	155	18	)	)	PUNCT
ap-7668	155	19	n	n	CCONJ
ap-7668	155	20	(	(	PUNCT
ap-7668	155	21	x	x	X
ap-7668	155	22	)	)	PUNCT
ap-7668	155	23	denotes	denote	VERB
ap-7668	155	24	the	the	DET
ap-7668	155	25	generalized	generalize	VERB
ap-7668	155	26	laguerre	laguerre	NOUN
ap-7668	155	27	polynomial	polynomial	ADJ
ap-7668	155	28	.	.	PUNCT
ap-7668	156	1	these	these	DET
ap-7668	156	2	solutions	solution	NOUN
ap-7668	156	3	are	be	AUX
ap-7668	156	4	associated	associate	VERB
ap-7668	156	5	with	with	ADP
ap-7668	156	6	a	a	DET
ap-7668	156	7	hidden	hide	VERB
ap-7668	156	8	sℓ(2,r	sℓ(2,r	VERB
ap-7668	156	9	)	)	PUNCT
ap-7668	156	10	lie	lie	NOUN
ap-7668	156	11	-	-	PUNCT
ap-7668	156	12	algebra	algebra	NOUN
ap-7668	156	13	.	.	PUNCT
ap-7668	157	1	6.2	6.2	NUM
ap-7668	157	2	.	.	PUNCT
ap-7668	158	1	arbitrary	arbitrary	ADJ
ap-7668	158	2	masses	masse	NOUN
ap-7668	158	3	:	:	PUNCT
ap-7668	158	4	moment	moment	NOUN
ap-7668	158	5	of	of	ADP
ap-7668	158	6	inertia	inertia	NOUN
ap-7668	158	7	a	a	DET
ap-7668	158	8	generalization	generalization	NOUN
ap-7668	158	9	of	of	ADP
ap-7668	158	10	the	the	DET
ap-7668	158	11	results	result	NOUN
ap-7668	158	12	presented	present	VERB
ap-7668	158	13	in	in	ADP
ap-7668	158	14	section	section	NOUN
ap-7668	158	15	6.1	6.1	NUM
ap-7668	158	16	can	can	AUX
ap-7668	158	17	be	be	AUX
ap-7668	158	18	derived	derive	VERB
ap-7668	158	19	from	from	ADP
ap-7668	158	20	the	the	DET
ap-7668	158	21	decomposition	decomposition	NOUN
ap-7668	158	22	of	of	ADP
ap-7668	158	23	∆rad	∆rad	PROPN
ap-7668	158	24	(	(	PUNCT
ap-7668	158	25	4	4	NUM
ap-7668	158	26	)	)	PUNCT
ap-7668	158	27	∆rad	∆rad	NOUN
ap-7668	158	28	=	=	PUNCT
ap-7668	159	1	∆i	∆i	PROPN
ap-7668	159	2	+	+	NUM
ap-7668	159	3	∆̃	∆̃	NOUN
ap-7668	159	4	,	,	PUNCT
ap-7668	159	5	(	(	PUNCT
ap-7668	159	6	22	22	NUM
ap-7668	159	7	)	)	PUNCT
ap-7668	159	8	where	where	SCONJ
ap-7668	159	9	∆i	∆i	PROPN
ap-7668	159	10	=	=	SYM
ap-7668	159	11	∆i(i	∆i(i	PROPN
ap-7668	159	12	)	)	PUNCT
ap-7668	159	13	is	be	AUX
ap-7668	159	14	an	an	DET
ap-7668	159	15	algebraic	algebraic	ADJ
ap-7668	159	16	operator	operator	NOUN
ap-7668	159	17	for	for	ADP
ap-7668	159	18	arbitrary	arbitrary	ADJ
ap-7668	159	19	d	d	X
ap-7668	159	20	≥	≥	NUM
ap-7668	159	21	1	1	NUM
ap-7668	159	22	.	.	PUNCT
ap-7668	160	1	it	it	PRON
ap-7668	160	2	depends	depend	VERB
ap-7668	160	3	on	on	ADP
ap-7668	160	4	the	the	DET
ap-7668	160	5	moment	moment	NOUN
ap-7668	160	6	of	of	ADP
ap-7668	160	7	inertial	inertial	NOUN
ap-7668	160	8	i	i	PRON
ap-7668	160	9	only	only	ADV
ap-7668	160	10	.	.	PUNCT
ap-7668	161	1	explicitly	explicitly	ADV
ap-7668	161	2	,	,	PUNCT
ap-7668	161	3	we	we	PRON
ap-7668	161	4	have	have	VERB
ap-7668	162	1	∆i	∆i	PROPN
ap-7668	162	2	=	=	SYM
ap-7668	162	3	2	2	NUM
ap-7668	162	4	i	i	PRON
ap-7668	162	5	∂2	∂2	VERB
ap-7668	163	1	i	i	PRON
ap-7668	163	2	,	,	PUNCT
ap-7668	163	3	i	i	PRON
ap-7668	163	4	+	+	NOUN
ap-7668	163	5	2	2	NUM
ap-7668	163	6	d	d	X
ap-7668	163	7	∂i	∂i	PROPN
ap-7668	163	8	.	.	PUNCT
ap-7668	164	1	(	(	PUNCT
ap-7668	164	2	23	23	NUM
ap-7668	164	3	)	)	PUNCT
ap-7668	164	4	the	the	DET
ap-7668	164	5	operator	operator	NOUN
ap-7668	164	6	∆̃	∆̃	PRON
ap-7668	164	7	=	=	SYM
ap-7668	164	8	∆̃(i	∆̃(i	X
ap-7668	164	9	,	,	PUNCT
ap-7668	164	10	q1	q1	PROPN
ap-7668	164	11	,	,	PUNCT
ap-7668	164	12	q2	q2	NOUN
ap-7668	164	13	)	)	PUNCT
ap-7668	164	14	depends	depend	VERB
ap-7668	164	15	on	on	ADP
ap-7668	164	16	i	i	PRON
ap-7668	164	17	and	and	CCONJ
ap-7668	164	18	two	two	NUM
ap-7668	164	19	more	more	ADJ
ap-7668	164	20	(	(	PUNCT
ap-7668	164	21	arbitrary	arbitrary	ADJ
ap-7668	164	22	)	)	PUNCT
ap-7668	164	23	variables	variables	PROPN
ap-7668	164	24	q1	q1	PROPN
ap-7668	164	25	,	,	PUNCT
ap-7668	164	26	q2	q2	NOUN
ap-7668	164	27	for	for	ADP
ap-7668	164	28	which	which	PRON
ap-7668	164	29	the	the	DET
ap-7668	164	30	coordinate	coordinate	NOUN
ap-7668	164	31	transformation	transformation	NOUN
ap-7668	164	32	{	{	PUNCT
ap-7668	164	33	ρij	ρij	NOUN
ap-7668	164	34	}	}	PUNCT
ap-7668	164	35	→	→	SYM
ap-7668	164	36	{	{	PUNCT
ap-7668	164	37	i	i	PROPN
ap-7668	164	38	,	,	PUNCT
ap-7668	164	39	q1	q1	PROPN
ap-7668	164	40	,	,	PUNCT
ap-7668	164	41	q2	q2	NOUN
ap-7668	164	42	}	}	PUNCT
ap-7668	164	43	is	be	AUX
ap-7668	164	44	invertible	invertible	ADJ
ap-7668	164	45	(	(	PUNCT
ap-7668	164	46	not	not	PART
ap-7668	164	47	singular	singular	ADJ
ap-7668	164	48	)	)	PUNCT
ap-7668	164	49	.	.	PUNCT
ap-7668	165	1	since	since	SCONJ
ap-7668	165	2	such	such	DET
ap-7668	165	3	an	an	DET
ap-7668	165	4	operator	operator	NOUN
ap-7668	165	5	∆̃	∆̃	PRON
ap-7668	165	6	annihilates	annihilate	VERB
ap-7668	165	7	any	any	DET
ap-7668	165	8	function	function	NOUN
ap-7668	165	9	f	f	NOUN
ap-7668	165	10	=	=	SYM
ap-7668	165	11	f	f	PROPN
ap-7668	165	12	(	(	PUNCT
ap-7668	165	13	i	i	NOUN
ap-7668	165	14	)	)	PUNCT
ap-7668	165	15	,	,	PUNCT
ap-7668	165	16	i.e.	i.e.	X
ap-7668	165	17	∆̃f	∆̃f	X
ap-7668	165	18	=	=	SYM
ap-7668	165	19	0	0	PROPN
ap-7668	165	20	,	,	PUNCT
ap-7668	165	21	the	the	DET
ap-7668	165	22	splitting	splitting	NOUN
ap-7668	165	23	(	(	PUNCT
ap-7668	165	24	22	22	NUM
ap-7668	165	25	)	)	PUNCT
ap-7668	165	26	indicates	indicate	VERB
ap-7668	165	27	that	that	SCONJ
ap-7668	165	28	for	for	ADP
ap-7668	165	29	any	any	DET
ap-7668	165	30	potential	potential	NOUN
ap-7668	165	31	of	of	ADP
ap-7668	165	32	the	the	DET
ap-7668	165	33	form	form	NOUN
ap-7668	165	34	v	v	ADP
ap-7668	165	35	=	=	SYM
ap-7668	165	36	v	v	PROPN
ap-7668	165	37	(	(	PUNCT
ap-7668	165	38	i	i	NOUN
ap-7668	165	39	)	)	PUNCT
ap-7668	165	40	,	,	PUNCT
ap-7668	165	41	(	(	PUNCT
ap-7668	165	42	24	24	NUM
ap-7668	165	43	)	)	PUNCT
ap-7668	165	44	the	the	DET
ap-7668	165	45	eigenvalue	eigenvalue	PROPN
ap-7668	165	46	problem	problem	NOUN
ap-7668	165	47	for	for	ADP
ap-7668	165	48	the	the	DET
ap-7668	165	49	operator	operator	NOUN
ap-7668	165	50	hrad	hrad	NOUN
ap-7668	165	51	=	=	PUNCT
ap-7668	166	1	−∆rad	−∆rad	NOUN
ap-7668	166	2	+	+	CCONJ
ap-7668	166	3	v	v	NOUN
ap-7668	166	4	is	be	AUX
ap-7668	166	5	further	far	ADV
ap-7668	166	6	reduced	reduce	VERB
ap-7668	166	7	to	to	ADP
ap-7668	166	8	a	a	DET
ap-7668	166	9	one	one	NUM
ap-7668	166	10	-	-	PUNCT
ap-7668	166	11	dimensional	dimensional	ADJ
ap-7668	166	12	spectral	spectral	ADJ
ap-7668	166	13	problem	problem	NOUN
ap-7668	166	14	,	,	PUNCT
ap-7668	166	15	namely	namely	ADV
ap-7668	166	16	[	[	PUNCT
ap-7668	166	17	−∆i	−∆i	X
ap-7668	166	18	+	+	CCONJ
ap-7668	166	19	v	v	NOUN
ap-7668	166	20	(	(	PUNCT
ap-7668	166	21	i	i	NOUN
ap-7668	166	22	)	)	PUNCT
ap-7668	166	23	]	]	PUNCT
ap-7668	166	24	ψ	ψ	X
ap-7668	166	25	=	=	SYM
ap-7668	166	26	e	e	NOUN
ap-7668	166	27	ψ	ψ	NOUN
ap-7668	166	28	,	,	PUNCT
ap-7668	166	29	(	(	PUNCT
ap-7668	166	30	25	25	NUM
ap-7668	166	31	)	)	PUNCT
ap-7668	166	32	which	which	PRON
ap-7668	166	33	can	can	AUX
ap-7668	166	34	be	be	AUX
ap-7668	166	35	called	call	VERB
ap-7668	166	36	the	the	DET
ap-7668	166	37	i−representation	i−representation	NOUN
ap-7668	166	38	.	.	PUNCT
ap-7668	167	1	in	in	ADP
ap-7668	167	2	the	the	DET
ap-7668	167	3	case	case	NOUN
ap-7668	167	4	of	of	ADP
ap-7668	167	5	equal	equal	ADJ
ap-7668	167	6	masses	masse	NOUN
ap-7668	167	7	m1	m1	NOUN
ap-7668	167	8	=	=	SYM
ap-7668	167	9	m2	m2	PROPN
ap-7668	167	10	=	=	PROPN
ap-7668	167	11	m3	m3	PROPN
ap-7668	167	12	the	the	DET
ap-7668	167	13	coordinate	coordinate	NOUN
ap-7668	167	14	i	i	PRON
ap-7668	167	15	is	be	AUX
ap-7668	167	16	proportional	proportional	ADJ
ap-7668	167	17	to	to	ADP
ap-7668	167	18	the	the	DET
ap-7668	167	19	hyperspherical	hyperspherical	ADJ
ap-7668	167	20	radius	radius	NOUN
ap-7668	167	21	(	(	PUNCT
ap-7668	167	22	hyperradious	hyperradious	ADJ
ap-7668	167	23	)	)	PUNCT
ap-7668	167	24	.	.	PUNCT
ap-7668	168	1	also	also	ADV
ap-7668	168	2	,	,	PUNCT
ap-7668	168	3	hi	hi	INTJ
ap-7668	168	4	(	(	PUNCT
ap-7668	168	5	25	25	NUM
ap-7668	168	6	)	)	PUNCT
ap-7668	168	7	is	be	AUX
ap-7668	168	8	gauge	gauge	NOUN
ap-7668	168	9	-	-	PUNCT
ap-7668	168	10	equivalent	equivalent	ADJ
ap-7668	168	11	to	to	ADP
ap-7668	168	12	a	a	DET
ap-7668	168	13	one	one	NUM
ap-7668	168	14	-	-	PUNCT
ap-7668	168	15	dimensional	dimensional	ADJ
ap-7668	168	16	the	the	DET
ap-7668	168	17	schrödinger	schrödinger	ADJ
ap-7668	168	18	operator	operator	NOUN
ap-7668	168	19	.	.	PUNCT
ap-7668	169	1	53	53	NUM
ap-7668	169	2	adrian	adrian	PROPN
ap-7668	169	3	m.	m.	NOUN
ap-7668	169	4	escobar	escobar	PROPN
ap-7668	169	5	-	-	PUNCT
ap-7668	169	6	ruiz	ruiz	NOUN
ap-7668	169	7	,	,	PUNCT
ap-7668	169	8	fidel	fidel	PROPN
ap-7668	169	9	montoya	montoya	PROPN
ap-7668	169	10	acta	acta	PROPN
ap-7668	169	11	polytechnica	polytechnica	PROPN
ap-7668	169	12	figure	figure	NOUN
ap-7668	169	13	2	2	NUM
ap-7668	169	14	.	.	PUNCT
ap-7668	169	15	classical	classical	ADJ
ap-7668	169	16	generalized	generalized	ADJ
ap-7668	169	17	three	three	NUM
ap-7668	169	18	-	-	PUNCT
ap-7668	169	19	body	body	NOUN
ap-7668	169	20	harmonic	harmonic	ADJ
ap-7668	169	21	oscillator	oscillator	NOUN
ap-7668	169	22	system	system	NOUN
ap-7668	169	23	:	:	PUNCT
ap-7668	169	24	average	average	ADJ
ap-7668	169	25	lyapunov	lyapunov	ADJ
ap-7668	169	26	exponent	exponent	NOUN
ap-7668	169	27	in	in	ADP
ap-7668	169	28	the	the	DET
ap-7668	169	29	space	space	NOUN
ap-7668	169	30	of	of	ADP
ap-7668	169	31	parameters	parameter	NOUN
ap-7668	169	32	(	(	PUNCT
ap-7668	169	33	h	h	NOUN
ap-7668	169	34	,	,	PUNCT
ap-7668	169	35	m1	m1	PROPN
ap-7668	169	36	)	)	PUNCT
ap-7668	169	37	.	.	PUNCT
ap-7668	170	1	the	the	DET
ap-7668	170	2	values	value	NOUN
ap-7668	170	3	m2	m2	PROPN
ap-7668	170	4	=	=	PROPN
ap-7668	170	5	m3	m3	PROPN
ap-7668	170	6	=	=	SYM
ap-7668	170	7	1	1	NUM
ap-7668	170	8	,	,	PUNCT
ap-7668	170	9	ω	ω	NOUN
ap-7668	170	10	=	=	SYM
ap-7668	170	11	1	1	NUM
ap-7668	170	12	,	,	PUNCT
ap-7668	170	13	ν12	ν12	NOUN
ap-7668	170	14	=	=	SYM
ap-7668	170	15	ν13	ν13	NOUN
ap-7668	170	16	=	=	SYM
ap-7668	170	17	ν23	ν23	PROPN
ap-7668	170	18	=	=	SYM
ap-7668	170	19	1	1	NUM
ap-7668	170	20	and	and	CCONJ
ap-7668	170	21	r12	r12	NOUN
ap-7668	170	22	=	=	SYM
ap-7668	170	23	r13	r13	NOUN
ap-7668	170	24	=	=	SYM
ap-7668	170	25	r23	r23	NOUN
ap-7668	170	26	=	=	SYM
ap-7668	170	27	1	1	NUM
ap-7668	170	28	were	be	AUX
ap-7668	170	29	used	use	VERB
ap-7668	170	30	.	.	PUNCT
ap-7668	171	1	7	7	X
ap-7668	171	2	.	.	NUM
ap-7668	171	3	generalized	generalize	VERB
ap-7668	171	4	three	three	NUM
ap-7668	171	5	body	body	NOUN
ap-7668	171	6	harmonic	harmonic	ADJ
ap-7668	171	7	oscillator	oscillator	NOUN
ap-7668	171	8	system	system	NOUN
ap-7668	171	9	now	now	ADV
ap-7668	171	10	,	,	PUNCT
ap-7668	171	11	let	let	VERB
ap-7668	171	12	us	we	PRON
ap-7668	171	13	consider	consider	VERB
ap-7668	171	14	the	the	DET
ap-7668	171	15	following	follow	VERB
ap-7668	171	16	potential	potential	ADJ
ap-7668	171	17	v	v	ADP
ap-7668	171	18	(	(	PUNCT
ap-7668	171	19	r	r	NOUN
ap-7668	171	20	)	)	PUNCT
ap-7668	172	1	=	=	SYM
ap-7668	172	2	2	2	NUM
ap-7668	172	3	ω2	ω2	NOUN
ap-7668	172	4	[	[	PUNCT
ap-7668	172	5	ν12	ν12	PROPN
ap-7668	172	6	(	(	PUNCT
ap-7668	172	7	√ρ12	√ρ12	X
ap-7668	172	8	−	−	PROPN
ap-7668	172	9	r12)2	r12)2	NOUN
ap-7668	172	10	+	+	CCONJ
ap-7668	172	11	ν13	ν13	NOUN
ap-7668	172	12	(	(	PUNCT
ap-7668	172	13	√ρ13	√ρ13	PROPN
ap-7668	172	14	−	−	PUNCT
ap-7668	172	15	r13)2	r13)2	VERB
ap-7668	172	16	+	+	NUM
ap-7668	172	17	ν23	ν23	ADJ
ap-7668	172	18	(	(	PUNCT
ap-7668	172	19	√ρ23	√ρ23	NOUN
ap-7668	172	20	−	−	PROPN
ap-7668	172	21	r23)2	r23)2	PROPN
ap-7668	172	22	]	]	PUNCT
ap-7668	172	23	,	,	PUNCT
ap-7668	172	24	(	(	PUNCT
ap-7668	172	25	26	26	NUM
ap-7668	172	26	)	)	PUNCT
ap-7668	172	27	where	where	SCONJ
ap-7668	172	28	r12	r12	NOUN
ap-7668	172	29	,	,	PUNCT
ap-7668	172	30	r13	r13	PROPN
ap-7668	172	31	,	,	PUNCT
ap-7668	172	32	r23	r23	NOUN
ap-7668	172	33	⩾	⩾	PROPN
ap-7668	172	34	0	0	NUM
ap-7668	172	35	denote	denote	VERB
ap-7668	172	36	the	the	DET
ap-7668	172	37	rest	rest	NOUN
ap-7668	172	38	lengths	length	NOUN
ap-7668	172	39	of	of	ADP
ap-7668	172	40	the	the	DET
ap-7668	172	41	system	system	NOUN
ap-7668	172	42	.	.	PUNCT
ap-7668	173	1	at	at	ADP
ap-7668	173	2	r12	r12	NOUN
ap-7668	173	3	=	=	SYM
ap-7668	173	4	r13	r13	NOUN
ap-7668	173	5	=	=	SYM
ap-7668	173	6	r23	r23	NOUN
ap-7668	173	7	=	=	SYM
ap-7668	173	8	0	0	NUM
ap-7668	173	9	we	we	PRON
ap-7668	173	10	recover	recover	VERB
ap-7668	173	11	the	the	DET
ap-7668	173	12	exactly	exactly	ADV
ap-7668	173	13	solvable	solvable	ADJ
ap-7668	173	14	3	3	NUM
ap-7668	173	15	-	-	PUNCT
ap-7668	173	16	body	body	NOUN
ap-7668	173	17	oscillator	oscillator	NOUN
ap-7668	173	18	system	system	NOUN
ap-7668	173	19	,	,	PUNCT
ap-7668	173	20	v	v	NOUN
ap-7668	173	21	(	(	PUNCT
ap-7668	173	22	r	r	NOUN
ap-7668	173	23	)	)	PUNCT
ap-7668	173	24	→	→	SYM
ap-7668	173	25	v	v	X
ap-7668	173	26	(	(	PUNCT
ap-7668	173	27	ho	ho	PROPN
ap-7668	173	28	)	)	PUNCT
ap-7668	173	29	.	.	PUNCT
ap-7668	174	1	the	the	DET
ap-7668	174	2	relevance	relevance	NOUN
ap-7668	174	3	of	of	ADP
ap-7668	174	4	v	v	NOUN
ap-7668	174	5	(	(	PUNCT
ap-7668	174	6	r	r	NOUN
ap-7668	174	7	)	)	PUNCT
ap-7668	174	8	comes	come	VERB
ap-7668	174	9	from	from	ADP
ap-7668	174	10	the	the	DET
ap-7668	174	11	fact	fact	NOUN
ap-7668	174	12	that	that	SCONJ
ap-7668	174	13	any	any	DET
ap-7668	174	14	arbitrary	arbitrary	ADJ
ap-7668	174	15	potential	potential	NOUN
ap-7668	174	16	v	v	NOUN
ap-7668	174	17	=	=	SYM
ap-7668	174	18	v	v	NOUN
ap-7668	174	19	(	(	PUNCT
ap-7668	174	20	rij	rij	ADJ
ap-7668	174	21	)	)	PUNCT
ap-7668	174	22	can	can	AUX
ap-7668	174	23	be	be	AUX
ap-7668	174	24	approximated	approximate	VERB
ap-7668	174	25	,	,	PUNCT
ap-7668	174	26	near	near	ADP
ap-7668	174	27	its	its	PRON
ap-7668	174	28	equilibrium	equilibrium	NOUN
ap-7668	174	29	points	point	NOUN
ap-7668	174	30	,	,	PUNCT
ap-7668	174	31	by	by	ADP
ap-7668	174	32	this	this	DET
ap-7668	174	33	generalized	generalize	VERB
ap-7668	174	34	3	3	NUM
ap-7668	174	35	-	-	PUNCT
ap-7668	174	36	body	body	NOUN
ap-7668	174	37	harmonic	harmonic	ADJ
ap-7668	174	38	potential	potential	NOUN
ap-7668	174	39	.	.	PUNCT
ap-7668	175	1	however	however	ADV
ap-7668	175	2	,	,	PUNCT
ap-7668	175	3	the	the	DET
ap-7668	175	4	existence	existence	NOUN
ap-7668	175	5	of	of	ADP
ap-7668	175	6	non	non	ADJ
ap-7668	175	7	-	-	ADJ
ap-7668	175	8	trivial	trivial	ADJ
ap-7668	175	9	exact	exact	ADJ
ap-7668	175	10	solutions	solution	NOUN
ap-7668	175	11	is	be	AUX
ap-7668	175	12	far	far	ADV
ap-7668	175	13	from	from	ADP
ap-7668	175	14	being	be	AUX
ap-7668	175	15	evident	evident	ADJ
ap-7668	175	16	.	.	PUNCT
ap-7668	176	1	even	even	ADV
ap-7668	176	2	for	for	ADP
ap-7668	176	3	the	the	DET
ap-7668	176	4	most	most	ADV
ap-7668	176	5	symmetric	symmetric	ADJ
ap-7668	176	6	case	case	NOUN
ap-7668	176	7	of	of	ADP
ap-7668	176	8	equal	equal	ADJ
ap-7668	176	9	masses	masse	NOUN
ap-7668	176	10	and	and	CCONJ
ap-7668	176	11	equal	equal	ADJ
ap-7668	176	12	spring	spring	NOUN
ap-7668	176	13	constants	constant	NOUN
ap-7668	176	14	,	,	PUNCT
ap-7668	176	15	we	we	PRON
ap-7668	176	16	were	be	AUX
ap-7668	176	17	not	not	PART
ap-7668	176	18	able	able	ADJ
ap-7668	176	19	to	to	PART
ap-7668	176	20	find	find	VERB
ap-7668	176	21	a	a	DET
ap-7668	176	22	hidden	hide	VERB
ap-7668	176	23	lie	lie	NOUN
ap-7668	176	24	algebra	algebra	NOUN
ap-7668	176	25	in	in	ADP
ap-7668	176	26	the	the	DET
ap-7668	176	27	corresponding	corresponding	ADJ
ap-7668	176	28	spectral	spectral	ADJ
ap-7668	176	29	problem	problem	NOUN
ap-7668	176	30	(	(	PUNCT
ap-7668	176	31	3	3	NUM
ap-7668	176	32	)	)	PUNCT
ap-7668	176	33	.	.	PUNCT
ap-7668	177	1	moreover	moreover	ADV
ap-7668	177	2	,	,	PUNCT
ap-7668	177	3	at	at	ADP
ap-7668	177	4	the	the	DET
ap-7668	177	5	classical	classical	ADJ
ap-7668	177	6	level	level	NOUN
ap-7668	177	7	such	such	DET
ap-7668	177	8	a	a	DET
ap-7668	177	9	system	system	NOUN
ap-7668	177	10	is	be	AUX
ap-7668	177	11	chaotic	chaotic	ADJ
ap-7668	177	12	.	.	PUNCT
ap-7668	178	1	this	this	PRON
ap-7668	178	2	can	can	AUX
ap-7668	178	3	be	be	AUX
ap-7668	178	4	easily	easily	ADV
ap-7668	178	5	seen	see	VERB
ap-7668	178	6	by	by	ADP
ap-7668	178	7	computing	compute	VERB
ap-7668	178	8	the	the	DET
ap-7668	178	9	average	average	ADJ
ap-7668	178	10	lyapunov	lyapunov	ADJ
ap-7668	178	11	exponent	exponent	NOUN
ap-7668	178	12	in	in	ADP
ap-7668	178	13	the	the	DET
ap-7668	178	14	space	space	NOUN
ap-7668	178	15	of	of	ADP
ap-7668	178	16	parameters	parameter	NOUN
ap-7668	178	17	(	(	PUNCT
ap-7668	178	18	h	h	NOUN
ap-7668	178	19	,	,	PUNCT
ap-7668	178	20	m1	m1	PROPN
ap-7668	178	21	)	)	PUNCT
ap-7668	178	22	,	,	PUNCT
ap-7668	178	23	see	see	VERB
ap-7668	178	24	figure	figure	NOUN
ap-7668	178	25	2	2	NUM
ap-7668	178	26	,	,	PUNCT
ap-7668	178	27	where	where	SCONJ
ap-7668	178	28	h	h	NOUN
ap-7668	178	29	is	be	AUX
ap-7668	178	30	the	the	DET
ap-7668	178	31	value	value	NOUN
ap-7668	178	32	of	of	ADP
ap-7668	178	33	the	the	DET
ap-7668	178	34	classical	classical	ADJ
ap-7668	178	35	hamiltonian	hamiltonian	NOUN
ap-7668	178	36	(	(	PUNCT
ap-7668	178	37	energy	energy	NOUN
ap-7668	178	38	)	)	PUNCT
ap-7668	178	39	with	with	ADP
ap-7668	178	40	potential	potential	ADJ
ap-7668	178	41	v	v	NOUN
ap-7668	178	42	(	(	PUNCT
ap-7668	178	43	r	r	NOUN
ap-7668	178	44	)	)	PUNCT
ap-7668	178	45	(	(	PUNCT
ap-7668	178	46	26	26	NUM
ap-7668	178	47	)	)	PUNCT
ap-7668	178	48	.	.	PUNCT
ap-7668	179	1	also	also	ADV
ap-7668	179	2	,	,	PUNCT
ap-7668	179	3	for	for	ADP
ap-7668	179	4	one	one	NUM
ap-7668	179	5	-	-	PUNCT
ap-7668	179	6	dimensional	dimensional	ADJ
ap-7668	179	7	systems	system	NOUN
ap-7668	179	8	it	it	PRON
ap-7668	179	9	is	be	AUX
ap-7668	179	10	said	say	VERB
ap-7668	179	11	(	(	PUNCT
ap-7668	179	12	see	see	VERB
ap-7668	179	13	[	[	X
ap-7668	179	14	11	11	NUM
ap-7668	179	15	]	]	PUNCT
ap-7668	179	16	)	)	PUNCT
ap-7668	179	17	that	that	SCONJ
ap-7668	179	18	a	a	DET
ap-7668	179	19	classical	classical	ADJ
ap-7668	179	20	orbit	orbit	NOUN
ap-7668	179	21	is	be	AUX
ap-7668	179	22	pt	pt	X
ap-7668	179	23	-symmetric	-symmetric	NOUN
ap-7668	179	24	if	if	SCONJ
ap-7668	179	25	the	the	DET
ap-7668	179	26	orbit	orbit	NOUN
ap-7668	179	27	remains	remain	VERB
ap-7668	179	28	unchanged	unchanged	ADJ
ap-7668	179	29	upon	upon	SCONJ
ap-7668	179	30	replacing	replace	VERB
ap-7668	179	31	x(t	x(t	PROPN
ap-7668	179	32	)	)	PUNCT
ap-7668	179	33	by	by	ADP
ap-7668	179	34	−x∗(−t	−x∗(−t	NOUN
ap-7668	179	35	)	)	PUNCT
ap-7668	179	36	.	.	PUNCT
ap-7668	180	1	there	there	PRON
ap-7668	180	2	are	be	VERB
ap-7668	180	3	several	several	ADJ
ap-7668	180	4	classes	class	NOUN
ap-7668	180	5	of	of	ADP
ap-7668	180	6	complex	complex	ADJ
ap-7668	180	7	pt	pt	X
ap-7668	180	8	-symmetric	-symmetric	ADJ
ap-7668	180	9	non	non	ADJ
ap-7668	180	10	-	-	ADJ
ap-7668	180	11	hermitian	hermitian	ADJ
ap-7668	180	12	quantum	quantum	ADJ
ap-7668	180	13	-	-	ADJ
ap-7668	180	14	mechanical	mechanical	ADJ
ap-7668	180	15	hamiltonians	hamiltonian	NOUN
ap-7668	180	16	whose	whose	DET
ap-7668	180	17	eigenvalues	eigenvalue	NOUN
ap-7668	180	18	are	be	AUX
ap-7668	180	19	real	real	ADJ
ap-7668	180	20	and	and	CCONJ
ap-7668	180	21	with	with	ADP
ap-7668	180	22	unitary	unitary	ADJ
ap-7668	180	23	time	time	NOUN
ap-7668	180	24	evolution	evolution	NOUN
ap-7668	180	25	[	[	X
ap-7668	180	26	12	12	NUM
ap-7668	180	27	,	,	PUNCT
ap-7668	180	28	13	13	NUM
ap-7668	180	29	]	]	PUNCT
ap-7668	180	30	.	.	PUNCT
ap-7668	181	1	however	however	ADV
ap-7668	181	2	,	,	PUNCT
ap-7668	181	3	while	while	SCONJ
ap-7668	181	4	the	the	DET
ap-7668	181	5	corresponding	correspond	VERB
ap-7668	181	6	quantum	quantum	ADJ
ap-7668	181	7	three	three	NUM
ap-7668	181	8	-	-	PUNCT
ap-7668	181	9	body	body	NOUN
ap-7668	181	10	oscillator	oscillator	NOUN
ap-7668	181	11	hamiltonian	hamiltonian	NOUN
ap-7668	181	12	is	be	AUX
ap-7668	181	13	hermitian	hermitian	ADJ
ap-7668	181	14	,	,	PUNCT
ap-7668	181	15	it	it	PRON
ap-7668	181	16	can	can	AUX
ap-7668	181	17	still	still	ADV
ap-7668	181	18	have	have	VERB
ap-7668	181	19	interesting	interesting	ADJ
ap-7668	181	20	complex	complex	ADJ
ap-7668	181	21	classical	classical	ADJ
ap-7668	181	22	trajectories	trajectory	NOUN
ap-7668	181	23	.	.	PUNCT
ap-7668	182	1	7.1	7.1	NUM
ap-7668	182	2	.	.	PUNCT
ap-7668	183	1	identical	identical	ADJ
ap-7668	183	2	particles	particle	NOUN
ap-7668	183	3	in	in	ADP
ap-7668	183	4	order	order	NOUN
ap-7668	183	5	to	to	PART
ap-7668	183	6	simplify	simplify	VERB
ap-7668	183	7	the	the	DET
ap-7668	183	8	problem	problem	NOUN
ap-7668	183	9	one	one	PRON
ap-7668	183	10	can	can	AUX
ap-7668	183	11	consider	consider	VERB
ap-7668	183	12	the	the	DET
ap-7668	183	13	simplest	simple	ADJ
ap-7668	183	14	case	case	NOUN
ap-7668	183	15	of	of	ADP
ap-7668	183	16	equal	equal	ADJ
ap-7668	183	17	masses	masse	NOUN
ap-7668	183	18	and	and	CCONJ
ap-7668	183	19	equal	equal	ADJ
ap-7668	183	20	spring	spring	NOUN
ap-7668	183	21	constants	constant	NOUN
ap-7668	183	22	(	(	PUNCT
ap-7668	183	23	19	19	NUM
ap-7668	183	24	)	)	PUNCT
ap-7668	183	25	with	with	ADP
ap-7668	183	26	ω	ω	PROPN
ap-7668	183	27	=	=	SYM
ap-7668	183	28	1	1	NUM
ap-7668	183	29	.	.	PUNCT
ap-7668	184	1	also	also	ADV
ap-7668	184	2	,	,	PUNCT
ap-7668	184	3	we	we	PRON
ap-7668	184	4	will	will	AUX
ap-7668	184	5	assume	assume	VERB
ap-7668	184	6	equal	equal	ADJ
ap-7668	184	7	rest	rest	NOUN
ap-7668	184	8	lengths	length	NOUN
ap-7668	184	9	r12	r12	NOUN
ap-7668	184	10	=	=	SYM
ap-7668	184	11	r13	r13	NOUN
ap-7668	184	12	=	=	SYM
ap-7668	184	13	r23	r23	NOUN
ap-7668	184	14	=	=	NOUN
ap-7668	184	15	r	r	NOUN
ap-7668	184	16	>	>	NOUN
ap-7668	184	17	0	0	NUM
ap-7668	184	18	.	.	PUNCT
ap-7668	184	19	ε0pt	ε0pt	PUNCT
ap-7668	185	1	[	[	X
ap-7668	185	2	0.5	0.5	NUM
ap-7668	185	3	,	,	PUNCT
ap-7668	185	4	r	r	NOUN
ap-7668	185	5	]	]	PUNCT
ap-7668	185	6	ε0pt	ε0pt	X
ap-7668	186	1	[	[	X
ap-7668	186	2	1	1	NUM
ap-7668	186	3	,	,	PUNCT
ap-7668	186	4	r	r	NOUN
ap-7668	186	5	]	]	PUNCT
ap-7668	186	6	ε0pt	ε0pt	X
ap-7668	187	1	[	[	X
ap-7668	187	2	2	2	NUM
ap-7668	187	3	,	,	PUNCT
ap-7668	187	4	r	r	NOUN
ap-7668	187	5	]	]	PUNCT
ap-7668	187	6	0.0	0.0	NUM
ap-7668	187	7	0.5	0.5	NUM
ap-7668	187	8	1.0	1.0	NUM
ap-7668	187	9	1.5	1.5	NUM
ap-7668	187	10	2.0	2.0	NUM
ap-7668	187	11	2.5	2.5	NUM
ap-7668	187	12	3.0	3.0	NUM
ap-7668	187	13	3.5	3.5	NUM
ap-7668	187	14	r	r	NOUN
ap-7668	187	15	5	5	NUM
ap-7668	187	16	10	10	NUM
ap-7668	187	17	15	15	NUM
ap-7668	187	18	20	20	NUM
ap-7668	187	19	ε0	ε0	PROPN
ap-7668	187	20	[	[	PUNCT
ap-7668	187	21	a	a	NOUN
ap-7668	187	22	,	,	PUNCT
ap-7668	187	23	r	r	NOUN
ap-7668	187	24	]	]	PUNCT
ap-7668	187	25	figure	figure	NOUN
ap-7668	187	26	3	3	NUM
ap-7668	187	27	.	.	PUNCT
ap-7668	187	28	ground	ground	NOUN
ap-7668	187	29	state	state	NOUN
ap-7668	187	30	energy	energy	NOUN
ap-7668	187	31	of	of	ADP
ap-7668	187	32	the	the	DET
ap-7668	187	33	generalized	generalized	ADJ
ap-7668	187	34	3body	3body	NUM
ap-7668	187	35	harmonic	harmonic	NOUN
ap-7668	187	36	oscillator	oscillator	NOUN
ap-7668	187	37	vs	vs	ADP
ap-7668	187	38	r	r	NOUN
ap-7668	187	39	for	for	ADP
ap-7668	187	40	different	different	ADJ
ap-7668	187	41	values	value	NOUN
ap-7668	187	42	of	of	ADP
ap-7668	187	43	the	the	DET
ap-7668	187	44	parameter	parameter	NOUN
ap-7668	187	45	a	a	PRON
ap-7668	187	46	which	which	PRON
ap-7668	187	47	defines	define	VERB
ap-7668	187	48	the	the	DET
ap-7668	187	49	spring	spring	NOUN
ap-7668	187	50	constant	constant	ADJ
ap-7668	187	51	,	,	PUNCT
ap-7668	187	52	see	see	VERB
ap-7668	187	53	text	text	NOUN
ap-7668	187	54	.	.	PUNCT
ap-7668	188	1	the	the	DET
ap-7668	188	2	solid	solid	ADJ
ap-7668	188	3	lines	line	NOUN
ap-7668	188	4	correspond	correspond	VERB
ap-7668	188	5	to	to	ADP
ap-7668	188	6	the	the	DET
ap-7668	188	7	variational	variational	ADJ
ap-7668	188	8	result	result	NOUN
ap-7668	188	9	whilst	whilst	SCONJ
ap-7668	188	10	the	the	DET
ap-7668	188	11	dashed	dash	VERB
ap-7668	188	12	ones	one	NOUN
ap-7668	188	13	refer	refer	VERB
ap-7668	188	14	to	to	ADP
ap-7668	188	15	the	the	DET
ap-7668	188	16	value	value	NOUN
ap-7668	188	17	calculated	calculate	VERB
ap-7668	188	18	by	by	ADP
ap-7668	188	19	perturbation	perturbation	NOUN
ap-7668	188	20	theory	theory	NOUN
ap-7668	188	21	up	up	ADP
ap-7668	188	22	to	to	ADP
ap-7668	188	23	first	first	ADJ
ap-7668	188	24	order	order	NOUN
ap-7668	188	25	.	.	PUNCT
ap-7668	189	1	in	in	ADP
ap-7668	189	2	this	this	DET
ap-7668	189	3	case	case	NOUN
ap-7668	189	4	,	,	PUNCT
ap-7668	189	5	approximate	approximate	ADJ
ap-7668	189	6	solutions	solution	NOUN
ap-7668	189	7	for	for	ADP
ap-7668	189	8	the	the	DET
ap-7668	189	9	schrödinger	schrödinger	ADJ
ap-7668	189	10	equation	equation	NOUN
ap-7668	189	11	can	can	AUX
ap-7668	189	12	be	be	AUX
ap-7668	189	13	obtained	obtain	VERB
ap-7668	189	14	using	use	VERB
ap-7668	189	15	perturbation	perturbation	NOUN
ap-7668	189	16	theory	theory	NOUN
ap-7668	189	17	in	in	ADP
ap-7668	189	18	powers	power	NOUN
ap-7668	189	19	of	of	ADP
ap-7668	189	20	r.	r.	PROPN
ap-7668	189	21	7.1.1	7.1.1	NUM
ap-7668	189	22	.	.	PUNCT
ap-7668	190	1	ground	ground	NOUN
ap-7668	190	2	state	state	NOUN
ap-7668	190	3	taking	take	VERB
ap-7668	190	4	the	the	DET
ap-7668	190	5	r−dependent	r−dependent	PROPN
ap-7668	190	6	terms	term	NOUN
ap-7668	190	7	in	in	ADP
ap-7668	190	8	(	(	PUNCT
ap-7668	190	9	26	26	NUM
ap-7668	190	10	)	)	PUNCT
ap-7668	190	11	as	as	ADP
ap-7668	190	12	a	a	DET
ap-7668	190	13	small	small	ADJ
ap-7668	190	14	perturbation	perturbation	NOUN
ap-7668	190	15	,	,	PUNCT
ap-7668	190	16	the	the	DET
ap-7668	190	17	first	first	ADJ
ap-7668	190	18	correction	correction	NOUN
ap-7668	190	19	e1,0	e1,0	PROPN
ap-7668	190	20	to	to	ADP
ap-7668	190	21	the	the	DET
ap-7668	190	22	ground	ground	NOUN
ap-7668	190	23	state	state	NOUN
ap-7668	190	24	energy	energy	NOUN
ap-7668	190	25	takes	take	VERB
ap-7668	190	26	the	the	DET
ap-7668	190	27	form	form	NOUN
ap-7668	190	28	e1,0	e1,0	PROPN
ap-7668	190	29	=	=	PROPN
ap-7668	190	30	3	3	NUM
ap-7668	190	31	a	a	DET
ap-7668	190	32	2π	2π	NOUN
ap-7668	190	33	(	(	PUNCT
ap-7668	190	34	3π	3π	NOUN
ap-7668	190	35	ar2	ar2	PART
ap-7668	190	36	−	−	PROPN
ap-7668	190	37	4r	4r	NUM
ap-7668	190	38	√	√	PROPN
ap-7668	190	39	6π	6π	NOUN
ap-7668	190	40	a	a	PRON
ap-7668	190	41	)	)	PUNCT
ap-7668	190	42	.	.	PUNCT
ap-7668	191	1	the	the	DET
ap-7668	191	2	domain	domain	NOUN
ap-7668	191	3	of	of	ADP
ap-7668	191	4	validity	validity	NOUN
ap-7668	191	5	of	of	ADP
ap-7668	191	6	this	this	DET
ap-7668	191	7	perturbative	perturbative	ADJ
ap-7668	191	8	approach	approach	NOUN
ap-7668	191	9	is	be	AUX
ap-7668	191	10	estimated	estimate	VERB
ap-7668	191	11	by	by	ADP
ap-7668	191	12	means	mean	NOUN
ap-7668	191	13	of	of	ADP
ap-7668	191	14	the	the	DET
ap-7668	191	15	variational	variational	ADJ
ap-7668	191	16	method	method	NOUN
ap-7668	191	17	.	.	PUNCT
ap-7668	192	1	the	the	DET
ap-7668	192	2	use	use	NOUN
ap-7668	192	3	of	of	ADP
ap-7668	192	4	the	the	DET
ap-7668	192	5	simple	simple	ADJ
ap-7668	192	6	trial	trial	NOUN
ap-7668	192	7	function	function	NOUN
ap-7668	192	8	ψtrial	ψtrial	NOUN
ap-7668	192	9	0	0	PUNCT
ap-7668	193	1	=	=	SYM
ap-7668	193	2	e−	e−	PROPN
ap-7668	193	3	ω	ω	NUM
ap-7668	193	4	2	2	NUM
ap-7668	193	5	a	a	DET
ap-7668	193	6	α	α	PROPN
ap-7668	193	7	(	(	PUNCT
ap-7668	193	8	ρ12	ρ12	NOUN
ap-7668	193	9	+	+	X
ap-7668	193	10	ρ13	ρ13	NOUN
ap-7668	193	11	+	+	CCONJ
ap-7668	193	12	ρ23	ρ23	NOUN
ap-7668	193	13	)	)	PUNCT
ap-7668	193	14	c.f	c.f	PROPN
ap-7668	193	15	.	.	PROPN
ap-7668	194	1	(	(	PUNCT
ap-7668	194	2	20	20	NUM
ap-7668	194	3	)	)	PUNCT
ap-7668	194	4	,	,	PUNCT
ap-7668	194	5	where	where	SCONJ
ap-7668	194	6	α	α	NOUN
ap-7668	194	7	is	be	AUX
ap-7668	194	8	a	a	DET
ap-7668	194	9	variational	variational	ADJ
ap-7668	194	10	parameter	parameter	NOUN
ap-7668	194	11	to	to	PART
ap-7668	194	12	be	be	AUX
ap-7668	194	13	fixed	fix	VERB
ap-7668	194	14	by	by	ADP
ap-7668	194	15	the	the	DET
ap-7668	194	16	procedure	procedure	NOUN
ap-7668	194	17	of	of	ADP
ap-7668	194	18	minimization	minimization	NOUN
ap-7668	194	19	,	,	PUNCT
ap-7668	194	20	leads	lead	VERB
ap-7668	194	21	to	to	ADP
ap-7668	194	22	the	the	DET
ap-7668	194	23	results	result	NOUN
ap-7668	194	24	shown	show	VERB
ap-7668	194	25	in	in	ADP
ap-7668	194	26	figure	figure	NOUN
ap-7668	194	27	3	3	NUM
ap-7668	194	28	.	.	PUNCT
ap-7668	195	1	7.1.2	7.1.2	X
ap-7668	195	2	.	.	PUNCT
ap-7668	195	3	first	first	PROPN
ap-7668	195	4	excited	excited	ADJ
ap-7668	195	5	state	state	NOUN
ap-7668	195	6	it	it	PRON
ap-7668	195	7	is	be	AUX
ap-7668	195	8	important	important	ADJ
ap-7668	195	9	to	to	PART
ap-7668	195	10	mention	mention	VERB
ap-7668	195	11	that	that	PRON
ap-7668	195	12	for	for	ADP
ap-7668	195	13	the	the	DET
ap-7668	195	14	3	3	NUM
ap-7668	195	15	-	-	PUNCT
ap-7668	195	16	body	body	NOUN
ap-7668	195	17	harmonic	harmonic	ADJ
ap-7668	195	18	oscillator	oscillator	NOUN
ap-7668	195	19	(	(	PUNCT
ap-7668	195	20	r	r	NOUN
ap-7668	195	21	=	=	SYM
ap-7668	195	22	0	0	NUM
ap-7668	195	23	)	)	PUNCT
ap-7668	195	24	the	the	DET
ap-7668	195	25	exact	exact	ADJ
ap-7668	195	26	first	first	ADV
ap-7668	195	27	excited	excited	ADJ
ap-7668	195	28	state	state	NOUN
ap-7668	195	29	possesses	possess	VERB
ap-7668	195	30	a	a	DET
ap-7668	195	31	degeneracy	degeneracy	NOUN
ap-7668	195	32	equal	equal	ADJ
ap-7668	195	33	to	to	ADP
ap-7668	195	34	3	3	NUM
ap-7668	195	35	.	.	PUNCT
ap-7668	196	1	for	for	ADP
ap-7668	196	2	r	r	NOUN
ap-7668	196	3	>	>	X
ap-7668	196	4	0	0	NUM
ap-7668	196	5	,	,	PUNCT
ap-7668	196	6	the	the	DET
ap-7668	196	7	perturbation	perturbation	NOUN
ap-7668	196	8	theory	theory	NOUN
ap-7668	196	9	partially	partially	ADV
ap-7668	196	10	breaks	break	VERB
ap-7668	196	11	this	this	DET
ap-7668	196	12	degeneracy	degeneracy	NOUN
ap-7668	196	13	.	.	PUNCT
ap-7668	197	1	the	the	DET
ap-7668	197	2	energy	energy	NOUN
ap-7668	197	3	of	of	ADP
ap-7668	197	4	the	the	DET
ap-7668	197	5	approximate	approximate	ADJ
ap-7668	197	6	first	first	ADJ
ap-7668	197	7	excited	excited	ADJ
ap-7668	197	8	state	state	NOUN
ap-7668	197	9	calculated	calculate	VERB
ap-7668	197	10	by	by	ADP
ap-7668	197	11	perturbation	perturbation	NOUN
ap-7668	197	12	theory	theory	NOUN
ap-7668	197	13	,	,	PUNCT
ap-7668	197	14	up	up	ADP
ap-7668	197	15	to	to	ADP
ap-7668	197	16	first	first	ADJ
ap-7668	197	17	order	order	NOUN
ap-7668	197	18	,	,	PUNCT
ap-7668	197	19	is	be	AUX
ap-7668	197	20	displayed	display	VERB
ap-7668	197	21	in	in	ADP
ap-7668	197	22	figure	figure	NOUN
ap-7668	197	23	4	4	NUM
ap-7668	197	24	.	.	NOUN
ap-7668	197	25	8	8	NUM
ap-7668	197	26	.	.	PUNCT
ap-7668	198	1	conclusions	conclusion	NOUN
ap-7668	198	2	in	in	ADP
ap-7668	198	3	this	this	DET
ap-7668	198	4	report	report	NOUN
ap-7668	198	5	for	for	ADP
ap-7668	198	6	a	a	DET
ap-7668	198	7	3	3	NUM
ap-7668	198	8	-	-	PUNCT
ap-7668	198	9	body	body	NOUN
ap-7668	198	10	harmonic	harmonic	ADJ
ap-7668	198	11	oscillator	oscillator	NOUN
ap-7668	198	12	in	in	ADP
ap-7668	198	13	euclidean	euclidean	ADJ
ap-7668	198	14	space	space	NOUN
ap-7668	198	15	rd	rd	NOUN
ap-7668	198	16	we	we	PRON
ap-7668	198	17	consider	consider	VERB
ap-7668	198	18	the	the	DET
ap-7668	198	19	schrödinger	schrödinger	ADJ
ap-7668	198	20	operator	operator	NOUN
ap-7668	198	21	in	in	ADP
ap-7668	198	22	ρ	ρ	NOUN
ap-7668	198	23	-	-	PUNCT
ap-7668	198	24	variables	variable	NOUN
ap-7668	198	25	ρij	ρij	NOUN
ap-7668	198	26	=	=	NOUN
ap-7668	198	27	r2	r2	PROPN
ap-7668	199	1	ij	ij	INTJ
ap-7668	199	2	,	,	PUNCT
ap-7668	199	3	hlb	hlb	PROPN
ap-7668	199	4	=	=	SYM
ap-7668	199	5	−∆lb(ρij	−∆lb(ρij	PROPN
ap-7668	199	6	)	)	PUNCT
ap-7668	200	1	+	+	NOUN
ap-7668	200	2	v	v	NOUN
ap-7668	200	3	(	(	PUNCT
ap-7668	200	4	ho)(ρij	ho)(ρij	NOUN
ap-7668	200	5	)	)	PUNCT
ap-7668	201	1	+	+	NOUN
ap-7668	201	2	v	v	ADJ
ap-7668	201	3	(	(	PUNCT
ap-7668	201	4	eff)(ρij	eff)(ρij	NOUN
ap-7668	201	5	)	)	PUNCT
ap-7668	201	6	,	,	PUNCT
ap-7668	201	7	(	(	PUNCT
ap-7668	201	8	27	27	NUM
ap-7668	201	9	)	)	PUNCT
ap-7668	201	10	where	where	SCONJ
ap-7668	201	11	the	the	DET
ap-7668	201	12	kinetic	kinetic	ADJ
ap-7668	201	13	energy	energy	NOUN
ap-7668	201	14	corresponds	correspond	VERB
ap-7668	201	15	to	to	ADP
ap-7668	201	16	a	a	DET
ap-7668	201	17	3dimensional	3dimensional	ADJ
ap-7668	201	18	particle	particle	NOUN
ap-7668	201	19	moving	move	VERB
ap-7668	201	20	in	in	ADP
ap-7668	201	21	a	a	DET
ap-7668	201	22	non	non	ADJ
ap-7668	201	23	-	-	ADJ
ap-7668	201	24	flat	flat	ADJ
ap-7668	201	25	space	space	NOUN
ap-7668	201	26	.	.	PUNCT
ap-7668	202	1	the	the	DET
ap-7668	202	2	54	54	NUM
ap-7668	202	3	vol	vol	NOUN
ap-7668	202	4	.	.	PUNCT
ap-7668	203	1	62	62	NUM
ap-7668	203	2	no	no	INTJ
ap-7668	203	3	.	.	PUNCT
ap-7668	204	1	1/2022	1/2022	NUM
ap-7668	204	2	generalized	generalized	ADJ
ap-7668	204	3	three	three	NUM
ap-7668	204	4	-	-	PUNCT
ap-7668	204	5	body	body	NOUN
ap-7668	204	6	harmonic	harmonic	ADJ
ap-7668	204	7	oscillator	oscillator	NOUN
ap-7668	204	8	system	system	NOUN
ap-7668	204	9	:	:	PUNCT
ap-7668	204	10	ground	ground	NOUN
ap-7668	204	11	state	state	NOUN
ap-7668	204	12	e1[0.5	e1[0.5	PROPN
ap-7668	204	13	,	,	PUNCT
ap-7668	204	14	r	r	NOUN
ap-7668	204	15	]	]	X
ap-7668	204	16	e1[1	e1[1	X
ap-7668	204	17	,	,	PUNCT
ap-7668	204	18	r	r	NOUN
ap-7668	204	19	]	]	X
ap-7668	204	20	e1[2	e1[2	NOUN
ap-7668	204	21	,	,	PUNCT
ap-7668	204	22	r	r	NOUN
ap-7668	204	23	]	]	X
ap-7668	204	24	0.2	0.2	NUM
ap-7668	204	25	0.4	0.4	NUM
ap-7668	204	26	0.6	0.6	NUM
ap-7668	204	27	0.8	0.8	NUM
ap-7668	204	28	1.0	1.0	NUM
ap-7668	204	29	r	r	NOUN
ap-7668	204	30	5	5	NUM
ap-7668	204	31	10	10	NUM
ap-7668	204	32	15	15	NUM
ap-7668	204	33	20	20	NUM
ap-7668	204	34	25	25	NUM
ap-7668	204	35	30	30	NUM
ap-7668	204	36	e1[a	e1[a	NOUN
ap-7668	204	37	,	,	PUNCT
ap-7668	204	38	r	r	NOUN
ap-7668	204	39	]	]	PUNCT
ap-7668	204	40	figure	figure	NOUN
ap-7668	204	41	4	4	NUM
ap-7668	204	42	.	.	PUNCT
ap-7668	204	43	first	first	ADV
ap-7668	204	44	excited	excited	ADJ
ap-7668	204	45	state	state	NOUN
ap-7668	204	46	of	of	ADP
ap-7668	204	47	the	the	DET
ap-7668	204	48	generalized	generalized	ADJ
ap-7668	204	49	3body	3body	NUM
ap-7668	204	50	harmonic	harmonic	NOUN
ap-7668	204	51	oscillator	oscillator	NOUN
ap-7668	204	52	vs	vs	ADP
ap-7668	204	53	r.	r.	PROPN
ap-7668	204	54	schrödinger	schrödinger	PROPN
ap-7668	204	55	operator	operator	NOUN
ap-7668	204	56	(	(	PUNCT
ap-7668	204	57	27	27	NUM
ap-7668	204	58	)	)	PUNCT
ap-7668	204	59	governs	govern	VERB
ap-7668	204	60	the	the	DET
ap-7668	204	61	s	s	NOUN
ap-7668	204	62	-	-	PUNCT
ap-7668	204	63	states	state	NOUN
ap-7668	204	64	solutions	solution	NOUN
ap-7668	204	65	of	of	ADP
ap-7668	204	66	the	the	DET
ap-7668	204	67	original	original	ADJ
ap-7668	204	68	three	three	NUM
ap-7668	204	69	-	-	PUNCT
ap-7668	204	70	body	body	NOUN
ap-7668	204	71	system	system	NOUN
ap-7668	204	72	(	(	PUNCT
ap-7668	204	73	1	1	NUM
ap-7668	204	74	)	)	PUNCT
ap-7668	204	75	,	,	PUNCT
ap-7668	204	76	in	in	ADP
ap-7668	204	77	particular	particular	ADJ
ap-7668	204	78	,	,	PUNCT
ap-7668	204	79	it	it	PRON
ap-7668	204	80	includes	include	VERB
ap-7668	204	81	the	the	DET
ap-7668	204	82	ground	ground	NOUN
ap-7668	204	83	state	state	NOUN
ap-7668	204	84	.	.	PUNCT
ap-7668	205	1	it	it	PRON
ap-7668	205	2	implies	imply	VERB
ap-7668	205	3	that	that	SCONJ
ap-7668	205	4	the	the	DET
ap-7668	205	5	solutions	solution	NOUN
ap-7668	205	6	of	of	ADP
ap-7668	205	7	corresponding	corresponding	PROPN
ap-7668	205	8	eigenvalue	eigenvalue	PROPN
ap-7668	205	9	problem	problem	NOUN
ap-7668	205	10	depend	depend	VERB
ap-7668	205	11	solely	solely	ADV
ap-7668	205	12	on	on	ADP
ap-7668	205	13	three	three	NUM
ap-7668	205	14	coordinates	coordinate	NOUN
ap-7668	205	15	,	,	PUNCT
ap-7668	205	16	contrary	contrary	ADJ
ap-7668	205	17	to	to	ADP
ap-7668	205	18	the	the	DET
ap-7668	205	19	(	(	PUNCT
ap-7668	205	20	3d)-dimensional	3d)-dimensional	ADJ
ap-7668	205	21	schrödinger	schrödinger	ADJ
ap-7668	205	22	equation	equation	NOUN
ap-7668	205	23	.	.	PUNCT
ap-7668	206	1	the	the	DET
ap-7668	206	2	reduced	reduce	VERB
ap-7668	206	3	hamiltonian	hamiltonian	PROPN
ap-7668	206	4	hlb	hlb	PROPN
ap-7668	206	5	is	be	AUX
ap-7668	206	6	an	an	DET
ap-7668	206	7	hermitian	hermitian	ADJ
ap-7668	206	8	operator	operator	NOUN
ap-7668	206	9	,	,	PUNCT
ap-7668	206	10	where	where	SCONJ
ap-7668	206	11	the	the	DET
ap-7668	206	12	variational	variational	ADJ
ap-7668	206	13	method	method	NOUN
ap-7668	206	14	can	can	AUX
ap-7668	206	15	be	be	AUX
ap-7668	206	16	more	more	ADV
ap-7668	206	17	easily	easily	ADV
ap-7668	206	18	implemented	implement	VERB
ap-7668	206	19	(	(	PUNCT
ap-7668	206	20	the	the	DET
ap-7668	206	21	energy	energy	NOUN
ap-7668	206	22	functional	functional	NOUN
ap-7668	206	23	is	be	AUX
ap-7668	206	24	a	a	DET
ap-7668	206	25	3	3	NUM
ap-7668	206	26	-	-	PUNCT
ap-7668	206	27	dimensional	dimensional	ADJ
ap-7668	206	28	integral	integral	ADJ
ap-7668	206	29	only	only	ADV
ap-7668	206	30	)	)	PUNCT
ap-7668	206	31	.	.	PUNCT
ap-7668	207	1	the	the	DET
ap-7668	207	2	classical	classical	ADJ
ap-7668	207	3	analogue	analogue	NOUN
ap-7668	207	4	of	of	ADP
ap-7668	207	5	(	(	PUNCT
ap-7668	207	6	27	27	NUM
ap-7668	207	7	)	)	PUNCT
ap-7668	207	8	was	be	AUX
ap-7668	207	9	presented	present	VERB
ap-7668	207	10	as	as	ADV
ap-7668	207	11	well	well	ADV
ap-7668	207	12	.	.	PUNCT
ap-7668	208	1	the	the	DET
ap-7668	208	2	operator	operator	NOUN
ap-7668	208	3	(	(	PUNCT
ap-7668	208	4	27	27	NUM
ap-7668	208	5	)	)	PUNCT
ap-7668	208	6	up	up	ADP
ap-7668	208	7	to	to	ADP
ap-7668	208	8	a	a	DET
ap-7668	208	9	gauge	gauge	ADJ
ap-7668	208	10	rotation	rotation	NOUN
ap-7668	208	11	is	be	AUX
ap-7668	208	12	equivalent	equivalent	ADJ
ap-7668	208	13	to	to	ADP
ap-7668	208	14	an	an	DET
ap-7668	208	15	algebraic	algebraic	ADJ
ap-7668	208	16	operator	operator	NOUN
ap-7668	208	17	with	with	ADP
ap-7668	208	18	hidden	hide	VERB
ap-7668	208	19	algebra	algebra	NOUN
ap-7668	208	20	sℓ(4,r	sℓ(4,r	ADJ
ap-7668	208	21	)	)	PUNCT
ap-7668	208	22	,	,	PUNCT
ap-7668	208	23	thus	thus	ADV
ap-7668	208	24	,	,	PUNCT
ap-7668	208	25	becoming	become	VERB
ap-7668	208	26	a	a	DET
ap-7668	208	27	lie	lie	NOUN
ap-7668	208	28	-	-	PUNCT
ap-7668	208	29	algebraic	algebraic	ADJ
ap-7668	208	30	operator	operator	NOUN
ap-7668	208	31	.	.	PUNCT
ap-7668	209	1	in	in	ADP
ap-7668	209	2	the	the	DET
ap-7668	209	3	case	case	NOUN
ap-7668	209	4	of	of	ADP
ap-7668	209	5	identical	identical	ADJ
ap-7668	209	6	masses	masse	NOUN
ap-7668	209	7	and	and	CCONJ
ap-7668	209	8	equal	equal	ADJ
ap-7668	209	9	frequencies	frequency	NOUN
ap-7668	209	10	the	the	DET
ap-7668	209	11	aforementioned	aforementioned	ADJ
ap-7668	209	12	model	model	NOUN
ap-7668	209	13	was	be	AUX
ap-7668	209	14	generalized	generalize	VERB
ap-7668	209	15	to	to	ADP
ap-7668	209	16	a	a	DET
ap-7668	209	17	3	3	NUM
ap-7668	209	18	-	-	PUNCT
ap-7668	209	19	body	body	NOUN
ap-7668	209	20	harmonic	harmonic	ADJ
ap-7668	209	21	system	system	NOUN
ap-7668	209	22	with	with	ADP
ap-7668	209	23	a	a	DET
ap-7668	209	24	non	non	ADJ
ap-7668	209	25	-	-	ADJ
ap-7668	209	26	zero	zero	NUM
ap-7668	209	27	rest	rest	NOUN
ap-7668	209	28	length	length	NOUN
ap-7668	209	29	r	r	NOUN
ap-7668	209	30	>	>	X
ap-7668	209	31	0	0	NUM
ap-7668	209	32	.	.	PUNCT
ap-7668	210	1	in	in	ADP
ap-7668	210	2	this	this	DET
ap-7668	210	3	case	case	NOUN
ap-7668	210	4	,	,	PUNCT
ap-7668	210	5	no	no	DET
ap-7668	210	6	hidden	hide	VERB
ap-7668	210	7	algebra	algebra	NOUN
ap-7668	210	8	nor	nor	CCONJ
ap-7668	210	9	exact	exact	ADJ
ap-7668	210	10	solutions	solution	NOUN
ap-7668	210	11	seem	seem	VERB
ap-7668	210	12	to	to	PART
ap-7668	210	13	occur	occur	VERB
ap-7668	210	14	.	.	PUNCT
ap-7668	211	1	an	an	DET
ap-7668	211	2	indication	indication	NOUN
ap-7668	211	3	of	of	ADP
ap-7668	211	4	the	the	DET
ap-7668	211	5	lost	lose	VERB
ap-7668	211	6	of	of	ADP
ap-7668	211	7	integrability	integrability	NOUN
ap-7668	211	8	is	be	AUX
ap-7668	211	9	the	the	DET
ap-7668	211	10	fact	fact	NOUN
ap-7668	211	11	that	that	SCONJ
ap-7668	211	12	the	the	DET
ap-7668	211	13	classical	classical	ADJ
ap-7668	211	14	counterpart	counterpart	NOUN
ap-7668	211	15	of	of	ADP
ap-7668	211	16	this	this	DET
ap-7668	211	17	model	model	NOUN
ap-7668	211	18	exhibits	exhibit	VERB
ap-7668	211	19	chaotic	chaotic	ADJ
ap-7668	211	20	motion	motion	NOUN
ap-7668	211	21	.	.	PUNCT
ap-7668	212	1	using	use	VERB
ap-7668	212	2	perturbation	perturbation	NOUN
ap-7668	212	3	theory	theory	NOUN
ap-7668	212	4	complemented	complement	VERB
ap-7668	212	5	by	by	ADP
ap-7668	212	6	the	the	DET
ap-7668	212	7	variational	variational	ADJ
ap-7668	212	8	method	method	NOUN
ap-7668	212	9	it	it	PRON
ap-7668	212	10	was	be	AUX
ap-7668	212	11	shown	show	VERB
ap-7668	212	12	that	that	SCONJ
ap-7668	212	13	the	the	DET
ap-7668	212	14	ground	ground	NOUN
ap-7668	212	15	state	state	NOUN
ap-7668	212	16	energy	energy	NOUN
ap-7668	212	17	vs	vs	ADP
ap-7668	212	18	r	r	NOUN
ap-7668	212	19	develops	develop	VERB
ap-7668	212	20	a	a	DET
ap-7668	212	21	global	global	ADJ
ap-7668	212	22	minimum	minimum	NOUN
ap-7668	212	23	,	,	PUNCT
ap-7668	212	24	hence	hence	ADV
ap-7668	212	25	,	,	PUNCT
ap-7668	212	26	defining	define	VERB
ap-7668	212	27	a	a	DET
ap-7668	212	28	configuration	configuration	NOUN
ap-7668	212	29	of	of	ADP
ap-7668	212	30	equilibrium	equilibrium	NOUN
ap-7668	212	31	.	.	PUNCT
ap-7668	213	1	acknowledgements	acknowledgement	NOUN
ap-7668	213	2	amer	amer	PROPN
ap-7668	213	3	thanks	thank	NOUN
ap-7668	213	4	the	the	DET
ap-7668	213	5	support	support	NOUN
ap-7668	213	6	through	through	ADP
ap-7668	213	7	the	the	DET
ap-7668	213	8	programa	programa	NOUN
ap-7668	213	9	especial	especial	X
ap-7668	213	10	de	de	PROPN
ap-7668	213	11	apoyo	apoyo	PROPN
ap-7668	213	12	a	a	PROPN
ap-7668	213	13	la	la	X
ap-7668	213	14	investigación	investigación	PROPN
ap-7668	213	15	2021	2021	NUM
ap-7668	213	16	,	,	PUNCT
ap-7668	213	17	uam	uam	PROPN
ap-7668	213	18	-	-	PUNCT
ap-7668	213	19	i.	i.	PROPN
ap-7668	213	20	fm	fm	PROPN
ap-7668	213	21	and	and	CCONJ
ap-7668	213	22	amer	amer	PROPN
ap-7668	213	23	are	be	AUX
ap-7668	213	24	thankful	thankful	ADJ
ap-7668	213	25	to	to	ADP
ap-7668	213	26	mario	mario	PROPN
ap-7668	213	27	alan	alan	PROPN
ap-7668	213	28	quiroz	quiroz	PROPN
ap-7668	213	29	for	for	ADP
ap-7668	213	30	helping	help	VERB
ap-7668	213	31	in	in	ADP
ap-7668	213	32	the	the	DET
ap-7668	213	33	numerical	numerical	ADJ
ap-7668	213	34	computations	computation	NOUN
ap-7668	213	35	.	.	PUNCT
ap-7668	214	1	references	reference	NOUN
ap-7668	214	2	[	[	X
ap-7668	214	3	1	1	NUM
ap-7668	214	4	]	]	X
ap-7668	214	5	f.	f.	PROPN
ap-7668	214	6	zernike	zernike	PROPN
ap-7668	214	7	,	,	PUNCT
ap-7668	214	8	h.	h.	PROPN
ap-7668	214	9	c.	c.	PROPN
ap-7668	214	10	brinkman	brinkman	PROPN
ap-7668	214	11	.	.	PUNCT
ap-7668	215	1	hypersphärische	hypersphärische	PROPN
ap-7668	215	2	funktionen	funktionen	PROPN
ap-7668	215	3	und	und	PROPN
ap-7668	215	4	die	die	VERB
ap-7668	215	5	in	in	ADP
ap-7668	215	6	sphärischen	sphärischen	ADV
ap-7668	215	7	bereichen	bereichen	ADV
ap-7668	215	8	orthogonalen	orthogonalen	ADJ
ap-7668	215	9	polynome	polynome	NOUN
ap-7668	215	10	.	.	PUNCT
ap-7668	216	1	koninklijke	koninklijke	PROPN
ap-7668	216	2	nederlandse	nederlandse	PROPN
ap-7668	216	3	akademie	akademie	PROPN
ap-7668	216	4	van	van	PROPN
ap-7668	216	5	wetenschappen	wetenschappen	PROPN
ap-7668	216	6	38:161–170	38:161–170	PROPN
ap-7668	216	7	,	,	PUNCT
ap-7668	216	8	1935	1935	NUM
ap-7668	216	9	.	.	PUNCT
ap-7668	217	1	[	[	X
ap-7668	217	2	2	2	NUM
ap-7668	217	3	]	]	PUNCT
ap-7668	217	4	l.	l.	PROPN
ap-7668	217	5	m.	m.	PROPN
ap-7668	217	6	delves	delf	NOUN
ap-7668	217	7	.	.	PUNCT
ap-7668	218	1	tertiary	tertiary	ADJ
ap-7668	218	2	and	and	CCONJ
ap-7668	218	3	general	general	ADJ
ap-7668	218	4	-	-	PUNCT
ap-7668	218	5	order	order	NOUN
ap-7668	218	6	collisions	collision	NOUN
ap-7668	218	7	(	(	PUNCT
ap-7668	218	8	i	i	NOUN
ap-7668	218	9	)	)	PUNCT
ap-7668	218	10	.	.	PUNCT
ap-7668	219	1	nuclear	nuclear	ADJ
ap-7668	219	2	physics	physics	PROPN
ap-7668	219	3	9(3):391–399	9(3):391–399	PROPN
ap-7668	219	4	,	,	PUNCT
ap-7668	219	5	1958	1958	NUM
ap-7668	219	6	.	.	PUNCT
ap-7668	220	1	https://doi.org/10.1016/0029-5582(58)90372-9	https://doi.org/10.1016/0029-5582(58)90372-9	NOUN
ap-7668	220	2	.	.	PUNCT
ap-7668	221	1	[	[	X
ap-7668	221	2	3	3	X
ap-7668	221	3	]	]	X
ap-7668	221	4	f.	f.	PROPN
ap-7668	221	5	smith	smith	PROPN
ap-7668	221	6	.	.	PUNCT
ap-7668	222	1	a	a	DET
ap-7668	222	2	symmetric	symmetric	ADJ
ap-7668	222	3	representation	representation	NOUN
ap-7668	222	4	for	for	ADP
ap-7668	222	5	three	three	NUM
ap-7668	222	6	-	-	PUNCT
ap-7668	222	7	body	body	NOUN
ap-7668	222	8	problems	problem	NOUN
ap-7668	222	9	.	.	PUNCT
ap-7668	223	1	i.	i.	PROPN
ap-7668	223	2	motion	motion	NOUN
ap-7668	223	3	in	in	ADP
ap-7668	223	4	a	a	DET
ap-7668	223	5	plane	plane	NOUN
ap-7668	223	6	.	.	PUNCT
ap-7668	224	1	journal	journal	PROPN
ap-7668	224	2	of	of	ADP
ap-7668	224	3	mathematical	mathematical	ADJ
ap-7668	224	4	physics	physics	NOUN
ap-7668	224	5	3(4):735	3(4):735	NUM
ap-7668	224	6	,	,	PUNCT
ap-7668	224	7	1962	1962	NUM
ap-7668	224	8	.	.	PUNCT
ap-7668	225	1	https://doi.org/10.1063/1.1724275	https://doi.org/10.1063/1.1724275	X
ap-7668	225	2	.	.	PUNCT
ap-7668	226	1	[	[	X
ap-7668	226	2	4	4	NUM
ap-7668	226	3	]	]	PUNCT
ap-7668	226	4	a.	a.	NOUN
ap-7668	226	5	turbiner	turbiner	NOUN
ap-7668	226	6	,	,	PUNCT
ap-7668	226	7	w.	w.	PROPN
ap-7668	226	8	miller	miller	PROPN
ap-7668	226	9	jr	jr	PROPN
ap-7668	226	10	,	,	PUNCT
ap-7668	226	11	m.	m.	NOUN
ap-7668	226	12	a.	a.	PROPN
ap-7668	226	13	escobar	escobar	PROPN
ap-7668	226	14	-	-	PUNCT
ap-7668	226	15	ruiz	ruiz	NOUN
ap-7668	226	16	.	.	PUNCT
ap-7668	227	1	three	three	NUM
ap-7668	227	2	-	-	PUNCT
ap-7668	227	3	body	body	NOUN
ap-7668	227	4	problem	problem	NOUN
ap-7668	227	5	in	in	ADP
ap-7668	227	6	d	d	ADJ
ap-7668	227	7	-	-	ADJ
ap-7668	227	8	dimensional	dimensional	ADJ
ap-7668	227	9	space	space	NOUN
ap-7668	227	10	:	:	PUNCT
ap-7668	227	11	ground	ground	NOUN
ap-7668	227	12	state	state	NOUN
ap-7668	227	13	,	,	PUNCT
ap-7668	227	14	(	(	PUNCT
ap-7668	227	15	quasi)-exact	quasi)-exact	NOUN
ap-7668	227	16	-	-	PUNCT
ap-7668	227	17	solvability	solvability	NOUN
ap-7668	227	18	.	.	PUNCT
ap-7668	228	1	journal	journal	PROPN
ap-7668	228	2	of	of	ADP
ap-7668	228	3	mathematical	mathematical	ADJ
ap-7668	228	4	physics	physics	NOUN
ap-7668	228	5	59(2):022108	59(2):022108	NUM
ap-7668	228	6	,	,	PUNCT
ap-7668	228	7	2018	2018	NUM
ap-7668	228	8	.	.	PUNCT
ap-7668	229	1	https://doi.org/10.1063/1.4994397	https://doi.org/10.1063/1.4994397	NOUN
ap-7668	229	2	.	.	PUNCT
ap-7668	230	1	[	[	X
ap-7668	230	2	5	5	NUM
ap-7668	230	3	]	]	PUNCT
ap-7668	230	4	a.	a.	NOUN
ap-7668	230	5	turbiner	turbiner	NOUN
ap-7668	230	6	,	,	PUNCT
ap-7668	230	7	w.	w.	PROPN
ap-7668	230	8	miller	miller	PROPN
ap-7668	230	9	jr	jr	PROPN
ap-7668	230	10	,	,	PUNCT
ap-7668	230	11	m.	m.	NOUN
ap-7668	230	12	a.	a.	PROPN
ap-7668	230	13	escobar	escobar	PROPN
ap-7668	230	14	-	-	PUNCT
ap-7668	230	15	ruiz	ruiz	NOUN
ap-7668	230	16	.	.	PUNCT
ap-7668	231	1	three	three	NUM
ap-7668	231	2	-	-	PUNCT
ap-7668	231	3	body	body	NOUN
ap-7668	231	4	problem	problem	NOUN
ap-7668	231	5	in	in	ADP
ap-7668	231	6	3d	3d	PROPN
ap-7668	231	7	space	space	NOUN
ap-7668	231	8	:	:	PUNCT
ap-7668	231	9	ground	ground	NOUN
ap-7668	231	10	state	state	NOUN
ap-7668	231	11	,	,	PUNCT
ap-7668	231	12	(	(	PUNCT
ap-7668	231	13	quasi)-exact	quasi)-exact	NOUN
ap-7668	231	14	-	-	PUNCT
ap-7668	231	15	solvability	solvability	NOUN
ap-7668	231	16	.	.	PUNCT
ap-7668	232	1	journal	journal	PROPN
ap-7668	232	2	of	of	ADP
ap-7668	232	3	physics	physics	PROPN
ap-7668	232	4	a	a	PRON
ap-7668	232	5	:	:	PUNCT
ap-7668	232	6	mathematical	mathematical	ADJ
ap-7668	232	7	and	and	CCONJ
ap-7668	232	8	theoretical	theoretical	ADJ
ap-7668	232	9	50(21):215201	50(21):215201	NUM
ap-7668	232	10	,	,	PUNCT
ap-7668	232	11	2017	2017	NUM
ap-7668	232	12	.	.	PUNCT
ap-7668	233	1	https://doi.org/10.1088/1751-8121/aa6cc2	https://doi.org/10.1088/1751-8121/aa6cc2	PROPN
ap-7668	233	2	.	.	PUNCT
ap-7668	234	1	[	[	X
ap-7668	234	2	6	6	NUM
ap-7668	234	3	]	]	PUNCT
ap-7668	234	4	w.	w.	PROPN
ap-7668	234	5	miller	miller	PROPN
ap-7668	234	6	jr	jr	PROPN
ap-7668	234	7	,	,	PUNCT
ap-7668	234	8	a.	a.	NOUN
ap-7668	234	9	turbiner	turbiner	NOUN
ap-7668	234	10	,	,	PUNCT
ap-7668	234	11	m.	m.	NOUN
ap-7668	234	12	a.	a.	PROPN
ap-7668	234	13	escobar	escobar	PROPN
ap-7668	234	14	-	-	PUNCT
ap-7668	234	15	ruiz	ruiz	NOUN
ap-7668	234	16	.	.	PUNCT
ap-7668	235	1	the	the	DET
ap-7668	235	2	quantum	quantum	PROPN
ap-7668	235	3	n	n	CCONJ
ap-7668	235	4	-	-	PUNCT
ap-7668	235	5	body	body	NOUN
ap-7668	235	6	problem	problem	NOUN
ap-7668	235	7	in	in	ADP
ap-7668	235	8	dimension	dimension	NOUN
ap-7668	235	9	d	d	PROPN
ap-7668	235	10	≥	≥	NUM
ap-7668	235	11	n	n	CCONJ
ap-7668	235	12	−	−	PROPN
ap-7668	235	13	1	1	NUM
ap-7668	235	14	:	:	PUNCT
ap-7668	235	15	ground	ground	NOUN
ap-7668	235	16	state	state	NOUN
ap-7668	235	17	.	.	PUNCT
ap-7668	236	1	journal	journal	PROPN
ap-7668	236	2	of	of	ADP
ap-7668	236	3	physics	physics	PROPN
ap-7668	236	4	a	a	PRON
ap-7668	236	5	:	:	PUNCT
ap-7668	236	6	mathematical	mathematical	ADJ
ap-7668	236	7	and	and	CCONJ
ap-7668	236	8	theoretical	theoretical	ADJ
ap-7668	236	9	51(20):205201	51(20):205201	NUM
ap-7668	236	10	,	,	PUNCT
ap-7668	236	11	2018	2018	NUM
ap-7668	236	12	.	.	PUNCT
ap-7668	237	1	https://doi.org/10.1088/1751-8121/aabb10	https://doi.org/10.1088/1751-8121/aabb10	NOUN
ap-7668	237	2	.	.	PUNCT
ap-7668	238	1	[	[	X
ap-7668	238	2	7	7	X
ap-7668	238	3	]	]	X
ap-7668	238	4	f.	f.	PROPN
ap-7668	238	5	m.	m.	PROPN
ap-7668	238	6	fernández	fernández	PROPN
ap-7668	238	7	.	.	PUNCT
ap-7668	239	1	born	bear	VERB
ap-7668	239	2	-	-	PUNCT
ap-7668	239	3	oppenheimer	oppenheimer	PROPN
ap-7668	239	4	approximation	approximation	NOUN
ap-7668	239	5	for	for	ADP
ap-7668	239	6	a	a	DET
ap-7668	239	7	harmonic	harmonic	ADJ
ap-7668	239	8	molecule	molecule	NOUN
ap-7668	239	9	.	.	PUNCT
ap-7668	240	1	arxiv:0810.2210v2	arxiv:0810.2210v2	ADJ
ap-7668	240	2	.	.	PUNCT
ap-7668	241	1	[	[	X
ap-7668	241	2	8	8	NUM
ap-7668	241	3	]	]	X
ap-7668	241	4	a.	a.	NOUN
ap-7668	241	5	v.	v.	PROPN
ap-7668	241	6	turbiner	turbiner	NOUN
ap-7668	241	7	.	.	PUNCT
ap-7668	242	1	quasi	quasi	ADJ
ap-7668	242	2	-	-	ADJ
ap-7668	242	3	exactly	exactly	ADV
ap-7668	242	4	-	-	PUNCT
ap-7668	242	5	solvable	solvable	ADJ
ap-7668	242	6	problems	problem	NOUN
ap-7668	242	7	and	and	CCONJ
ap-7668	242	8	the	the	DET
ap-7668	242	9	sl(2	sl(2	PROPN
ap-7668	242	10	,	,	PUNCT
ap-7668	242	11	r	r	NOUN
ap-7668	242	12	)	)	PUNCT
ap-7668	242	13	algebra	algebra	NOUN
ap-7668	242	14	.	.	PUNCT
ap-7668	243	1	communications	communication	NOUN
ap-7668	243	2	in	in	ADP
ap-7668	243	3	mathematical	mathematical	ADJ
ap-7668	243	4	physics	physics	NOUN
ap-7668	243	5	118:467–474	118:467–474	NOUN
ap-7668	243	6	,	,	PUNCT
ap-7668	243	7	1988	1988	NUM
ap-7668	243	8	.	.	PUNCT
ap-7668	244	1	https://doi.org/10.1007/bf01466727	https://doi.org/10.1007/bf01466727	X
ap-7668	244	2	.	.	PUNCT
ap-7668	245	1	[	[	X
ap-7668	245	2	9	9	NUM
ap-7668	245	3	]	]	PUNCT
ap-7668	245	4	a.	a.	NOUN
ap-7668	245	5	v.	v.	PROPN
ap-7668	245	6	turbiner	turbiner	NOUN
ap-7668	245	7	.	.	PUNCT
ap-7668	246	1	one	one	NUM
ap-7668	246	2	-	-	PUNCT
ap-7668	246	3	dimensional	dimensional	ADJ
ap-7668	246	4	quasi	quasi	ADJ
ap-7668	246	5	-	-	ADJ
ap-7668	246	6	exactly	exactly	ADV
ap-7668	246	7	-	-	PUNCT
ap-7668	246	8	solvable	solvable	ADJ
ap-7668	246	9	schrödinger	schrödinger	ADJ
ap-7668	246	10	equations	equation	NOUN
ap-7668	246	11	.	.	PUNCT
ap-7668	247	1	physics	physics	NOUN
ap-7668	247	2	reports	report	VERB
ap-7668	247	3	642:1–71	642:1–71	NUM
ap-7668	247	4	,	,	PUNCT
ap-7668	247	5	2016	2016	NUM
ap-7668	247	6	.	.	PUNCT
ap-7668	248	1	https://doi.org/10.1016/j.physrep.2016.06.002	https://doi.org/10.1016/j.physrep.2016.06.002	NOUN
ap-7668	248	2	.	.	PUNCT
ap-7668	249	1	[	[	X
ap-7668	249	2	10	10	NUM
ap-7668	249	3	]	]	X
ap-7668	249	4	l.	l.	PROPN
ap-7668	249	5	m.	m.	PROPN
ap-7668	249	6	delves	delf	NOUN
ap-7668	249	7	.	.	PUNCT
ap-7668	250	1	tertiary	tertiary	ADJ
ap-7668	250	2	and	and	CCONJ
ap-7668	250	3	general	general	ADJ
ap-7668	250	4	-	-	PUNCT
ap-7668	250	5	order	order	NOUN
ap-7668	250	6	collisions	collision	NOUN
ap-7668	250	7	(	(	PUNCT
ap-7668	250	8	ii	ii	NOUN
ap-7668	250	9	)	)	PUNCT
ap-7668	250	10	.	.	PUNCT
ap-7668	251	1	nuclear	nuclear	ADJ
ap-7668	251	2	physics	physics	PROPN
ap-7668	251	3	20:275–308	20:275–308	NUM
ap-7668	251	4	,	,	PUNCT
ap-7668	251	5	1960	1960	NUM
ap-7668	251	6	.	.	PUNCT
ap-7668	252	1	https://doi.org/10.1016/0029-5582(60)90174-7	https://doi.org/10.1016/0029-5582(60)90174-7	PROPN
ap-7668	252	2	.	.	PUNCT
ap-7668	253	1	[	[	X
ap-7668	253	2	11	11	NUM
ap-7668	253	3	]	]	X
ap-7668	253	4	c.	c.	PROPN
ap-7668	253	5	m.	m.	PROPN
ap-7668	253	6	bender	bender	PROPN
ap-7668	253	7	,	,	PUNCT
ap-7668	253	8	j.-h	j.-h	PROPN
ap-7668	253	9	.	.	PUNCT
ap-7668	254	1	chen	chen	PROPN
ap-7668	254	2	,	,	PUNCT
ap-7668	254	3	d.	d.	PROPN
ap-7668	254	4	w.	w.	PROPN
ap-7668	254	5	darg	darg	PROPN
ap-7668	254	6	,	,	PUNCT
ap-7668	254	7	k.	k.	PROPN
ap-7668	254	8	a.	a.	PROPN
ap-7668	254	9	milton	milton	PROPN
ap-7668	254	10	.	.	PUNCT
ap-7668	255	1	classical	classical	ADJ
ap-7668	255	2	trajectories	trajectory	NOUN
ap-7668	255	3	for	for	ADP
ap-7668	255	4	complex	complex	ADJ
ap-7668	255	5	hamiltonians	hamiltonian	NOUN
ap-7668	255	6	.	.	PUNCT
ap-7668	256	1	journal	journal	PROPN
ap-7668	256	2	of	of	ADP
ap-7668	256	3	physics	physics	PROPN
ap-7668	256	4	a	a	PRON
ap-7668	256	5	:	:	PUNCT
ap-7668	256	6	mathematical	mathematical	ADJ
ap-7668	256	7	and	and	CCONJ
ap-7668	256	8	general	general	ADJ
ap-7668	256	9	39(16):4219–4238	39(16):4219–4238	NUM
ap-7668	256	10	,	,	PUNCT
ap-7668	256	11	2006	2006	NUM
ap-7668	256	12	.	.	PUNCT
ap-7668	257	1	https://doi.org/10.1088/0305-4470/39/16/009	https://doi.org/10.1088/0305-4470/39/16/009	X
ap-7668	257	2	.	.	PUNCT
ap-7668	258	1	[	[	X
ap-7668	258	2	12	12	NUM
ap-7668	258	3	]	]	X
ap-7668	258	4	c.	c.	PROPN
ap-7668	258	5	m.	m.	PROPN
ap-7668	258	6	bender	bender	PROPN
ap-7668	258	7	,	,	PUNCT
ap-7668	258	8	s.	s.	PROPN
ap-7668	258	9	boettcher	boettcher	PROPN
ap-7668	258	10	.	.	PUNCT
ap-7668	259	1	real	real	ADJ
ap-7668	259	2	spectra	spectra	NOUN
ap-7668	259	3	in	in	ADP
ap-7668	259	4	non	non	ADJ
ap-7668	259	5	-	-	ADJ
ap-7668	259	6	hermitian	hermitian	ADJ
ap-7668	259	7	hamiltonians	hamiltonian	NOUN
ap-7668	259	8	having	have	VERB
ap-7668	259	9	pt	pt	PRON
ap-7668	259	10	symmetry	symmetry	NOUN
ap-7668	259	11	.	.	PUNCT
ap-7668	260	1	physical	physical	PROPN
ap-7668	260	2	review	review	PROPN
ap-7668	260	3	letters	letter	NOUN
ap-7668	260	4	80(24):5243–5246	80(24):5243–5246	NUM
ap-7668	260	5	,	,	PUNCT
ap-7668	260	6	1998	1998	NUM
ap-7668	260	7	.	.	PUNCT
ap-7668	261	1	https://doi.org/10.1103/physrevlett.80.5243	https://doi.org/10.1103/physrevlett.80.5243	NOUN
ap-7668	261	2	.	.	PUNCT
ap-7668	262	1	[	[	X
ap-7668	262	2	13	13	NUM
ap-7668	262	3	]	]	PUNCT
ap-7668	262	4	p.	p.	PROPN
ap-7668	262	5	dorey	dorey	PROPN
ap-7668	262	6	,	,	PUNCT
ap-7668	262	7	c.	c.	PROPN
ap-7668	262	8	dunning	dunning	NOUN
ap-7668	262	9	,	,	PUNCT
ap-7668	262	10	r.	r.	NOUN
ap-7668	262	11	tateo	tateo	NOUN
ap-7668	262	12	.	.	PUNCT
ap-7668	263	1	supersymmetry	supersymmetry	NOUN
ap-7668	263	2	and	and	CCONJ
ap-7668	263	3	the	the	DET
ap-7668	263	4	spontaneous	spontaneous	ADJ
ap-7668	263	5	breakdown	breakdown	NOUN
ap-7668	263	6	of	of	ADP
ap-7668	263	7	pt	pt	NOUN
ap-7668	263	8	symmetry	symmetry	NOUN
ap-7668	263	9	.	.	PUNCT
ap-7668	264	1	journal	journal	PROPN
ap-7668	264	2	of	of	ADP
ap-7668	264	3	physics	physics	PROPN
ap-7668	264	4	a	a	PRON
ap-7668	264	5	:	:	PUNCT
ap-7668	264	6	mathematical	mathematical	ADJ
ap-7668	264	7	and	and	CCONJ
ap-7668	264	8	general	general	ADJ
ap-7668	264	9	34(28):l391	34(28):l391	NUM
ap-7668	264	10	,	,	PUNCT
ap-7668	264	11	2001	2001	NUM
ap-7668	264	12	.	.	PUNCT
ap-7668	265	1	https://doi.org/10.1088/0305-4470/34/28/102	https://doi.org/10.1088/0305-4470/34/28/102	PROPN
ap-7668	265	2	.	.	PUNCT
ap-7668	266	1	55	55	NUM
ap-7668	266	2	https://doi.org/10.1016/0029-5582(58)90372-9	https://doi.org/10.1016/0029-5582(58)90372-9	NOUN
ap-7668	266	3	https://doi.org/10.1063/1.1724275	https://doi.org/10.1063/1.1724275	PROPN
ap-7668	266	4	https://doi.org/10.1063/1.4994397	https://doi.org/10.1063/1.4994397	X
ap-7668	266	5	https://doi.org/10.1088/1751-8121/aa6cc2	https://doi.org/10.1088/1751-8121/aa6cc2	X
ap-7668	266	6	https://doi.org/10.1088/1751-8121/aabb10	https://doi.org/10.1088/1751-8121/aabb10	NOUN
ap-7668	266	7	http://arxiv.org/abs/0810.2210v2	http://arxiv.org/abs/0810.2210v2	NOUN
ap-7668	266	8	https://doi.org/10.1007/bf01466727	https://doi.org/10.1007/bf01466727	NOUN
ap-7668	266	9	https://doi.org/10.1016/j.physrep.2016.06.002	https://doi.org/10.1016/j.physrep.2016.06.002	NOUN
ap-7668	266	10	https://doi.org/10.1016/0029-5582(60)90174-7	https://doi.org/10.1016/0029-5582(60)90174-7	PROPN
ap-7668	266	11	https://doi.org/10.1088/0305-4470/39/16/009	https://doi.org/10.1088/0305-4470/39/16/009	NOUN
ap-7668	266	12	https://doi.org/10.1103/physrevlett.80.5243	https://doi.org/10.1103/physrevlett.80.5243	VERB
ap-7668	266	13	https://doi.org/10.1088/0305-4470/34/28/102	https://doi.org/10.1088/0305-4470/34/28/102	PROPN
ap-7668	266	14	acta	acta	PROPN
ap-7668	266	15	polytechnica	polytechnica	PROPN
ap-7668	266	16	62(1):50–55	62(1):50–55	ADP
ap-7668	266	17	,	,	PUNCT
ap-7668	266	18	2022	2022	NUM
ap-7668	266	19	1	1	NUM
ap-7668	266	20	introduction	introduction	NOUN
ap-7668	266	21	2	2	NUM
ap-7668	266	22	generalities	generality	NOUN
ap-7668	266	23	2.1	2.1	NUM
ap-7668	266	24	case	case	NOUN
ap-7668	266	25	of	of	ADP
ap-7668	266	26	identical	identical	ADJ
ap-7668	266	27	particles	particle	NOUN
ap-7668	266	28	:	:	PUNCT
ap-7668	266	29	-representation	-representation	NOUN
ap-7668	266	30	3	3	NUM
ap-7668	266	31	laplace	laplace	NOUN
ap-7668	266	32	-	-	PUNCT
ap-7668	266	33	beltrami	beltrami	NOUN
ap-7668	266	34	operator	operator	NOUN
ap-7668	266	35	4	4	NUM
ap-7668	266	36	three	three	NUM
ap-7668	266	37	body	body	NOUN
ap-7668	266	38	harmonic	harmonic	ADJ
ap-7668	266	39	oscillator	oscillator	NOUN
ap-7668	266	40	system	system	NOUN
ap-7668	266	41	4.1	4.1	NUM
ap-7668	266	42	solution	solution	NOUN
ap-7668	266	43	for	for	ADP
ap-7668	266	44	the	the	DET
ap-7668	266	45	ground	ground	NOUN
ap-7668	266	46	state	state	NOUN
ap-7668	266	47	5	5	NUM
ap-7668	266	48	lie	lie	NOUN
ap-7668	266	49	algebraic	algebraic	ADJ
ap-7668	266	50	structure	structure	NOUN
ap-7668	266	51	6	6	NUM
ap-7668	266	52	relation	relation	NOUN
ap-7668	266	53	with	with	ADP
ap-7668	266	54	the	the	DET
ap-7668	266	55	jacobi	jacobi	PROPN
ap-7668	266	56	oscillator	oscillator	NOUN
ap-7668	266	57	6.1	6.1	NUM
ap-7668	266	58	identical	identical	ADJ
ap-7668	266	59	particles	particle	NOUN
ap-7668	266	60	:	:	PUNCT
ap-7668	266	61	hyperradious	hyperradious	ADJ
ap-7668	266	62	6.2	6.2	NUM
ap-7668	266	63	arbitrary	arbitrary	ADJ
ap-7668	266	64	masses	masse	NOUN
ap-7668	266	65	:	:	PUNCT
ap-7668	266	66	moment	moment	NOUN
ap-7668	266	67	of	of	ADP
ap-7668	266	68	inertia	inertia	NOUN
ap-7668	266	69	7	7	NUM
ap-7668	266	70	generalized	generalize	VERB
ap-7668	266	71	three	three	NUM
ap-7668	266	72	body	body	NOUN
ap-7668	266	73	harmonic	harmonic	ADJ
ap-7668	266	74	oscillator	oscillator	NOUN
ap-7668	266	75	system	system	NOUN
ap-7668	266	76	7.1	7.1	NUM
ap-7668	266	77	identical	identical	ADJ
ap-7668	266	78	particles	particle	NOUN
ap-7668	266	79	7.1.1	7.1.1	NUM
ap-7668	266	80	ground	ground	NOUN
ap-7668	266	81	state	state	NOUN
ap-7668	266	82	7.1.2	7.1.2	NUM
ap-7668	266	83	first	first	ADV
ap-7668	266	84	excited	excited	ADJ
ap-7668	266	85	state	state	NOUN
ap-7668	266	86	8	8	NUM
ap-7668	266	87	conclusions	conclusion	NOUN
ap-7668	266	88	acknowledgements	acknowledgement	NOUN
ap-7668	266	89	references	reference	NOUN