id	sid	tid	token	lemma	pos
ap-10691	1	1	acta	acta	PROPN
ap-10691	1	2	polytechnica	polytechnica	PROPN
ap-10691	1	3	https://doi.org/10.14311/ap.2025.65.0520	https://doi.org/10.14311/ap.2025.65.0520	PROPN
ap-10691	1	4	acta	acta	PROPN
ap-10691	1	5	polytechnica	polytechnica	PROPN
ap-10691	1	6	65(5):520–533	65(5):520–533	PROPN
ap-10691	1	7	,	,	PUNCT
ap-10691	1	8	2025	2025	NUM
ap-10691	1	9	©	©	ADP
ap-10691	1	10	2025	2025	NUM
ap-10691	1	11	the	the	DET
ap-10691	1	12	author(s	author(s	NOUN
ap-10691	1	13	)	)	PUNCT
ap-10691	1	14	.	.	PUNCT
ap-10691	2	1	licensed	license	VERB
ap-10691	2	2	under	under	ADP
ap-10691	2	3	a	a	DET
ap-10691	2	4	cc	cc	NOUN
ap-10691	2	5	-	-	PUNCT
ap-10691	2	6	by	by	ADP
ap-10691	2	7	4.0	4.0	NUM
ap-10691	2	8	licence	licence	NOUN
ap-10691	2	9	published	publish	VERB
ap-10691	2	10	by	by	ADP
ap-10691	2	11	the	the	DET
ap-10691	2	12	czech	czech	PROPN
ap-10691	2	13	technical	technical	PROPN
ap-10691	2	14	university	university	PROPN
ap-10691	2	15	in	in	ADP
ap-10691	2	16	prague	prague	PROPN
ap-10691	2	17	classical	classical	ADJ
ap-10691	2	18	and	and	CCONJ
ap-10691	2	19	quantum	quantum	ADJ
ap-10691	2	20	superintegrable	superintegrable	ADJ
ap-10691	2	21	systems	system	NOUN
ap-10691	2	22	on	on	ADP
ap-10691	2	23	the	the	DET
ap-10691	2	24	sphere	sphere	NOUN
ap-10691	2	25	and	and	CCONJ
ap-10691	2	26	the	the	DET
ap-10691	2	27	hyperbolic	hyperbolic	ADJ
ap-10691	2	28	2	2	NUM
ap-10691	2	29	-	-	PUNCT
ap-10691	2	30	space	space	NOUN
ap-10691	2	31	mariano	mariano	PROPN
ap-10691	2	32	a.	a.	PROPN
ap-10691	2	33	del	del	PROPN
ap-10691	2	34	olmoa,∗	olmoa,∗	PROPN
ap-10691	2	35	,	,	PUNCT
ap-10691	2	36	álvaro	álvaro	PROPN
ap-10691	2	37	romaniegab	romaniegab	VERB
ap-10691	2	38	a	a	DET
ap-10691	2	39	universidad	universidad	PROPN
ap-10691	2	40	de	de	PROPN
ap-10691	2	41	valladolid	valladolid	PROPN
ap-10691	2	42	,	,	PUNCT
ap-10691	2	43	departamento	departamento	PROPN
ap-10691	2	44	de	de	PROPN
ap-10691	2	45	física	física	PROPN
ap-10691	2	46	teórica	teórica	PROPN
ap-10691	2	47	,	,	PUNCT
ap-10691	2	48	atómica	atómica	PROPN
ap-10691	2	49	y	y	PROPN
ap-10691	2	50	optica	optica	PROPN
ap-10691	2	51	and	and	CCONJ
ap-10691	2	52	imuva	imuva	PROPN
ap-10691	2	53	,	,	PUNCT
ap-10691	2	54	paseo	paseo	PROPN
ap-10691	2	55	belén	belén	PROPN
ap-10691	2	56	7	7	NUM
ap-10691	2	57	,	,	PUNCT
ap-10691	2	58	47011	47011	NUM
ap-10691	2	59	valladolid	valladolid	PROPN
ap-10691	2	60	,	,	PUNCT
ap-10691	2	61	spain	spain	PROPN
ap-10691	2	62	b	b	PROPN
ap-10691	2	63	universidad	universidad	PROPN
ap-10691	2	64	de	de	PROPN
ap-10691	2	65	las	las	PROPN
ap-10691	2	66	hespérides	hespéride	NOUN
ap-10691	2	67	,	,	PUNCT
ap-10691	2	68	c.	c.	PROPN
ap-10691	2	69	los	los	PROPN
ap-10691	2	70	balcones	balcones	PROPN
ap-10691	2	71	10	10	NUM
ap-10691	2	72	,	,	PUNCT
ap-10691	2	73	35001	35001	NUM
ap-10691	2	74	las	las	PROPN
ap-10691	2	75	palmas	palmas	PROPN
ap-10691	2	76	de	de	PROPN
ap-10691	2	77	gran	gran	PROPN
ap-10691	2	78	canaria	canaria	PROPN
ap-10691	2	79	,	,	PUNCT
ap-10691	2	80	spain	spain	PROPN
ap-10691	2	81	∗	∗	NOUN
ap-10691	2	82	corresponding	correspond	VERB
ap-10691	2	83	author	author	NOUN
ap-10691	2	84	:	:	PUNCT
ap-10691	2	85	marianoantonio.olmo@uva.es	marianoantonio.olmo@uva.es	PROPN
ap-10691	2	86	abstract	abstract	NOUN
ap-10691	2	87	.	.	PUNCT
ap-10691	3	1	we	we	PRON
ap-10691	3	2	present	present	VERB
ap-10691	3	3	two	two	NUM
ap-10691	3	4	superintegrable	superintegrable	ADJ
ap-10691	3	5	hamiltonian	hamiltonian	ADJ
ap-10691	3	6	systems	system	NOUN
ap-10691	3	7	in	in	ADP
ap-10691	3	8	two	two	NUM
ap-10691	3	9	dimensions	dimension	NOUN
ap-10691	3	10	,	,	PUNCT
ap-10691	3	11	defined	define	VERB
ap-10691	3	12	on	on	ADP
ap-10691	3	13	the	the	DET
ap-10691	3	14	sphere	sphere	NOUN
ap-10691	3	15	and	and	CCONJ
ap-10691	3	16	on	on	ADP
ap-10691	3	17	the	the	DET
ap-10691	3	18	hyperbolic	hyperbolic	ADJ
ap-10691	3	19	plane	plane	NOUN
ap-10691	3	20	.	.	PUNCT
ap-10691	4	1	these	these	DET
ap-10691	4	2	systems	system	NOUN
ap-10691	4	3	are	be	AUX
ap-10691	4	4	generalised	generalise	VERB
ap-10691	4	5	à	à	X
ap-10691	4	6	la	la	DET
ap-10691	4	7	tremblay	tremblay	NOUN
ap-10691	4	8	-	-	PUNCT
ap-10691	4	9	turbiner	turbiner	NOUN
ap-10691	4	10	-	-	PUNCT
ap-10691	4	11	winternitz	winternitz	NOUN
ap-10691	4	12	(	(	PUNCT
ap-10691	4	13	ttw	ttw	PROPN
ap-10691	4	14	)	)	PUNCT
ap-10691	4	15	,	,	PUNCT
ap-10691	4	16	involving	involve	VERB
ap-10691	4	17	the	the	DET
ap-10691	4	18	introduction	introduction	NOUN
ap-10691	4	19	of	of	ADP
ap-10691	4	20	a	a	DET
ap-10691	4	21	real	real	ADJ
ap-10691	4	22	parameter	parameter	NOUN
ap-10691	5	1	k	k	PROPN
ap-10691	5	2	>	>	X
ap-10691	5	3	0	0	PROPN
ap-10691	5	4	,	,	PUNCT
ap-10691	5	5	with	with	ADP
ap-10691	5	6	the	the	DET
ap-10691	5	7	aim	aim	NOUN
ap-10691	5	8	of	of	ADP
ap-10691	5	9	extending	extend	VERB
ap-10691	5	10	superintegrable	superintegrable	ADJ
ap-10691	5	11	hamiltonian	hamiltonian	ADJ
ap-10691	5	12	systems	system	NOUN
ap-10691	5	13	to	to	ADP
ap-10691	5	14	curved	curved	ADJ
ap-10691	5	15	spaces	space	NOUN
ap-10691	5	16	in	in	ADP
ap-10691	5	17	a	a	DET
ap-10691	5	18	way	way	NOUN
ap-10691	5	19	similar	similar	ADJ
ap-10691	5	20	to	to	ADP
ap-10691	5	21	the	the	DET
ap-10691	5	22	ttw	ttw	PROPN
ap-10691	5	23	system	system	NOUN
ap-10691	5	24	on	on	ADP
ap-10691	5	25	the	the	DET
ap-10691	5	26	plane	plane	NOUN
ap-10691	5	27	.	.	PUNCT
ap-10691	6	1	we	we	PRON
ap-10691	6	2	carry	carry	VERB
ap-10691	6	3	out	out	ADP
ap-10691	6	4	both	both	CCONJ
ap-10691	6	5	classical	classical	ADJ
ap-10691	6	6	and	and	CCONJ
ap-10691	6	7	quantum	quantum	ADJ
ap-10691	6	8	analyses	analysis	NOUN
ap-10691	6	9	of	of	ADP
ap-10691	6	10	these	these	DET
ap-10691	6	11	new	new	ADJ
ap-10691	6	12	systems	system	NOUN
ap-10691	6	13	.	.	PUNCT
ap-10691	7	1	we	we	PRON
ap-10691	7	2	prove	prove	VERB
ap-10691	7	3	that	that	SCONJ
ap-10691	7	4	the	the	DET
ap-10691	7	5	superintegrability	superintegrability	NOUN
ap-10691	7	6	of	of	ADP
ap-10691	7	7	the	the	DET
ap-10691	7	8	initial	initial	ADJ
ap-10691	7	9	systems	system	NOUN
ap-10691	7	10	(	(	PUNCT
ap-10691	7	11	i.e.	i.e.	X
ap-10691	7	12	when	when	SCONJ
ap-10691	7	13	k	k	PROPN
ap-10691	7	14	=	=	SYM
ap-10691	7	15	1	1	X
ap-10691	7	16	)	)	PUNCT
ap-10691	7	17	is	be	AUX
ap-10691	7	18	preserved	preserve	VERB
ap-10691	7	19	when	when	SCONJ
ap-10691	7	20	k	k	PROPN
ap-10691	7	21	is	be	AUX
ap-10691	7	22	rational	rational	ADJ
ap-10691	7	23	,	,	PUNCT
ap-10691	7	24	as	as	ADP
ap-10691	7	25	in	in	ADP
ap-10691	7	26	the	the	DET
ap-10691	7	27	ttw	ttw	PROPN
ap-10691	7	28	case	case	NOUN
ap-10691	7	29	.	.	PUNCT
ap-10691	8	1	a	a	DET
ap-10691	8	2	detailed	detailed	ADJ
ap-10691	8	3	study	study	NOUN
ap-10691	8	4	of	of	ADP
ap-10691	8	5	their	their	PRON
ap-10691	8	6	classical	classical	ADJ
ap-10691	8	7	counterparts	counterpart	NOUN
ap-10691	8	8	and	and	CCONJ
ap-10691	8	9	trajectories	trajectory	NOUN
ap-10691	8	10	is	be	AUX
ap-10691	8	11	also	also	ADV
ap-10691	8	12	included	include	VERB
ap-10691	8	13	.	.	PUNCT
ap-10691	9	1	keywords	keyword	NOUN
ap-10691	9	2	:	:	PUNCT
ap-10691	9	3	superintegrable	superintegrable	ADJ
ap-10691	9	4	systems	system	NOUN
ap-10691	9	5	,	,	PUNCT
ap-10691	9	6	factorisation	factorisation	NOUN
ap-10691	9	7	of	of	ADP
ap-10691	9	8	hamiltonians	hamiltonian	NOUN
ap-10691	9	9	,	,	PUNCT
ap-10691	9	10	tremblay	tremblay	NOUN
ap-10691	9	11	-	-	PUNCT
ap-10691	9	12	turbiner	turbiner	NOUN
ap-10691	9	13	-	-	PUNCT
ap-10691	9	14	winternitz	winternitz	NOUN
ap-10691	9	15	hamiltonan	hamiltonan	PROPN
ap-10691	9	16	systems	system	NOUN
ap-10691	9	17	.	.	PUNCT
ap-10691	10	1	1	1	X
ap-10691	10	2	.	.	X
ap-10691	10	3	introduction	introduction	NOUN
ap-10691	10	4	in	in	ADP
ap-10691	10	5	[	[	X
ap-10691	10	6	1	1	NUM
ap-10691	10	7	]	]	PUNCT
ap-10691	10	8	,	,	PUNCT
ap-10691	10	9	a	a	DET
ap-10691	10	10	family	family	NOUN
ap-10691	10	11	of	of	ADP
ap-10691	10	12	superintegrable	superintegrable	ADJ
ap-10691	10	13	systems	system	NOUN
ap-10691	10	14	defined	define	VERB
ap-10691	10	15	on	on	ADP
ap-10691	10	16	a	a	DET
ap-10691	10	17	homogeneous	homogeneous	ADJ
ap-10691	10	18	space	space	NOUN
ap-10691	10	19	of	of	ADP
ap-10691	10	20	the	the	DET
ap-10691	10	21	pseudo	pseudo	NOUN
ap-10691	10	22	-	-	ADJ
ap-10691	10	23	orthogonal	orthogonal	ADJ
ap-10691	10	24	lie	lie	NOUN
ap-10691	10	25	group	group	NOUN
ap-10691	10	26	o(p	o(p	PROPN
ap-10691	10	27	,	,	PUNCT
ap-10691	10	28	q	q	NOUN
ap-10691	10	29	)	)	PUNCT
ap-10691	10	30	was	be	AUX
ap-10691	10	31	introduced	introduce	VERB
ap-10691	10	32	.	.	PUNCT
ap-10691	11	1	this	this	DET
ap-10691	11	2	work	work	NOUN
ap-10691	11	3	increased	increase	VERB
ap-10691	11	4	the	the	DET
ap-10691	11	5	number	number	NOUN
ap-10691	11	6	of	of	ADP
ap-10691	11	7	known	know	VERB
ap-10691	11	8	superintegrable	superintegrable	ADJ
ap-10691	11	9	systems	system	NOUN
ap-10691	11	10	at	at	ADP
ap-10691	11	11	the	the	DET
ap-10691	11	12	time	time	NOUN
ap-10691	11	13	[	[	X
ap-10691	11	14	2	2	NUM
ap-10691	11	15	]	]	PUNCT
ap-10691	11	16	.	.	PUNCT
ap-10691	12	1	this	this	DET
ap-10691	12	2	family	family	NOUN
ap-10691	12	3	of	of	ADP
ap-10691	12	4	superintegrable	superintegrable	ADJ
ap-10691	12	5	hamiltonian	hamiltonian	ADJ
ap-10691	12	6	systems	system	NOUN
ap-10691	12	7	(	(	PUNCT
ap-10691	12	8	shss	shss	PROPN
ap-10691	12	9	)	)	PUNCT
ap-10691	12	10	has	have	AUX
ap-10691	12	11	since	since	ADV
ap-10691	12	12	been	be	AUX
ap-10691	12	13	studied	study	VERB
ap-10691	12	14	from	from	ADP
ap-10691	12	15	various	various	ADJ
ap-10691	12	16	perspectives	perspective	NOUN
ap-10691	12	17	[	[	X
ap-10691	12	18	3–8	3–8	NUM
ap-10691	12	19	]	]	X
ap-10691	12	20	.	.	PUNCT
ap-10691	13	1	in	in	ADP
ap-10691	13	2	2010	2010	NUM
ap-10691	13	3	,	,	PUNCT
ap-10691	13	4	tremblay	tremblay	NOUN
ap-10691	13	5	,	,	PUNCT
ap-10691	13	6	turbiner	turbiner	NOUN
ap-10691	13	7	,	,	PUNCT
ap-10691	13	8	and	and	CCONJ
ap-10691	13	9	winternitz	winternitz	PROPN
ap-10691	13	10	introduced	introduce	VERB
ap-10691	13	11	the	the	DET
ap-10691	13	12	well	well	ADV
ap-10691	13	13	-	-	PUNCT
ap-10691	13	14	known	know	VERB
ap-10691	13	15	ttw	ttw	PROPN
ap-10691	13	16	integrable	integrable	ADJ
ap-10691	13	17	system	system	NOUN
ap-10691	13	18	[	[	X
ap-10691	13	19	9	9	NUM
ap-10691	13	20	,	,	PUNCT
ap-10691	13	21	10	10	NUM
ap-10691	13	22	]	]	PUNCT
ap-10691	13	23	,	,	PUNCT
ap-10691	13	24	which	which	PRON
ap-10691	13	25	generalises	generalise	VERB
ap-10691	13	26	the	the	DET
ap-10691	13	27	smorodinsky	smorodinsky	PROPN
ap-10691	13	28	-	-	PUNCT
ap-10691	13	29	winternitz	winternitz	ADJ
ap-10691	13	30	superintegrable	superintegrable	ADJ
ap-10691	13	31	system	system	NOUN
ap-10691	13	32	[	[	X
ap-10691	13	33	11	11	NUM
ap-10691	13	34	,	,	PUNCT
ap-10691	13	35	12	12	NUM
ap-10691	13	36	]	]	PUNCT
ap-10691	13	37	.	.	PUNCT
ap-10691	14	1	its	its	PRON
ap-10691	14	2	introduction	introduction	NOUN
ap-10691	14	3	renewed	renew	VERB
ap-10691	14	4	the	the	DET
ap-10691	14	5	scientific	scientific	ADJ
ap-10691	14	6	community	community	NOUN
ap-10691	14	7	’s	’s	PART
ap-10691	14	8	interest	interest	NOUN
ap-10691	14	9	in	in	ADP
ap-10691	14	10	superintegrable	superintegrable	ADJ
ap-10691	14	11	systems	system	NOUN
ap-10691	14	12	,	,	PUNCT
ap-10691	14	13	and	and	CCONJ
ap-10691	14	14	the	the	DET
ap-10691	14	15	number	number	NOUN
ap-10691	14	16	of	of	ADP
ap-10691	14	17	new	new	ADJ
ap-10691	14	18	shss	shss	PROPN
ap-10691	14	19	has	have	AUX
ap-10691	14	20	steadily	steadily	ADV
ap-10691	14	21	grown	grow	VERB
ap-10691	14	22	since	since	SCONJ
ap-10691	14	23	then	then	ADV
ap-10691	14	24	[	[	X
ap-10691	14	25	13–18	13–18	NUM
ap-10691	14	26	]	]	PUNCT
ap-10691	14	27	.	.	PUNCT
ap-10691	15	1	the	the	DET
ap-10691	15	2	classical	classical	ADJ
ap-10691	15	3	ttw	ttw	NOUN
ap-10691	15	4	system	system	NOUN
ap-10691	15	5	[	[	X
ap-10691	15	6	9	9	NUM
ap-10691	15	7	,	,	PUNCT
ap-10691	15	8	10	10	NUM
ap-10691	15	9	]	]	PUNCT
ap-10691	15	10	is	be	AUX
ap-10691	15	11	characterised	characterise	VERB
ap-10691	15	12	by	by	ADP
ap-10691	15	13	the	the	DET
ap-10691	15	14	hamiltonian	hamiltonian	NOUN
ap-10691	15	15	:	:	PUNCT
ap-10691	15	16	h	h	NOUN
ap-10691	15	17	=	=	NOUN
ap-10691	15	18	p2	p2	PROPN
ap-10691	15	19	r	r	NOUN
ap-10691	15	20	+	+	CCONJ
ap-10691	15	21	1	1	NUM
ap-10691	15	22	r2	r2	NOUN
ap-10691	15	23	p	p	NOUN
ap-10691	15	24	2	2	NUM
ap-10691	15	25	ϕ	ϕ	NOUN
ap-10691	15	26	+	+	NOUN
ap-10691	15	27	ωr2	ωr2	ADJ
ap-10691	15	28	+	+	CCONJ
ap-10691	15	29	k2	k2	ADJ
ap-10691	15	30	r2	r2	PROPN
ap-10691	15	31	(	(	PUNCT
ap-10691	15	32	a	a	DET
ap-10691	15	33	cos2	cos2	NOUN
ap-10691	16	1	kϕ	kϕ	INTJ
ap-10691	16	2	+	+	CCONJ
ap-10691	16	3	b	b	PROPN
ap-10691	16	4	sin2	sin2	NOUN
ap-10691	16	5	kϕ	kϕ	PROPN
ap-10691	16	6	)	)	PUNCT
ap-10691	16	7	,	,	PUNCT
ap-10691	16	8	(	(	PUNCT
ap-10691	16	9	1	1	X
ap-10691	16	10	)	)	PUNCT
ap-10691	16	11	where	where	SCONJ
ap-10691	16	12	r	r	NOUN
ap-10691	16	13	∈	∈	PROPN
ap-10691	16	14	(	(	PUNCT
ap-10691	16	15	0,∞	0,∞	NOUN
ap-10691	16	16	)	)	PUNCT
ap-10691	16	17	,	,	PUNCT
ap-10691	17	1	0	0	PUNCT
ap-10691	17	2	<	<	X
ap-10691	17	3	ϕ	ϕ	X
ap-10691	17	4	<	<	X
ap-10691	17	5	π	π	PROPN
ap-10691	17	6	2k	2k	NUM
ap-10691	17	7	;	;	PUNCT
ap-10691	17	8	k	k	X
ap-10691	17	9	,	,	PUNCT
ap-10691	17	10	ω	ω	PROPN
ap-10691	17	11	,	,	PUNCT
ap-10691	17	12	a	a	DET
ap-10691	17	13	,	,	PUNCT
ap-10691	17	14	b	b	NOUN
ap-10691	17	15	are	be	AUX
ap-10691	17	16	real	real	ADJ
ap-10691	17	17	numbers	number	NOUN
ap-10691	17	18	with	with	ADP
ap-10691	17	19	k	k	PROPN
ap-10691	17	20	,	,	PUNCT
ap-10691	17	21	ω	ω	NOUN
ap-10691	17	22	=	=	NOUN
ap-10691	17	23	̸	̸	NUM
ap-10691	17	24	0	0	NUM
ap-10691	17	25	,	,	PUNCT
ap-10691	17	26	and	and	CCONJ
ap-10691	17	27	a	a	DET
ap-10691	17	28	,	,	PUNCT
ap-10691	17	29	b	b	X
ap-10691	17	30	>	>	X
ap-10691	17	31	0	0	NUM
ap-10691	17	32	,	,	PUNCT
ap-10691	17	33	respectively	respectively	ADV
ap-10691	17	34	.	.	PUNCT
ap-10691	18	1	the	the	DET
ap-10691	18	2	quantum	quantum	ADJ
ap-10691	18	3	version	version	NOUN
ap-10691	18	4	of	of	ADP
ap-10691	18	5	this	this	DET
ap-10691	18	6	system	system	NOUN
ap-10691	18	7	is	be	AUX
ap-10691	18	8	:	:	PUNCT
ap-10691	18	9	h	h	NOUN
ap-10691	18	10	=	=	PUNCT
ap-10691	18	11	−∂2	−∂2	PROPN
ap-10691	18	12	r	r	NOUN
ap-10691	18	13	−	−	NUM
ap-10691	18	14	1	1	NUM
ap-10691	18	15	r	r	NOUN
ap-10691	18	16	∂r	∂r	NOUN
ap-10691	19	1	+	+	NUM
ap-10691	19	2	ωr2	ωr2	NOUN
ap-10691	20	1	+	+	ADJ
ap-10691	20	2	k2	k2	ADJ
ap-10691	20	3	r2	r2	PROPN
ap-10691	20	4	(	(	PUNCT
ap-10691	20	5	−	−	PROPN
ap-10691	20	6	1	1	NUM
ap-10691	20	7	k2	k2	NOUN
ap-10691	20	8	∂	∂	NOUN
ap-10691	20	9	2	2	NUM
ap-10691	20	10	ϕ	ϕ	NOUN
ap-10691	20	11	+	+	CCONJ
ap-10691	20	12	a	a	DET
ap-10691	20	13	cos2	cos2	NOUN
ap-10691	20	14	kϕ	kϕ	NOUN
ap-10691	20	15	+	+	CCONJ
ap-10691	20	16	b	b	PROPN
ap-10691	20	17	sin2	sin2	NOUN
ap-10691	20	18	kϕ	kϕ	PROPN
ap-10691	20	19	)	)	PUNCT
ap-10691	20	20	.	.	PUNCT
ap-10691	21	1	(	(	PUNCT
ap-10691	21	2	2	2	X
ap-10691	21	3	)	)	PUNCT
ap-10691	21	4	now	now	ADV
ap-10691	21	5	,	,	PUNCT
ap-10691	21	6	by	by	ADP
ap-10691	21	7	making	make	VERB
ap-10691	21	8	the	the	DET
ap-10691	21	9	change	change	NOUN
ap-10691	21	10	of	of	ADP
ap-10691	21	11	variables	variable	NOUN
ap-10691	21	12	k	k	PROPN
ap-10691	21	13	ϕ	ϕ	PROPN
ap-10691	21	14	=	=	SYM
ap-10691	21	15	θ	θ	PROPN
ap-10691	21	16	,	,	PUNCT
ap-10691	21	17	and	and	CCONJ
ap-10691	21	18	replacing	replace	VERB
ap-10691	21	19	a	a	PRON
ap-10691	21	20	and	and	CCONJ
ap-10691	21	21	b	b	NOUN
ap-10691	21	22	with	with	ADP
ap-10691	21	23	α2	α2	ADJ
ap-10691	21	24	−	−	PROPN
ap-10691	21	25	1	1	NUM
ap-10691	21	26	4	4	NUM
ap-10691	21	27	and	and	CCONJ
ap-10691	21	28	β2	β2	VERB
ap-10691	21	29	−	−	PROPN
ap-10691	21	30	1	1	NUM
ap-10691	21	31	4	4	NUM
ap-10691	21	32	,	,	PUNCT
ap-10691	21	33	respectively	respectively	ADV
ap-10691	21	34	,	,	PUNCT
ap-10691	21	35	(	(	PUNCT
ap-10691	21	36	as	as	ADP
ap-10691	21	37	in	in	ADP
ap-10691	21	38	[	[	X
ap-10691	21	39	19	19	NUM
ap-10691	21	40	]	]	NUM
ap-10691	21	41	)	)	PUNCT
ap-10691	21	42	,	,	PUNCT
ap-10691	21	43	the	the	DET
ap-10691	21	44	hamiltonian	hamiltonian	NOUN
ap-10691	21	45	(	(	PUNCT
ap-10691	21	46	2	2	X
ap-10691	21	47	)	)	PUNCT
ap-10691	21	48	becomes	become	VERB
ap-10691	21	49	:	:	PUNCT
ap-10691	21	50	h	h	NOUN
ap-10691	21	51	=	=	PUNCT
ap-10691	21	52	−∂2	−∂2	PROPN
ap-10691	21	53	r	r	NOUN
ap-10691	21	54	−	−	NUM
ap-10691	21	55	1	1	NUM
ap-10691	21	56	r	r	NOUN
ap-10691	21	57	∂r	∂r	NOUN
ap-10691	22	1	+	+	NUM
ap-10691	22	2	ωr2	ωr2	NOUN
ap-10691	23	1	+	+	ADJ
ap-10691	23	2	k2	k2	ADJ
ap-10691	23	3	r2	r2	PROPN
ap-10691	23	4	(	(	PUNCT
ap-10691	23	5	−∂2	−∂2	PROPN
ap-10691	23	6	θ	θ	PROPN
ap-10691	23	7	+	+	CCONJ
ap-10691	23	8	α2	α2	ADJ
ap-10691	23	9	−	−	PROPN
ap-10691	23	10	1	1	NUM
ap-10691	23	11	4	4	NUM
ap-10691	23	12	cos2	cos2	NOUN
ap-10691	23	13	θ	θ	PROPN
ap-10691	24	1	+	+	CCONJ
ap-10691	24	2	β2	β2	VERB
ap-10691	24	3	−	−	PROPN
ap-10691	24	4	1	1	NUM
ap-10691	24	5	4	4	NUM
ap-10691	24	6	sin2	sin2	NOUN
ap-10691	24	7	θ	θ	PROPN
ap-10691	24	8	)	)	PUNCT
ap-10691	24	9	,	,	PUNCT
ap-10691	24	10	(	(	PUNCT
ap-10691	24	11	3	3	X
ap-10691	24	12	)	)	PUNCT
ap-10691	24	13	where	where	SCONJ
ap-10691	24	14	0	0	NUM
ap-10691	24	15	<	<	X
ap-10691	24	16	θ	θ	X
ap-10691	24	17	<	<	X
ap-10691	24	18	θ	θ	PROPN
ap-10691	24	19	2	2	NUM
ap-10691	24	20	and	and	CCONJ
ap-10691	24	21	α2	α2	ADJ
ap-10691	24	22	,	,	PUNCT
ap-10691	24	23	β2	β2	VERB
ap-10691	24	24	>	>	X
ap-10691	24	25	1	1	NUM
ap-10691	24	26	4	4	NUM
ap-10691	24	27	.	.	PUNCT
ap-10691	25	1	in	in	ADP
ap-10691	25	2	this	this	DET
ap-10691	25	3	paper	paper	NOUN
ap-10691	25	4	,	,	PUNCT
ap-10691	25	5	we	we	PRON
ap-10691	25	6	present	present	VERB
ap-10691	25	7	a	a	DET
ap-10691	25	8	generalisation	generalisation	NOUN
ap-10691	25	9	à	à	X
ap-10691	25	10	la	la	PROPN
ap-10691	25	11	ttw	ttw	PROPN
ap-10691	25	12	of	of	ADP
ap-10691	25	13	two	two	NUM
ap-10691	25	14	superintegrable	superintegrable	ADJ
ap-10691	25	15	hamiltonian	hamiltonian	ADJ
ap-10691	25	16	systems	system	NOUN
ap-10691	25	17	defined	define	VERB
ap-10691	25	18	in	in	ADP
ap-10691	25	19	two	two	NUM
ap-10691	25	20	-	-	PUNCT
ap-10691	25	21	dimensional	dimensional	ADJ
ap-10691	25	22	curved	curved	ADJ
ap-10691	25	23	spaces	space	NOUN
ap-10691	25	24	,	,	PUNCT
ap-10691	25	25	specifically	specifically	ADV
ap-10691	25	26	the	the	DET
ap-10691	25	27	sphere	sphere	NOUN
ap-10691	25	28	s2	s2	NOUN
ap-10691	25	29	and	and	CCONJ
ap-10691	25	30	the	the	DET
ap-10691	25	31	hyperbolic	hyperbolic	ADJ
ap-10691	25	32	plane	plane	NOUN
ap-10691	25	33	h2	h2	NOUN
ap-10691	25	34	.	.	PUNCT
ap-10691	26	1	a	a	DET
ap-10691	26	2	direct	direct	ADJ
ap-10691	26	3	extension	extension	NOUN
ap-10691	26	4	of	of	ADP
ap-10691	26	5	the	the	DET
ap-10691	26	6	original	original	ADJ
ap-10691	26	7	ttw	ttw	NOUN
ap-10691	26	8	system	system	NOUN
ap-10691	26	9	to	to	ADP
ap-10691	26	10	two	two	NUM
ap-10691	26	11	-	-	PUNCT
ap-10691	26	12	dimensional	dimensional	ADJ
ap-10691	26	13	spherical	spherical	ADJ
ap-10691	26	14	and	and	CCONJ
ap-10691	26	15	hyperbolic	hyperbolic	ADJ
ap-10691	26	16	spaces	space	NOUN
ap-10691	26	17	can	can	AUX
ap-10691	26	18	be	be	AUX
ap-10691	26	19	found	find	VERB
ap-10691	26	20	in	in	ADP
ap-10691	26	21	[	[	X
ap-10691	26	22	20–23	20–23	NOUN
ap-10691	26	23	]	]	PUNCT
ap-10691	26	24	.	.	PUNCT
ap-10691	27	1	the	the	DET
ap-10691	27	2	structure	structure	NOUN
ap-10691	27	3	of	of	ADP
ap-10691	27	4	the	the	DET
ap-10691	27	5	paper	paper	NOUN
ap-10691	27	6	is	be	AUX
ap-10691	27	7	as	as	SCONJ
ap-10691	27	8	follows	follow	VERB
ap-10691	27	9	:	:	PUNCT
ap-10691	27	10	in	in	ADP
ap-10691	27	11	section	section	NOUN
ap-10691	27	12	2	2	NUM
ap-10691	27	13	,	,	PUNCT
ap-10691	27	14	we	we	PRON
ap-10691	27	15	introduce	introduce	VERB
ap-10691	27	16	the	the	DET
ap-10691	27	17	original	original	ADJ
ap-10691	27	18	system	system	NOUN
ap-10691	27	19	defined	define	VERB
ap-10691	27	20	on	on	ADP
ap-10691	27	21	s2	s2	PROPN
ap-10691	27	22	,	,	PUNCT
ap-10691	27	23	as	as	ADV
ap-10691	27	24	well	well	ADV
ap-10691	27	25	as	as	ADP
ap-10691	27	26	its	its	PRON
ap-10691	27	27	ttw	ttw	NOUN
ap-10691	27	28	-	-	PUNCT
ap-10691	27	29	type	type	NOUN
ap-10691	27	30	generalisation	generalisation	NOUN
ap-10691	27	31	.	.	PUNCT
ap-10691	28	1	in	in	ADP
ap-10691	28	2	addition	addition	NOUN
ap-10691	28	3	,	,	PUNCT
ap-10691	28	4	we	we	PRON
ap-10691	28	5	present	present	VERB
ap-10691	28	6	a	a	DET
ap-10691	28	7	mathematical	mathematical	ADJ
ap-10691	28	8	overview	overview	NOUN
ap-10691	28	9	of	of	ADP
ap-10691	28	10	the	the	DET
ap-10691	28	11	factorisation	factorisation	NOUN
ap-10691	28	12	method	method	NOUN
ap-10691	28	13	for	for	ADP
ap-10691	28	14	hamiltonians	hamiltonian	NOUN
ap-10691	28	15	–	–	PUNCT
ap-10691	28	16	originating	originate	VERB
ap-10691	28	17	in	in	ADP
ap-10691	28	18	the	the	DET
ap-10691	28	19	work	work	NOUN
ap-10691	28	20	of	of	ADP
ap-10691	28	21	schrödinger	schrödinger	NOUN
ap-10691	28	22	–	–	PUNCT
ap-10691	28	23	which	which	PRON
ap-10691	28	24	allows	allow	VERB
ap-10691	28	25	us	we	PRON
ap-10691	28	26	to	to	PART
ap-10691	28	27	construct	construct	VERB
ap-10691	28	28	generalised	generalised	ADJ
ap-10691	28	29	ladder	ladder	NOUN
ap-10691	28	30	and	and	CCONJ
ap-10691	28	31	shift	shift	NOUN
ap-10691	28	32	operators	operator	NOUN
ap-10691	28	33	.	.	PUNCT
ap-10691	29	1	we	we	PRON
ap-10691	29	2	also	also	ADV
ap-10691	29	3	present	present	VERB
ap-10691	29	4	a	a	DET
ap-10691	29	5	theorem	theorem	NOUN
ap-10691	29	6	that	that	PRON
ap-10691	29	7	establishes	establish	VERB
ap-10691	29	8	a	a	DET
ap-10691	29	9	systematic	systematic	ADJ
ap-10691	29	10	method	method	NOUN
ap-10691	29	11	for	for	ADP
ap-10691	29	12	constructing	construct	VERB
ap-10691	29	13	two	two	NUM
ap-10691	29	14	symmetries	symmetry	NOUN
ap-10691	29	15	(	(	PUNCT
ap-10691	29	16	or	or	CCONJ
ap-10691	29	17	integrals	integral	NOUN
ap-10691	29	18	of	of	ADP
ap-10691	29	19	motion	motion	NOUN
ap-10691	29	20	)	)	PUNCT
ap-10691	29	21	that	that	PRON
ap-10691	29	22	commute	commute	VERB
ap-10691	29	23	with	with	ADP
ap-10691	29	24	the	the	DET
ap-10691	29	25	hamiltonian	hamiltonian	NOUN
ap-10691	29	26	,	,	PUNCT
ap-10691	29	27	thereby	thereby	ADV
ap-10691	29	28	demonstrating	demonstrate	VERB
ap-10691	29	29	the	the	DET
ap-10691	29	30	superintegrability	superintegrability	NOUN
ap-10691	29	31	of	of	ADP
ap-10691	29	32	the	the	DET
ap-10691	29	33	new	new	ADJ
ap-10691	29	34	system	system	NOUN
ap-10691	29	35	.	.	PUNCT
ap-10691	30	1	section	section	NOUN
ap-10691	30	2	3	3	NUM
ap-10691	30	3	is	be	AUX
ap-10691	30	4	devoted	devote	VERB
ap-10691	30	5	to	to	ADP
ap-10691	30	6	the	the	DET
ap-10691	30	7	explicit	explicit	ADJ
ap-10691	30	8	construction	construction	NOUN
ap-10691	30	9	of	of	ADP
ap-10691	30	10	these	these	DET
ap-10691	30	11	symmetries	symmetry	NOUN
ap-10691	30	12	,	,	PUNCT
ap-10691	30	13	which	which	PRON
ap-10691	30	14	are	be	AUX
ap-10691	30	15	obtained	obtain	VERB
ap-10691	30	16	by	by	ADP
ap-10691	30	17	factorising	factorise	VERB
ap-10691	30	18	two	two	NUM
ap-10691	30	19	subhamiltonians	subhamiltonian	NOUN
ap-10691	30	20	derived	derive	VERB
ap-10691	30	21	from	from	ADP
ap-10691	30	22	the	the	DET
ap-10691	30	23	original	original	ADJ
ap-10691	30	24	system	system	NOUN
ap-10691	30	25	through	through	ADP
ap-10691	30	26	the	the	DET
ap-10691	30	27	separation	separation	NOUN
ap-10691	30	28	of	of	ADP
ap-10691	30	29	variables	variable	NOUN
ap-10691	30	30	method	method	NOUN
ap-10691	30	31	.	.	PUNCT
ap-10691	31	1	in	in	ADP
ap-10691	31	2	section	section	NOUN
ap-10691	31	3	4	4	NUM
ap-10691	31	4	,	,	PUNCT
ap-10691	31	5	we	we	PRON
ap-10691	31	6	study	study	VERB
ap-10691	31	7	the	the	DET
ap-10691	31	8	classical	classical	ADJ
ap-10691	31	9	counterpart	counterpart	NOUN
ap-10691	31	10	of	of	ADP
ap-10691	31	11	this	this	DET
ap-10691	31	12	hamiltonian	hamiltonian	NOUN
ap-10691	31	13	and	and	CCONJ
ap-10691	31	14	derive	derive	VERB
ap-10691	31	15	its	its	PRON
ap-10691	31	16	classical	classical	ADJ
ap-10691	31	17	trajectories	trajectory	NOUN
ap-10691	31	18	in	in	ADP
ap-10691	31	19	an	an	DET
ap-10691	31	20	algebraic	algebraic	ADJ
ap-10691	31	21	way	way	NOUN
ap-10691	31	22	.	.	PUNCT
ap-10691	32	1	the	the	DET
ap-10691	32	2	hyperbolic	hyperbolic	ADJ
ap-10691	32	3	case	case	NOUN
ap-10691	32	4	is	be	AUX
ap-10691	32	5	presented	present	VERB
ap-10691	32	6	in	in	ADP
ap-10691	32	7	section	section	NOUN
ap-10691	32	8	5	5	NUM
ap-10691	32	9	,	,	PUNCT
ap-10691	32	10	where	where	SCONJ
ap-10691	32	11	we	we	PRON
ap-10691	32	12	follow	follow	VERB
ap-10691	32	13	an	an	DET
ap-10691	32	14	analogous	analogous	ADJ
ap-10691	32	15	approach	approach	NOUN
ap-10691	32	16	,	,	PUNCT
ap-10691	32	17	as	as	SCONJ
ap-10691	32	18	the	the	DET
ap-10691	32	19	hamiltonian	hamiltonian	ADJ
ap-10691	32	20	systems	system	NOUN
ap-10691	32	21	exhibit	exhibit	VERB
ap-10691	32	22	formal	formal	ADJ
ap-10691	32	23	similarities	similarity	NOUN
ap-10691	32	24	.	.	PUNCT
ap-10691	33	1	we	we	PRON
ap-10691	33	2	conclude	conclude	VERB
ap-10691	33	3	with	with	ADP
ap-10691	33	4	some	some	DET
ap-10691	33	5	final	final	ADJ
ap-10691	33	6	remarks	remark	NOUN
ap-10691	33	7	and	and	CCONJ
ap-10691	33	8	an	an	DET
ap-10691	33	9	appendix	appendix	NOUN
ap-10691	33	10	,	,	PUNCT
ap-10691	33	11	where	where	SCONJ
ap-10691	33	12	we	we	PRON
ap-10691	33	13	present	present	VERB
ap-10691	33	14	a	a	DET
ap-10691	33	15	more	more	ADV
ap-10691	33	16	general	general	ADJ
ap-10691	33	17	version	version	NOUN
ap-10691	33	18	of	of	ADP
ap-10691	33	19	theorem	theorem	NOUN
ap-10691	33	20	1	1	NUM
ap-10691	33	21	from	from	ADP
ap-10691	33	22	section	section	NOUN
ap-10691	33	23	2	2	NUM
ap-10691	33	24	.	.	NOUN
ap-10691	33	25	2	2	NUM
ap-10691	33	26	.	.	X
ap-10691	34	1	ttw	ttw	PROPN
ap-10691	34	2	so(3)-hamiltonian	so(3)-hamiltonian	PROPN
ap-10691	34	3	let	let	VERB
ap-10691	34	4	us	we	PRON
ap-10691	34	5	consider	consider	VERB
ap-10691	34	6	the	the	DET
ap-10691	34	7	hamiltonian	hamiltonian	NOUN
ap-10691	35	1	[	[	X
ap-10691	35	2	6	6	NUM
ap-10691	35	3	]	]	PUNCT
ap-10691	35	4	:	:	PUNCT
ap-10691	35	5	h	h	NOUN
ap-10691	35	6	:	:	PUNCT
ap-10691	35	7	=	=	PUNCT
ap-10691	36	1	−	−	NOUN
ap-10691	36	2	2∑	2∑	NUM
ap-10691	36	3	i=0	i=0	PROPN
ap-10691	36	4	j2	j2	PROPN
ap-10691	36	5	i	i	PROPN
ap-10691	37	1	+	+	PROPN
ap-10691	37	2	l2i	l2i	NOUN
ap-10691	37	3	−	−	NOUN
ap-10691	37	4	1	1	NUM
ap-10691	37	5	4	4	NUM
ap-10691	37	6	s2	s2	NOUN
ap-10691	37	7	i	i	PRON
ap-10691	37	8	,	,	PUNCT
ap-10691	37	9	(	(	PUNCT
ap-10691	37	10	4	4	X
ap-10691	37	11	)	)	PUNCT
ap-10691	37	12	520	520	NUM
ap-10691	37	13	https://doi.org/10.14311/ap.2025.65.0520	https://doi.org/10.14311/ap.2025.65.0520	NOUN
ap-10691	37	14	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10691	37	15	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-10691	37	16	vol	vol	NOUN
ap-10691	37	17	.	.	PROPN
ap-10691	38	1	65	65	NUM
ap-10691	38	2	no	no	NOUN
ap-10691	38	3	.	.	PUNCT
ap-10691	39	1	5/2025	5/2025	NUM
ap-10691	39	2	classical	classical	ADJ
ap-10691	39	3	and	and	CCONJ
ap-10691	39	4	quantum	quantum	ADJ
ap-10691	39	5	superintegrable	superintegrable	ADJ
ap-10691	39	6	systems	system	NOUN
ap-10691	39	7	on	on	ADP
ap-10691	39	8	the	the	DET
ap-10691	39	9	sphere	sphere	NOUN
ap-10691	39	10	.	.	PUNCT
ap-10691	39	11	.	.	PUNCT
ap-10691	39	12	.	.	PUNCT
ap-10691	40	1	where	where	SCONJ
ap-10691	40	2	(	(	PUNCT
ap-10691	40	3	si	si	NOUN
ap-10691	40	4	)	)	PUNCT
ap-10691	40	5	≡	≡	PROPN
ap-10691	40	6	(	(	PUNCT
ap-10691	40	7	s0	s0	PROPN
ap-10691	40	8	,	,	PUNCT
ap-10691	40	9	s1	s1	NOUN
ap-10691	40	10	,	,	PUNCT
ap-10691	40	11	s2	s2	PROPN
ap-10691	40	12	)	)	PUNCT
ap-10691	40	13	∈	∈	PROPN
ap-10691	40	14	r3	r3	PROPN
ap-10691	40	15	verifies	verifie	NOUN
ap-10691	40	16	s2	s2	VERB
ap-10691	40	17	0	0	NUM
ap-10691	41	1	+	+	CCONJ
ap-10691	41	2	s2	s2	VERB
ap-10691	41	3	1	1	NUM
ap-10691	41	4	+	+	NOUN
ap-10691	41	5	s2	s2	VERB
ap-10691	41	6	2	2	NUM
ap-10691	41	7	=	=	SYM
ap-10691	41	8	1	1	NUM
ap-10691	41	9	and	and	CCONJ
ap-10691	41	10	li	li	PROPN
ap-10691	41	11	∈	∈	PROPN
ap-10691	41	12	r.	r.	PROPN
ap-10691	41	13	the	the	DET
ap-10691	41	14	differential	differential	PROPN
ap-10691	41	15	operators	operator	NOUN
ap-10691	41	16	ji	ji	INTJ
ap-10691	41	17	:	:	PUNCT
ap-10691	41	18	=	=	NOUN
ap-10691	41	19	εijk	εijk	NOUN
ap-10691	41	20	sj	sj	PROPN
ap-10691	41	21	∂sk	∂sk	PROPN
ap-10691	41	22	(	(	PUNCT
ap-10691	41	23	εijk	εijk	NOUN
ap-10691	41	24	is	be	AUX
ap-10691	41	25	the	the	DET
ap-10691	41	26	levi	levi	NOUN
ap-10691	41	27	-	-	PUNCT
ap-10691	41	28	civita	civita	NOUN
ap-10691	41	29	symbol	symbol	NOUN
ap-10691	41	30	)	)	PUNCT
ap-10691	41	31	span	span	VERB
ap-10691	41	32	the	the	DET
ap-10691	41	33	lie	lie	NOUN
ap-10691	41	34	algebra	algebra	NOUN
ap-10691	41	35	so(3	so(3	NOUN
ap-10691	41	36	)	)	PUNCT
ap-10691	41	37	since	since	SCONJ
ap-10691	41	38	they	they	PRON
ap-10691	41	39	are	be	AUX
ap-10691	41	40	the	the	DET
ap-10691	41	41	infinitesimal	infinitesimal	ADJ
ap-10691	41	42	generators	generator	NOUN
ap-10691	41	43	in	in	ADP
ap-10691	41	44	the	the	DET
ap-10691	41	45	vector	vector	NOUN
ap-10691	41	46	field	field	NOUN
ap-10691	41	47	representation	representation	NOUN
ap-10691	41	48	.	.	PUNCT
ap-10691	42	1	it	it	PRON
ap-10691	42	2	is	be	AUX
ap-10691	42	3	worth	worth	ADJ
ap-10691	42	4	noting	note	VERB
ap-10691	42	5	that	that	SCONJ
ap-10691	42	6	∑2	∑2	PROPN
ap-10691	42	7	i=0	i=0	PROPN
ap-10691	42	8	j	j	PROPN
ap-10691	42	9	2	2	NUM
ap-10691	42	10	i	i	PRON
ap-10691	42	11	is	be	AUX
ap-10691	42	12	the	the	DET
ap-10691	42	13	quadratic	quadratic	ADJ
ap-10691	42	14	casimir	casimir	NOUN
ap-10691	42	15	operator	operator	NOUN
ap-10691	42	16	of	of	ADP
ap-10691	42	17	so(3	so(3	NOUN
ap-10691	42	18	)	)	PUNCT
ap-10691	42	19	,	,	PUNCT
ap-10691	42	20	which	which	PRON
ap-10691	42	21	is	be	AUX
ap-10691	42	22	the	the	DET
ap-10691	42	23	laplacebeltrami	laplacebeltrami	ADJ
ap-10691	42	24	operator	operator	NOUN
ap-10691	42	25	on	on	ADP
ap-10691	42	26	the	the	DET
ap-10691	42	27	sphere	sphere	NOUN
ap-10691	42	28	s2	s2	PROPN
ap-10691	42	29	,	,	PUNCT
ap-10691	42	30	which	which	PRON
ap-10691	42	31	is	be	AUX
ap-10691	42	32	,	,	PUNCT
ap-10691	42	33	in	in	ADP
ap-10691	42	34	turn	turn	NOUN
ap-10691	42	35	,	,	PUNCT
ap-10691	42	36	the	the	DET
ap-10691	42	37	orbit	orbit	NOUN
ap-10691	42	38	(	(	PUNCT
ap-10691	42	39	symmetric	symmetric	ADJ
ap-10691	42	40	space	space	NOUN
ap-10691	42	41	)	)	PUNCT
ap-10691	42	42	of	of	ADP
ap-10691	42	43	so(3	so(3	NOUN
ap-10691	42	44	)	)	PUNCT
ap-10691	42	45	.	.	PUNCT
ap-10691	43	1	considering	consider	VERB
ap-10691	43	2	spherical	spherical	ADJ
ap-10691	43	3	coordinates	coordinate	NOUN
ap-10691	43	4	(	(	PUNCT
ap-10691	43	5	ϕ1	ϕ1	NOUN
ap-10691	43	6	,	,	PUNCT
ap-10691	43	7	ϕ2	ϕ2	ADV
ap-10691	43	8	)	)	PUNCT
ap-10691	43	9	such	such	ADJ
ap-10691	43	10	that	that	SCONJ
ap-10691	43	11	:	:	PUNCT
ap-10691	43	12	s0	s0	PROPN
ap-10691	43	13	=	=	PUNCT
ap-10691	43	14	cosϕ2	cosϕ2	PROPN
ap-10691	43	15	cosϕ1	cosϕ1	PROPN
ap-10691	43	16	,	,	PUNCT
ap-10691	43	17	s1	s1	PROPN
ap-10691	43	18	=	=	SYM
ap-10691	43	19	cosϕ2	cosϕ2	PROPN
ap-10691	43	20	sinϕ1	sinϕ1	PROPN
ap-10691	43	21	,	,	PUNCT
ap-10691	43	22	s2	s2	PROPN
ap-10691	43	23	=	=	SYM
ap-10691	43	24	sinϕ2	sinϕ2	PROPN
ap-10691	43	25	,	,	PUNCT
ap-10691	43	26	(	(	PUNCT
ap-10691	43	27	5	5	X
ap-10691	43	28	)	)	PUNCT
ap-10691	43	29	the	the	DET
ap-10691	43	30	hamiltonian	hamiltonian	NOUN
ap-10691	43	31	(	(	PUNCT
ap-10691	43	32	4	4	X
ap-10691	43	33	)	)	PUNCT
ap-10691	43	34	becomes	become	VERB
ap-10691	43	35	:	:	PUNCT
ap-10691	43	36	h	h	NOUN
ap-10691	43	37	=	=	PUNCT
ap-10691	44	1	−	−	PROPN
ap-10691	44	2	∂2	∂2	NOUN
ap-10691	44	3	ϕ2	ϕ2	ADV
ap-10691	44	4	+	+	CCONJ
ap-10691	44	5	tanϕ2	tanϕ2	ADJ
ap-10691	44	6	∂ϕ2	∂ϕ2	NOUN
ap-10691	44	7	+	+	CCONJ
ap-10691	44	8	l22	l22	NOUN
ap-10691	44	9	−	−	PROPN
ap-10691	44	10	1	1	NUM
ap-10691	44	11	4	4	NUM
ap-10691	44	12	sin2	sin2	NOUN
ap-10691	44	13	ϕ2	ϕ2	ADV
ap-10691	44	14	+	+	CCONJ
ap-10691	44	15	1	1	NUM
ap-10691	44	16	cos2	cos2	NOUN
ap-10691	44	17	ϕ2	ϕ2	ADV
ap-10691	44	18	[	[	PUNCT
ap-10691	44	19	−∂2	−∂2	PROPN
ap-10691	44	20	ϕ1	ϕ1	NOUN
ap-10691	44	21	+	+	CCONJ
ap-10691	44	22	l20	l20	NOUN
ap-10691	44	23	−	−	PROPN
ap-10691	44	24	1	1	NUM
ap-10691	44	25	4	4	NUM
ap-10691	44	26	cos2	cos2	NOUN
ap-10691	44	27	ϕ1	ϕ1	NOUN
ap-10691	44	28	+	+	CCONJ
ap-10691	44	29	l21	l21	NOUN
ap-10691	44	30	−	−	PROPN
ap-10691	44	31	1	1	NUM
ap-10691	44	32	4	4	NUM
ap-10691	44	33	sin2	sin2	NOUN
ap-10691	44	34	ϕ1	ϕ1	NOUN
ap-10691	44	35	]	]	PUNCT
ap-10691	44	36	,	,	PUNCT
ap-10691	44	37	(	(	PUNCT
ap-10691	44	38	6	6	NUM
ap-10691	44	39	)	)	PUNCT
ap-10691	44	40	with	with	ADP
ap-10691	44	41	0	0	NUM
ap-10691	44	42	<	<	X
ap-10691	44	43	ϕ1	ϕ1	PROPN
ap-10691	44	44	<	<	X
ap-10691	44	45	π	π	PROPN
ap-10691	44	46	2	2	NUM
ap-10691	44	47	,	,	PUNCT
ap-10691	44	48	0	0	NUM
ap-10691	44	49	<	<	X
ap-10691	44	50	ϕ2	ϕ2	ADV
ap-10691	44	51	<	<	X
ap-10691	44	52	π	π	PROPN
ap-10691	44	53	2	2	NUM
ap-10691	44	54	.	.	PUNCT
ap-10691	45	1	now	now	ADV
ap-10691	45	2	we	we	PRON
ap-10691	45	3	modify	modify	VERB
ap-10691	45	4	this	this	DET
ap-10691	45	5	hamiltonian	hamiltonian	NOUN
ap-10691	45	6	following	follow	VERB
ap-10691	45	7	the	the	DET
ap-10691	45	8	ttw	ttw	PROPN
ap-10691	45	9	-	-	PUNCT
ap-10691	45	10	hamiltonians	hamiltonians	PROPN
ap-10691	45	11	(	(	PUNCT
ap-10691	45	12	2	2	NUM
ap-10691	45	13	)	)	PUNCT
ap-10691	45	14	and	and	CCONJ
ap-10691	45	15	(	(	PUNCT
ap-10691	45	16	3	3	X
ap-10691	45	17	)	)	PUNCT
ap-10691	45	18	obtaining	obtain	VERB
ap-10691	45	19	a	a	DET
ap-10691	45	20	one	one	NUM
ap-10691	45	21	-	-	PUNCT
ap-10691	45	22	parameter	parameter	NOUN
ap-10691	45	23	family	family	NOUN
ap-10691	45	24	of	of	ADP
ap-10691	45	25	hamiltonians	hamiltonian	NOUN
ap-10691	45	26	depending	depend	VERB
ap-10691	45	27	on	on	ADP
ap-10691	45	28	k	k	PROPN
ap-10691	45	29	∈	∈	PROPN
ap-10691	45	30	r∗	r∗	PROPN
ap-10691	45	31	:	:	PUNCT
ap-10691	46	1	hk	hk	PROPN
ap-10691	46	2	=	=	PUNCT
ap-10691	46	3	−	−	PROPN
ap-10691	46	4	∂2	∂2	NOUN
ap-10691	46	5	ϕ2	ϕ2	ADV
ap-10691	46	6	+	+	CCONJ
ap-10691	46	7	tanϕ2	tanϕ2	ADJ
ap-10691	46	8	∂ϕ2	∂ϕ2	NOUN
ap-10691	46	9	+	+	CCONJ
ap-10691	46	10	l22	l22	NOUN
ap-10691	46	11	−	−	PROPN
ap-10691	46	12	1	1	NUM
ap-10691	46	13	4	4	NUM
ap-10691	46	14	sin2	sin2	NOUN
ap-10691	46	15	ϕ2	ϕ2	ADV
ap-10691	46	16	+	+	CCONJ
ap-10691	46	17	k2	k2	ADJ
ap-10691	46	18	cos2	cos2	NOUN
ap-10691	46	19	ϕ2	ϕ2	ADV
ap-10691	46	20	[	[	PUNCT
ap-10691	46	21	−∂2	−∂2	PROPN
ap-10691	46	22	kϕ1	kϕ1	PROPN
ap-10691	46	23	+	+	CCONJ
ap-10691	46	24	l20	l20	NOUN
ap-10691	46	25	−	−	PROPN
ap-10691	46	26	1	1	NUM
ap-10691	46	27	4	4	NUM
ap-10691	46	28	cos2	cos2	NOUN
ap-10691	46	29	kϕ1	kϕ1	VERB
ap-10691	46	30	+	+	CCONJ
ap-10691	46	31	l21	l21	PROPN
ap-10691	46	32	−	−	PROPN
ap-10691	46	33	1	1	NUM
ap-10691	46	34	4	4	NUM
ap-10691	46	35	sin2	sin2	NOUN
ap-10691	46	36	kϕ1	kϕ1	PROPN
ap-10691	46	37	]	]	PUNCT
ap-10691	46	38	,	,	PUNCT
ap-10691	46	39	(	(	PUNCT
ap-10691	46	40	7	7	X
ap-10691	46	41	)	)	PUNCT
ap-10691	46	42	with	with	ADP
ap-10691	46	43	now	now	ADV
ap-10691	46	44	0	0	NUM
ap-10691	46	45	<	<	X
ap-10691	46	46	ϕ1	ϕ1	PROPN
ap-10691	46	47	<	<	X
ap-10691	46	48	π	π	PROPN
ap-10691	46	49	2k	2k	PROPN
ap-10691	46	50	,	,	PUNCT
ap-10691	46	51	0	0	PUNCT
ap-10691	46	52	<	<	X
ap-10691	47	1	ϕ2	ϕ2	ADV
ap-10691	47	2	<	<	X
ap-10691	47	3	π	π	PROPN
ap-10691	47	4	2	2	NUM
ap-10691	47	5	.	.	PUNCT
ap-10691	48	1	to	to	PART
ap-10691	48	2	simplify	simplify	VERB
ap-10691	48	3	the	the	DET
ap-10691	48	4	notation	notation	NOUN
ap-10691	48	5	,	,	PUNCT
ap-10691	48	6	we	we	PRON
ap-10691	48	7	introduce	introduce	VERB
ap-10691	48	8	the	the	DET
ap-10691	48	9	change	change	NOUN
ap-10691	48	10	of	of	ADP
ap-10691	48	11	variables	variable	NOUN
ap-10691	48	12	(	(	PUNCT
ap-10691	48	13	kϕ1	kϕ1	PROPN
ap-10691	48	14	,	,	PUNCT
ap-10691	48	15	ϕ2	ϕ2	ADV
ap-10691	48	16	)	)	PUNCT
ap-10691	48	17	→	→	SYM
ap-10691	48	18	(	(	PUNCT
ap-10691	48	19	θ	θ	PROPN
ap-10691	48	20	,	,	PUNCT
ap-10691	48	21	ϕ	ϕ	NOUN
ap-10691	48	22	)	)	PUNCT
ap-10691	48	23	such	such	ADJ
ap-10691	48	24	that	that	SCONJ
ap-10691	48	25	0	0	NUM
ap-10691	48	26	<	<	X
ap-10691	48	27	θ	θ	PROPN
ap-10691	48	28	,	,	PUNCT
ap-10691	48	29	ϕ	ϕ	X
ap-10691	48	30	<	<	X
ap-10691	48	31	π	π	X
ap-10691	48	32	2	2	NUM
ap-10691	48	33	[	[	X
ap-10691	48	34	19	19	NUM
ap-10691	48	35	]	]	X
ap-10691	48	36	:	:	PUNCT
ap-10691	49	1	hk	hk	PROPN
ap-10691	49	2	=	=	PUNCT
ap-10691	50	1	−	−	PROPN
ap-10691	50	2	∂2	∂2	PROPN
ap-10691	50	3	ϕ	ϕ	NOUN
ap-10691	50	4	+	+	CCONJ
ap-10691	50	5	tanϕ∂ϕ	tanϕ∂ϕ	NUM
ap-10691	50	6	+	+	NUM
ap-10691	50	7	l22	l22	NOUN
ap-10691	50	8	−	−	NOUN
ap-10691	50	9	1	1	NUM
ap-10691	50	10	4	4	NUM
ap-10691	50	11	sin2	sin2	NOUN
ap-10691	50	12	ϕ	ϕ	PROPN
ap-10691	50	13	+	+	CCONJ
ap-10691	50	14	k2	k2	ADJ
ap-10691	50	15	cos2	cos2	PROPN
ap-10691	50	16	ϕ	ϕ	X
ap-10691	50	17	[	[	PUNCT
ap-10691	50	18	−∂2	−∂2	PROPN
ap-10691	50	19	θ	θ	PROPN
ap-10691	50	20	+	+	CCONJ
ap-10691	50	21	l20	l20	PROPN
ap-10691	50	22	−	−	PROPN
ap-10691	50	23	1	1	NUM
ap-10691	50	24	4	4	NUM
ap-10691	50	25	cos2	cos2	NOUN
ap-10691	50	26	θ	θ	PROPN
ap-10691	51	1	+	+	CCONJ
ap-10691	51	2	l21	l21	PROPN
ap-10691	51	3	−	−	NOUN
ap-10691	51	4	1	1	NUM
ap-10691	51	5	4	4	NUM
ap-10691	51	6	sin2	sin2	NOUN
ap-10691	51	7	θ	θ	PROPN
ap-10691	51	8	]	]	PUNCT
ap-10691	51	9	.	.	PUNCT
ap-10691	52	1	(	(	PUNCT
ap-10691	52	2	8)	8)	NUM
ap-10691	52	3	note	note	NOUN
ap-10691	52	4	that	that	SCONJ
ap-10691	52	5	we	we	PRON
ap-10691	52	6	actually	actually	ADV
ap-10691	52	7	have	have	VERB
ap-10691	52	8	a	a	DET
ap-10691	52	9	family	family	NOUN
ap-10691	52	10	of	of	ADP
ap-10691	52	11	hamiltonians	hamiltonian	NOUN
ap-10691	52	12	depending	depend	VERB
ap-10691	52	13	on	on	ADP
ap-10691	52	14	four	four	NUM
ap-10691	52	15	real	real	ADJ
ap-10691	52	16	parameters	parameter	NOUN
ap-10691	52	17	(	(	PUNCT
ap-10691	52	18	k	k	X
ap-10691	52	19	,	,	PUNCT
ap-10691	52	20	l0	l0	PROPN
ap-10691	52	21	,	,	PUNCT
ap-10691	52	22	l1	l1	PROPN
ap-10691	52	23	,	,	PUNCT
ap-10691	52	24	l2	l2	NOUN
ap-10691	52	25	)	)	PUNCT
ap-10691	52	26	.	.	PUNCT
ap-10691	53	1	taking	take	VERB
ap-10691	53	2	into	into	ADP
ap-10691	53	3	account	account	NOUN
ap-10691	53	4	the	the	DET
ap-10691	53	5	variable	variable	ADJ
ap-10691	53	6	separation	separation	NOUN
ap-10691	53	7	,	,	PUNCT
ap-10691	53	8	i.e.	i.e.	X
ap-10691	53	9	ψ(θ	ψ(θ	PROPN
ap-10691	53	10	,	,	PUNCT
ap-10691	53	11	ϕ	ϕ	NOUN
ap-10691	53	12	)	)	PUNCT
ap-10691	53	13	=	=	PUNCT
ap-10691	53	14	ψ(θ)φ(ϕ	ψ(θ)φ(ϕ	PROPN
ap-10691	53	15	)	)	PUNCT
ap-10691	53	16	,	,	PUNCT
ap-10691	53	17	the	the	DET
ap-10691	53	18	well	well	ADV
ap-10691	53	19	-	-	PUNCT
ap-10691	53	20	known	know	VERB
ap-10691	53	21	eigenvalue	eigenvalue	NOUN
ap-10691	53	22	equation	equation	NOUN
ap-10691	53	23	hk	hk	NOUN
ap-10691	53	24	ψ	ψ	NOUN
ap-10691	53	25	=	=	X
ap-10691	53	26	eψ	eψ	NOUN
ap-10691	53	27	splits	split	VERB
ap-10691	53	28	in	in	ADP
ap-10691	53	29	two	two	NUM
ap-10691	53	30	equations	equation	NOUN
ap-10691	53	31	:	:	PUNCT
ap-10691	53	32	hϕ	hϕ	PROPN
ap-10691	53	33	mk	mk	PROPN
ap-10691	53	34	φ(ϕ	φ(ϕ	PROPN
ap-10691	53	35	)	)	PUNCT
ap-10691	53	36	=	=	PUNCT
ap-10691	53	37	e	e	X
ap-10691	53	38	φ(ϕ	φ(ϕ	PROPN
ap-10691	53	39	)	)	PUNCT
ap-10691	53	40	,	,	PUNCT
ap-10691	53	41	hθψ(θ	hθψ(θ	NOUN
ap-10691	53	42	)	)	PUNCT
ap-10691	53	43	=	=	SYM
ap-10691	53	44	e′	e′	X
ap-10691	53	45	ψ(θ	ψ(θ	PROPN
ap-10691	53	46	)	)	PUNCT
ap-10691	53	47	,	,	PUNCT
ap-10691	53	48	(	(	PUNCT
ap-10691	53	49	9	9	X
ap-10691	53	50	)	)	PUNCT
ap-10691	53	51	where	where	SCONJ
ap-10691	53	52	:	:	PUNCT
ap-10691	53	53	hϕ	hϕ	PROPN
ap-10691	53	54	mk	mk	NOUN
ap-10691	53	55	=	=	PUNCT
ap-10691	53	56	−∂2	−∂2	PROPN
ap-10691	53	57	ϕ	ϕ	PROPN
ap-10691	53	58	+	+	CCONJ
ap-10691	53	59	tanϕ∂ϕ	tanϕ∂ϕ	NUM
ap-10691	53	60	+	+	CCONJ
ap-10691	53	61	l	l	NOUN
ap-10691	53	62	2	2	NUM
ap-10691	53	63	2	2	NUM
ap-10691	53	64	−	−	NOUN
ap-10691	53	65	1	1	NUM
ap-10691	53	66	4	4	NUM
ap-10691	53	67	sin2	sin2	NOUN
ap-10691	53	68	ϕ	ϕ	PROPN
ap-10691	54	1	+	+	CCONJ
ap-10691	54	2	m2	m2	PROPN
ap-10691	54	3	k	k	PROPN
ap-10691	54	4	cos2	cos2	PROPN
ap-10691	54	5	ϕ	ϕ	PROPN
ap-10691	54	6	=	=	PUNCT
ap-10691	54	7	hϕ	hϕ	PROPN
ap-10691	54	8	+	+	CCONJ
ap-10691	54	9	m2	m2	PROPN
ap-10691	54	10	k	k	PROPN
ap-10691	54	11	cos2	cos2	PROPN
ap-10691	54	12	ϕ	ϕ	PROPN
ap-10691	54	13	,	,	PUNCT
ap-10691	54	14	(	(	PUNCT
ap-10691	54	15	10	10	NUM
ap-10691	54	16	)	)	PUNCT
ap-10691	54	17	hθ	hθ	NOUN
ap-10691	54	18	=	=	PUNCT
ap-10691	54	19	−∂2	−∂2	PROPN
ap-10691	54	20	θ	θ	PROPN
ap-10691	54	21	+	+	CCONJ
ap-10691	54	22	l20	l20	PROPN
ap-10691	54	23	−	−	PROPN
ap-10691	54	24	1	1	NUM
ap-10691	54	25	4	4	NUM
ap-10691	54	26	cos2	cos2	NOUN
ap-10691	54	27	θ	θ	PROPN
ap-10691	55	1	+	+	CCONJ
ap-10691	55	2	l21	l21	PROPN
ap-10691	55	3	−	−	NOUN
ap-10691	55	4	1	1	NUM
ap-10691	55	5	4	4	NUM
ap-10691	55	6	sin2	sin2	NOUN
ap-10691	55	7	θ	θ	PROPN
ap-10691	55	8	,	,	PUNCT
ap-10691	55	9	(	(	PUNCT
ap-10691	55	10	11	11	NUM
ap-10691	55	11	)	)	PUNCT
ap-10691	55	12	with	with	ADP
ap-10691	55	13	mk	mk	NOUN
ap-10691	55	14	:	:	PUNCT
ap-10691	56	1	=	=	SYM
ap-10691	56	2	k	k	X
ap-10691	56	3	√	√	NUM
ap-10691	56	4	e′	e′	PROPN
ap-10691	56	5	the	the	DET
ap-10691	56	6	separation	separation	NOUN
ap-10691	56	7	constant	constant	ADJ
ap-10691	56	8	.	.	PUNCT
ap-10691	57	1	in	in	ADP
ap-10691	57	2	the	the	DET
ap-10691	57	3	following	following	NOUN
ap-10691	57	4	we	we	PRON
ap-10691	57	5	will	will	AUX
ap-10691	57	6	use	use	VERB
ap-10691	57	7	β	β	X
ap-10691	57	8	instead	instead	ADV
ap-10691	57	9	e′	e′	ADJ
ap-10691	57	10	,	,	PUNCT
ap-10691	57	11	such	such	ADJ
ap-10691	57	12	that	that	SCONJ
ap-10691	57	13	β2	β2	NOUN
ap-10691	57	14	:	:	PUNCT
ap-10691	57	15	=	=	SYM
ap-10691	57	16	e′	e′	ADJ
ap-10691	57	17	,	,	PUNCT
ap-10691	57	18	hence	hence	ADV
ap-10691	57	19	mk	mk	NOUN
ap-10691	57	20	:	:	PUNCT
ap-10691	58	1	=	=	SYM
ap-10691	58	2	kβ	kβ	PROPN
ap-10691	58	3	.	.	PUNCT
ap-10691	59	1	thus	thus	ADV
ap-10691	59	2	the	the	DET
ap-10691	59	3	new	new	ADJ
ap-10691	59	4	hamiltonian	hamiltonian	NOUN
ap-10691	59	5	(	(	PUNCT
ap-10691	59	6	8)	8)	NUM
ap-10691	59	7	becomes	become	VERB
ap-10691	59	8	:	:	PUNCT
ap-10691	59	9	hk	hk	PROPN
ap-10691	59	10	=	=	SYM
ap-10691	59	11	hϕ	hϕ	PROPN
ap-10691	59	12	mk	mk	NOUN
ap-10691	59	13	+	+	CCONJ
ap-10691	59	14	k2(hθ	k2(hθ	PROPN
ap-10691	59	15	−	−	PROPN
ap-10691	59	16	β2	β2	NOUN
ap-10691	59	17	)	)	PUNCT
ap-10691	59	18	cos2	cos2	PROPN
ap-10691	59	19	ϕ	ϕ	PROPN
ap-10691	59	20	.	.	PUNCT
ap-10691	60	1	(	(	PUNCT
ap-10691	60	2	12	12	NUM
ap-10691	60	3	)	)	PUNCT
ap-10691	60	4	2.1	2.1	NUM
ap-10691	60	5	.	.	PUNCT
ap-10691	61	1	hamiltonian	hamiltonian	ADJ
ap-10691	61	2	factorisation	factorisation	NOUN
ap-10691	61	3	as	as	SCONJ
ap-10691	61	4	it	it	PRON
ap-10691	61	5	is	be	AUX
ap-10691	61	6	well	well	ADV
ap-10691	61	7	know	know	ADJ
ap-10691	61	8	from	from	ADP
ap-10691	61	9	the	the	DET
ap-10691	61	10	paper	paper	NOUN
ap-10691	61	11	by	by	ADP
ap-10691	61	12	infeld	infeld	NOUN
ap-10691	61	13	and	and	CCONJ
ap-10691	61	14	hull	hull	NOUN
ap-10691	61	15	[	[	X
ap-10691	61	16	24	24	NUM
ap-10691	61	17	]	]	PUNCT
ap-10691	61	18	in	in	ADP
ap-10691	61	19	order	order	NOUN
ap-10691	61	20	to	to	PART
ap-10691	61	21	construct	construct	VERB
ap-10691	61	22	the	the	DET
ap-10691	61	23	shift	shift	NOUN
ap-10691	61	24	operators	operator	NOUN
ap-10691	61	25	,	,	PUNCT
ap-10691	61	26	we	we	PRON
ap-10691	61	27	factorise	factorise	VERB
ap-10691	61	28	the	the	DET
ap-10691	61	29	hamiltonian	hamiltonian	NOUN
ap-10691	62	1	[	[	X
ap-10691	62	2	25	25	NUM
ap-10691	62	3	,	,	PUNCT
ap-10691	62	4	26	26	NUM
ap-10691	62	5	]	]	PUNCT
ap-10691	62	6	.	.	PUNCT
ap-10691	63	1	let	let	VERB
ap-10691	63	2	{	{	PUNCT
ap-10691	63	3	hm}m∈z	hm}m∈z	AUX
ap-10691	63	4	be	be	AUX
ap-10691	63	5	a	a	DET
ap-10691	63	6	family	family	NOUN
ap-10691	63	7	of	of	ADP
ap-10691	63	8	hamiltonians	hamiltonian	NOUN
ap-10691	63	9	such	such	ADJ
ap-10691	63	10	that	that	SCONJ
ap-10691	63	11	∀m	∀m	PROPN
ap-10691	63	12	∈	∈	PROPN
ap-10691	64	1	z	z	NOUN
ap-10691	64	2	:	:	PUNCT
ap-10691	64	3	hm	hm	INTJ
ap-10691	64	4	=	=	SYM
ap-10691	64	5	a+	a+	PUNCT
ap-10691	64	6	ma	ma	PROPN
ap-10691	64	7	−	−	PROPN
ap-10691	65	1	m	m	PROPN
ap-10691	65	2	+	+	X
ap-10691	65	3	λm	λm	X
ap-10691	65	4	=	=	SYM
ap-10691	65	5	a−	a−	NOUN
ap-10691	65	6	m−1a	m−1a	NOUN
ap-10691	66	1	+	+	CCONJ
ap-10691	66	2	m−1	m−1	PROPN
ap-10691	66	3	+	+	CCONJ
ap-10691	66	4	λm−1	λm−1	PROPN
ap-10691	66	5	.	.	PUNCT
ap-10691	67	1	(	(	PUNCT
ap-10691	67	2	13	13	NUM
ap-10691	67	3	)	)	PUNCT
ap-10691	67	4	then	then	ADV
ap-10691	67	5	,	,	PUNCT
ap-10691	67	6	it	it	PRON
ap-10691	67	7	is	be	AUX
ap-10691	67	8	straightforward	straightforward	ADJ
ap-10691	67	9	to	to	PART
ap-10691	67	10	prove	prove	VERB
ap-10691	67	11	that	that	SCONJ
ap-10691	67	12	a±	a±	PROPN
ap-10691	67	13	m	m	VERB
ap-10691	67	14	are	be	AUX
ap-10691	67	15	shift	shift	NOUN
ap-10691	67	16	operators	operator	NOUN
ap-10691	67	17	(	(	PUNCT
ap-10691	67	18	13	13	NUM
ap-10691	67	19	)	)	PUNCT
ap-10691	67	20	,	,	PUNCT
ap-10691	67	21	verifying	verifying	NOUN
ap-10691	67	22	:	:	PUNCT
ap-10691	67	23	a−	a−	PROPN
ap-10691	67	24	m	m	VERB
ap-10691	67	25	:	:	PUNCT
ap-10691	67	26	hm	hm	INTJ
ap-10691	67	27	→	→	SYM
ap-10691	67	28	hm+1	hm+1	PROPN
ap-10691	67	29	,	,	PUNCT
ap-10691	67	30	a+	a+	X
ap-10691	67	31	m	m	VERB
ap-10691	67	32	:	:	PUNCT
ap-10691	67	33	hm+1	hm+1	PROPN
ap-10691	67	34	→	→	SYM
ap-10691	67	35	hm	hm	INTJ
ap-10691	67	36	,	,	PUNCT
ap-10691	67	37	(	(	PUNCT
ap-10691	67	38	14	14	NUM
ap-10691	67	39	)	)	PUNCT
ap-10691	67	40	where	where	SCONJ
ap-10691	67	41	by	by	ADP
ap-10691	67	42	hm	hm	INTJ
ap-10691	67	43	,	,	PUNCT
ap-10691	67	44	we	we	PRON
ap-10691	67	45	design	design	VERB
ap-10691	67	46	the	the	DET
ap-10691	67	47	eigenfunction	eigenfunction	NOUN
ap-10691	67	48	space	space	NOUN
ap-10691	67	49	of	of	ADP
ap-10691	67	50	the	the	DET
ap-10691	67	51	hamiltonian	hamiltonian	ADJ
ap-10691	68	1	hm	hm	INTJ
ap-10691	68	2	(	(	PUNCT
ap-10691	68	3	as	as	ADP
ap-10691	68	4	differential	differential	ADJ
ap-10691	68	5	operators	operator	NOUN
ap-10691	68	6	)	)	PUNCT
ap-10691	68	7	.	.	PUNCT
ap-10691	69	1	in	in	ADP
ap-10691	69	2	addition	addition	NOUN
ap-10691	69	3	,	,	PUNCT
ap-10691	69	4	the	the	DET
ap-10691	69	5	operators	operator	NOUN
ap-10691	69	6	a±	a±	PROPN
ap-10691	69	7	m	m	AUX
ap-10691	69	8	are	be	AUX
ap-10691	69	9	intertwining	intertwine	VERB
ap-10691	69	10	operators	operator	NOUN
ap-10691	69	11	,	,	PUNCT
ap-10691	69	12	i.e.	i.e.	X
ap-10691	69	13	:	:	PUNCT
ap-10691	69	14	a+	a+	PUNCT
ap-10691	69	15	m	m	VERB
ap-10691	69	16	hm+1	hm+1	X
ap-10691	69	17	=	=	ADJ
ap-10691	69	18	hm	hm	INTJ
ap-10691	69	19	a+	a+	X
ap-10691	69	20	m	m	PROPN
ap-10691	69	21	,	,	PUNCT
ap-10691	69	22	a−	a−	PROPN
ap-10691	69	23	m	m	NOUN
ap-10691	69	24	hm	hm	NOUN
ap-10691	69	25	=	=	ADJ
ap-10691	69	26	hm+1	hm+1	PROPN
ap-10691	69	27	a	a	DET
ap-10691	69	28	−	−	PROPN
ap-10691	69	29	m.	m.	NOUN
ap-10691	69	30	(	(	PUNCT
ap-10691	69	31	15	15	NUM
ap-10691	69	32	)	)	PUNCT
ap-10691	69	33	an	an	DET
ap-10691	69	34	important	important	ADJ
ap-10691	69	35	consequence	consequence	NOUN
ap-10691	69	36	of	of	ADP
ap-10691	69	37	this	this	DET
ap-10691	69	38	result	result	NOUN
ap-10691	69	39	is	be	AUX
ap-10691	69	40	that	that	SCONJ
ap-10691	69	41	we	we	PRON
ap-10691	69	42	can	can	AUX
ap-10691	69	43	obtain	obtain	VERB
ap-10691	69	44	the	the	DET
ap-10691	69	45	eigenvectors	eigenvector	NOUN
ap-10691	69	46	and	and	CCONJ
ap-10691	69	47	the	the	DET
ap-10691	69	48	eigenvalues	eigenvalue	NOUN
ap-10691	69	49	of	of	ADP
ap-10691	69	50	the	the	DET
ap-10691	69	51	discrete	discrete	ADJ
ap-10691	69	52	spectrum	spectrum	NOUN
ap-10691	69	53	of	of	ADP
ap-10691	69	54	the	the	DET
ap-10691	69	55	original	original	ADJ
ap-10691	69	56	hamiltonian	hamiltonian	NOUN
ap-10691	69	57	knowing	know	VERB
ap-10691	69	58	the	the	DET
ap-10691	69	59	ground	ground	NOUN
ap-10691	69	60	states	state	NOUN
ap-10691	69	61	of	of	ADP
ap-10691	69	62	the	the	DET
ap-10691	69	63	hamiltonians	hamiltonian	NOUN
ap-10691	69	64	hm	hm	INTJ
ap-10691	69	65	of	of	ADP
ap-10691	69	66	the	the	DET
ap-10691	69	67	family	family	NOUN
ap-10691	69	68	.	.	PUNCT
ap-10691	70	1	effectively	effectively	ADV
ap-10691	70	2	,	,	PUNCT
ap-10691	70	3	let	let	VERB
ap-10691	70	4	us	we	PRON
ap-10691	70	5	suppose	suppose	VERB
ap-10691	70	6	that	that	SCONJ
ap-10691	70	7	ψ0	ψ0	PROPN
ap-10691	70	8	(	(	PUNCT
ap-10691	70	9	m	m	NOUN
ap-10691	70	10	)	)	PUNCT
ap-10691	70	11	are	be	AUX
ap-10691	70	12	the	the	DET
ap-10691	70	13	ground	ground	NOUN
ap-10691	70	14	states	state	NOUN
ap-10691	70	15	of	of	ADP
ap-10691	70	16	the	the	DET
ap-10691	70	17	hamiltonians	hamiltonian	NOUN
ap-10691	70	18	hm	hm	INTJ
ap-10691	70	19	of	of	ADP
ap-10691	70	20	the	the	DET
ap-10691	70	21	hierarchy	hierarchy	NOUN
ap-10691	70	22	.	.	PUNCT
ap-10691	71	1	they	they	PRON
ap-10691	71	2	are	be	AUX
ap-10691	71	3	determined	determine	VERB
ap-10691	71	4	by	by	ADP
ap-10691	71	5	the	the	DET
ap-10691	71	6	condition	condition	NOUN
ap-10691	71	7	:	:	PUNCT
ap-10691	71	8	a−	a−	PROPN
ap-10691	71	9	mψ	mψ	PROPN
ap-10691	71	10	0	0	NUM
ap-10691	71	11	(	(	PUNCT
ap-10691	71	12	m	m	NOUN
ap-10691	71	13	)	)	PUNCT
ap-10691	71	14	=	=	SYM
ap-10691	71	15	0	0	NUM
ap-10691	71	16	,	,	PUNCT
ap-10691	71	17	(	(	PUNCT
ap-10691	71	18	16	16	NUM
ap-10691	71	19	)	)	PUNCT
ap-10691	71	20	hence	hence	ADV
ap-10691	71	21	from	from	ADP
ap-10691	71	22	equation	equation	NOUN
ap-10691	71	23	(	(	PUNCT
ap-10691	71	24	13	13	NUM
ap-10691	71	25	):	):	PUNCT
ap-10691	71	26	hm	hm	INTJ
ap-10691	71	27	ψ0	ψ0	ADV
ap-10691	71	28	(	(	PUNCT
ap-10691	71	29	m	m	NOUN
ap-10691	71	30	)	)	PUNCT
ap-10691	72	1	=	=	SYM
ap-10691	72	2	(	(	PUNCT
ap-10691	72	3	a+	a+	PUNCT
ap-10691	72	4	m	m	VERB
ap-10691	72	5	a−	a−	PROPN
ap-10691	72	6	m	m	PROPN
ap-10691	72	7	+	+	X
ap-10691	72	8	λm	λm	X
ap-10691	72	9	)	)	PUNCT
ap-10691	72	10	ψ0	ψ0	ADV
ap-10691	72	11	(	(	PUNCT
ap-10691	72	12	m	m	NOUN
ap-10691	72	13	)	)	PUNCT
ap-10691	72	14	=	=	SYM
ap-10691	73	1	λmψ	λmψ	ADJ
ap-10691	73	2	0	0	PUNCT
ap-10691	73	3	(	(	PUNCT
ap-10691	73	4	m	m	NOUN
ap-10691	73	5	)	)	PUNCT
ap-10691	73	6	.	.	PUNCT
ap-10691	74	1	(	(	PUNCT
ap-10691	74	2	17	17	NUM
ap-10691	74	3	)	)	PUNCT
ap-10691	74	4	thus	thus	ADV
ap-10691	74	5	,	,	PUNCT
ap-10691	74	6	the	the	DET
ap-10691	74	7	scalars	scalar	NOUN
ap-10691	74	8	λm	λm	ADP
ap-10691	74	9	appearing	appear	VERB
ap-10691	74	10	in	in	ADP
ap-10691	74	11	the	the	DET
ap-10691	74	12	factorisation	factorisation	NOUN
ap-10691	74	13	are	be	AUX
ap-10691	74	14	the	the	DET
ap-10691	74	15	energies	energy	NOUN
ap-10691	74	16	of	of	ADP
ap-10691	74	17	the	the	DET
ap-10691	74	18	grounds	ground	NOUN
ap-10691	74	19	states	state	NOUN
ap-10691	74	20	.	.	PUNCT
ap-10691	75	1	then	then	ADV
ap-10691	75	2	,	,	PUNCT
ap-10691	75	3	defining	define	VERB
ap-10691	75	4	:	:	PUNCT
ap-10691	75	5	m∏	m∏	PROPN
ap-10691	75	6	i=0	i=0	PROPN
ap-10691	75	7	a+	a+	PUNCT
ap-10691	76	1	i	i	PRON
ap-10691	76	2	:	:	PUNCT
ap-10691	76	3	=	=	SYM
ap-10691	76	4	a+	a+	X
ap-10691	76	5	0	0	NUM
ap-10691	76	6	·	·	PUNCT
ap-10691	76	7	·	·	PUNCT
ap-10691	76	8	·	·	PUNCT
ap-10691	76	9	a+	a+	X
ap-10691	76	10	m	m	PROPN
ap-10691	76	11	,	,	PUNCT
ap-10691	76	12	m	m	VERB
ap-10691	76	13	∈	∈	PROPN
ap-10691	76	14	n	n	CCONJ
ap-10691	76	15	,	,	PUNCT
ap-10691	76	16	(	(	PUNCT
ap-10691	76	17	18	18	NUM
ap-10691	76	18	)	)	PUNCT
ap-10691	76	19	and	and	CCONJ
ap-10691	76	20	taking	take	VERB
ap-10691	76	21	into	into	ADP
ap-10691	76	22	account	account	NOUN
ap-10691	76	23	(	(	PUNCT
ap-10691	76	24	15	15	NUM
ap-10691	76	25	)	)	PUNCT
ap-10691	76	26	,	,	PUNCT
ap-10691	76	27	by	by	ADP
ap-10691	76	28	induction	induction	NOUN
ap-10691	76	29	,	,	PUNCT
ap-10691	76	30	we	we	PRON
ap-10691	76	31	obtain	obtain	VERB
ap-10691	76	32	:	:	PUNCT
ap-10691	76	33	h0	h0	PROPN
ap-10691	76	34	m∏	m∏	PROPN
ap-10691	76	35	i=0	i=0	PROPN
ap-10691	76	36	a+	a+	PUNCT
ap-10691	77	1	i	i	NOUN
ap-10691	77	2	=	=	PUNCT
ap-10691	77	3	(	(	PUNCT
ap-10691	77	4	m∏	m∏	PROPN
ap-10691	77	5	i=0	i=0	PROPN
ap-10691	77	6	a+	a+	PUNCT
ap-10691	77	7	i	i	PROPN
ap-10691	77	8	)	)	PUNCT
ap-10691	77	9	hm+1	hm+1	PROPN
ap-10691	77	10	.	.	PUNCT
ap-10691	78	1	(	(	PUNCT
ap-10691	78	2	19	19	NUM
ap-10691	78	3	)	)	PUNCT
ap-10691	78	4	therefore	therefore	ADV
ap-10691	78	5	,	,	PUNCT
ap-10691	78	6	we	we	PRON
ap-10691	78	7	conclude	conclude	VERB
ap-10691	78	8	that	that	SCONJ
ap-10691	78	9	the	the	DET
ap-10691	78	10	mth	mth	NOUN
ap-10691	78	11	excited	excite	VERB
ap-10691	78	12	eigenfunction	eigenfunction	NOUN
ap-10691	78	13	ψm	ψm	INTJ
ap-10691	78	14	(	(	PUNCT
ap-10691	78	15	0	0	NUM
ap-10691	78	16	)	)	PUNCT
ap-10691	78	17	of	of	ADP
ap-10691	78	18	the	the	DET
ap-10691	78	19	original	original	ADJ
ap-10691	78	20	hamiltonian	hamiltonian	NOUN
ap-10691	78	21	h0	h0	NOUN
ap-10691	78	22	is	be	AUX
ap-10691	78	23	obtained	obtain	VERB
ap-10691	78	24	by	by	ADP
ap-10691	78	25	the	the	DET
ap-10691	78	26	consecutive	consecutive	ADJ
ap-10691	78	27	application	application	NOUN
ap-10691	78	28	of	of	ADP
ap-10691	78	29	the	the	DET
ap-10691	78	30	operators	operator	NOUN
ap-10691	78	31	a+	a+	PUNCT
ap-10691	78	32	over	over	ADP
ap-10691	78	33	the	the	DET
ap-10691	78	34	ground	ground	NOUN
ap-10691	78	35	state	state	NOUN
ap-10691	78	36	ψ0	ψ0	PROPN
ap-10691	78	37	(	(	PUNCT
ap-10691	78	38	m	m	NOUN
ap-10691	78	39	)	)	PUNCT
ap-10691	78	40	of	of	ADP
ap-10691	78	41	hm	hm	INTJ
ap-10691	78	42	:	:	PUNCT
ap-10691	78	43	ψm	ψm	PROPN
ap-10691	78	44	(	(	PUNCT
ap-10691	78	45	0	0	NUM
ap-10691	78	46	)	)	PUNCT
ap-10691	79	1	=	=	SYM
ap-10691	79	2	m−1∏	m−1∏	PROPN
ap-10691	79	3	i=0	i=0	PROPN
ap-10691	79	4	a+	a+	PUNCT
ap-10691	79	5	i	i	NOUN
ap-10691	79	6	ψ	ψ	PROPN
ap-10691	79	7	0	0	PUNCT
ap-10691	79	8	(	(	PUNCT
ap-10691	79	9	m	m	NOUN
ap-10691	79	10	)	)	PUNCT
ap-10691	79	11	.	.	PUNCT
ap-10691	80	1	(	(	PUNCT
ap-10691	80	2	20	20	NUM
ap-10691	80	3	)	)	PUNCT
ap-10691	80	4	hence	hence	ADV
ap-10691	80	5	,	,	PUNCT
ap-10691	80	6	the	the	DET
ap-10691	80	7	eigenvalues	eigenvalue	NOUN
ap-10691	80	8	of	of	ADP
ap-10691	80	9	the	the	DET
ap-10691	80	10	hamiltonian	hamiltonian	ADJ
ap-10691	80	11	h0	h0	PROPN
ap-10691	80	12	are	be	AUX
ap-10691	80	13	obtained	obtain	VERB
ap-10691	80	14	in	in	ADP
ap-10691	80	15	an	an	DET
ap-10691	80	16	algebraic	algebraic	ADJ
ap-10691	80	17	way	way	NOUN
ap-10691	80	18	.	.	PUNCT
ap-10691	81	1	521	521	NUM
ap-10691	81	2	mariano	mariano	PROPN
ap-10691	81	3	a.	a.	PROPN
ap-10691	81	4	del	del	PROPN
ap-10691	81	5	olmo	olmo	PROPN
ap-10691	81	6	,	,	PUNCT
ap-10691	81	7	álvaro	álvaro	PROPN
ap-10691	81	8	romaniega	romaniega	PROPN
ap-10691	81	9	acta	acta	PROPN
ap-10691	81	10	polytechnica	polytechnica	PROPN
ap-10691	81	11	2.2	2.2	NUM
ap-10691	81	12	.	.	PUNCT
ap-10691	81	13	higher	high	ADJ
ap-10691	81	14	rank	rank	NOUN
ap-10691	81	15	ladder	ladder	NOUN
ap-10691	81	16	/	/	SYM
ap-10691	81	17	shift	shift	NOUN
ap-10691	81	18	operators	operator	NOUN
ap-10691	81	19	let	let	VERB
ap-10691	81	20	us	we	PRON
ap-10691	81	21	begin	begin	VERB
ap-10691	81	22	by	by	ADP
ap-10691	81	23	considering	consider	VERB
ap-10691	81	24	a	a	DET
ap-10691	81	25	family	family	NOUN
ap-10691	81	26	of	of	ADP
ap-10691	81	27	hamiltonians	hamiltonian	NOUN
ap-10691	81	28	{	{	PUNCT
ap-10691	81	29	hm}m∈i	hm}m∈i	NOUN
ap-10691	81	30	,	,	PUNCT
ap-10691	81	31	and	and	CCONJ
ap-10691	81	32	introduce	introduce	VERB
ap-10691	81	33	some	some	DET
ap-10691	81	34	general	general	ADJ
ap-10691	81	35	definitions	definition	NOUN
ap-10691	81	36	concerning	concern	VERB
ap-10691	81	37	two	two	NUM
ap-10691	81	38	types	type	NOUN
ap-10691	81	39	of	of	ADP
ap-10691	81	40	operators	operator	NOUN
ap-10691	81	41	:	:	PUNCT
ap-10691	81	42	•	•	NUM
ap-10691	81	43	ladder	ladder	NOUN
ap-10691	81	44	operators	operator	NOUN
ap-10691	81	45	,	,	PUNCT
ap-10691	81	46	which	which	PRON
ap-10691	81	47	connect	connect	VERB
ap-10691	81	48	eigenvectors	eigenvector	NOUN
ap-10691	81	49	of	of	ADP
ap-10691	81	50	a	a	DET
ap-10691	81	51	fixed	fix	VERB
ap-10691	81	52	hamiltonian	hamiltonian	ADJ
ap-10691	81	53	hk	hk	PROPN
ap-10691	81	54	(	(	PUNCT
ap-10691	81	55	with	with	ADP
ap-10691	81	56	k	k	PROPN
ap-10691	81	57	∈	∈	PROPN
ap-10691	81	58	i	i	PRON
ap-10691	81	59	fixed	fix	VERB
ap-10691	81	60	)	)	PUNCT
ap-10691	81	61	,	,	PUNCT
ap-10691	81	62	corresponding	correspond	VERB
ap-10691	81	63	to	to	ADP
ap-10691	81	64	different	different	ADJ
ap-10691	81	65	eigenvalues	eigenvalue	NOUN
ap-10691	81	66	.	.	PUNCT
ap-10691	82	1	•	•	NUM
ap-10691	82	2	shift	shift	NOUN
ap-10691	82	3	operators	operator	NOUN
ap-10691	82	4	,	,	PUNCT
ap-10691	82	5	which	which	PRON
ap-10691	82	6	connect	connect	VERB
ap-10691	82	7	eigenvectors	eigenvector	NOUN
ap-10691	82	8	of	of	ADP
ap-10691	82	9	different	different	ADJ
ap-10691	82	10	hamiltonians	hamiltonian	NOUN
ap-10691	82	11	within	within	ADP
ap-10691	82	12	the	the	DET
ap-10691	82	13	family	family	NOUN
ap-10691	82	14	{	{	PUNCT
ap-10691	82	15	hm}m∈i	hm}m∈i	NOUN
ap-10691	82	16	,	,	PUNCT
ap-10691	82	17	corresponding	correspond	VERB
ap-10691	82	18	to	to	ADP
ap-10691	82	19	the	the	DET
ap-10691	82	20	same	same	ADJ
ap-10691	82	21	eigenvalue	eigenvalue	NOUN
ap-10691	82	22	.	.	PUNCT
ap-10691	83	1	let	let	VERB
ap-10691	83	2	hm	hm	PRON
ap-10691	83	3	be	be	AUX
ap-10691	83	4	a	a	DET
ap-10691	83	5	hamiltonian	hamiltonian	NOUN
ap-10691	83	6	,	,	PUNCT
ap-10691	83	7	hm	hm	INTJ
ap-10691	84	1	the	the	DET
ap-10691	84	2	hilbert	hilbert	PROPN
ap-10691	84	3	space	space	NOUN
ap-10691	84	4	spanned	span	VERB
ap-10691	84	5	by	by	ADP
ap-10691	84	6	its	its	PRON
ap-10691	84	7	eigenvectors	eigenvector	NOUN
ap-10691	84	8	and	and	CCONJ
ap-10691	84	9	ψm	ψm	ADP
ap-10691	84	10	λ	λ	PROPN
ap-10691	84	11	an	an	DET
ap-10691	84	12	eigenvector	eigenvector	NOUN
ap-10691	84	13	of	of	ADP
ap-10691	84	14	hm	hm	INTJ
ap-10691	84	15	with	with	ADP
ap-10691	84	16	eigenvalue	eigenvalue	PROPN
ap-10691	84	17	λ	λ	PROPN
ap-10691	84	18	.	.	PUNCT
ap-10691	84	19	an	an	DET
ap-10691	84	20	operator	operator	NOUN
ap-10691	84	21	l±n	l±n	PROPN
ap-10691	84	22	(	(	PUNCT
ap-10691	84	23	with	with	ADP
ap-10691	84	24	n	n	PRON
ap-10691	84	25	∈	∈	PROPN
ap-10691	84	26	n	n	CCONJ
ap-10691	84	27	)	)	PUNCT
ap-10691	84	28	satisfying	satisfying	NOUN
ap-10691	84	29	:	:	PUNCT
ap-10691	84	30	l±n	l±n	VERB
ap-10691	84	31	:	:	PUNCT
ap-10691	84	32	hm	hm	INTJ
ap-10691	85	1	−→	−→	NOUN
ap-10691	86	1	hm	hm	INTJ
ap-10691	86	2	ψm	ψm	PROPN
ap-10691	87	1	λ	λ	PROPN
ap-10691	87	2	7−→	7−→	NUM
ap-10691	87	3	ψm	ψm	INTJ
ap-10691	88	1	λ±n	λ±n	PROPN
ap-10691	88	2	=	=	PUNCT
ap-10691	89	1	l±nψ	l±nψ	PROPN
ap-10691	89	2	m	m	VERB
ap-10691	89	3	λ	λ	X
ap-10691	89	4	(	(	PUNCT
ap-10691	89	5	21	21	NUM
ap-10691	89	6	)	)	PUNCT
ap-10691	89	7	is	be	AUX
ap-10691	89	8	called	call	VERB
ap-10691	89	9	a	a	DET
ap-10691	89	10	generalised	generalise	VERB
ap-10691	89	11	ladder	ladder	NOUN
ap-10691	89	12	operator	operator	NOUN
ap-10691	89	13	.	.	PUNCT
ap-10691	90	1	the	the	DET
ap-10691	90	2	standard	standard	ADJ
ap-10691	90	3	ladder	ladder	NOUN
ap-10691	90	4	operator	operator	NOUN
ap-10691	90	5	corresponds	correspond	VERB
ap-10691	90	6	to	to	ADP
ap-10691	90	7	the	the	DET
ap-10691	90	8	case	case	NOUN
ap-10691	90	9	n	n	NOUN
ap-10691	90	10	=	=	SYM
ap-10691	90	11	1	1	X
ap-10691	90	12	.	.	PUNCT
ap-10691	90	13	an	an	DET
ap-10691	90	14	operator	operator	NOUN
ap-10691	90	15	s±n	s±n	PROPN
ap-10691	90	16	(	(	PUNCT
ap-10691	90	17	with	with	ADP
ap-10691	90	18	n	n	PRON
ap-10691	90	19	∈	∈	PROPN
ap-10691	90	20	n	n	CCONJ
ap-10691	90	21	)	)	PUNCT
ap-10691	90	22	satisfying	satisfying	NOUN
ap-10691	90	23	:	:	PUNCT
ap-10691	90	24	s±n	s±n	NUM
ap-10691	90	25	:	:	PUNCT
ap-10691	90	26	hm	hm	INTJ
ap-10691	90	27	−→	−→	ADJ
ap-10691	90	28	hm±n	hm±n	PROPN
ap-10691	90	29	ψm	ψm	NOUN
ap-10691	90	30	λ	λ	NOUN
ap-10691	90	31	7−→	7−→	PROPN
ap-10691	90	32	ψm±n	ψm±n	PUNCT
ap-10691	90	33	λ	λ	NOUN
ap-10691	90	34	=	=	SYM
ap-10691	91	1	s±ψ	s±ψ	PROPN
ap-10691	91	2	m	m	VERB
ap-10691	91	3	λ	λ	NOUN
ap-10691	91	4	(	(	PUNCT
ap-10691	91	5	22	22	NUM
ap-10691	91	6	)	)	PUNCT
ap-10691	91	7	is	be	AUX
ap-10691	91	8	called	call	VERB
ap-10691	91	9	a	a	DET
ap-10691	91	10	generalised	generalise	VERB
ap-10691	91	11	shift	shift	NOUN
ap-10691	91	12	operador	operador	NOUN
ap-10691	91	13	.	.	PUNCT
ap-10691	92	1	to	to	PART
ap-10691	92	2	summarise	summarise	VERB
ap-10691	92	3	:	:	PUNCT
ap-10691	92	4	ladder	ladder	NOUN
ap-10691	92	5	operators	operator	NOUN
ap-10691	92	6	connect	connect	VERB
ap-10691	92	7	eigenstates	eigenstate	NOUN
ap-10691	92	8	of	of	ADP
ap-10691	92	9	a	a	DET
ap-10691	92	10	single	single	ADJ
ap-10691	92	11	hamiltonian	hamiltonian	NOUN
ap-10691	92	12	with	with	ADP
ap-10691	92	13	different	different	ADJ
ap-10691	92	14	eigenvalues	eigenvalue	NOUN
ap-10691	92	15	.	.	PUNCT
ap-10691	93	1	shift	shift	NOUN
ap-10691	93	2	operators	operator	NOUN
ap-10691	93	3	connect	connect	VERB
ap-10691	93	4	eigenstates	eigenstate	NOUN
ap-10691	93	5	of	of	ADP
ap-10691	93	6	different	different	ADJ
ap-10691	93	7	hamiltonians	hamiltonian	NOUN
ap-10691	93	8	within	within	ADP
ap-10691	93	9	the	the	DET
ap-10691	93	10	family	family	NOUN
ap-10691	93	11	{	{	PUNCT
ap-10691	93	12	hm	hm	INTJ
ap-10691	93	13	}	}	PUNCT
ap-10691	93	14	with	with	ADP
ap-10691	93	15	the	the	DET
ap-10691	93	16	same	same	ADJ
ap-10691	93	17	eigenvalue	eigenvalue	NOUN
ap-10691	93	18	.	.	PUNCT
ap-10691	94	1	2.3	2.3	NUM
ap-10691	94	2	.	.	PUNCT
ap-10691	94	3	superintegrability	superintegrability	NOUN
ap-10691	94	4	of	of	ADP
ap-10691	94	5	the	the	DET
ap-10691	94	6	ttw	ttw	PROPN
ap-10691	94	7	so(3)-hamiltonian	so(3)-hamiltonian	NUM
ap-10691	94	8	by	by	ADP
ap-10691	94	9	combining	combine	VERB
ap-10691	94	10	both	both	DET
ap-10691	94	11	types	type	NOUN
ap-10691	94	12	of	of	ADP
ap-10691	94	13	operators	operator	NOUN
ap-10691	94	14	in	in	ADP
ap-10691	94	15	a	a	DET
ap-10691	94	16	suitable	suitable	ADJ
ap-10691	94	17	way	way	NOUN
ap-10691	94	18	,	,	PUNCT
ap-10691	94	19	we	we	PRON
ap-10691	94	20	can	can	AUX
ap-10691	94	21	construct	construct	VERB
ap-10691	94	22	a	a	DET
ap-10691	94	23	symmetry	symmetry	NOUN
ap-10691	94	24	of	of	ADP
ap-10691	94	25	the	the	DET
ap-10691	94	26	hamiltonian	hamiltonian	ADJ
ap-10691	94	27	system	system	NOUN
ap-10691	94	28	–	–	PUNCT
ap-10691	94	29	namely	namely	ADV
ap-10691	94	30	,	,	PUNCT
ap-10691	94	31	a	a	DET
ap-10691	94	32	finite	finite	ADJ
ap-10691	94	33	differential	differential	NOUN
ap-10691	94	34	operator	operator	NOUN
ap-10691	94	35	x	x	PUNCT
ap-10691	94	36	that	that	PRON
ap-10691	94	37	commutes	commute	VERB
ap-10691	94	38	with	with	ADP
ap-10691	94	39	the	the	DET
ap-10691	94	40	hamiltonian	hamiltonian	NOUN
ap-10691	95	1	[	[	X
ap-10691	95	2	27–29	27–29	NUM
ap-10691	95	3	]	]	PUNCT
ap-10691	95	4	.	.	PUNCT
ap-10691	96	1	at	at	ADP
ap-10691	96	2	the	the	DET
ap-10691	96	3	classical	classical	ADJ
ap-10691	96	4	level	level	NOUN
ap-10691	96	5	,	,	PUNCT
ap-10691	96	6	these	these	DET
ap-10691	96	7	symmetries	symmetry	NOUN
ap-10691	96	8	correspond	correspond	VERB
ap-10691	96	9	to	to	ADP
ap-10691	96	10	integrals	integral	NOUN
ap-10691	96	11	of	of	ADP
ap-10691	96	12	motion	motion	NOUN
ap-10691	96	13	,	,	PUNCT
ap-10691	96	14	also	also	ADV
ap-10691	96	15	known	know	VERB
ap-10691	96	16	as	as	ADP
ap-10691	96	17	constants	constant	NOUN
ap-10691	96	18	of	of	ADP
ap-10691	96	19	motion	motion	NOUN
ap-10691	96	20	.	.	PUNCT
ap-10691	97	1	theorem	theorem	NOUN
ap-10691	97	2	1	1	NUM
ap-10691	97	3	.	.	PUNCT
ap-10691	98	1	let	let	VERB
ap-10691	98	2	hk	hk	PROPN
ap-10691	98	3	be	be	AUX
ap-10691	98	4	the	the	DET
ap-10691	98	5	hamiltonian	hamiltonian	NOUN
ap-10691	98	6	given	give	VERB
ap-10691	98	7	in	in	ADP
ap-10691	98	8	equation	equation	NOUN
ap-10691	98	9	(	(	PUNCT
ap-10691	98	10	12	12	NUM
ap-10691	98	11	)	)	PUNCT
ap-10691	98	12	.	.	PUNCT
ap-10691	99	1	suppose	suppose	VERB
ap-10691	99	2	there	there	PRON
ap-10691	99	3	exist	exist	VERB
ap-10691	99	4	ladder	ladder	NOUN
ap-10691	99	5	and	and	CCONJ
ap-10691	99	6	shift	shift	VERB
ap-10691	99	7	operators	operator	NOUN
ap-10691	99	8	as	as	SCONJ
ap-10691	99	9	defined	define	VERB
ap-10691	99	10	in	in	ADP
ap-10691	99	11	equations	equation	NOUN
ap-10691	99	12	(	(	PUNCT
ap-10691	99	13	21	21	NUM
ap-10691	99	14	)	)	PUNCT
ap-10691	99	15	and	and	CCONJ
ap-10691	99	16	(	(	PUNCT
ap-10691	99	17	22	22	NUM
ap-10691	99	18	)	)	PUNCT
ap-10691	99	19	,	,	PUNCT
ap-10691	99	20	respectively	respectively	ADV
ap-10691	99	21	:	:	PUNCT
ap-10691	100	1	ψβ	ψβ	PROPN
ap-10691	100	2	∈	∈	PROPN
ap-10691	100	3	hθ	hθ	VERB
ap-10691	100	4	l±2n−−−→	l±2n−−−→	NOUN
ap-10691	100	5	n∈n∗	n∈n∗	PROPN
ap-10691	100	6	ψβ±2n	ψβ±2n	PROPN
ap-10691	100	7	∈	∈	PROPN
ap-10691	100	8	hθ	hθ	NOUN
ap-10691	100	9	,	,	PUNCT
ap-10691	100	10	φmk	φmk	NOUN
ap-10691	100	11	∈	∈	PROPN
ap-10691	100	12	hϕ	hϕ	NOUN
ap-10691	100	13	mk	mk	PROPN
ap-10691	100	14	s±2m−−−−→	s±2m−−−−→	PROPN
ap-10691	100	15	m∈n∗	m∈n∗	PROPN
ap-10691	100	16	φmk±2	φmk±2	PROPN
ap-10691	100	17	m	m	PROPN
ap-10691	100	18	∈	∈	PROPN
ap-10691	100	19	hϕ	hϕ	PROPN
ap-10691	100	20	mk±2	mk±2	PROPN
ap-10691	100	21	m	m	PROPN
ap-10691	100	22	,	,	PUNCT
ap-10691	100	23	(	(	PUNCT
ap-10691	100	24	23	23	NUM
ap-10691	100	25	)	)	PUNCT
ap-10691	100	26	where	where	SCONJ
ap-10691	100	27	ψβ	ψβ	PROPN
ap-10691	100	28	∈	∈	PROPN
ap-10691	101	1	hθ	hθ	PROPN
ap-10691	101	2	is	be	AUX
ap-10691	101	3	an	an	DET
ap-10691	101	4	eigenvector	eigenvector	NOUN
ap-10691	101	5	of	of	ADP
ap-10691	101	6	hθ	hθ	PROPN
ap-10691	101	7	with	with	ADP
ap-10691	101	8	eigenvalue	eigenvalue	PROPN
ap-10691	101	9	β2	β2	PROPN
ap-10691	101	10	and	and	CCONJ
ap-10691	101	11	φmk	φmk	NOUN
ap-10691	101	12	∈	∈	PROPN
ap-10691	101	13	hϕ	hϕ	NOUN
ap-10691	101	14	mk	mk	PROPN
ap-10691	101	15	is	be	AUX
ap-10691	101	16	an	an	DET
ap-10691	101	17	eigenvector	eigenvector	NOUN
ap-10691	101	18	of	of	ADP
ap-10691	101	19	hϕ	hϕ	PROPN
ap-10691	101	20	mk	mk	PROPN
ap-10691	101	21	as	as	SCONJ
ap-10691	101	22	given	give	VERB
ap-10691	101	23	in	in	ADP
ap-10691	101	24	(	(	PUNCT
ap-10691	101	25	10	10	NUM
ap-10691	101	26	)	)	PUNCT
ap-10691	101	27	,	,	PUNCT
ap-10691	102	1	such	such	ADJ
ap-10691	102	2	that	that	SCONJ
ap-10691	102	3	k	k	PROPN
ap-10691	102	4	β	β	X
ap-10691	102	5	=	=	SYM
ap-10691	102	6	mk	mk	PROPN
ap-10691	102	7	.	.	PUNCT
ap-10691	103	1	then	then	ADV
ap-10691	103	2	,	,	PUNCT
ap-10691	103	3	if	if	SCONJ
ap-10691	103	4	k	k	PROPN
ap-10691	103	5	=	=	VERB
ap-10691	103	6	m	m	VERB
ap-10691	103	7	n	n	INTJ
ap-10691	103	8	,	,	PUNCT
ap-10691	103	9	there	there	PRON
ap-10691	103	10	are	be	VERB
ap-10691	103	11	two	two	NUM
ap-10691	103	12	symmetry	symmetry	NOUN
ap-10691	103	13	operators	operator	NOUN
ap-10691	103	14	(	(	PUNCT
ap-10691	103	15	x±	x±	PROPN
ap-10691	103	16	)	)	PUNCT
ap-10691	103	17	of	of	ADP
ap-10691	103	18	the	the	DET
ap-10691	103	19	hamiltonian	hamiltonian	PROPN
ap-10691	103	20	hk	hk	PROPN
ap-10691	103	21	,	,	PUNCT
ap-10691	103	22	(	(	PUNCT
ap-10691	103	23	i.e.	i.e.	X
ap-10691	103	24	operators	operator	NOUN
ap-10691	103	25	that	that	PRON
ap-10691	103	26	commute	commute	VERB
ap-10691	103	27	with	with	ADP
ap-10691	103	28	hk	hk	PROPN
ap-10691	103	29	)	)	PUNCT
ap-10691	103	30	,	,	PUNCT
ap-10691	103	31	defined	define	VERB
ap-10691	103	32	as	as	ADP
ap-10691	103	33	:	:	PUNCT
ap-10691	103	34	x±	x±	PROPN
ap-10691	103	35	:	:	PUNCT
ap-10691	103	36	=	=	PUNCT
ap-10691	103	37	l±2n	l±2n	ADJ
ap-10691	103	38	s±2	s±2	NOUN
ap-10691	103	39	m	m	PROPN
ap-10691	103	40	,	,	PUNCT
ap-10691	103	41	m	m	PROPN
ap-10691	103	42	,	,	PUNCT
ap-10691	103	43	n	n	PRON
ap-10691	103	44	∈	∈	PROPN
ap-10691	103	45	n∗	n∗	PROPN
ap-10691	103	46	≡	≡	PROPN
ap-10691	103	47	n	n	CCONJ
ap-10691	103	48	−	−	PROPN
ap-10691	103	49	{	{	PUNCT
ap-10691	103	50	0	0	NUM
ap-10691	103	51	}	}	PUNCT
ap-10691	103	52	.	.	PUNCT
ap-10691	104	1	(	(	PUNCT
ap-10691	104	2	24	24	NUM
ap-10691	104	3	)	)	PUNCT
ap-10691	104	4	since	since	SCONJ
ap-10691	104	5	there	there	PRON
ap-10691	104	6	are	be	VERB
ap-10691	104	7	2	2	NUM
ap-10691	104	8	×	×	NOUN
ap-10691	104	9	2	2	NUM
ap-10691	104	10	−	−	NOUN
ap-10691	104	11	1	1	NUM
ap-10691	104	12	independent	independent	ADJ
ap-10691	104	13	symmetries	symmetry	NOUN
ap-10691	104	14	,	,	PUNCT
ap-10691	104	15	namely	namely	ADV
ap-10691	104	16	x±	x±	PROPN
ap-10691	104	17	and	and	CCONJ
ap-10691	104	18	hk	hk	PROPN
ap-10691	104	19	,	,	PUNCT
ap-10691	104	20	the	the	DET
ap-10691	104	21	system	system	NOUN
ap-10691	104	22	is	be	AUX
ap-10691	104	23	maximally	maximally	ADV
ap-10691	104	24	superintegrable	superintegrable	ADJ
ap-10691	104	25	.	.	PUNCT
ap-10691	105	1	proof	proof	NOUN
ap-10691	105	2	.	.	PUNCT
ap-10691	106	1	we	we	PRON
ap-10691	106	2	only	only	ADV
ap-10691	106	3	need	need	VERB
ap-10691	106	4	to	to	PART
ap-10691	106	5	prove	prove	VERB
ap-10691	106	6	that	that	SCONJ
ap-10691	106	7	the	the	DET
ap-10691	106	8	two	two	NUM
ap-10691	106	9	operators	operator	NOUN
ap-10691	106	10	x±	x±	PROPN
ap-10691	106	11	defined	define	VERB
ap-10691	106	12	in	in	ADP
ap-10691	106	13	equation	equation	NOUN
ap-10691	106	14	(	(	PUNCT
ap-10691	106	15	24	24	NUM
ap-10691	106	16	)	)	PUNCT
ap-10691	106	17	commute	commute	NOUN
ap-10691	106	18	with	with	ADP
ap-10691	106	19	the	the	DET
ap-10691	106	20	hamiltonian	hamiltonian	NOUN
ap-10691	106	21	,	,	PUNCT
ap-10691	106	22	i.e.	i.e.	X
ap-10691	106	23	:	:	PUNCT
ap-10691	106	24	[	[	X
ap-10691	106	25	hk	hk	X
ap-10691	106	26	,	,	PUNCT
ap-10691	106	27	x	x	X
ap-10691	106	28	±	±	NUM
ap-10691	106	29	]	]	PUNCT
ap-10691	106	30	=	=	SYM
ap-10691	106	31	0	0	NUM
ap-10691	106	32	,	,	PUNCT
ap-10691	106	33	∀mk	∀mk	PROPN
ap-10691	106	34	,	,	PUNCT
ap-10691	106	35	β	β	X
ap-10691	106	36	,	,	PUNCT
ap-10691	106	37	e	e	NOUN
ap-10691	106	38	,	,	PUNCT
ap-10691	106	39	(	(	PUNCT
ap-10691	106	40	25	25	NUM
ap-10691	106	41	)	)	PUNCT
ap-10691	106	42	as	as	SCONJ
ap-10691	106	43	shown	show	VERB
ap-10691	106	44	in	in	ADP
ap-10691	106	45	[	[	X
ap-10691	106	46	28	28	NUM
ap-10691	106	47	]	]	PUNCT
ap-10691	106	48	.	.	PUNCT
ap-10691	107	1	let	let	VERB
ap-10691	107	2	us	we	PRON
ap-10691	107	3	consider	consider	VERB
ap-10691	107	4	the	the	DET
ap-10691	107	5	eigenfunction	eigenfunction	NOUN
ap-10691	107	6	φmk	φmk	NOUN
ap-10691	107	7	ψβ	ψβ	NOUN
ap-10691	107	8	of	of	ADP
ap-10691	107	9	hk	hk	PROPN
ap-10691	107	10	with	with	ADP
ap-10691	107	11	eigenvalue	eigenvalue	PROPN
ap-10691	107	12	e.	e.	PROPN
ap-10691	107	13	then	then	ADV
ap-10691	107	14	:	:	PUNCT
ap-10691	108	1	[	[	X
ap-10691	108	2	hk	hk	X
ap-10691	108	3	,	,	PUNCT
ap-10691	108	4	x	x	X
ap-10691	108	5	±]φmk	±]φmk	NOUN
ap-10691	108	6	ψβ	ψβ	NOUN
ap-10691	108	7	=	=	PRON
ap-10691	108	8	(	(	PUNCT
ap-10691	108	9	hk	hk	PROPN
ap-10691	108	10	−	−	PROPN
ap-10691	108	11	e)x±φmk	e)x±φmk	PROPN
ap-10691	108	12	ψβ	ψβ	NOUN
ap-10691	108	13	.	.	PUNCT
ap-10691	109	1	(	(	PUNCT
ap-10691	109	2	26	26	NUM
ap-10691	109	3	)	)	PUNCT
ap-10691	109	4	on	on	ADP
ap-10691	109	5	the	the	DET
ap-10691	109	6	other	other	ADJ
ap-10691	109	7	hand	hand	NOUN
ap-10691	109	8	,	,	PUNCT
ap-10691	109	9	from	from	ADP
ap-10691	109	10	equations	equation	NOUN
ap-10691	109	11	(	(	PUNCT
ap-10691	109	12	23	23	NUM
ap-10691	109	13	)	)	PUNCT
ap-10691	109	14	and	and	CCONJ
ap-10691	109	15	(	(	PUNCT
ap-10691	109	16	24	24	NUM
ap-10691	109	17	)	)	PUNCT
ap-10691	109	18	,	,	PUNCT
ap-10691	109	19	we	we	PRON
ap-10691	109	20	have	have	VERB
ap-10691	109	21	:	:	PUNCT
ap-10691	110	1	x±φmk	x±φmk	PROPN
ap-10691	110	2	ψβ	ψβ	PROPN
ap-10691	110	3	=	=	PUNCT
ap-10691	110	4	ψβ±2nφmk±2	ψβ±2nφmk±2	PROPN
ap-10691	110	5	m.	m.	NOUN
ap-10691	110	6	(	(	PUNCT
ap-10691	110	7	27	27	NUM
ap-10691	110	8	)	)	PUNCT
ap-10691	110	9	the	the	DET
ap-10691	110	10	hamiltonian	hamiltonian	PROPN
ap-10691	110	11	hk	hk	PROPN
ap-10691	110	12	,	,	PUNCT
ap-10691	110	13	using	use	VERB
ap-10691	110	14	equations	equation	NOUN
ap-10691	110	15	(	(	PUNCT
ap-10691	110	16	10	10	NUM
ap-10691	110	17	)	)	PUNCT
ap-10691	110	18	and	and	CCONJ
ap-10691	110	19	(	(	PUNCT
ap-10691	110	20	12	12	NUM
ap-10691	110	21	)	)	PUNCT
ap-10691	110	22	,	,	PUNCT
ap-10691	110	23	can	can	AUX
ap-10691	110	24	be	be	AUX
ap-10691	110	25	rewritten	rewrite	VERB
ap-10691	110	26	as	as	ADP
ap-10691	110	27	:	:	PUNCT
ap-10691	110	28	hk	hk	PROPN
ap-10691	110	29	=	=	SYM
ap-10691	110	30	hϕ	hϕ	PROPN
ap-10691	110	31	+	+	NUM
ap-10691	110	32	mk	mk	PROPN
ap-10691	110	33	2	2	NUM
ap-10691	110	34	cos2	cos2	PROPN
ap-10691	110	35	ϕ	ϕ	NOUN
ap-10691	110	36	+	+	CCONJ
ap-10691	110	37	k2(hθ	k2(hθ	PROPN
ap-10691	110	38	−	−	PROPN
ap-10691	110	39	β2	β2	NOUN
ap-10691	110	40	)	)	PUNCT
ap-10691	110	41	cos2	cos2	PROPN
ap-10691	110	42	ϕ	ϕ	PROPN
ap-10691	110	43	.	.	PUNCT
ap-10691	111	1	(	(	PUNCT
ap-10691	111	2	28	28	NUM
ap-10691	111	3	)	)	PUNCT
ap-10691	111	4	since	since	SCONJ
ap-10691	111	5	mk	mk	PROPN
ap-10691	111	6	2	2	NUM
ap-10691	111	7	=	=	SYM
ap-10691	111	8	(	(	PUNCT
ap-10691	111	9	mk	mk	NOUN
ap-10691	111	10	±2m)2	±2m)2	NUM
ap-10691	111	11	−(2m)2	−(2m)2	PROPN
ap-10691	111	12	∓4mk	∓4mk	PROPN
ap-10691	111	13	m	m	PROPN
ap-10691	111	14	,	,	PUNCT
ap-10691	111	15	we	we	PRON
ap-10691	111	16	obtain	obtain	VERB
ap-10691	111	17	:	:	PUNCT
ap-10691	111	18	hk	hk	PROPN
ap-10691	111	19	=	=	PROPN
ap-10691	111	20	hϕ	hϕ	PROPN
ap-10691	111	21	mk±2	mk±2	PROPN
ap-10691	111	22	m	m	PROPN
ap-10691	111	23	−	−	PROPN
ap-10691	111	24	(	(	PUNCT
ap-10691	111	25	2m)2	2m)2	NUM
ap-10691	111	26	cos2	cos2	PROPN
ap-10691	112	1	ϕ	ϕ	PROPN
ap-10691	112	2	∓	∓	PROPN
ap-10691	112	3	4mkm	4mkm	NUM
ap-10691	112	4	cos2	cos2	PROPN
ap-10691	112	5	ϕ	ϕ	PROPN
ap-10691	112	6	+	+	CCONJ
ap-10691	112	7	k2(hθ	k2(hθ	PROPN
ap-10691	112	8	−	−	PROPN
ap-10691	112	9	β2	β2	NOUN
ap-10691	112	10	)	)	PUNCT
ap-10691	112	11	cos2	cos2	PROPN
ap-10691	112	12	ϕ	ϕ	PROPN
ap-10691	112	13	.	.	PUNCT
ap-10691	113	1	(	(	PUNCT
ap-10691	113	2	29	29	NUM
ap-10691	113	3	)	)	PUNCT
ap-10691	113	4	from	from	ADP
ap-10691	113	5	equations	equation	NOUN
ap-10691	113	6	(	(	PUNCT
ap-10691	113	7	27	27	NUM
ap-10691	113	8	)	)	PUNCT
ap-10691	113	9	and	and	CCONJ
ap-10691	113	10	(	(	PUNCT
ap-10691	113	11	29	29	NUM
ap-10691	113	12	)	)	PUNCT
ap-10691	113	13	,	,	PUNCT
ap-10691	113	14	it	it	PRON
ap-10691	113	15	follows	follow	VERB
ap-10691	113	16	that	that	SCONJ
ap-10691	113	17	:	:	PUNCT
ap-10691	114	1	hk	hk	PROPN
ap-10691	114	2	x	x	X
ap-10691	114	3	±φmk	±φmk	PROPN
ap-10691	114	4	ψβ	ψβ	PROPN
ap-10691	115	1	=	=	PUNCT
ap-10691	115	2	eφmk±2mψβ±2n	eφmk±2mψβ±2n	PROPN
ap-10691	115	3	,	,	PUNCT
ap-10691	115	4	(	(	PUNCT
ap-10691	115	5	30	30	NUM
ap-10691	115	6	)	)	PUNCT
ap-10691	115	7	where	where	SCONJ
ap-10691	115	8	we	we	PRON
ap-10691	115	9	used	use	VERB
ap-10691	115	10	the	the	DET
ap-10691	115	11	relation	relation	NOUN
ap-10691	115	12	mk	mk	NOUN
ap-10691	115	13	=	=	NOUN
ap-10691	115	14	kβ	kβ	VERB
ap-10691	115	15	together	together	ADV
ap-10691	115	16	with	with	ADP
ap-10691	115	17	the	the	DET
ap-10691	115	18	rationality	rationality	NOUN
ap-10691	115	19	condition	condition	NOUN
ap-10691	115	20	k	k	PROPN
ap-10691	116	1	=	=	PUNCT
ap-10691	116	2	m	m	VERB
ap-10691	116	3	n	n	ADV
ap-10691	116	4	.	.	PUNCT
ap-10691	117	1	by	by	ADP
ap-10691	117	2	substituting	substitute	VERB
ap-10691	117	3	equations	equation	NOUN
ap-10691	117	4	(	(	PUNCT
ap-10691	117	5	27	27	NUM
ap-10691	117	6	)	)	PUNCT
ap-10691	117	7	and	and	CCONJ
ap-10691	117	8	(	(	PUNCT
ap-10691	117	9	30	30	NUM
ap-10691	117	10	)	)	PUNCT
ap-10691	117	11	into	into	ADP
ap-10691	117	12	(	(	PUNCT
ap-10691	117	13	26	26	NUM
ap-10691	117	14	)	)	PUNCT
ap-10691	117	15	,	,	PUNCT
ap-10691	117	16	we	we	PRON
ap-10691	117	17	find	find	VERB
ap-10691	117	18	that	that	SCONJ
ap-10691	117	19	[	[	X
ap-10691	117	20	hk	hk	PROPN
ap-10691	117	21	,	,	PUNCT
ap-10691	117	22	x	x	X
ap-10691	117	23	±	±	NUM
ap-10691	117	24	]	]	PUNCT
ap-10691	117	25	=	=	SYM
ap-10691	117	26	0	0	NUM
ap-10691	117	27	,	,	PUNCT
ap-10691	117	28	as	as	SCONJ
ap-10691	117	29	claimed	claim	VERB
ap-10691	117	30	.	.	PUNCT
ap-10691	118	1	3	3	X
ap-10691	118	2	.	.	X
ap-10691	118	3	analysis	analysis	NOUN
ap-10691	118	4	of	of	ADP
ap-10691	118	5	the	the	DET
ap-10691	118	6	ttw	ttw	NOUN
ap-10691	118	7	so(3)-hamiltonian	so(3)-hamiltonian	NOUN
ap-10691	118	8	we	we	PRON
ap-10691	118	9	will	will	AUX
ap-10691	118	10	use	use	VERB
ap-10691	118	11	the	the	DET
ap-10691	118	12	theory	theory	NOUN
ap-10691	118	13	of	of	ADP
ap-10691	118	14	hamiltonian	hamiltonian	ADJ
ap-10691	118	15	factorisation	factorisation	NOUN
ap-10691	118	16	[	[	X
ap-10691	118	17	24	24	NUM
ap-10691	118	18	]	]	PUNCT
ap-10691	118	19	to	to	PART
ap-10691	118	20	study	study	VERB
ap-10691	118	21	the	the	DET
ap-10691	118	22	ttw	ttw	NOUN
ap-10691	118	23	so(3)-hamiltonian	so(3)-hamiltonian	NOUN
ap-10691	118	24	given	give	VERB
ap-10691	118	25	in	in	ADP
ap-10691	118	26	equation	equation	NOUN
ap-10691	118	27	(	(	PUNCT
ap-10691	118	28	8)	8)	NUM
ap-10691	118	29	.	.	NOUN
ap-10691	118	30	3.1	3.1	NUM
ap-10691	118	31	.	.	PUNCT
ap-10691	118	32	factorisation	factorisation	NOUN
ap-10691	118	33	of	of	ADP
ap-10691	118	34	hθ	hθ	NOUN
ap-10691	118	35	let	let	VERB
ap-10691	118	36	us	we	PRON
ap-10691	118	37	start	start	VERB
ap-10691	118	38	with	with	ADP
ap-10691	118	39	the	the	DET
ap-10691	118	40	hamiltonian	hamiltonian	ADJ
ap-10691	118	41	hθ	hθ	NOUN
ap-10691	118	42	(	(	PUNCT
ap-10691	118	43	11	11	NUM
ap-10691	118	44	)	)	PUNCT
ap-10691	118	45	,	,	PUNCT
ap-10691	118	46	which	which	PRON
ap-10691	118	47	is	be	AUX
ap-10691	118	48	a	a	DET
ap-10691	118	49	trigonometric	trigonometric	ADJ
ap-10691	118	50	pöschl	pöschl	NOUN
ap-10691	118	51	-	-	PUNCT
ap-10691	118	52	teller	teller	NOUN
ap-10691	118	53	hamiltonian	hamiltonian	NOUN
ap-10691	119	1	[	[	X
ap-10691	119	2	30	30	NUM
ap-10691	119	3	]	]	PUNCT
ap-10691	119	4	:	:	PUNCT
ap-10691	119	5	hθ	hθ	NOUN
ap-10691	119	6	=	=	PUNCT
ap-10691	119	7	−∂2	−∂2	PROPN
ap-10691	119	8	θ	θ	PROPN
ap-10691	119	9	+	+	CCONJ
ap-10691	119	10	l20	l20	PROPN
ap-10691	119	11	−	−	PROPN
ap-10691	119	12	1	1	NUM
ap-10691	119	13	4	4	NUM
ap-10691	119	14	cos2	cos2	NOUN
ap-10691	119	15	θ	θ	PROPN
ap-10691	120	1	+	+	CCONJ
ap-10691	120	2	l21	l21	PROPN
ap-10691	120	3	−	−	NOUN
ap-10691	120	4	1	1	NUM
ap-10691	120	5	4	4	NUM
ap-10691	120	6	sin2	sin2	NOUN
ap-10691	120	7	θ	θ	PROPN
ap-10691	120	8	.	.	PUNCT
ap-10691	121	1	(	(	PUNCT
ap-10691	121	2	31	31	NUM
ap-10691	121	3	)	)	PUNCT
ap-10691	121	4	the	the	DET
ap-10691	121	5	corresponding	correspond	VERB
ap-10691	121	6	operators	operator	NOUN
ap-10691	121	7	a±	a±	PROPN
ap-10691	121	8	n	n	PROPN
ap-10691	121	9	and	and	CCONJ
ap-10691	121	10	λn	λn	PROPN
ap-10691	121	11	(	(	PUNCT
ap-10691	121	12	13	13	NUM
ap-10691	121	13	)	)	PUNCT
ap-10691	121	14	,	,	PUNCT
ap-10691	121	15	relative	relative	ADJ
ap-10691	121	16	to	to	ADP
ap-10691	121	17	hθ	hθ	PROPN
ap-10691	121	18	are	be	AUX
ap-10691	121	19	[	[	X
ap-10691	121	20	6	6	NUM
ap-10691	121	21	]	]	PUNCT
ap-10691	121	22	:	:	PUNCT
ap-10691	121	23	a±	a±	PROPN
ap-10691	121	24	n	n	PROPN
ap-10691	121	25	=	=	SYM
ap-10691	121	26	±	±	NUM
ap-10691	121	27	∂θ	∂θ	PROPN
ap-10691	122	1	−	−	PROPN
ap-10691	122	2	(	(	PUNCT
ap-10691	122	3	l0	l0	NOUN
ap-10691	122	4	+	+	CCONJ
ap-10691	122	5	n+	n+	NUM
ap-10691	122	6	1	1	NUM
ap-10691	122	7	2	2	NUM
ap-10691	122	8	)	)	PUNCT
ap-10691	122	9	tan	tan	NOUN
ap-10691	122	10	θ	θ	PROPN
ap-10691	122	11	+	+	CCONJ
ap-10691	122	12	(	(	PUNCT
ap-10691	122	13	l1	l1	PROPN
ap-10691	122	14	+	+	CCONJ
ap-10691	122	15	n+	n+	NUM
ap-10691	122	16	1	1	NUM
ap-10691	122	17	2	2	NUM
ap-10691	122	18	)	)	PUNCT
ap-10691	122	19	cot	cot	NOUN
ap-10691	122	20	θ	θ	NOUN
ap-10691	122	21	,	,	PUNCT
ap-10691	122	22	λn	λn	PROPN
ap-10691	122	23	≡e′	≡e′	PROPN
ap-10691	122	24	n	n	PRON
ap-10691	122	25	≡	≡	PROPN
ap-10691	122	26	β2	β2	PROPN
ap-10691	122	27	=	=	SYM
ap-10691	122	28	(	(	PUNCT
ap-10691	122	29	l0	l0	PROPN
ap-10691	122	30	+	+	CCONJ
ap-10691	122	31	l1	l1	PROPN
ap-10691	122	32	+	+	CCONJ
ap-10691	122	33	2n+	2n+	NUM
ap-10691	122	34	1)2	1)2	NUM
ap-10691	122	35	.	.	PUNCT
ap-10691	123	1	(	(	PUNCT
ap-10691	123	2	32	32	NUM
ap-10691	123	3	)	)	PUNCT
ap-10691	123	4	522	522	NUM
ap-10691	123	5	vol	vol	NOUN
ap-10691	123	6	.	.	PUNCT
ap-10691	124	1	65	65	NUM
ap-10691	124	2	no	no	NOUN
ap-10691	124	3	.	.	PUNCT
ap-10691	125	1	5/2025	5/2025	NUM
ap-10691	125	2	classical	classical	ADJ
ap-10691	125	3	and	and	CCONJ
ap-10691	125	4	quantum	quantum	ADJ
ap-10691	125	5	superintegrable	superintegrable	ADJ
ap-10691	125	6	systems	system	NOUN
ap-10691	125	7	on	on	ADP
ap-10691	125	8	the	the	DET
ap-10691	125	9	sphere	sphere	NOUN
ap-10691	125	10	.	.	PUNCT
ap-10691	125	11	.	.	PUNCT
ap-10691	125	12	.	.	PUNCT
ap-10691	126	1	the	the	DET
ap-10691	126	2	hierarchy	hierarchy	NOUN
ap-10691	126	3	of	of	ADP
ap-10691	126	4	hamiltonians	hamiltonian	NOUN
ap-10691	126	5	hθ	hθ	PROPN
ap-10691	126	6	n	n	CCONJ
ap-10691	126	7	obtained	obtain	VERB
ap-10691	126	8	by	by	ADP
ap-10691	126	9	using	use	VERB
ap-10691	126	10	equation	equation	NOUN
ap-10691	126	11	(	(	PUNCT
ap-10691	126	12	13	13	NUM
ap-10691	126	13	)	)	PUNCT
ap-10691	126	14	have	have	VERB
ap-10691	126	15	the	the	DET
ap-10691	126	16	same	same	ADJ
ap-10691	126	17	expression	expression	NOUN
ap-10691	126	18	of	of	ADP
ap-10691	126	19	hθ	hθ	PROPN
ap-10691	126	20	(	(	PUNCT
ap-10691	126	21	equation	equation	NOUN
ap-10691	126	22	(	(	PUNCT
ap-10691	126	23	11	11	NUM
ap-10691	126	24	)	)	PUNCT
ap-10691	126	25	)	)	PUNCT
ap-10691	126	26	,	,	PUNCT
ap-10691	126	27	that	that	SCONJ
ap-10691	126	28	it	it	PRON
ap-10691	126	29	is	be	AUX
ap-10691	126	30	the	the	DET
ap-10691	126	31	hamiltonian	hamiltonian	NOUN
ap-10691	126	32	with	with	ADP
ap-10691	126	33	n	n	NOUN
ap-10691	126	34	=	=	SYM
ap-10691	126	35	0	0	NUM
ap-10691	126	36	of	of	ADP
ap-10691	126	37	the	the	DET
ap-10691	126	38	hierarchy	hierarchy	NOUN
ap-10691	126	39	,	,	PUNCT
ap-10691	126	40	after	after	ADP
ap-10691	126	41	the	the	DET
ap-10691	126	42	changes	change	NOUN
ap-10691	126	43	l0	l0	PROPN
ap-10691	126	44	→	→	SYM
ap-10691	126	45	l0	l0	PROPN
ap-10691	126	46	+	+	CCONJ
ap-10691	126	47	n	n	PROPN
ap-10691	126	48	and	and	CCONJ
ap-10691	126	49	l1	l1	PROPN
ap-10691	126	50	→	→	SYM
ap-10691	126	51	l1	l1	PROPN
ap-10691	126	52	+	+	CCONJ
ap-10691	126	53	n.	n.	VERB
ap-10691	126	54	the	the	DET
ap-10691	126	55	hierarchy	hierarchy	NOUN
ap-10691	126	56	of	of	ADP
ap-10691	126	57	hamiltonians	hamiltonian	NOUN
ap-10691	126	58	hθ	hθ	PROPN
ap-10691	126	59	n	n	CCONJ
ap-10691	126	60	,	,	PUNCT
ap-10691	126	61	defined	define	VERB
ap-10691	126	62	via	via	ADP
ap-10691	126	63	equation	equation	NOUN
ap-10691	126	64	(	(	PUNCT
ap-10691	126	65	13	13	NUM
ap-10691	126	66	)	)	PUNCT
ap-10691	126	67	,	,	PUNCT
ap-10691	126	68	all	all	PRON
ap-10691	126	69	share	share	VERB
ap-10691	126	70	the	the	DET
ap-10691	126	71	same	same	ADJ
ap-10691	126	72	functional	functional	ADJ
ap-10691	126	73	form	form	NOUN
ap-10691	126	74	as	as	ADP
ap-10691	126	75	hθ	hθ	PROPN
ap-10691	126	76	in	in	ADP
ap-10691	126	77	equation	equation	NOUN
ap-10691	126	78	(	(	PUNCT
ap-10691	126	79	11	11	NUM
ap-10691	126	80	)	)	PUNCT
ap-10691	126	81	–	–	PUNCT
ap-10691	126	82	which	which	PRON
ap-10691	126	83	corresponds	correspond	VERB
ap-10691	126	84	to	to	ADP
ap-10691	126	85	the	the	DET
ap-10691	126	86	case	case	NOUN
ap-10691	126	87	n	n	NOUN
ap-10691	126	88	=	=	SYM
ap-10691	126	89	0	0	NUM
ap-10691	126	90	,	,	PUNCT
ap-10691	126	91	up	up	ADP
ap-10691	126	92	to	to	ADP
ap-10691	126	93	the	the	DET
ap-10691	126	94	parameter	parameter	NOUN
ap-10691	126	95	shifts	shift	NOUN
ap-10691	126	96	l0	l0	PROPN
ap-10691	126	97	→	→	SYM
ap-10691	126	98	l0	l0	PROPN
ap-10691	126	99	+	+	CCONJ
ap-10691	126	100	n	n	PROPN
ap-10691	126	101	and	and	CCONJ
ap-10691	126	102	l1	l1	PROPN
ap-10691	126	103	→	→	SYM
ap-10691	126	104	l1	l1	PROPN
ap-10691	126	105	+	+	CCONJ
ap-10691	126	106	n.	n.	PROPN
ap-10691	126	107	the	the	DET
ap-10691	126	108	fundamental	fundamental	ADJ
ap-10691	126	109	states	state	NOUN
ap-10691	126	110	of	of	ADP
ap-10691	126	111	hθ	hθ	PROPN
ap-10691	126	112	n	n	PRON
ap-10691	126	113	are	be	AUX
ap-10691	126	114	obtained	obtain	VERB
ap-10691	126	115	by	by	ADP
ap-10691	126	116	equation	equation	NOUN
ap-10691	126	117	(	(	PUNCT
ap-10691	126	118	16	16	NUM
ap-10691	126	119	)	)	PUNCT
ap-10691	126	120	and	and	CCONJ
ap-10691	126	121	they	they	PRON
ap-10691	126	122	are	be	AUX
ap-10691	126	123	:	:	PUNCT
ap-10691	126	124	ψ0	ψ0	PROPN
ap-10691	126	125	(	(	PUNCT
ap-10691	126	126	n)(θ	n)(θ	PROPN
ap-10691	126	127	)	)	PUNCT
ap-10691	126	128	=	=	PUNCT
ap-10691	126	129	cosl0+n+	cosl0+n+	NOUN
ap-10691	126	130	1	1	NUM
ap-10691	126	131	2	2	NUM
ap-10691	126	132	θ	θ	NOUN
ap-10691	126	133	sinl1+n+	sinl1+n+	PROPN
ap-10691	126	134	1	1	NUM
ap-10691	126	135	2	2	NUM
ap-10691	126	136	θ	θ	NOUN
ap-10691	126	137	,	,	PUNCT
ap-10691	126	138	(	(	PUNCT
ap-10691	126	139	33	33	NUM
ap-10691	126	140	)	)	PUNCT
ap-10691	126	141	and	and	CCONJ
ap-10691	126	142	the	the	DET
ap-10691	126	143	excited	excited	ADJ
ap-10691	126	144	states	state	NOUN
ap-10691	126	145	of	of	ADP
ap-10691	126	146	the	the	DET
ap-10691	126	147	initial	initial	ADJ
ap-10691	126	148	hamiltonian	hamiltonian	NOUN
ap-10691	126	149	hθ	hθ	PROPN
ap-10691	126	150	≡	≡	PROPN
ap-10691	126	151	hθ	hθ	INTJ
ap-10691	126	152	0	0	NUM
ap-10691	126	153	are	be	AUX
ap-10691	126	154	given	give	VERB
ap-10691	126	155	by	by	ADP
ap-10691	126	156	:	:	PUNCT
ap-10691	126	157	ψn	ψn	PROPN
ap-10691	126	158	(	(	PUNCT
ap-10691	126	159	0)(θ	0)(θ	NOUN
ap-10691	126	160	)	)	PUNCT
ap-10691	126	161	=	=	SYM
ap-10691	127	1	n	n	PRON
ap-10691	127	2	cosl0	cosl0	ADJ
ap-10691	127	3	+	+	CCONJ
ap-10691	127	4	1	1	NUM
ap-10691	127	5	2	2	NUM
ap-10691	127	6	θ	θ	NOUN
ap-10691	127	7	sinl1	sinl1	NOUN
ap-10691	128	1	+	+	CCONJ
ap-10691	128	2	1	1	NUM
ap-10691	128	3	2	2	NUM
ap-10691	128	4	θ	θ	NOUN
ap-10691	128	5	p	p	X
ap-10691	128	6	(	(	PUNCT
ap-10691	128	7	l0,l1	l0,l1	PROPN
ap-10691	128	8	)	)	PUNCT
ap-10691	128	9	n	n	CCONJ
ap-10691	128	10	(	(	PUNCT
ap-10691	128	11	cos	cos	ADJ
ap-10691	128	12	2θ	2θ	NUM
ap-10691	128	13	)	)	PUNCT
ap-10691	128	14	,	,	PUNCT
ap-10691	128	15	(	(	PUNCT
ap-10691	128	16	34	34	NUM
ap-10691	128	17	)	)	PUNCT
ap-10691	128	18	where	where	SCONJ
ap-10691	128	19	n	n	PRON
ap-10691	128	20	is	be	AUX
ap-10691	128	21	the	the	DET
ap-10691	128	22	normalisation	normalisation	NOUN
ap-10691	128	23	constant	constant	ADJ
ap-10691	128	24	and	and	CCONJ
ap-10691	128	25	p	p	X
ap-10691	128	26	(	(	PUNCT
ap-10691	128	27	l0,l1	l0,l1	PROPN
ap-10691	128	28	)	)	PUNCT
ap-10691	128	29	n	n	CCONJ
ap-10691	128	30	are	be	AUX
ap-10691	128	31	jacobi	jacobi	NOUN
ap-10691	128	32	polynomials	polynomial	NOUN
ap-10691	128	33	.	.	PUNCT
ap-10691	129	1	the	the	DET
ap-10691	129	2	energy	energy	NOUN
ap-10691	129	3	of	of	ADP
ap-10691	129	4	these	these	DET
ap-10691	129	5	states	state	NOUN
ap-10691	129	6	is	be	AUX
ap-10691	129	7	e′	e′	PROPN
ap-10691	129	8	n	n	X
ap-10691	129	9	=	=	PUNCT
ap-10691	129	10	β2	β2	NOUN
ap-10691	129	11	=	=	NOUN
ap-10691	129	12	λn	λn	NOUN
ap-10691	129	13	as	as	SCONJ
ap-10691	129	14	given	give	VERB
ap-10691	129	15	in	in	ADP
ap-10691	129	16	equation	equation	NOUN
ap-10691	129	17	(	(	PUNCT
ap-10691	129	18	32	32	NUM
ap-10691	129	19	)	)	PUNCT
ap-10691	129	20	.	.	PUNCT
ap-10691	130	1	from	from	ADP
ap-10691	130	2	[	[	X
ap-10691	130	3	8	8	NUM
ap-10691	130	4	]	]	PUNCT
ap-10691	130	5	,	,	PUNCT
ap-10691	130	6	the	the	DET
ap-10691	130	7	ladder	ladder	NOUN
ap-10691	130	8	operators	operator	NOUN
ap-10691	130	9	are	be	AUX
ap-10691	130	10	:	:	PUNCT
ap-10691	130	11	l±	l±	X
ap-10691	130	12	β	β	X
ap-10691	130	13	:	:	PUNCT
ap-10691	130	14	=	=	SYM
ap-10691	130	15	±	±	NUM
ap-10691	130	16	(	(	PUNCT
ap-10691	130	17	β	β	X
ap-10691	130	18	±	±	NUM
ap-10691	130	19	1	1	NUM
ap-10691	130	20	)	)	PUNCT
ap-10691	130	21	sin	sin	NOUN
ap-10691	130	22	2θ	2θ	NUM
ap-10691	130	23	∂θ	∂θ	NOUN
ap-10691	131	1	+	+	CCONJ
ap-10691	131	2	β(β	β(β	VERB
ap-10691	131	3	±	±	NUM
ap-10691	131	4	1	1	NUM
ap-10691	131	5	)	)	PUNCT
ap-10691	131	6	cos	cos	ADP
ap-10691	131	7	2θ	2θ	NUM
ap-10691	131	8	−	−	PROPN
ap-10691	131	9	l20	l20	NOUN
ap-10691	131	10	+	+	NUM
ap-10691	131	11	l21	l21	NOUN
ap-10691	131	12	.	.	PUNCT
ap-10691	132	1	(	(	PUNCT
ap-10691	132	2	35	35	NUM
ap-10691	132	3	)	)	PUNCT
ap-10691	132	4	they	they	PRON
ap-10691	132	5	act	act	VERB
ap-10691	132	6	as	as	ADP
ap-10691	132	7	:	:	PUNCT
ap-10691	132	8	hθ	hθ	PROPN
ap-10691	132	9	∋	∋	NOUN
ap-10691	132	10	ψβ	ψβ	PROPN
ap-10691	132	11	l+	l+	X
ap-10691	132	12	β−−→	β−−→	PUNCT
ap-10691	132	13	ψβ+2	ψβ+2	PROPN
ap-10691	132	14	∈	∈	PROPN
ap-10691	133	1	hθ	hθ	INTJ
ap-10691	133	2	,	,	PUNCT
ap-10691	133	3	hθ	hθ	NOUN
ap-10691	133	4	∋	∋	NOUN
ap-10691	133	5	ψβ+2	ψβ+2	PROPN
ap-10691	133	6	l−	l−	PROPN
ap-10691	133	7	β−−→	β−−→	PUNCT
ap-10691	133	8	ψβ	ψβ	PROPN
ap-10691	133	9	∈	∈	PROPN
ap-10691	133	10	hθ	hθ	PROPN
ap-10691	133	11	.	.	PUNCT
ap-10691	134	1	(	(	PUNCT
ap-10691	134	2	36	36	NUM
ap-10691	134	3	)	)	PUNCT
ap-10691	134	4	we	we	PRON
ap-10691	134	5	can	can	AUX
ap-10691	134	6	define	define	VERB
ap-10691	134	7	generalised	generalised	ADJ
ap-10691	134	8	ladder	ladder	NOUN
ap-10691	134	9	operators	operator	NOUN
ap-10691	134	10	as	as	ADP
ap-10691	134	11	:	:	PUNCT
ap-10691	134	12	l+	l+	NOUN
ap-10691	134	13	β→β+2n	β→β+2n	NOUN
ap-10691	134	14	:	:	PUNCT
ap-10691	134	15	=	=	SYM
ap-10691	135	1	0∏	0∏	X
ap-10691	135	2	i=2(n−1	i=2(n−1	ADJ
ap-10691	135	3	)	)	PUNCT
ap-10691	135	4	l+	l+	NOUN
ap-10691	135	5	β+i	β+i	PROPN
ap-10691	135	6	,	,	PUNCT
ap-10691	135	7	l−	l−	NOUN
ap-10691	135	8	β→β−2n	β→β−2n	X
ap-10691	136	1	:	:	PUNCT
ap-10691	136	2	=	=	SYM
ap-10691	137	1	2∏	2∏	NUM
ap-10691	137	2	i=2n	i=2n	NOUN
ap-10691	137	3	l+	l+	X
ap-10691	137	4	β−i	β−i	X
ap-10691	137	5	,	,	PUNCT
ap-10691	137	6	(	(	PUNCT
ap-10691	137	7	37	37	NUM
ap-10691	137	8	)	)	PUNCT
ap-10691	137	9	that	that	PRON
ap-10691	137	10	act	act	VERB
ap-10691	137	11	as	as	ADP
ap-10691	137	12	:	:	PUNCT
ap-10691	137	13	hθ	hθ	PROPN
ap-10691	137	14	∋	∋	NOUN
ap-10691	137	15	ψβ	ψβ	PROPN
ap-10691	137	16	l+	l+	PROPN
ap-10691	137	17	β→β+2n−−−−−−→	β→β+2n−−−−−−→	PROPN
ap-10691	137	18	ψβ+2n	ψβ+2n	PROPN
ap-10691	137	19	∈	∈	PROPN
ap-10691	137	20	hθ	hθ	NOUN
ap-10691	137	21	,	,	PUNCT
ap-10691	137	22	hθ	hθ	PROPN
ap-10691	137	23	∋	∋	NOUN
ap-10691	137	24	ψβ	ψβ	PROPN
ap-10691	137	25	l−	l−	PROPN
ap-10691	137	26	β→β−2n−−−−−−→	β→β−2n−−−−−−→	PUNCT
ap-10691	137	27	ψβ−2n	ψβ−2n	PROPN
ap-10691	137	28	∈	∈	PROPN
ap-10691	138	1	hθ	hθ	NOUN
ap-10691	138	2	.	.	PUNCT
ap-10691	139	1	(	(	PUNCT
ap-10691	139	2	38	38	NUM
ap-10691	139	3	)	)	PUNCT
ap-10691	139	4	we	we	PRON
ap-10691	139	5	now	now	ADV
ap-10691	139	6	consider	consider	VERB
ap-10691	139	7	index	index	NOUN
ap-10691	139	8	-	-	PUNCT
ap-10691	139	9	free	free	ADJ
ap-10691	139	10	operators	operator	NOUN
ap-10691	139	11	l±	l±	VERB
ap-10691	139	12	and	and	CCONJ
ap-10691	139	13	(	(	PUNCT
ap-10691	139	14	l±)n	l±)n	ADJ
ap-10691	139	15	,	,	PUNCT
ap-10691	139	16	defined	define	VERB
ap-10691	139	17	by	by	ADP
ap-10691	139	18	removing	remove	VERB
ap-10691	139	19	the	the	DET
ap-10691	139	20	subscript	subscript	NOUN
ap-10691	139	21	β	β	NOUN
ap-10691	139	22	from	from	ADP
ap-10691	139	23	the	the	DET
ap-10691	139	24	operators	operator	NOUN
ap-10691	139	25	l±	l±	VERB
ap-10691	139	26	β	β	PROPN
ap-10691	139	27	defined	define	VERB
ap-10691	139	28	in	in	ADP
ap-10691	139	29	equation	equation	NOUN
ap-10691	139	30	(	(	PUNCT
ap-10691	139	31	36	36	NUM
ap-10691	139	32	)	)	PUNCT
ap-10691	139	33	,	,	PUNCT
ap-10691	139	34	as	as	SCONJ
ap-10691	139	35	follows	follow	VERB
ap-10691	139	36	:	:	PUNCT
ap-10691	139	37	l+ψβ	l+ψβ	ADJ
ap-10691	139	38	:	:	PUNCT
ap-10691	139	39	=	=	PUNCT
ap-10691	139	40	l+	l+	X
ap-10691	139	41	β	β	X
ap-10691	139	42	ψβ	ψβ	PROPN
ap-10691	139	43	,	,	PUNCT
ap-10691	139	44	l−ψβ	l−ψβ	INTJ
ap-10691	139	45	:	:	PUNCT
ap-10691	139	46	=	=	PUNCT
ap-10691	139	47	l−	l−	PROPN
ap-10691	139	48	β−2ψβ	β−2ψβ	NOUN
ap-10691	139	49	,	,	PUNCT
ap-10691	139	50	∀β	∀β	PROPN
ap-10691	139	51	.	.	PUNCT
ap-10691	140	1	(	(	PUNCT
ap-10691	140	2	39	39	NUM
ap-10691	140	3	)	)	PUNCT
ap-10691	140	4	this	this	DET
ap-10691	140	5	notation	notation	NOUN
ap-10691	140	6	also	also	ADV
ap-10691	140	7	extends	extend	VERB
ap-10691	140	8	to	to	ADP
ap-10691	140	9	the	the	DET
ap-10691	140	10	generalised	generalise	VERB
ap-10691	140	11	ladder	ladder	NOUN
ap-10691	140	12	operators	operator	NOUN
ap-10691	140	13	l±	l±	X
ap-10691	140	14	β→β±2n	β→β±2n	PROPN
ap-10691	140	15	defined	define	VERB
ap-10691	140	16	in	in	ADP
ap-10691	140	17	equation	equation	NOUN
ap-10691	140	18	(	(	PUNCT
ap-10691	140	19	37	37	NUM
ap-10691	140	20	):	):	PUNCT
ap-10691	140	21	(	(	PUNCT
ap-10691	140	22	l+)n	l+)n	PROPN
ap-10691	140	23	ψβ	ψβ	NOUN
ap-10691	140	24	:	:	PUNCT
ap-10691	140	25	=	=	SYM
ap-10691	140	26	l+	l+	NOUN
ap-10691	140	27	β→β+2nψβ	β→β+2nψβ	PUNCT
ap-10691	140	28	,	,	PUNCT
ap-10691	140	29	(	(	PUNCT
ap-10691	140	30	l−)n	l−)n	PROPN
ap-10691	140	31	ψβ	ψβ	PROPN
ap-10691	140	32	:	:	PUNCT
ap-10691	141	1	=	=	PUNCT
ap-10691	141	2	l−	l−	NOUN
ap-10691	141	3	β→β−2nψβ	β→β−2nψβ	NOUN
ap-10691	141	4	,	,	PUNCT
ap-10691	141	5	∀β	∀β	PROPN
ap-10691	141	6	.	.	PUNCT
ap-10691	142	1	(	(	PUNCT
ap-10691	142	2	40	40	NUM
ap-10691	142	3	)	)	PUNCT
ap-10691	142	4	we	we	PRON
ap-10691	142	5	state	state	VERB
ap-10691	142	6	the	the	DET
ap-10691	142	7	following	follow	VERB
ap-10691	142	8	interesting	interesting	ADJ
ap-10691	142	9	result	result	NOUN
ap-10691	142	10	and	and	CCONJ
ap-10691	142	11	leave	leave	VERB
ap-10691	142	12	its	its	PRON
ap-10691	142	13	proof	proof	NOUN
ap-10691	142	14	to	to	ADP
ap-10691	142	15	the	the	DET
ap-10691	142	16	reader:[√	reader:[√	NOUN
ap-10691	142	17	hθ	hθ	NOUN
ap-10691	142	18	,	,	PUNCT
ap-10691	142	19	(	(	PUNCT
ap-10691	142	20	l±)n	l±)n	ADJ
ap-10691	142	21	]	]	PUNCT
ap-10691	143	1	=	=	SYM
ap-10691	143	2	±2n	±2n	PROPN
ap-10691	143	3	(	(	PUNCT
ap-10691	143	4	l±)n	l±)n	NOUN
ap-10691	143	5	.	.	PUNCT
ap-10691	144	1	(	(	PUNCT
ap-10691	144	2	41	41	NUM
ap-10691	144	3	)	)	PUNCT
ap-10691	144	4	3.2	3.2	NUM
ap-10691	144	5	.	.	PUNCT
ap-10691	145	1	factorisation	factorisation	NOUN
ap-10691	145	2	of	of	ADP
ap-10691	145	3	hϕ	hϕ	PROPN
ap-10691	145	4	mk	mk	NOUN
ap-10691	145	5	our	our	PRON
ap-10691	145	6	task	task	NOUN
ap-10691	145	7	now	now	ADV
ap-10691	145	8	is	be	AUX
ap-10691	145	9	to	to	PART
ap-10691	145	10	find	find	VERB
ap-10691	145	11	intertwining	intertwine	VERB
ap-10691	145	12	operators	operator	NOUN
ap-10691	145	13	m±	m±	NOUN
ap-10691	145	14	that	that	PRON
ap-10691	145	15	factorise	factorise	VERB
ap-10691	145	16	the	the	DET
ap-10691	145	17	hamiltonian	hamiltonian	PROPN
ap-10691	145	18	hϕ	hϕ	PROPN
ap-10691	145	19	mk	mk	NOUN
ap-10691	145	20	given	give	VERB
ap-10691	145	21	in	in	ADP
ap-10691	145	22	equation	equation	NOUN
ap-10691	145	23	(	(	PUNCT
ap-10691	145	24	10	10	NUM
ap-10691	145	25	)	)	PUNCT
ap-10691	145	26	,	,	PUNCT
ap-10691	145	27	that	that	PRON
ap-10691	145	28	is	be	AUX
ap-10691	145	29	:	:	PUNCT
ap-10691	145	30	hϕ	hϕ	PROPN
ap-10691	145	31	mk	mk	NOUN
ap-10691	145	32	=	=	PUNCT
ap-10691	146	1	m+m−	m+m−	PROPN
ap-10691	146	2	+	+	CCONJ
ap-10691	146	3	µ.	µ.	NOUN
ap-10691	146	4	(	(	PUNCT
ap-10691	146	5	42	42	NUM
ap-10691	146	6	)	)	PUNCT
ap-10691	146	7	we	we	PRON
ap-10691	146	8	have	have	AUX
ap-10691	146	9	identified	identify	VERB
ap-10691	146	10	four	four	NUM
ap-10691	146	11	families	family	NOUN
ap-10691	146	12	of	of	ADP
ap-10691	146	13	ladder	ladder	NOUN
ap-10691	146	14	operators	operator	NOUN
ap-10691	146	15	,	,	PUNCT
ap-10691	146	16	denoted	denote	VERB
ap-10691	146	17	m±,i	m±,i	PROPN
ap-10691	146	18	with	with	ADP
ap-10691	146	19	i	i	PRON
ap-10691	146	20	=	=	NOUN
ap-10691	146	21	1	1	NUM
ap-10691	146	22	,	,	PUNCT
ap-10691	146	23	2	2	NUM
ap-10691	146	24	,	,	PUNCT
ap-10691	146	25	3	3	NUM
ap-10691	146	26	,	,	PUNCT
ap-10691	146	27	4	4	NUM
ap-10691	146	28	,	,	PUNCT
ap-10691	146	29	which	which	PRON
ap-10691	146	30	yield	yield	VERB
ap-10691	146	31	the	the	DET
ap-10691	146	32	same	same	ADJ
ap-10691	146	33	factorisation	factorisation	NOUN
ap-10691	146	34	of	of	ADP
ap-10691	146	35	the	the	DET
ap-10691	146	36	hamiltonian	hamiltonian	NOUN
ap-10691	146	37	,	,	PUNCT
ap-10691	146	38	but	but	CCONJ
ap-10691	146	39	satisfy	satisfy	VERB
ap-10691	146	40	different	different	ADJ
ap-10691	146	41	intertwining	intertwine	VERB
ap-10691	146	42	relations	relation	NOUN
ap-10691	146	43	[	[	X
ap-10691	146	44	29	29	NUM
ap-10691	146	45	]	]	PUNCT
ap-10691	146	46	.	.	PUNCT
ap-10691	147	1	these	these	DET
ap-10691	147	2	families	family	NOUN
ap-10691	147	3	are	be	AUX
ap-10691	147	4	:	:	PUNCT
ap-10691	147	5	solution	solution	NOUN
ap-10691	147	6	1	1	NUM
ap-10691	147	7	:	:	PUNCT
ap-10691	147	8	m+,1	m+,1	X
ap-10691	148	1	=	=	PUNCT
ap-10691	148	2	∂ϕ	∂ϕ	PROPN
ap-10691	149	1	+	+	CCONJ
ap-10691	149	2	(	(	PUNCT
ap-10691	149	3	kβ	kβ	INTJ
ap-10691	149	4	−	−	PROPN
ap-10691	149	5	1	1	NUM
ap-10691	149	6	)	)	PUNCT
ap-10691	149	7	tanϕ+	tanϕ+	X
ap-10691	149	8	−2l2	−2l2	PUNCT
ap-10691	150	1	+	+	CCONJ
ap-10691	150	2	1	1	NUM
ap-10691	150	3	2	2	NUM
ap-10691	150	4	cotϕ	cotϕ	NOUN
ap-10691	150	5	,	,	PUNCT
ap-10691	150	6	m−,1	m−,1	NOUN
ap-10691	150	7	=	=	SYM
ap-10691	150	8	−∂ϕ	−∂ϕ	NOUN
ap-10691	150	9	+	+	CCONJ
ap-10691	150	10	kβ	kβ	X
ap-10691	150	11	tanϕ+	tanϕ+	X
ap-10691	150	12	−2l2	−2l2	PUNCT
ap-10691	151	1	+	+	CCONJ
ap-10691	151	2	1	1	NUM
ap-10691	151	3	2	2	NUM
ap-10691	151	4	cotϕ	cotϕ	NOUN
ap-10691	151	5	,	,	PUNCT
ap-10691	151	6	µ1	µ1	PROPN
ap-10691	151	7	=	=	SYM
ap-10691	151	8	(	(	PUNCT
ap-10691	151	9	kβ	kβ	NOUN
ap-10691	151	10	+	+	X
ap-10691	151	11	l2	l2	NOUN
ap-10691	151	12	−	−	NOUN
ap-10691	151	13	3	3	NUM
ap-10691	151	14	2	2	NUM
ap-10691	151	15	)	)	PUNCT
ap-10691	151	16	(	(	PUNCT
ap-10691	151	17	kβ	kβ	X
ap-10691	151	18	+	+	X
ap-10691	151	19	l2	l2	NOUN
ap-10691	151	20	−	−	NOUN
ap-10691	151	21	1	1	NUM
ap-10691	151	22	2	2	NUM
ap-10691	151	23	)	)	PUNCT
ap-10691	151	24	.	.	PUNCT
ap-10691	152	1	(	(	PUNCT
ap-10691	152	2	43	43	NUM
ap-10691	152	3	)	)	PUNCT
ap-10691	152	4	by	by	ADP
ap-10691	152	5	computing	compute	VERB
ap-10691	152	6	m−,1	m−,1	PROPN
ap-10691	152	7	m+,1	m+,1	NOUN
ap-10691	153	1	+	+	SYM
ap-10691	153	2	µ1	µ1	ADJ
ap-10691	153	3	,	,	PUNCT
ap-10691	153	4	we	we	PRON
ap-10691	153	5	get	get	VERB
ap-10691	153	6	that	that	SCONJ
ap-10691	153	7	it	it	PRON
ap-10691	153	8	is	be	AUX
ap-10691	153	9	equal	equal	ADJ
ap-10691	153	10	to	to	PART
ap-10691	153	11	:	:	PUNCT
ap-10691	153	12	−∂2	−∂2	PROPN
ap-10691	153	13	ϕ	ϕ	PROPN
ap-10691	153	14	+	+	CCONJ
ap-10691	153	15	tanϕ∂ϕ	tanϕ∂ϕ	NUM
ap-10691	153	16	+	+	CCONJ
ap-10691	153	17	(	(	PUNCT
ap-10691	153	18	kβ	kβ	INTJ
ap-10691	153	19	−	−	PROPN
ap-10691	153	20	1)2	1)2	NUM
ap-10691	153	21	cos2	cos2	PROPN
ap-10691	153	22	ϕ	ϕ	NOUN
ap-10691	153	23	+	+	CCONJ
ap-10691	153	24	(	(	PUNCT
ap-10691	153	25	l2	l2	NOUN
ap-10691	153	26	−	−	PROPN
ap-10691	153	27	1)2	1)2	NUM
ap-10691	153	28	−	−	NOUN
ap-10691	153	29	1	1	NUM
ap-10691	153	30	4	4	NUM
ap-10691	153	31	sin2	sin2	NOUN
ap-10691	153	32	ϕ	ϕ	PROPN
ap-10691	153	33	.	.	PUNCT
ap-10691	154	1	(	(	PUNCT
ap-10691	154	2	44	44	NUM
ap-10691	154	3	)	)	PUNCT
ap-10691	154	4	thus	thus	ADV
ap-10691	154	5	,	,	PUNCT
ap-10691	154	6	the	the	DET
ap-10691	154	7	hamiltonian	hamiltonian	NOUN
ap-10691	154	8	given	give	VERB
ap-10691	154	9	in	in	ADP
ap-10691	154	10	equation	equation	NOUN
ap-10691	154	11	(	(	PUNCT
ap-10691	154	12	44	44	NUM
ap-10691	154	13	)	)	PUNCT
ap-10691	154	14	has	have	VERB
ap-10691	154	15	the	the	DET
ap-10691	154	16	same	same	ADJ
ap-10691	154	17	form	form	NOUN
ap-10691	154	18	as	as	ADP
ap-10691	154	19	hϕ	hϕ	PROPN
ap-10691	154	20	mk	mk	PROPN
ap-10691	154	21	in	in	ADP
ap-10691	154	22	equation	equation	NOUN
ap-10691	154	23	(	(	PUNCT
ap-10691	154	24	10	10	NUM
ap-10691	154	25	)	)	PUNCT
ap-10691	154	26	,	,	PUNCT
ap-10691	154	27	but	but	CCONJ
ap-10691	154	28	with	with	ADP
ap-10691	154	29	the	the	DET
ap-10691	154	30	parameters	parameter	NOUN
ap-10691	154	31	kβ	kβ	ADP
ap-10691	154	32	and	and	CCONJ
ap-10691	154	33	l2	l2	NOUN
ap-10691	154	34	replaced	replace	VERB
ap-10691	154	35	by	by	ADP
ap-10691	154	36	kβ	kβ	INTJ
ap-10691	154	37	−	−	PROPN
ap-10691	154	38	1	1	NUM
ap-10691	154	39	and	and	CCONJ
ap-10691	154	40	l2	l2	VERB
ap-10691	154	41	−	−	PROPN
ap-10691	154	42	1	1	NUM
ap-10691	154	43	,	,	PUNCT
ap-10691	154	44	respectively	respectively	ADV
ap-10691	154	45	.	.	PUNCT
ap-10691	155	1	solution	solution	NOUN
ap-10691	155	2	2	2	NUM
ap-10691	155	3	:	:	PUNCT
ap-10691	155	4	m+,2	m+,2	X
ap-10691	155	5	=	=	PUNCT
ap-10691	155	6	∂ϕ	∂ϕ	PROPN
ap-10691	156	1	+	+	CCONJ
ap-10691	156	2	(	(	PUNCT
ap-10691	156	3	kβ	kβ	INTJ
ap-10691	156	4	−	−	PROPN
ap-10691	156	5	1	1	NUM
ap-10691	156	6	)	)	PUNCT
ap-10691	156	7	tanϕ+	tanϕ+	X
ap-10691	157	1	2l2	2l2	NUM
ap-10691	157	2	+	+	CCONJ
ap-10691	157	3	1	1	NUM
ap-10691	157	4	2	2	NUM
ap-10691	157	5	cotϕ	cotϕ	NOUN
ap-10691	157	6	,	,	PUNCT
ap-10691	157	7	m−,2	m−,2	NOUN
ap-10691	157	8	=	=	SYM
ap-10691	157	9	−∂ϕ	−∂ϕ	NOUN
ap-10691	157	10	+	+	CCONJ
ap-10691	157	11	kβ	kβ	X
ap-10691	157	12	tanϕ+	tanϕ+	X
ap-10691	157	13	2l2	2l2	NUM
ap-10691	158	1	+	+	CCONJ
ap-10691	158	2	1	1	NUM
ap-10691	158	3	2	2	NUM
ap-10691	158	4	cotϕ	cotϕ	NOUN
ap-10691	158	5	,	,	PUNCT
ap-10691	158	6	µ2	µ2	PROPN
ap-10691	158	7	=	=	PUNCT
ap-10691	158	8	(	(	PUNCT
ap-10691	158	9	−kβ	−kβ	X
ap-10691	158	10	+	+	CCONJ
ap-10691	158	11	l2	l2	NOUN
ap-10691	158	12	+	+	CCONJ
ap-10691	158	13	1	1	NUM
ap-10691	158	14	2	2	NUM
ap-10691	158	15	)	)	PUNCT
ap-10691	158	16	(	(	PUNCT
ap-10691	158	17	−kβ	−kβ	X
ap-10691	158	18	+	+	CCONJ
ap-10691	158	19	l2	l2	NOUN
ap-10691	158	20	+	+	CCONJ
ap-10691	158	21	3	3	NUM
ap-10691	158	22	2	2	NUM
ap-10691	158	23	)	)	PUNCT
ap-10691	158	24	.	.	PUNCT
ap-10691	159	1	(	(	PUNCT
ap-10691	159	2	45	45	NUM
ap-10691	159	3	)	)	PUNCT
ap-10691	159	4	here	here	ADV
ap-10691	159	5	,	,	PUNCT
ap-10691	159	6	m−,2m+,2	m−,2m+,2	PROPN
ap-10691	160	1	+	+	CCONJ
ap-10691	160	2	µ2	µ2	PROPN
ap-10691	160	3	gives	give	VERB
ap-10691	160	4	:	:	PUNCT
ap-10691	160	5	−∂2	−∂2	PROPN
ap-10691	160	6	ϕ	ϕ	PROPN
ap-10691	160	7	+	+	CCONJ
ap-10691	160	8	tanϕ∂ϕ	tanϕ∂ϕ	NUM
ap-10691	160	9	+	+	CCONJ
ap-10691	160	10	(	(	PUNCT
ap-10691	160	11	kβ	kβ	INTJ
ap-10691	160	12	−	−	PROPN
ap-10691	160	13	1)2	1)2	NUM
ap-10691	160	14	cos2	cos2	PROPN
ap-10691	160	15	ϕ	ϕ	NOUN
ap-10691	160	16	+	+	X
ap-10691	160	17	(	(	PUNCT
ap-10691	160	18	l2	l2	NOUN
ap-10691	160	19	+	+	CCONJ
ap-10691	160	20	1)2	1)2	NUM
ap-10691	160	21	−	−	NOUN
ap-10691	160	22	1	1	NUM
ap-10691	160	23	4	4	NUM
ap-10691	160	24	)	)	PUNCT
ap-10691	160	25	sin2	sin2	PROPN
ap-10691	160	26	ϕ	ϕ	PROPN
ap-10691	160	27	.	.	PUNCT
ap-10691	161	1	(	(	PUNCT
ap-10691	161	2	46	46	NUM
ap-10691	161	3	)	)	PUNCT
ap-10691	161	4	in	in	ADP
ap-10691	161	5	this	this	DET
ap-10691	161	6	case	case	NOUN
ap-10691	161	7	,	,	PUNCT
ap-10691	161	8	the	the	DET
ap-10691	161	9	hamiltonian	hamiltonian	NOUN
ap-10691	161	10	(	(	PUNCT
ap-10691	161	11	45	45	NUM
ap-10691	161	12	)	)	PUNCT
ap-10691	161	13	has	have	VERB
ap-10691	161	14	the	the	DET
ap-10691	161	15	same	same	ADJ
ap-10691	161	16	form	form	NOUN
ap-10691	161	17	as	as	ADP
ap-10691	161	18	hϕ	hϕ	PROPN
ap-10691	161	19	mk	mk	PROPN
ap-10691	161	20	in	in	ADP
ap-10691	161	21	equation	equation	NOUN
ap-10691	161	22	(	(	PUNCT
ap-10691	161	23	10	10	NUM
ap-10691	161	24	)	)	PUNCT
ap-10691	161	25	,	,	PUNCT
ap-10691	161	26	but	but	CCONJ
ap-10691	161	27	with	with	ADP
ap-10691	161	28	the	the	DET
ap-10691	161	29	parameters	parameter	NOUN
ap-10691	161	30	kβ	kβ	ADP
ap-10691	161	31	and	and	CCONJ
ap-10691	161	32	l2	l2	NOUN
ap-10691	161	33	replaced	replace	VERB
ap-10691	161	34	by	by	ADP
ap-10691	161	35	kβ	kβ	INTJ
ap-10691	161	36	−	−	PROPN
ap-10691	161	37	1	1	NUM
ap-10691	161	38	and	and	CCONJ
ap-10691	161	39	l2	l2	VERB
ap-10691	161	40	+	+	CCONJ
ap-10691	161	41	1	1	NUM
ap-10691	161	42	,	,	PUNCT
ap-10691	161	43	respectively	respectively	ADV
ap-10691	161	44	.	.	PUNCT
ap-10691	162	1	solution	solution	NOUN
ap-10691	162	2	3	3	NUM
ap-10691	162	3	:	:	PUNCT
ap-10691	162	4	m+,3	m+,3	X
ap-10691	163	1	=	=	PUNCT
ap-10691	163	2	∂ϕ	∂ϕ	NUM
ap-10691	164	1	−	−	PROPN
ap-10691	164	2	(	(	PUNCT
ap-10691	164	3	kβ	kβ	PROPN
ap-10691	164	4	+	+	NOUN
ap-10691	164	5	1	1	NUM
ap-10691	164	6	)	)	PUNCT
ap-10691	164	7	tanϕ+	tanϕ+	SYM
ap-10691	164	8	2l2	2l2	NUM
ap-10691	165	1	+	+	CCONJ
ap-10691	165	2	1	1	NUM
ap-10691	165	3	2	2	NUM
ap-10691	165	4	cotϕ	cotϕ	NOUN
ap-10691	165	5	,	,	PUNCT
ap-10691	165	6	m−,3	m−,3	NOUN
ap-10691	165	7	=	=	SYM
ap-10691	165	8	−∂ϕ	−∂ϕ	ADV
ap-10691	165	9	−	−	PROPN
ap-10691	166	1	kβ	kβ	INTJ
ap-10691	166	2	tanϕ+	tanϕ+	X
ap-10691	166	3	2l2	2l2	NUM
ap-10691	167	1	+	+	CCONJ
ap-10691	167	2	1	1	NUM
ap-10691	167	3	2	2	NUM
ap-10691	167	4	cotϕ	cotϕ	NOUN
ap-10691	167	5	,	,	PUNCT
ap-10691	167	6	µ3	µ3	NOUN
ap-10691	167	7	=	=	SYM
ap-10691	167	8	(	(	PUNCT
ap-10691	167	9	kβ	kβ	NOUN
ap-10691	167	10	+	+	X
ap-10691	167	11	l2	l2	NOUN
ap-10691	167	12	+	+	CCONJ
ap-10691	167	13	1	1	NUM
ap-10691	167	14	2	2	NUM
ap-10691	167	15	)	)	PUNCT
ap-10691	167	16	(	(	PUNCT
ap-10691	167	17	kβ	kβ	NOUN
ap-10691	167	18	+	+	X
ap-10691	167	19	l2	l2	NOUN
ap-10691	167	20	+	+	CCONJ
ap-10691	167	21	3	3	NUM
ap-10691	167	22	2	2	NUM
ap-10691	167	23	)	)	PUNCT
ap-10691	167	24	.	.	PUNCT
ap-10691	168	1	(	(	PUNCT
ap-10691	168	2	47	47	NUM
ap-10691	168	3	)	)	PUNCT
ap-10691	168	4	in	in	ADP
ap-10691	168	5	this	this	DET
ap-10691	168	6	case	case	NOUN
ap-10691	168	7	,	,	PUNCT
ap-10691	168	8	from	from	ADP
ap-10691	168	9	m−,3m+,3	m−,3m+,3	PROPN
ap-10691	169	1	+	+	CCONJ
ap-10691	169	2	µ3	µ3	NOUN
ap-10691	169	3	,	,	PUNCT
ap-10691	169	4	we	we	PRON
ap-10691	169	5	get	get	VERB
ap-10691	169	6	:	:	PUNCT
ap-10691	169	7	−∂2	−∂2	PROPN
ap-10691	169	8	ϕ	ϕ	PROPN
ap-10691	169	9	+	+	CCONJ
ap-10691	169	10	tanϕ∂ϕ	tanϕ∂ϕ	NUM
ap-10691	169	11	+	+	CCONJ
ap-10691	169	12	(	(	PUNCT
ap-10691	169	13	kβ	kβ	X
ap-10691	169	14	+	+	ADJ
ap-10691	169	15	1)2	1)2	NUM
ap-10691	169	16	cos2	cos2	NOUN
ap-10691	169	17	ϕ	ϕ	NOUN
ap-10691	169	18	+	+	X
ap-10691	169	19	(	(	PUNCT
ap-10691	169	20	l2	l2	NOUN
ap-10691	169	21	+	+	CCONJ
ap-10691	169	22	1)2	1)2	NUM
ap-10691	169	23	−	−	NOUN
ap-10691	169	24	1	1	NUM
ap-10691	169	25	4	4	NUM
ap-10691	169	26	)	)	PUNCT
ap-10691	169	27	sin2	sin2	PROPN
ap-10691	169	28	ϕ	ϕ	PROPN
ap-10691	169	29	,	,	PUNCT
ap-10691	169	30	(	(	PUNCT
ap-10691	169	31	48	48	NUM
ap-10691	169	32	)	)	PUNCT
ap-10691	169	33	where	where	SCONJ
ap-10691	169	34	the	the	DET
ap-10691	169	35	parameters	parameter	NOUN
ap-10691	169	36	kβ	kβ	VERB
ap-10691	169	37	and	and	CCONJ
ap-10691	169	38	l2	l2	NOUN
ap-10691	169	39	are	be	AUX
ap-10691	169	40	replaced	replace	VERB
ap-10691	169	41	by	by	ADP
ap-10691	169	42	kβ+1	kβ+1	PROPN
ap-10691	169	43	and	and	CCONJ
ap-10691	169	44	l2	l2	VERB
ap-10691	169	45	+	+	CCONJ
ap-10691	169	46	1	1	NUM
ap-10691	169	47	,	,	PUNCT
ap-10691	169	48	respectively	respectively	ADV
ap-10691	169	49	.	.	PUNCT
ap-10691	170	1	523	523	NUM
ap-10691	170	2	mariano	mariano	PROPN
ap-10691	170	3	a.	a.	PROPN
ap-10691	170	4	del	del	PROPN
ap-10691	170	5	olmo	olmo	PROPN
ap-10691	170	6	,	,	PUNCT
ap-10691	170	7	álvaro	álvaro	PROPN
ap-10691	170	8	romaniega	romaniega	PROPN
ap-10691	170	9	acta	acta	PROPN
ap-10691	170	10	polytechnica	polytechnica	PROPN
ap-10691	170	11	solution	solution	NOUN
ap-10691	170	12	4	4	NUM
ap-10691	170	13	:	:	PUNCT
ap-10691	170	14	m+,4	m+,4	X
ap-10691	171	1	=	=	PUNCT
ap-10691	172	1	∂ϕ	∂ϕ	NUM
ap-10691	173	1	−	−	PROPN
ap-10691	173	2	(	(	PUNCT
ap-10691	173	3	kβ	kβ	PROPN
ap-10691	173	4	+	+	NOUN
ap-10691	173	5	1	1	NUM
ap-10691	173	6	)	)	PUNCT
ap-10691	173	7	tanϕ+	tanϕ+	X
ap-10691	173	8	−2l2	−2l2	PUNCT
ap-10691	174	1	+	+	CCONJ
ap-10691	174	2	1	1	NUM
ap-10691	174	3	2	2	NUM
ap-10691	174	4	cotϕ	cotϕ	NOUN
ap-10691	174	5	,	,	PUNCT
ap-10691	174	6	m−,4	m−,4	X
ap-10691	174	7	=	=	SYM
ap-10691	174	8	−∂ϕ	−∂ϕ	ADV
ap-10691	174	9	−	−	PROPN
ap-10691	175	1	kβ	kβ	INTJ
ap-10691	175	2	tanϕ+	tanϕ+	X
ap-10691	175	3	−2l2	−2l2	PUNCT
ap-10691	176	1	+	+	CCONJ
ap-10691	176	2	1	1	NUM
ap-10691	176	3	2	2	NUM
ap-10691	176	4	cotϕ	cotϕ	NOUN
ap-10691	176	5	,	,	PUNCT
ap-10691	176	6	µ4	µ4	PROPN
ap-10691	176	7	=	=	PUNCT
ap-10691	176	8	(	(	PUNCT
ap-10691	176	9	−kβ	−kβ	X
ap-10691	176	10	+	+	NOUN
ap-10691	176	11	l2	l2	NOUN
ap-10691	176	12	−	−	NOUN
ap-10691	176	13	3	3	NUM
ap-10691	176	14	2	2	NUM
ap-10691	176	15	)	)	PUNCT
ap-10691	176	16	(	(	PUNCT
ap-10691	176	17	−kβ	−kβ	X
ap-10691	176	18	+	+	CCONJ
ap-10691	176	19	l2	l2	NOUN
ap-10691	176	20	−	−	NOUN
ap-10691	176	21	1	1	NUM
ap-10691	176	22	2	2	NUM
ap-10691	176	23	)	)	PUNCT
ap-10691	176	24	.	.	PUNCT
ap-10691	177	1	(	(	PUNCT
ap-10691	177	2	49	49	NUM
ap-10691	177	3	)	)	PUNCT
ap-10691	177	4	now	now	ADV
ap-10691	177	5	,	,	PUNCT
ap-10691	177	6	m−,4m+,4	m−,4m+,4	PROPN
ap-10691	178	1	+	+	CCONJ
ap-10691	178	2	µ4	µ4	PROPN
ap-10691	178	3	gives	give	VERB
ap-10691	178	4	:	:	PUNCT
ap-10691	178	5	−∂2	−∂2	PROPN
ap-10691	178	6	ϕ	ϕ	PROPN
ap-10691	178	7	+	+	CCONJ
ap-10691	178	8	tanϕ∂ϕ	tanϕ∂ϕ	NUM
ap-10691	178	9	+	+	CCONJ
ap-10691	178	10	(	(	PUNCT
ap-10691	178	11	kβ	kβ	X
ap-10691	178	12	+	+	ADJ
ap-10691	178	13	1)2	1)2	NUM
ap-10691	178	14	cos2	cos2	NOUN
ap-10691	178	15	ϕ	ϕ	NOUN
ap-10691	178	16	+	+	CCONJ
ap-10691	178	17	(	(	PUNCT
ap-10691	178	18	l2	l2	NOUN
ap-10691	178	19	−	−	PROPN
ap-10691	178	20	1)2	1)2	NUM
ap-10691	178	21	−	−	NOUN
ap-10691	178	22	1	1	NUM
ap-10691	178	23	4	4	NUM
ap-10691	178	24	)	)	PUNCT
ap-10691	178	25	sin2	sin2	PROPN
ap-10691	178	26	ϕ	ϕ	PROPN
ap-10691	178	27	,	,	PUNCT
ap-10691	178	28	(	(	PUNCT
ap-10691	178	29	50	50	NUM
ap-10691	178	30	)	)	PUNCT
ap-10691	178	31	where	where	SCONJ
ap-10691	178	32	the	the	DET
ap-10691	178	33	parameters	parameter	NOUN
ap-10691	178	34	kβ	kβ	VERB
ap-10691	178	35	and	and	CCONJ
ap-10691	178	36	l2	l2	NOUN
ap-10691	178	37	are	be	AUX
ap-10691	178	38	replaced	replace	VERB
ap-10691	178	39	by	by	ADP
ap-10691	178	40	kβ+1	kβ+1	PROPN
ap-10691	178	41	and	and	CCONJ
ap-10691	178	42	l2	l2	VERB
ap-10691	178	43	−	−	PROPN
ap-10691	178	44	1	1	NUM
ap-10691	178	45	,	,	PUNCT
ap-10691	178	46	respectively	respectively	ADV
ap-10691	178	47	.	.	PUNCT
ap-10691	179	1	we	we	PRON
ap-10691	179	2	have	have	AUX
ap-10691	179	3	obtained	obtain	VERB
ap-10691	179	4	eight	eight	NUM
ap-10691	179	5	operators	operator	NOUN
ap-10691	179	6	that	that	PRON
ap-10691	179	7	modify	modify	VERB
ap-10691	179	8	the	the	DET
ap-10691	179	9	parameters	parameter	NOUN
ap-10691	179	10	β	β	PROPN
ap-10691	179	11	k	k	NOUN
ap-10691	179	12	and	and	CCONJ
ap-10691	179	13	l2	l2	NOUN
ap-10691	179	14	by	by	ADP
ap-10691	179	15	±1	±1	NOUN
ap-10691	179	16	,	,	PUNCT
ap-10691	179	17	allowing	allow	VERB
ap-10691	179	18	movement	movement	NOUN
ap-10691	179	19	in	in	ADP
ap-10691	179	20	both	both	DET
ap-10691	179	21	directions	direction	NOUN
ap-10691	179	22	along	along	ADP
ap-10691	179	23	the	the	DET
ap-10691	179	24	kβ	kβ	NOUN
ap-10691	179	25	and	and	CCONJ
ap-10691	179	26	l2	l2	NOUN
ap-10691	179	27	axes	axis	NOUN
ap-10691	179	28	.	.	PUNCT
ap-10691	180	1	this	this	PRON
ap-10691	180	2	enables	enable	VERB
ap-10691	180	3	us	we	PRON
ap-10691	180	4	to	to	PART
ap-10691	180	5	construct	construct	VERB
ap-10691	180	6	a	a	DET
ap-10691	180	7	hierarchy	hierarchy	NOUN
ap-10691	180	8	of	of	ADP
ap-10691	180	9	hamiltonians	hamiltonian	NOUN
ap-10691	180	10	,	,	PUNCT
ap-10691	180	11	denoted	denote	VERB
ap-10691	180	12	by	by	ADP
ap-10691	180	13	{	{	PUNCT
ap-10691	180	14	hϕ	hϕ	PROPN
ap-10691	180	15	mk;n	mk;n	ADJ
ap-10691	180	16	,	,	PUNCT
ap-10691	180	17	m}n	m}n	PROPN
ap-10691	180	18	,	,	PUNCT
ap-10691	180	19	m∈z	m∈z	NOUN
ap-10691	180	20	,	,	PUNCT
ap-10691	180	21	associated	associate	VERB
ap-10691	180	22	with	with	ADP
ap-10691	180	23	the	the	DET
ap-10691	180	24	initial	initial	ADJ
ap-10691	180	25	hamiltonianhϕ	hamiltonianhϕ	ADJ
ap-10691	180	26	mk	mk	NOUN
ap-10691	180	27	in	in	ADP
ap-10691	180	28	equation	equation	NOUN
ap-10691	180	29	(	(	PUNCT
ap-10691	180	30	10	10	NUM
ap-10691	180	31	)	)	PUNCT
ap-10691	180	32	,	,	PUNCT
ap-10691	180	33	through	through	ADP
ap-10691	180	34	the	the	DET
ap-10691	180	35	repeated	repeat	VERB
ap-10691	180	36	application	application	NOUN
ap-10691	180	37	of	of	ADP
ap-10691	180	38	the	the	DET
ap-10691	180	39	intertwining	intertwine	VERB
ap-10691	180	40	operators	operator	NOUN
ap-10691	180	41	m±,3	m±,3	PRON
ap-10691	180	42	,	,	PUNCT
ap-10691	180	43	as	as	SCONJ
ap-10691	180	44	described	describe	VERB
ap-10691	180	45	in	in	ADP
ap-10691	180	46	equation	equation	NOUN
ap-10691	180	47	(	(	PUNCT
ap-10691	180	48	13	13	NUM
ap-10691	180	49	)	)	PUNCT
ap-10691	180	50	.	.	PUNCT
ap-10691	181	1	the	the	DET
ap-10691	181	2	elements	element	NOUN
ap-10691	181	3	of	of	ADP
ap-10691	181	4	this	this	DET
ap-10691	181	5	hierarchy	hierarchy	NOUN
ap-10691	181	6	are	be	AUX
ap-10691	181	7	explicitly	explicitly	ADV
ap-10691	181	8	given	give	VERB
ap-10691	181	9	by	by	ADP
ap-10691	181	10	:	:	PUNCT
ap-10691	181	11	hϕ	hϕ	PROPN
ap-10691	181	12	mk;n	mk;n	ADJ
ap-10691	181	13	,	,	PUNCT
ap-10691	181	14	m	m	NOUN
ap-10691	181	15	=	=	PUNCT
ap-10691	181	16	−	−	PROPN
ap-10691	181	17	∂2	∂2	PROPN
ap-10691	181	18	ϕ	ϕ	NOUN
ap-10691	181	19	+	+	CCONJ
ap-10691	181	20	tanϕ∂ϕ	tanϕ∂ϕ	NUM
ap-10691	181	21	+	+	CCONJ
ap-10691	181	22	(	(	PUNCT
ap-10691	181	23	mk	mk	PROPN
ap-10691	181	24	+	+	PROPN
ap-10691	181	25	n)2	n)2	PROPN
ap-10691	181	26	cos2(ϕ	cos2(ϕ	NOUN
ap-10691	181	27	)	)	PUNCT
ap-10691	181	28	+	+	CCONJ
ap-10691	181	29	(	(	PUNCT
ap-10691	181	30	l2	l2	VERB
ap-10691	181	31	+	+	CCONJ
ap-10691	181	32	m)2	m)2	NOUN
ap-10691	181	33	−	−	NUM
ap-10691	181	34	1	1	NUM
ap-10691	181	35	4	4	NUM
ap-10691	181	36	sin2(ϕ	sin2(ϕ	NOUN
ap-10691	181	37	)	)	PUNCT
ap-10691	181	38	,	,	PUNCT
ap-10691	181	39	(	(	PUNCT
ap-10691	181	40	51	51	NUM
ap-10691	181	41	)	)	PUNCT
ap-10691	181	42	where	where	SCONJ
ap-10691	181	43	we	we	PRON
ap-10691	181	44	have	have	AUX
ap-10691	181	45	taken	take	VERB
ap-10691	181	46	into	into	ADP
ap-10691	181	47	account	account	NOUN
ap-10691	181	48	that	that	SCONJ
ap-10691	181	49	mk	mk	X
ap-10691	181	50	=	=	PUNCT
ap-10691	181	51	k	k	PROPN
ap-10691	181	52	β	β	X
ap-10691	181	53	.	.	PUNCT
ap-10691	181	54	note	note	VERB
ap-10691	181	55	that	that	SCONJ
ap-10691	181	56	for	for	ADP
ap-10691	181	57	n	n	NOUN
ap-10691	181	58	=	=	SYM
ap-10691	181	59	0	0	NUM
ap-10691	181	60	we	we	PRON
ap-10691	181	61	recover	recover	VERB
ap-10691	181	62	the	the	DET
ap-10691	181	63	initial	initial	ADJ
ap-10691	181	64	hamiltonian	hamiltonian	NOUN
ap-10691	181	65	hϕ	hϕ	PROPN
ap-10691	181	66	mk	mk	NOUN
ap-10691	181	67	given	give	VERB
ap-10691	181	68	in	in	ADP
ap-10691	181	69	equation	equation	NOUN
ap-10691	181	70	(	(	PUNCT
ap-10691	181	71	10	10	NUM
ap-10691	181	72	)	)	PUNCT
ap-10691	181	73	.	.	PUNCT
ap-10691	182	1	the	the	DET
ap-10691	182	2	fundamental	fundamental	ADJ
ap-10691	182	3	states	state	NOUN
ap-10691	182	4	of	of	ADP
ap-10691	182	5	the	the	DET
ap-10691	182	6	hamiltonians	hamiltonian	NOUN
ap-10691	182	7	hkβ	hkβ	NOUN
ap-10691	182	8	ϕ,0,m	ϕ,0,m	PROPN
ap-10691	182	9	are	be	AUX
ap-10691	182	10	obtained	obtain	VERB
ap-10691	182	11	using	use	VERB
ap-10691	182	12	equation	equation	NOUN
ap-10691	182	13	(	(	PUNCT
ap-10691	182	14	16	16	NUM
ap-10691	182	15	)	)	PUNCT
ap-10691	182	16	,	,	PUNCT
ap-10691	182	17	and	and	CCONJ
ap-10691	182	18	are	be	AUX
ap-10691	182	19	given	give	VERB
ap-10691	182	20	by	by	ADP
ap-10691	182	21	[	[	X
ap-10691	182	22	6	6	NUM
ap-10691	182	23	]	]	SYM
ap-10691	182	24	:	:	PUNCT
ap-10691	182	25	φ0	φ0	PROPN
ap-10691	182	26	(	(	PUNCT
ap-10691	182	27	m)(ϕ	m)(ϕ	PROPN
ap-10691	182	28	)	)	PUNCT
ap-10691	182	29	=	=	SYM
ap-10691	182	30	coskβ	coskβ	PROPN
ap-10691	182	31	ϕ	ϕ	PROPN
ap-10691	182	32	,	,	PUNCT
ap-10691	182	33	sinl2+m+	sinl2+m+	VERB
ap-10691	182	34	1	1	NUM
ap-10691	182	35	2	2	NUM
ap-10691	182	36	ϕ	ϕ	NOUN
ap-10691	182	37	,	,	PUNCT
ap-10691	182	38	(	(	PUNCT
ap-10691	182	39	52	52	NUM
ap-10691	182	40	)	)	PUNCT
ap-10691	182	41	with	with	ADP
ap-10691	182	42	β	β	X
ap-10691	182	43	=	=	SYM
ap-10691	182	44	l0	l0	PROPN
ap-10691	182	45	+	+	NOUN
ap-10691	182	46	l1	l1	PROPN
ap-10691	182	47	+	+	NOUN
ap-10691	182	48	n′	n′	PROPN
ap-10691	182	49	+	+	CCONJ
ap-10691	182	50	1	1	NUM
ap-10691	182	51	2	2	NUM
ap-10691	182	52	,	,	PUNCT
ap-10691	182	53	as	as	ADP
ap-10691	182	54	in	in	ADP
ap-10691	182	55	equation	equation	NOUN
ap-10691	182	56	(	(	PUNCT
ap-10691	182	57	32	32	NUM
ap-10691	182	58	)	)	PUNCT
ap-10691	182	59	,	,	PUNCT
ap-10691	182	60	where	where	SCONJ
ap-10691	182	61	we	we	PRON
ap-10691	182	62	fix	fix	VERB
ap-10691	182	63	an	an	DET
ap-10691	182	64	arbitrary	arbitrary	ADJ
ap-10691	182	65	value	value	NOUN
ap-10691	182	66	n	n	NOUN
ap-10691	182	67	=	=	SYM
ap-10691	182	68	n′	n′	NOUN
ap-10691	182	69	∈	∈	PROPN
ap-10691	182	70	n	n	CCONJ
ap-10691	182	71	(	(	PUNCT
ap-10691	182	72	see	see	VERB
ap-10691	182	73	subsection	subsection	NOUN
ap-10691	182	74	3.1	3.1	NUM
ap-10691	182	75	)	)	PUNCT
ap-10691	182	76	.	.	PUNCT
ap-10691	183	1	the	the	DET
ap-10691	183	2	excited	excited	ADJ
ap-10691	183	3	states	state	NOUN
ap-10691	183	4	of	of	ADP
ap-10691	183	5	the	the	DET
ap-10691	183	6	initial	initial	ADJ
ap-10691	183	7	hamiltonian	hamiltonian	NOUN
ap-10691	183	8	hϕ	hϕ	PROPN
ap-10691	183	9	mk;0,0	mk;0,0	NOUN
ap-10691	183	10	,	,	PUNCT
ap-10691	183	11	obtained	obtain	VERB
ap-10691	183	12	by	by	ADP
ap-10691	183	13	applying	apply	VERB
ap-10691	183	14	equation	equation	NOUN
ap-10691	183	15	(	(	PUNCT
ap-10691	183	16	20	20	NUM
ap-10691	183	17	)	)	PUNCT
ap-10691	183	18	,	,	PUNCT
ap-10691	183	19	are	be	AUX
ap-10691	183	20	:	:	PUNCT
ap-10691	183	21	φm	φm	X
ap-10691	183	22	(	(	PUNCT
ap-10691	183	23	0)(ϕ	0)(ϕ	NUM
ap-10691	183	24	)	)	PUNCT
ap-10691	183	25	=	=	SYM
ap-10691	184	1	n	n	NOUN
ap-10691	184	2	cosβ	cosβ	NOUN
ap-10691	184	3	k	k	PROPN
ap-10691	185	1	ϕ	ϕ	PROPN
ap-10691	185	2	sinl2	sinl2	PROPN
ap-10691	185	3	+	+	CCONJ
ap-10691	185	4	1	1	NUM
ap-10691	185	5	2	2	NUM
ap-10691	185	6	ϕ	ϕ	NOUN
ap-10691	185	7	×	×	NOUN
ap-10691	185	8	p	p	X
ap-10691	185	9	(	(	PUNCT
ap-10691	185	10	l2	l2	NOUN
ap-10691	185	11	+	+	CCONJ
ap-10691	185	12	1	1	NUM
ap-10691	185	13	2	2	NUM
ap-10691	185	14	,	,	PUNCT
ap-10691	185	15	β	β	X
ap-10691	185	16	k	k	X
ap-10691	185	17	)	)	PUNCT
ap-10691	185	18	m	m	VERB
ap-10691	185	19	(	(	PUNCT
ap-10691	185	20	cos	cos	ADP
ap-10691	185	21	2ϕ	2ϕ	NUM
ap-10691	185	22	)	)	PUNCT
ap-10691	185	23	,	,	PUNCT
ap-10691	185	24	(	(	PUNCT
ap-10691	185	25	53	53	NUM
ap-10691	185	26	)	)	PUNCT
ap-10691	185	27	where	where	SCONJ
ap-10691	185	28	n	n	PRON
ap-10691	185	29	is	be	AUX
ap-10691	185	30	the	the	DET
ap-10691	185	31	normalisation	normalisation	NOUN
ap-10691	185	32	constant	constant	ADJ
ap-10691	185	33	and	and	CCONJ
ap-10691	185	34	p	p	X
ap-10691	185	35	(	(	PUNCT
ap-10691	185	36	l0,l1	l0,l1	PROPN
ap-10691	185	37	)	)	PUNCT
ap-10691	185	38	m	m	VERB
ap-10691	185	39	are	be	AUX
ap-10691	185	40	jacobi	jacobi	NOUN
ap-10691	185	41	polynomials	polynomial	NOUN
ap-10691	185	42	.	.	PUNCT
ap-10691	186	1	the	the	DET
ap-10691	186	2	energy	energy	NOUN
ap-10691	186	3	associated	associate	VERB
ap-10691	186	4	with	with	ADP
ap-10691	186	5	these	these	DET
ap-10691	186	6	states	state	NOUN
ap-10691	186	7	is	be	AUX
ap-10691	186	8	:	:	PUNCT
ap-10691	186	9	eβ	eβ	PROPN
ap-10691	186	10	k	k	PROPN
ap-10691	186	11	,	,	PUNCT
ap-10691	186	12	m	m	PROPN
ap-10691	186	13	(	(	PUNCT
ap-10691	186	14	0	0	NUM
ap-10691	186	15	)	)	PUNCT
ap-10691	186	16	=	=	SYM
ap-10691	186	17	(	(	PUNCT
ap-10691	186	18	β	β	X
ap-10691	186	19	+	+	CCONJ
ap-10691	186	20	l2	l2	NOUN
ap-10691	186	21	+	+	CCONJ
ap-10691	186	22	2m+	2m+	NUM
ap-10691	186	23	1	1	NUM
ap-10691	186	24	2	2	NUM
ap-10691	186	25	)	)	PUNCT
ap-10691	186	26	(	(	PUNCT
ap-10691	186	27	β	β	X
ap-10691	186	28	+	+	CCONJ
ap-10691	186	29	l2	l2	NOUN
ap-10691	186	30	+	+	CCONJ
ap-10691	186	31	2m+	2m+	NUM
ap-10691	186	32	3	3	NUM
ap-10691	186	33	2	2	NUM
ap-10691	186	34	)	)	PUNCT
ap-10691	186	35	.	.	PUNCT
ap-10691	187	1	(	(	PUNCT
ap-10691	187	2	54	54	NUM
ap-10691	187	3	)	)	PUNCT
ap-10691	187	4	3.3	3.3	NUM
ap-10691	187	5	.	.	PUNCT
ap-10691	188	1	factorisation	factorisation	NOUN
ap-10691	188	2	of	of	ADP
ap-10691	188	3	multi	multi	ADJ
ap-10691	188	4	-	-	ADJ
ap-10691	188	5	parametric	parametric	ADJ
ap-10691	188	6	hamiltonian	hamiltonian	NOUN
ap-10691	188	7	given	give	VERB
ap-10691	188	8	that	that	SCONJ
ap-10691	188	9	the	the	DET
ap-10691	188	10	hamiltonians	hamiltonian	NOUN
ap-10691	188	11	now	now	ADV
ap-10691	188	12	depend	depend	VERB
ap-10691	188	13	on	on	ADP
ap-10691	188	14	multiple	multiple	ADJ
ap-10691	188	15	indices	index	NOUN
ap-10691	188	16	,	,	PUNCT
ap-10691	188	17	we	we	PRON
ap-10691	188	18	shall	shall	AUX
ap-10691	188	19	establish	establish	VERB
ap-10691	188	20	a	a	DET
ap-10691	188	21	generalisation	generalisation	NOUN
ap-10691	188	22	of	of	ADP
ap-10691	188	23	subsection	subsection	NOUN
ap-10691	188	24	2.1	2.1	NUM
ap-10691	188	25	,	,	PUNCT
ap-10691	188	26	since	since	SCONJ
ap-10691	188	27	the	the	DET
ap-10691	188	28	original	original	ADJ
ap-10691	188	29	statement	statement	NOUN
ap-10691	188	30	does	do	AUX
ap-10691	188	31	not	not	PART
ap-10691	188	32	apply	apply	VERB
ap-10691	188	33	to	to	ADP
ap-10691	188	34	this	this	DET
ap-10691	188	35	extended	extended	ADJ
ap-10691	188	36	setting	setting	NOUN
ap-10691	188	37	.	.	PUNCT
ap-10691	189	1	proposition	proposition	NOUN
ap-10691	189	2	2	2	NUM
ap-10691	189	3	.	.	PUNCT
ap-10691	190	1	let	let	VERB
ap-10691	190	2	{	{	PUNCT
ap-10691	190	3	hm}m∈z|i|	hm}m∈z|i|	VERB
ap-10691	190	4	be	be	AUX
ap-10691	190	5	a	a	DET
ap-10691	190	6	family	family	NOUN
ap-10691	190	7	of	of	ADP
ap-10691	190	8	operators	operator	NOUN
ap-10691	190	9	depending	depend	VERB
ap-10691	190	10	on	on	ADP
ap-10691	190	11	a	a	DET
ap-10691	190	12	multi	multi	ADJ
ap-10691	190	13	-	-	NOUN
ap-10691	190	14	index	index	NOUN
ap-10691	190	15	m	m	NOUN
ap-10691	190	16	=	=	PUNCT
ap-10691	190	17	(	(	PUNCT
ap-10691	190	18	mi)i∈i	mi)i∈i	NUM
ap-10691	190	19	,	,	PUNCT
ap-10691	190	20	where	where	SCONJ
ap-10691	190	21	|i|	|i|	VERB
ap-10691	190	22	denotes	denote	VERB
ap-10691	190	23	the	the	DET
ap-10691	190	24	cardinality	cardinality	NOUN
ap-10691	190	25	of	of	ADP
ap-10691	190	26	the	the	DET
ap-10691	190	27	index	index	NOUN
ap-10691	190	28	set	set	VERB
ap-10691	190	29	i.	i.	PROPN
ap-10691	190	30	assume	assume	VERB
ap-10691	190	31	that	that	SCONJ
ap-10691	190	32	for	for	ADP
ap-10691	190	33	all	all	DET
ap-10691	190	34	m	m	NOUN
ap-10691	190	35	∈	∈	PROPN
ap-10691	190	36	z|i|	z|i|	NOUN
ap-10691	190	37	:	:	PUNCT
ap-10691	190	38	hm	hm	INTJ
ap-10691	190	39	=	=	SYM
ap-10691	190	40	a+	a+	PUNCT
ap-10691	190	41	ma	ma	PROPN
ap-10691	190	42	−	−	PROPN
ap-10691	191	1	m	m	PROPN
ap-10691	191	2	+	+	X
ap-10691	191	3	λm	λm	X
ap-10691	191	4	=	=	SYM
ap-10691	191	5	a−	a−	PROPN
ap-10691	191	6	f(m)a	f(m)a	PROPN
ap-10691	191	7	+	+	CCONJ
ap-10691	191	8	f(m	f(m	PROPN
ap-10691	191	9	)	)	PUNCT
ap-10691	191	10	+	+	NUM
ap-10691	191	11	λf(m	λf(m	X
ap-10691	191	12	)	)	PUNCT
ap-10691	191	13	,	,	PUNCT
ap-10691	191	14	(	(	PUNCT
ap-10691	191	15	55	55	NUM
ap-10691	191	16	)	)	PUNCT
ap-10691	191	17	where	where	SCONJ
ap-10691	191	18	f	f	NOUN
ap-10691	191	19	:	:	PUNCT
ap-10691	191	20	z|i|	z|i|	NOUN
ap-10691	191	21	→	→	SYM
ap-10691	191	22	z|i|	z|i|	NOUN
ap-10691	191	23	acts	act	VERB
ap-10691	191	24	,	,	PUNCT
ap-10691	191	25	component	component	NOUN
ap-10691	191	26	-	-	PUNCT
ap-10691	191	27	wise	wise	ADJ
ap-10691	191	28	,	,	PUNCT
ap-10691	191	29	as	as	ADP
ap-10691	191	30	f(m	f(m	PROPN
ap-10691	191	31	)	)	PUNCT
ap-10691	191	32	=	=	PUNCT
ap-10691	192	1	(	(	PUNCT
ap-10691	192	2	fi(mi))i∈i	fi(mi))i∈i	NOUN
ap-10691	192	3	with	with	ADP
ap-10691	192	4	each	each	DET
ap-10691	192	5	fi	fi	NOUN
ap-10691	192	6	:	:	PUNCT
ap-10691	192	7	z	z	X
ap-10691	192	8	→	→	SYM
ap-10691	192	9	z	z	NOUN
ap-10691	192	10	invertible	invertible	ADJ
ap-10691	192	11	on	on	ADP
ap-10691	192	12	its	its	PRON
ap-10691	192	13	domain	domain	NOUN
ap-10691	192	14	.	.	PUNCT
ap-10691	193	1	then	then	ADV
ap-10691	193	2	a±	a±	PROPN
ap-10691	193	3	m	m	VERB
ap-10691	193	4	are	be	AUX
ap-10691	193	5	shift	shift	NOUN
ap-10691	193	6	operators	operator	NOUN
ap-10691	193	7	(	(	PUNCT
ap-10691	193	8	cf	cf	NOUN
ap-10691	193	9	.	.	PUNCT
ap-10691	194	1	equation	equation	NOUN
ap-10691	194	2	(	(	PUNCT
ap-10691	194	3	14	14	NUM
ap-10691	194	4	)	)	PUNCT
ap-10691	194	5	)	)	PUNCT
ap-10691	195	1	satisfying	satisfy	VERB
ap-10691	195	2	:	:	PUNCT
ap-10691	195	3	a−	a−	PROPN
ap-10691	195	4	m	m	VERB
ap-10691	195	5	:	:	PUNCT
ap-10691	195	6	hm	hm	INTJ
ap-10691	195	7	→	→	SYM
ap-10691	195	8	hf−1(m	hf−1(m	PROPN
ap-10691	195	9	)	)	PUNCT
ap-10691	195	10	,	,	PUNCT
ap-10691	195	11	a+	a+	X
ap-10691	195	12	m	m	VERB
ap-10691	195	13	:	:	PUNCT
ap-10691	195	14	hf−1(m	hf−1(m	ADJ
ap-10691	195	15	)	)	PUNCT
ap-10691	195	16	→	→	SYM
ap-10691	195	17	hm	hm	INTJ
ap-10691	195	18	,	,	PUNCT
ap-10691	195	19	(	(	PUNCT
ap-10691	195	20	56	56	NUM
ap-10691	195	21	)	)	PUNCT
ap-10691	195	22	where	where	SCONJ
ap-10691	195	23	hm	hm	PRON
ap-10691	195	24	is	be	AUX
ap-10691	195	25	the	the	DET
ap-10691	195	26	the	the	DET
ap-10691	195	27	eigenfunction	eigenfunction	NOUN
ap-10691	195	28	space	space	NOUN
ap-10691	195	29	of	of	ADP
ap-10691	195	30	the	the	DET
ap-10691	195	31	hamiltonian	hamiltonian	ADJ
ap-10691	195	32	hm	hm	INTJ
ap-10691	195	33	.	.	PUNCT
ap-10691	195	34	proof	proof	NOUN
ap-10691	195	35	.	.	PUNCT
ap-10691	196	1	effectively	effectively	ADV
ap-10691	196	2	,	,	PUNCT
ap-10691	196	3	let	let	VERB
ap-10691	196	4	ψe	ψe	VERB
ap-10691	196	5	m	m	VERB
ap-10691	196	6	∈	∈	NOUN
ap-10691	196	7	hm	hm	INTJ
ap-10691	196	8	be	be	AUX
ap-10691	196	9	an	an	DET
ap-10691	196	10	eigenvector	eigenvector	NOUN
ap-10691	196	11	of	of	ADP
ap-10691	196	12	hm	hm	INTJ
ap-10691	196	13	with	with	ADP
ap-10691	196	14	eigenvalue	eigenvalue	PROPN
ap-10691	196	15	e	e	NOUN
ap-10691	196	16	,	,	PUNCT
ap-10691	196	17	i.e.	i.e.	X
ap-10691	196	18	hm	hm	INTJ
ap-10691	196	19	ψe	ψe	NOUN
ap-10691	196	20	m	m	NOUN
ap-10691	196	21	=	=	PUNCT
ap-10691	196	22	e	e	X
ap-10691	196	23	ψe	ψe	NOUN
ap-10691	196	24	m.	m.	NOUN
ap-10691	196	25	from	from	ADP
ap-10691	196	26	equation	equation	NOUN
ap-10691	196	27	(	(	PUNCT
ap-10691	196	28	55	55	NUM
ap-10691	196	29	):	):	PUNCT
ap-10691	196	30	hf−1	hf−1	PROPN
ap-10691	196	31	i	i	PRON
ap-10691	196	32	(	(	PUNCT
ap-10691	196	33	m	m	PROPN
ap-10691	196	34	)	)	PUNCT
ap-10691	196	35	a	a	DET
ap-10691	196	36	−	−	NOUN
ap-10691	196	37	m	m	PRON
ap-10691	196	38	ψe	ψe	NOUN
ap-10691	196	39	m	m	NOUN
ap-10691	196	40	=	=	SYM
ap-10691	196	41	a−	a−	PROPN
ap-10691	196	42	m	m	PROPN
ap-10691	196	43	(	(	PUNCT
ap-10691	196	44	a+	a+	PUNCT
ap-10691	196	45	ma	ma	PROPN
ap-10691	197	1	−	−	PROPN
ap-10691	198	1	m	m	PROPN
ap-10691	198	2	+	+	NUM
ap-10691	198	3	λm)ψe	λm)ψe	ADP
ap-10691	198	4	m	m	VERB
ap-10691	198	5	=	=	SYM
ap-10691	198	6	a−	a−	PROPN
ap-10691	198	7	m	m	VERB
ap-10691	198	8	hm	hm	INTJ
ap-10691	198	9	ψe	ψe	NOUN
ap-10691	198	10	m	m	NOUN
ap-10691	198	11	=	=	SYM
ap-10691	198	12	e	e	X
ap-10691	198	13	(	(	PUNCT
ap-10691	198	14	a−	a−	PROPN
ap-10691	198	15	m	m	PROPN
ap-10691	198	16	ψe	ψe	NOUN
ap-10691	198	17	m	m	PROPN
ap-10691	198	18	)	)	PUNCT
ap-10691	198	19	,	,	PUNCT
ap-10691	198	20	(	(	PUNCT
ap-10691	198	21	57	57	NUM
ap-10691	198	22	)	)	PUNCT
ap-10691	198	23	since	since	SCONJ
ap-10691	198	24	f(f−1(m	f(f−1(m	PROPN
ap-10691	198	25	)	)	PUNCT
ap-10691	198	26	)	)	PUNCT
ap-10691	199	1	=	=	PUNCT
ap-10691	199	2	m	m	VERB
ap-10691	199	3	by	by	ADP
ap-10691	199	4	definition	definition	NOUN
ap-10691	199	5	of	of	ADP
ap-10691	199	6	f−1	f−1	PROPN
ap-10691	199	7	.	.	PUNCT
ap-10691	200	1	thus	thus	ADV
ap-10691	200	2	,	,	PUNCT
ap-10691	200	3	a−	a−	PROPN
ap-10691	200	4	m	m	PROPN
ap-10691	200	5	maps	map	NOUN
ap-10691	200	6	ψe	ψe	VERB
ap-10691	200	7	m	m	VERB
ap-10691	200	8	to	to	ADP
ap-10691	200	9	an	an	DET
ap-10691	200	10	eigenvector	eigenvector	NOUN
ap-10691	200	11	of	of	ADP
ap-10691	200	12	hf−1(m	hf−1(m	PROPN
ap-10691	200	13	)	)	PUNCT
ap-10691	200	14	with	with	ADP
ap-10691	200	15	the	the	DET
ap-10691	200	16	same	same	ADJ
ap-10691	200	17	eigenvalue	eigenvalue	NOUN
ap-10691	200	18	.	.	PUNCT
ap-10691	201	1	similarly	similarly	ADV
ap-10691	201	2	,	,	PUNCT
ap-10691	201	3	for	for	ADP
ap-10691	201	4	a+	a+	PRON
ap-10691	201	5	m	m	PROPN
ap-10691	201	6	:	:	PUNCT
ap-10691	201	7	hm	hm	INTJ
ap-10691	201	8	a+	a+	X
ap-10691	201	9	m	m	VERB
ap-10691	201	10	ψe	ψe	ADP
ap-10691	201	11	f−1(m	f−1(m	ADJ
ap-10691	201	12	)	)	PUNCT
ap-10691	201	13	=	=	SYM
ap-10691	201	14	a+	a+	PUNCT
ap-10691	201	15	m(a−	m(a−	PROPN
ap-10691	201	16	ma	ma	PROPN
ap-10691	201	17	+	+	NOUN
ap-10691	201	18	m	m	PROPN
ap-10691	201	19	+	+	X
ap-10691	201	20	λm)ψe	λm)ψe	X
ap-10691	201	21	f−1(m	f−1(m	ADJ
ap-10691	201	22	)	)	PUNCT
ap-10691	201	23	=	=	PRON
ap-10691	201	24	a+	a+	PUNCT
ap-10691	201	25	m	m	PROPN
ap-10691	201	26	hf−1(m	hf−1(m	NOUN
ap-10691	201	27	)	)	PUNCT
ap-10691	201	28	ψ	ψ	X
ap-10691	201	29	e	e	X
ap-10691	201	30	f−1(m	f−1(m	ADJ
ap-10691	201	31	)	)	PUNCT
ap-10691	201	32	=	=	SYM
ap-10691	201	33	e(a+	e(a+	NOUN
ap-10691	201	34	m	m	VERB
ap-10691	201	35	ψe	ψe	ADP
ap-10691	201	36	f−1(m	f−1(m	ADJ
ap-10691	201	37	)	)	PUNCT
ap-10691	201	38	)	)	PUNCT
ap-10691	201	39	.	.	PUNCT
ap-10691	202	1	(	(	PUNCT
ap-10691	202	2	58	58	X
ap-10691	202	3	)	)	PUNCT
ap-10691	202	4	this	this	PRON
ap-10691	202	5	completes	complete	VERB
ap-10691	202	6	the	the	DET
ap-10691	202	7	proof	proof	NOUN
ap-10691	202	8	.	.	PUNCT
ap-10691	203	1	it	it	PRON
ap-10691	203	2	is	be	AUX
ap-10691	203	3	worth	worth	ADJ
ap-10691	203	4	noting	note	VERB
ap-10691	203	5	that	that	SCONJ
ap-10691	203	6	a±	a±	PROPN
ap-10691	203	7	m	m	AUX
ap-10691	203	8	preserve	preserve	VERB
ap-10691	203	9	the	the	DET
ap-10691	203	10	eigenvalues	eigenvalue	NOUN
ap-10691	203	11	.	.	PUNCT
ap-10691	204	1	3.4	3.4	NUM
ap-10691	204	2	.	.	PUNCT
ap-10691	205	1	on	on	ADP
ap-10691	205	2	the	the	DET
ap-10691	205	3	factorisation	factorisation	NOUN
ap-10691	205	4	of	of	ADP
ap-10691	205	5	the	the	DET
ap-10691	205	6	multi	multi	ADJ
ap-10691	205	7	-	-	ADJ
ap-10691	205	8	indexed	indexed	ADJ
ap-10691	205	9	hamiltonian	hamiltonian	NOUN
ap-10691	205	10	hϕ	hϕ	PROPN
ap-10691	205	11	mk	mk	PROPN
ap-10691	205	12	in	in	ADP
ap-10691	205	13	the	the	DET
ap-10691	205	14	following	following	ADJ
ap-10691	205	15	section	section	NOUN
ap-10691	205	16	,	,	PUNCT
ap-10691	205	17	we	we	PRON
ap-10691	205	18	analyse	analyse	VERB
ap-10691	205	19	the	the	DET
ap-10691	205	20	solutions	solution	NOUN
ap-10691	205	21	arising	arise	VERB
ap-10691	205	22	from	from	ADP
ap-10691	205	23	the	the	DET
ap-10691	205	24	factorisation	factorisation	NOUN
ap-10691	205	25	of	of	ADP
ap-10691	205	26	the	the	DET
ap-10691	205	27	hamiltonian	hamiltonian	PROPN
ap-10691	205	28	hϕ	hϕ	PROPN
ap-10691	205	29	mk	mk	PROPN
ap-10691	205	30	,	,	PUNCT
ap-10691	205	31	in	in	ADP
ap-10691	205	32	the	the	DET
ap-10691	205	33	context	context	NOUN
ap-10691	205	34	of	of	ADP
ap-10691	205	35	the	the	DET
ap-10691	205	36	results	result	NOUN
ap-10691	205	37	of	of	ADP
ap-10691	205	38	the	the	DET
ap-10691	205	39	preceding	precede	VERB
ap-10691	205	40	subsection	subsection	NOUN
ap-10691	205	41	,	,	PUNCT
ap-10691	205	42	with	with	ADP
ap-10691	205	43	the	the	DET
ap-10691	205	44	objective	objective	NOUN
ap-10691	205	45	of	of	ADP
ap-10691	205	46	constructing	construct	VERB
ap-10691	205	47	shift	shift	NOUN
ap-10691	205	48	operators	operator	NOUN
ap-10691	205	49	that	that	PRON
ap-10691	205	50	facilitate	facilitate	VERB
ap-10691	205	51	the	the	DET
ap-10691	205	52	determination	determination	NOUN
ap-10691	205	53	of	of	ADP
ap-10691	205	54	the	the	DET
ap-10691	205	55	symmetries	symmetry	NOUN
ap-10691	205	56	x±.	x±.	PUNCT
ap-10691	205	57	let	let	VERB
ap-10691	205	58	us	we	PRON
ap-10691	205	59	define	define	VERB
ap-10691	205	60	the	the	DET
ap-10691	205	61	generalised	generalise	VERB
ap-10691	205	62	operators	operator	NOUN
ap-10691	205	63	m±,i	m±,i	PROPN
ap-10691	205	64	n	n	CCONJ
ap-10691	205	65	,	,	PUNCT
ap-10691	205	66	m	m	VERB
ap-10691	205	67	in	in	ADP
ap-10691	205	68	terms	term	NOUN
ap-10691	205	69	of	of	ADP
ap-10691	205	70	the	the	DET
ap-10691	205	71	operators	operator	NOUN
ap-10691	205	72	m±	m±	NOUN
ap-10691	205	73	i	i	PRON
ap-10691	205	74	given	give	VERB
ap-10691	205	75	in	in	ADP
ap-10691	205	76	equations	equation	NOUN
ap-10691	205	77	(	(	PUNCT
ap-10691	205	78	43	43	NUM
ap-10691	205	79	)	)	PUNCT
ap-10691	205	80	,	,	PUNCT
ap-10691	205	81	(	(	PUNCT
ap-10691	205	82	45	45	NUM
ap-10691	205	83	)	)	PUNCT
ap-10691	205	84	,	,	PUNCT
ap-10691	205	85	(	(	PUNCT
ap-10691	205	86	47	47	NUM
ap-10691	205	87	)	)	PUNCT
ap-10691	205	88	,	,	PUNCT
ap-10691	205	89	and	and	CCONJ
ap-10691	205	90	(	(	PUNCT
ap-10691	205	91	49	49	NUM
ap-10691	205	92	)	)	PUNCT
ap-10691	205	93	by	by	ADP
ap-10691	205	94	performing	perform	VERB
ap-10691	205	95	the	the	DET
ap-10691	205	96	replacements	replacement	NOUN
ap-10691	205	97	kβ	kβ	INTJ
ap-10691	205	98	→	→	PUNCT
ap-10691	205	99	kβ	kβ	X
ap-10691	205	100	+	+	CCONJ
ap-10691	205	101	n	n	NOUN
ap-10691	205	102	and	and	CCONJ
ap-10691	205	103	l2	l2	NOUN
ap-10691	205	104	→	→	SYM
ap-10691	205	105	l2	l2	NOUN
ap-10691	205	106	+	+	NOUN
ap-10691	205	107	m	m	NOUN
ap-10691	205	108	with	with	ADP
ap-10691	205	109	n	n	CCONJ
ap-10691	205	110	,	,	PUNCT
ap-10691	205	111	m	m	PROPN
ap-10691	205	112	∈	∈	PROPN
ap-10691	205	113	z	z	NOUN
ap-10691	205	114	,	,	PUNCT
ap-10691	205	115	that	that	PRON
ap-10691	205	116	is	be	AUX
ap-10691	205	117	:	:	PUNCT
ap-10691	205	118	m±,i	m±,i	PROPN
ap-10691	205	119	n	n	CCONJ
ap-10691	205	120	,	,	PUNCT
ap-10691	205	121	m	m	VERB
ap-10691	205	122	:	:	PUNCT
ap-10691	205	123	=	=	PUNCT
ap-10691	205	124	m±	m±	NOUN
ap-10691	205	125	i	i	PRON
ap-10691	205	126	(	(	PUNCT
ap-10691	205	127	kβ	kβ	PROPN
ap-10691	205	128	→	→	SYM
ap-10691	205	129	kβ	kβ	NOUN
ap-10691	205	130	+	+	CCONJ
ap-10691	205	131	n	n	CCONJ
ap-10691	205	132	,	,	PUNCT
ap-10691	205	133	l2	l2	NOUN
ap-10691	205	134	→	→	SYM
ap-10691	205	135	l2	l2	NOUN
ap-10691	205	136	+	+	NOUN
ap-10691	205	137	m	m	NOUN
ap-10691	205	138	)	)	PUNCT
ap-10691	205	139	,	,	PUNCT
ap-10691	205	140	(	(	PUNCT
ap-10691	205	141	59	59	NUM
ap-10691	205	142	)	)	PUNCT
ap-10691	205	143	where	where	SCONJ
ap-10691	205	144	i	i	PRON
ap-10691	205	145	=	=	NOUN
ap-10691	205	146	1	1	NUM
ap-10691	205	147	,	,	PUNCT
ap-10691	205	148	.	.	PUNCT
ap-10691	205	149	.	.	PUNCT
ap-10691	206	1	.	.	PUNCT
ap-10691	207	1	,	,	PUNCT
ap-10691	207	2	4	4	X
ap-10691	207	3	.	.	PUNCT
ap-10691	208	1	from	from	ADP
ap-10691	208	2	their	their	PRON
ap-10691	208	3	definition	definition	NOUN
ap-10691	208	4	(	(	PUNCT
ap-10691	208	5	59	59	NUM
ap-10691	208	6	)	)	PUNCT
ap-10691	208	7	and	and	CCONJ
ap-10691	208	8	from	from	ADP
ap-10691	208	9	the	the	DET
ap-10691	208	10	substitutions	substitution	NOUN
ap-10691	208	11	β	β	X
ap-10691	208	12	k	k	X
ap-10691	208	13	→	→	X
ap-10691	208	14	β	β	X
ap-10691	208	15	k	k	NOUN
ap-10691	208	16	+	+	CCONJ
ap-10691	208	17	n	n	NOUN
ap-10691	208	18	and	and	CCONJ
ap-10691	208	19	l2	l2	NOUN
ap-10691	208	20	→	→	SYM
ap-10691	208	21	l2	l2	NOUN
ap-10691	208	22	+	+	CCONJ
ap-10691	208	23	m	m	VERB
ap-10691	208	24	in	in	ADP
ap-10691	208	25	the	the	DET
ap-10691	208	26	factorisation	factorisation	NOUN
ap-10691	208	27	equations	equation	NOUN
ap-10691	208	28	(	(	PUNCT
ap-10691	208	29	43)–(50	43)–(50	NUM
ap-10691	208	30	)	)	PUNCT
ap-10691	208	31	,	,	PUNCT
ap-10691	208	32	we	we	PRON
ap-10691	208	33	can	can	AUX
ap-10691	208	34	see	see	VERB
ap-10691	208	35	that	that	PRON
ap-10691	208	36	for	for	ADP
ap-10691	208	37	each	each	DET
ap-10691	208	38	i	i	PRON
ap-10691	208	39	∈	∈	PROPN
ap-10691	208	40	{	{	PUNCT
ap-10691	208	41	1	1	NUM
ap-10691	208	42	,	,	PUNCT
ap-10691	208	43	2	2	NUM
ap-10691	208	44	,	,	PUNCT
ap-10691	208	45	3	3	NUM
ap-10691	208	46	,	,	PUNCT
ap-10691	208	47	4	4	NUM
ap-10691	208	48	}	}	PUNCT
ap-10691	208	49	,	,	PUNCT
ap-10691	208	50	the	the	DET
ap-10691	208	51	operators	operator	NOUN
ap-10691	208	52	m±,i	m±,i	PROPN
ap-10691	208	53	n	n	CCONJ
ap-10691	208	54	,	,	PUNCT
ap-10691	208	55	m	m	PROPN
ap-10691	208	56	act	act	VERB
ap-10691	208	57	on	on	ADP
ap-10691	208	58	the	the	DET
ap-10691	208	59	hierarchy	hierarchy	NOUN
ap-10691	208	60	of	of	ADP
ap-10691	208	61	hamiltonians	hamiltonian	NOUN
ap-10691	208	62	{	{	PUNCT
ap-10691	208	63	hϕ	hϕ	NOUN
ap-10691	208	64	mk;n	mk;n	ADJ
ap-10691	208	65	,	,	PUNCT
ap-10691	208	66	m}n	m}n	ADV
ap-10691	208	67	,	,	PUNCT
ap-10691	208	68	m∈z	m∈z	VERB
ap-10691	208	69	as	as	SCONJ
ap-10691	208	70	follows	follow	VERB
ap-10691	208	71	:	:	PUNCT
ap-10691	208	72	m+,i	m+,i	NOUN
ap-10691	208	73	n	n	CCONJ
ap-10691	208	74	,	,	PUNCT
ap-10691	208	75	m	m	PROPN
ap-10691	208	76	m−,i	m−,i	NUM
ap-10691	208	77	n	n	CCONJ
ap-10691	208	78	,	,	PUNCT
ap-10691	208	79	m	m	VERB
ap-10691	208	80	+	+	CCONJ
ap-10691	208	81	µi	µi	PROPN
ap-10691	208	82	n	n	CCONJ
ap-10691	208	83	,	,	PUNCT
ap-10691	208	84	m	m	PROPN
ap-10691	208	85	=	=	NOUN
ap-10691	208	86	hϕ	hϕ	PROPN
ap-10691	208	87	mk;n	mk;n	PROPN
ap-10691	208	88	,	,	PUNCT
ap-10691	208	89	m	m	PROPN
ap-10691	208	90	,	,	PUNCT
ap-10691	208	91	m−,i	m−,i	PROPN
ap-10691	208	92	n	n	CCONJ
ap-10691	208	93	,	,	PUNCT
ap-10691	208	94	m	m	VERB
ap-10691	208	95	m+,i	m+,i	NOUN
ap-10691	208	96	n	n	CCONJ
ap-10691	208	97	,	,	PUNCT
ap-10691	208	98	m	m	VERB
ap-10691	208	99	+	+	CCONJ
ap-10691	208	100	µi	µi	PROPN
ap-10691	208	101	n	n	CCONJ
ap-10691	208	102	,	,	PUNCT
ap-10691	208	103	m	m	PROPN
ap-10691	208	104	=	=	NOUN
ap-10691	208	105	hϕ	hϕ	PROPN
ap-10691	208	106	mk;f−1	mk;f−1	ADJ
ap-10691	208	107	1,i	1,i	PROPN
ap-10691	208	108	(	(	PUNCT
ap-10691	208	109	n),f−1	n),f−1	PROPN
ap-10691	208	110	2,i	2,i	NUM
ap-10691	208	111	(	(	PUNCT
ap-10691	208	112	m	m	PROPN
ap-10691	208	113	)	)	PUNCT
ap-10691	208	114	,	,	PUNCT
ap-10691	208	115	(	(	PUNCT
ap-10691	208	116	60	60	NUM
ap-10691	208	117	)	)	PUNCT
ap-10691	208	118	524	524	NUM
ap-10691	208	119	vol	vol	NOUN
ap-10691	208	120	.	.	PUNCT
ap-10691	209	1	65	65	NUM
ap-10691	209	2	no	no	NOUN
ap-10691	209	3	.	.	PUNCT
ap-10691	210	1	5/2025	5/2025	NUM
ap-10691	210	2	classical	classical	ADJ
ap-10691	210	3	and	and	CCONJ
ap-10691	210	4	quantum	quantum	ADJ
ap-10691	210	5	superintegrable	superintegrable	ADJ
ap-10691	210	6	systems	system	NOUN
ap-10691	210	7	on	on	ADP
ap-10691	210	8	the	the	DET
ap-10691	210	9	sphere	sphere	NOUN
ap-10691	210	10	.	.	PUNCT
ap-10691	210	11	.	.	PUNCT
ap-10691	210	12	.	.	PUNCT
ap-10691	211	1	with	with	ADP
ap-10691	211	2	f−1	f−1	PROPN
ap-10691	211	3	1,i	1,i	PROPN
ap-10691	211	4	,	,	PUNCT
ap-10691	211	5	f	f	PROPN
ap-10691	211	6	−1	−1	NOUN
ap-10691	211	7	2,i	2,i	NUM
ap-10691	211	8	:	:	PUNCT
ap-10691	211	9	z	z	X
ap-10691	211	10	→	→	SYM
ap-10691	211	11	z	z	PROPN
ap-10691	211	12	invertible	invertible	ADJ
ap-10691	211	13	index	index	NOUN
ap-10691	211	14	maps	map	NOUN
ap-10691	211	15	such	such	ADJ
ap-10691	211	16	that	that	SCONJ
ap-10691	211	17	f−1	f−1	PROPN
ap-10691	211	18	1,i	1,i	PROPN
ap-10691	211	19	(	(	PUNCT
ap-10691	211	20	r	r	NOUN
ap-10691	211	21	)	)	PUNCT
ap-10691	211	22	,	,	PUNCT
ap-10691	211	23	f−1	f−1	PROPN
ap-10691	211	24	2,i	2,i	NUM
ap-10691	211	25	(	(	PUNCT
ap-10691	211	26	r	r	NOUN
ap-10691	211	27	)	)	PUNCT
ap-10691	211	28	:	:	PUNCT
ap-10691	212	1	r	r	NOUN
ap-10691	212	2	→	→	SYM
ap-10691	212	3	r	r	NOUN
ap-10691	212	4	±	±	NUM
ap-10691	212	5	1	1	NUM
ap-10691	212	6	depending	depend	VERB
ap-10691	212	7	on	on	ADP
ap-10691	212	8	i	i	PRON
ap-10691	212	9	=	=	NOUN
ap-10691	212	10	1	1	NUM
ap-10691	212	11	,	,	PUNCT
ap-10691	212	12	2	2	NUM
ap-10691	212	13	,	,	PUNCT
ap-10691	212	14	3	3	NUM
ap-10691	212	15	,	,	PUNCT
ap-10691	212	16	4	4	NUM
ap-10691	212	17	.	.	X
ap-10691	212	18	in	in	ADP
ap-10691	212	19	other	other	ADJ
ap-10691	212	20	words	word	NOUN
ap-10691	212	21	,	,	PUNCT
ap-10691	212	22	their	their	PRON
ap-10691	212	23	definitions	definition	NOUN
ap-10691	212	24	are	be	AUX
ap-10691	212	25	determined	determine	VERB
ap-10691	212	26	by	by	ADP
ap-10691	212	27	the	the	DET
ap-10691	212	28	index	index	NOUN
ap-10691	212	29	changes	change	NOUN
ap-10691	212	30	dictated	dictate	VERB
ap-10691	212	31	by	by	ADP
ap-10691	212	32	the	the	DET
ap-10691	212	33	intertwining	intertwine	VERB
ap-10691	212	34	equations	equation	NOUN
ap-10691	212	35	(	(	PUNCT
ap-10691	212	36	43)–(50	43)–(50	NOUN
ap-10691	212	37	)	)	PUNCT
ap-10691	212	38	.	.	PUNCT
ap-10691	213	1	for	for	ADP
ap-10691	213	2	instance	instance	NOUN
ap-10691	213	3	,	,	PUNCT
ap-10691	213	4	f−1	f−1	PROPN
ap-10691	213	5	1,4	1,4	NUM
ap-10691	213	6	(	(	PUNCT
ap-10691	213	7	n	n	CCONJ
ap-10691	213	8	)	)	PUNCT
ap-10691	213	9	=	=	SYM
ap-10691	213	10	n	n	PROPN
ap-10691	213	11	+	+	CCONJ
ap-10691	213	12	1	1	NUM
ap-10691	213	13	and	and	CCONJ
ap-10691	213	14	f−1	f−1	PROPN
ap-10691	213	15	2,4	2,4	NUM
ap-10691	213	16	(	(	PUNCT
ap-10691	213	17	m	m	NOUN
ap-10691	213	18	)	)	PUNCT
ap-10691	213	19	=	=	SYM
ap-10691	214	1	m−1	m−1	PROPN
ap-10691	214	2	.	.	PUNCT
ap-10691	215	1	moreover	moreover	ADV
ap-10691	215	2	,	,	PUNCT
ap-10691	215	3	the	the	DET
ap-10691	215	4	action	action	NOUN
ap-10691	215	5	on	on	ADP
ap-10691	215	6	the	the	DET
ap-10691	215	7	spaces	space	NOUN
ap-10691	215	8	of	of	ADP
ap-10691	215	9	eigenfunctions	eigenfunction	NOUN
ap-10691	215	10	hϕ	hϕ	PRON
ap-10691	215	11	mk;n	mk;n	ADJ
ap-10691	215	12	,	,	PUNCT
ap-10691	215	13	m	m	PROPN
ap-10691	215	14	of	of	ADP
ap-10691	215	15	the	the	DET
ap-10691	215	16	hierarchy	hierarchy	NOUN
ap-10691	215	17	hamiltonians	hamiltonian	NOUN
ap-10691	215	18	is	be	AUX
ap-10691	215	19	as	as	SCONJ
ap-10691	215	20	follows	follow	VERB
ap-10691	215	21	:	:	PUNCT
ap-10691	215	22	m−,i	m−,i	PROPN
ap-10691	215	23	n	n	CCONJ
ap-10691	215	24	,	,	PUNCT
ap-10691	215	25	m	m	VERB
ap-10691	215	26	:	:	PUNCT
ap-10691	215	27	hϕ	hϕ	PROPN
ap-10691	215	28	mk;n	mk;n	PROPN
ap-10691	215	29	,	,	PUNCT
ap-10691	215	30	m	m	PROPN
ap-10691	215	31	→	→	SYM
ap-10691	215	32	hϕ	hϕ	X
ap-10691	215	33	mk;f−1	mk;f−1	ADJ
ap-10691	215	34	1,i	1,i	PROPN
ap-10691	215	35	(	(	PUNCT
ap-10691	215	36	n),f−1	n),f−1	PROPN
ap-10691	215	37	2,i	2,i	NUM
ap-10691	215	38	(	(	PUNCT
ap-10691	215	39	m	m	PROPN
ap-10691	215	40	)	)	PUNCT
ap-10691	215	41	,	,	PUNCT
ap-10691	215	42	m+,i	m+,i	NOUN
ap-10691	215	43	n	n	CCONJ
ap-10691	215	44	,	,	PUNCT
ap-10691	215	45	m	m	VERB
ap-10691	215	46	:	:	PUNCT
ap-10691	215	47	hϕ	hϕ	PROPN
ap-10691	215	48	mk;f−1	mk;f−1	ADJ
ap-10691	215	49	1,i	1,i	PROPN
ap-10691	215	50	(	(	PUNCT
ap-10691	215	51	n),f−1	n),f−1	PROPN
ap-10691	215	52	2,i	2,i	NUM
ap-10691	215	53	(	(	PUNCT
ap-10691	215	54	m	m	PROPN
ap-10691	215	55	)	)	PUNCT
ap-10691	215	56	→	→	SYM
ap-10691	215	57	hϕ	hϕ	X
ap-10691	215	58	mk;n	mk;n	ADJ
ap-10691	215	59	,	,	PUNCT
ap-10691	215	60	m.	m.	NOUN
ap-10691	215	61	(	(	PUNCT
ap-10691	215	62	61	61	NUM
ap-10691	215	63	)	)	PUNCT
ap-10691	215	64	we	we	PRON
ap-10691	215	65	have	have	AUX
ap-10691	215	66	identified	identify	VERB
ap-10691	215	67	eight	eight	NUM
ap-10691	215	68	operators	operator	NOUN
ap-10691	215	69	m±,i	m±,i	PROPN
ap-10691	215	70	n	n	CCONJ
ap-10691	215	71	,	,	PUNCT
ap-10691	215	72	m	m	VERB
ap-10691	215	73	that	that	PRON
ap-10691	215	74	transform	transform	VERB
ap-10691	215	75	the	the	DET
ap-10691	215	76	eigenstates	eigenstate	NOUN
ap-10691	215	77	according	accord	VERB
ap-10691	215	78	to	to	ADP
ap-10691	215	79	:	:	PUNCT
ap-10691	215	80	m±,i	m±,i	PROPN
ap-10691	215	81	n	n	CCONJ
ap-10691	215	82	,	,	PUNCT
ap-10691	215	83	m	m	VERB
ap-10691	215	84	:	:	PUNCT
ap-10691	215	85	hϕ	hϕ	PROPN
ap-10691	215	86	mk;n	mk;n	PROPN
ap-10691	215	87	,	,	PUNCT
ap-10691	215	88	m	m	PROPN
ap-10691	215	89	→	→	SYM
ap-10691	215	90	hϕ	hϕ	PROPN
ap-10691	215	91	mk;n+a	mk;n+a	PROPN
ap-10691	215	92	,	,	PUNCT
ap-10691	215	93	m+b	m+b	NUM
ap-10691	215	94	,	,	PUNCT
ap-10691	215	95	(	(	PUNCT
ap-10691	215	96	62	62	NUM
ap-10691	215	97	)	)	PUNCT
ap-10691	215	98	where	where	SCONJ
ap-10691	215	99	a	a	PRON
ap-10691	215	100	,	,	PUNCT
ap-10691	215	101	b	b	X
ap-10691	215	102	∈	∈	PROPN
ap-10691	215	103	{	{	PUNCT
ap-10691	215	104	−1,+1	−1,+1	NOUN
ap-10691	215	105	}	}	PUNCT
ap-10691	215	106	.	.	PUNCT
ap-10691	216	1	in	in	ADP
ap-10691	216	2	figures	figure	NOUN
ap-10691	216	3	1	1	NUM
ap-10691	216	4	and	and	CCONJ
ap-10691	216	5	2	2	NUM
ap-10691	216	6	,	,	PUNCT
ap-10691	216	7	we	we	PRON
ap-10691	216	8	illustrate	illustrate	VERB
ap-10691	216	9	the	the	DET
ap-10691	216	10	action	action	NOUN
ap-10691	216	11	of	of	ADP
ap-10691	216	12	the	the	DET
ap-10691	216	13	operators	operator	NOUN
ap-10691	216	14	m±,i	m±,i	PROPN
ap-10691	216	15	0,0	0,0	NUM
ap-10691	216	16	≡	≡	PROPN
ap-10691	216	17	m±,i	m±,i	PROPN
ap-10691	216	18	,	,	PUNCT
ap-10691	216	19	which	which	PRON
ap-10691	216	20	coincide	coincide	VERB
ap-10691	216	21	with	with	ADP
ap-10691	216	22	those	those	PRON
ap-10691	216	23	defined	define	VERB
ap-10691	216	24	in	in	ADP
ap-10691	216	25	equations	equation	NOUN
ap-10691	216	26	(	(	PUNCT
ap-10691	216	27	43	43	NUM
ap-10691	216	28	)	)	PUNCT
ap-10691	216	29	,	,	PUNCT
ap-10691	216	30	(	(	PUNCT
ap-10691	216	31	45	45	NUM
ap-10691	216	32	)	)	PUNCT
ap-10691	216	33	,	,	PUNCT
ap-10691	216	34	(	(	PUNCT
ap-10691	216	35	47	47	NUM
ap-10691	216	36	)	)	PUNCT
ap-10691	216	37	,	,	PUNCT
ap-10691	216	38	and	and	CCONJ
ap-10691	216	39	(	(	PUNCT
ap-10691	216	40	49	49	NUM
ap-10691	216	41	)	)	PUNCT
ap-10691	216	42	.	.	PUNCT
ap-10691	217	1	note	note	VERB
ap-10691	217	2	that	that	SCONJ
ap-10691	217	3	,	,	PUNCT
ap-10691	217	4	for	for	ADP
ap-10691	217	5	our	our	PRON
ap-10691	217	6	purposes	purpose	NOUN
ap-10691	217	7	,	,	PUNCT
ap-10691	217	8	it	it	PRON
ap-10691	217	9	is	be	AUX
ap-10691	217	10	sufficient	sufficient	ADJ
ap-10691	217	11	to	to	PART
ap-10691	217	12	consider	consider	VERB
ap-10691	217	13	only	only	ADV
ap-10691	217	14	one	one	NUM
ap-10691	217	15	set	set	NOUN
ap-10691	217	16	,	,	PUNCT
ap-10691	217	17	either	either	CCONJ
ap-10691	217	18	the	the	DET
ap-10691	217	19	m+	m+	NOUN
ap-10691	217	20	or	or	CCONJ
ap-10691	217	21	the	the	DET
ap-10691	217	22	m−	m−	PROPN
ap-10691	217	23	operators	operator	NOUN
ap-10691	217	24	,	,	PUNCT
ap-10691	217	25	as	as	SCONJ
ap-10691	217	26	they	they	PRON
ap-10691	217	27	act	act	VERB
ap-10691	217	28	in	in	ADP
ap-10691	217	29	a	a	DET
ap-10691	217	30	similar	similar	ADJ
ap-10691	217	31	manner	manner	NOUN
ap-10691	217	32	.	.	PUNCT
ap-10691	218	1	we	we	PRON
ap-10691	218	2	can	can	AUX
ap-10691	218	3	define	define	VERB
ap-10691	218	4	index	index	NOUN
ap-10691	218	5	-	-	PUNCT
ap-10691	218	6	free	free	ADJ
ap-10691	218	7	operators	operator	NOUN
ap-10691	218	8	ma	ma	PROPN
ap-10691	218	9	,	,	PUNCT
ap-10691	218	10	b	b	NOUN
ap-10691	218	11	in	in	ADP
ap-10691	218	12	terms	term	NOUN
ap-10691	218	13	of	of	ADP
ap-10691	218	14	,	,	PUNCT
ap-10691	218	15	for	for	ADP
ap-10691	218	16	instance	instance	NOUN
ap-10691	218	17	,	,	PUNCT
ap-10691	218	18	the	the	DET
ap-10691	218	19	operators	operator	NOUN
ap-10691	218	20	m−,i	m−,i	PROPN
ap-10691	218	21	m	m	PROPN
ap-10691	218	22	,	,	PUNCT
ap-10691	218	23	n	n	CCONJ
ap-10691	218	24	(	(	PUNCT
ap-10691	218	25	for	for	ADP
ap-10691	218	26	all	all	DET
ap-10691	218	27	n	n	CCONJ
ap-10691	218	28	,	,	PUNCT
ap-10691	218	29	m	m	PROPN
ap-10691	218	30	∈	∈	PROPN
ap-10691	218	31	z	z	PROPN
ap-10691	218	32	)	)	PUNCT
ap-10691	218	33	as	as	SCONJ
ap-10691	218	34	follows	follow	VERB
ap-10691	218	35	:	:	PUNCT
ap-10691	218	36	ma	ma	PROPN
ap-10691	218	37	,	,	PUNCT
ap-10691	218	38	b	b	PROPN
ap-10691	218	39	ψm	ψm	PROPN
ap-10691	218	40	,	,	PUNCT
ap-10691	218	41	n	n	PRON
ap-10691	218	42	:	:	PUNCT
ap-10691	218	43	=	=	SYM
ap-10691	218	44	m−,i	m−,i	NUM
ap-10691	218	45	m	m	PROPN
ap-10691	218	46	,	,	PUNCT
ap-10691	218	47	n	n	PROPN
ap-10691	218	48	ψm	ψm	PROPN
ap-10691	218	49	,	,	PUNCT
ap-10691	218	50	n	n	CCONJ
ap-10691	218	51	,	,	PUNCT
ap-10691	218	52	a	a	PRON
ap-10691	218	53	,	,	PUNCT
ap-10691	218	54	b	b	NOUN
ap-10691	218	55	=	=	PUNCT
ap-10691	218	56	±1	±1	VERB
ap-10691	218	57	.	.	PUNCT
ap-10691	219	1	(	(	PUNCT
ap-10691	219	2	63	63	NUM
ap-10691	219	3	)	)	PUNCT
ap-10691	219	4	thus	thus	ADV
ap-10691	219	5	,	,	PUNCT
ap-10691	219	6	from	from	ADP
ap-10691	219	7	figure	figure	NOUN
ap-10691	219	8	1	1	NUM
ap-10691	219	9	and	and	CCONJ
ap-10691	219	10	figure	figure	VERB
ap-10691	219	11	2	2	NUM
ap-10691	219	12	it	it	PRON
ap-10691	219	13	can	can	AUX
ap-10691	219	14	be	be	AUX
ap-10691	219	15	seen	see	VERB
ap-10691	219	16	that	that	SCONJ
ap-10691	219	17	m1,1	m1,1	NOUN
ap-10691	220	1	=	=	NOUN
ap-10691	220	2	m−,3	m−,3	NOUN
ap-10691	220	3	m	m	NOUN
ap-10691	220	4	,	,	PUNCT
ap-10691	220	5	n	n	CCONJ
ap-10691	220	6	,	,	PUNCT
ap-10691	220	7	m	m	VERB
ap-10691	220	8	1,−1	1,−1	NUM
ap-10691	220	9	=	=	SYM
ap-10691	220	10	m−,2	m−,2	NUM
ap-10691	220	11	m	m	NOUN
ap-10691	220	12	,	,	PUNCT
ap-10691	220	13	n	n	CCONJ
ap-10691	220	14	,	,	PUNCT
ap-10691	220	15	m	m	NOUN
ap-10691	220	16	−1,1	−1,1	NOUN
ap-10691	220	17	=	=	SYM
ap-10691	220	18	m−,4	m−,4	NUM
ap-10691	220	19	m	m	PROPN
ap-10691	220	20	,	,	PUNCT
ap-10691	220	21	n	n	CCONJ
ap-10691	220	22	,	,	PUNCT
ap-10691	220	23	and	and	CCONJ
ap-10691	220	24	m−1,−1	m−1,−1	NOUN
ap-10691	220	25	=	=	SYM
ap-10691	220	26	m−,1	m−,1	PROPN
ap-10691	220	27	m	m	NOUN
ap-10691	220	28	,	,	PUNCT
ap-10691	220	29	n.	n.	VERB
ap-10691	220	30	by	by	ADP
ap-10691	220	31	composing	compose	VERB
ap-10691	220	32	two	two	NUM
ap-10691	220	33	such	such	ADJ
ap-10691	220	34	operators	operator	NOUN
ap-10691	220	35	,	,	PUNCT
ap-10691	220	36	we	we	PRON
ap-10691	220	37	can	can	AUX
ap-10691	220	38	construct	construct	VERB
ap-10691	220	39	the	the	DET
ap-10691	220	40	shift	shift	NOUN
ap-10691	220	41	operators	operator	NOUN
ap-10691	220	42	s	s	AUX
ap-10691	220	43	defined	define	VERB
ap-10691	220	44	in	in	ADP
ap-10691	220	45	equation	equation	NOUN
ap-10691	220	46	(	(	PUNCT
ap-10691	220	47	22	22	NUM
ap-10691	220	48	)	)	PUNCT
ap-10691	220	49	,	,	PUNCT
ap-10691	220	50	which	which	PRON
ap-10691	220	51	move	move	VERB
ap-10691	220	52	only	only	ADV
ap-10691	220	53	in	in	ADP
ap-10691	220	54	one	one	NUM
ap-10691	220	55	direction	direction	NOUN
ap-10691	220	56	.	.	PUNCT
ap-10691	221	1	in	in	ADP
ap-10691	221	2	our	our	PRON
ap-10691	221	3	case	case	NOUN
ap-10691	221	4	,	,	PUNCT
ap-10691	221	5	we	we	PRON
ap-10691	221	6	choose	choose	VERB
ap-10691	221	7	the	the	DET
ap-10691	221	8	direction	direction	NOUN
ap-10691	221	9	along	along	ADP
ap-10691	221	10	kβ	kβ	PROPN
ap-10691	221	11	(	(	PUNCT
ap-10691	221	12	i.e.	i.e.	X
ap-10691	221	13	direction	direction	NOUN
ap-10691	221	14	n	n	CCONJ
ap-10691	221	15	)	)	PUNCT
ap-10691	221	16	.	.	PUNCT
ap-10691	222	1	considering	consider	VERB
ap-10691	222	2	the	the	DET
ap-10691	222	3	composition	composition	NOUN
ap-10691	222	4	of	of	ADP
ap-10691	222	5	operators	operator	NOUN
ap-10691	222	6	acting	act	VERB
ap-10691	222	7	as	as	ADP
ap-10691	222	8	ma	ma	PROPN
ap-10691	222	9	,	,	PUNCT
ap-10691	222	10	bψm	bψm	NOUN
ap-10691	222	11	,	,	PUNCT
ap-10691	222	12	n	n	NOUN
ap-10691	222	13	=	=	SYM
ap-10691	222	14	ψm+a	ψm+a	NOUN
ap-10691	222	15	,	,	PUNCT
ap-10691	222	16	n+b	n+b	NUM
ap-10691	222	17	,	,	PUNCT
ap-10691	222	18	we	we	PRON
ap-10691	222	19	find	find	VERB
ap-10691	222	20	that	that	SCONJ
ap-10691	222	21	:	:	PUNCT
ap-10691	222	22	ma	ma	PROPN
ap-10691	222	23	,	,	PUNCT
ap-10691	222	24	bm−a	bm−a	NOUN
ap-10691	222	25	,	,	PUNCT
ap-10691	222	26	bψm	bψm	NOUN
ap-10691	222	27	,	,	PUNCT
ap-10691	222	28	n	n	PROPN
ap-10691	222	29	=	=	SYM
ap-10691	222	30	ma	ma	PROPN
ap-10691	222	31	,	,	PUNCT
ap-10691	222	32	bψm−a	bψm−a	NOUN
ap-10691	222	33	,	,	PUNCT
ap-10691	222	34	n+b	n+b	NUM
ap-10691	222	35	=	=	SYM
ap-10691	222	36	ψm	ψm	PROPN
ap-10691	222	37	,	,	PUNCT
ap-10691	222	38	n+2b	n+2b	PROPN
ap-10691	222	39	,	,	PUNCT
ap-10691	222	40	(	(	PUNCT
ap-10691	222	41	64	64	NUM
ap-10691	222	42	)	)	PUNCT
ap-10691	222	43	where	where	SCONJ
ap-10691	222	44	a	a	DET
ap-10691	222	45	,	,	PUNCT
ap-10691	222	46	b	b	NOUN
ap-10691	222	47	=	=	PUNCT
ap-10691	222	48	±1	±1	VERB
ap-10691	222	49	.	.	PUNCT
ap-10691	223	1	equation	equation	NOUN
ap-10691	223	2	(	(	PUNCT
ap-10691	223	3	63	63	NUM
ap-10691	223	4	)	)	PUNCT
ap-10691	223	5	allows	allow	VERB
ap-10691	223	6	us	we	PRON
ap-10691	223	7	to	to	PART
ap-10691	223	8	define	define	VERB
ap-10691	223	9	the	the	DET
ap-10691	223	10	shift	shift	NOUN
ap-10691	223	11	operators	operator	NOUN
ap-10691	223	12	(	(	PUNCT
ap-10691	223	13	22	22	NUM
ap-10691	223	14	)	)	PUNCT
ap-10691	223	15	as	as	SCONJ
ap-10691	223	16	follows	follow	VERB
ap-10691	223	17	:	:	PUNCT
ap-10691	223	18	s±	s±	PROPN
ap-10691	223	19	:	:	PUNCT
ap-10691	223	20	=	=	SYM
ap-10691	223	21	ma,±1	ma,±1	PROPN
ap-10691	223	22	m−a,±1	m−a,±1	PROPN
ap-10691	223	23	,	,	PUNCT
ap-10691	223	24	(	(	PUNCT
ap-10691	223	25	65	65	NUM
ap-10691	223	26	)	)	PUNCT
ap-10691	223	27	that	that	PRON
ap-10691	223	28	act	act	VERB
ap-10691	223	29	as	as	ADP
ap-10691	223	30	:	:	PUNCT
ap-10691	223	31	s±	s±	PROPN
ap-10691	223	32	:	:	PUNCT
ap-10691	223	33	hϕ	hϕ	PROPN
ap-10691	223	34	mk;m	mk;m	PROPN
ap-10691	223	35	,	,	PUNCT
ap-10691	223	36	n	n	PROPN
ap-10691	223	37	→	→	SYM
ap-10691	223	38	hϕ	hϕ	PROPN
ap-10691	223	39	mk;m	mk;m	PROPN
ap-10691	223	40	,	,	PUNCT
ap-10691	223	41	n±2	n±2	NUM
ap-10691	223	42	.	.	PUNCT
ap-10691	224	1	(	(	PUNCT
ap-10691	224	2	66	66	NUM
ap-10691	224	3	)	)	PUNCT
ap-10691	224	4	in	in	ADP
ap-10691	224	5	figure	figure	NOUN
ap-10691	224	6	3	3	NUM
ap-10691	224	7	we	we	PRON
ap-10691	224	8	show	show	VERB
ap-10691	224	9	how	how	SCONJ
ap-10691	224	10	the	the	DET
ap-10691	224	11	shift	shift	NOUN
ap-10691	224	12	operator	operator	NOUN
ap-10691	224	13	s+	s+	ADV
ap-10691	224	14	can	can	AUX
ap-10691	224	15	be	be	AUX
ap-10691	224	16	expressed	express	VERB
ap-10691	224	17	in	in	ADP
ap-10691	224	18	terms	term	NOUN
ap-10691	224	19	of	of	ADP
ap-10691	224	20	the	the	DET
ap-10691	224	21	operators	operator	NOUN
ap-10691	224	22	m−1,1	m−1,1	VERB
ap-10691	224	23	and	and	CCONJ
ap-10691	225	1	m1,1	m1,1	INTJ
ap-10691	225	2	.	.	PUNCT
ap-10691	226	1	although	although	SCONJ
ap-10691	226	2	s−	s−	PROPN
ap-10691	226	3	is	be	AUX
ap-10691	226	4	not	not	PART
ap-10691	226	5	depicted	depict	VERB
ap-10691	226	6	,	,	PUNCT
ap-10691	226	7	the	the	DET
ap-10691	226	8	reader	reader	NOUN
ap-10691	226	9	can	can	AUX
ap-10691	226	10	infer	infer	VERB
ap-10691	226	11	that	that	SCONJ
ap-10691	226	12	it	it	PRON
ap-10691	226	13	is	be	AUX
ap-10691	226	14	defined	define	VERB
ap-10691	226	15	analogously	analogously	ADV
ap-10691	226	16	in	in	ADP
ap-10691	226	17	terms	term	NOUN
ap-10691	226	18	of	of	ADP
ap-10691	226	19	the	the	DET
ap-10691	226	20	operators	operator	NOUN
ap-10691	226	21	m−1,−1	m−1,−1	PROPN
ap-10691	226	22	and	and	CCONJ
ap-10691	226	23	m1,−1	m1,−1	NOUN
ap-10691	226	24	.	.	PUNCT
ap-10691	227	1	taking	take	VERB
ap-10691	227	2	into	into	ADP
ap-10691	227	3	account	account	NOUN
ap-10691	227	4	equation	equation	NOUN
ap-10691	227	5	(	(	PUNCT
ap-10691	227	6	40	40	NUM
ap-10691	227	7	)	)	PUNCT
ap-10691	227	8	,	,	PUNCT
ap-10691	227	9	we	we	PRON
ap-10691	227	10	can	can	AUX
ap-10691	227	11	then	then	ADV
ap-10691	227	12	obtain	obtain	VERB
ap-10691	227	13	the	the	DET
ap-10691	227	14	shift	shift	NOUN
ap-10691	227	15	operators	operator	NOUN
ap-10691	227	16	s±2	s±2	NOUN
ap-10691	227	17	m	m	AUX
ap-10691	227	18	defined	define	VERB
ap-10691	227	19	in	in	ADP
ap-10691	227	20	equation	equation	NOUN
ap-10691	227	21	(	(	PUNCT
ap-10691	227	22	23	23	NUM
ap-10691	227	23	)	)	PUNCT
ap-10691	227	24	by	by	ADP
ap-10691	227	25	:	:	PUNCT
ap-10691	227	26	s±2	s±2	NOUN
ap-10691	227	27	m	m	VERB
ap-10691	227	28	=	=	PUNCT
ap-10691	227	29	(	(	PUNCT
ap-10691	227	30	s±)m	s±)m	PROPN
ap-10691	227	31	.	.	PUNCT
ap-10691	228	1	(	(	PUNCT
ap-10691	228	2	67	67	NUM
ap-10691	228	3	)	)	PUNCT
ap-10691	228	4	.	.	PUNCT
ap-10691	229	1	figure	figure	VERB
ap-10691	229	2	1	1	NUM
ap-10691	229	3	.	.	PUNCT
ap-10691	230	1	action	action	NOUN
ap-10691	230	2	of	of	ADP
ap-10691	230	3	the	the	DET
ap-10691	230	4	operators	operator	NOUN
ap-10691	230	5	m±,1	m±,1	NOUN
ap-10691	230	6	(	(	PUNCT
ap-10691	230	7	equation	equation	NOUN
ap-10691	230	8	(	(	PUNCT
ap-10691	230	9	43	43	NUM
ap-10691	230	10	)	)	PUNCT
ap-10691	230	11	)	)	PUNCT
ap-10691	230	12	and	and	CCONJ
ap-10691	230	13	m±,2	m±,2	PROPN
ap-10691	230	14	(	(	PUNCT
ap-10691	230	15	equation	equation	NOUN
ap-10691	230	16	(	(	PUNCT
ap-10691	230	17	45	45	NUM
ap-10691	230	18	)	)	PUNCT
ap-10691	230	19	)	)	PUNCT
ap-10691	230	20	figure	figure	NOUN
ap-10691	230	21	2	2	NUM
ap-10691	230	22	.	.	PUNCT
ap-10691	231	1	action	action	NOUN
ap-10691	231	2	of	of	ADP
ap-10691	231	3	the	the	DET
ap-10691	231	4	operators	operator	NOUN
ap-10691	231	5	m±,3	m±,3	PROPN
ap-10691	231	6	(	(	PUNCT
ap-10691	231	7	equation	equation	NOUN
ap-10691	231	8	(	(	PUNCT
ap-10691	231	9	47	47	NUM
ap-10691	231	10	)	)	PUNCT
ap-10691	231	11	)	)	PUNCT
ap-10691	231	12	and	and	CCONJ
ap-10691	231	13	m±,4	m±,4	PROPN
ap-10691	231	14	(	(	PUNCT
ap-10691	231	15	equation	equation	NOUN
ap-10691	231	16	(	(	PUNCT
ap-10691	231	17	49	49	NUM
ap-10691	231	18	)	)	PUNCT
ap-10691	231	19	)	)	PUNCT
ap-10691	231	20	.	.	PUNCT
ap-10691	232	1	figure	figure	VERB
ap-10691	232	2	3	3	NUM
ap-10691	232	3	.	.	PUNCT
ap-10691	232	4	shift	shift	NOUN
ap-10691	232	5	operator	operator	NOUN
ap-10691	232	6	(	(	PUNCT
ap-10691	232	7	65	65	NUM
ap-10691	232	8	)	)	PUNCT
ap-10691	232	9	s+	s+	PUNCT
ap-10691	233	1	=	=	PUNCT
ap-10691	233	2	m1,1	m1,1	ADJ
ap-10691	233	3	m−1,1	m−1,1	NOUN
ap-10691	233	4	.	.	PUNCT
ap-10691	234	1	finally	finally	ADV
ap-10691	234	2	,	,	PUNCT
ap-10691	234	3	we	we	PRON
ap-10691	234	4	have	have	AUX
ap-10691	234	5	constructed	construct	VERB
ap-10691	234	6	the	the	DET
ap-10691	234	7	operators	operator	NOUN
ap-10691	234	8	l±	l±	VERB
ap-10691	234	9	±2n	±2n	PROPN
ap-10691	234	10	(	(	PUNCT
ap-10691	234	11	40	40	NUM
ap-10691	234	12	)	)	PUNCT
ap-10691	234	13	and	and	CCONJ
ap-10691	234	14	s±2	s±2	NOUN
ap-10691	234	15	m	m	VERB
ap-10691	234	16	(	(	PUNCT
ap-10691	234	17	67	67	NUM
ap-10691	234	18	)	)	PUNCT
ap-10691	234	19	,	,	PUNCT
ap-10691	234	20	which	which	PRON
ap-10691	234	21	enable	enable	VERB
ap-10691	234	22	us	we	PRON
ap-10691	234	23	to	to	PART
ap-10691	234	24	build	build	VERB
ap-10691	234	25	the	the	DET
ap-10691	234	26	symmetries	symmetry	NOUN
ap-10691	234	27	x±	x±	PROPN
ap-10691	235	1	=	=	SYM
ap-10691	235	2	l±2n	l±2n	ADJ
ap-10691	235	3	s±2	s±2	NOUN
ap-10691	235	4	m	m	PROPN
ap-10691	235	5	(	(	PUNCT
ap-10691	235	6	24	24	NUM
ap-10691	235	7	)	)	PUNCT
ap-10691	235	8	that	that	PRON
ap-10691	235	9	commute	commute	VERB
ap-10691	235	10	with	with	ADP
ap-10691	235	11	the	the	DET
ap-10691	235	12	hamiltonian	hamiltonian	NOUN
ap-10691	235	13	.	.	PUNCT
ap-10691	236	1	this	this	DET
ap-10691	236	2	construction	construction	NOUN
ap-10691	236	3	allows	allow	VERB
ap-10691	236	4	us	we	PRON
ap-10691	236	5	to	to	PART
ap-10691	236	6	prove	prove	VERB
ap-10691	236	7	that	that	SCONJ
ap-10691	236	8	the	the	DET
ap-10691	236	9	hamiltonian	hamiltonian	ADJ
ap-10691	236	10	system	system	NOUN
ap-10691	236	11	hk	hk	PROPN
ap-10691	236	12	(	(	PUNCT
ap-10691	236	13	8)	8)	NUM
ap-10691	236	14	is	be	AUX
ap-10691	236	15	superintegrable	superintegrable	ADJ
ap-10691	236	16	.	.	PUNCT
ap-10691	237	1	it	it	PRON
ap-10691	237	2	is	be	AUX
ap-10691	237	3	worth	worth	ADJ
ap-10691	237	4	noting	note	VERB
ap-10691	237	5	that	that	SCONJ
ap-10691	237	6	the	the	DET
ap-10691	237	7	operators	operator	NOUN
ap-10691	237	8	x±	x±	PROPN
ap-10691	237	9	do	do	AUX
ap-10691	237	10	not	not	PART
ap-10691	237	11	commute	commute	VERB
ap-10691	237	12	,	,	PUNCT
ap-10691	237	13	since	since	SCONJ
ap-10691	237	14	[	[	X
ap-10691	237	15	x+	x+	ADJ
ap-10691	237	16	,	,	PUNCT
ap-10691	237	17	x−	x−	PROPN
ap-10691	237	18	]	]	X
ap-10691	237	19	̸=	̸=	PROPN
ap-10691	237	20	0	0	NUM
ap-10691	237	21	,	,	PUNCT
ap-10691	237	22	which	which	PRON
ap-10691	237	23	is	be	AUX
ap-10691	237	24	a	a	DET
ap-10691	237	25	fact	fact	NOUN
ap-10691	237	26	that	that	PRON
ap-10691	237	27	can	can	AUX
ap-10691	237	28	be	be	AUX
ap-10691	237	29	directly	directly	ADV
ap-10691	237	30	verified	verify	VERB
ap-10691	237	31	.	.	PUNCT
ap-10691	238	1	recall	recall	VERB
ap-10691	238	2	that	that	PRON
ap-10691	238	3	k	k	PROPN
ap-10691	239	1	=	=	PUNCT
ap-10691	239	2	m	m	VERB
ap-10691	239	3	n	n	ADJ
ap-10691	239	4	,	,	PUNCT
ap-10691	239	5	with	with	ADP
ap-10691	239	6	m	m	PROPN
ap-10691	239	7	and	and	CCONJ
ap-10691	239	8	n	n	NUM
ap-10691	239	9	integers	integer	NOUN
ap-10691	239	10	,	,	PUNCT
ap-10691	239	11	which	which	PRON
ap-10691	239	12	can	can	AUX
ap-10691	239	13	,	,	PUNCT
ap-10691	239	14	without	without	ADP
ap-10691	239	15	loss	loss	NOUN
ap-10691	239	16	of	of	ADP
ap-10691	239	17	generality	generality	NOUN
ap-10691	239	18	,	,	PUNCT
ap-10691	239	19	be	be	AUX
ap-10691	239	20	taken	take	VERB
ap-10691	239	21	an	an	DET
ap-10691	239	22	irreducible	irreducible	ADJ
ap-10691	239	23	form	form	NOUN
ap-10691	239	24	,	,	PUNCT
ap-10691	239	25	i.e.	i.e.	X
ap-10691	239	26	with	with	ADP
ap-10691	239	27	m	m	PROPN
ap-10691	239	28	and	and	CCONJ
ap-10691	239	29	n	n	CCONJ
ap-10691	239	30	>	>	NOUN
ap-10691	239	31	0	0	PUNCT
ap-10691	239	32	coprime	coprime	NOUN
ap-10691	239	33	.	.	PUNCT
ap-10691	240	1	although	although	SCONJ
ap-10691	240	2	k	k	PROPN
ap-10691	240	3	can	can	AUX
ap-10691	240	4	equivalently	equivalently	ADV
ap-10691	240	5	be	be	AUX
ap-10691	240	6	written	write	VERB
ap-10691	240	7	as	as	ADP
ap-10691	240	8	k	k	NOUN
ap-10691	240	9	=	=	X
ap-10691	240	10	γm	γm	ADJ
ap-10691	240	11	γn	γn	NOUN
ap-10691	240	12	for	for	ADP
ap-10691	240	13	any	any	DET
ap-10691	240	14	γ	γ	NOUN
ap-10691	240	15	̸=	̸=	PROPN
ap-10691	240	16	0	0	NUM
ap-10691	240	17	,	,	PUNCT
ap-10691	240	18	the	the	DET
ap-10691	240	19	operators	operator	NOUN
ap-10691	240	20	l±2n	l±2n	ADJ
ap-10691	240	21	and	and	CCONJ
ap-10691	240	22	s±2	s±2	NOUN
ap-10691	240	23	m	m	PROPN
ap-10691	240	24	,	,	PUNCT
ap-10691	240	25	depending	depend	VERB
ap-10691	240	26	on	on	ADP
ap-10691	240	27	θ	θ	PROPN
ap-10691	240	28	and	and	CCONJ
ap-10691	240	29	ϕ	ϕ	X
ap-10691	240	30	respectively	respectively	ADV
ap-10691	240	31	,	,	PUNCT
ap-10691	240	32	commute	commute	NOUN
ap-10691	240	33	.	.	PUNCT
ap-10691	240	34	using	use	VERB
ap-10691	240	35	l±2n	l±2n	NOUN
ap-10691	240	36	=	=	SYM
ap-10691	240	37	(	(	PUNCT
ap-10691	240	38	l±)n	l±)n	ADJ
ap-10691	240	39	and	and	CCONJ
ap-10691	240	40	s±2	s±2	NOUN
ap-10691	240	41	m	m	VERB
ap-10691	240	42	=	=	PUNCT
ap-10691	240	43	(	(	PUNCT
ap-10691	240	44	s±)m	s±)m	PROPN
ap-10691	240	45	,	,	PUNCT
ap-10691	240	46	we	we	PRON
ap-10691	240	47	obtain	obtain	VERB
ap-10691	240	48	l±2nγs±2mγ	l±2nγs±2mγ	X
ap-10691	240	49	=	=	PUNCT
ap-10691	240	50	(	(	PUNCT
ap-10691	240	51	x±)γ	x±)γ	PROPN
ap-10691	240	52	,	,	PUNCT
ap-10691	240	53	implying	imply	VERB
ap-10691	240	54	that	that	SCONJ
ap-10691	240	55	the	the	DET
ap-10691	240	56	expression	expression	NOUN
ap-10691	240	57	depends	depend	VERB
ap-10691	240	58	only	only	ADV
ap-10691	240	59	on	on	ADP
ap-10691	240	60	x±.	x±.	PUNCT
ap-10691	240	61	thus	thus	ADV
ap-10691	240	62	,	,	PUNCT
ap-10691	240	63	it	it	PRON
ap-10691	240	64	is	be	AUX
ap-10691	240	65	natural	natural	ADJ
ap-10691	240	66	and	and	CCONJ
ap-10691	240	67	sufficient	sufficient	ADJ
ap-10691	240	68	to	to	PART
ap-10691	240	69	restrict	restrict	VERB
ap-10691	240	70	k	k	PROPN
ap-10691	240	71	to	to	ADP
ap-10691	240	72	its	its	PRON
ap-10691	240	73	irreducible	irreducible	ADJ
ap-10691	240	74	form	form	NOUN
ap-10691	240	75	.	.	PUNCT
ap-10691	241	1	525	525	NUM
ap-10691	241	2	mariano	mariano	PROPN
ap-10691	241	3	a.	a.	PROPN
ap-10691	241	4	del	del	PROPN
ap-10691	241	5	olmo	olmo	PROPN
ap-10691	241	6	,	,	PUNCT
ap-10691	241	7	álvaro	álvaro	PROPN
ap-10691	241	8	romaniega	romaniega	PROPN
ap-10691	241	9	acta	acta	PROPN
ap-10691	241	10	polytechnica	polytechnica	PROPN
ap-10691	241	11	4	4	NUM
ap-10691	241	12	.	.	PUNCT
ap-10691	241	13	associated	associate	VERB
ap-10691	241	14	classical	classical	ADJ
ap-10691	241	15	system	system	NOUN
ap-10691	241	16	the	the	DET
ap-10691	241	17	classical	classical	ADJ
ap-10691	241	18	version	version	NOUN
ap-10691	241	19	of	of	ADP
ap-10691	241	20	the	the	DET
ap-10691	241	21	quantum	quantum	ADJ
ap-10691	241	22	hamiltonian	hamiltonian	NOUN
ap-10691	241	23	(	(	PUNCT
ap-10691	241	24	8)	8)	NUM
ap-10691	241	25	is	be	AUX
ap-10691	241	26	:	:	PUNCT
ap-10691	241	27	hk	hk	PROPN
ap-10691	241	28	=	=	NOUN
ap-10691	241	29	p2	p2	PROPN
ap-10691	241	30	ϕ	ϕ	PROPN
ap-10691	242	1	+	+	CCONJ
ap-10691	242	2	c2	c2	PROPN
ap-10691	242	3	sin2	sin2	PROPN
ap-10691	242	4	ϕ	ϕ	PROPN
ap-10691	243	1	+	+	CCONJ
ap-10691	243	2	k2	k2	ADJ
ap-10691	243	3	cos2	cos2	PROPN
ap-10691	243	4	ϕ	ϕ	PROPN
ap-10691	243	5	×	×	PROPN
ap-10691	243	6	(	(	PUNCT
ap-10691	243	7	p2	p2	PROPN
ap-10691	243	8	θ	θ	PROPN
ap-10691	243	9	+	+	CCONJ
ap-10691	243	10	a2	a2	PROPN
ap-10691	243	11	cos2	cos2	NOUN
ap-10691	243	12	θ	θ	PROPN
ap-10691	243	13	+	+	CCONJ
ap-10691	243	14	b2	b2	NOUN
ap-10691	243	15	sin2	sin2	NOUN
ap-10691	243	16	θ	θ	PROPN
ap-10691	243	17	)	)	PUNCT
ap-10691	243	18	.	.	PUNCT
ap-10691	244	1	(	(	PUNCT
ap-10691	244	2	68	68	NUM
ap-10691	244	3	)	)	PUNCT
ap-10691	244	4	we	we	PRON
ap-10691	244	5	can	can	AUX
ap-10691	244	6	group	group	VERB
ap-10691	244	7	the	the	DET
ap-10691	244	8	terms	term	NOUN
ap-10691	244	9	as	as	ADP
ap-10691	244	10	:	:	PUNCT
ap-10691	244	11	hθ	hθ	NOUN
ap-10691	244	12	=	=	PUNCT
ap-10691	244	13	p2	p2	PROPN
ap-10691	244	14	θ	θ	PROPN
ap-10691	244	15	+	+	CCONJ
ap-10691	244	16	a2	a2	PROPN
ap-10691	244	17	cos2	cos2	NOUN
ap-10691	244	18	θ	θ	PROPN
ap-10691	244	19	+	+	CCONJ
ap-10691	244	20	b2	b2	NOUN
ap-10691	244	21	sin2	sin2	NOUN
ap-10691	244	22	θ	θ	PROPN
ap-10691	244	23	,	,	PUNCT
ap-10691	244	24	(	(	PUNCT
ap-10691	244	25	69	69	NUM
ap-10691	244	26	)	)	PUNCT
ap-10691	244	27	hϕ	hϕ	PROPN
ap-10691	244	28	mk	mk	NOUN
ap-10691	244	29	=	=	PUNCT
ap-10691	244	30	p2	p2	PROPN
ap-10691	244	31	ϕ	ϕ	PROPN
ap-10691	244	32	+	+	CCONJ
ap-10691	245	1	m2	m2	PROPN
ap-10691	245	2	k	k	PROPN
ap-10691	245	3	cos2	cos2	PROPN
ap-10691	245	4	ϕ	ϕ	PROPN
ap-10691	246	1	+	+	PROPN
ap-10691	246	2	c2	c2	PROPN
ap-10691	246	3	sin2	sin2	PROPN
ap-10691	246	4	ϕ	ϕ	PROPN
ap-10691	246	5	,	,	PUNCT
ap-10691	246	6	(	(	PUNCT
ap-10691	246	7	70	70	NUM
ap-10691	246	8	)	)	PUNCT
ap-10691	246	9	where	where	SCONJ
ap-10691	246	10	mk	mk	NOUN
ap-10691	246	11	:	:	PUNCT
ap-10691	246	12	=	=	SYM
ap-10691	247	1	k	k	ADJ
ap-10691	247	2	√	√	NUM
ap-10691	247	3	hθ	hθ	INTJ
ap-10691	247	4	.	.	PUNCT
ap-10691	248	1	note	note	VERB
ap-10691	248	2	that	that	SCONJ
ap-10691	248	3	hk	hk	PROPN
ap-10691	248	4	=	=	SYM
ap-10691	248	5	hk(pϕ	hk(pϕ	PROPN
ap-10691	248	6	,	,	PUNCT
ap-10691	248	7	ϕ	ϕ	NOUN
ap-10691	248	8	,	,	PUNCT
ap-10691	248	9	pθ	pθ	VERB
ap-10691	248	10	,	,	PUNCT
ap-10691	248	11	θ	θ	NOUN
ap-10691	248	12	)	)	PUNCT
ap-10691	248	13	and	and	CCONJ
ap-10691	248	14	hθ	hθ	NOUN
ap-10691	248	15	=	=	SYM
ap-10691	248	16	hθ(pθ	hθ(pθ	PROPN
ap-10691	248	17	,	,	PUNCT
ap-10691	248	18	θ	θ	PROPN
ap-10691	248	19	)	)	PUNCT
ap-10691	248	20	.	.	PUNCT
ap-10691	249	1	4.1	4.1	NUM
ap-10691	249	2	.	.	PUNCT
ap-10691	249	3	superintegrability	superintegrability	NOUN
ap-10691	249	4	in	in	ADP
ap-10691	249	5	analogy	analogy	NOUN
ap-10691	249	6	with	with	ADP
ap-10691	249	7	the	the	DET
ap-10691	249	8	quantum	quantum	ADJ
ap-10691	249	9	case	case	NOUN
ap-10691	249	10	[	[	X
ap-10691	249	11	31	31	NUM
ap-10691	249	12	]	]	PUNCT
ap-10691	249	13	,	,	PUNCT
ap-10691	249	14	we	we	PRON
ap-10691	249	15	can	can	AUX
ap-10691	249	16	consider	consider	VERB
ap-10691	249	17	the	the	DET
ap-10691	249	18	ladder	ladder	NOUN
ap-10691	249	19	functions	function	NOUN
ap-10691	249	20	l±(θ	l±(θ	PROPN
ap-10691	249	21	,	,	PUNCT
ap-10691	249	22	pθ	pθ	VERB
ap-10691	249	23	):	):	PUNCT
ap-10691	249	24	l±	l±	X
ap-10691	249	25	=	=	SYM
ap-10691	249	26	(	(	PUNCT
ap-10691	249	27	b2	b2	NOUN
ap-10691	249	28	−	−	PROPN
ap-10691	249	29	a2	a2	PROPN
ap-10691	249	30	)	)	PUNCT
ap-10691	249	31	1√	1√	NOUN
ap-10691	249	32	hθ	hθ	NOUN
ap-10691	249	33	+	+	CCONJ
ap-10691	249	34	cos	cos	ADJ
ap-10691	249	35	2θ	2θ	NUM
ap-10691	249	36	√	√	INTJ
ap-10691	249	37	hθ	hθ	PROPN
ap-10691	249	38	±	±	PROPN
ap-10691	249	39	ipθ	ipθ	ADJ
ap-10691	249	40	sin	sin	NOUN
ap-10691	249	41	2θ	2θ	NUM
ap-10691	249	42	,	,	PUNCT
ap-10691	249	43	(	(	PUNCT
ap-10691	249	44	71	71	NUM
ap-10691	249	45	)	)	PUNCT
ap-10691	249	46	such	such	ADJ
ap-10691	249	47	that	that	SCONJ
ap-10691	249	48	they	they	PRON
ap-10691	249	49	verify	verify	VERB
ap-10691	249	50	:	:	PUNCT
ap-10691	249	51	{	{	PUNCT
ap-10691	249	52	hθ	hθ	INTJ
ap-10691	249	53	,	,	PUNCT
ap-10691	249	54	l±}θ	l±}θ	PROPN
ap-10691	249	55	=	=	SYM
ap-10691	249	56	∓i	∓i	PROPN
ap-10691	249	57	4	4	NUM
ap-10691	249	58	√	√	NOUN
ap-10691	249	59	hθ	hθ	PROPN
ap-10691	249	60	l±	l±	PROPN
ap-10691	249	61	,	,	PUNCT
ap-10691	249	62	(	(	PUNCT
ap-10691	249	63	72	72	NUM
ap-10691	249	64	)	)	PUNCT
ap-10691	249	65	and	and	CCONJ
ap-10691	249	66	also	also	ADV
ap-10691	249	67	:	:	PUNCT
ap-10691	249	68	{	{	PUNCT
ap-10691	249	69	hk	hk	NOUN
ap-10691	249	70	,	,	PUNCT
ap-10691	249	71	(	(	PUNCT
ap-10691	249	72	l±)n	l±)n	ADJ
ap-10691	249	73	}	}	PUNCT
ap-10691	249	74	=	=	SYM
ap-10691	249	75	{	{	PUNCT
ap-10691	249	76	hθ	hθ	NOUN
ap-10691	249	77	,	,	PUNCT
ap-10691	249	78	(	(	PUNCT
ap-10691	249	79	l±)n}θ	l±)n}θ	NOUN
ap-10691	249	80	=	=	PUNCT
ap-10691	249	81	∓nα	∓nα	NOUN
ap-10691	249	82	(	(	PUNCT
ap-10691	249	83	l±)n	l±)n	ADJ
ap-10691	249	84	,	,	PUNCT
ap-10691	249	85	(	(	PUNCT
ap-10691	249	86	73	73	NUM
ap-10691	249	87	)	)	PUNCT
ap-10691	250	1	where	where	SCONJ
ap-10691	250	2	:	:	PUNCT
ap-10691	251	1	α	α	X
ap-10691	251	2	=	=	NOUN
ap-10691	251	3	4i	4i	NUM
ap-10691	252	1	√	√	INTJ
ap-10691	252	2	hθ	hθ	PROPN
ap-10691	252	3	k2	k2	PROPN
ap-10691	252	4	cos2	cos2	PROPN
ap-10691	252	5	θ	θ	PROPN
ap-10691	252	6	=	=	SYM
ap-10691	252	7	4i	4i	NUM
ap-10691	252	8	kmk	kmk	PROPN
ap-10691	252	9	sec2	sec2	PROPN
ap-10691	252	10	ϕ.	ϕ.	PROPN
ap-10691	252	11	(	(	PUNCT
ap-10691	252	12	74	74	NUM
ap-10691	252	13	)	)	PUNCT
ap-10691	252	14	the	the	DET
ap-10691	252	15	poisson	poisson	NOUN
ap-10691	252	16	brackets	bracket	NOUN
ap-10691	252	17	{	{	PUNCT
ap-10691	252	18	·	·	PUNCT
ap-10691	252	19	,	,	PUNCT
ap-10691	252	20	·	·	PUNCT
ap-10691	252	21	}	}	PUNCT
ap-10691	252	22	θ	θ	PROPN
ap-10691	252	23	and	and	CCONJ
ap-10691	252	24	{	{	PUNCT
ap-10691	252	25	·	·	PUNCT
ap-10691	252	26	,	,	PUNCT
ap-10691	252	27	·	·	PUNCT
ap-10691	252	28	}	}	PUNCT
ap-10691	252	29	refer	refer	VERB
ap-10691	252	30	to	to	ADP
ap-10691	252	31	the	the	DET
ap-10691	252	32	canonical	canonical	ADJ
ap-10691	252	33	variables	variable	NOUN
ap-10691	252	34	(	(	PUNCT
ap-10691	252	35	θ	θ	NOUN
ap-10691	252	36	,	,	PUNCT
ap-10691	252	37	pθ	pθ	VERB
ap-10691	252	38	)	)	PUNCT
ap-10691	252	39	and	and	CCONJ
ap-10691	252	40	(	(	PUNCT
ap-10691	252	41	ϕ	ϕ	NOUN
ap-10691	252	42	,	,	PUNCT
ap-10691	252	43	pϕ	pϕ	NOUN
ap-10691	252	44	;	;	PUNCT
ap-10691	252	45	θ	θ	PROPN
ap-10691	252	46	,	,	PUNCT
ap-10691	252	47	pθ	pθ	NOUN
ap-10691	252	48	)	)	PUNCT
ap-10691	252	49	,	,	PUNCT
ap-10691	252	50	respectively	respectively	ADV
ap-10691	252	51	.	.	PUNCT
ap-10691	253	1	it	it	PRON
ap-10691	253	2	is	be	AUX
ap-10691	253	3	worth	worth	ADJ
ap-10691	253	4	noting	note	VERB
ap-10691	253	5	that	that	SCONJ
ap-10691	253	6	from	from	ADP
ap-10691	253	7	equation	equation	NOUN
ap-10691	253	8	(	(	PUNCT
ap-10691	253	9	72	72	NUM
ap-10691	253	10	)	)	PUNCT
ap-10691	253	11	,	,	PUNCT
ap-10691	253	12	we	we	PRON
ap-10691	253	13	obtain	obtain	VERB
ap-10691	253	14	{	{	PUNCT
ap-10691	253	15	√	√	NUM
ap-10691	253	16	hθ	hθ	PROPN
ap-10691	253	17	,	,	PUNCT
ap-10691	253	18	l±}θ	l±}θ	PROPN
ap-10691	253	19	=	=	SYM
ap-10691	253	20	∓i	∓i	PROPN
ap-10691	253	21	2	2	NUM
ap-10691	253	22	l±	l±	NOUN
ap-10691	253	23	,	,	PUNCT
ap-10691	253	24	which	which	PRON
ap-10691	253	25	corresponds	correspond	VERB
ap-10691	253	26	to	to	ADP
ap-10691	253	27	the	the	DET
ap-10691	253	28	classical	classical	ADJ
ap-10691	253	29	analogue	analogue	NOUN
ap-10691	253	30	of	of	ADP
ap-10691	253	31	equation	equation	NOUN
ap-10691	253	32	(	(	PUNCT
ap-10691	253	33	41	41	NUM
ap-10691	253	34	)	)	PUNCT
ap-10691	253	35	.	.	PUNCT
ap-10691	254	1	similarly	similarly	ADV
ap-10691	254	2	,	,	PUNCT
ap-10691	254	3	we	we	PRON
ap-10691	254	4	obtain	obtain	VERB
ap-10691	254	5	shift	shift	NOUN
ap-10691	254	6	functions	function	NOUN
ap-10691	254	7	s±(ϕ	s±(ϕ	VERB
ap-10691	254	8	,	,	PUNCT
ap-10691	254	9	pϕ	pϕ	NOUN
ap-10691	254	10	)	)	PUNCT
ap-10691	254	11	associated	associate	VERB
ap-10691	254	12	with	with	ADP
ap-10691	254	13	solutions	solution	NOUN
ap-10691	254	14	3	3	NUM
ap-10691	254	15	and	and	CCONJ
ap-10691	254	16	4	4	NUM
ap-10691	254	17	from	from	ADP
ap-10691	254	18	subsection	subsection	NOUN
ap-10691	254	19	3.1	3.1	NUM
ap-10691	254	20	:	:	PUNCT
ap-10691	254	21	s±	s±	PROPN
ap-10691	254	22	=	=	SYM
ap-10691	254	23	−l22	−l22	PUNCT
ap-10691	254	24	cot2	cot2	NOUN
ap-10691	254	25	ϕ−	ϕ−	PROPN
ap-10691	254	26	(	(	PUNCT
ap-10691	254	27	pϕ	pϕ	NOUN
ap-10691	254	28	∓	∓	PROPN
ap-10691	254	29	imk	imk	PROPN
ap-10691	254	30	tanϕ)2	tanϕ)2	PROPN
ap-10691	254	31	.	.	PUNCT
ap-10691	255	1	(	(	PUNCT
ap-10691	255	2	75	75	NUM
ap-10691	255	3	)	)	PUNCT
ap-10691	255	4	they	they	PRON
ap-10691	255	5	verify	verify	VERB
ap-10691	255	6	:	:	PUNCT
ap-10691	255	7	{	{	PUNCT
ap-10691	255	8	hϕ	hϕ	PROPN
ap-10691	255	9	mk	mk	PROPN
ap-10691	255	10	,	,	PUNCT
ap-10691	255	11	s±	s±	PROPN
ap-10691	255	12	}	}	PUNCT
ap-10691	255	13	=	=	SYM
ap-10691	255	14	±	±	NUM
ap-10691	255	15	4imk	4imk	PROPN
ap-10691	255	16	sec2	sec2	PROPN
ap-10691	255	17	ϕs±	ϕs±	PROPN
ap-10691	255	18	,	,	PUNCT
ap-10691	255	19	{	{	PUNCT
ap-10691	255	20	h	h	NOUN
ap-10691	255	21	,	,	PUNCT
ap-10691	255	22	(	(	PUNCT
ap-10691	255	23	s±)m	s±)m	ADJ
ap-10691	255	24	}	}	PUNCT
ap-10691	255	25	=	=	SYM
ap-10691	255	26	±	±	NUM
ap-10691	255	27	mα	mα	PROPN
ap-10691	255	28	(	(	PUNCT
ap-10691	255	29	s±)m	s±)m	NOUN
ap-10691	255	30	.	.	PUNCT
ap-10691	256	1	(	(	PUNCT
ap-10691	256	2	76	76	NUM
ap-10691	256	3	)	)	PUNCT
ap-10691	256	4	now	now	ADV
ap-10691	256	5	,	,	PUNCT
ap-10691	256	6	considering	consider	VERB
ap-10691	256	7	the	the	DET
ap-10691	256	8	functions	function	NOUN
ap-10691	256	9	:	:	PUNCT
ap-10691	256	10	x±	x±	PROPN
ap-10691	257	1	=	=	PRON
ap-10691	257	2	(	(	PUNCT
ap-10691	257	3	s±)m(l±)n	s±)m(l±)n	PROPN
ap-10691	257	4	,	,	PUNCT
ap-10691	257	5	(	(	PUNCT
ap-10691	257	6	77	77	X
ap-10691	257	7	)	)	PUNCT
ap-10691	257	8	we	we	PRON
ap-10691	257	9	obtain	obtain	VERB
ap-10691	257	10	the	the	DET
ap-10691	257	11	following	follow	VERB
ap-10691	257	12	poisson	poisson	NOUN
ap-10691	257	13	commutation	commutation	NOUN
ap-10691	257	14	relations	relation	NOUN
ap-10691	257	15	:	:	PUNCT
ap-10691	257	16	{	{	PUNCT
ap-10691	257	17	h	h	NOUN
ap-10691	257	18	,	,	PUNCT
ap-10691	257	19	x±	x±	PROPN
ap-10691	257	20	}	}	PUNCT
ap-10691	257	21	=	=	SYM
ap-10691	257	22	0	0	PUNCT
ap-10691	258	1	if	if	SCONJ
ap-10691	258	2	k	k	PROPN
ap-10691	258	3	=	=	VERB
ap-10691	258	4	m	m	VERB
ap-10691	258	5	n	n	PRON
ap-10691	258	6	,	,	PUNCT
ap-10691	258	7	(	(	PUNCT
ap-10691	258	8	78	78	NUM
ap-10691	258	9	)	)	PUNCT
ap-10691	258	10	which	which	PRON
ap-10691	258	11	show	show	VERB
ap-10691	258	12	that	that	SCONJ
ap-10691	258	13	x±	x±	PROPN
ap-10691	258	14	are	be	AUX
ap-10691	258	15	integrals	integral	NOUN
ap-10691	258	16	of	of	ADP
ap-10691	258	17	motion	motion	NOUN
ap-10691	258	18	.	.	PUNCT
ap-10691	259	1	this	this	PRON
ap-10691	259	2	establishes	establish	VERB
ap-10691	259	3	the	the	DET
ap-10691	259	4	superintegrability	superintegrability	NOUN
ap-10691	259	5	of	of	ADP
ap-10691	259	6	the	the	DET
ap-10691	259	7	classical	classical	ADJ
ap-10691	259	8	system	system	NOUN
ap-10691	259	9	described	describe	VERB
ap-10691	259	10	by	by	ADP
ap-10691	259	11	equation	equation	NOUN
ap-10691	259	12	(	(	PUNCT
ap-10691	259	13	68	68	NUM
ap-10691	259	14	)	)	PUNCT
ap-10691	259	15	.	.	PUNCT
ap-10691	260	1	4.2	4.2	NUM
ap-10691	260	2	.	.	PUNCT
ap-10691	261	1	classical	classical	ADJ
ap-10691	261	2	trajectories	trajectory	NOUN
ap-10691	261	3	from	from	ADP
ap-10691	261	4	the	the	DET
ap-10691	261	5	constants	constant	NOUN
ap-10691	261	6	of	of	ADP
ap-10691	261	7	motion	motion	NOUN
ap-10691	261	8	x±	x±	PROPN
ap-10691	262	1	(	(	PUNCT
ap-10691	262	2	equation	equation	NOUN
ap-10691	262	3	(	(	PUNCT
ap-10691	262	4	77	77	NUM
ap-10691	262	5	)	)	PUNCT
ap-10691	262	6	)	)	PUNCT
ap-10691	262	7	,	,	PUNCT
ap-10691	262	8	by	by	ADP
ap-10691	262	9	substituting	substitute	VERB
ap-10691	262	10	hθ	hθ	NOUN
ap-10691	262	11	with	with	ADP
ap-10691	262	12	its	its	PRON
ap-10691	262	13	expression	expression	NOUN
ap-10691	262	14	in	in	ADP
ap-10691	262	15	terms	term	NOUN
ap-10691	262	16	on	on	ADP
ap-10691	262	17	mk	mk	X
ap-10691	262	18	=	=	PROPN
ap-10691	262	19	k	k	PROPN
ap-10691	262	20	√	√	NUM
ap-10691	263	1	hθ	hθ	INTJ
ap-10691	263	2	,	,	PUNCT
ap-10691	263	3	we	we	PRON
ap-10691	263	4	get	get	VERB
ap-10691	263	5	:	:	PUNCT
ap-10691	263	6	x±	x±	PROPN
ap-10691	264	1	=	=	PRON
ap-10691	264	2	(	(	PUNCT
ap-10691	264	3	−l22	−l22	PUNCT
ap-10691	264	4	cot2	cot2	NOUN
ap-10691	264	5	ϕ−	ϕ−	PROPN
ap-10691	264	6	(	(	PUNCT
ap-10691	264	7	pϕ	pϕ	NOUN
ap-10691	264	8	∓	∓	PROPN
ap-10691	264	9	imk	imk	PROPN
ap-10691	264	10	tanϕ)2)m	tanϕ)2)m	PROPN
ap-10691	264	11	×	×	PROPN
ap-10691	264	12	(	(	PUNCT
ap-10691	264	13	b2	b2	NOUN
ap-10691	264	14	−	−	PROPN
ap-10691	264	15	a2√	a2√	PROPN
ap-10691	264	16	a2	a2	PROPN
ap-10691	264	17	sec2	sec2	PROPN
ap-10691	264	18	θ	θ	PROPN
ap-10691	264	19	+	+	CCONJ
ap-10691	264	20	b2	b2	NOUN
ap-10691	264	21	csc2	csc2	NOUN
ap-10691	264	22	θ	θ	PROPN
ap-10691	264	23	+	+	CCONJ
ap-10691	264	24	p2	p2	PROPN
ap-10691	264	25	θ	θ	PROPN
ap-10691	265	1	+	+	CCONJ
ap-10691	265	2	cos	cos	ADJ
ap-10691	265	3	2θ	2θ	NUM
ap-10691	265	4	×	×	NOUN
ap-10691	265	5	√	√	NOUN
ap-10691	265	6	a2	a2	PROPN
ap-10691	265	7	sec2	sec2	PROPN
ap-10691	265	8	θ	θ	PROPN
ap-10691	265	9	+	+	CCONJ
ap-10691	265	10	b2	b2	NOUN
ap-10691	265	11	csc2	csc2	NOUN
ap-10691	265	12	θ	θ	PROPN
ap-10691	265	13	+	+	CCONJ
ap-10691	265	14	p2	p2	PROPN
ap-10691	265	15	θ	θ	NOUN
ap-10691	265	16	±	±	NOUN
ap-10691	266	1	i	i	PRON
ap-10691	266	2	pθ	pθ	VERB
ap-10691	266	3	sin	sin	NOUN
ap-10691	266	4	2θ	2θ	NUM
ap-10691	266	5	)	)	PUNCT
ap-10691	267	1	n	n	CCONJ
ap-10691	267	2	.	.	PUNCT
ap-10691	268	1	(	(	PUNCT
ap-10691	268	2	79	79	NUM
ap-10691	268	3	)	)	PUNCT
ap-10691	268	4	in	in	ADP
ap-10691	268	5	this	this	DET
ap-10691	268	6	system	system	NOUN
ap-10691	268	7	,	,	PUNCT
ap-10691	268	8	h	h	NOUN
ap-10691	268	9	,	,	PUNCT
ap-10691	268	10	hθ	hθ	PROPN
ap-10691	268	11	,	,	PUNCT
ap-10691	268	12	x±	x±	PROPN
ap-10691	268	13	,	,	PUNCT
ap-10691	268	14	and	and	CCONJ
ap-10691	268	15	mk	mk	NOUN
ap-10691	268	16	are	be	AUX
ap-10691	268	17	constants	constant	NOUN
ap-10691	268	18	of	of	ADP
ap-10691	268	19	motion	motion	NOUN
ap-10691	268	20	,	,	PUNCT
ap-10691	268	21	but	but	CCONJ
ap-10691	268	22	only	only	ADV
ap-10691	268	23	three	three	NUM
ap-10691	268	24	are	be	AUX
ap-10691	268	25	functionally	functionally	ADV
ap-10691	268	26	independent	independent	ADJ
ap-10691	268	27	.	.	PUNCT
ap-10691	269	1	by	by	ADP
ap-10691	269	2	fixing	fix	VERB
ap-10691	269	3	the	the	DET
ap-10691	269	4	total	total	ADJ
ap-10691	269	5	energy	energy	NOUN
ap-10691	269	6	h	h	NOUN
ap-10691	269	7	=	=	SYM
ap-10691	269	8	e	e	NOUN
ap-10691	269	9	,	,	PUNCT
ap-10691	269	10	both	both	PRON
ap-10691	269	11	e	e	NOUN
ap-10691	269	12	and	and	CCONJ
ap-10691	269	13	mk	mk	PROPN
ap-10691	269	14	remain	remain	VERB
ap-10691	269	15	constant	constant	ADJ
ap-10691	269	16	along	along	ADP
ap-10691	269	17	the	the	DET
ap-10691	269	18	classical	classical	ADJ
ap-10691	269	19	trajectory	trajectory	NOUN
ap-10691	269	20	.	.	PUNCT
ap-10691	270	1	this	this	PRON
ap-10691	270	2	allows	allow	VERB
ap-10691	270	3	us	we	PRON
ap-10691	270	4	to	to	PART
ap-10691	270	5	express	express	VERB
ap-10691	270	6	the	the	DET
ap-10691	270	7	generalised	generalise	VERB
ap-10691	270	8	momenta	momenta	NOUN
ap-10691	270	9	in	in	ADP
ap-10691	270	10	terms	term	NOUN
ap-10691	270	11	of	of	ADP
ap-10691	270	12	the	the	DET
ap-10691	270	13	generalised	generalise	VERB
ap-10691	270	14	coordinates	coordinate	NOUN
ap-10691	270	15	:	:	PUNCT
ap-10691	270	16	pθ	pθ	ADP
ap-10691	270	17	=	=	SYM
ap-10691	270	18	εθ	εθ	NOUN
ap-10691	270	19	√	√	PROPN
ap-10691	270	20	m2	m2	PROPN
ap-10691	270	21	k	k	PROPN
ap-10691	270	22	k2	k2	PROPN
ap-10691	270	23	−	−	PROPN
ap-10691	271	1	(	(	PUNCT
ap-10691	271	2	a2	a2	PROPN
ap-10691	271	3	cos2	cos2	PROPN
ap-10691	271	4	θ	θ	PROPN
ap-10691	271	5	+	+	CCONJ
ap-10691	271	6	b2	b2	NOUN
ap-10691	271	7	sin2	sin2	NOUN
ap-10691	271	8	θ	θ	PROPN
ap-10691	271	9	)	)	PUNCT
ap-10691	271	10	,	,	PUNCT
ap-10691	271	11	pϕ	pϕ	NOUN
ap-10691	271	12	=	=	NOUN
ap-10691	272	1	εϕ	εϕ	NOUN
ap-10691	272	2	√	√	NUM
ap-10691	272	3	e	e	X
ap-10691	272	4	−	−	PROPN
ap-10691	272	5	(	(	PUNCT
ap-10691	272	6	l22	l22	PROPN
ap-10691	272	7	sin2	sin2	PROPN
ap-10691	272	8	ϕ	ϕ	PROPN
ap-10691	273	1	+	+	CCONJ
ap-10691	273	2	m2	m2	PROPN
ap-10691	273	3	k	k	PROPN
ap-10691	273	4	cos2	cos2	PROPN
ap-10691	273	5	ϕ	ϕ	PROPN
ap-10691	273	6	)	)	PUNCT
ap-10691	273	7	,	,	PUNCT
ap-10691	273	8	(	(	PUNCT
ap-10691	273	9	80	80	NUM
ap-10691	273	10	)	)	PUNCT
ap-10691	273	11	where	where	SCONJ
ap-10691	273	12	εθ	εθ	NOUN
ap-10691	273	13	,	,	PUNCT
ap-10691	273	14	εϕ	εϕ	PROPN
ap-10691	273	15	∈	∈	PROPN
ap-10691	273	16	{	{	PUNCT
ap-10691	273	17	±1	±1	NOUN
ap-10691	273	18	}	}	PUNCT
ap-10691	273	19	.	.	PUNCT
ap-10691	274	1	the	the	DET
ap-10691	274	2	symmetry	symmetry	NOUN
ap-10691	274	3	functions	function	NOUN
ap-10691	274	4	x±	x±	PROPN
ap-10691	274	5	are	be	AUX
ap-10691	274	6	complex	complex	ADV
ap-10691	274	7	-	-	PUNCT
ap-10691	274	8	valued	value	VERB
ap-10691	274	9	,	,	PUNCT
ap-10691	274	10	and	and	CCONJ
ap-10691	274	11	therefore	therefore	ADV
ap-10691	274	12	the	the	DET
ap-10691	274	13	constants	constant	NOUN
ap-10691	274	14	of	of	ADP
ap-10691	274	15	motion	motion	NOUN
ap-10691	274	16	are	be	AUX
ap-10691	274	17	,	,	PUNCT
ap-10691	274	18	in	in	ADP
ap-10691	274	19	general	general	ADJ
ap-10691	274	20	,	,	PUNCT
ap-10691	274	21	complex	complex	ADJ
ap-10691	274	22	numbers	number	NOUN
ap-10691	274	23	c.	c.	NOUN
ap-10691	274	24	to	to	PART
ap-10691	274	25	obtain	obtain	VERB
ap-10691	274	26	physically	physically	ADV
ap-10691	274	27	meaningful	meaningful	ADJ
ap-10691	274	28	(	(	PUNCT
ap-10691	274	29	real	real	ADJ
ap-10691	274	30	)	)	PUNCT
ap-10691	274	31	representations	representation	NOUN
ap-10691	274	32	,	,	PUNCT
ap-10691	274	33	we	we	PRON
ap-10691	274	34	make	make	VERB
ap-10691	274	35	use	use	NOUN
ap-10691	274	36	of	of	ADP
ap-10691	274	37	the	the	DET
ap-10691	274	38	reality	reality	NOUN
ap-10691	274	39	condition	condition	NOUN
ap-10691	274	40	(	(	PUNCT
ap-10691	274	41	x+)∗	x+)∗	PROPN
ap-10691	274	42	=	=	SYM
ap-10691	274	43	x−	x−	PROPN
ap-10691	274	44	,	,	PUNCT
ap-10691	274	45	and	and	CCONJ
ap-10691	274	46	define	define	VERB
ap-10691	274	47	:	:	PUNCT
ap-10691	275	1	x+	x+	ADJ
ap-10691	275	2	=	=	SYM
ap-10691	275	3	c	c	X
ap-10691	275	4	,	,	PUNCT
ap-10691	275	5	x−	x−	PROPN
ap-10691	275	6	=	=	PUNCT
ap-10691	275	7	c∗.	c∗.	X
ap-10691	275	8	(	(	PUNCT
ap-10691	275	9	81	81	NUM
ap-10691	275	10	)	)	PUNCT
ap-10691	275	11	we	we	PRON
ap-10691	275	12	then	then	ADV
ap-10691	275	13	consider	consider	VERB
ap-10691	275	14	the	the	DET
ap-10691	275	15	real	real	ADJ
ap-10691	275	16	and	and	CCONJ
ap-10691	275	17	imaginary	imaginary	ADJ
ap-10691	275	18	parts	part	NOUN
ap-10691	275	19	of	of	ADP
ap-10691	275	20	x+	x+	ADJ
ap-10691	275	21	:	:	PUNCT
ap-10691	275	22	re(x+	re(x+	ADJ
ap-10691	275	23	)	)	PUNCT
ap-10691	275	24	=	=	SYM
ap-10691	276	1	x+	x+	PUNCT
ap-10691	276	2	+	+	NUM
ap-10691	276	3	x−	x−	PROPN
ap-10691	276	4	2	2	NUM
ap-10691	276	5	=	=	SYM
ap-10691	276	6	re(c	re(c	NUM
ap-10691	276	7	)	)	PUNCT
ap-10691	276	8	,	,	PUNCT
ap-10691	276	9	im(x+	im(x+	PROPN
ap-10691	276	10	)	)	PUNCT
ap-10691	276	11	=	=	SYM
ap-10691	277	1	x+	x+	NUM
ap-10691	277	2	−	−	PROPN
ap-10691	277	3	x−	x−	PROPN
ap-10691	277	4	2i	2i	PROPN
ap-10691	277	5	=	=	SYM
ap-10691	277	6	im(c	im(c	NOUN
ap-10691	277	7	)	)	PUNCT
ap-10691	277	8	.	.	PUNCT
ap-10691	278	1	(	(	PUNCT
ap-10691	278	2	82	82	X
ap-10691	278	3	)	)	PUNCT
ap-10691	278	4	these	these	DET
ap-10691	278	5	two	two	NUM
ap-10691	278	6	real	real	ADJ
ap-10691	278	7	functions	function	NOUN
ap-10691	278	8	can	can	AUX
ap-10691	278	9	be	be	AUX
ap-10691	278	10	used	use	VERB
ap-10691	278	11	to	to	PART
ap-10691	278	12	describe	describe	VERB
ap-10691	278	13	the	the	DET
ap-10691	278	14	trajectories	trajectory	NOUN
ap-10691	278	15	of	of	ADP
ap-10691	278	16	the	the	DET
ap-10691	278	17	system	system	NOUN
ap-10691	278	18	.	.	PUNCT
ap-10691	279	1	the	the	DET
ap-10691	279	2	classical	classical	ADJ
ap-10691	279	3	trajectories	trajectory	NOUN
ap-10691	279	4	t0	t0	NOUN
ap-10691	279	5	are	be	AUX
ap-10691	279	6	implicitly	implicitly	ADV
ap-10691	279	7	defined	define	VERB
ap-10691	279	8	as	as	ADP
ap-10691	279	9	the	the	DET
ap-10691	279	10	set	set	NOUN
ap-10691	279	11	of	of	ADP
ap-10691	279	12	points	point	NOUN
ap-10691	279	13	x	x	X
ap-10691	279	14	∈	∈	PROPN
ap-10691	279	15	r3	r3	NOUN
ap-10691	279	16	satisfying	satisfy	VERB
ap-10691	279	17	the	the	DET
ap-10691	279	18	condition	condition	NOUN
ap-10691	279	19	:	:	PUNCT
ap-10691	279	20	x(x	x(x	X
ap-10691	279	21	)	)	PUNCT
ap-10691	279	22	=	=	SYM
ap-10691	279	23	c0	c0	NOUN
ap-10691	279	24	,	,	PUNCT
ap-10691	279	25	(	(	PUNCT
ap-10691	279	26	83	83	NUM
ap-10691	279	27	)	)	PUNCT
ap-10691	279	28	where	where	SCONJ
ap-10691	279	29	c0	c0	PROPN
ap-10691	279	30	is	be	AUX
ap-10691	279	31	the	the	DET
ap-10691	279	32	fixed	fix	VERB
ap-10691	279	33	complex	complex	ADJ
ap-10691	279	34	constant	constant	ADJ
ap-10691	279	35	determined	determine	VERB
ap-10691	279	36	by	by	ADP
ap-10691	279	37	the	the	DET
ap-10691	279	38	initial	initial	ADJ
ap-10691	279	39	conditions	condition	NOUN
ap-10691	279	40	.	.	PUNCT
ap-10691	280	1	figures	figure	NOUN
ap-10691	280	2	4	4	NUM
ap-10691	280	3	and	and	CCONJ
ap-10691	280	4	5	5	NUM
ap-10691	280	5	show	show	NOUN
ap-10691	280	6	trajectories	trajectory	NOUN
ap-10691	280	7	corresponding	correspond	VERB
ap-10691	280	8	to	to	ADP
ap-10691	280	9	different	different	ADJ
ap-10691	280	10	values	value	NOUN
ap-10691	280	11	of	of	ADP
ap-10691	280	12	k	k	PROPN
ap-10691	280	13	=	=	PUNCT
ap-10691	280	14	m	m	VERB
ap-10691	280	15	n	n	PRON
ap-10691	280	16	,	,	PUNCT
ap-10691	280	17	as	as	SCONJ
ap-10691	280	18	presented	present	VERB
ap-10691	280	19	[	[	X
ap-10691	280	20	29	29	NUM
ap-10691	280	21	]	]	PUNCT
ap-10691	280	22	.	.	PUNCT
ap-10691	281	1	these	these	DET
ap-10691	281	2	plots	plot	NOUN
ap-10691	281	3	were	be	AUX
ap-10691	281	4	generated	generate	VERB
ap-10691	281	5	using	use	VERB
ap-10691	281	6	mathematica	mathematica	PROPN
ap-10691	281	7	.	.	PUNCT
ap-10691	282	1	5	5	NUM
ap-10691	282	2	.	.	X
ap-10691	282	3	hyperbolic	hyperbolic	PROPN
ap-10691	282	4	ttw	ttw	PROPN
ap-10691	282	5	so(2	so(2	NOUN
ap-10691	282	6	,	,	PUNCT
ap-10691	282	7	1)-hamiltonian	1)-hamiltonian	NUM
ap-10691	282	8	in	in	ADP
ap-10691	282	9	this	this	DET
ap-10691	282	10	case	case	NOUN
ap-10691	282	11	,	,	PUNCT
ap-10691	282	12	we	we	PRON
ap-10691	282	13	consider	consider	VERB
ap-10691	282	14	the	the	DET
ap-10691	282	15	hamiltonian	hamiltonian	NOUN
ap-10691	282	16	introduced	introduce	VERB
ap-10691	282	17	in	in	ADP
ap-10691	282	18	[	[	X
ap-10691	282	19	7	7	NUM
ap-10691	282	20	]	]	SYM
ap-10691	282	21	:	:	PUNCT
ap-10691	282	22	h	h	NOUN
ap-10691	282	23	:	:	PUNCT
ap-10691	282	24	=	=	SYM
ap-10691	282	25	j2	j2	PROPN
ap-10691	282	26	2	2	NUM
ap-10691	282	27	−j2	−j2	NOUN
ap-10691	282	28	1	1	NUM
ap-10691	283	1	−j2	−j2	NOUN
ap-10691	283	2	0	0	NUM
ap-10691	283	3	−	−	NOUN
ap-10691	283	4	l	l	NOUN
ap-10691	283	5	2	2	NUM
ap-10691	283	6	2	2	NUM
ap-10691	283	7	−	−	NOUN
ap-10691	283	8	1	1	NUM
ap-10691	283	9	4	4	NUM
ap-10691	283	10	s2	s2	NOUN
ap-10691	283	11	2	2	NUM
ap-10691	284	1	+	+	CCONJ
ap-10691	284	2	l21	l21	NOUN
ap-10691	284	3	−	−	NOUN
ap-10691	284	4	1	1	NUM
ap-10691	284	5	4	4	NUM
ap-10691	284	6	s2	s2	NOUN
ap-10691	284	7	1	1	NUM
ap-10691	284	8	+	+	CCONJ
ap-10691	284	9	l20	l20	NOUN
ap-10691	284	10	−	−	NOUN
ap-10691	284	11	1	1	NUM
ap-10691	284	12	4	4	NUM
ap-10691	284	13	s2	s2	NOUN
ap-10691	284	14	0	0	NUM
ap-10691	284	15	,	,	PUNCT
ap-10691	284	16	(	(	PUNCT
ap-10691	284	17	84	84	NUM
ap-10691	284	18	)	)	PUNCT
ap-10691	284	19	526	526	NUM
ap-10691	284	20	vol	vol	NOUN
ap-10691	284	21	.	.	PUNCT
ap-10691	284	22	65	65	NUM
ap-10691	285	1	no	no	NOUN
ap-10691	285	2	.	.	PUNCT
ap-10691	286	1	5/2025	5/2025	NUM
ap-10691	286	2	classical	classical	ADJ
ap-10691	286	3	and	and	CCONJ
ap-10691	286	4	quantum	quantum	ADJ
ap-10691	286	5	superintegrable	superintegrable	ADJ
ap-10691	286	6	systems	system	NOUN
ap-10691	286	7	on	on	ADP
ap-10691	286	8	the	the	DET
ap-10691	286	9	sphere	sphere	NOUN
ap-10691	286	10	.	.	PUNCT
ap-10691	286	11	.	.	PUNCT
ap-10691	286	12	.	.	PUNCT
ap-10691	287	1	(	(	PUNCT
ap-10691	287	2	a	a	X
ap-10691	287	3	)	)	PUNCT
ap-10691	287	4	.	.	PUNCT
ap-10691	288	1	m	m	VERB
ap-10691	288	2	=	=	NOUN
ap-10691	288	3	1	1	NUM
ap-10691	288	4	,	,	PUNCT
ap-10691	288	5	n	n	NOUN
ap-10691	288	6	=	=	SYM
ap-10691	288	7	1	1	NUM
ap-10691	288	8	.	.	PUNCT
ap-10691	289	1	(	(	PUNCT
ap-10691	289	2	b	b	NOUN
ap-10691	289	3	)	)	PUNCT
ap-10691	289	4	.	.	PUNCT
ap-10691	290	1	m	m	VERB
ap-10691	290	2	=	=	SYM
ap-10691	290	3	2	2	NUM
ap-10691	290	4	,	,	PUNCT
ap-10691	290	5	n	n	NOUN
ap-10691	290	6	=	=	SYM
ap-10691	290	7	1	1	X
ap-10691	290	8	.	.	X
ap-10691	290	9	figure	figure	NOUN
ap-10691	290	10	4	4	NUM
ap-10691	290	11	.	.	PUNCT
ap-10691	290	12	trajectories	trajectory	NOUN
ap-10691	290	13	for	for	ADP
ap-10691	290	14	m	m	PROPN
ap-10691	290	15	=	=	SYM
ap-10691	290	16	1	1	NUM
ap-10691	290	17	,	,	PUNCT
ap-10691	290	18	n	n	NOUN
ap-10691	290	19	=	=	SYM
ap-10691	290	20	1	1	NUM
ap-10691	290	21	and	and	CCONJ
ap-10691	290	22	m	m	PROPN
ap-10691	290	23	=	=	ADJ
ap-10691	290	24	2	2	NUM
ap-10691	290	25	,	,	PUNCT
ap-10691	290	26	n	n	NOUN
ap-10691	290	27	=	=	SYM
ap-10691	290	28	1	1	NUM
ap-10691	290	29	,	,	PUNCT
ap-10691	290	30	respectively	respectively	ADV
ap-10691	290	31	.	.	PUNCT
ap-10691	291	1	(	(	PUNCT
ap-10691	291	2	a	a	NOUN
ap-10691	291	3	)	)	PUNCT
ap-10691	291	4	.	.	PUNCT
ap-10691	292	1	m	m	VERB
ap-10691	292	2	=	=	NOUN
ap-10691	292	3	1	1	NUM
ap-10691	292	4	,	,	PUNCT
ap-10691	292	5	n	n	NOUN
ap-10691	292	6	=	=	SYM
ap-10691	292	7	3	3	X
ap-10691	292	8	.	.	PUNCT
ap-10691	292	9	(	(	PUNCT
ap-10691	292	10	b	b	NOUN
ap-10691	292	11	)	)	PUNCT
ap-10691	292	12	.	.	PUNCT
ap-10691	293	1	m	m	VERB
ap-10691	294	1	=	=	SYM
ap-10691	294	2	3	3	NUM
ap-10691	294	3	,	,	PUNCT
ap-10691	294	4	n	n	NOUN
ap-10691	294	5	=	=	SYM
ap-10691	294	6	3	3	X
ap-10691	294	7	.	.	X
ap-10691	294	8	figure	figure	NOUN
ap-10691	294	9	5	5	NUM
ap-10691	294	10	.	.	PUNCT
ap-10691	294	11	trajectories	trajectory	NOUN
ap-10691	294	12	for	for	ADP
ap-10691	294	13	m	m	PROPN
ap-10691	294	14	=	=	SYM
ap-10691	294	15	1	1	NUM
ap-10691	294	16	,	,	PUNCT
ap-10691	294	17	n	n	NOUN
ap-10691	294	18	=	=	SYM
ap-10691	294	19	3	3	NUM
ap-10691	294	20	and	and	CCONJ
ap-10691	294	21	m	m	PROPN
ap-10691	294	22	=	=	SYM
ap-10691	294	23	3	3	NUM
ap-10691	294	24	,	,	PUNCT
ap-10691	294	25	n	n	NOUN
ap-10691	294	26	=	=	SYM
ap-10691	294	27	3	3	NUM
ap-10691	294	28	,	,	PUNCT
ap-10691	294	29	respectively	respectively	ADV
ap-10691	294	30	.	.	PUNCT
ap-10691	295	1	where	where	SCONJ
ap-10691	295	2	the	the	DET
ap-10691	295	3	coordinates	coordinate	NOUN
ap-10691	295	4	of	of	ADP
ap-10691	295	5	the	the	DET
ap-10691	295	6	ambient	ambient	ADJ
ap-10691	295	7	space	space	NOUN
ap-10691	295	8	(	(	PUNCT
ap-10691	295	9	si	si	NOUN
ap-10691	295	10	)	)	PUNCT
ap-10691	295	11	≡	≡	PROPN
ap-10691	295	12	(	(	PUNCT
ap-10691	295	13	s0	s0	PROPN
ap-10691	295	14	,	,	PUNCT
ap-10691	295	15	s1	s1	NOUN
ap-10691	295	16	,	,	PUNCT
ap-10691	295	17	s2	s2	PROPN
ap-10691	295	18	)	)	PUNCT
ap-10691	295	19	∈	∈	PROPN
ap-10691	295	20	r3	r3	PROPN
ap-10691	295	21	satisfy	satisfy	VERB
ap-10691	295	22	the	the	DET
ap-10691	295	23	constraint	constraint	NOUN
ap-10691	295	24	s2	s2	NOUN
ap-10691	295	25	0+s1	0+s1	NOUN
ap-10691	295	26	1−s2	1−s2	NUM
ap-10691	295	27	2	2	NUM
ap-10691	295	28	=	=	SYM
ap-10691	295	29	−1	−1	NOUN
ap-10691	295	30	.	.	PUNCT
ap-10691	296	1	the	the	DET
ap-10691	296	2	differential	differential	ADJ
ap-10691	296	3	operators	operator	NOUN
ap-10691	296	4	ji	ji	PROPN
ap-10691	296	5	are	be	AUX
ap-10691	296	6	given	give	VERB
ap-10691	296	7	by	by	ADP
ap-10691	296	8	:	:	PUNCT
ap-10691	296	9	j0	j0	PROPN
ap-10691	296	10	=	=	SYM
ap-10691	296	11	s1∂2	s1∂2	PROPN
ap-10691	296	12	+	+	CCONJ
ap-10691	296	13	s2∂1	s2∂1	PROPN
ap-10691	296	14	,	,	PUNCT
ap-10691	296	15	j1	j1	NOUN
ap-10691	296	16	=	=	PUNCT
ap-10691	296	17	s2∂0	s2∂0	PROPN
ap-10691	296	18	+	+	PROPN
ap-10691	296	19	s0∂2	s0∂2	PROPN
ap-10691	296	20	,	,	PUNCT
ap-10691	296	21	j2	j2	NOUN
ap-10691	296	22	=	=	SYM
ap-10691	296	23	s0∂1	s0∂1	PROPN
ap-10691	296	24	−	−	PROPN
ap-10691	296	25	s1∂0	s1∂0	NOUN
ap-10691	296	26	,	,	PUNCT
ap-10691	296	27	(	(	PUNCT
ap-10691	296	28	85	85	NUM
ap-10691	296	29	)	)	PUNCT
ap-10691	296	30	and	and	CCONJ
ap-10691	296	31	they	they	PRON
ap-10691	296	32	generate	generate	VERB
ap-10691	296	33	the	the	DET
ap-10691	296	34	lie	lie	NOUN
ap-10691	296	35	algebra	algebra	NOUN
ap-10691	296	36	so(2	so(2	NOUN
ap-10691	296	37	,	,	PUNCT
ap-10691	296	38	1	1	NUM
ap-10691	296	39	)	)	PUNCT
ap-10691	296	40	,	,	PUNCT
ap-10691	296	41	with	with	ADP
ap-10691	296	42	commutation	commutation	NOUN
ap-10691	296	43	relations	relation	NOUN
ap-10691	296	44	:	:	PUNCT
ap-10691	297	1	[	[	X
ap-10691	297	2	j0	j0	PROPN
ap-10691	297	3	,	,	PUNCT
ap-10691	297	4	j1	j1	PROPN
ap-10691	297	5	]	]	PUNCT
ap-10691	297	6	=	=	SYM
ap-10691	297	7	−j2	−j2	NOUN
ap-10691	297	8	,	,	PUNCT
ap-10691	297	9	[	[	X
ap-10691	297	10	j2	j2	PROPN
ap-10691	297	11	,	,	PUNCT
ap-10691	297	12	j0	j0	PROPN
ap-10691	297	13	]	]	X
ap-10691	297	14	=	=	SYM
ap-10691	297	15	j1	j1	PROPN
ap-10691	297	16	,	,	PUNCT
ap-10691	297	17	[	[	X
ap-10691	297	18	j1	j1	PROPN
ap-10691	297	19	,	,	PUNCT
ap-10691	297	20	j2	j2	PROPN
ap-10691	297	21	]	]	X
ap-10691	297	22	=	=	SYM
ap-10691	297	23	j0	j0	PROPN
ap-10691	297	24	.	.	PUNCT
ap-10691	297	25	(	(	PUNCT
ap-10691	297	26	86	86	NUM
ap-10691	297	27	)	)	PUNCT
ap-10691	297	28	next	next	ADV
ap-10691	297	29	,	,	PUNCT
ap-10691	297	30	we	we	PRON
ap-10691	297	31	introduce	introduce	VERB
ap-10691	297	32	coordinates	coordinate	NOUN
ap-10691	297	33	analogous	analogous	ADJ
ap-10691	297	34	to	to	ADP
ap-10691	297	35	the	the	DET
ap-10691	297	36	spherical	spherical	ADJ
ap-10691	297	37	coordinates	coordinate	NOUN
ap-10691	297	38	,	,	PUNCT
ap-10691	297	39	denoted	denote	VERB
ap-10691	297	40	by	by	ADP
ap-10691	297	41	(	(	PUNCT
ap-10691	297	42	ξ	ξ	PROPN
ap-10691	297	43	,	,	PUNCT
ap-10691	297	44	θ	θ	NOUN
ap-10691	297	45	)	)	PUNCT
ap-10691	297	46	,	,	PUNCT
ap-10691	297	47	to	to	PART
ap-10691	297	48	proceed	proceed	VERB
ap-10691	297	49	with	with	ADP
ap-10691	297	50	the	the	DET
ap-10691	297	51	analysis	analysis	NOUN
ap-10691	297	52	:	:	PUNCT
ap-10691	297	53	s0	s0	PROPN
ap-10691	297	54	=	=	PUNCT
ap-10691	297	55	cos	cos	PROPN
ap-10691	297	56	θ	θ	PROPN
ap-10691	297	57	sinh	sinh	PROPN
ap-10691	297	58	ξ	ξ	PROPN
ap-10691	297	59	,	,	PUNCT
ap-10691	297	60	s1	s1	NOUN
ap-10691	297	61	=	=	PUNCT
ap-10691	297	62	sin	sin	NOUN
ap-10691	297	63	θ	θ	PROPN
ap-10691	297	64	sinh	sinh	NOUN
ap-10691	297	65	ξ	ξ	PROPN
ap-10691	297	66	,	,	PUNCT
ap-10691	297	67	s2	s2	NOUN
ap-10691	297	68	=	=	SYM
ap-10691	297	69	cosh	cosh	PROPN
ap-10691	297	70	ξ	ξ	PROPN
ap-10691	297	71	,	,	PUNCT
ap-10691	297	72	(	(	PUNCT
ap-10691	297	73	87	87	NUM
ap-10691	297	74	)	)	PUNCT
ap-10691	297	75	where	where	SCONJ
ap-10691	297	76	0	0	NUM
ap-10691	297	77	≤	≤	NUM
ap-10691	297	78	θ	θ	PROPN
ap-10691	297	79	<	<	X
ap-10691	297	80	2π	2π	NOUN
ap-10691	297	81	and	and	CCONJ
ap-10691	297	82	0	0	NUM
ap-10691	297	83	≤	≤	NOUN
ap-10691	298	1	ξ	ξ	PUNCT
ap-10691	298	2	<	<	X
ap-10691	298	3	∞	∞	NUM
ap-10691	298	4	.	.	PUNCT
ap-10691	299	1	the	the	DET
ap-10691	299	2	hamiltonian	hamiltonian	NOUN
ap-10691	299	3	(	(	PUNCT
ap-10691	299	4	84	84	NUM
ap-10691	299	5	)	)	PUNCT
ap-10691	299	6	can	can	AUX
ap-10691	299	7	be	be	AUX
ap-10691	299	8	rewritten	rewrite	VERB
ap-10691	299	9	in	in	ADP
ap-10691	299	10	terms	term	NOUN
ap-10691	299	11	of	of	ADP
ap-10691	299	12	the	the	DET
ap-10691	299	13	variables	variable	NOUN
ap-10691	299	14	(	(	PUNCT
ap-10691	299	15	ξ	ξ	PROPN
ap-10691	299	16	,	,	PUNCT
ap-10691	299	17	θ	θ	NOUN
ap-10691	299	18	)	)	PUNCT
ap-10691	299	19	as	as	ADP
ap-10691	299	20	:	:	PUNCT
ap-10691	299	21	h	h	NOUN
ap-10691	299	22	=	=	PUNCT
ap-10691	299	23	−	−	PROPN
ap-10691	299	24	∂2	∂2	NUM
ap-10691	300	1	ξ	ξ	X
ap-10691	300	2	−	−	PROPN
ap-10691	300	3	coth	coth	NOUN
ap-10691	300	4	ξ	ξ	PROPN
ap-10691	300	5	∂ξ	∂ξ	NOUN
ap-10691	300	6	−	−	NOUN
ap-10691	300	7	l	l	NOUN
ap-10691	300	8	2	2	NUM
ap-10691	300	9	2	2	NUM
ap-10691	300	10	−	−	NOUN
ap-10691	300	11	1	1	NUM
ap-10691	300	12	4	4	NUM
ap-10691	300	13	cosh2	cosh2	VERB
ap-10691	300	14	ξ	ξ	X
ap-10691	300	15	+	+	SYM
ap-10691	300	16	1	1	NUM
ap-10691	300	17	sinh2	sinh2	NOUN
ap-10691	300	18	ξ	ξ	X
ap-10691	300	19	[	[	PUNCT
ap-10691	300	20	−∂θ	−∂θ	X
ap-10691	300	21	+	+	NUM
ap-10691	300	22	l21	l21	NOUN
ap-10691	300	23	−	−	NOUN
ap-10691	300	24	1	1	NUM
ap-10691	300	25	4	4	NUM
ap-10691	300	26	sin2	sin2	NOUN
ap-10691	300	27	θ	θ	PROPN
ap-10691	300	28	+	+	CCONJ
ap-10691	300	29	l20	l20	NOUN
ap-10691	300	30	−	−	PROPN
ap-10691	300	31	1	1	NUM
ap-10691	300	32	4	4	NUM
ap-10691	300	33	cos2	cos2	NOUN
ap-10691	300	34	θ	θ	PROPN
ap-10691	300	35	]	]	PUNCT
ap-10691	300	36	.	.	PUNCT
ap-10691	301	1	(	(	PUNCT
ap-10691	301	2	88	88	NUM
ap-10691	301	3	)	)	PUNCT
ap-10691	301	4	by	by	ADP
ap-10691	301	5	deforming	deform	VERB
ap-10691	301	6	this	this	DET
ap-10691	301	7	hamiltonian	hamiltonian	ADJ
ap-10691	301	8	à	à	X
ap-10691	301	9	la	la	PROPN
ap-10691	301	10	ttw	ttw	PROPN
ap-10691	301	11	,	,	PUNCT
ap-10691	301	12	using	use	VERB
ap-10691	301	13	the	the	DET
ap-10691	301	14	real	real	ADJ
ap-10691	301	15	parameter	parameter	NOUN
ap-10691	301	16	k	k	PROPN
ap-10691	301	17	̸=	̸=	PROPN
ap-10691	301	18	0	0	PUNCT
ap-10691	301	19	as	as	ADP
ap-10691	301	20	in	in	ADP
ap-10691	301	21	section	section	NOUN
ap-10691	301	22	2	2	NUM
ap-10691	301	23	,	,	PUNCT
ap-10691	301	24	we	we	PRON
ap-10691	301	25	arrive	arrive	VERB
ap-10691	301	26	at	at	ADP
ap-10691	301	27	the	the	DET
ap-10691	301	28	ttw	ttw	NOUN
ap-10691	301	29	-	-	PUNCT
ap-10691	301	30	hamiltonian	hamiltonian	NOUN
ap-10691	301	31	:	:	PUNCT
ap-10691	301	32	hk	hk	PROPN
ap-10691	301	33	=	=	PUNCT
ap-10691	302	1	−	−	PROPN
ap-10691	302	2	∂2	∂2	PROPN
ap-10691	302	3	ξ	ξ	PROPN
ap-10691	302	4	−	−	PROPN
ap-10691	302	5	coth	coth	NOUN
ap-10691	302	6	ξ∂ξ	ξ∂ξ	PROPN
ap-10691	302	7	−	−	PROPN
ap-10691	302	8	l	l	NOUN
ap-10691	302	9	2	2	NUM
ap-10691	302	10	2	2	NUM
ap-10691	302	11	−	−	NOUN
ap-10691	302	12	1	1	NUM
ap-10691	302	13	4	4	NUM
ap-10691	302	14	cosh2	cosh2	VERB
ap-10691	302	15	ξ	ξ	X
ap-10691	302	16	+	+	PUNCT
ap-10691	302	17	k2	k2	ADJ
ap-10691	302	18	sinh2	sinh2	NOUN
ap-10691	302	19	ξ	ξ	X
ap-10691	303	1	[	[	PUNCT
ap-10691	303	2	−∂θ	−∂θ	X
ap-10691	303	3	+	+	NUM
ap-10691	303	4	l21	l21	NOUN
ap-10691	303	5	−	−	NOUN
ap-10691	303	6	1	1	NUM
ap-10691	303	7	4	4	NUM
ap-10691	303	8	sin2	sin2	NOUN
ap-10691	303	9	θ	θ	PROPN
ap-10691	303	10	+	+	CCONJ
ap-10691	303	11	l20	l20	NOUN
ap-10691	303	12	−	−	PROPN
ap-10691	303	13	1	1	NUM
ap-10691	303	14	4	4	NUM
ap-10691	303	15	cos2	cos2	NOUN
ap-10691	303	16	θ	θ	PROPN
ap-10691	303	17	]	]	PUNCT
ap-10691	303	18	,	,	PUNCT
ap-10691	303	19	(	(	PUNCT
ap-10691	303	20	89	89	NUM
ap-10691	303	21	)	)	PUNCT
ap-10691	304	1	where	where	SCONJ
ap-10691	304	2	0	0	NUM
ap-10691	304	3	≤	≤	NUM
ap-10691	304	4	θ	θ	X
ap-10691	304	5	<	<	X
ap-10691	304	6	π	π	X
ap-10691	304	7	2	2	NUM
ap-10691	304	8	and	and	CCONJ
ap-10691	304	9	0	0	NUM
ap-10691	304	10	≤	≤	NOUN
ap-10691	304	11	ξ	ξ	PUNCT
ap-10691	304	12	<	<	X
ap-10691	304	13	∞.	∞.	PROPN
ap-10691	304	14	in	in	ADP
ap-10691	304	15	this	this	DET
ap-10691	304	16	way	way	NOUN
ap-10691	304	17	we	we	PRON
ap-10691	304	18	have	have	AUX
ap-10691	304	19	constructed	construct	VERB
ap-10691	304	20	a	a	DET
ap-10691	304	21	family	family	NOUN
ap-10691	304	22	of	of	ADP
ap-10691	304	23	hamiltonians	hamiltonian	NOUN
ap-10691	304	24	{	{	PUNCT
ap-10691	304	25	hk	hk	NOUN
ap-10691	304	26	}	}	PUNCT
ap-10691	304	27	,	,	PUNCT
ap-10691	304	28	depending	depend	VERB
ap-10691	304	29	on	on	ADP
ap-10691	304	30	four	four	NUM
ap-10691	304	31	real	real	ADJ
ap-10691	304	32	parameters	parameter	NOUN
ap-10691	304	33	(	(	PUNCT
ap-10691	304	34	k	k	X
ap-10691	304	35	,	,	PUNCT
ap-10691	304	36	l0	l0	PROPN
ap-10691	304	37	,	,	PUNCT
ap-10691	304	38	l1	l1	PROPN
ap-10691	304	39	,	,	PUNCT
ap-10691	304	40	l2	l2	NOUN
ap-10691	304	41	)	)	PUNCT
ap-10691	304	42	.	.	PUNCT
ap-10691	305	1	the	the	DET
ap-10691	305	2	hamiltonian	hamiltonian	NOUN
ap-10691	305	3	may	may	AUX
ap-10691	305	4	be	be	AUX
ap-10691	305	5	separated	separate	VERB
ap-10691	305	6	in	in	ADP
ap-10691	305	7	two	two	NUM
ap-10691	305	8	“	"	PUNCT
ap-10691	305	9	sub	sub	NOUN
ap-10691	305	10	-	-	NOUN
ap-10691	305	11	hamiltonians	hamiltonian	NOUN
ap-10691	305	12	”	"	PUNCT
ap-10691	305	13	through	through	ADP
ap-10691	305	14	variable	variable	ADJ
ap-10691	305	15	separation	separation	NOUN
ap-10691	305	16	in	in	ADP
ap-10691	305	17	the	the	DET
ap-10691	305	18	schrödinger	schrödinger	ADJ
ap-10691	305	19	equation	equation	NOUN
ap-10691	305	20	hk	hk	PROPN
ap-10691	305	21	ψ(θ	ψ(θ	PROPN
ap-10691	305	22	,	,	PUNCT
ap-10691	305	23	ξ	ξ	X
ap-10691	305	24	)	)	PUNCT
ap-10691	305	25	=	=	SYM
ap-10691	305	26	eψ(θ	eψ(θ	X
ap-10691	305	27	,	,	PUNCT
ap-10691	305	28	ξ	ξ	X
ap-10691	305	29	)	)	PUNCT
ap-10691	305	30	by	by	ADP
ap-10691	305	31	assuming	assume	VERB
ap-10691	305	32	a	a	DET
ap-10691	305	33	factorised	factorise	VERB
ap-10691	305	34	solution	solution	NOUN
ap-10691	305	35	of	of	ADP
ap-10691	305	36	the	the	DET
ap-10691	305	37	form	form	NOUN
ap-10691	305	38	ψ(θ	ψ(θ	PROPN
ap-10691	305	39	,	,	PUNCT
ap-10691	305	40	ξ	ξ	X
ap-10691	305	41	)	)	PUNCT
ap-10691	305	42	=	=	SYM
ap-10691	305	43	ψ(θ)φ(ξ	ψ(θ)φ(ξ	NOUN
ap-10691	305	44	)	)	PUNCT
ap-10691	305	45	.	.	PUNCT
ap-10691	306	1	this	this	PRON
ap-10691	306	2	leads	lead	VERB
ap-10691	306	3	to	to	ADP
ap-10691	306	4	two	two	NUM
ap-10691	306	5	eigenvalue	eigenvalue	NOUN
ap-10691	306	6	equations	equation	NOUN
ap-10691	306	7	:	:	PUNCT
ap-10691	306	8	hθψ	hθψ	PROPN
ap-10691	306	9	=	=	SYM
ap-10691	306	10	e′ψ	e′ψ	PROPN
ap-10691	306	11	,	,	PUNCT
ap-10691	306	12	hξ	hξ	PROPN
ap-10691	306	13	mk	mk	PROPN
ap-10691	306	14	φ	φ	PROPN
ap-10691	306	15	=	=	SYM
ap-10691	306	16	eφ	eφ	PROPN
ap-10691	306	17	,	,	PUNCT
ap-10691	306	18	(	(	PUNCT
ap-10691	306	19	90	90	NUM
ap-10691	306	20	)	)	PUNCT
ap-10691	306	21	with	with	ADP
ap-10691	306	22	e′	e′	PROPN
ap-10691	306	23	=	=	SYM
ap-10691	306	24	β2	β2	PROPN
ap-10691	306	25	,	,	PUNCT
ap-10691	306	26	and	and	CCONJ
ap-10691	306	27	mk	mk	NOUN
ap-10691	306	28	=	=	NOUN
ap-10691	306	29	kβ	kβ	X
ap-10691	306	30	is	be	AUX
ap-10691	306	31	the	the	DET
ap-10691	306	32	separation	separation	NOUN
ap-10691	306	33	constant	constant	ADJ
ap-10691	306	34	,	,	PUNCT
ap-10691	307	1	where	where	SCONJ
ap-10691	307	2	:	:	PUNCT
ap-10691	307	3	hθ	hθ	X
ap-10691	307	4	:	:	PUNCT
ap-10691	307	5	=	=	SYM
ap-10691	308	1	−∂θ	−∂θ	PROPN
ap-10691	308	2	+	+	NUM
ap-10691	308	3	l21	l21	NOUN
ap-10691	308	4	−	−	NOUN
ap-10691	308	5	1	1	NUM
ap-10691	308	6	4	4	NUM
ap-10691	308	7	sin2	sin2	NOUN
ap-10691	308	8	θ	θ	PROPN
ap-10691	309	1	+	+	CCONJ
ap-10691	309	2	l20	l20	NOUN
ap-10691	309	3	−	−	PROPN
ap-10691	309	4	1	1	NUM
ap-10691	309	5	4	4	NUM
ap-10691	309	6	cos2	cos2	NOUN
ap-10691	309	7	θ	θ	PROPN
ap-10691	309	8	,	,	PUNCT
ap-10691	309	9	(	(	PUNCT
ap-10691	309	10	91	91	NUM
ap-10691	309	11	)	)	PUNCT
ap-10691	309	12	hξ	hξ	PROPN
ap-10691	309	13	mk	mk	NOUN
ap-10691	309	14	:	:	PUNCT
ap-10691	309	15	=	=	SYM
ap-10691	309	16	−∂2	−∂2	PROPN
ap-10691	309	17	ξ	ξ	X
ap-10691	309	18	−	−	PROPN
ap-10691	309	19	coth	coth	NOUN
ap-10691	309	20	ξ∂ξ	ξ∂ξ	PROPN
ap-10691	309	21	−	−	PROPN
ap-10691	309	22	l	l	NOUN
ap-10691	309	23	2	2	NUM
ap-10691	309	24	2	2	NUM
ap-10691	309	25	−	−	NOUN
ap-10691	309	26	1	1	NUM
ap-10691	309	27	4	4	NUM
ap-10691	309	28	cosh2	cosh2	VERB
ap-10691	309	29	ξ	ξ	PROPN
ap-10691	309	30	+	+	NUM
ap-10691	309	31	m2	m2	PROPN
ap-10691	309	32	k	k	PROPN
ap-10691	309	33	sinh2	sinh2	PROPN
ap-10691	309	34	ξ	ξ	PROPN
ap-10691	309	35	.	.	PUNCT
ap-10691	310	1	(	(	PUNCT
ap-10691	310	2	92	92	NUM
ap-10691	310	3	)	)	PUNCT
ap-10691	310	4	it	it	PRON
ap-10691	310	5	is	be	AUX
ap-10691	310	6	worth	worth	ADJ
ap-10691	310	7	noting	note	VERB
ap-10691	310	8	that	that	SCONJ
ap-10691	310	9	the	the	DET
ap-10691	310	10	hamiltonian	hamiltonian	ADJ
ap-10691	310	11	hθ	hθ	NOUN
ap-10691	310	12	(	(	PUNCT
ap-10691	310	13	equation	equation	NOUN
ap-10691	310	14	(	(	PUNCT
ap-10691	310	15	91	91	NUM
ap-10691	310	16	)	)	PUNCT
ap-10691	310	17	)	)	PUNCT
ap-10691	310	18	coincides	coincide	VERB
ap-10691	310	19	with	with	ADP
ap-10691	310	20	the	the	DET
ap-10691	310	21	hamiltonian	hamiltonian	NOUN
ap-10691	310	22	(	(	PUNCT
ap-10691	310	23	equation	equation	NOUN
ap-10691	310	24	(	(	PUNCT
ap-10691	310	25	11	11	NUM
ap-10691	310	26	)	)	PUNCT
ap-10691	310	27	)	)	PUNCT
ap-10691	310	28	that	that	PRON
ap-10691	310	29	appeared	appear	VERB
ap-10691	310	30	in	in	ADP
ap-10691	310	31	the	the	DET
ap-10691	310	32	ttw	ttw	PROPN
ap-10691	310	33	so(3)hamiltonian	so(3)hamiltonian	PROPN
ap-10691	310	34	discussed	discuss	VERB
ap-10691	310	35	in	in	ADP
ap-10691	310	36	section	section	NOUN
ap-10691	310	37	2	2	NUM
ap-10691	310	38	,	,	PUNCT
ap-10691	310	39	whose	whose	DET
ap-10691	310	40	factorisation	factorisation	NOUN
ap-10691	310	41	carried	carry	VERB
ap-10691	310	42	out	out	ADP
ap-10691	310	43	in	in	ADP
ap-10691	310	44	subsection	subsection	NOUN
ap-10691	310	45	3.1	3.1	NUM
ap-10691	310	46	.	.	PUNCT
ap-10691	311	1	5.1	5.1	NUM
ap-10691	311	2	.	.	PUNCT
ap-10691	311	3	factorisation	factorisation	NOUN
ap-10691	311	4	of	of	ADP
ap-10691	311	5	hξ	hξ	PROPN
ap-10691	311	6	mk	mk	NOUN
ap-10691	311	7	we	we	PRON
ap-10691	311	8	further	far	ADV
ap-10691	311	9	identify	identify	VERB
ap-10691	311	10	four	four	NUM
ap-10691	311	11	distinct	distinct	ADJ
ap-10691	311	12	families	family	NOUN
ap-10691	311	13	of	of	ADP
ap-10691	311	14	ladder	ladder	NOUN
ap-10691	311	15	operators	operator	NOUN
ap-10691	311	16	n±,i	n±,i	PROPN
ap-10691	311	17	,	,	PUNCT
ap-10691	311	18	(	(	PUNCT
ap-10691	312	1	i	i	NOUN
ap-10691	312	2	=	=	NOUN
ap-10691	312	3	1	1	NUM
ap-10691	312	4	,	,	PUNCT
ap-10691	312	5	2	2	NUM
ap-10691	312	6	,	,	PUNCT
ap-10691	312	7	3	3	NUM
ap-10691	312	8	,	,	PUNCT
ap-10691	312	9	4	4	NUM
ap-10691	312	10	)	)	PUNCT
ap-10691	312	11	,	,	PUNCT
ap-10691	312	12	analogous	analogous	ADJ
ap-10691	312	13	to	to	ADP
ap-10691	312	14	those	those	PRON
ap-10691	312	15	arising	arise	VERB
ap-10691	312	16	from	from	ADP
ap-10691	312	17	the	the	DET
ap-10691	312	18	ttw	ttw	NOUN
ap-10691	312	19	so(3)-hamiltonian	so(3)-hamiltonian	PROPN
ap-10691	312	20	case	case	NOUN
ap-10691	312	21	(	(	PUNCT
ap-10691	312	22	subsection	subsection	NOUN
ap-10691	312	23	3.2	3.2	NUM
ap-10691	312	24	):	):	PUNCT
ap-10691	312	25	hξ	hξ	PROPN
ap-10691	312	26	mk	mk	NOUN
ap-10691	312	27	=	=	PUNCT
ap-10691	312	28	n+,in−,i	n+,in−,i	PROPN
ap-10691	312	29	+	+	NOUN
ap-10691	312	30	µi	µi	PROPN
ap-10691	312	31	.	.	PUNCT
ap-10691	313	1	(	(	PUNCT
ap-10691	313	2	93	93	NUM
ap-10691	313	3	)	)	PUNCT
ap-10691	313	4	as	as	ADP
ap-10691	313	5	in	in	ADP
ap-10691	313	6	the	the	DET
ap-10691	313	7	spherical	spherical	ADJ
ap-10691	313	8	case	case	NOUN
ap-10691	313	9	,	,	PUNCT
ap-10691	313	10	these	these	DET
ap-10691	313	11	operators	operator	NOUN
ap-10691	313	12	yield	yield	VERB
ap-10691	313	13	the	the	DET
ap-10691	313	14	same	same	ADJ
ap-10691	313	15	factorisation	factorisation	NOUN
ap-10691	313	16	of	of	ADP
ap-10691	313	17	the	the	DET
ap-10691	313	18	hamiltonian	hamiltonian	NOUN
ap-10691	313	19	(	(	PUNCT
ap-10691	313	20	92	92	NUM
ap-10691	313	21	)	)	PUNCT
ap-10691	313	22	,	,	PUNCT
ap-10691	313	23	although	although	SCONJ
ap-10691	313	24	they	they	PRON
ap-10691	313	25	differ	differ	VERB
ap-10691	313	26	in	in	ADP
ap-10691	313	27	their	their	PRON
ap-10691	313	28	intertwining	intertwine	VERB
ap-10691	313	29	relations	relation	NOUN
ap-10691	313	30	.	.	PUNCT
ap-10691	314	1	they	they	PRON
ap-10691	314	2	are	be	AUX
ap-10691	314	3	:	:	PUNCT
ap-10691	314	4	solution	solution	NOUN
ap-10691	314	5	1	1	NUM
ap-10691	314	6	:	:	PUNCT
ap-10691	314	7	n+,1	n+,1	X
ap-10691	315	1	=	=	PUNCT
ap-10691	315	2	∂ξ	∂ξ	NOUN
ap-10691	316	1	+	+	CCONJ
ap-10691	316	2	(	(	PUNCT
ap-10691	316	3	1	1	NUM
ap-10691	316	4	2	2	NUM
ap-10691	316	5	−	−	NOUN
ap-10691	316	6	l2	l2	NOUN
ap-10691	316	7	)	)	PUNCT
ap-10691	316	8	tanh	tanh	PROPN
ap-10691	316	9	ξ	ξ	PROPN
ap-10691	316	10	+	+	CCONJ
ap-10691	316	11	(	(	PUNCT
ap-10691	316	12	1	1	NUM
ap-10691	316	13	−mk	−mk	NOUN
ap-10691	316	14	)	)	PUNCT
ap-10691	316	15	coth	coth	PROPN
ap-10691	316	16	ξ	ξ	PROPN
ap-10691	316	17	,	,	PUNCT
ap-10691	316	18	n−,1	n−,1	ADJ
ap-10691	316	19	=	=	SYM
ap-10691	316	20	−∂ξ	−∂ξ	PROPN
ap-10691	316	21	+	+	CCONJ
ap-10691	316	22	(	(	PUNCT
ap-10691	316	23	1	1	NUM
ap-10691	316	24	2	2	NUM
ap-10691	316	25	−	−	NOUN
ap-10691	316	26	l2	l2	NOUN
ap-10691	316	27	)	)	PUNCT
ap-10691	316	28	tanh	tanh	PROPN
ap-10691	316	29	ξ	ξ	PROPN
ap-10691	316	30	−mk	−mk	PROPN
ap-10691	316	31	coth	coth	PROPN
ap-10691	316	32	ξ	ξ	PROPN
ap-10691	316	33	,	,	PUNCT
ap-10691	316	34	µ1	µ1	NOUN
ap-10691	316	35	=	=	SYM
ap-10691	316	36	−1	−1	NOUN
ap-10691	316	37	4(2l2	4(2l2	NOUN
ap-10691	317	1	+	+	CCONJ
ap-10691	317	2	2mk	2mk	ADJ
ap-10691	317	3	−	−	X
ap-10691	317	4	3)(2l2	3)(2l2	NOUN
ap-10691	318	1	+	+	CCONJ
ap-10691	318	2	2mk	2mk	ADJ
ap-10691	318	3	−	−	NOUN
ap-10691	318	4	1	1	NUM
ap-10691	318	5	)	)	PUNCT
ap-10691	318	6	.	.	PUNCT
ap-10691	319	1	(	(	PUNCT
ap-10691	319	2	94	94	NUM
ap-10691	319	3	)	)	PUNCT
ap-10691	319	4	for	for	ADP
ap-10691	319	5	this	this	DET
ap-10691	319	6	solution	solution	NOUN
ap-10691	319	7	,	,	PUNCT
ap-10691	319	8	we	we	PRON
ap-10691	319	9	obtain	obtain	VERB
ap-10691	319	10	the	the	DET
ap-10691	319	11	following	follow	VERB
ap-10691	319	12	expression	expression	NOUN
ap-10691	319	13	for	for	ADP
ap-10691	319	14	n−,1n+,1	n−,1n+,1	NOUN
ap-10691	320	1	+	+	CCONJ
ap-10691	320	2	µ1	µ1	ADJ
ap-10691	320	3	:	:	PUNCT
ap-10691	320	4	−∂2	−∂2	PROPN
ap-10691	320	5	ξ	ξ	PROPN
ap-10691	320	6	−	−	PROPN
ap-10691	320	7	coth	coth	NOUN
ap-10691	320	8	ξ	ξ	PROPN
ap-10691	320	9	∂ξ	∂ξ	NOUN
ap-10691	320	10	−	−	NOUN
ap-10691	320	11	(	(	PUNCT
ap-10691	320	12	l2	l2	NOUN
ap-10691	320	13	−	−	PROPN
ap-10691	320	14	1)2	1)2	NUM
ap-10691	320	15	−	−	NOUN
ap-10691	320	16	1	1	NUM
ap-10691	320	17	4	4	NUM
ap-10691	320	18	cosh2	cosh2	VERB
ap-10691	320	19	ξ	ξ	SYM
ap-10691	320	20	+	+	CCONJ
ap-10691	320	21	(	(	PUNCT
ap-10691	320	22	mk	mk	NOUN
ap-10691	320	23	−	−	PROPN
ap-10691	321	1	1)2	1)2	NUM
ap-10691	321	2	sinh2	sinh2	NOUN
ap-10691	321	3	ξ	ξ	X
ap-10691	321	4	.	.	PUNCT
ap-10691	322	1	(	(	PUNCT
ap-10691	322	2	95	95	NUM
ap-10691	322	3	)	)	PUNCT
ap-10691	322	4	the	the	DET
ap-10691	322	5	hamiltonian	hamiltonian	NOUN
ap-10691	322	6	given	give	VERB
ap-10691	322	7	in	in	ADP
ap-10691	322	8	equation	equation	NOUN
ap-10691	322	9	(	(	PUNCT
ap-10691	322	10	95	95	NUM
ap-10691	322	11	)	)	PUNCT
ap-10691	322	12	has	have	VERB
ap-10691	322	13	the	the	DET
ap-10691	322	14	same	same	ADJ
ap-10691	322	15	form	form	NOUN
ap-10691	322	16	as	as	ADP
ap-10691	322	17	hξ	hξ	PROPN
ap-10691	322	18	mk	mk	PROPN
ap-10691	322	19	in	in	ADP
ap-10691	322	20	equation	equation	NOUN
ap-10691	322	21	(	(	PUNCT
ap-10691	322	22	92	92	NUM
ap-10691	322	23	)	)	PUNCT
ap-10691	322	24	,	,	PUNCT
ap-10691	322	25	but	but	CCONJ
ap-10691	322	26	with	with	ADP
ap-10691	322	27	the	the	DET
ap-10691	322	28	parameters	parameter	NOUN
ap-10691	322	29	mk	mk	NOUN
ap-10691	322	30	and	and	CCONJ
ap-10691	322	31	l2	l2	NOUN
ap-10691	322	32	replaced	replace	VERB
ap-10691	322	33	by	by	ADP
ap-10691	322	34	mk	mk	PROPN
ap-10691	322	35	−	−	PROPN
ap-10691	322	36	1	1	NUM
ap-10691	322	37	and	and	CCONJ
ap-10691	322	38	l2	l2	VERB
ap-10691	322	39	−	−	PROPN
ap-10691	322	40	1	1	NUM
ap-10691	322	41	,	,	PUNCT
ap-10691	322	42	respectively	respectively	ADV
ap-10691	322	43	.	.	PUNCT
ap-10691	323	1	527	527	NUM
ap-10691	323	2	mariano	mariano	PROPN
ap-10691	323	3	a.	a.	PROPN
ap-10691	323	4	del	del	PROPN
ap-10691	323	5	olmo	olmo	PROPN
ap-10691	323	6	,	,	PUNCT
ap-10691	323	7	álvaro	álvaro	PROPN
ap-10691	323	8	romaniega	romaniega	PROPN
ap-10691	323	9	acta	acta	PROPN
ap-10691	323	10	polytechnica	polytechnica	PROPN
ap-10691	323	11	solution	solution	NOUN
ap-10691	323	12	2	2	NUM
ap-10691	323	13	:	:	PUNCT
ap-10691	323	14	n+,2	n+,2	X
ap-10691	323	15	=	=	PUNCT
ap-10691	324	1	∂ξ	∂ξ	NOUN
ap-10691	325	1	+	+	CCONJ
ap-10691	325	2	(	(	PUNCT
ap-10691	325	3	1	1	NUM
ap-10691	325	4	2	2	NUM
ap-10691	325	5	+	+	NUM
ap-10691	325	6	l2	l2	NOUN
ap-10691	325	7	)	)	PUNCT
ap-10691	325	8	tanh	tanh	PROPN
ap-10691	325	9	ξ	ξ	PROPN
ap-10691	326	1	+	+	CCONJ
ap-10691	326	2	(	(	PUNCT
ap-10691	326	3	1	1	NUM
ap-10691	326	4	−mk	−mk	NOUN
ap-10691	326	5	)	)	PUNCT
ap-10691	326	6	coth	coth	PROPN
ap-10691	326	7	ξ	ξ	PROPN
ap-10691	326	8	,	,	PUNCT
ap-10691	326	9	n−,2	n−,2	PRON
ap-10691	326	10	=	=	SYM
ap-10691	326	11	−∂ξ	−∂ξ	NOUN
ap-10691	326	12	+	+	CCONJ
ap-10691	326	13	(	(	PUNCT
ap-10691	326	14	1	1	NUM
ap-10691	326	15	2	2	NUM
ap-10691	326	16	+	+	NUM
ap-10691	326	17	l2	l2	NOUN
ap-10691	326	18	)	)	PUNCT
ap-10691	326	19	tanh	tanh	PROPN
ap-10691	326	20	ξ	ξ	PROPN
ap-10691	326	21	−mk	−mk	PROPN
ap-10691	326	22	coth	coth	PROPN
ap-10691	326	23	ξ	ξ	PROPN
ap-10691	326	24	,	,	PUNCT
ap-10691	326	25	µ2	µ2	PROPN
ap-10691	326	26	=	=	SYM
ap-10691	326	27	−1	−1	NOUN
ap-10691	326	28	4(2l2	4(2l2	NOUN
ap-10691	326	29	−	−	ADV
ap-10691	326	30	2mk	2mk	ADJ
ap-10691	327	1	+	+	CCONJ
ap-10691	328	1	1)(2l2	1)(2l2	NUM
ap-10691	328	2	−	−	NOUN
ap-10691	328	3	2mk	2mk	NOUN
ap-10691	329	1	+	+	CCONJ
ap-10691	330	1	3	3	NUM
ap-10691	330	2	)	)	PUNCT
ap-10691	330	3	.	.	PUNCT
ap-10691	331	1	(	(	PUNCT
ap-10691	331	2	96	96	NUM
ap-10691	331	3	)	)	PUNCT
ap-10691	331	4	in	in	ADP
ap-10691	331	5	this	this	DET
ap-10691	331	6	case	case	NOUN
ap-10691	331	7	n−,2n+,2	n−,2n+,2	PROPN
ap-10691	332	1	+	+	CCONJ
ap-10691	332	2	µ2	µ2	NOUN
ap-10691	332	3	yields	yield	VERB
ap-10691	332	4	:	:	PUNCT
ap-10691	332	5	−∂2	−∂2	PROPN
ap-10691	332	6	ξ	ξ	X
ap-10691	332	7	−	−	PROPN
ap-10691	332	8	coth	coth	NOUN
ap-10691	332	9	ξ	ξ	PROPN
ap-10691	332	10	∂ξ	∂ξ	NOUN
ap-10691	332	11	−	−	NOUN
ap-10691	332	12	(	(	PUNCT
ap-10691	332	13	l2	l2	NOUN
ap-10691	332	14	+	+	CCONJ
ap-10691	333	1	1)2	1)2	NUM
ap-10691	333	2	−	−	NOUN
ap-10691	333	3	1	1	NUM
ap-10691	333	4	4	4	NUM
ap-10691	333	5	cosh2	cosh2	VERB
ap-10691	333	6	ξ	ξ	SYM
ap-10691	333	7	+	+	CCONJ
ap-10691	333	8	(	(	PUNCT
ap-10691	333	9	mk	mk	NOUN
ap-10691	333	10	−	−	PROPN
ap-10691	333	11	1)2	1)2	NUM
ap-10691	333	12	sinh2	sinh2	NOUN
ap-10691	333	13	ξ	ξ	X
ap-10691	333	14	,	,	PUNCT
ap-10691	333	15	(	(	PUNCT
ap-10691	333	16	97	97	NUM
ap-10691	333	17	)	)	PUNCT
ap-10691	333	18	where	where	SCONJ
ap-10691	333	19	the	the	DET
ap-10691	333	20	parameters	parameter	NOUN
ap-10691	333	21	mk	mk	NOUN
ap-10691	333	22	and	and	CCONJ
ap-10691	333	23	l2	l2	NOUN
ap-10691	333	24	are	be	AUX
ap-10691	333	25	replaced	replace	VERB
ap-10691	333	26	by	by	ADP
ap-10691	333	27	mk−1	mk−1	NOUN
ap-10691	333	28	and	and	CCONJ
ap-10691	333	29	l2	l2	NOUN
ap-10691	333	30	+	+	CCONJ
ap-10691	333	31	1	1	NUM
ap-10691	333	32	,	,	PUNCT
ap-10691	333	33	respectively	respectively	ADV
ap-10691	333	34	.	.	PUNCT
ap-10691	334	1	solution	solution	NOUN
ap-10691	334	2	3	3	NUM
ap-10691	334	3	:	:	PUNCT
ap-10691	334	4	n+,3	n+,3	ADP
ap-10691	334	5	=	=	SYM
ap-10691	335	1	∂ξ	∂ξ	NOUN
ap-10691	336	1	+	+	CCONJ
ap-10691	336	2	(	(	PUNCT
ap-10691	336	3	1	1	NUM
ap-10691	336	4	2	2	NUM
ap-10691	336	5	+	+	NUM
ap-10691	336	6	l2	l2	NOUN
ap-10691	336	7	)	)	PUNCT
ap-10691	336	8	tanh	tanh	PROPN
ap-10691	336	9	ξ	ξ	PROPN
ap-10691	337	1	+	+	CCONJ
ap-10691	337	2	(	(	PUNCT
ap-10691	337	3	mk	mk	NOUN
ap-10691	337	4	+	+	CCONJ
ap-10691	337	5	1	1	X
ap-10691	337	6	)	)	PUNCT
ap-10691	337	7	coth	coth	PROPN
ap-10691	337	8	ξ	ξ	PROPN
ap-10691	337	9	,	,	PUNCT
ap-10691	337	10	n−,3	n−,3	X
ap-10691	337	11	=	=	SYM
ap-10691	337	12	−∂ξ	−∂ξ	PROPN
ap-10691	337	13	+	+	CCONJ
ap-10691	337	14	(	(	PUNCT
ap-10691	337	15	1	1	NUM
ap-10691	337	16	2	2	NUM
ap-10691	337	17	+	+	NUM
ap-10691	337	18	l2	l2	NOUN
ap-10691	337	19	)	)	PUNCT
ap-10691	337	20	tanh	tanh	PROPN
ap-10691	337	21	ξ	ξ	PROPN
ap-10691	337	22	+	+	PROPN
ap-10691	337	23	mk	mk	PROPN
ap-10691	337	24	coth	coth	PROPN
ap-10691	337	25	ξ	ξ	PROPN
ap-10691	337	26	,	,	PUNCT
ap-10691	337	27	µ3	µ3	NOUN
ap-10691	337	28	=	=	SYM
ap-10691	337	29	−1	−1	NOUN
ap-10691	337	30	4(1	4(1	NUM
ap-10691	337	31	+	+	CCONJ
ap-10691	337	32	2l2	2l2	NUM
ap-10691	338	1	+	+	CCONJ
ap-10691	338	2	2mk)(3	2mk)(3	NUM
ap-10691	338	3	+	+	CCONJ
ap-10691	338	4	2l2	2l2	NUM
ap-10691	338	5	+	+	CCONJ
ap-10691	338	6	2mk	2mk	ADJ
ap-10691	338	7	)	)	PUNCT
ap-10691	338	8	.	.	PUNCT
ap-10691	339	1	(	(	PUNCT
ap-10691	339	2	98	98	NUM
ap-10691	339	3	)	)	PUNCT
ap-10691	339	4	here	here	ADV
ap-10691	339	5	,	,	PUNCT
ap-10691	339	6	the	the	DET
ap-10691	339	7	expression	expression	NOUN
ap-10691	339	8	n−,3n+,3	n−,3n+,3	PUNCT
ap-10691	340	1	+	+	CCONJ
ap-10691	340	2	µ3	µ3	NOUN
ap-10691	340	3	results	result	VERB
ap-10691	340	4	in	in	ADP
ap-10691	340	5	:	:	PUNCT
ap-10691	340	6	−∂2	−∂2	PROPN
ap-10691	340	7	ξ	ξ	PROPN
ap-10691	340	8	−	−	PROPN
ap-10691	340	9	coth	coth	NOUN
ap-10691	340	10	ξ	ξ	PROPN
ap-10691	340	11	∂ξ	∂ξ	NOUN
ap-10691	340	12	−	−	NOUN
ap-10691	340	13	(	(	PUNCT
ap-10691	340	14	l2	l2	NOUN
ap-10691	340	15	+	+	CCONJ
ap-10691	341	1	1)2	1)2	NUM
ap-10691	341	2	−	−	NOUN
ap-10691	341	3	1	1	NUM
ap-10691	341	4	4	4	NUM
ap-10691	341	5	cosh2	cosh2	VERB
ap-10691	341	6	ξ	ξ	SYM
ap-10691	341	7	+	+	CCONJ
ap-10691	341	8	(	(	PUNCT
ap-10691	341	9	mk	mk	X
ap-10691	341	10	+	+	X
ap-10691	341	11	1)2	1)2	NUM
ap-10691	341	12	sinh2	sinh2	NOUN
ap-10691	341	13	ξ	ξ	X
ap-10691	341	14	,	,	PUNCT
ap-10691	341	15	(	(	PUNCT
ap-10691	341	16	99	99	NUM
ap-10691	341	17	)	)	PUNCT
ap-10691	341	18	where	where	SCONJ
ap-10691	341	19	the	the	DET
ap-10691	341	20	parameters	parameter	NOUN
ap-10691	341	21	mk	mk	NOUN
ap-10691	341	22	and	and	CCONJ
ap-10691	341	23	l2	l2	NOUN
ap-10691	341	24	are	be	AUX
ap-10691	341	25	replaced	replace	VERB
ap-10691	341	26	by	by	ADP
ap-10691	341	27	mk+1	mk+1	NUM
ap-10691	341	28	and	and	CCONJ
ap-10691	341	29	l2	l2	VERB
ap-10691	341	30	+	+	CCONJ
ap-10691	341	31	1	1	NUM
ap-10691	341	32	,	,	PUNCT
ap-10691	341	33	respectively	respectively	ADV
ap-10691	341	34	.	.	PUNCT
ap-10691	341	35	solution	solution	NOUN
ap-10691	341	36	4	4	NUM
ap-10691	341	37	:	:	PUNCT
ap-10691	341	38	n+,4	n+,4	X
ap-10691	341	39	=	=	SYM
ap-10691	342	1	∂ξ	∂ξ	NOUN
ap-10691	343	1	+	+	CCONJ
ap-10691	343	2	(	(	PUNCT
ap-10691	343	3	1	1	NUM
ap-10691	343	4	2	2	NUM
ap-10691	343	5	−	−	NOUN
ap-10691	343	6	l2	l2	NOUN
ap-10691	343	7	)	)	PUNCT
ap-10691	343	8	tanh	tanh	PROPN
ap-10691	343	9	ξ	ξ	PROPN
ap-10691	344	1	+	+	CCONJ
ap-10691	344	2	(	(	PUNCT
ap-10691	344	3	mk	mk	NOUN
ap-10691	344	4	+	+	CCONJ
ap-10691	344	5	1	1	X
ap-10691	344	6	)	)	PUNCT
ap-10691	344	7	coth	coth	PROPN
ap-10691	344	8	ξ	ξ	PROPN
ap-10691	344	9	,	,	PUNCT
ap-10691	344	10	n−,4	n−,4	X
ap-10691	344	11	=	=	SYM
ap-10691	344	12	−∂ξ	−∂ξ	PROPN
ap-10691	344	13	+	+	CCONJ
ap-10691	344	14	(	(	PUNCT
ap-10691	344	15	1	1	NUM
ap-10691	344	16	2	2	NUM
ap-10691	344	17	−	−	NOUN
ap-10691	344	18	l2	l2	NOUN
ap-10691	344	19	)	)	PUNCT
ap-10691	344	20	tanh	tanh	PROPN
ap-10691	344	21	ξ	ξ	PROPN
ap-10691	344	22	+	+	PROPN
ap-10691	344	23	mk	mk	PROPN
ap-10691	344	24	coth	coth	PROPN
ap-10691	344	25	ξ	ξ	PROPN
ap-10691	344	26	,	,	PUNCT
ap-10691	344	27	µ4	µ4	PROPN
ap-10691	344	28	=	=	SYM
ap-10691	344	29	−1	−1	NOUN
ap-10691	344	30	4(2l2	4(2l2	NOUN
ap-10691	345	1	−	−	ADV
ap-10691	345	2	2mk	2mk	ADJ
ap-10691	345	3	−	−	PROPN
ap-10691	345	4	3)(2l2	3)(2l2	NOUN
ap-10691	346	1	−	−	NOUN
ap-10691	346	2	2mk	2mk	ADJ
ap-10691	347	1	−	−	NOUN
ap-10691	347	2	1	1	NUM
ap-10691	347	3	)	)	PUNCT
ap-10691	347	4	.	.	PUNCT
ap-10691	348	1	(	(	PUNCT
ap-10691	348	2	100	100	X
ap-10691	348	3	)	)	PUNCT
ap-10691	348	4	evaluating	evaluate	VERB
ap-10691	348	5	n−,4n+,4	n−,4n+,4	PUNCT
ap-10691	349	1	+	+	CCONJ
ap-10691	349	2	µ4	µ4	PROPN
ap-10691	349	3	results	result	VERB
ap-10691	349	4	in	in	ADP
ap-10691	349	5	:	:	PUNCT
ap-10691	349	6	−∂2	−∂2	PROPN
ap-10691	349	7	ξ	ξ	PROPN
ap-10691	349	8	−	−	PROPN
ap-10691	349	9	coth	coth	NOUN
ap-10691	349	10	ξ	ξ	PROPN
ap-10691	349	11	∂ξ	∂ξ	NOUN
ap-10691	349	12	−	−	NOUN
ap-10691	349	13	(	(	PUNCT
ap-10691	349	14	l2	l2	NOUN
ap-10691	349	15	−	−	PROPN
ap-10691	349	16	1)2	1)2	NUM
ap-10691	349	17	−	−	NOUN
ap-10691	349	18	1	1	NUM
ap-10691	349	19	4	4	NUM
ap-10691	349	20	cosh2	cosh2	VERB
ap-10691	349	21	ξ	ξ	SYM
ap-10691	349	22	+	+	CCONJ
ap-10691	349	23	(	(	PUNCT
ap-10691	349	24	mk	mk	X
ap-10691	349	25	+	+	X
ap-10691	349	26	1)2	1)2	NUM
ap-10691	349	27	sinh2	sinh2	NOUN
ap-10691	349	28	ξ	ξ	PROPN
ap-10691	349	29	,	,	PUNCT
ap-10691	349	30	(	(	PUNCT
ap-10691	349	31	101	101	NUM
ap-10691	349	32	)	)	PUNCT
ap-10691	349	33	where	where	SCONJ
ap-10691	349	34	the	the	DET
ap-10691	349	35	parameters	parameter	NOUN
ap-10691	349	36	mk	mk	NOUN
ap-10691	349	37	and	and	CCONJ
ap-10691	349	38	l2	l2	NOUN
ap-10691	349	39	are	be	AUX
ap-10691	349	40	replaced	replace	VERB
ap-10691	349	41	by	by	ADP
ap-10691	349	42	mk+1	mk+1	NUM
ap-10691	349	43	and	and	CCONJ
ap-10691	349	44	l2	l2	VERB
ap-10691	349	45	−	−	PROPN
ap-10691	349	46	1	1	NUM
ap-10691	349	47	,	,	PUNCT
ap-10691	349	48	respectively	respectively	ADV
ap-10691	349	49	.	.	PUNCT
ap-10691	350	1	we	we	PRON
ap-10691	350	2	have	have	AUX
ap-10691	350	3	identified	identify	VERB
ap-10691	350	4	eight	eight	NUM
ap-10691	350	5	operators	operator	NOUN
ap-10691	350	6	that	that	PRON
ap-10691	350	7	shift	shift	VERB
ap-10691	350	8	the	the	DET
ap-10691	350	9	parameters	parameter	NOUN
ap-10691	350	10	β	β	PROPN
ap-10691	350	11	k	k	NOUN
ap-10691	350	12	and	and	CCONJ
ap-10691	350	13	l2	l2	NOUN
ap-10691	350	14	by	by	ADP
ap-10691	350	15	±1	±1	NOUN
ap-10691	350	16	,	,	PUNCT
ap-10691	350	17	allowing	allow	VERB
ap-10691	350	18	movement	movement	NOUN
ap-10691	350	19	in	in	ADP
ap-10691	350	20	both	both	DET
ap-10691	350	21	directions	direction	NOUN
ap-10691	350	22	along	along	ADP
ap-10691	350	23	the	the	DET
ap-10691	350	24	kβ	kβ	NOUN
ap-10691	350	25	and	and	CCONJ
ap-10691	350	26	l2	l2	NOUN
ap-10691	350	27	axes	axis	NOUN
ap-10691	350	28	.	.	PUNCT
ap-10691	351	1	we	we	PRON
ap-10691	351	2	also	also	ADV
ap-10691	351	3	construct	construct	VERB
ap-10691	351	4	a	a	DET
ap-10691	351	5	hierarchy	hierarchy	NOUN
ap-10691	351	6	of	of	ADP
ap-10691	351	7	hamiltonians	hamiltonian	NOUN
ap-10691	351	8	,	,	PUNCT
ap-10691	351	9	{	{	PUNCT
ap-10691	351	10	hξ	hξ	X
ap-10691	351	11	mk;n	mk;n	ADJ
ap-10691	351	12	,	,	PUNCT
ap-10691	351	13	m}n	m}n	PROPN
ap-10691	351	14	,	,	PUNCT
ap-10691	351	15	m∈z	m∈z	NOUN
ap-10691	351	16	,	,	PUNCT
ap-10691	351	17	associated	associate	VERB
ap-10691	351	18	with	with	ADP
ap-10691	351	19	the	the	DET
ap-10691	351	20	initial	initial	ADJ
ap-10691	351	21	hamiltonian	hamiltonian	NOUN
ap-10691	351	22	hξ	hξ	X
ap-10691	351	23	mk	mk	PROPN
ap-10691	351	24	(	(	PUNCT
ap-10691	351	25	equation	equation	NOUN
ap-10691	351	26	(	(	PUNCT
ap-10691	351	27	92	92	NUM
ap-10691	351	28	)	)	PUNCT
ap-10691	351	29	)	)	PUNCT
ap-10691	351	30	,	,	PUNCT
ap-10691	351	31	by	by	ADP
ap-10691	351	32	the	the	DET
ap-10691	351	33	repeatedly	repeatedly	ADV
ap-10691	351	34	applying	apply	VERB
ap-10691	351	35	the	the	DET
ap-10691	351	36	intertwining	intertwine	VERB
ap-10691	351	37	operators	operator	NOUN
ap-10691	351	38	n±,3	n±,3	PRON
ap-10691	351	39	as	as	SCONJ
ap-10691	351	40	described	describe	VERB
ap-10691	351	41	in	in	ADP
ap-10691	351	42	equation	equation	NOUN
ap-10691	351	43	(	(	PUNCT
ap-10691	351	44	13	13	NUM
ap-10691	351	45	)	)	PUNCT
ap-10691	351	46	.	.	PUNCT
ap-10691	352	1	the	the	DET
ap-10691	352	2	elements	element	NOUN
ap-10691	352	3	of	of	ADP
ap-10691	352	4	this	this	DET
ap-10691	352	5	hierarchy	hierarchy	NOUN
ap-10691	352	6	are	be	AUX
ap-10691	352	7	explicitly	explicitly	ADV
ap-10691	352	8	given	give	VERB
ap-10691	352	9	by	by	ADP
ap-10691	352	10	:	:	PUNCT
ap-10691	352	11	hξ	hξ	NOUN
ap-10691	352	12	mk;n	mk;n	ADJ
ap-10691	352	13	,	,	PUNCT
ap-10691	352	14	m	m	NOUN
ap-10691	352	15	=	=	PUNCT
ap-10691	352	16	−	−	PROPN
ap-10691	352	17	∂2	∂2	NUM
ap-10691	353	1	ξ	ξ	X
ap-10691	353	2	−	−	PROPN
ap-10691	353	3	coth	coth	NOUN
ap-10691	353	4	ξ	ξ	PROPN
ap-10691	353	5	∂ξ	∂ξ	NOUN
ap-10691	353	6	−	−	NOUN
ap-10691	353	7	(	(	PUNCT
ap-10691	353	8	l2	l2	VERB
ap-10691	353	9	+	+	CCONJ
ap-10691	353	10	m)2	m)2	PROPN
ap-10691	353	11	−	−	NUM
ap-10691	353	12	1	1	NUM
ap-10691	353	13	4	4	NUM
ap-10691	353	14	cosh2	cosh2	NOUN
ap-10691	353	15	ϕ	ϕ	NOUN
ap-10691	353	16	+	+	CCONJ
ap-10691	353	17	(	(	PUNCT
ap-10691	353	18	kβ	kβ	PROPN
ap-10691	353	19	+	+	PROPN
ap-10691	353	20	n)2	n)2	PROPN
ap-10691	353	21	sinh2	sinh2	PROPN
ap-10691	353	22	ϕ	ϕ	PROPN
ap-10691	353	23	,	,	PUNCT
ap-10691	353	24	(	(	PUNCT
ap-10691	353	25	102	102	NUM
ap-10691	353	26	)	)	PUNCT
ap-10691	353	27	where	where	SCONJ
ap-10691	353	28	we	we	PRON
ap-10691	353	29	have	have	AUX
ap-10691	353	30	used	use	VERB
ap-10691	353	31	the	the	DET
ap-10691	353	32	relation	relation	NOUN
ap-10691	353	33	mk	mk	NOUN
ap-10691	353	34	=	=	PUNCT
ap-10691	353	35	k	k	PROPN
ap-10691	353	36	β	β	X
ap-10691	353	37	.	.	PUNCT
ap-10691	354	1	for	for	ADP
ap-10691	354	2	m	m	PROPN
ap-10691	354	3	=	=	SYM
ap-10691	354	4	n	n	PROPN
ap-10691	354	5	=	=	SYM
ap-10691	354	6	0	0	NUM
ap-10691	354	7	,	,	PUNCT
ap-10691	354	8	we	we	PRON
ap-10691	354	9	obtain	obtain	VERB
ap-10691	354	10	the	the	DET
ap-10691	354	11	initial	initial	ADJ
ap-10691	354	12	hamiltonian	hamiltonian	NOUN
ap-10691	354	13	hξ	hξ	ADP
ap-10691	354	14	mk	mk	PROPN
ap-10691	354	15	given	give	VERB
ap-10691	354	16	by	by	ADP
ap-10691	354	17	equation	equation	NOUN
ap-10691	354	18	(	(	PUNCT
ap-10691	354	19	92	92	NUM
ap-10691	354	20	)	)	PUNCT
ap-10691	354	21	.	.	PUNCT
ap-10691	355	1	the	the	DET
ap-10691	355	2	fundamental	fundamental	ADJ
ap-10691	355	3	states	state	NOUN
ap-10691	355	4	of	of	ADP
ap-10691	355	5	the	the	DET
ap-10691	355	6	hamiltonians	hamiltonian	NOUN
ap-10691	355	7	hξ	hξ	PROPN
ap-10691	355	8	mk;0,m	mk;0,m	ADV
ap-10691	355	9	are	be	AUX
ap-10691	355	10	obtained	obtain	VERB
ap-10691	355	11	via	via	ADP
ap-10691	355	12	equation	equation	NOUN
ap-10691	355	13	(	(	PUNCT
ap-10691	355	14	16	16	NUM
ap-10691	355	15	)	)	PUNCT
ap-10691	355	16	and	and	CCONJ
ap-10691	355	17	are	be	AUX
ap-10691	355	18	given	give	VERB
ap-10691	355	19	by	by	ADP
ap-10691	355	20	[	[	X
ap-10691	355	21	7	7	NUM
ap-10691	355	22	]	]	SYM
ap-10691	355	23	:	:	PUNCT
ap-10691	355	24	φ0	φ0	PROPN
ap-10691	355	25	(	(	PUNCT
ap-10691	355	26	m)(ξ	m)(ξ	NOUN
ap-10691	355	27	)	)	PUNCT
ap-10691	355	28	=	=	PUNCT
ap-10691	356	1	coshl2+m+	coshl2+m+	VERB
ap-10691	356	2	1	1	NUM
ap-10691	356	3	2	2	NUM
ap-10691	356	4	ξ	ξ	X
ap-10691	356	5	sinhkβ	sinhkβ	NOUN
ap-10691	356	6	ξ	ξ	PROPN
ap-10691	356	7	,	,	PUNCT
ap-10691	356	8	(	(	PUNCT
ap-10691	356	9	103	103	NUM
ap-10691	356	10	)	)	PUNCT
ap-10691	356	11	with	with	ADP
ap-10691	356	12	β	β	X
ap-10691	356	13	=	=	SYM
ap-10691	356	14	l0	l0	PROPN
ap-10691	356	15	+	+	NUM
ap-10691	356	16	l1	l1	PROPN
ap-10691	356	17	+	+	CCONJ
ap-10691	356	18	n′	n′	PROPN
ap-10691	357	1	+	+	CCONJ
ap-10691	357	2	1	1	NUM
ap-10691	357	3	2	2	NUM
ap-10691	357	4	(	(	PUNCT
ap-10691	357	5	equation	equation	NOUN
ap-10691	357	6	(	(	PUNCT
ap-10691	357	7	32	32	NUM
ap-10691	357	8	)	)	PUNCT
ap-10691	357	9	)	)	PUNCT
ap-10691	357	10	,	,	PUNCT
ap-10691	357	11	where	where	SCONJ
ap-10691	357	12	we	we	PRON
ap-10691	357	13	have	have	AUX
ap-10691	357	14	taken	take	VERB
ap-10691	357	15	a	a	DET
ap-10691	357	16	fixed	fix	VERB
ap-10691	357	17	,	,	PUNCT
ap-10691	357	18	but	but	CCONJ
ap-10691	357	19	arbitrary	arbitrary	ADJ
ap-10691	357	20	value	value	NOUN
ap-10691	357	21	of	of	ADP
ap-10691	357	22	n	n	NOUN
ap-10691	357	23	=	=	SYM
ap-10691	357	24	n′	n′	PRON
ap-10691	357	25	∈	∈	PROPN
ap-10691	357	26	n	n	CCONJ
ap-10691	357	27	(	(	PUNCT
ap-10691	357	28	see	see	VERB
ap-10691	357	29	subsection	subsection	NOUN
ap-10691	357	30	3.1	3.1	NUM
ap-10691	357	31	)	)	PUNCT
ap-10691	357	32	,	,	PUNCT
ap-10691	357	33	the	the	DET
ap-10691	357	34	excited	excited	ADJ
ap-10691	357	35	states	state	NOUN
ap-10691	357	36	of	of	ADP
ap-10691	357	37	the	the	DET
ap-10691	357	38	original	original	ADJ
ap-10691	357	39	hamiltonian	hamiltonian	ADJ
ap-10691	357	40	hkβ	hkβ	PROPN
ap-10691	357	41	ϕ,0,0	ϕ,0,0	NOUN
ap-10691	357	42	,	,	PUNCT
ap-10691	357	43	obtained	obtain	VERB
ap-10691	357	44	using	use	VERB
ap-10691	357	45	equation	equation	NOUN
ap-10691	357	46	(	(	PUNCT
ap-10691	357	47	32	32	NUM
ap-10691	357	48	)	)	PUNCT
ap-10691	357	49	,	,	PUNCT
ap-10691	357	50	are	be	AUX
ap-10691	357	51	[	[	X
ap-10691	357	52	32	32	NUM
ap-10691	357	53	]	]	PUNCT
ap-10691	357	54	:	:	PUNCT
ap-10691	357	55	φm	φm	X
ap-10691	357	56	(	(	PUNCT
ap-10691	357	57	0)(ξ	0)(ξ	NUM
ap-10691	357	58	)	)	PUNCT
ap-10691	357	59	=	=	SYM
ap-10691	357	60	n	n	PRON
ap-10691	358	1	coshl2	coshl2	NOUN
ap-10691	358	2	+	+	CCONJ
ap-10691	358	3	1	1	NUM
ap-10691	358	4	2	2	NUM
ap-10691	358	5	ξ	ξ	PRON
ap-10691	358	6	sinhβ	sinhβ	NOUN
ap-10691	358	7	k	k	PROPN
ap-10691	358	8	ξ	ξ	X
ap-10691	358	9	×	×	NOUN
ap-10691	358	10	p	p	X
ap-10691	358	11	(	(	PUNCT
ap-10691	358	12	l2	l2	NOUN
ap-10691	358	13	+	+	CCONJ
ap-10691	358	14	1	1	NUM
ap-10691	358	15	2	2	NUM
ap-10691	358	16	,	,	PUNCT
ap-10691	358	17	β	β	X
ap-10691	358	18	k	k	X
ap-10691	358	19	)	)	PUNCT
ap-10691	358	20	m	m	PROPN
ap-10691	358	21	(	(	PUNCT
ap-10691	358	22	cosh	cosh	PROPN
ap-10691	358	23	2ξ	2ξ	NUM
ap-10691	358	24	)	)	PUNCT
ap-10691	358	25	,	,	PUNCT
ap-10691	358	26	(	(	PUNCT
ap-10691	358	27	104	104	X
ap-10691	358	28	)	)	PUNCT
ap-10691	358	29	where	where	SCONJ
ap-10691	358	30	n	n	PRON
ap-10691	358	31	is	be	AUX
ap-10691	358	32	the	the	DET
ap-10691	358	33	normalisation	normalisation	NOUN
ap-10691	358	34	constant	constant	ADJ
ap-10691	358	35	and	and	CCONJ
ap-10691	358	36	p	p	X
ap-10691	358	37	(	(	PUNCT
ap-10691	358	38	l0,l1	l0,l1	PROPN
ap-10691	358	39	)	)	PUNCT
ap-10691	358	40	m	m	VERB
ap-10691	358	41	are	be	AUX
ap-10691	358	42	jacobi	jacobi	NOUN
ap-10691	358	43	polynomials	polynomial	NOUN
ap-10691	358	44	.	.	PUNCT
ap-10691	359	1	the	the	DET
ap-10691	359	2	energy	energy	NOUN
ap-10691	359	3	of	of	ADP
ap-10691	359	4	these	these	DET
ap-10691	359	5	states	state	NOUN
ap-10691	359	6	is	be	AUX
ap-10691	359	7	:	:	PUNCT
ap-10691	359	8	eβ	eβ	PROPN
ap-10691	359	9	k	k	PROPN
ap-10691	359	10	,	,	PUNCT
ap-10691	359	11	m	m	PROPN
ap-10691	359	12	(	(	PUNCT
ap-10691	359	13	0	0	NUM
ap-10691	359	14	)	)	PUNCT
ap-10691	359	15	=	=	SYM
ap-10691	360	1	−	−	PROPN
ap-10691	360	2	(	(	PUNCT
ap-10691	360	3	βk	βk	ADP
ap-10691	360	4	+	+	X
ap-10691	360	5	l2	l2	NOUN
ap-10691	360	6	+	+	CCONJ
ap-10691	360	7	2m+	2m+	NUM
ap-10691	360	8	1	1	NUM
ap-10691	360	9	2	2	NUM
ap-10691	360	10	)	)	PUNCT
ap-10691	360	11	×	×	NOUN
ap-10691	360	12	(	(	PUNCT
ap-10691	360	13	βk	βk	ADP
ap-10691	360	14	+	+	X
ap-10691	360	15	l2	l2	NOUN
ap-10691	360	16	+	+	CCONJ
ap-10691	360	17	2m+	2m+	NUM
ap-10691	360	18	3	3	NUM
ap-10691	360	19	2	2	NUM
ap-10691	360	20	)	)	PUNCT
ap-10691	360	21	.	.	PUNCT
ap-10691	361	1	(	(	PUNCT
ap-10691	361	2	105	105	NUM
ap-10691	361	3	)	)	PUNCT
ap-10691	361	4	we	we	PRON
ap-10691	361	5	can	can	AUX
ap-10691	361	6	define	define	VERB
ap-10691	361	7	generalised	generalised	ADJ
ap-10691	361	8	operators	operator	NOUN
ap-10691	361	9	n±,i	n±,i	PROPN
ap-10691	361	10	n	n	CCONJ
ap-10691	361	11	,	,	PUNCT
ap-10691	361	12	m	m	VERB
ap-10691	361	13	in	in	ADP
ap-10691	361	14	terms	term	NOUN
ap-10691	361	15	of	of	ADP
ap-10691	361	16	the	the	DET
ap-10691	361	17	operators	operator	NOUN
ap-10691	361	18	n±	n±	ADV
ap-10691	361	19	i	i	PRON
ap-10691	361	20	given	give	VERB
ap-10691	361	21	in	in	ADP
ap-10691	361	22	equations	equation	NOUN
ap-10691	361	23	(	(	PUNCT
ap-10691	361	24	94	94	NUM
ap-10691	361	25	)	)	PUNCT
ap-10691	361	26	,	,	PUNCT
ap-10691	361	27	(	(	PUNCT
ap-10691	361	28	96	96	NUM
ap-10691	361	29	)	)	PUNCT
ap-10691	361	30	,	,	PUNCT
ap-10691	361	31	(	(	PUNCT
ap-10691	361	32	98	98	NUM
ap-10691	361	33	)	)	PUNCT
ap-10691	361	34	,	,	PUNCT
ap-10691	361	35	and	and	CCONJ
ap-10691	361	36	(	(	PUNCT
ap-10691	361	37	100	100	NUM
ap-10691	361	38	)	)	PUNCT
ap-10691	361	39	,	,	PUNCT
ap-10691	361	40	by	by	ADP
ap-10691	361	41	replacing	replace	VERB
ap-10691	361	42	kβ	kβ	ADP
ap-10691	361	43	with	with	ADP
ap-10691	361	44	kβ	kβ	NOUN
ap-10691	361	45	+	+	CCONJ
ap-10691	361	46	n	n	NOUN
ap-10691	361	47	and	and	CCONJ
ap-10691	361	48	l2	l2	NOUN
ap-10691	361	49	by	by	ADP
ap-10691	361	50	l2	l2	NOUN
ap-10691	361	51	+	+	PROPN
ap-10691	361	52	m	m	NOUN
ap-10691	361	53	with	with	ADP
ap-10691	361	54	n	n	CCONJ
ap-10691	361	55	,	,	PUNCT
ap-10691	361	56	m	m	PROPN
ap-10691	361	57	∈	∈	PROPN
ap-10691	361	58	z.	z.	PROPN
ap-10691	362	1	that	that	PRON
ap-10691	362	2	is	be	AUX
ap-10691	362	3	:	:	PUNCT
ap-10691	362	4	n±,i	n±,i	PROPN
ap-10691	362	5	n	n	CCONJ
ap-10691	362	6	,	,	PUNCT
ap-10691	362	7	m	m	VERB
ap-10691	362	8	:	:	PUNCT
ap-10691	362	9	=	=	PUNCT
ap-10691	363	1	n±	n±	ADJ
ap-10691	363	2	i	i	PRON
ap-10691	363	3	(	(	PUNCT
ap-10691	363	4	kβ	kβ	PROPN
ap-10691	363	5	→	→	SYM
ap-10691	363	6	kβ	kβ	NOUN
ap-10691	363	7	+	+	CCONJ
ap-10691	363	8	n	n	CCONJ
ap-10691	363	9	,	,	PUNCT
ap-10691	363	10	l2	l2	NOUN
ap-10691	363	11	→	→	SYM
ap-10691	363	12	l2	l2	NOUN
ap-10691	363	13	+	+	NOUN
ap-10691	363	14	m	m	NOUN
ap-10691	363	15	)	)	PUNCT
ap-10691	363	16	,	,	PUNCT
ap-10691	363	17	(	(	PUNCT
ap-10691	363	18	106	106	NUM
ap-10691	363	19	)	)	PUNCT
ap-10691	363	20	for	for	ADP
ap-10691	363	21	i	i	PRON
ap-10691	363	22	=	=	NOUN
ap-10691	363	23	1	1	NUM
ap-10691	363	24	,	,	PUNCT
ap-10691	363	25	.	.	PUNCT
ap-10691	363	26	.	.	PUNCT
ap-10691	363	27	.	.	PUNCT
ap-10691	364	1	,	,	PUNCT
ap-10691	364	2	4	4	X
ap-10691	364	3	.	.	PUNCT
ap-10691	365	1	similarly	similarly	ADV
ap-10691	365	2	to	to	ADP
ap-10691	365	3	the	the	DET
ap-10691	365	4	sphere	sphere	NOUN
ap-10691	365	5	case	case	NOUN
ap-10691	365	6	(	(	PUNCT
ap-10691	365	7	subsection	subsection	NOUN
ap-10691	365	8	3.4	3.4	NUM
ap-10691	365	9	)	)	PUNCT
ap-10691	365	10	,	,	PUNCT
ap-10691	365	11	we	we	PRON
ap-10691	365	12	can	can	AUX
ap-10691	365	13	consider	consider	VERB
ap-10691	365	14	index	index	NOUN
ap-10691	365	15	-	-	PUNCT
ap-10691	365	16	free	free	ADJ
ap-10691	365	17	operators	operator	NOUN
ap-10691	365	18	na	na	ADP
ap-10691	365	19	,	,	PUNCT
ap-10691	365	20	b	b	PROPN
ap-10691	365	21	defined	define	VERB
ap-10691	365	22	,	,	PUNCT
ap-10691	365	23	for	for	ADP
ap-10691	365	24	example	example	NOUN
ap-10691	365	25	,	,	PUNCT
ap-10691	365	26	in	in	ADP
ap-10691	365	27	terms	term	NOUN
ap-10691	365	28	of	of	ADP
ap-10691	365	29	the	the	DET
ap-10691	365	30	operators	operator	NOUN
ap-10691	366	1	n−,i	n−,i	PROPN
ap-10691	366	2	m	m	PROPN
ap-10691	366	3	,	,	PUNCT
ap-10691	366	4	n	n	CCONJ
ap-10691	366	5	for	for	ADP
ap-10691	366	6	all	all	DET
ap-10691	366	7	n	n	CCONJ
ap-10691	366	8	,	,	PUNCT
ap-10691	366	9	m	m	VERB
ap-10691	366	10	∈	∈	ADJ
ap-10691	366	11	z	z	NOUN
ap-10691	366	12	as	as	SCONJ
ap-10691	366	13	follows	follow	VERB
ap-10691	366	14	:	:	PUNCT
ap-10691	366	15	na	na	NOUN
ap-10691	366	16	,	,	PUNCT
ap-10691	366	17	b	b	NOUN
ap-10691	366	18	φm	φm	X
ap-10691	366	19	,	,	PUNCT
ap-10691	366	20	n	n	CCONJ
ap-10691	366	21	:	:	PUNCT
ap-10691	366	22	=	=	PUNCT
ap-10691	366	23	n−,i	n−,i	NUM
ap-10691	366	24	m	m	NOUN
ap-10691	366	25	,	,	PUNCT
ap-10691	366	26	n	n	PRON
ap-10691	366	27	φm	φm	X
ap-10691	366	28	,	,	PUNCT
ap-10691	366	29	n	n	CCONJ
ap-10691	366	30	,	,	PUNCT
ap-10691	366	31	a	a	PRON
ap-10691	366	32	,	,	PUNCT
ap-10691	366	33	b	b	NOUN
ap-10691	366	34	=	=	PUNCT
ap-10691	366	35	±1	±1	VERB
ap-10691	366	36	,	,	PUNCT
ap-10691	366	37	(	(	PUNCT
ap-10691	366	38	107	107	NUM
ap-10691	366	39	)	)	PUNCT
ap-10691	366	40	such	such	ADJ
ap-10691	366	41	that	that	SCONJ
ap-10691	366	42	n1,1	n1,1	PROPN
ap-10691	366	43	=	=	PUNCT
ap-10691	366	44	n−,3	n−,3	PROPN
ap-10691	366	45	m	m	PROPN
ap-10691	366	46	,	,	PUNCT
ap-10691	366	47	n	n	CCONJ
ap-10691	366	48	,	,	PUNCT
ap-10691	366	49	n	n	PROPN
ap-10691	366	50	1,−1	1,−1	NUM
ap-10691	366	51	=	=	PUNCT
ap-10691	367	1	n−,2	n−,2	NUM
ap-10691	367	2	m	m	PROPN
ap-10691	367	3	,	,	PUNCT
ap-10691	367	4	n	n	CCONJ
ap-10691	367	5	,	,	PUNCT
ap-10691	367	6	n−1,1	n−1,1	NOUN
ap-10691	367	7	=	=	NOUN
ap-10691	367	8	n−,4	n−,4	NUM
ap-10691	367	9	m	m	PROPN
ap-10691	367	10	,	,	PUNCT
ap-10691	367	11	n	n	CCONJ
ap-10691	367	12	,	,	PUNCT
ap-10691	367	13	and	and	CCONJ
ap-10691	367	14	n−1,−1	n−1,−1	ADV
ap-10691	367	15	=	=	SYM
ap-10691	367	16	n−,1	n−,1	PROPN
ap-10691	367	17	m	m	NOUN
ap-10691	367	18	,	,	PUNCT
ap-10691	367	19	n.	n.	NOUN
ap-10691	367	20	by	by	ADP
ap-10691	367	21	composing	compose	VERB
ap-10691	367	22	two	two	NUM
ap-10691	367	23	of	of	ADP
ap-10691	367	24	these	these	DET
ap-10691	367	25	operators	operator	NOUN
ap-10691	367	26	,	,	PUNCT
ap-10691	367	27	we	we	PRON
ap-10691	367	28	can	can	AUX
ap-10691	367	29	construct	construct	VERB
ap-10691	367	30	the	the	DET
ap-10691	367	31	shift	shift	NOUN
ap-10691	367	32	operators	operator	NOUN
ap-10691	367	33	,	,	PUNCT
ap-10691	367	34	defined	define	VERB
ap-10691	367	35	in	in	ADP
ap-10691	367	36	equation	equation	NOUN
ap-10691	367	37	(	(	PUNCT
ap-10691	367	38	22	22	NUM
ap-10691	367	39	)	)	PUNCT
ap-10691	367	40	,	,	PUNCT
ap-10691	367	41	which	which	PRON
ap-10691	367	42	move	move	VERB
ap-10691	367	43	only	only	ADV
ap-10691	367	44	in	in	ADP
ap-10691	367	45	a	a	DET
ap-10691	367	46	single	single	ADJ
ap-10691	367	47	direction	direction	NOUN
ap-10691	367	48	.	.	PUNCT
ap-10691	368	1	in	in	ADP
ap-10691	368	2	our	our	PRON
ap-10691	368	3	case	case	NOUN
ap-10691	368	4	,	,	PUNCT
ap-10691	368	5	we	we	PRON
ap-10691	368	6	choose	choose	VERB
ap-10691	368	7	the	the	DET
ap-10691	368	8	direction	direction	NOUN
ap-10691	368	9	along	along	ADP
ap-10691	368	10	kβ	kβ	PROPN
ap-10691	368	11	(	(	PUNCT
ap-10691	368	12	i.e.	i.e.	X
ap-10691	368	13	the	the	DET
ap-10691	368	14	n	n	NUM
ap-10691	368	15	direction	direction	NOUN
ap-10691	368	16	)	)	PUNCT
ap-10691	368	17	.	.	PUNCT
ap-10691	369	1	considering	consider	VERB
ap-10691	369	2	the	the	DET
ap-10691	369	3	composition	composition	NOUN
ap-10691	369	4	of	of	ADP
ap-10691	369	5	these	these	DET
ap-10691	369	6	operators	operator	NOUN
ap-10691	369	7	acting	act	VERB
ap-10691	369	8	as	as	ADP
ap-10691	369	9	na	na	PROPN
ap-10691	369	10	,	,	PUNCT
ap-10691	369	11	bφm	bφm	PROPN
ap-10691	369	12	,	,	PUNCT
ap-10691	369	13	n	n	NOUN
ap-10691	369	14	=	=	SYM
ap-10691	369	15	φm+a	φm+a	NOUN
ap-10691	369	16	,	,	PUNCT
ap-10691	369	17	n+b	n+b	NUM
ap-10691	369	18	,	,	PUNCT
ap-10691	369	19	where	where	SCONJ
ap-10691	369	20	φm	φm	X
ap-10691	369	21	,	,	PUNCT
ap-10691	369	22	n	n	PRON
ap-10691	369	23	∈	∈	NOUN
ap-10691	369	24	hξ	hξ	ADP
ap-10691	369	25	mk;n	mk;n	PROPN
ap-10691	369	26	,	,	PUNCT
ap-10691	369	27	m	m	PRON
ap-10691	369	28	,	,	PUNCT
ap-10691	369	29	we	we	PRON
ap-10691	369	30	obtain	obtain	VERB
ap-10691	369	31	that	that	DET
ap-10691	369	32	:	:	PUNCT
ap-10691	369	33	na	na	NOUN
ap-10691	369	34	,	,	PUNCT
ap-10691	369	35	bn−a	bn−a	PROPN
ap-10691	369	36	,	,	PUNCT
ap-10691	369	37	bφm	bφm	PROPN
ap-10691	369	38	,	,	PUNCT
ap-10691	369	39	n	n	NOUN
ap-10691	369	40	=	=	SYM
ap-10691	369	41	na	na	NOUN
ap-10691	369	42	,	,	PUNCT
ap-10691	369	43	bφm−a	bφm−a	NOUN
ap-10691	369	44	,	,	PUNCT
ap-10691	369	45	n+b	n+b	NUM
ap-10691	369	46	=	=	SYM
ap-10691	369	47	φm	φm	X
ap-10691	369	48	,	,	PUNCT
ap-10691	369	49	n+2b	n+2b	PROPN
ap-10691	369	50	,	,	PUNCT
ap-10691	369	51	(	(	PUNCT
ap-10691	369	52	108	108	NUM
ap-10691	369	53	)	)	PUNCT
ap-10691	369	54	with	with	ADP
ap-10691	369	55	a	a	DET
ap-10691	369	56	,	,	PUNCT
ap-10691	369	57	b	b	NOUN
ap-10691	369	58	=	=	PUNCT
ap-10691	369	59	±1	±1	VERB
ap-10691	369	60	.	.	PUNCT
ap-10691	370	1	equation	equation	NOUN
ap-10691	370	2	(	(	PUNCT
ap-10691	370	3	107	107	NUM
ap-10691	370	4	)	)	PUNCT
ap-10691	370	5	allows	allow	VERB
ap-10691	370	6	us	we	PRON
ap-10691	370	7	to	to	PART
ap-10691	370	8	define	define	VERB
ap-10691	370	9	the	the	DET
ap-10691	370	10	shift	shift	NOUN
ap-10691	370	11	operators	operator	NOUN
ap-10691	370	12	(	(	PUNCT
ap-10691	370	13	22	22	NUM
ap-10691	370	14	)	)	PUNCT
ap-10691	370	15	as	as	ADP
ap-10691	370	16	:	:	PUNCT
ap-10691	370	17	s±	s±	PROPN
ap-10691	370	18	:	:	PUNCT
ap-10691	370	19	=	=	PUNCT
ap-10691	370	20	na,±1	na,±1	PROPN
ap-10691	370	21	n−a,±1	n−a,±1	PROPN
ap-10691	370	22	,	,	PUNCT
ap-10691	370	23	(	(	PUNCT
ap-10691	370	24	109	109	NUM
ap-10691	370	25	)	)	PUNCT
ap-10691	370	26	such	such	ADJ
ap-10691	370	27	that	that	SCONJ
ap-10691	370	28	:	:	PUNCT
ap-10691	370	29	s±	s±	PROPN
ap-10691	370	30	:	:	PUNCT
ap-10691	370	31	hξ	hξ	PROPN
ap-10691	370	32	mk;m	mk;m	PROPN
ap-10691	370	33	,	,	PUNCT
ap-10691	370	34	n	n	CCONJ
ap-10691	370	35	→	→	X
ap-10691	370	36	hξ	hξ	PRON
ap-10691	370	37	mk;m	mk;m	PROPN
ap-10691	370	38	,	,	PUNCT
ap-10691	370	39	n±2	n±2	NUM
ap-10691	370	40	.	.	PUNCT
ap-10691	371	1	(	(	PUNCT
ap-10691	371	2	110	110	NUM
ap-10691	371	3	)	)	SYM
ap-10691	371	4	528	528	NUM
ap-10691	371	5	vol	vol	NOUN
ap-10691	371	6	.	.	PUNCT
ap-10691	372	1	65	65	NUM
ap-10691	372	2	no	no	NOUN
ap-10691	372	3	.	.	PUNCT
ap-10691	373	1	5/2025	5/2025	NUM
ap-10691	373	2	classical	classical	ADJ
ap-10691	373	3	and	and	CCONJ
ap-10691	373	4	quantum	quantum	ADJ
ap-10691	373	5	superintegrable	superintegrable	ADJ
ap-10691	373	6	systems	system	NOUN
ap-10691	373	7	on	on	ADP
ap-10691	373	8	the	the	DET
ap-10691	373	9	sphere	sphere	NOUN
ap-10691	373	10	.	.	PUNCT
ap-10691	373	11	.	.	PUNCT
ap-10691	373	12	.	.	PUNCT
ap-10691	374	1	taking	take	VERB
ap-10691	374	2	into	into	ADP
ap-10691	374	3	account	account	NOUN
ap-10691	374	4	equation	equation	NOUN
ap-10691	374	5	(	(	PUNCT
ap-10691	374	6	40	40	NUM
ap-10691	374	7	)	)	PUNCT
ap-10691	374	8	,	,	PUNCT
ap-10691	374	9	we	we	PRON
ap-10691	374	10	can	can	AUX
ap-10691	374	11	obtain	obtain	VERB
ap-10691	374	12	the	the	DET
ap-10691	374	13	shift	shift	NOUN
ap-10691	374	14	operators	operator	NOUN
ap-10691	374	15	s±2	s±2	NOUN
ap-10691	374	16	m	m	AUX
ap-10691	374	17	defined	define	VERB
ap-10691	374	18	in	in	ADP
ap-10691	374	19	equation	equation	NOUN
ap-10691	374	20	(	(	PUNCT
ap-10691	374	21	23	23	NUM
ap-10691	374	22	)	)	PUNCT
ap-10691	374	23	as	as	ADP
ap-10691	374	24	:	:	PUNCT
ap-10691	374	25	s±2	s±2	NOUN
ap-10691	374	26	m	m	VERB
ap-10691	374	27	=	=	PUNCT
ap-10691	374	28	(	(	PUNCT
ap-10691	374	29	s±)m	s±)m	X
ap-10691	374	30	.	.	PUNCT
ap-10691	375	1	(	(	PUNCT
ap-10691	375	2	111	111	NUM
ap-10691	375	3	)	)	PUNCT
ap-10691	375	4	thus	thus	ADV
ap-10691	375	5	,	,	PUNCT
ap-10691	375	6	together	together	ADV
ap-10691	375	7	with	with	ADP
ap-10691	375	8	the	the	DET
ap-10691	375	9	operators	operator	NOUN
ap-10691	375	10	l±	l±	VERB
ap-10691	375	11	±2n	±2n	PROPN
ap-10691	375	12	(	(	PUNCT
ap-10691	375	13	equation	equation	NOUN
ap-10691	375	14	(	(	PUNCT
ap-10691	375	15	23	23	NUM
ap-10691	375	16	)	)	PUNCT
ap-10691	375	17	)	)	PUNCT
ap-10691	375	18	and	and	CCONJ
ap-10691	375	19	s±2	s±2	NOUN
ap-10691	375	20	m	m	VERB
ap-10691	375	21	(	(	PUNCT
ap-10691	375	22	equation	equation	NOUN
ap-10691	375	23	(	(	PUNCT
ap-10691	375	24	111	111	NUM
ap-10691	375	25	)	)	PUNCT
ap-10691	375	26	)	)	PUNCT
ap-10691	375	27	,	,	PUNCT
ap-10691	375	28	we	we	PRON
ap-10691	375	29	can	can	AUX
ap-10691	375	30	construct	construct	VERB
ap-10691	375	31	the	the	DET
ap-10691	375	32	symmetries	symmetry	NOUN
ap-10691	375	33	x±	x±	PROPN
ap-10691	376	1	(	(	PUNCT
ap-10691	376	2	equation	equation	NOUN
ap-10691	376	3	(	(	PUNCT
ap-10691	376	4	15	15	NUM
ap-10691	376	5	)	)	PUNCT
ap-10691	376	6	)	)	PUNCT
ap-10691	376	7	,	,	PUNCT
ap-10691	376	8	that	that	PRON
ap-10691	376	9	commute	commute	VERB
ap-10691	376	10	with	with	ADP
ap-10691	376	11	the	the	DET
ap-10691	376	12	hamiltonian	hamiltonian	NOUN
ap-10691	376	13	.	.	PUNCT
ap-10691	377	1	this	this	PRON
ap-10691	377	2	allows	allow	VERB
ap-10691	377	3	us	we	PRON
ap-10691	377	4	to	to	PART
ap-10691	377	5	prove	prove	VERB
ap-10691	377	6	that	that	SCONJ
ap-10691	377	7	the	the	DET
ap-10691	377	8	hamiltonian	hamiltonian	ADJ
ap-10691	377	9	system	system	NOUN
ap-10691	377	10	hk	hk	PROPN
ap-10691	377	11	(	(	PUNCT
ap-10691	377	12	equation	equation	NOUN
ap-10691	377	13	(	(	PUNCT
ap-10691	377	14	89	89	NUM
ap-10691	377	15	)	)	PUNCT
ap-10691	377	16	)	)	PUNCT
ap-10691	377	17	is	be	AUX
ap-10691	377	18	superintegrable	superintegrable	ADJ
ap-10691	377	19	whenever	whenever	SCONJ
ap-10691	377	20	k	k	PROPN
ap-10691	377	21	=	=	VERB
ap-10691	377	22	m	m	VERB
ap-10691	377	23	n	n	VERB
ap-10691	377	24	is	be	AUX
ap-10691	377	25	a	a	DET
ap-10691	377	26	rational	rational	ADJ
ap-10691	377	27	number	number	NOUN
ap-10691	377	28	.	.	PUNCT
ap-10691	378	1	as	as	SCONJ
ap-10691	378	2	mentioned	mention	VERB
ap-10691	378	3	in	in	ADP
ap-10691	378	4	the	the	DET
ap-10691	378	5	ttw	ttw	NOUN
ap-10691	378	6	so(3)-hamiltonian	so(3)-hamiltonian	PROPN
ap-10691	378	7	case	case	NOUN
ap-10691	378	8	,	,	PUNCT
ap-10691	378	9	we	we	PRON
ap-10691	378	10	also	also	ADV
ap-10691	378	11	find	find	VERB
ap-10691	378	12	that	that	SCONJ
ap-10691	378	13	[	[	X
ap-10691	378	14	x+	x+	ADJ
ap-10691	378	15	,	,	PUNCT
ap-10691	378	16	x−	x−	PROPN
ap-10691	378	17	]	]	X
ap-10691	378	18	̸=	̸=	PROPN
ap-10691	378	19	0	0	NUM
ap-10691	378	20	.	.	PUNCT
ap-10691	379	1	by	by	ADP
ap-10691	379	2	evaluating	evaluate	VERB
ap-10691	379	3	the	the	DET
ap-10691	379	4	double	double	ADJ
ap-10691	379	5	commutators	commutator	NOUN
ap-10691	380	1	[	[	X
ap-10691	380	2	x±	x±	PROPN
ap-10691	380	3	,	,	PUNCT
ap-10691	381	1	[	[	X
ap-10691	381	2	x+	x+	ADJ
ap-10691	381	3	,	,	PUNCT
ap-10691	381	4	x−	x−	PROPN
ap-10691	381	5	]	]	X
ap-10691	381	6	]	]	X
ap-10691	381	7	,	,	PUNCT
ap-10691	381	8	one	one	PRON
ap-10691	381	9	paves	pave	VERB
ap-10691	381	10	the	the	DET
ap-10691	381	11	way	way	NOUN
ap-10691	381	12	for	for	ADP
ap-10691	381	13	constructing	construct	VERB
ap-10691	381	14	the	the	DET
ap-10691	381	15	algebra	algebra	NOUN
ap-10691	381	16	of	of	ADP
ap-10691	381	17	integrals	integral	NOUN
ap-10691	381	18	of	of	ADP
ap-10691	381	19	motion	motion	NOUN
ap-10691	381	20	.	.	PUNCT
ap-10691	382	1	incidentally	incidentally	ADV
ap-10691	382	2	,	,	PUNCT
ap-10691	382	3	[	[	X
ap-10691	382	4	33	33	NUM
ap-10691	382	5	]	]	PUNCT
ap-10691	382	6	shows	show	VERB
ap-10691	382	7	that	that	SCONJ
ap-10691	382	8	,	,	PUNCT
ap-10691	382	9	for	for	ADP
ap-10691	382	10	both	both	DET
ap-10691	382	11	initial	initial	ADJ
ap-10691	382	12	hamiltonians	hamiltonian	NOUN
ap-10691	382	13	(	(	PUNCT
ap-10691	382	14	so(3	so(3	NOUN
ap-10691	382	15	)	)	PUNCT
ap-10691	382	16	and	and	CCONJ
ap-10691	382	17	so(2	so(2	NOUN
ap-10691	382	18	,	,	PUNCT
ap-10691	382	19	1	1	NUM
ap-10691	382	20	)	)	PUNCT
ap-10691	382	21	,	,	PUNCT
ap-10691	382	22	when	when	SCONJ
ap-10691	382	23	k	k	PROPN
ap-10691	382	24	=	=	SYM
ap-10691	382	25	1	1	NUM
ap-10691	382	26	,	,	PUNCT
ap-10691	382	27	the	the	DET
ap-10691	382	28	algebra	algebra	NOUN
ap-10691	382	29	of	of	ADP
ap-10691	382	30	integrals	integral	NOUN
ap-10691	382	31	of	of	ADP
ap-10691	382	32	motion	motion	NOUN
ap-10691	382	33	coincides	coincide	VERB
ap-10691	382	34	with	with	ADP
ap-10691	382	35	the	the	DET
ap-10691	382	36	racah	racah	NOUN
ap-10691	382	37	algebra	algebra	PROPN
ap-10691	382	38	r(3	r(3	NOUN
ap-10691	382	39	)	)	PUNCT
ap-10691	382	40	.	.	PUNCT
ap-10691	383	1	furthermore	furthermore	ADV
ap-10691	383	2	,	,	PUNCT
ap-10691	383	3	in	in	ADP
ap-10691	383	4	[	[	PUNCT
ap-10691	383	5	34	34	NUM
ap-10691	383	6	]	]	X
ap-10691	383	7	a	a	DET
ap-10691	383	8	new	new	ADJ
ap-10691	383	9	algebraic	algebraic	ADJ
ap-10691	383	10	method	method	NOUN
ap-10691	383	11	to	to	PART
ap-10691	383	12	describe	describe	VERB
ap-10691	383	13	the	the	DET
ap-10691	383	14	symmetry	symmetry	NOUN
ap-10691	383	15	of	of	ADP
ap-10691	383	16	a	a	DET
ap-10691	383	17	quadratically	quadratically	ADV
ap-10691	383	18	superintegrable	superintegrable	ADJ
ap-10691	383	19	system	system	NOUN
ap-10691	383	20	on	on	ADP
ap-10691	383	21	the	the	DET
ap-10691	383	22	two	two	NUM
ap-10691	383	23	-	-	PUNCT
ap-10691	383	24	spherecommonly	spherecommonly	ADV
ap-10691	383	25	associated	associate	VERB
ap-10691	383	26	with	with	ADP
ap-10691	383	27	r(3	r(3	NOUN
ap-10691	383	28	)	)	PUNCT
ap-10691	383	29	.	.	PUNCT
ap-10691	384	1	instead	instead	ADV
ap-10691	384	2	of	of	ADP
ap-10691	384	3	relying	rely	VERB
ap-10691	384	4	on	on	ADP
ap-10691	384	5	explicit	explicit	ADJ
ap-10691	384	6	operator	operator	NOUN
ap-10691	384	7	realisations	realisation	NOUN
ap-10691	384	8	,	,	PUNCT
ap-10691	384	9	the	the	DET
ap-10691	384	10	symmetry	symmetry	NOUN
ap-10691	384	11	algebra	algebra	NOUN
ap-10691	384	12	is	be	AUX
ap-10691	384	13	built	build	VERB
ap-10691	384	14	directly	directly	ADV
ap-10691	384	15	from	from	ADP
ap-10691	384	16	the	the	DET
ap-10691	384	17	enveloping	enveloping	NOUN
ap-10691	384	18	algebra	algebra	NOUN
ap-10691	384	19	of	of	ADP
ap-10691	384	20	su(3	su(3	PROPN
ap-10691	384	21	)	)	PUNCT
ap-10691	384	22	,	,	PUNCT
ap-10691	384	23	using	use	VERB
ap-10691	384	24	polynomials	polynomial	NOUN
ap-10691	384	25	of	of	ADP
ap-10691	384	26	degrees	degree	NOUN
ap-10691	384	27	2–4	2–4	NUM
ap-10691	384	28	in	in	ADP
ap-10691	384	29	a	a	DET
ap-10691	384	30	maximal	maximal	ADJ
ap-10691	384	31	abelian	abelian	ADJ
ap-10691	384	32	subalgebra	subalgebra	NOUN
ap-10691	384	33	.	.	PUNCT
ap-10691	385	1	this	this	PRON
ap-10691	385	2	leads	lead	VERB
ap-10691	385	3	to	to	ADP
ap-10691	385	4	a	a	DET
ap-10691	385	5	new	new	ADJ
ap-10691	385	6	six	six	NUM
ap-10691	385	7	-	-	PUNCT
ap-10691	385	8	dimensional	dimensional	ADJ
ap-10691	385	9	cubic	cubic	ADJ
ap-10691	385	10	algebra	algebra	NOUN
ap-10691	385	11	with	with	ADP
ap-10691	385	12	integer	integer	NOUN
ap-10691	385	13	structure	structure	NOUN
ap-10691	385	14	constants	constant	NOUN
ap-10691	385	15	,	,	PUNCT
ap-10691	385	16	which	which	PRON
ap-10691	385	17	in	in	ADP
ap-10691	385	18	specific	specific	ADJ
ap-10691	385	19	realisations	realisation	NOUN
ap-10691	385	20	reduces	reduce	VERB
ap-10691	385	21	to	to	ADP
ap-10691	385	22	r(3	r(3	NOUN
ap-10691	385	23	)	)	PUNCT
ap-10691	385	24	.	.	PUNCT
ap-10691	386	1	moreover	moreover	ADV
ap-10691	386	2	,	,	PUNCT
ap-10691	386	3	a	a	DET
ap-10691	386	4	contraction	contraction	NOUN
ap-10691	386	5	of	of	ADP
ap-10691	386	6	this	this	DET
ap-10691	386	7	cubic	cubic	ADJ
ap-10691	386	8	algebra	algebra	NOUN
ap-10691	386	9	to	to	ADP
ap-10691	386	10	the	the	DET
ap-10691	386	11	symmetry	symmetry	NOUN
ap-10691	386	12	algebra	algebra	NOUN
ap-10691	386	13	of	of	ADP
ap-10691	386	14	a	a	DET
ap-10691	386	15	smorodinsky	smorodinsky	NOUN
ap-10691	386	16	-	-	PUNCT
ap-10691	386	17	winternitz	winternitz	NOUN
ap-10691	386	18	model	model	NOUN
ap-10691	386	19	on	on	ADP
ap-10691	386	20	the	the	DET
ap-10691	386	21	sphere	sphere	NOUN
ap-10691	386	22	is	be	AUX
ap-10691	386	23	shown	show	VERB
ap-10691	386	24	.	.	PUNCT
ap-10691	387	1	in	in	ADP
ap-10691	387	2	a	a	DET
ap-10691	387	3	recent	recent	ADJ
ap-10691	387	4	work	work	NOUN
ap-10691	387	5	[	[	X
ap-10691	387	6	35	35	NUM
ap-10691	387	7	]	]	PUNCT
ap-10691	387	8	,	,	PUNCT
ap-10691	387	9	it	it	PRON
ap-10691	387	10	was	be	AUX
ap-10691	387	11	demonstrated	demonstrate	VERB
ap-10691	387	12	that	that	SCONJ
ap-10691	387	13	for	for	ADP
ap-10691	387	14	integer	integer	NOUN
ap-10691	387	15	values	value	NOUN
ap-10691	387	16	of	of	ADP
ap-10691	387	17	the	the	DET
ap-10691	387	18	ttw	ttw	PROPN
ap-10691	387	19	parameter	parameter	PROPN
ap-10691	387	20	k	k	PROPN
ap-10691	387	21	,	,	PUNCT
ap-10691	387	22	the	the	DET
ap-10691	387	23	ttwhamiltonian	ttwhamiltonian	ADJ
ap-10691	387	24	,	,	PUNCT
ap-10691	387	25	together	together	ADV
ap-10691	387	26	with	with	ADP
ap-10691	387	27	two	two	NUM
ap-10691	387	28	independent	independent	ADJ
ap-10691	387	29	integrals	integral	NOUN
ap-10691	387	30	of	of	ADP
ap-10691	387	31	motion	motion	NOUN
ap-10691	387	32	and	and	CCONJ
ap-10691	387	33	their	their	PRON
ap-10691	387	34	commutator	commutator	NOUN
ap-10691	387	35	generate	generate	VERB
ap-10691	387	36	a	a	DET
ap-10691	387	37	finitedimensional	finitedimensional	ADJ
ap-10691	387	38	polynomial	polynomial	ADJ
ap-10691	387	39	algebra	algebra	NOUN
ap-10691	387	40	of	of	ADP
ap-10691	387	41	k	k	PROPN
ap-10691	387	42	+	+	CCONJ
ap-10691	387	43	1	1	NUM
ap-10691	387	44	order	order	NOUN
ap-10691	387	45	.	.	PUNCT
ap-10691	388	1	this	this	DET
ap-10691	388	2	algebra	algebra	NOUN
ap-10691	388	3	exhibits	exhibit	VERB
ap-10691	388	4	polynomial	polynomial	ADJ
ap-10691	388	5	,	,	PUNCT
ap-10691	388	6	rather	rather	ADV
ap-10691	388	7	than	than	ADP
ap-10691	388	8	linear	linear	ADJ
ap-10691	388	9	,	,	PUNCT
ap-10691	388	10	closure	closure	NOUN
ap-10691	388	11	and	and	CCONJ
ap-10691	388	12	is	be	AUX
ap-10691	388	13	referred	refer	VERB
ap-10691	388	14	to	to	ADP
ap-10691	388	15	as	as	ADP
ap-10691	388	16	the	the	DET
ap-10691	388	17	hidden	hide	VERB
ap-10691	388	18	algebra	algebra	NOUN
ap-10691	388	19	g(k	g(k	NOUN
ap-10691	388	20	)	)	PUNCT
ap-10691	388	21	.	.	PUNCT
ap-10691	389	1	for	for	ADP
ap-10691	389	2	k	k	PROPN
ap-10691	389	3	=	=	SYM
ap-10691	389	4	1	1	NUM
ap-10691	389	5	,	,	PUNCT
ap-10691	389	6	2	2	NUM
ap-10691	389	7	,	,	PUNCT
ap-10691	389	8	3	3	NUM
ap-10691	389	9	,	,	PUNCT
ap-10691	389	10	4	4	NUM
ap-10691	389	11	the	the	DET
ap-10691	389	12	polynomial	polynomial	ADJ
ap-10691	389	13	structure	structure	NOUN
ap-10691	389	14	has	have	AUX
ap-10691	389	15	been	be	AUX
ap-10691	389	16	explicitly	explicitly	ADV
ap-10691	389	17	established	establish	VERB
ap-10691	389	18	,	,	PUNCT
ap-10691	389	19	and	and	CCONJ
ap-10691	389	20	it	it	PRON
ap-10691	389	21	is	be	AUX
ap-10691	389	22	conjectured	conjecture	VERB
ap-10691	389	23	that	that	SCONJ
ap-10691	389	24	the	the	DET
ap-10691	389	25	same	same	ADJ
ap-10691	389	26	holds	hold	VERB
ap-10691	389	27	for	for	ADP
ap-10691	389	28	all	all	DET
ap-10691	389	29	positive	positive	ADJ
ap-10691	389	30	integer	integer	NOUN
ap-10691	389	31	k.	k.	PROPN
ap-10691	390	1	the	the	DET
ap-10691	390	2	polynomial	polynomial	ADJ
ap-10691	390	3	degree	degree	NOUN
ap-10691	390	4	increases	increase	NOUN
ap-10691	390	5	with	with	ADP
ap-10691	390	6	k	k	NOUN
ap-10691	390	7	,	,	PUNCT
ap-10691	390	8	reflecting	reflect	VERB
ap-10691	390	9	the	the	DET
ap-10691	390	10	higher	high	ADJ
ap-10691	390	11	-	-	PUNCT
ap-10691	390	12	order	order	NOUN
ap-10691	390	13	nature	nature	NOUN
ap-10691	390	14	of	of	ADP
ap-10691	390	15	the	the	DET
ap-10691	390	16	additional	additional	ADJ
ap-10691	390	17	integral	integral	NOUN
ap-10691	390	18	of	of	ADP
ap-10691	390	19	motion	motion	NOUN
ap-10691	390	20	.	.	PUNCT
ap-10691	391	1	the	the	DET
ap-10691	391	2	specific	specific	ADJ
ap-10691	391	3	cases	case	NOUN
ap-10691	391	4	we	we	PRON
ap-10691	391	5	have	have	AUX
ap-10691	391	6	analysed	analyse	VERB
ap-10691	391	7	in	in	ADP
ap-10691	391	8	this	this	DET
ap-10691	391	9	paper	paper	NOUN
ap-10691	391	10	fall	fall	NOUN
ap-10691	391	11	within	within	ADP
ap-10691	391	12	this	this	DET
ap-10691	391	13	framework	framework	NOUN
ap-10691	391	14	and	and	CCONJ
ap-10691	391	15	will	will	AUX
ap-10691	391	16	be	be	AUX
ap-10691	391	17	the	the	DET
ap-10691	391	18	subject	subject	NOUN
ap-10691	391	19	of	of	ADP
ap-10691	391	20	a	a	DET
ap-10691	391	21	forthcoming	forthcoming	ADJ
ap-10691	391	22	publication	publication	NOUN
ap-10691	391	23	elsewhere	elsewhere	ADV
ap-10691	391	24	.	.	PUNCT
ap-10691	392	1	5.2	5.2	NUM
ap-10691	392	2	.	.	PUNCT
ap-10691	393	1	associated	associate	VERB
ap-10691	393	2	classical	classical	ADJ
ap-10691	393	3	hamiltonian	hamiltonian	NOUN
ap-10691	393	4	the	the	DET
ap-10691	393	5	classical	classical	ADJ
ap-10691	393	6	counterpart	counterpart	NOUN
ap-10691	393	7	of	of	ADP
ap-10691	393	8	the	the	DET
ap-10691	393	9	hamiltonian	hamiltonian	NOUN
ap-10691	393	10	(	(	PUNCT
ap-10691	393	11	89	89	NUM
ap-10691	393	12	)	)	PUNCT
ap-10691	393	13	,	,	PUNCT
ap-10691	393	14	including	include	VERB
ap-10691	393	15	the	the	DET
ap-10691	393	16	“	"	PUNCT
ap-10691	393	17	coupling	couple	VERB
ap-10691	393	18	constant	constant	ADJ
ap-10691	393	19	”	"	PUNCT
ap-10691	393	20	k	k	NOUN
ap-10691	393	21	,	,	PUNCT
ap-10691	393	22	is	be	AUX
ap-10691	393	23	:	:	PUNCT
ap-10691	393	24	hk	hk	PROPN
ap-10691	393	25	=	=	PUNCT
ap-10691	393	26	p2	p2	PROPN
ap-10691	393	27	ξ	ξ	X
ap-10691	393	28	−	−	NOUN
ap-10691	393	29	l22	l22	NOUN
ap-10691	393	30	cosh2	cosh2	PUNCT
ap-10691	394	1	ξ	ξ	X
ap-10691	394	2	+	+	SYM
ap-10691	394	3	k2	k2	ADJ
ap-10691	394	4	hθ	hθ	NOUN
ap-10691	394	5	sinh2ξ	sinh2ξ	PROPN
ap-10691	394	6	,	,	PUNCT
ap-10691	394	7	(	(	PUNCT
ap-10691	394	8	112	112	NUM
ap-10691	394	9	)	)	PUNCT
ap-10691	394	10	where	where	SCONJ
ap-10691	394	11	hθ	hθ	PROPN
ap-10691	394	12	is	be	AUX
ap-10691	394	13	given	give	VERB
ap-10691	394	14	by	by	ADP
ap-10691	394	15	equation	equation	NOUN
ap-10691	394	16	(	(	PUNCT
ap-10691	394	17	69	69	NUM
ap-10691	394	18	)	)	PUNCT
ap-10691	394	19	,	,	PUNCT
ap-10691	394	20	and	and	CCONJ
ap-10691	394	21	hξ	hξ	PROPN
ap-10691	394	22	mk	mk	PROPN
ap-10691	394	23	is	be	AUX
ap-10691	394	24	defined	define	VERB
ap-10691	394	25	by	by	ADP
ap-10691	394	26	:	:	PUNCT
ap-10691	394	27	hξ	hξ	PROPN
ap-10691	394	28	mk	mk	PROPN
ap-10691	394	29	=	=	PUNCT
ap-10691	394	30	p2	p2	PROPN
ap-10691	395	1	ξ	ξ	X
ap-10691	395	2	−	−	NOUN
ap-10691	395	3	l22	l22	NOUN
ap-10691	395	4	cosh2	cosh2	X
ap-10691	396	1	ξ	ξ	X
ap-10691	396	2	+	+	NUM
ap-10691	396	3	m2	m2	PROPN
ap-10691	396	4	k	k	PROPN
ap-10691	396	5	sinh2ξ	sinh2ξ	PROPN
ap-10691	396	6	,	,	PUNCT
ap-10691	396	7	(	(	PUNCT
ap-10691	396	8	113	113	NUM
ap-10691	396	9	)	)	PUNCT
ap-10691	396	10	with	with	ADP
ap-10691	396	11	m	m	PROPN
ap-10691	396	12	2	2	NUM
ap-10691	396	13	k	k	NOUN
ap-10691	396	14	=	=	SYM
ap-10691	396	15	k2	k2	PROPN
ap-10691	396	16	hθ	hθ	PROPN
ap-10691	396	17	.	.	PUNCT
ap-10691	397	1	it	it	PRON
ap-10691	397	2	is	be	AUX
ap-10691	397	3	worth	worth	ADJ
ap-10691	397	4	noting	note	VERB
ap-10691	397	5	that	that	SCONJ
ap-10691	397	6	,	,	PUNCT
ap-10691	397	7	unlike	unlike	ADP
ap-10691	397	8	in	in	ADP
ap-10691	397	9	the	the	DET
ap-10691	397	10	quantum	quantum	NOUN
ap-10691	397	11	case	case	NOUN
ap-10691	397	12	,	,	PUNCT
ap-10691	397	13	it	it	PRON
ap-10691	397	14	now	now	ADV
ap-10691	397	15	depends	depend	VERB
ap-10691	397	16	on	on	ADP
ap-10691	397	17	θ	θ	PROPN
ap-10691	397	18	.	.	PROPN
ap-10691	397	19	for	for	ADP
ap-10691	397	20	hθ	hθ	PROPN
ap-10691	397	21	(	(	PUNCT
ap-10691	397	22	equation	equation	NOUN
ap-10691	397	23	(	(	PUNCT
ap-10691	397	24	69	69	NUM
ap-10691	397	25	)	)	PUNCT
ap-10691	397	26	)	)	PUNCT
ap-10691	397	27	,	,	PUNCT
ap-10691	397	28	we	we	PRON
ap-10691	397	29	obtained	obtain	VERB
ap-10691	397	30	the	the	DET
ap-10691	397	31	ladder	ladder	NOUN
ap-10691	397	32	functions	function	NOUN
ap-10691	397	33	l±	l±	X
ap-10691	397	34	(	(	PUNCT
ap-10691	397	35	equation	equation	NOUN
ap-10691	397	36	(	(	PUNCT
ap-10691	397	37	71	71	NUM
ap-10691	397	38	)	)	PUNCT
ap-10691	397	39	)	)	PUNCT
ap-10691	397	40	in	in	ADP
ap-10691	397	41	subsection	subsection	NOUN
ap-10691	397	42	4.1	4.1	NUM
ap-10691	397	43	,	,	PUNCT
ap-10691	397	44	and	and	CCONJ
ap-10691	397	45	for	for	ADP
ap-10691	397	46	hmk	hmk	NOUN
ap-10691	397	47	ξ	ξ	PROPN
ap-10691	397	48	(	(	PUNCT
ap-10691	397	49	equation	equation	NOUN
ap-10691	397	50	(	(	PUNCT
ap-10691	397	51	113	113	NUM
ap-10691	397	52	)	)	PUNCT
ap-10691	397	53	)	)	PUNCT
ap-10691	398	1	we	we	PRON
ap-10691	398	2	have	have	VERB
ap-10691	398	3	the	the	DET
ap-10691	398	4	shift	shift	NOUN
ap-10691	398	5	functions	function	NOUN
ap-10691	398	6	:	:	PUNCT
ap-10691	398	7	s±	s±	PROPN
ap-10691	398	8	=	=	SYM
ap-10691	398	9	(	(	PUNCT
ap-10691	398	10	−l2	−l2	PROPN
ap-10691	398	11	tanh	tanh	PROPN
ap-10691	398	12	ξ	ξ	X
ap-10691	398	13	∓	∓	PROPN
ap-10691	398	14	mk	mk	NOUN
ap-10691	398	15	coth	coth	PROPN
ap-10691	398	16	ξ	ξ	PROPN
ap-10691	398	17	+	+	PUNCT
ap-10691	398	18	ipξ	ipξ	PROPN
ap-10691	398	19	)	)	PUNCT
ap-10691	398	20	×	×	NOUN
ap-10691	398	21	(	(	PUNCT
ap-10691	398	22	l2	l2	NOUN
ap-10691	398	23	tanh	tanh	PROPN
ap-10691	398	24	ξ	ξ	PROPN
ap-10691	398	25	∓	∓	PROPN
ap-10691	398	26	mk	mk	NOUN
ap-10691	398	27	coth	coth	PROPN
ap-10691	398	28	ξ	ξ	PROPN
ap-10691	398	29	+	+	PUNCT
ap-10691	398	30	ipξ	ipξ	PROPN
ap-10691	398	31	)	)	PUNCT
ap-10691	398	32	.	.	PUNCT
ap-10691	399	1	(	(	PUNCT
ap-10691	399	2	114	114	NUM
ap-10691	399	3	)	)	PUNCT
ap-10691	399	4	both	both	DET
ap-10691	399	5	operators	operator	NOUN
ap-10691	399	6	satisfy	satisfy	VERB
ap-10691	399	7	:	:	PUNCT
ap-10691	399	8	{	{	PUNCT
ap-10691	399	9	hk	hk	PROPN
ap-10691	399	10	,	,	PUNCT
ap-10691	399	11	s±	s±	PROPN
ap-10691	399	12	}	}	PUNCT
ap-10691	399	13	=	=	SYM
ap-10691	399	14	±α	±α	PROPN
ap-10691	399	15	s±	s±	ADJ
ap-10691	399	16	,	,	PUNCT
ap-10691	399	17	{	{	PUNCT
ap-10691	399	18	h	h	NOUN
ap-10691	399	19	,	,	PUNCT
ap-10691	399	20	l±	l±	PROPN
ap-10691	399	21	}	}	PUNCT
ap-10691	399	22	=	=	SYM
ap-10691	399	23	∓kα	∓kα	PROPN
ap-10691	399	24	l±	l±	PROPN
ap-10691	399	25	,	,	PUNCT
ap-10691	399	26	(	(	PUNCT
ap-10691	399	27	115	115	NUM
ap-10691	399	28	)	)	PUNCT
ap-10691	399	29	with	with	ADP
ap-10691	399	30	:	:	PUNCT
ap-10691	399	31	α	α	X
ap-10691	399	32	=	=	PUNCT
ap-10691	399	33	4mk	4mk	NOUN
ap-10691	400	1	i	i	PRON
ap-10691	400	2	sinh2	sinh2	NOUN
ap-10691	401	1	ξ	ξ	X
ap-10691	401	2	.	.	PUNCT
ap-10691	402	1	(	(	PUNCT
ap-10691	402	2	116	116	NUM
ap-10691	402	3	)	)	PUNCT
ap-10691	402	4	then	then	ADV
ap-10691	402	5	,	,	PUNCT
ap-10691	402	6	the	the	DET
ap-10691	402	7	functions	function	NOUN
ap-10691	402	8	x±	x±	PROPN
ap-10691	403	1	:	:	PUNCT
ap-10691	403	2	=	=	SYM
ap-10691	403	3	(	(	PUNCT
ap-10691	403	4	s±)m(l±)n	s±)m(l±)n	NOUN
ap-10691	403	5	satisfy	satisfy	NOUN
ap-10691	403	6	:	:	PUNCT
ap-10691	403	7	{	{	PUNCT
ap-10691	403	8	hk	hk	PROPN
ap-10691	403	9	,	,	PUNCT
ap-10691	403	10	x±	x±	PROPN
ap-10691	403	11	}	}	PUNCT
ap-10691	404	1	=	=	SYM
ap-10691	404	2	0	0	PUNCT
ap-10691	405	1	if	if	SCONJ
ap-10691	405	2	k	k	PROPN
ap-10691	405	3	=	=	VERB
ap-10691	405	4	m	m	VERB
ap-10691	405	5	n	n	NUM
ap-10691	405	6	∈	∈	PROPN
ap-10691	405	7	q.	q.	NOUN
ap-10691	405	8	(	(	PUNCT
ap-10691	405	9	117	117	NUM
ap-10691	405	10	)	)	PUNCT
ap-10691	405	11	thus	thus	ADV
ap-10691	405	12	,	,	PUNCT
ap-10691	405	13	for	for	ADP
ap-10691	405	14	each	each	DET
ap-10691	405	15	rational	rational	ADJ
ap-10691	405	16	value	value	NOUN
ap-10691	405	17	of	of	ADP
ap-10691	405	18	k	k	NOUN
ap-10691	405	19	,	,	PUNCT
ap-10691	405	20	there	there	PRON
ap-10691	405	21	exist	exist	VERB
ap-10691	405	22	two	two	NUM
ap-10691	405	23	independent	independent	ADJ
ap-10691	405	24	integrals	integral	NOUN
ap-10691	405	25	of	of	ADP
ap-10691	405	26	motion	motion	NOUN
ap-10691	405	27	,	,	PUNCT
ap-10691	405	28	explicitly	explicitly	ADV
ap-10691	405	29	given	give	VERB
ap-10691	405	30	by	by	ADP
ap-10691	405	31	:	:	PUNCT
ap-10691	405	32	x±	x±	PROPN
ap-10691	406	1	=	=	PRON
ap-10691	406	2	(	(	PUNCT
ap-10691	406	3	m2	m2	PROPN
ap-10691	406	4	k	k	PROPN
ap-10691	406	5	coth2	coth2	PROPN
ap-10691	406	6	ξ	ξ	X
ap-10691	407	1	−	−	PROPN
ap-10691	407	2	l22	l22	NOUN
ap-10691	407	3	tanh2	tanh2	NOUN
ap-10691	407	4	ξ	ξ	PROPN
ap-10691	407	5	∓2imkpξ	∓2imkpξ	NOUN
ap-10691	407	6	coth	coth	PROPN
ap-10691	407	7	ξ	ξ	PROPN
ap-10691	407	8	−	−	PROPN
ap-10691	407	9	p2	p2	X
ap-10691	407	10	ξ	ξ	PROPN
ap-10691	407	11	)	)	PUNCT
ap-10691	407	12	m	m	PROPN
ap-10691	407	13	×	×	NOUN
ap-10691	407	14			PROPN
ap-10691	407	15	b2	b2	NOUN
ap-10691	407	16	−	−	PROPN
ap-10691	407	17	a2√	a2√	PROPN
ap-10691	407	18	a2	a2	PROPN
ap-10691	407	19	cos2	cos2	PROPN
ap-10691	407	20	θ	θ	PROPN
ap-10691	407	21	+	+	CCONJ
ap-10691	407	22	b2	b2	NOUN
ap-10691	407	23	sin2	sin2	NOUN
ap-10691	407	24	θ	θ	PROPN
ap-10691	407	25	+	+	CCONJ
ap-10691	407	26	p2	p2	PROPN
ap-10691	407	27	θ	θ	PROPN
ap-10691	407	28	+	+	CCONJ
ap-10691	407	29	cos	cos	ADJ
ap-10691	407	30	2θ	2θ	NUM
ap-10691	407	31	×	×	NOUN
ap-10691	407	32	√	√	NOUN
ap-10691	407	33	a2	a2	PROPN
ap-10691	407	34	cos2	cos2	PROPN
ap-10691	407	35	θ	θ	PROPN
ap-10691	407	36	+	+	CCONJ
ap-10691	407	37	b2	b2	NOUN
ap-10691	407	38	sin2	sin2	NOUN
ap-10691	407	39	θ	θ	PROPN
ap-10691	407	40	+	+	CCONJ
ap-10691	407	41	p2	p2	PROPN
ap-10691	407	42	θ	θ	PROPN
ap-10691	407	43	±	±	NUM
ap-10691	407	44	ipθ	ipθ	ADP
ap-10691	407	45	sin	sin	NOUN
ap-10691	407	46	2θ	2θ	NUM
ap-10691	407	47			NOUN
ap-10691	407	48	n	n	X
ap-10691	407	49	,	,	PUNCT
ap-10691	407	50	(	(	PUNCT
ap-10691	407	51	118	118	NUM
ap-10691	407	52	)	)	PUNCT
ap-10691	407	53	where	where	SCONJ
ap-10691	407	54	a	a	DET
ap-10691	407	55	,	,	PUNCT
ap-10691	407	56	b	b	X
ap-10691	407	57	∈	∈	PROPN
ap-10691	407	58	r	r	NOUN
ap-10691	407	59	(	(	PUNCT
ap-10691	407	60	see	see	VERB
ap-10691	407	61	equation	equation	NOUN
ap-10691	407	62	(	(	PUNCT
ap-10691	407	63	68	68	NUM
ap-10691	407	64	)	)	PUNCT
ap-10691	407	65	)	)	PUNCT
ap-10691	407	66	,	,	PUNCT
ap-10691	407	67	which	which	PRON
ap-10691	407	68	satisfy	satisfy	VERB
ap-10691	407	69	the	the	DET
ap-10691	407	70	reality	reality	NOUN
ap-10691	407	71	condition	condition	NOUN
ap-10691	407	72	(	(	PUNCT
ap-10691	407	73	x+)∗	x+)∗	PROPN
ap-10691	407	74	=	=	PUNCT
ap-10691	408	1	x−.	x−.	ADV
ap-10691	408	2	this	this	DET
ap-10691	408	3	condition	condition	NOUN
ap-10691	408	4	will	will	AUX
ap-10691	408	5	be	be	AUX
ap-10691	408	6	used	use	VERB
ap-10691	408	7	to	to	PART
ap-10691	408	8	compute	compute	VERB
ap-10691	408	9	the	the	DET
ap-10691	408	10	classical	classical	ADJ
ap-10691	408	11	trajectories	trajectory	NOUN
ap-10691	408	12	,	,	PUNCT
ap-10691	408	13	similarly	similarly	ADV
ap-10691	408	14	to	to	ADP
ap-10691	408	15	the	the	DET
ap-10691	408	16	spherical	spherical	ADJ
ap-10691	408	17	case	case	NOUN
ap-10691	408	18	.	.	PUNCT
ap-10691	409	1	for	for	ADP
ap-10691	409	2	our	our	PRON
ap-10691	409	3	system	system	NOUN
ap-10691	409	4	,	,	PUNCT
ap-10691	409	5	hk	hk	PROPN
ap-10691	409	6	,	,	PUNCT
ap-10691	409	7	hθ	hθ	PROPN
ap-10691	409	8	,	,	PUNCT
ap-10691	409	9	x±	x±	PROPN
ap-10691	409	10	,	,	PUNCT
ap-10691	409	11	and	and	CCONJ
ap-10691	409	12	mk	mk	NOUN
ap-10691	409	13	are	be	AUX
ap-10691	409	14	all	all	PRON
ap-10691	409	15	constants	constant	NOUN
ap-10691	409	16	of	of	ADP
ap-10691	409	17	motion	motion	NOUN
ap-10691	409	18	,	,	PUNCT
ap-10691	409	19	but	but	CCONJ
ap-10691	409	20	only	only	ADV
ap-10691	409	21	three	three	NUM
ap-10691	409	22	are	be	AUX
ap-10691	409	23	functionally	functionally	ADV
ap-10691	409	24	independent	independent	ADJ
ap-10691	409	25	.	.	PUNCT
ap-10691	410	1	by	by	ADP
ap-10691	410	2	fixing	fix	VERB
ap-10691	410	3	the	the	DET
ap-10691	410	4	value	value	NOUN
ap-10691	410	5	of	of	ADP
ap-10691	410	6	hk	hk	PROPN
ap-10691	410	7	=	=	SYM
ap-10691	410	8	e	e	NOUN
ap-10691	410	9	,	,	PUNCT
ap-10691	410	10	both	both	PRON
ap-10691	410	11	e	e	NOUN
ap-10691	410	12	and	and	CCONJ
ap-10691	410	13	mk	mk	PROPN
ap-10691	410	14	remain	remain	VERB
ap-10691	410	15	constant	constant	ADJ
ap-10691	410	16	along	along	ADP
ap-10691	410	17	the	the	DET
ap-10691	410	18	trajectory	trajectory	NOUN
ap-10691	410	19	.	.	PUNCT
ap-10691	411	1	thus	thus	ADV
ap-10691	411	2	,	,	PUNCT
ap-10691	411	3	the	the	DET
ap-10691	411	4	generalised	generalise	VERB
ap-10691	411	5	momenta	momenta	NOUN
ap-10691	411	6	can	can	AUX
ap-10691	411	7	be	be	AUX
ap-10691	411	8	expressed	express	VERB
ap-10691	411	9	in	in	ADP
ap-10691	411	10	terms	term	NOUN
ap-10691	411	11	of	of	ADP
ap-10691	411	12	the	the	DET
ap-10691	411	13	generalised	generalise	VERB
ap-10691	411	14	coordinates	coordinate	NOUN
ap-10691	411	15	as	as	SCONJ
ap-10691	411	16	follows	follow	VERB
ap-10691	411	17	:	:	PUNCT
ap-10691	411	18	pθ	pθ	ADP
ap-10691	411	19	=	=	SYM
ap-10691	411	20	εθ	εθ	NOUN
ap-10691	411	21	√	√	PROPN
ap-10691	411	22	m2	m2	PROPN
ap-10691	411	23	k	k	PROPN
ap-10691	411	24	k2	k2	PROPN
ap-10691	411	25	−	−	PROPN
ap-10691	412	1	(	(	PUNCT
ap-10691	412	2	α2	α2	ADJ
ap-10691	412	3	cos2	cos2	PROPN
ap-10691	412	4	θ	θ	PROPN
ap-10691	412	5	+	+	CCONJ
ap-10691	412	6	β2	β2	PROPN
ap-10691	412	7	sin2	sin2	NOUN
ap-10691	412	8	θ	θ	PROPN
ap-10691	412	9	)	)	PUNCT
ap-10691	412	10	,	,	PUNCT
ap-10691	412	11	pξ	pξ	ADP
ap-10691	412	12	=	=	PUNCT
ap-10691	412	13	εξ	εξ	NOUN
ap-10691	413	1	√	√	PROPN
ap-10691	413	2	e	e	PROPN
ap-10691	413	3	+	+	CCONJ
ap-10691	413	4	(	(	PUNCT
ap-10691	413	5	l22	l22	NOUN
ap-10691	413	6	cosh2	cosh2	VERB
ap-10691	414	1	ξ	ξ	X
ap-10691	414	2	−	−	PROPN
ap-10691	414	3	m2	m2	PROPN
ap-10691	414	4	k	k	PROPN
ap-10691	414	5	sinh2	sinh2	PROPN
ap-10691	414	6	ξ	ξ	PROPN
ap-10691	414	7	)	)	PUNCT
ap-10691	415	1	,	,	PUNCT
ap-10691	415	2	(	(	PUNCT
ap-10691	415	3	119	119	NUM
ap-10691	415	4	)	)	PUNCT
ap-10691	415	5	with	with	ADP
ap-10691	415	6	εθ	εθ	PROPN
ap-10691	415	7	,	,	PUNCT
ap-10691	415	8	εξ	εξ	PROPN
ap-10691	415	9	∈	∈	PROPN
ap-10691	415	10	{	{	PUNCT
ap-10691	415	11	±1	±1	NOUN
ap-10691	415	12	}	}	PUNCT
ap-10691	415	13	.	.	PUNCT
ap-10691	416	1	since	since	SCONJ
ap-10691	416	2	the	the	DET
ap-10691	416	3	symmetry	symmetry	NOUN
ap-10691	416	4	functions	function	NOUN
ap-10691	416	5	x±	x±	PROPN
ap-10691	416	6	are	be	AUX
ap-10691	416	7	complex	complex	ADJ
ap-10691	416	8	,	,	PUNCT
ap-10691	416	9	the	the	DET
ap-10691	416	10	constants	constant	NOUN
ap-10691	416	11	of	of	ADP
ap-10691	416	12	motion	motion	NOUN
ap-10691	416	13	will	will	AUX
ap-10691	416	14	be	be	AUX
ap-10691	416	15	complex	complex	ADJ
ap-10691	416	16	numbers	number	NOUN
ap-10691	416	17	c.	c.	NOUN
ap-10691	416	18	to	to	PART
ap-10691	416	19	obtain	obtain	VERB
ap-10691	416	20	real	real	ADJ
ap-10691	416	21	representations	representation	NOUN
ap-10691	416	22	,	,	PUNCT
ap-10691	416	23	and	and	CCONJ
ap-10691	416	24	considering	consider	VERB
ap-10691	416	25	the	the	DET
ap-10691	416	26	reality	reality	NOUN
ap-10691	416	27	condition	condition	NOUN
ap-10691	416	28	for	for	ADP
ap-10691	416	29	x±	x±	PROPN
ap-10691	416	30	,	,	PUNCT
ap-10691	416	31	we	we	PRON
ap-10691	416	32	set	set	VERB
ap-10691	416	33	x+	x+	ADJ
ap-10691	416	34	=	=	SYM
ap-10691	416	35	c	c	NOUN
ap-10691	416	36	,	,	PUNCT
ap-10691	416	37	and	and	CCONJ
ap-10691	416	38	x−	x−	PROPN
ap-10691	416	39	=	=	SYM
ap-10691	416	40	c∗	c∗	PROPN
ap-10691	416	41	,	,	PUNCT
ap-10691	416	42	we	we	PRON
ap-10691	416	43	can	can	AUX
ap-10691	416	44	consider	consider	VERB
ap-10691	416	45	:	:	PUNCT
ap-10691	416	46	re(x+	re(x+	ADJ
ap-10691	416	47	)	)	PUNCT
ap-10691	416	48	=	=	SYM
ap-10691	417	1	x+	x+	PUNCT
ap-10691	417	2	+	+	NUM
ap-10691	417	3	x−	x−	PROPN
ap-10691	417	4	2	2	NUM
ap-10691	417	5	=	=	SYM
ap-10691	417	6	re(c	re(c	NUM
ap-10691	417	7	)	)	PUNCT
ap-10691	417	8	,	,	PUNCT
ap-10691	417	9	im(x+	im(x+	PROPN
ap-10691	417	10	)	)	PUNCT
ap-10691	417	11	=	=	SYM
ap-10691	418	1	x+	x+	NUM
ap-10691	418	2	−	−	PROPN
ap-10691	418	3	x−	x−	PROPN
ap-10691	418	4	2i	2i	PROPN
ap-10691	418	5	=	=	SYM
ap-10691	418	6	im(c	im(c	NOUN
ap-10691	418	7	)	)	PUNCT
ap-10691	418	8	.	.	PUNCT
ap-10691	419	1	(	(	PUNCT
ap-10691	419	2	120	120	NUM
ap-10691	419	3	)	)	PUNCT
ap-10691	419	4	529	529	NUM
ap-10691	419	5	mariano	mariano	PROPN
ap-10691	419	6	a.	a.	PROPN
ap-10691	419	7	del	del	PROPN
ap-10691	419	8	olmo	olmo	PROPN
ap-10691	419	9	,	,	PUNCT
ap-10691	419	10	álvaro	álvaro	PROPN
ap-10691	419	11	romaniega	romaniega	PROPN
ap-10691	419	12	acta	acta	PROPN
ap-10691	419	13	polytechnica	polytechnica	PROPN
ap-10691	419	14	(	(	PUNCT
ap-10691	419	15	a	a	NOUN
ap-10691	419	16	)	)	PUNCT
ap-10691	419	17	.	.	PUNCT
ap-10691	420	1	m	m	VERB
ap-10691	420	2	=	=	NOUN
ap-10691	420	3	1	1	NUM
ap-10691	420	4	,	,	PUNCT
ap-10691	420	5	n	n	NOUN
ap-10691	420	6	=	=	SYM
ap-10691	420	7	1	1	NUM
ap-10691	420	8	.	.	PUNCT
ap-10691	421	1	(	(	PUNCT
ap-10691	421	2	b	b	NOUN
ap-10691	421	3	)	)	PUNCT
ap-10691	421	4	.	.	PUNCT
ap-10691	422	1	m	m	VERB
ap-10691	422	2	=	=	SYM
ap-10691	422	3	2	2	NUM
ap-10691	422	4	,	,	PUNCT
ap-10691	422	5	n	n	NOUN
ap-10691	422	6	=	=	SYM
ap-10691	422	7	1	1	X
ap-10691	422	8	.	.	X
ap-10691	422	9	figure	figure	NOUN
ap-10691	422	10	6	6	NUM
ap-10691	422	11	.	.	PUNCT
ap-10691	423	1	trajectories	trajectory	NOUN
ap-10691	423	2	for	for	ADP
ap-10691	423	3	m	m	PROPN
ap-10691	423	4	=	=	SYM
ap-10691	423	5	1	1	NUM
ap-10691	423	6	,	,	PUNCT
ap-10691	423	7	n	n	NOUN
ap-10691	423	8	=	=	SYM
ap-10691	423	9	1	1	NUM
ap-10691	423	10	and	and	CCONJ
ap-10691	423	11	m	m	PROPN
ap-10691	423	12	=	=	ADJ
ap-10691	423	13	2	2	NUM
ap-10691	423	14	,	,	PUNCT
ap-10691	423	15	n	n	NOUN
ap-10691	423	16	=	=	SYM
ap-10691	423	17	1	1	NUM
ap-10691	423	18	,	,	PUNCT
ap-10691	423	19	respectively	respectively	ADV
ap-10691	423	20	.	.	PUNCT
ap-10691	424	1	thus	thus	ADV
ap-10691	424	2	,	,	PUNCT
ap-10691	424	3	the	the	DET
ap-10691	424	4	trajectories	trajectory	NOUN
ap-10691	424	5	t0	t0	PROPN
ap-10691	424	6	are	be	AUX
ap-10691	424	7	implicitly	implicitly	ADV
ap-10691	424	8	defined	define	VERB
ap-10691	424	9	by	by	ADP
ap-10691	424	10	the	the	DET
ap-10691	424	11	set	set	NOUN
ap-10691	424	12	of	of	ADP
ap-10691	424	13	points	point	NOUN
ap-10691	424	14	x	x	X
ap-10691	424	15	∈	∈	PROPN
ap-10691	424	16	r3	r3	PROPN
ap-10691	424	17	satisfying	satisfying	NOUN
ap-10691	424	18	:	:	PUNCT
ap-10691	424	19	x(x	x(x	X
ap-10691	424	20	)	)	PUNCT
ap-10691	425	1	=	=	SYM
ap-10691	425	2	c0	c0	NOUN
ap-10691	425	3	,	,	PUNCT
ap-10691	425	4	(	(	PUNCT
ap-10691	425	5	121	121	NUM
ap-10691	425	6	)	)	PUNCT
ap-10691	425	7	where	where	SCONJ
ap-10691	425	8	c0	c0	PROPN
ap-10691	425	9	is	be	AUX
ap-10691	425	10	a	a	DET
ap-10691	425	11	fixed	fix	VERB
ap-10691	425	12	complex	complex	ADJ
ap-10691	425	13	constant	constant	ADJ
ap-10691	425	14	.	.	PUNCT
ap-10691	426	1	in	in	ADP
ap-10691	426	2	figures	figure	NOUN
ap-10691	426	3	6–8	6–8	INTJ
ap-10691	426	4	we	we	PRON
ap-10691	426	5	present	present	VERB
ap-10691	426	6	trajectories	trajectory	NOUN
ap-10691	426	7	plotted	plot	VERB
ap-10691	426	8	using	use	VERB
ap-10691	426	9	mathematica	mathematica	PROPN
ap-10691	426	10	for	for	ADP
ap-10691	426	11	various	various	ADJ
ap-10691	426	12	values	value	NOUN
ap-10691	426	13	of	of	ADP
ap-10691	426	14	k	k	PROPN
ap-10691	426	15	=	=	PUNCT
ap-10691	426	16	m	m	VERB
ap-10691	426	17	n	n	NOUN
ap-10691	426	18	.	.	PUNCT
ap-10691	427	1	6	6	X
ap-10691	427	2	.	.	X
ap-10691	427	3	conclusions	conclusion	NOUN
ap-10691	427	4	we	we	PRON
ap-10691	427	5	have	have	AUX
ap-10691	427	6	examined	examine	VERB
ap-10691	427	7	in	in	ADP
ap-10691	427	8	detail	detail	NOUN
ap-10691	427	9	two	two	NUM
ap-10691	427	10	new	new	ADJ
ap-10691	427	11	families	family	NOUN
ap-10691	427	12	of	of	ADP
ap-10691	427	13	hamiltonians	hamiltonian	NOUN
ap-10691	427	14	defined	define	VERB
ap-10691	427	15	on	on	ADP
ap-10691	427	16	curved	curved	ADJ
ap-10691	427	17	spaces	space	NOUN
ap-10691	427	18	,	,	PUNCT
ap-10691	427	19	derived	derive	VERB
ap-10691	427	20	from	from	ADP
ap-10691	427	21	wellknown	wellknown	ADJ
ap-10691	427	22	superintegrable	superintegrable	ADJ
ap-10691	427	23	hamiltonians	hamiltonian	NOUN
ap-10691	427	24	on	on	ADP
ap-10691	427	25	the	the	DET
ap-10691	427	26	sphere	sphere	NOUN
ap-10691	428	1	[	[	X
ap-10691	428	2	6	6	NUM
ap-10691	428	3	]	]	PUNCT
ap-10691	428	4	and	and	CCONJ
ap-10691	428	5	hyperbolic	hyperbolic	ADJ
ap-10691	428	6	2	2	NUM
ap-10691	428	7	-	-	PUNCT
ap-10691	428	8	space	space	NOUN
ap-10691	428	9	[	[	X
ap-10691	428	10	7	7	X
ap-10691	428	11	]	]	PUNCT
ap-10691	428	12	through	through	ADP
ap-10691	428	13	a	a	DET
ap-10691	428	14	ttw	ttw	NOUN
ap-10691	428	15	procedure	procedure	NOUN
ap-10691	428	16	analogous	analogous	ADJ
ap-10691	428	17	to	to	ADP
ap-10691	428	18	that	that	PRON
ap-10691	428	19	used	use	VERB
ap-10691	428	20	in	in	ADP
ap-10691	428	21	[	[	X
ap-10691	428	22	9	9	NUM
ap-10691	428	23	]	]	PUNCT
ap-10691	428	24	to	to	PART
ap-10691	428	25	generate	generate	VERB
ap-10691	428	26	the	the	DET
ap-10691	428	27	ttw	ttw	PROPN
ap-10691	428	28	hamiltonians	hamiltonian	NOUN
ap-10691	428	29	from	from	ADP
ap-10691	428	30	the	the	DET
ap-10691	428	31	smorodinsky	smorodinsky	NOUN
ap-10691	428	32	-	-	PUNCT
ap-10691	428	33	winternitz	winternitz	NOUN
ap-10691	428	34	system	system	NOUN
ap-10691	428	35	[	[	X
ap-10691	428	36	12	12	NUM
ap-10691	428	37	]	]	PUNCT
ap-10691	428	38	.	.	PUNCT
ap-10691	429	1	this	this	DET
ap-10691	429	2	procedure	procedure	NOUN
ap-10691	429	3	involves	involve	VERB
ap-10691	429	4	deforming	deform	VERB
ap-10691	429	5	the	the	DET
ap-10691	429	6	initial	initial	ADJ
ap-10691	429	7	hamiltonian	hamiltonian	NOUN
ap-10691	429	8	by	by	ADP
ap-10691	429	9	a	a	DET
ap-10691	429	10	real	real	ADJ
ap-10691	429	11	parameter	parameter	NOUN
ap-10691	429	12	k	k	PROPN
ap-10691	429	13	̸=	̸=	PROPN
ap-10691	429	14	0	0	NUM
ap-10691	429	15	,	,	PUNCT
ap-10691	429	16	which	which	PRON
ap-10691	429	17	recovers	recover	VERB
ap-10691	429	18	the	the	DET
ap-10691	429	19	initial	initial	ADJ
ap-10691	429	20	system	system	NOUN
ap-10691	429	21	in	in	ADP
ap-10691	429	22	the	the	DET
ap-10691	429	23	limit	limit	NOUN
ap-10691	429	24	k	k	X
ap-10691	430	1	→	→	SYM
ap-10691	430	2	1	1	X
ap-10691	430	3	.	.	PUNCT
ap-10691	430	4	to	to	PART
ap-10691	430	5	prove	prove	VERB
ap-10691	430	6	the	the	DET
ap-10691	430	7	superintegrability	superintegrability	NOUN
ap-10691	430	8	of	of	ADP
ap-10691	430	9	these	these	DET
ap-10691	430	10	new	new	ADJ
ap-10691	430	11	ttw	ttw	PROPN
ap-10691	430	12	hamiltonian	hamiltonian	ADJ
ap-10691	430	13	families	family	NOUN
ap-10691	430	14	,	,	PUNCT
ap-10691	430	15	we	we	PRON
ap-10691	430	16	construct	construct	VERB
ap-10691	430	17	generalised	generalised	ADJ
ap-10691	430	18	ladder	ladder	NOUN
ap-10691	430	19	and	and	CCONJ
ap-10691	430	20	shift	shift	VERB
ap-10691	430	21	operators	operator	NOUN
ap-10691	430	22	via	via	ADP
ap-10691	430	23	the	the	DET
ap-10691	430	24	factorisation	factorisation	NOUN
ap-10691	430	25	method	method	NOUN
ap-10691	430	26	.	.	PUNCT
ap-10691	431	1	these	these	DET
ap-10691	431	2	operators	operator	NOUN
ap-10691	431	3	yield	yield	VERB
ap-10691	431	4	two	two	NUM
ap-10691	431	5	symmetries	symmetry	NOUN
ap-10691	431	6	of	of	ADP
ap-10691	431	7	the	the	DET
ap-10691	431	8	ttw	ttw	PROPN
ap-10691	431	9	hamiltonian	hamiltonian	NOUN
ap-10691	431	10	,	,	PUNCT
ap-10691	431	11	demonstrating	demonstrate	VERB
ap-10691	431	12	that	that	DET
ap-10691	431	13	superintegrability	superintegrability	NOUN
ap-10691	431	14	is	be	AUX
ap-10691	431	15	preserved	preserve	VERB
ap-10691	431	16	when	when	SCONJ
ap-10691	431	17	k	k	PROPN
ap-10691	431	18	is	be	AUX
ap-10691	431	19	rational	rational	ADJ
ap-10691	431	20	.	.	PUNCT
ap-10691	432	1	furthermore	furthermore	ADV
ap-10691	432	2	,	,	PUNCT
ap-10691	432	3	we	we	PRON
ap-10691	432	4	study	study	VERB
ap-10691	432	5	the	the	DET
ap-10691	432	6	classical	classical	ADJ
ap-10691	432	7	counterparts	counterpart	NOUN
ap-10691	432	8	of	of	ADP
ap-10691	432	9	these	these	DET
ap-10691	432	10	hamiltonians	hamiltonian	NOUN
ap-10691	432	11	by	by	ADP
ap-10691	432	12	following	follow	VERB
ap-10691	432	13	a	a	DET
ap-10691	432	14	procedure	procedure	NOUN
ap-10691	432	15	parallel	parallel	NOUN
ap-10691	432	16	to	to	ADP
ap-10691	432	17	the	the	DET
ap-10691	432	18	quantum	quantum	NOUN
ap-10691	432	19	case	case	NOUN
ap-10691	432	20	and	and	CCONJ
ap-10691	432	21	guided	guide	VERB
ap-10691	432	22	by	by	ADP
ap-10691	432	23	the	the	DET
ap-10691	432	24	correspondence	correspondence	NOUN
ap-10691	432	25	principle	principle	NOUN
ap-10691	433	1	[	[	X
ap-10691	433	2	31	31	NUM
ap-10691	433	3	]	]	PUNCT
ap-10691	433	4	.	.	PUNCT
ap-10691	434	1	we	we	PRON
ap-10691	434	2	derive	derive	VERB
ap-10691	434	3	classical	classical	ADJ
ap-10691	434	4	analogues	analogue	NOUN
ap-10691	434	5	of	of	ADP
ap-10691	434	6	the	the	DET
ap-10691	434	7	ladder	ladder	NOUN
ap-10691	434	8	and	and	CCONJ
ap-10691	434	9	shift	shift	VERB
ap-10691	434	10	quantum	quantum	ADJ
ap-10691	434	11	operators	operator	NOUN
ap-10691	434	12	as	as	ADP
ap-10691	434	13	classical	classical	ADJ
ap-10691	434	14	functions	function	NOUN
ap-10691	434	15	,	,	PUNCT
ap-10691	434	16	and	and	CCONJ
ap-10691	434	17	identify	identify	VERB
ap-10691	434	18	two	two	NUM
ap-10691	434	19	functions	function	NOUN
ap-10691	434	20	in	in	ADP
ap-10691	434	21	involution	involution	NOUN
ap-10691	434	22	with	with	ADP
ap-10691	434	23	the	the	DET
ap-10691	434	24	hamiltonian	hamiltonian	NOUN
ap-10691	434	25	,	,	PUNCT
ap-10691	434	26	proving	prove	VERB
ap-10691	434	27	classical	classical	ADJ
ap-10691	434	28	superintegrability	superintegrability	NOUN
ap-10691	434	29	for	for	ADP
ap-10691	434	30	rational	rational	ADJ
ap-10691	434	31	k.	k.	PROPN
ap-10691	434	32	additionally	additionally	ADV
ap-10691	434	33	,	,	PUNCT
ap-10691	434	34	the	the	DET
ap-10691	434	35	classical	classical	ADJ
ap-10691	434	36	trajectories	trajectory	NOUN
ap-10691	434	37	are	be	AUX
ap-10691	434	38	obtained	obtain	VERB
ap-10691	434	39	through	through	ADP
ap-10691	434	40	an	an	DET
ap-10691	434	41	algebraic	algebraic	ADJ
ap-10691	434	42	approach	approach	NOUN
ap-10691	434	43	.	.	PUNCT
ap-10691	435	1	an	an	DET
ap-10691	435	2	open	open	ADJ
ap-10691	435	3	and	and	CCONJ
ap-10691	435	4	mathematically	mathematically	ADV
ap-10691	435	5	significant	significant	ADJ
ap-10691	435	6	problem	problem	NOUN
ap-10691	435	7	,	,	PUNCT
ap-10691	435	8	particularly	particularly	ADV
ap-10691	435	9	in	in	ADP
ap-10691	435	10	light	light	NOUN
ap-10691	435	11	of	of	ADP
ap-10691	435	12	[	[	X
ap-10691	435	13	33–35	33–35	NUM
ap-10691	435	14	]	]	PUNCT
ap-10691	435	15	,	,	PUNCT
ap-10691	435	16	is	be	AUX
ap-10691	435	17	the	the	DET
ap-10691	435	18	explicit	explicit	ADJ
ap-10691	435	19	determination	determination	NOUN
ap-10691	435	20	of	of	ADP
ap-10691	435	21	the	the	DET
ap-10691	435	22	polynomial	polynomial	ADJ
ap-10691	435	23	algebra	algebra	NOUN
ap-10691	435	24	underlying	underlie	VERB
ap-10691	435	25	the	the	DET
ap-10691	435	26	integrals	integral	NOUN
ap-10691	435	27	of	of	ADP
ap-10691	435	28	motion	motion	NOUN
ap-10691	435	29	in	in	ADP
ap-10691	435	30	both	both	DET
ap-10691	435	31	cases	case	NOUN
ap-10691	435	32	.	.	PUNCT
ap-10691	436	1	a	a	DET
ap-10691	436	2	deeper	deep	ADJ
ap-10691	436	3	understanding	understanding	NOUN
ap-10691	436	4	of	of	ADP
ap-10691	436	5	this	this	DET
ap-10691	436	6	algebraic	algebraic	ADJ
ap-10691	436	7	structure	structure	NOUN
ap-10691	436	8	could	could	AUX
ap-10691	436	9	provide	provide	VERB
ap-10691	436	10	new	new	ADJ
ap-10691	436	11	insights	insight	NOUN
ap-10691	436	12	into	into	ADP
ap-10691	436	13	the	the	DET
ap-10691	436	14	symmetry	symmetry	NOUN
ap-10691	436	15	properties	property	NOUN
ap-10691	436	16	and	and	CCONJ
ap-10691	436	17	superintegrability	superintegrability	NOUN
ap-10691	436	18	of	of	ADP
ap-10691	436	19	these	these	DET
ap-10691	436	20	two	two	NUM
ap-10691	436	21	hamiltonian	hamiltonian	ADJ
ap-10691	436	22	systems	system	NOUN
ap-10691	436	23	.	.	PUNCT
ap-10691	437	1	(	(	PUNCT
ap-10691	437	2	a	a	NOUN
ap-10691	437	3	)	)	PUNCT
ap-10691	437	4	.	.	PUNCT
ap-10691	438	1	m	m	VERB
ap-10691	438	2	=	=	NOUN
ap-10691	438	3	1	1	NUM
ap-10691	438	4	,	,	PUNCT
ap-10691	438	5	n	n	NOUN
ap-10691	438	6	=	=	SYM
ap-10691	438	7	2	2	NUM
ap-10691	438	8	.	.	PUNCT
ap-10691	438	9	(	(	PUNCT
ap-10691	438	10	b	b	NOUN
ap-10691	438	11	)	)	PUNCT
ap-10691	438	12	.	.	PUNCT
ap-10691	439	1	m	m	VERB
ap-10691	440	1	=	=	SYM
ap-10691	440	2	3	3	NUM
ap-10691	440	3	,	,	PUNCT
ap-10691	440	4	n	n	NOUN
ap-10691	440	5	=	=	SYM
ap-10691	440	6	3	3	X
ap-10691	440	7	.	.	X
ap-10691	440	8	figure	figure	NOUN
ap-10691	440	9	7	7	NUM
ap-10691	440	10	.	.	PUNCT
ap-10691	441	1	trajectories	trajectory	NOUN
ap-10691	441	2	for	for	ADP
ap-10691	441	3	m	m	PROPN
ap-10691	441	4	=	=	SYM
ap-10691	441	5	1	1	NUM
ap-10691	441	6	,	,	PUNCT
ap-10691	441	7	n	n	NOUN
ap-10691	441	8	=	=	SYM
ap-10691	441	9	2	2	NUM
ap-10691	441	10	and	and	CCONJ
ap-10691	441	11	m	m	PROPN
ap-10691	441	12	=	=	SYM
ap-10691	441	13	3	3	NUM
ap-10691	441	14	,	,	PUNCT
ap-10691	441	15	n	n	NOUN
ap-10691	441	16	=	=	SYM
ap-10691	441	17	3	3	NUM
ap-10691	441	18	,	,	PUNCT
ap-10691	441	19	respectively	respectively	ADV
ap-10691	441	20	.	.	PUNCT
ap-10691	442	1	(	(	PUNCT
ap-10691	442	2	a	a	NOUN
ap-10691	442	3	)	)	PUNCT
ap-10691	442	4	.	.	PUNCT
ap-10691	443	1	m	m	VERB
ap-10691	444	1	=	=	NOUN
ap-10691	444	2	4	4	NUM
ap-10691	444	3	,	,	PUNCT
ap-10691	444	4	n	n	NOUN
ap-10691	444	5	=	=	SYM
ap-10691	444	6	4	4	NUM
ap-10691	444	7	.	.	PUNCT
ap-10691	444	8	(	(	PUNCT
ap-10691	444	9	b	b	NOUN
ap-10691	444	10	)	)	PUNCT
ap-10691	444	11	.	.	PUNCT
ap-10691	445	1	m	m	VERB
ap-10691	446	1	=	=	NOUN
ap-10691	446	2	4	4	NUM
ap-10691	446	3	,	,	PUNCT
ap-10691	446	4	n	n	NOUN
ap-10691	446	5	=	=	SYM
ap-10691	446	6	5	5	X
ap-10691	446	7	.	.	X
ap-10691	446	8	figure	figure	NOUN
ap-10691	446	9	8	8	NUM
ap-10691	446	10	.	.	PUNCT
ap-10691	447	1	trajectories	trajectory	NOUN
ap-10691	447	2	for	for	ADP
ap-10691	447	3	m	m	PROPN
ap-10691	447	4	=	=	SYM
ap-10691	447	5	4	4	NUM
ap-10691	447	6	,	,	PUNCT
ap-10691	447	7	n	n	NOUN
ap-10691	447	8	=	=	SYM
ap-10691	447	9	4	4	NUM
ap-10691	447	10	and	and	CCONJ
ap-10691	447	11	m	m	VERB
ap-10691	447	12	=	=	ADJ
ap-10691	447	13	4	4	NUM
ap-10691	447	14	,	,	PUNCT
ap-10691	447	15	n	n	NOUN
ap-10691	447	16	=	=	SYM
ap-10691	447	17	5	5	NUM
ap-10691	447	18	,	,	PUNCT
ap-10691	447	19	respectively	respectively	ADV
ap-10691	447	20	.	.	PUNCT
ap-10691	448	1	acknowledgements	acknowledgement	NOUN
ap-10691	448	2	mariano	mariano	PROPN
ap-10691	448	3	a.	a.	PROPN
ap-10691	448	4	del	del	PROPN
ap-10691	448	5	olmo	olmo	PROPN
ap-10691	448	6	is	be	AUX
ap-10691	448	7	supported	support	VERB
ap-10691	448	8	by	by	ADP
ap-10691	448	9	pid2023	pid2023	NOUN
ap-10691	448	10	-	-	PUNCT
ap-10691	448	11	149560nbc21	149560nbc21	NOUN
ap-10691	448	12	financed	finance	VERB
ap-10691	448	13	by	by	ADP
ap-10691	448	14	miciu	miciu	PROPN
ap-10691	448	15	/	/	SYM
ap-10691	448	16	aei/10.13039/501100011033	aei/10.13039/501100011033	PROPN
ap-10691	448	17	of	of	ADP
ap-10691	448	18	spain	spain	PROPN
ap-10691	448	19	.	.	PUNCT
ap-10691	449	1	this	this	DET
ap-10691	449	2	article	article	NOUN
ap-10691	449	3	/	/	SYM
ap-10691	449	4	publication	publication	NOUN
ap-10691	449	5	is	be	AUX
ap-10691	449	6	based	base	VERB
ap-10691	449	7	upon	upon	SCONJ
ap-10691	449	8	work	work	NOUN
ap-10691	449	9	from	from	ADP
ap-10691	449	10	cost	cost	NOUN
ap-10691	449	11	action	action	NOUN
ap-10691	449	12	calista	calista	PROPN
ap-10691	449	13	ca21109	ca21109	PROPN
ap-10691	449	14	supported	support	VERB
ap-10691	449	15	by	by	ADP
ap-10691	449	16	cost	cost	NOUN
ap-10691	449	17	(	(	PUNCT
ap-10691	449	18	european	european	ADJ
ap-10691	449	19	cooperation	cooperation	NOUN
ap-10691	449	20	in	in	ADP
ap-10691	449	21	science	science	NOUN
ap-10691	449	22	and	and	CCONJ
ap-10691	449	23	technology	technology	NOUN
ap-10691	449	24	)	)	PUNCT
ap-10691	449	25	.	.	PUNCT
ap-10691	450	1	references	reference	NOUN
ap-10691	450	2	[	[	X
ap-10691	450	3	1	1	NUM
ap-10691	450	4	]	]	PUNCT
ap-10691	450	5	m.	m.	NOUN
ap-10691	450	6	a.	a.	PROPN
ap-10691	450	7	del	del	PROPN
ap-10691	450	8	olmo	olmo	PROPN
ap-10691	450	9	,	,	PUNCT
ap-10691	450	10	m.	m.	NOUN
ap-10691	450	11	a.	a.	NOUN
ap-10691	450	12	rodríguez	rodríguez	PROPN
ap-10691	450	13	,	,	PUNCT
ap-10691	450	14	p.	p.	PROPN
ap-10691	450	15	winternitz	winternitz	PROPN
ap-10691	450	16	.	.	PUNCT
ap-10691	451	1	integrable	integrable	ADJ
ap-10691	451	2	systems	system	NOUN
ap-10691	451	3	based	base	VERB
ap-10691	451	4	on	on	ADP
ap-10691	451	5	su(p	su(p	NOUN
ap-10691	451	6	,	,	PUNCT
ap-10691	451	7	q	q	ADJ
ap-10691	451	8	)	)	PUNCT
ap-10691	451	9	homogeneous	homogeneous	ADJ
ap-10691	451	10	manifolds	manifold	NOUN
ap-10691	451	11	.	.	PUNCT
ap-10691	452	1	journal	journal	PROPN
ap-10691	452	2	of	of	ADP
ap-10691	452	3	mathematical	mathematical	ADJ
ap-10691	452	4	physics	physics	NOUN
ap-10691	452	5	34(11):5118	34(11):5118	NUM
ap-10691	452	6	–	–	PUNCT
ap-10691	452	7	5139	5139	NUM
ap-10691	452	8	,	,	PUNCT
ap-10691	452	9	1993	1993	NUM
ap-10691	452	10	.	.	PUNCT
ap-10691	453	1	https://doi.org/10.1063/1.530346	https://doi.org/10.1063/1.530346	PROPN
ap-10691	454	1	[	[	X
ap-10691	454	2	2	2	NUM
ap-10691	454	3	]	]	X
ap-10691	454	4	n.	n.	PROPN
ap-10691	454	5	w.	w.	PROPN
ap-10691	454	6	evans	evans	PROPN
ap-10691	454	7	.	.	PUNCT
ap-10691	455	1	superintegrability	superintegrability	NOUN
ap-10691	455	2	in	in	ADP
ap-10691	455	3	classical	classical	ADJ
ap-10691	455	4	mechanics	mechanic	NOUN
ap-10691	455	5	.	.	PUNCT
ap-10691	456	1	physical	physical	ADJ
ap-10691	456	2	review	review	NOUN
ap-10691	456	3	a	a	DET
ap-10691	456	4	41(10):5666–5676	41(10):5666–5676	NUM
ap-10691	456	5	,	,	PUNCT
ap-10691	456	6	1990	1990	NUM
ap-10691	456	7	.	.	PUNCT
ap-10691	457	1	https://doi.org/10.1103/physreva.41.5666	https://doi.org/10.1103/physreva.41.5666	PROPN
ap-10691	458	1	[	[	X
ap-10691	458	2	3	3	X
ap-10691	458	3	]	]	PUNCT
ap-10691	458	4	j.	j.	PROPN
ap-10691	458	5	a.	a.	PROPN
ap-10691	458	6	calzada	calzada	PROPN
ap-10691	458	7	,	,	PUNCT
ap-10691	458	8	m.	m.	NOUN
ap-10691	458	9	a.	a.	PROPN
ap-10691	458	10	del	del	PROPN
ap-10691	458	11	olmo	olmo	PROPN
ap-10691	458	12	,	,	PUNCT
ap-10691	458	13	m.	m.	NOUN
ap-10691	458	14	a.	a.	NOUN
ap-10691	458	15	rodríguez	rodríguez	PROPN
ap-10691	458	16	.	.	PUNCT
ap-10691	459	1	classical	classical	ADJ
ap-10691	459	2	superintegrable	superintegrable	ADJ
ap-10691	459	3	so(p	so(p	NOUN
ap-10691	459	4	,	,	PUNCT
ap-10691	459	5	q	q	ADJ
ap-10691	459	6	)	)	PUNCT
ap-10691	459	7	hamiltonian	hamiltonian	ADJ
ap-10691	459	8	systems	system	NOUN
ap-10691	459	9	.	.	PUNCT
ap-10691	460	1	journal	journal	NOUN
ap-10691	460	2	of	of	ADP
ap-10691	460	3	geometry	geometry	NOUN
ap-10691	460	4	and	and	CCONJ
ap-10691	460	5	physics	physics	NOUN
ap-10691	460	6	23(1):14–30	23(1):14–30	NUM
ap-10691	460	7	,	,	PUNCT
ap-10691	460	8	1997	1997	NUM
ap-10691	460	9	.	.	PUNCT
ap-10691	461	1	https://doi.org/10.1016/s0393-0440(96)00043-5	https://doi.org/10.1016/s0393-0440(96)00043-5	PROPN
ap-10691	462	1	[	[	X
ap-10691	462	2	4	4	NUM
ap-10691	462	3	]	]	PUNCT
ap-10691	462	4	j.	j.	PROPN
ap-10691	462	5	a.	a.	PROPN
ap-10691	462	6	calzada	calzada	PROPN
ap-10691	462	7	,	,	PUNCT
ap-10691	462	8	m.	m.	NOUN
ap-10691	462	9	a.	a.	PROPN
ap-10691	462	10	del	del	PROPN
ap-10691	462	11	olmo	olmo	PROPN
ap-10691	462	12	,	,	PUNCT
ap-10691	462	13	m.	m.	NOUN
ap-10691	462	14	a.	a.	NOUN
ap-10691	462	15	rodríguez	rodríguez	PROPN
ap-10691	462	16	.	.	PUNCT
ap-10691	463	1	pseudo	pseudo	NOUN
ap-10691	463	2	-	-	ADJ
ap-10691	463	3	orthogonal	orthogonal	ADJ
ap-10691	463	4	groups	group	NOUN
ap-10691	463	5	and	and	CCONJ
ap-10691	463	6	integrable	integrable	ADJ
ap-10691	463	7	dynamical	dynamical	ADJ
ap-10691	463	8	systems	system	NOUN
ap-10691	463	9	in	in	ADP
ap-10691	463	10	two	two	NUM
ap-10691	463	11	dimensions	dimension	NOUN
ap-10691	463	12	.	.	PUNCT
ap-10691	464	1	journal	journal	PROPN
ap-10691	464	2	of	of	ADP
ap-10691	464	3	mathematical	mathematical	ADJ
ap-10691	464	4	physics	physics	NOUN
ap-10691	464	5	40(1):188–209	40(1):188–209	PROPN
ap-10691	464	6	,	,	PUNCT
ap-10691	464	7	1999	1999	NUM
ap-10691	464	8	.	.	PUNCT
ap-10691	465	1	https://doi.org/10.1063/1.532768	https://doi.org/10.1063/1.532768	NOUN
ap-10691	466	1	[	[	X
ap-10691	466	2	5	5	X
ap-10691	466	3	]	]	PUNCT
ap-10691	466	4	j.	j.	PROPN
ap-10691	466	5	a.	a.	PROPN
ap-10691	466	6	calzada	calzada	PROPN
ap-10691	466	7	,	,	PUNCT
ap-10691	466	8	j.	j.	PROPN
ap-10691	466	9	negro	negro	PROPN
ap-10691	466	10	,	,	PUNCT
ap-10691	466	11	m.	m.	NOUN
ap-10691	466	12	a.	a.	PROPN
ap-10691	466	13	del	del	PROPN
ap-10691	466	14	olmo	olmo	PROPN
ap-10691	466	15	,	,	PUNCT
ap-10691	466	16	m.	m.	NOUN
ap-10691	466	17	a.	a.	NOUN
ap-10691	466	18	rodríguez	rodríguez	PROPN
ap-10691	466	19	.	.	PUNCT
ap-10691	467	1	contraction	contraction	NOUN
ap-10691	467	2	of	of	ADP
ap-10691	467	3	superintegrable	superintegrable	ADJ
ap-10691	467	4	hamiltonian	hamiltonian	ADJ
ap-10691	467	5	systems	system	NOUN
ap-10691	467	6	.	.	PUNCT
ap-10691	468	1	journal	journal	PROPN
ap-10691	468	2	of	of	ADP
ap-10691	468	3	mathematical	mathematical	ADJ
ap-10691	468	4	physics	physics	PROPN
ap-10691	468	5	41(1):317–336	41(1):317–336	PROPN
ap-10691	468	6	,	,	PUNCT
ap-10691	468	7	2000	2000	NUM
ap-10691	468	8	.	.	PUNCT
ap-10691	469	1	https://doi.org/10.1063/1.533147	https://doi.org/10.1063/1.533147	PROPN
ap-10691	469	2	530	530	NUM
ap-10691	469	3	https://doi.org/10.1063/1.530346	https://doi.org/10.1063/1.530346	PROPN
ap-10691	469	4	https://doi.org/10.1103/physreva.41.5666	https://doi.org/10.1103/physreva.41.5666	NOUN
ap-10691	469	5	https://doi.org/10.1016/s0393-0440(96)00043-5	https://doi.org/10.1016/s0393-0440(96)00043-5	NOUN
ap-10691	469	6	https://doi.org/10.1063/1.532768	https://doi.org/10.1063/1.532768	NOUN
ap-10691	469	7	https://doi.org/10.1063/1.533147	https://doi.org/10.1063/1.533147	PROPN
ap-10691	469	8	vol	vol	NOUN
ap-10691	469	9	.	.	PUNCT
ap-10691	470	1	65	65	NUM
ap-10691	470	2	no	no	NOUN
ap-10691	470	3	.	.	PUNCT
ap-10691	471	1	5/2025	5/2025	NUM
ap-10691	471	2	classical	classical	ADJ
ap-10691	471	3	and	and	CCONJ
ap-10691	471	4	quantum	quantum	ADJ
ap-10691	471	5	superintegrable	superintegrable	ADJ
ap-10691	471	6	systems	system	NOUN
ap-10691	471	7	on	on	ADP
ap-10691	471	8	the	the	DET
ap-10691	471	9	sphere	sphere	NOUN
ap-10691	471	10	.	.	PUNCT
ap-10691	471	11	.	.	PUNCT
ap-10691	471	12	.	.	PUNCT
ap-10691	472	1	[	[	X
ap-10691	472	2	6	6	NUM
ap-10691	472	3	]	]	PUNCT
ap-10691	472	4	j.	j.	PROPN
ap-10691	472	5	a.	a.	PROPN
ap-10691	472	6	calzada	calzada	PROPN
ap-10691	472	7	,	,	PUNCT
ap-10691	472	8	j.	j.	PROPN
ap-10691	472	9	negro	negro	PROPN
ap-10691	472	10	,	,	PUNCT
ap-10691	472	11	m.	m.	NOUN
ap-10691	472	12	a.	a.	PROPN
ap-10691	472	13	del	del	PROPN
ap-10691	472	14	olmo	olmo	PROPN
ap-10691	472	15	.	.	PUNCT
ap-10691	472	16	superintegrable	superintegrable	ADJ
ap-10691	472	17	quantum	quantum	PROPN
ap-10691	472	18	u(3	u(3	PROPN
ap-10691	472	19	)	)	PUNCT
ap-10691	472	20	systems	system	NOUN
ap-10691	472	21	and	and	CCONJ
ap-10691	472	22	higher	high	ADJ
ap-10691	472	23	rank	rank	NOUN
ap-10691	472	24	factorizations	factorization	NOUN
ap-10691	472	25	.	.	PUNCT
ap-10691	473	1	journal	journal	NOUN
ap-10691	473	2	of	of	ADP
ap-10691	473	3	mathematical	mathematical	ADJ
ap-10691	473	4	physics	physics	PROPN
ap-10691	473	5	47(4):043511	47(4):043511	PROPN
ap-10691	473	6	,	,	PUNCT
ap-10691	473	7	2006	2006	NUM
ap-10691	473	8	.	.	PUNCT
ap-10691	474	1	https://doi.org/10.1063/1.2191360	https://doi.org/10.1063/1.2191360	VERB
ap-10691	475	1	[	[	X
ap-10691	475	2	7	7	X
ap-10691	475	3	]	]	PUNCT
ap-10691	475	4	j.	j.	PROPN
ap-10691	475	5	a.	a.	PROPN
ap-10691	475	6	calzada	calzada	PROPN
ap-10691	475	7	,	,	PUNCT
ap-10691	475	8	ş	ş	PROPN
ap-10691	475	9	.	.	PUNCT
ap-10691	475	10	kuru	kuru	PROPN
ap-10691	475	11	,	,	PUNCT
ap-10691	475	12	j.	j.	PROPN
ap-10691	475	13	negro	negro	PROPN
ap-10691	475	14	,	,	PUNCT
ap-10691	475	15	m.	m.	PROPN
ap-10691	475	16	a.	a.	PROPN
ap-10691	475	17	d.	d.	PROPN
ap-10691	475	18	olmo	olmo	PROPN
ap-10691	475	19	.	.	PUNCT
ap-10691	476	1	intertwining	intertwine	VERB
ap-10691	476	2	symmetry	symmetry	NOUN
ap-10691	476	3	algebras	algebra	NOUN
ap-10691	476	4	of	of	ADP
ap-10691	476	5	quantum	quantum	ADJ
ap-10691	476	6	superintegrable	superintegrable	ADJ
ap-10691	476	7	systems	system	NOUN
ap-10691	476	8	on	on	ADP
ap-10691	476	9	the	the	DET
ap-10691	476	10	hyperboloid	hyperboloid	NOUN
ap-10691	476	11	.	.	PUNCT
ap-10691	477	1	journal	journal	PROPN
ap-10691	477	2	of	of	ADP
ap-10691	477	3	physics	physics	PROPN
ap-10691	477	4	a	a	PRON
ap-10691	477	5	:	:	PUNCT
ap-10691	477	6	mathematical	mathematical	ADJ
ap-10691	477	7	and	and	CCONJ
ap-10691	477	8	theoretical	theoretical	ADJ
ap-10691	477	9	41(25):255201	41(25):255201	NUM
ap-10691	477	10	,	,	PUNCT
ap-10691	477	11	2008	2008	NUM
ap-10691	477	12	.	.	PUNCT
ap-10691	478	1	https://doi.org/10.1088/1751-8113/41/25/255201	https://doi.org/10.1088/1751-8113/41/25/255201	ADP
ap-10691	478	2	[	[	X
ap-10691	478	3	8	8	NUM
ap-10691	478	4	]	]	PUNCT
ap-10691	478	5	j.	j.	PROPN
ap-10691	478	6	a.	a.	PROPN
ap-10691	478	7	calzada	calzada	PROPN
ap-10691	478	8	,	,	PUNCT
ap-10691	478	9	ş	ş	PROPN
ap-10691	478	10	.	.	PUNCT
ap-10691	478	11	kuru	kuru	PROPN
ap-10691	478	12	,	,	PUNCT
ap-10691	478	13	j.	j.	PROPN
ap-10691	478	14	negro	negro	PROPN
ap-10691	478	15	,	,	PUNCT
ap-10691	478	16	m.	m.	NOUN
ap-10691	478	17	a.	a.	PROPN
ap-10691	478	18	del	del	PROPN
ap-10691	478	19	olmo	olmo	PROPN
ap-10691	478	20	.	.	PUNCT
ap-10691	479	1	dynamical	dynamical	ADJ
ap-10691	479	2	algebras	algebra	NOUN
ap-10691	479	3	of	of	ADP
ap-10691	479	4	general	general	ADJ
ap-10691	479	5	two	two	NUM
ap-10691	479	6	-	-	PUNCT
ap-10691	479	7	parametric	parametric	NOUN
ap-10691	479	8	pöschl	pöschl	NOUN
ap-10691	479	9	–	–	PUNCT
ap-10691	479	10	teller	teller	NOUN
ap-10691	479	11	hamiltonians	hamiltonian	NOUN
ap-10691	479	12	.	.	PUNCT
ap-10691	480	1	annals	annal	NOUN
ap-10691	480	2	of	of	ADP
ap-10691	480	3	physics	physics	NOUN
ap-10691	480	4	327(3):808–822	327(3):808–822	NUM
ap-10691	480	5	,	,	PUNCT
ap-10691	480	6	2012	2012	NUM
ap-10691	480	7	.	.	PUNCT
ap-10691	481	1	https://doi.org/10.1016/j.aop.2011.12.014	https://doi.org/10.1016/j.aop.2011.12.014	NOUN
ap-10691	482	1	[	[	X
ap-10691	482	2	9	9	NUM
ap-10691	482	3	]	]	X
ap-10691	482	4	f.	f.	PROPN
ap-10691	482	5	tremblay	tremblay	PROPN
ap-10691	482	6	,	,	PUNCT
ap-10691	482	7	a.	a.	NOUN
ap-10691	482	8	v.	v.	PROPN
ap-10691	482	9	turbiner	turbiner	NOUN
ap-10691	482	10	,	,	PUNCT
ap-10691	482	11	p.	p.	PROPN
ap-10691	482	12	winternitz	winternitz	PROPN
ap-10691	482	13	.	.	PUNCT
ap-10691	483	1	an	an	DET
ap-10691	483	2	infinite	infinite	ADJ
ap-10691	483	3	family	family	NOUN
ap-10691	483	4	of	of	ADP
ap-10691	483	5	solvable	solvable	ADJ
ap-10691	483	6	and	and	CCONJ
ap-10691	483	7	integrable	integrable	ADJ
ap-10691	483	8	quantum	quantum	NOUN
ap-10691	483	9	systems	system	NOUN
ap-10691	483	10	on	on	ADP
ap-10691	483	11	a	a	DET
ap-10691	483	12	plane	plane	NOUN
ap-10691	483	13	.	.	PUNCT
ap-10691	484	1	journal	journal	PROPN
ap-10691	484	2	of	of	ADP
ap-10691	484	3	physics	physics	PROPN
ap-10691	484	4	a	a	PRON
ap-10691	484	5	:	:	PUNCT
ap-10691	484	6	mathematical	mathematical	ADJ
ap-10691	484	7	and	and	CCONJ
ap-10691	484	8	theoretical	theoretical	ADJ
ap-10691	484	9	42(24):242001	42(24):242001	NUM
ap-10691	484	10	,	,	PUNCT
ap-10691	484	11	2009	2009	NUM
ap-10691	484	12	.	.	PUNCT
ap-10691	485	1	https://doi.org/10.1088/1751-8113/42/24/242001	https://doi.org/10.1088/1751-8113/42/24/242001	X
ap-10691	486	1	[	[	X
ap-10691	486	2	10	10	NUM
ap-10691	486	3	]	]	X
ap-10691	486	4	f.	f.	PROPN
ap-10691	486	5	tremblay	tremblay	PROPN
ap-10691	486	6	,	,	PUNCT
ap-10691	486	7	a.	a.	NOUN
ap-10691	486	8	v.	v.	PROPN
ap-10691	486	9	turbiner	turbiner	NOUN
ap-10691	486	10	,	,	PUNCT
ap-10691	486	11	p.	p.	PROPN
ap-10691	486	12	winternitz	winternitz	PROPN
ap-10691	486	13	.	.	PUNCT
ap-10691	487	1	periodic	periodic	ADJ
ap-10691	487	2	orbits	orbit	NOUN
ap-10691	487	3	for	for	ADP
ap-10691	487	4	an	an	DET
ap-10691	487	5	infinite	infinite	ADJ
ap-10691	487	6	family	family	NOUN
ap-10691	487	7	of	of	ADP
ap-10691	487	8	classical	classical	ADJ
ap-10691	487	9	superintegrable	superintegrable	ADJ
ap-10691	487	10	systems	system	NOUN
ap-10691	487	11	.	.	PUNCT
ap-10691	488	1	journal	journal	PROPN
ap-10691	488	2	of	of	ADP
ap-10691	488	3	physics	physics	PROPN
ap-10691	488	4	a	a	PRON
ap-10691	488	5	:	:	PUNCT
ap-10691	488	6	mathematical	mathematical	ADJ
ap-10691	488	7	and	and	CCONJ
ap-10691	488	8	theoretical	theoretical	ADJ
ap-10691	488	9	43(1):015202	43(1):015202	PROPN
ap-10691	488	10	,	,	PUNCT
ap-10691	488	11	2010	2010	NUM
ap-10691	488	12	.	.	PUNCT
ap-10691	489	1	https://doi.org/10.1088/1751-8113/43/1/015202	https://doi.org/10.1088/1751-8113/43/1/015202	PROPN
ap-10691	490	1	[	[	X
ap-10691	490	2	11	11	NUM
ap-10691	490	3	]	]	PUNCT
ap-10691	490	4	j.	j.	PROPN
ap-10691	490	5	friš	friš	PROPN
ap-10691	490	6	,	,	PUNCT
ap-10691	490	7	v.	v.	PROPN
ap-10691	490	8	mandrosov	mandrosov	NOUN
ap-10691	490	9	,	,	PUNCT
ap-10691	490	10	y.	y.	PROPN
ap-10691	490	11	a.	a.	PROPN
ap-10691	490	12	smorodinsky	smorodinsky	PROPN
ap-10691	490	13	,	,	PUNCT
ap-10691	490	14	et	et	PROPN
ap-10691	490	15	al	al	PROPN
ap-10691	490	16	.	.	PROPN
ap-10691	491	1	on	on	ADP
ap-10691	491	2	higher	high	ADJ
ap-10691	491	3	symmetries	symmetry	NOUN
ap-10691	491	4	in	in	ADP
ap-10691	491	5	quantum	quantum	ADJ
ap-10691	491	6	mechanics	mechanic	NOUN
ap-10691	491	7	.	.	PUNCT
ap-10691	492	1	physics	physics	NOUN
ap-10691	492	2	letters	letter	NOUN
ap-10691	492	3	16(3):354–356	16(3):354–356	NUM
ap-10691	492	4	,	,	PUNCT
ap-10691	492	5	1965	1965	NUM
ap-10691	492	6	.	.	PUNCT
ap-10691	493	1	https://doi.org/10.1016/0031-9163(65)90885-1	https://doi.org/10.1016/0031-9163(65)90885-1	NOUN
ap-10691	494	1	[	[	X
ap-10691	494	2	12	12	NUM
ap-10691	494	3	]	]	PUNCT
ap-10691	494	4	p.	p.	NOUN
ap-10691	494	5	winternitz	winternitz	PROPN
ap-10691	494	6	,	,	PUNCT
ap-10691	494	7	y.	y.	PROPN
ap-10691	494	8	a.	a.	PROPN
ap-10691	494	9	smorodinsky	smorodinsky	PROPN
ap-10691	494	10	,	,	PUNCT
ap-10691	494	11	m.	m.	NOUN
ap-10691	494	12	uhlíř	uhlíř	PROPN
ap-10691	494	13	,	,	PUNCT
ap-10691	494	14	j.	j.	PROPN
ap-10691	494	15	friš	friš	PROPN
ap-10691	494	16	.	.	PUNCT
ap-10691	495	1	symmetry	symmetry	NOUN
ap-10691	495	2	groups	group	NOUN
ap-10691	495	3	in	in	ADP
ap-10691	495	4	classical	classical	ADJ
ap-10691	495	5	and	and	CCONJ
ap-10691	495	6	quantum	quantum	ADJ
ap-10691	495	7	mechanics	mechanic	NOUN
ap-10691	495	8	.	.	PUNCT
ap-10691	496	1	soviet	soviet	ADJ
ap-10691	496	2	journal	journal	PROPN
ap-10691	496	3	of	of	ADP
ap-10691	496	4	nuclear	nuclear	ADJ
ap-10691	496	5	physics	physics	NOUN
ap-10691	496	6	4:444–450	4:444–450	NUM
ap-10691	496	7	,	,	PUNCT
ap-10691	496	8	1967	1967	NUM
ap-10691	496	9	.	.	PUNCT
ap-10691	497	1	[	[	X
ap-10691	497	2	13	13	NUM
ap-10691	497	3	]	]	PUNCT
ap-10691	497	4	m.	m.	PROPN
ap-10691	497	5	f.	f.	PROPN
ap-10691	497	6	rañada	rañada	PROPN
ap-10691	497	7	,	,	PUNCT
ap-10691	497	8	m.	m.	NOUN
ap-10691	497	9	santander	santander	NOUN
ap-10691	497	10	.	.	PUNCT
ap-10691	497	11	superintegrable	superintegrable	ADJ
ap-10691	497	12	systems	system	NOUN
ap-10691	497	13	on	on	ADP
ap-10691	497	14	the	the	DET
ap-10691	497	15	two	two	NUM
ap-10691	497	16	-	-	PUNCT
ap-10691	497	17	dimensional	dimensional	ADJ
ap-10691	497	18	sphere	sphere	NOUN
ap-10691	497	19	s2	s2	NOUN
ap-10691	497	20	and	and	CCONJ
ap-10691	497	21	the	the	DET
ap-10691	497	22	hyperbolic	hyperbolic	ADJ
ap-10691	497	23	plane	plane	NOUN
ap-10691	497	24	h2	h2	PROPN
ap-10691	497	25	.	.	PUNCT
ap-10691	498	1	journal	journal	PROPN
ap-10691	498	2	of	of	ADP
ap-10691	498	3	mathematical	mathematical	ADJ
ap-10691	498	4	physics	physics	NOUN
ap-10691	498	5	40(10):5026	40(10):5026	PROPN
ap-10691	498	6	–	–	PUNCT
ap-10691	498	7	5057	5057	NUM
ap-10691	498	8	,	,	PUNCT
ap-10691	498	9	1999	1999	NUM
ap-10691	498	10	.	.	PUNCT
ap-10691	499	1	https://doi.org/10.1063/1.533014	https://doi.org/10.1063/1.533014	PRON
ap-10691	500	1	[	[	X
ap-10691	500	2	14	14	NUM
ap-10691	500	3	]	]	X
ap-10691	500	4	i.	i.	PROPN
ap-10691	500	5	marquette	marquette	PROPN
ap-10691	500	6	,	,	PUNCT
ap-10691	500	7	c.	c.	PROPN
ap-10691	500	8	quesne	quesne	NOUN
ap-10691	500	9	.	.	PUNCT
ap-10691	501	1	new	new	ADJ
ap-10691	501	2	families	family	NOUN
ap-10691	501	3	of	of	ADP
ap-10691	501	4	superintegrable	superintegrable	ADJ
ap-10691	501	5	systems	system	NOUN
ap-10691	501	6	from	from	ADP
ap-10691	501	7	hermite	hermite	PROPN
ap-10691	501	8	and	and	CCONJ
ap-10691	501	9	laguerre	laguerre	VERB
ap-10691	501	10	exceptional	exceptional	ADJ
ap-10691	501	11	orthogonal	orthogonal	ADJ
ap-10691	501	12	polynomials	polynomial	NOUN
ap-10691	501	13	.	.	PUNCT
ap-10691	502	1	journal	journal	PROPN
ap-10691	502	2	of	of	ADP
ap-10691	502	3	mathematical	mathematical	ADJ
ap-10691	502	4	physics	physics	NOUN
ap-10691	502	5	54(4):042102	54(4):042102	NUM
ap-10691	502	6	,	,	PUNCT
ap-10691	502	7	2013	2013	NUM
ap-10691	502	8	.	.	PUNCT
ap-10691	503	1	https://doi.org/10.1063/1.4798807	https://doi.org/10.1063/1.4798807	PROPN
ap-10691	504	1	[	[	X
ap-10691	504	2	15	15	NUM
ap-10691	504	3	]	]	X
ap-10691	504	4	g.	g.	PROPN
ap-10691	504	5	s.	s.	PROPN
ap-10691	504	6	pogosyan	pogosyan	PROPN
ap-10691	504	7	,	,	PUNCT
ap-10691	504	8	k.	k.	PROPN
ap-10691	504	9	b.	b.	PROPN
ap-10691	504	10	wolf	wolf	PROPN
ap-10691	504	11	,	,	PUNCT
ap-10691	505	1	a.	a.	NOUN
ap-10691	505	2	yakhno	yakhno	NOUN
ap-10691	505	3	.	.	PUNCT
ap-10691	506	1	superintegrable	superintegrable	ADJ
ap-10691	506	2	classical	classical	ADJ
ap-10691	506	3	zernike	zernike	NOUN
ap-10691	506	4	system	system	NOUN
ap-10691	506	5	.	.	PUNCT
ap-10691	507	1	journal	journal	PROPN
ap-10691	507	2	of	of	ADP
ap-10691	507	3	mathematical	mathematical	ADJ
ap-10691	507	4	physics	physics	NOUN
ap-10691	507	5	58(7):072901	58(7):072901	NUM
ap-10691	507	6	,	,	PUNCT
ap-10691	507	7	2017	2017	NUM
ap-10691	507	8	.	.	PUNCT
ap-10691	508	1	https://doi.org/10.1063/1.4990793	https://doi.org/10.1063/1.4990793	PROPN
ap-10691	508	2	[	[	X
ap-10691	508	3	16	16	NUM
ap-10691	508	4	]	]	X
ap-10691	508	5	g.	g.	PROPN
ap-10691	508	6	s.	s.	PROPN
ap-10691	508	7	pogosyan	pogosyan	PROPN
ap-10691	508	8	,	,	PUNCT
ap-10691	508	9	c.	c.	PROPN
ap-10691	508	10	salto	salto	PROPN
ap-10691	508	11	-	-	PUNCT
ap-10691	508	12	alegre	alegre	PROPN
ap-10691	508	13	,	,	PUNCT
ap-10691	508	14	k.	k.	PROPN
ap-10691	508	15	b.	b.	PROPN
ap-10691	508	16	wolf	wolf	PROPN
ap-10691	508	17	,	,	PUNCT
ap-10691	508	18	a.	a.	NOUN
ap-10691	508	19	yakhno	yakhno	NOUN
ap-10691	508	20	.	.	PUNCT
ap-10691	509	1	quantum	quantum	PROPN
ap-10691	509	2	superintegrable	superintegrable	ADJ
ap-10691	509	3	zernike	zernike	NOUN
ap-10691	509	4	system	system	NOUN
ap-10691	509	5	.	.	PUNCT
ap-10691	510	1	journal	journal	PROPN
ap-10691	510	2	of	of	ADP
ap-10691	510	3	mathematical	mathematical	ADJ
ap-10691	510	4	physics	physics	NOUN
ap-10691	510	5	58(7):072101	58(7):072101	NUM
ap-10691	510	6	,	,	PUNCT
ap-10691	510	7	2017	2017	NUM
ap-10691	510	8	.	.	PUNCT
ap-10691	511	1	https://doi.org/10.1063/1.4990794	https://doi.org/10.1063/1.4990794	PROPN
ap-10691	512	1	[	[	X
ap-10691	512	2	17	17	NUM
ap-10691	512	3	]	]	PUNCT
ap-10691	512	4	a.	a.	NOUN
ap-10691	512	5	m.	m.	NOUN
ap-10691	512	6	escobar	escobar	PROPN
ap-10691	512	7	-	-	PUNCT
ap-10691	512	8	ruiz	ruiz	NOUN
ap-10691	512	9	,	,	PUNCT
ap-10691	512	10	p.	p.	NOUN
ap-10691	512	11	winternitz	winternitz	PROPN
ap-10691	512	12	,	,	PUNCT
ap-10691	512	13	i̇.	i̇.	VERB
ap-10691	512	14	yurduşen	yurduşen	NOUN
ap-10691	512	15	.	.	PUNCT
ap-10691	513	1	general	general	ADJ
ap-10691	513	2	n	n	CCONJ
ap-10691	513	3	th	th	ADJ
ap-10691	513	4	-	-	PUNCT
ap-10691	513	5	order	order	NOUN
ap-10691	513	6	superintegrable	superintegrable	ADJ
ap-10691	513	7	systems	system	NOUN
ap-10691	513	8	separating	separate	VERB
ap-10691	513	9	in	in	ADP
ap-10691	513	10	polar	polar	ADJ
ap-10691	513	11	coordinates	coordinate	NOUN
ap-10691	513	12	.	.	PUNCT
ap-10691	514	1	journal	journal	PROPN
ap-10691	514	2	of	of	ADP
ap-10691	514	3	physics	physics	PROPN
ap-10691	514	4	a	a	PRON
ap-10691	514	5	:	:	PUNCT
ap-10691	514	6	mathematical	mathematical	ADJ
ap-10691	514	7	and	and	CCONJ
ap-10691	514	8	theoretical	theoretical	ADJ
ap-10691	514	9	51(40):40lt01	51(40):40lt01	NUM
ap-10691	514	10	,	,	PUNCT
ap-10691	514	11	2018	2018	NUM
ap-10691	514	12	.	.	PUNCT
ap-10691	515	1	https://doi.org/10.1088/1751-8121/aadc23	https://doi.org/10.1088/1751-8121/aadc23	X
ap-10691	516	1	[	[	X
ap-10691	516	2	18	18	NUM
ap-10691	516	3	]	]	X
ap-10691	516	4	f.	f.	PROPN
ap-10691	516	5	correa	correa	PROPN
ap-10691	516	6	,	,	PUNCT
ap-10691	516	7	l.	l.	PROPN
ap-10691	516	8	inzunza	inzunza	PROPN
ap-10691	516	9	,	,	PUNCT
ap-10691	516	10	i.	i.	PROPN
ap-10691	516	11	marquette	marquette	PROPN
ap-10691	516	12	.	.	PUNCT
ap-10691	517	1	non	non	ADJ
ap-10691	517	2	-	-	ADJ
ap-10691	517	3	hermitian	hermitian	ADJ
ap-10691	517	4	superintegrable	superintegrable	ADJ
ap-10691	517	5	systems	system	NOUN
ap-10691	517	6	.	.	PUNCT
ap-10691	518	1	journal	journal	PROPN
ap-10691	518	2	of	of	ADP
ap-10691	518	3	physics	physics	PROPN
ap-10691	518	4	a	a	PRON
ap-10691	518	5	:	:	PUNCT
ap-10691	518	6	mathematical	mathematical	ADJ
ap-10691	518	7	and	and	CCONJ
ap-10691	518	8	theoretical	theoretical	ADJ
ap-10691	518	9	56(34):345207	56(34):345207	NOUN
ap-10691	518	10	,	,	PUNCT
ap-10691	518	11	2023	2023	NUM
ap-10691	518	12	.	.	PUNCT
ap-10691	519	1	https://doi.org/10.1088/1751-8121/ace506	https://doi.org/10.1088/1751-8121/ace506	PROPN
ap-10691	520	1	[	[	X
ap-10691	520	2	19	19	NUM
ap-10691	520	3	]	]	X
ap-10691	520	4	e.	e.	PROPN
ap-10691	520	5	celeghini	celeghini	PROPN
ap-10691	520	6	,	,	PUNCT
ap-10691	520	7	ş	ş	X
ap-10691	520	8	.	.	PUNCT
ap-10691	520	9	kuru	kuru	PROPN
ap-10691	520	10	,	,	PUNCT
ap-10691	520	11	j.	j.	PROPN
ap-10691	520	12	negro	negro	PROPN
ap-10691	520	13	,	,	PUNCT
ap-10691	520	14	m.	m.	NOUN
ap-10691	520	15	a.	a.	PROPN
ap-10691	520	16	del	del	PROPN
ap-10691	520	17	olmo	olmo	PROPN
ap-10691	520	18	.	.	PUNCT
ap-10691	521	1	a	a	DET
ap-10691	521	2	unified	unified	ADJ
ap-10691	521	3	approach	approach	NOUN
ap-10691	521	4	to	to	ADP
ap-10691	521	5	quantum	quantum	NOUN
ap-10691	521	6	and	and	CCONJ
ap-10691	521	7	classical	classical	ADJ
ap-10691	521	8	ttw	ttw	PROPN
ap-10691	521	9	systems	system	NOUN
ap-10691	521	10	based	base	VERB
ap-10691	521	11	on	on	ADP
ap-10691	521	12	factorizations	factorization	NOUN
ap-10691	521	13	.	.	PUNCT
ap-10691	522	1	annals	annal	NOUN
ap-10691	522	2	of	of	ADP
ap-10691	522	3	physics	physics	NOUN
ap-10691	522	4	332:27–37	332:27–37	PROPN
ap-10691	522	5	,	,	PUNCT
ap-10691	522	6	2012	2012	NUM
ap-10691	522	7	.	.	PUNCT
ap-10691	523	1	https://doi.org/10.1016/j.aop.2013.01.008	https://doi.org/10.1016/j.aop.2013.01.008	NOUN
ap-10691	524	1	[	[	X
ap-10691	524	2	20	20	NUM
ap-10691	524	3	]	]	PUNCT
ap-10691	524	4	t.	t.	PROPN
ap-10691	524	5	hakobyan	hakobyan	PROPN
ap-10691	524	6	,	,	PUNCT
ap-10691	524	7	o.	o.	PROPN
ap-10691	524	8	lechtenfeld	lechtenfeld	PROPN
ap-10691	524	9	,	,	PUNCT
ap-10691	524	10	a.	a.	NOUN
ap-10691	524	11	nersessian	nersessian	PROPN
ap-10691	524	12	,	,	PUNCT
ap-10691	524	13	et	et	PROPN
ap-10691	524	14	al	al	PROPN
ap-10691	524	15	.	.	PROPN
ap-10691	525	1	integrable	integrable	ADJ
ap-10691	525	2	generalizations	generalization	NOUN
ap-10691	525	3	of	of	ADP
ap-10691	525	4	oscillator	oscillator	NOUN
ap-10691	525	5	and	and	CCONJ
ap-10691	525	6	coulomb	coulomb	NOUN
ap-10691	525	7	systems	system	NOUN
ap-10691	525	8	via	via	ADP
ap-10691	525	9	action	action	NOUN
ap-10691	525	10	-	-	PUNCT
ap-10691	525	11	angle	angle	NOUN
ap-10691	525	12	variables	variable	NOUN
ap-10691	525	13	.	.	PUNCT
ap-10691	526	1	physics	physics	NOUN
ap-10691	526	2	letters	letter	NOUN
ap-10691	526	3	a	a	DET
ap-10691	526	4	376(5):679–686	376(5):679–686	NUM
ap-10691	526	5	,	,	PUNCT
ap-10691	526	6	2012	2012	NUM
ap-10691	526	7	.	.	PUNCT
ap-10691	527	1	https://doi.org/10.1016/j.physleta.2011.12.034	https://doi.org/10.1016/j.physleta.2011.12.034	PUNCT
ap-10691	527	2	[	[	X
ap-10691	527	3	21	21	NUM
ap-10691	527	4	]	]	PUNCT
ap-10691	527	5	t.	t.	PROPN
ap-10691	527	6	hakobyan	hakobyan	PROPN
ap-10691	527	7	,	,	PUNCT
ap-10691	527	8	o.	o.	PROPN
ap-10691	527	9	lechtenfeld	lechtenfeld	PROPN
ap-10691	527	10	,	,	PUNCT
ap-10691	527	11	a.	a.	NOUN
ap-10691	527	12	nersessian	nersessian	PROPN
ap-10691	527	13	,	,	PUNCT
ap-10691	527	14	et	et	PROPN
ap-10691	527	15	al	al	PROPN
ap-10691	527	16	.	.	PUNCT
ap-10691	527	17	action	action	NOUN
ap-10691	527	18	-	-	PUNCT
ap-10691	527	19	angle	angle	NOUN
ap-10691	527	20	variables	variable	NOUN
ap-10691	527	21	and	and	CCONJ
ap-10691	527	22	novel	novel	ADJ
ap-10691	527	23	superintegrable	superintegrable	ADJ
ap-10691	527	24	systems	system	NOUN
ap-10691	527	25	.	.	PUNCT
ap-10691	528	1	physics	physic	NOUN
ap-10691	528	2	of	of	ADP
ap-10691	528	3	particles	particle	NOUN
ap-10691	528	4	and	and	CCONJ
ap-10691	528	5	nuclei	nucleus	NOUN
ap-10691	528	6	43(5):577–582	43(5):577–582	PROPN
ap-10691	528	7	,	,	PUNCT
ap-10691	528	8	2012	2012	NUM
ap-10691	528	9	.	.	PUNCT
ap-10691	529	1	https://doi.org/10.1134/s1063779612050152	https://doi.org/10.1134/s1063779612050152	PROPN
ap-10691	529	2	[	[	X
ap-10691	529	3	22	22	NUM
ap-10691	529	4	]	]	PUNCT
ap-10691	529	5	m.	m.	PROPN
ap-10691	529	6	f.	f.	PROPN
ap-10691	529	7	rañada	rañada	PROPN
ap-10691	529	8	.	.	PUNCT
ap-10691	530	1	the	the	DET
ap-10691	530	2	tremblay	tremblay	NOUN
ap-10691	530	3	-	-	PUNCT
ap-10691	530	4	turbiner	turbiner	NOUN
ap-10691	530	5	-	-	PUNCT
ap-10691	530	6	winternitz	winternitz	NOUN
ap-10691	530	7	system	system	NOUN
ap-10691	530	8	on	on	ADP
ap-10691	530	9	spherical	spherical	ADJ
ap-10691	530	10	and	and	CCONJ
ap-10691	530	11	hyperbolic	hyperbolic	ADJ
ap-10691	530	12	spaces	space	NOUN
ap-10691	530	13	:	:	PUNCT
ap-10691	530	14	superintegrability	superintegrability	NOUN
ap-10691	530	15	,	,	PUNCT
ap-10691	530	16	curvature	curvature	NOUN
ap-10691	530	17	-	-	PUNCT
ap-10691	530	18	dependent	dependent	ADJ
ap-10691	530	19	formalism	formalism	NOUN
ap-10691	530	20	and	and	CCONJ
ap-10691	530	21	complex	complex	ADJ
ap-10691	530	22	factorization	factorization	NOUN
ap-10691	530	23	.	.	PUNCT
ap-10691	531	1	journal	journal	PROPN
ap-10691	531	2	of	of	ADP
ap-10691	531	3	physics	physics	PROPN
ap-10691	531	4	a	a	PRON
ap-10691	531	5	:	:	PUNCT
ap-10691	531	6	mathematical	mathematical	ADJ
ap-10691	531	7	and	and	CCONJ
ap-10691	531	8	theoretical	theoretical	ADJ
ap-10691	531	9	47(16):165203	47(16):165203	NUM
ap-10691	531	10	,	,	PUNCT
ap-10691	531	11	2014	2014	NUM
ap-10691	531	12	.	.	PUNCT
ap-10691	532	1	https://doi.org/10.1088/1751-8113/47/16/165203	https://doi.org/10.1088/1751-8113/47/16/165203	PUNCT
ap-10691	533	1	[	[	X
ap-10691	533	2	23	23	NUM
ap-10691	533	3	]	]	X
ap-10691	533	4	i.	i.	PROPN
ap-10691	533	5	marquette	marquette	PROPN
ap-10691	533	6	,	,	PUNCT
ap-10691	533	7	a.	a.	NOUN
ap-10691	533	8	parr	parr	PROPN
ap-10691	533	9	.	.	PUNCT
ap-10691	534	1	superintegrability	superintegrability	NOUN
ap-10691	534	2	and	and	CCONJ
ap-10691	534	3	deformed	deform	VERB
ap-10691	534	4	oscillator	oscillator	NOUN
ap-10691	534	5	realizations	realization	NOUN
ap-10691	534	6	of	of	ADP
ap-10691	534	7	quantum	quantum	PROPN
ap-10691	534	8	ttw	ttw	PROPN
ap-10691	534	9	hamiltonians	hamiltonian	NOUN
ap-10691	534	10	on	on	ADP
ap-10691	534	11	constant	constant	ADJ
ap-10691	534	12	-	-	PUNCT
ap-10691	534	13	curvature	curvature	NOUN
ap-10691	534	14	manifolds	manifold	NOUN
ap-10691	534	15	and	and	CCONJ
ap-10691	534	16	with	with	ADP
ap-10691	534	17	reflections	reflection	NOUN
ap-10691	534	18	in	in	ADP
ap-10691	534	19	a	a	DET
ap-10691	534	20	plane	plane	NOUN
ap-10691	534	21	.	.	PUNCT
ap-10691	535	1	journal	journal	PROPN
ap-10691	535	2	of	of	ADP
ap-10691	535	3	physics	physics	PROPN
ap-10691	535	4	a	a	PRON
ap-10691	535	5	:	:	PUNCT
ap-10691	535	6	mathematical	mathematical	ADJ
ap-10691	535	7	and	and	CCONJ
ap-10691	535	8	theoretical	theoretical	ADJ
ap-10691	535	9	57(13):135201	57(13):135201	NUM
ap-10691	535	10	,	,	PUNCT
ap-10691	535	11	2024	2024	NUM
ap-10691	535	12	.	.	PUNCT
ap-10691	536	1	https://doi.org/10.1088/1751-8121/ad2e3f	https://doi.org/10.1088/1751-8121/ad2e3f	PROPN
ap-10691	536	2	[	[	X
ap-10691	536	3	24	24	NUM
ap-10691	536	4	]	]	X
ap-10691	536	5	l.	l.	PROPN
ap-10691	536	6	infeld	infeld	PROPN
ap-10691	536	7	,	,	PUNCT
ap-10691	536	8	t.	t.	PROPN
ap-10691	536	9	e.	e.	PROPN
ap-10691	536	10	hull	hull	PROPN
ap-10691	536	11	.	.	PUNCT
ap-10691	537	1	the	the	DET
ap-10691	537	2	factorization	factorization	NOUN
ap-10691	537	3	method	method	NOUN
ap-10691	537	4	.	.	PUNCT
ap-10691	538	1	reviews	review	NOUN
ap-10691	538	2	of	of	ADP
ap-10691	538	3	modern	modern	ADJ
ap-10691	538	4	physics	physic	NOUN
ap-10691	538	5	23(1):21–68	23(1):21–68	NUM
ap-10691	538	6	,	,	PUNCT
ap-10691	538	7	1951	1951	NUM
ap-10691	538	8	.	.	PUNCT
ap-10691	539	1	https://doi.org/10.1103/revmodphys.23.21	https://doi.org/10.1103/revmodphys.23.21	PROPN
ap-10691	539	2	[	[	X
ap-10691	539	3	25	25	NUM
ap-10691	539	4	]	]	PUNCT
ap-10691	539	5	e.	e.	PROPN
ap-10691	539	6	schrödinger	schrödinger	PROPN
ap-10691	539	7	.	.	PUNCT
ap-10691	540	1	a	a	DET
ap-10691	540	2	method	method	NOUN
ap-10691	540	3	of	of	ADP
ap-10691	540	4	determining	determine	VERB
ap-10691	540	5	quantum	quantum	ADJ
ap-10691	540	6	-	-	ADJ
ap-10691	540	7	mechanical	mechanical	ADJ
ap-10691	540	8	eigenvalues	eigenvalue	NOUN
ap-10691	540	9	and	and	CCONJ
ap-10691	540	10	eigenfunctions	eigenfunction	NOUN
ap-10691	540	11	.	.	PUNCT
ap-10691	541	1	in	in	ADP
ap-10691	541	2	proceedings	proceeding	NOUN
ap-10691	541	3	of	of	ADP
ap-10691	541	4	the	the	DET
ap-10691	541	5	royal	royal	PROPN
ap-10691	541	6	irish	irish	PROPN
ap-10691	541	7	academy	academy	PROPN
ap-10691	541	8	.	.	PUNCT
ap-10691	542	1	section	section	PROPN
ap-10691	542	2	a	a	DET
ap-10691	542	3	:	:	PUNCT
ap-10691	542	4	mathematical	mathematical	ADJ
ap-10691	542	5	and	and	CCONJ
ap-10691	542	6	physical	physical	ADJ
ap-10691	542	7	sciences	science	NOUN
ap-10691	542	8	,	,	PUNCT
ap-10691	542	9	vol	vol	NOUN
ap-10691	542	10	.	.	PROPN
ap-10691	542	11	46	46	NUM
ap-10691	542	12	,	,	PUNCT
ap-10691	542	13	pp	pp	ADJ
ap-10691	542	14	.	.	PUNCT
ap-10691	543	1	9–16	9–16	NOUN
ap-10691	543	2	.	.	PUNCT
ap-10691	544	1	royal	royal	PROPN
ap-10691	544	2	irish	irish	PROPN
ap-10691	544	3	academy	academy	PROPN
ap-10691	544	4	,	,	PUNCT
ap-10691	544	5	1940	1940	NUM
ap-10691	544	6	.	.	PUNCT
ap-10691	545	1	http://www.jstor.org/stable/20490744	http://www.jstor.org/stable/20490744	NOUN
ap-10691	546	1	[	[	X
ap-10691	546	2	26	26	NUM
ap-10691	546	3	]	]	PUNCT
ap-10691	546	4	e.	e.	PROPN
ap-10691	546	5	schrödinger	schrödinger	PROPN
ap-10691	546	6	.	.	PUNCT
ap-10691	547	1	further	further	ADJ
ap-10691	547	2	studies	study	NOUN
ap-10691	547	3	on	on	ADP
ap-10691	547	4	solving	solve	VERB
ap-10691	547	5	eigenvalue	eigenvalue	NOUN
ap-10691	547	6	problems	problem	NOUN
ap-10691	547	7	by	by	ADP
ap-10691	547	8	factorization	factorization	NOUN
ap-10691	547	9	.	.	PUNCT
ap-10691	548	1	in	in	ADP
ap-10691	548	2	proceedings	proceeding	NOUN
ap-10691	548	3	of	of	ADP
ap-10691	548	4	the	the	DET
ap-10691	548	5	royal	royal	PROPN
ap-10691	548	6	irish	irish	PROPN
ap-10691	548	7	academy	academy	PROPN
ap-10691	548	8	.	.	PUNCT
ap-10691	549	1	section	section	PROPN
ap-10691	549	2	a	a	DET
ap-10691	549	3	:	:	PUNCT
ap-10691	549	4	mathematical	mathematical	ADJ
ap-10691	549	5	and	and	CCONJ
ap-10691	549	6	physical	physical	ADJ
ap-10691	549	7	sciences	science	NOUN
ap-10691	549	8	,	,	PUNCT
ap-10691	549	9	vol	vol	NOUN
ap-10691	549	10	.	.	PROPN
ap-10691	549	11	46	46	NUM
ap-10691	549	12	,	,	PUNCT
ap-10691	549	13	pp	pp	ADJ
ap-10691	549	14	.	.	PUNCT
ap-10691	550	1	183–206	183–206	NUM
ap-10691	550	2	.	.	PUNCT
ap-10691	551	1	royal	royal	PROPN
ap-10691	551	2	irish	irish	PROPN
ap-10691	551	3	academy	academy	PROPN
ap-10691	551	4	,	,	PUNCT
ap-10691	551	5	1941	1941	NUM
ap-10691	551	6	.	.	PUNCT
ap-10691	552	1	http://www.jstor.org/stable/20490756	http://www.jstor.org/stable/20490756	PRON
ap-10691	553	1	[	[	X
ap-10691	553	2	27	27	NUM
ap-10691	553	3	]	]	X
ap-10691	553	4	e.	e.	PROPN
ap-10691	553	5	g.	g.	PROPN
ap-10691	553	6	kalnins	kalnins	PROPN
ap-10691	553	7	,	,	PUNCT
ap-10691	553	8	j.	j.	PROPN
ap-10691	553	9	m.	m.	PROPN
ap-10691	553	10	kress	kress	PROPN
ap-10691	553	11	,	,	PUNCT
ap-10691	553	12	w.	w.	PROPN
ap-10691	553	13	miller	miller	PROPN
ap-10691	553	14	.	.	PUNCT
ap-10691	554	1	superintegrability	superintegrability	NOUN
ap-10691	554	2	and	and	CCONJ
ap-10691	554	3	higher	high	ADJ
ap-10691	554	4	order	order	NOUN
ap-10691	554	5	integrals	integral	NOUN
ap-10691	554	6	for	for	ADP
ap-10691	554	7	quantum	quantum	NOUN
ap-10691	554	8	systems	system	NOUN
ap-10691	554	9	.	.	PUNCT
ap-10691	555	1	journal	journal	PROPN
ap-10691	555	2	of	of	ADP
ap-10691	555	3	physics	physics	PROPN
ap-10691	555	4	a	a	PRON
ap-10691	555	5	:	:	PUNCT
ap-10691	555	6	mathematical	mathematical	ADJ
ap-10691	555	7	and	and	CCONJ
ap-10691	555	8	theoretical	theoretical	ADJ
ap-10691	555	9	43(26):265205	43(26):265205	NUM
ap-10691	555	10	,	,	PUNCT
ap-10691	555	11	2010	2010	NUM
ap-10691	555	12	.	.	PUNCT
ap-10691	556	1	https://doi.org/10.1088/1751-8113/43/26/265205	https://doi.org/10.1088/1751-8113/43/26/265205	NOUN
ap-10691	556	2	[	[	X
ap-10691	556	3	28	28	NUM
ap-10691	556	4	]	]	X
ap-10691	556	5	w.	w.	PROPN
ap-10691	556	6	miller	miller	PROPN
ap-10691	556	7	,	,	PUNCT
ap-10691	556	8	s.	s.	PROPN
ap-10691	556	9	post	post	PROPN
ap-10691	556	10	,	,	PUNCT
ap-10691	556	11	p.	p.	PROPN
ap-10691	556	12	winternitz	winternitz	PROPN
ap-10691	556	13	.	.	PUNCT
ap-10691	557	1	classical	classical	ADJ
ap-10691	557	2	and	and	CCONJ
ap-10691	557	3	quantum	quantum	ADJ
ap-10691	557	4	superintegrability	superintegrability	NOUN
ap-10691	557	5	with	with	ADP
ap-10691	557	6	applications	application	NOUN
ap-10691	557	7	.	.	PUNCT
ap-10691	558	1	journal	journal	PROPN
ap-10691	558	2	of	of	ADP
ap-10691	558	3	physics	physics	PROPN
ap-10691	558	4	a	a	PRON
ap-10691	558	5	:	:	PUNCT
ap-10691	558	6	mathematical	mathematical	ADJ
ap-10691	558	7	and	and	CCONJ
ap-10691	558	8	theoretical	theoretical	ADJ
ap-10691	558	9	46(42):423001	46(42):423001	NUM
ap-10691	558	10	,	,	PUNCT
ap-10691	558	11	2013	2013	NUM
ap-10691	558	12	.	.	PUNCT
ap-10691	559	1	https://doi.org/10.1088/1751-8113/46/42/423001	https://doi.org/10.1088/1751-8113/46/42/423001	PROPN
ap-10691	560	1	[	[	X
ap-10691	560	2	29	29	NUM
ap-10691	560	3	]	]	PUNCT
ap-10691	560	4	a.	a.	NOUN
ap-10691	560	5	romaniega	romaniega	PROPN
ap-10691	560	6	.	.	PUNCT
ap-10691	561	1	sistemas	sistemas	PROPN
ap-10691	561	2	superintegrables	superintegrable	NOUN
ap-10691	561	3	en	en	PROPN
ap-10691	561	4	mecánica	mecánica	PROPN
ap-10691	561	5	clásica	clásica	PROPN
ap-10691	561	6	y	y	PROPN
ap-10691	561	7	en	en	PROPN
ap-10691	561	8	mecánica	mecánica	PROPN
ap-10691	561	9	cuántica	cuántica	PROPN
ap-10691	561	10	:	:	PUNCT
ap-10691	561	11	generalización	generalización	PROPN
ap-10691	561	12	en	en	X
ap-10691	561	13	la	la	PROPN
ap-10691	561	14	ésfera	ésfera	PROPN
ap-10691	561	15	s2	s2	PROPN
ap-10691	561	16	y	y	PROPN
ap-10691	561	17	formulación	formulación	PROPN
ap-10691	561	18	geométrica	geométrica	PROPN
ap-10691	561	19	de	de	PROPN
ap-10691	561	20	la	la	PROPN
ap-10691	561	21	mecánica	mecánica	PROPN
ap-10691	562	1	[	[	X
ap-10691	562	2	in	in	ADP
ap-10691	562	3	spanish	spanish	ADJ
ap-10691	562	4	;	;	PUNCT
ap-10691	562	5	superintegrable	superintegrable	ADJ
ap-10691	562	6	systems	system	NOUN
ap-10691	562	7	in	in	ADP
ap-10691	562	8	classical	classical	ADJ
ap-10691	562	9	and	and	CCONJ
ap-10691	562	10	quantum	quantum	ADJ
ap-10691	562	11	mechanics	mechanic	NOUN
ap-10691	562	12	:	:	PUNCT
ap-10691	562	13	generalisation	generalisation	NOUN
ap-10691	562	14	on	on	ADP
ap-10691	562	15	the	the	DET
ap-10691	562	16	s2	s2	NOUN
ap-10691	562	17	-	-	PUNCT
ap-10691	562	18	sphere	sphere	NOUN
ap-10691	562	19	and	and	CCONJ
ap-10691	562	20	the	the	DET
ap-10691	562	21	geometric	geometric	ADJ
ap-10691	562	22	formulation	formulation	NOUN
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ap-10691	562	24	mechanics	mechanic	NOUN
ap-10691	562	25	]	]	PUNCT
ap-10691	562	26	.	.	PUNCT
ap-10691	563	1	bachelor	bachelor	PROPN
ap-10691	563	2	’s	’s	PART
ap-10691	563	3	thesis	thesis	NOUN
ap-10691	563	4	,	,	PUNCT
ap-10691	563	5	university	university	NOUN
ap-10691	563	6	of	of	ADP
ap-10691	563	7	valladolid	valladolid	PROPN
ap-10691	563	8	,	,	PUNCT
ap-10691	563	9	2016	2016	NUM
ap-10691	563	10	.	.	PUNCT
ap-10691	564	1	[	[	X
ap-10691	564	2	30	30	NUM
ap-10691	564	3	]	]	X
ap-10691	564	4	g.	g.	NOUN
ap-10691	564	5	pöschl	pöschl	PROPN
ap-10691	564	6	,	,	PUNCT
ap-10691	564	7	e.	e.	PROPN
ap-10691	564	8	teller	teller	PROPN
ap-10691	564	9	.	.	PUNCT
ap-10691	565	1	bemerkungen	bemerkungen	PROPN
ap-10691	565	2	zur	zur	PROPN
ap-10691	565	3	quantenmechanik	quantenmechanik	X
ap-10691	565	4	des	des	PROPN
ap-10691	565	5	anharmonischen	anharmonischen	PROPN
ap-10691	565	6	oszillators	oszillator	NOUN
ap-10691	566	1	[	[	X
ap-10691	566	2	in	in	ADP
ap-10691	566	3	german	german	ADJ
ap-10691	566	4	;	;	PUNCT
ap-10691	566	5	remarks	remark	NOUN
ap-10691	566	6	on	on	ADP
ap-10691	566	7	the	the	DET
ap-10691	566	8	quantum	quantum	ADJ
ap-10691	566	9	mechanics	mechanic	NOUN
ap-10691	566	10	of	of	ADP
ap-10691	566	11	the	the	DET
ap-10691	566	12	anharmonic	anharmonic	ADJ
ap-10691	566	13	oscillator	oscillator	NOUN
ap-10691	566	14	]	]	PUNCT
ap-10691	566	15	.	.	PUNCT
ap-10691	567	1	zeitschrift	zeitschrift	PROPN
ap-10691	567	2	für	für	PROPN
ap-10691	567	3	physik	physik	PROPN
ap-10691	567	4	83(3):143	83(3):143	PROPN
ap-10691	567	5	–	–	PUNCT
ap-10691	567	6	151	151	NUM
ap-10691	567	7	,	,	PUNCT
ap-10691	567	8	1933	1933	NUM
ap-10691	567	9	.	.	PUNCT
ap-10691	568	1	https://doi.org/10.1007/bf01331132	https://doi.org/10.1007/bf01331132	PRON
ap-10691	568	2	531	531	NUM
ap-10691	568	3	https://doi.org/10.1063/1.2191360	https://doi.org/10.1063/1.2191360	NOUN
ap-10691	568	4	https://doi.org/10.1088/1751-8113/41/25/255201	https://doi.org/10.1088/1751-8113/41/25/255201	SCONJ
ap-10691	568	5	https://doi.org/10.1016/j.aop.2011.12.014	https://doi.org/10.1016/j.aop.2011.12.014	NOUN
ap-10691	568	6	https://doi.org/10.1088/1751-8113/42/24/242001	https://doi.org/10.1088/1751-8113/42/24/242001	VERB
ap-10691	568	7	https://doi.org/10.1088/1751-8113/43/1/015202	https://doi.org/10.1088/1751-8113/43/1/015202	PROPN
ap-10691	568	8	https://doi.org/10.1016/0031-9163(65)90885-1	https://doi.org/10.1016/0031-9163(65)90885-1	INTJ
ap-10691	568	9	https://doi.org/10.1063/1.533014	https://doi.org/10.1063/1.533014	NOUN
ap-10691	568	10	https://doi.org/10.1063/1.4798807	https://doi.org/10.1063/1.4798807	NOUN
ap-10691	568	11	https://doi.org/10.1063/1.4990793	https://doi.org/10.1063/1.4990793	PROPN
ap-10691	568	12	https://doi.org/10.1063/1.4990794	https://doi.org/10.1063/1.4990794	PROPN
ap-10691	568	13	https://doi.org/10.1088/1751-8121/aadc23	https://doi.org/10.1088/1751-8121/aadc23	NOUN
ap-10691	569	1	https://doi.org/10.1088/1751-8121/ace506	https://doi.org/10.1088/1751-8121/ace506	PROPN
ap-10691	569	2	https://doi.org/10.1016/j.aop.2013.01.008	https://doi.org/10.1016/j.aop.2013.01.008	NOUN
ap-10691	569	3	https://doi.org/10.1016/j.physleta.2011.12.034	https://doi.org/10.1016/j.physleta.2011.12.034	PUNCT
ap-10691	569	4	https://doi.org/10.1134/s1063779612050152	https://doi.org/10.1134/s1063779612050152	PROPN
ap-10691	569	5	https://doi.org/10.1088/1751-8113/47/16/165203	https://doi.org/10.1088/1751-8113/47/16/165203	NUM
ap-10691	569	6	https://doi.org/10.1088/1751-8121/ad2e3f	https://doi.org/10.1088/1751-8121/ad2e3f	PROPN
ap-10691	569	7	https://doi.org/10.1103/revmodphys.23.21	https://doi.org/10.1103/revmodphys.23.21	PROPN
ap-10691	569	8	http://www.jstor.org/stable/20490744	http://www.jstor.org/stable/20490744	NOUN
ap-10691	569	9	http://www.jstor.org/stable/20490756	http://www.jstor.org/stable/20490756	PROPN
ap-10691	569	10	https://doi.org/10.1088/1751-8113/43/26/265205	https://doi.org/10.1088/1751-8113/43/26/265205	NOUN
ap-10691	569	11	https://doi.org/10.1088/1751-8113/46/42/423001	https://doi.org/10.1088/1751-8113/46/42/423001	PROPN
ap-10691	570	1	https://doi.org/10.1007/bf01331132	https://doi.org/10.1007/bf01331132	PROPN
ap-10691	570	2	mariano	mariano	PROPN
ap-10691	570	3	a.	a.	PROPN
ap-10691	570	4	del	del	PROPN
ap-10691	570	5	olmo	olmo	PROPN
ap-10691	570	6	,	,	PUNCT
ap-10691	570	7	álvaro	álvaro	PROPN
ap-10691	570	8	romaniega	romaniega	PROPN
ap-10691	570	9	acta	acta	PROPN
ap-10691	570	10	polytechnica	polytechnica	PROPN
ap-10691	571	1	[	[	X
ap-10691	571	2	31	31	NUM
ap-10691	571	3	]	]	SYM
ap-10691	571	4	ş	ş	PROPN
ap-10691	571	5	.	.	PUNCT
ap-10691	571	6	kuru	kuru	PROPN
ap-10691	571	7	,	,	PUNCT
ap-10691	571	8	j.	j.	PROPN
ap-10691	571	9	negro	negro	PROPN
ap-10691	571	10	.	.	PUNCT
ap-10691	572	1	factorizations	factorization	NOUN
ap-10691	572	2	of	of	ADP
ap-10691	572	3	one	one	NUM
ap-10691	572	4	-	-	PUNCT
ap-10691	572	5	dimensional	dimensional	ADJ
ap-10691	572	6	classical	classical	ADJ
ap-10691	572	7	systems	system	NOUN
ap-10691	572	8	.	.	PUNCT
ap-10691	573	1	annals	annal	NOUN
ap-10691	573	2	of	of	ADP
ap-10691	573	3	physics	physics	NOUN
ap-10691	573	4	323(2):413–431	323(2):413–431	NUM
ap-10691	573	5	,	,	PUNCT
ap-10691	573	6	2008	2008	NUM
ap-10691	573	7	.	.	PUNCT
ap-10691	574	1	https://doi.org/10.1016/j.aop.2007.10.004	https://doi.org/10.1016/j.aop.2007.10.004	PROPN
ap-10691	574	2	[	[	X
ap-10691	574	3	32	32	NUM
ap-10691	574	4	]	]	PUNCT
ap-10691	574	5	m.	m.	NOUN
ap-10691	574	6	blazquez	blazquez	NOUN
ap-10691	574	7	,	,	PUNCT
ap-10691	574	8	j.	j.	PROPN
ap-10691	574	9	negro	negro	PROPN
ap-10691	574	10	.	.	PUNCT
ap-10691	575	1	so(2	so(2	ADJ
ap-10691	575	2	,	,	PUNCT
ap-10691	575	3	2	2	X
ap-10691	575	4	)	)	PUNCT
ap-10691	575	5	representations	representation	NOUN
ap-10691	575	6	in	in	ADP
ap-10691	575	7	polar	polar	ADJ
ap-10691	575	8	coordinates	coordinate	NOUN
ap-10691	575	9	and	and	CCONJ
ap-10691	575	10	pöschl	pöschl	NOUN
ap-10691	575	11	-	-	PUNCT
ap-10691	575	12	teller	teller	NOUN
ap-10691	575	13	potentials	potential	NOUN
ap-10691	575	14	.	.	PUNCT
ap-10691	576	1	journal	journal	PROPN
ap-10691	576	2	of	of	ADP
ap-10691	576	3	physics	physics	PROPN
ap-10691	576	4	a	a	PRON
ap-10691	576	5	:	:	PUNCT
ap-10691	576	6	mathematical	mathematical	ADJ
ap-10691	576	7	and	and	CCONJ
ap-10691	576	8	theoretical	theoretical	ADJ
ap-10691	576	9	57(19):195204	57(19):195204	NUM
ap-10691	576	10	,	,	PUNCT
ap-10691	576	11	2024	2024	NUM
ap-10691	576	12	.	.	PUNCT
ap-10691	577	1	https://doi.org/10.1088/1751-8121/ad3d45	https://doi.org/10.1088/1751-8121/ad3d45	X
ap-10691	578	1	[	[	X
ap-10691	578	2	33	33	NUM
ap-10691	578	3	]	]	SYM
ap-10691	578	4	ş	ş	X
ap-10691	578	5	.	.	PUNCT
ap-10691	578	6	kuru	kuru	PROPN
ap-10691	578	7	,	,	PUNCT
ap-10691	578	8	i.	i.	PROPN
ap-10691	578	9	marquette	marquette	PROPN
ap-10691	578	10	,	,	PUNCT
ap-10691	578	11	j.	j.	PROPN
ap-10691	578	12	negro	negro	PROPN
ap-10691	578	13	.	.	PUNCT
ap-10691	579	1	the	the	DET
ap-10691	579	2	general	general	ADJ
ap-10691	579	3	racah	racah	PROPN
ap-10691	579	4	algebra	algebra	PROPN
ap-10691	579	5	as	as	ADP
ap-10691	579	6	the	the	DET
ap-10691	579	7	symmetry	symmetry	NOUN
ap-10691	579	8	algebra	algebra	NOUN
ap-10691	579	9	of	of	ADP
ap-10691	579	10	generic	generic	ADJ
ap-10691	579	11	systems	system	NOUN
ap-10691	579	12	on	on	ADP
ap-10691	579	13	pseudo	pseudo	NOUN
ap-10691	579	14	-	-	NOUN
ap-10691	579	15	spheres	sphere	NOUN
ap-10691	579	16	.	.	PUNCT
ap-10691	580	1	journal	journal	PROPN
ap-10691	580	2	of	of	ADP
ap-10691	580	3	physics	physics	PROPN
ap-10691	580	4	a	a	PRON
ap-10691	580	5	:	:	PUNCT
ap-10691	580	6	mathematical	mathematical	ADJ
ap-10691	580	7	and	and	CCONJ
ap-10691	580	8	theoretical	theoretical	ADJ
ap-10691	580	9	53(40):405203	53(40):405203	NUM
ap-10691	580	10	,	,	PUNCT
ap-10691	580	11	2020	2020	NUM
ap-10691	580	12	.	.	PUNCT
ap-10691	581	1	https://doi.org/10.1088/1751-8121/abadb7	https://doi.org/10.1088/1751-8121/abadb7	VERB
ap-10691	582	1	[	[	X
ap-10691	582	2	34	34	NUM
ap-10691	582	3	]	]	X
ap-10691	582	4	f.	f.	PROPN
ap-10691	582	5	correa	correa	PROPN
ap-10691	582	6	,	,	PUNCT
ap-10691	582	7	m.	m.	NOUN
ap-10691	582	8	a.	a.	PROPN
ap-10691	582	9	del	del	PROPN
ap-10691	582	10	olmo	olmo	PROPN
ap-10691	582	11	,	,	PUNCT
ap-10691	582	12	i.	i.	PROPN
ap-10691	582	13	marquette	marquette	PROPN
ap-10691	582	14	,	,	PUNCT
ap-10691	582	15	j.	j.	PROPN
ap-10691	582	16	negro	negro	PROPN
ap-10691	582	17	.	.	PUNCT
ap-10691	583	1	polynomial	polynomial	PROPN
ap-10691	583	2	algebras	algebras	PROPN
ap-10691	583	3	from	from	ADP
ap-10691	583	4	su(3	su(3	PROPN
ap-10691	583	5	)	)	PUNCT
ap-10691	583	6	and	and	CCONJ
ap-10691	583	7	a	a	DET
ap-10691	583	8	quadratically	quadratically	ADV
ap-10691	583	9	superintegrable	superintegrable	ADJ
ap-10691	583	10	model	model	NOUN
ap-10691	583	11	on	on	ADP
ap-10691	583	12	the	the	DET
ap-10691	583	13	two	two	NUM
ap-10691	583	14	sphere	sphere	NOUN
ap-10691	583	15	.	.	PUNCT
ap-10691	584	1	journal	journal	PROPN
ap-10691	584	2	of	of	ADP
ap-10691	584	3	physics	physics	PROPN
ap-10691	584	4	a	a	PRON
ap-10691	584	5	:	:	PUNCT
ap-10691	584	6	mathematical	mathematical	ADJ
ap-10691	584	7	and	and	CCONJ
ap-10691	584	8	theoretical	theoretical	ADJ
ap-10691	584	9	54(1):015205	54(1):015205	NUM
ap-10691	584	10	,	,	PUNCT
ap-10691	584	11	2020	2020	NUM
ap-10691	584	12	.	.	PUNCT
ap-10691	585	1	https://doi.org/10.1088/1751-8121/abc909	https://doi.org/10.1088/1751-8121/abc909	PROPN
ap-10691	585	2	[	[	X
ap-10691	585	3	35	35	NUM
ap-10691	585	4	]	]	X
ap-10691	585	5	j.	j.	PROPN
ap-10691	585	6	c.	c.	PROPN
ap-10691	585	7	l.	l.	PROPN
ap-10691	585	8	vieyra	vieyra	PROPN
ap-10691	585	9	,	,	PUNCT
ap-10691	585	10	a.	a.	NOUN
ap-10691	585	11	v.	v.	PROPN
ap-10691	585	12	turbiner	turbiner	PROPN
ap-10691	585	13	.	.	PUNCT
ap-10691	586	1	tremblay	tremblay	NOUN
ap-10691	586	2	-	-	PUNCT
ap-10691	586	3	turbinerwinternitz	turbinerwinternitz	NOUN
ap-10691	586	4	(	(	PUNCT
ap-10691	586	5	ttw	ttw	PROPN
ap-10691	586	6	)	)	PUNCT
ap-10691	586	7	system	system	NOUN
ap-10691	586	8	at	at	ADP
ap-10691	586	9	integer	integer	PROPN
ap-10691	586	10	index	index	NOUN
ap-10691	586	11	k	k	NOUN
ap-10691	586	12	:	:	PUNCT
ap-10691	586	13	polynomial	polynomial	ADJ
ap-10691	586	14	algebras	algebra	NOUN
ap-10691	586	15	of	of	ADP
ap-10691	586	16	integrals	integral	NOUN
ap-10691	586	17	.	.	PUNCT
ap-10691	587	1	arxiv	arxiv	PROPN
ap-10691	587	2	math	math	PROPN
ap-10691	587	3	-	-	PUNCT
ap-10691	587	4	ph:2503.09502	ph:2503.09502	PROPN
ap-10691	587	5	,	,	PUNCT
ap-10691	587	6	2025	2025	NUM
ap-10691	587	7	.	.	PUNCT
ap-10691	588	1	https://doi.org/10.48550/arxiv.2503.09502	https://doi.org/10.48550/arxiv.2503.09502	PROPN
ap-10691	588	2	532	532	NUM
ap-10691	588	3	https://doi.org/10.1016/j.aop.2007.10.004	https://doi.org/10.1016/j.aop.2007.10.004	PROPN
ap-10691	588	4	https://doi.org/10.1088/1751-8121/ad3d45	https://doi.org/10.1088/1751-8121/ad3d45	ADP
ap-10691	588	5	https://doi.org/10.1088/1751-8121/abadb7	https://doi.org/10.1088/1751-8121/abadb7	VERB
ap-10691	589	1	https://doi.org/10.1088/1751-8121/abc909	https://doi.org/10.1088/1751-8121/abc909	PROPN
ap-10691	589	2	https://doi.org/10.48550/arxiv.2503.09502	https://doi.org/10.48550/arxiv.2503.09502	PROPN
ap-10691	589	3	vol	vol	NOUN
ap-10691	589	4	.	.	PUNCT
ap-10691	590	1	65	65	NUM
ap-10691	590	2	no	no	NOUN
ap-10691	590	3	.	.	PUNCT
ap-10691	591	1	5/2025	5/2025	NUM
ap-10691	591	2	classical	classical	ADJ
ap-10691	591	3	and	and	CCONJ
ap-10691	591	4	quantum	quantum	ADJ
ap-10691	591	5	superintegrable	superintegrable	ADJ
ap-10691	591	6	systems	system	NOUN
ap-10691	591	7	on	on	ADP
ap-10691	591	8	the	the	DET
ap-10691	591	9	sphere	sphere	NOUN
ap-10691	591	10	.	.	PUNCT
ap-10691	591	11	.	.	PUNCT
ap-10691	591	12	.	.	PUNCT
ap-10691	592	1	appendix	appendix	VERB
ap-10691	592	2	a.	a.	NOUN
ap-10691	592	3	generalisation	generalisation	NOUN
ap-10691	592	4	of	of	ADP
ap-10691	592	5	theorem	theorem	ADJ
ap-10691	592	6	1	1	NUM
ap-10691	592	7	let	let	VERB
ap-10691	592	8	us	we	PRON
ap-10691	592	9	consider	consider	VERB
ap-10691	592	10	a	a	DET
ap-10691	592	11	hamiltonian	hamiltonian	NOUN
ap-10691	592	12	of	of	ADP
ap-10691	592	13	the	the	DET
ap-10691	592	14	form	form	NOUN
ap-10691	592	15	:	:	PUNCT
ap-10691	592	16	hk	hk	PROPN
ap-10691	592	17	=	=	SYM
ap-10691	592	18	hx	hx	PROPN
ap-10691	592	19	mk	mk	PROPN
ap-10691	592	20	+	+	CCONJ
ap-10691	592	21	k2(hy	k2(hy	PROPN
ap-10691	592	22	−	−	PROPN
ap-10691	592	23	e′	e′	PROPN
ap-10691	592	24	)	)	PUNCT
ap-10691	592	25	f(x	f(x	PROPN
ap-10691	592	26	)	)	PUNCT
ap-10691	592	27	,	,	PUNCT
ap-10691	592	28	hx	hx	PROPN
ap-10691	592	29	mk	mk	PROPN
ap-10691	592	30	=	=	PROPN
ap-10691	592	31	hx	hx	PROPN
ap-10691	592	32	+	+	CCONJ
ap-10691	592	33	m2	m2	PROPN
ap-10691	592	34	k	k	PROPN
ap-10691	592	35	f(x	f(x	PROPN
ap-10691	592	36	)	)	PUNCT
ap-10691	592	37	,	,	PUNCT
ap-10691	592	38	(	(	PUNCT
ap-10691	592	39	122	122	NUM
ap-10691	592	40	)	)	PUNCT
ap-10691	592	41	where	where	SCONJ
ap-10691	592	42	(	(	PUNCT
ap-10691	592	43	x	x	NOUN
ap-10691	592	44	,	,	PUNCT
ap-10691	592	45	y	y	NOUN
ap-10691	592	46	)	)	PUNCT
ap-10691	592	47	are	be	AUX
ap-10691	592	48	the	the	DET
ap-10691	592	49	configuration	configuration	NOUN
ap-10691	592	50	space	space	NOUN
ap-10691	592	51	variables	variable	NOUN
ap-10691	592	52	,	,	PUNCT
ap-10691	592	53	hx	hx	PROPN
ap-10691	592	54	and	and	CCONJ
ap-10691	592	55	hy	hy	PROPN
ap-10691	592	56	are	be	AUX
ap-10691	592	57	hamiltonians	hamiltonian	NOUN
ap-10691	592	58	,	,	PUNCT
ap-10691	592	59	depending	depend	VERB
ap-10691	592	60	only	only	ADV
ap-10691	592	61	on	on	ADP
ap-10691	592	62	x	x	PUNCT
ap-10691	592	63	and	and	CCONJ
ap-10691	592	64	y	y	PROPN
ap-10691	592	65	,	,	PUNCT
ap-10691	592	66	respectively	respectively	ADV
ap-10691	592	67	,	,	PUNCT
ap-10691	592	68	and	and	CCONJ
ap-10691	592	69	f(x	f(x	PROPN
ap-10691	592	70	)	)	PUNCT
ap-10691	592	71	is	be	AUX
ap-10691	592	72	a	a	DET
ap-10691	592	73	smooth	smooth	ADJ
ap-10691	592	74	function	function	NOUN
ap-10691	592	75	.	.	PUNCT
ap-10691	593	1	here	here	ADV
ap-10691	593	2	,	,	PUNCT
ap-10691	593	3	mk	mk	PROPN
ap-10691	593	4	=	=	SYM
ap-10691	593	5	kβ	kβ	PROPN
ap-10691	593	6	,	,	PUNCT
ap-10691	593	7	k	k	PROPN
ap-10691	593	8	̸=	̸=	PROPN
ap-10691	593	9	0	0	NUM
ap-10691	593	10	is	be	AUX
ap-10691	593	11	a	a	DET
ap-10691	593	12	real	real	ADJ
ap-10691	593	13	number	number	NOUN
ap-10691	593	14	,	,	PUNCT
ap-10691	593	15	and	and	CCONJ
ap-10691	593	16	e′	e′	NOUN
ap-10691	593	17	=	=	NOUN
ap-10691	593	18	β2	β2	PROPN
ap-10691	593	19	is	be	AUX
ap-10691	593	20	an	an	DET
ap-10691	593	21	eigenvalue	eigenvalue	NOUN
ap-10691	593	22	of	of	ADP
ap-10691	593	23	hy	hy	PROPN
ap-10691	593	24	.	.	PUNCT
ap-10691	594	1	suppose	suppose	VERB
ap-10691	594	2	that	that	SCONJ
ap-10691	594	3	there	there	PRON
ap-10691	594	4	exist	exist	VERB
ap-10691	594	5	ladder	ladder	NOUN
ap-10691	594	6	and	and	CCONJ
ap-10691	594	7	shift	shift	VERB
ap-10691	594	8	operators	operator	NOUN
ap-10691	594	9	ly	ly	ADP
ap-10691	594	10	n	n	PROPN
ap-10691	594	11	and	and	CCONJ
ap-10691	594	12	sx	sx	PROPN
ap-10691	594	13	m	m	PROPN
ap-10691	594	14	,	,	PUNCT
ap-10691	594	15	respectively	respectively	ADV
ap-10691	594	16	,	,	PUNCT
ap-10691	594	17	acting	act	VERB
ap-10691	594	18	as	as	ADP
ap-10691	594	19	equation	equation	NOUN
ap-10691	594	20	(	(	PUNCT
ap-10691	594	21	23	23	NUM
ap-10691	594	22	):	):	PUNCT
ap-10691	594	23	ly	ly	ADP
ap-10691	594	24	±n	±n	PROPN
ap-10691	594	25	:	:	PUNCT
ap-10691	594	26	hy	hy	PROPN
ap-10691	594	27	→	→	SYM
ap-10691	594	28	hy	hy	PROPN
ap-10691	594	29	,	,	PUNCT
ap-10691	594	30	sx	sx	PROPN
ap-10691	594	31	±m	±m	PROPN
ap-10691	594	32	:	:	PUNCT
ap-10691	594	33	hx	hx	PROPN
ap-10691	594	34	mk	mk	PROPN
ap-10691	594	35	→	→	SYM
ap-10691	594	36	hx	hx	PROPN
ap-10691	594	37	mk±m	mk±m	PROPN
ap-10691	594	38	,	,	PUNCT
ap-10691	594	39	ψβ(y	ψβ(y	PUNCT
ap-10691	594	40	)	)	PUNCT
ap-10691	594	41	7→	7→	NUM
ap-10691	594	42	ψβ±n	ψβ±n	ADJ
ap-10691	594	43	=	=	SYM
ap-10691	594	44	l±nψβ(y	l±nψβ(y	NOUN
ap-10691	594	45	)	)	PUNCT
ap-10691	594	46	,	,	PUNCT
ap-10691	594	47	φmk	φmk	INTJ
ap-10691	594	48	(	(	PUNCT
ap-10691	594	49	x	x	NOUN
ap-10691	594	50	)	)	PUNCT
ap-10691	594	51	7→	7→	NUM
ap-10691	594	52	φmk±m(x	φmk±m(x	NOUN
ap-10691	594	53	)	)	PUNCT
ap-10691	594	54	=	=	SYM
ap-10691	594	55	sx	sx	PROPN
ap-10691	594	56	±mφ	±mφ	PROPN
ap-10691	594	57	mk	mk	PROPN
ap-10691	594	58	(	(	PUNCT
ap-10691	594	59	x	x	NOUN
ap-10691	594	60	)	)	PUNCT
ap-10691	594	61	,	,	PUNCT
ap-10691	594	62	(	(	PUNCT
ap-10691	594	63	123	123	NUM
ap-10691	594	64	)	)	PUNCT
ap-10691	594	65	where	where	SCONJ
ap-10691	594	66	ψβ	ψβ	PROPN
ap-10691	594	67	∈	∈	PROPN
ap-10691	595	1	hθ	hθ	PROPN
ap-10691	595	2	is	be	AUX
ap-10691	595	3	an	an	DET
ap-10691	595	4	eigenvector	eigenvector	NOUN
ap-10691	595	5	of	of	ADP
ap-10691	595	6	hy	hy	NOUN
ap-10691	595	7	with	with	ADP
ap-10691	595	8	eigenvalue	eigenvalue	PROPN
ap-10691	595	9	β2	β2	PROPN
ap-10691	595	10	and	and	CCONJ
ap-10691	595	11	φmk	φmk	ADJ
ap-10691	595	12	∈	∈	PROPN
ap-10691	595	13	hx	hx	PROPN
ap-10691	595	14	mk	mk	PROPN
ap-10691	595	15	is	be	AUX
ap-10691	595	16	an	an	DET
ap-10691	595	17	eigenvector	eigenvector	NOUN
ap-10691	595	18	of	of	ADP
ap-10691	595	19	hx	hx	PROPN
ap-10691	595	20	mk	mk	PROPN
ap-10691	595	21	.	.	PUNCT
ap-10691	596	1	then	then	ADV
ap-10691	596	2	,	,	PUNCT
ap-10691	596	3	if	if	SCONJ
ap-10691	596	4	k	k	PROPN
ap-10691	596	5	=	=	VERB
ap-10691	596	6	m	m	VERB
ap-10691	596	7	n	n	VERB
ap-10691	596	8	is	be	AUX
ap-10691	596	9	a	a	DET
ap-10691	596	10	rational	rational	ADJ
ap-10691	596	11	number	number	NOUN
ap-10691	596	12	,	,	PUNCT
ap-10691	596	13	there	there	PRON
ap-10691	596	14	are	be	VERB
ap-10691	596	15	two	two	NUM
ap-10691	596	16	symmetry	symmetry	NOUN
ap-10691	596	17	operators	operator	NOUN
ap-10691	596	18	(	(	PUNCT
ap-10691	596	19	x±	x±	PROPN
ap-10691	596	20	)	)	PUNCT
ap-10691	596	21	of	of	ADP
ap-10691	596	22	the	the	DET
ap-10691	596	23	hamiltonian	hamiltonian	PROPN
ap-10691	596	24	hk	hk	PROPN
ap-10691	596	25	,	,	PUNCT
ap-10691	596	26	(	(	PUNCT
ap-10691	596	27	i.e.	i.e.	X
ap-10691	596	28	operators	operator	NOUN
ap-10691	596	29	that	that	PRON
ap-10691	596	30	commute	commute	VERB
ap-10691	596	31	with	with	ADP
ap-10691	596	32	hk	hk	PROPN
ap-10691	596	33	)	)	PUNCT
ap-10691	596	34	,	,	PUNCT
ap-10691	596	35	defined	define	VERB
ap-10691	596	36	as	as	ADP
ap-10691	596	37	:	:	PUNCT
ap-10691	596	38	x±	x±	PROPN
ap-10691	596	39	:	:	PUNCT
ap-10691	596	40	=	=	SYM
ap-10691	596	41	ly	ly	ADP
ap-10691	596	42	±n	±n	PROPN
ap-10691	596	43	s	s	PART
ap-10691	596	44	x	x	SYM
ap-10691	596	45	±m	±m	PROPN
ap-10691	596	46	,	,	PUNCT
ap-10691	596	47	m	m	PROPN
ap-10691	596	48	,	,	PUNCT
ap-10691	596	49	n	n	PRON
ap-10691	596	50	∈	∈	PROPN
ap-10691	596	51	n∗	n∗	PROPN
ap-10691	596	52	≡	≡	PROPN
ap-10691	596	53	n	n	CCONJ
ap-10691	596	54	−	−	PROPN
ap-10691	596	55	{	{	PUNCT
ap-10691	596	56	0	0	NUM
ap-10691	596	57	}	}	PUNCT
ap-10691	596	58	.	.	PUNCT
ap-10691	597	1	(	(	PUNCT
ap-10691	597	2	124	124	NUM
ap-10691	597	3	)	)	PUNCT
ap-10691	597	4	since	since	SCONJ
ap-10691	597	5	there	there	PRON
ap-10691	597	6	are	be	VERB
ap-10691	597	7	2	2	NUM
ap-10691	597	8	×	×	NOUN
ap-10691	597	9	2	2	NUM
ap-10691	597	10	−	−	NOUN
ap-10691	597	11	1	1	NUM
ap-10691	597	12	independent	independent	ADJ
ap-10691	597	13	symmetries	symmetry	NOUN
ap-10691	597	14	,	,	PUNCT
ap-10691	597	15	(	(	PUNCT
ap-10691	597	16	namely	namely	ADV
ap-10691	597	17	x±	x±	PROPN
ap-10691	597	18	and	and	CCONJ
ap-10691	597	19	hk	hk	PROPN
ap-10691	597	20	)	)	PUNCT
ap-10691	597	21	,	,	PUNCT
ap-10691	597	22	the	the	DET
ap-10691	597	23	system	system	NOUN
ap-10691	597	24	is	be	AUX
ap-10691	597	25	maximally	maximally	ADV
ap-10691	597	26	superintegrable	superintegrable	ADJ
ap-10691	597	27	.	.	PUNCT
ap-10691	598	1	proof	proof	NOUN
ap-10691	598	2	.	.	PUNCT
ap-10691	599	1	by	by	ADP
ap-10691	599	2	computing	compute	VERB
ap-10691	599	3	the	the	DET
ap-10691	599	4	action	action	NOUN
ap-10691	599	5	of	of	ADP
ap-10691	599	6	the	the	DET
ap-10691	599	7	commutator	commutator	NOUN
ap-10691	600	1	[	[	X
ap-10691	600	2	hk	hk	PROPN
ap-10691	600	3	,	,	PUNCT
ap-10691	600	4	l	l	PROPN
ap-10691	600	5	y	y	PROPN
ap-10691	600	6	ns	ns	NUM
ap-10691	600	7	x	x	PROPN
ap-10691	600	8	m	m	VERB
ap-10691	600	9	]	]	X
ap-10691	600	10	on	on	ADP
ap-10691	600	11	an	an	DET
ap-10691	600	12	eigenfunction	eigenfunction	NOUN
ap-10691	600	13	ψ(x	ψ(x	PROPN
ap-10691	600	14	,	,	PUNCT
ap-10691	600	15	y	y	NOUN
ap-10691	600	16	)	)	PUNCT
ap-10691	600	17	=	=	SYM
ap-10691	600	18	φmk	φmk	NOUN
ap-10691	600	19	(	(	PUNCT
ap-10691	600	20	x)ψβ(y	x)ψβ(y	NOUN
ap-10691	600	21	)	)	PUNCT
ap-10691	600	22	of	of	ADP
ap-10691	600	23	hk	hk	PROPN
ap-10691	600	24	with	with	ADP
ap-10691	600	25	eigenvalue	eigenvalue	PROPN
ap-10691	600	26	e	e	NOUN
ap-10691	600	27	,	,	PUNCT
ap-10691	600	28	we	we	PRON
ap-10691	600	29	obtain	obtain	VERB
ap-10691	600	30	:	:	PUNCT
ap-10691	601	1	[	[	X
ap-10691	601	2	hk	hk	PROPN
ap-10691	601	3	,	,	PUNCT
ap-10691	601	4	l	l	PROPN
ap-10691	601	5	y	y	PROPN
ap-10691	601	6	ns	ns	NUM
ap-10691	601	7	x	x	PROPN
ap-10691	601	8	m]φmk	m]φmk	NOUN
ap-10691	601	9	ψβ	ψβ	NOUN
ap-10691	601	10	=	=	PUNCT
ap-10691	601	11	(	(	PUNCT
ap-10691	601	12	hk	hk	PROPN
ap-10691	601	13	−	−	PROPN
ap-10691	601	14	e)ly	e)ly	PROPN
ap-10691	601	15	ns	ns	NUM
ap-10691	601	16	x	x	PROPN
ap-10691	601	17	mφmk	mφmk	NOUN
ap-10691	601	18	ψβ	ψβ	PROPN
ap-10691	601	19	,	,	PUNCT
ap-10691	601	20	(	(	PUNCT
ap-10691	601	21	125	125	NUM
ap-10691	601	22	)	)	PUNCT
ap-10691	601	23	since	since	SCONJ
ap-10691	601	24	φmk	φmk	ADJ
ap-10691	601	25	ψβ	ψβ	PROPN
ap-10691	601	26	is	be	AUX
ap-10691	601	27	an	an	DET
ap-10691	601	28	eigenfunction	eigenfunction	NOUN
ap-10691	601	29	of	of	ADP
ap-10691	601	30	hk	hk	PROPN
ap-10691	601	31	with	with	ADP
ap-10691	601	32	eigenvalue	eigenvalue	PROPN
ap-10691	601	33	e.	e.	PROPN
ap-10691	601	34	this	this	PRON
ap-10691	601	35	follows	follow	VERB
ap-10691	601	36	directly	directly	ADV
ap-10691	601	37	from	from	ADP
ap-10691	601	38	the	the	DET
ap-10691	601	39	nested	nested	ADJ
ap-10691	601	40	structure	structure	NOUN
ap-10691	601	41	of	of	ADP
ap-10691	601	42	the	the	DET
ap-10691	601	43	hamiltonian	hamiltonian	NOUN
ap-10691	601	44	(	(	PUNCT
ap-10691	601	45	122	122	NUM
ap-10691	601	46	)	)	PUNCT
ap-10691	601	47	and	and	CCONJ
ap-10691	601	48	the	the	DET
ap-10691	601	49	fact	fact	NOUN
ap-10691	601	50	that	that	SCONJ
ap-10691	601	51	hx	hx	PROPN
ap-10691	601	52	mk	mk	PROPN
ap-10691	601	53	φmk	φmk	ADV
ap-10691	601	54	=	=	PUNCT
ap-10691	601	55	eφmk	eφmk	ADJ
ap-10691	601	56	.	.	PUNCT
ap-10691	602	1	by	by	ADP
ap-10691	602	2	computing	compute	VERB
ap-10691	602	3	ly	ly	ADP
ap-10691	602	4	ns	ns	NUM
ap-10691	602	5	x	x	NOUN
ap-10691	602	6	mφmk	mφmk	NOUN
ap-10691	602	7	ψβ	ψβ	PROPN
ap-10691	602	8	,	,	PUNCT
ap-10691	602	9	we	we	PRON
ap-10691	602	10	obtain	obtain	VERB
ap-10691	602	11	:	:	PUNCT
ap-10691	602	12	ly	ly	X
ap-10691	602	13	ns	ns	NUM
ap-10691	602	14	x	x	NOUN
ap-10691	602	15	mφmk	mφmk	NOUN
ap-10691	602	16	ψβ	ψβ	NOUN
ap-10691	602	17	=	=	PUNCT
ap-10691	602	18	ψβ+nφmk+m	ψβ+nφmk+m	PROPN
ap-10691	602	19	,	,	PUNCT
ap-10691	602	20	(	(	PUNCT
ap-10691	602	21	126	126	NUM
ap-10691	602	22	)	)	PUNCT
ap-10691	602	23	from	from	ADP
ap-10691	602	24	the	the	DET
ap-10691	602	25	definitions	definition	NOUN
ap-10691	602	26	of	of	ADP
ap-10691	602	27	the	the	DET
ap-10691	602	28	ladder	ladder	NOUN
ap-10691	602	29	and	and	CCONJ
ap-10691	602	30	shift	shift	NOUN
ap-10691	602	31	operators	operator	NOUN
ap-10691	602	32	ly	ly	ADP
ap-10691	602	33	n	n	PROPN
ap-10691	602	34	(	(	PUNCT
ap-10691	602	35	equation	equation	NOUN
ap-10691	602	36	(	(	PUNCT
ap-10691	602	37	21	21	NUM
ap-10691	602	38	)	)	PUNCT
ap-10691	602	39	)	)	PUNCT
ap-10691	603	1	and	and	CCONJ
ap-10691	603	2	sx	sx	PROPN
ap-10691	603	3	m	m	PROPN
ap-10691	603	4	(	(	PUNCT
ap-10691	603	5	equation	equation	NOUN
ap-10691	603	6	(	(	PUNCT
ap-10691	603	7	13	13	NUM
ap-10691	603	8	)	)	PUNCT
ap-10691	603	9	)	)	PUNCT
ap-10691	603	10	,	,	PUNCT
ap-10691	603	11	where	where	SCONJ
ap-10691	603	12	m	m	VERB
ap-10691	603	13	and	and	CCONJ
ap-10691	603	14	n	n	PROPN
ap-10691	603	15	are	be	AUX
ap-10691	603	16	integers	integer	NOUN
ap-10691	603	17	.	.	PUNCT
ap-10691	604	1	taking	take	VERB
ap-10691	604	2	this	this	DET
ap-10691	604	3	fact	fact	NOUN
ap-10691	604	4	into	into	ADP
ap-10691	604	5	account	account	NOUN
ap-10691	604	6	,	,	PUNCT
ap-10691	604	7	the	the	DET
ap-10691	604	8	hamiltonian	hamiltonian	ADJ
ap-10691	604	9	hk	hk	PROPN
ap-10691	604	10	(	(	PUNCT
ap-10691	604	11	equation	equation	NOUN
ap-10691	604	12	(	(	PUNCT
ap-10691	604	13	122	122	NUM
ap-10691	604	14	)	)	PUNCT
ap-10691	604	15	)	)	PUNCT
ap-10691	604	16	takes	take	VERB
ap-10691	604	17	the	the	DET
ap-10691	604	18	form	form	NOUN
ap-10691	604	19	:	:	PUNCT
ap-10691	605	1	hk	hk	PROPN
ap-10691	605	2	=	=	SYM
ap-10691	605	3	hx	hx	PROPN
ap-10691	606	1	+	+	CCONJ
ap-10691	606	2	(	(	PUNCT
ap-10691	606	3	mk	mk	PROPN
ap-10691	606	4	+	+	ADJ
ap-10691	606	5	m)2	m)2	PROPN
ap-10691	606	6	f(x	f(x	PROPN
ap-10691	606	7	)	)	PUNCT
ap-10691	607	1	+	+	CCONJ
ap-10691	607	2	−m2	−m2	NOUN
ap-10691	607	3	−	−	PROPN
ap-10691	607	4	2mkm	2mkm	NUM
ap-10691	607	5	f(x	f(x	PROPN
ap-10691	607	6	)	)	PUNCT
ap-10691	608	1	+	+	CCONJ
ap-10691	608	2	k2(hy	k2(hy	PROPN
ap-10691	608	3	−	−	PROPN
ap-10691	608	4	e′	e′	PROPN
ap-10691	608	5	)	)	PUNCT
ap-10691	608	6	f(x	f(x	PROPN
ap-10691	608	7	)	)	PUNCT
ap-10691	609	1	=	=	SYM
ap-10691	609	2	hx	hx	PROPN
ap-10691	609	3	mk+m	mk+m	PROPN
ap-10691	609	4	+	+	CCONJ
ap-10691	609	5	−m2	−m2	NOUN
ap-10691	609	6	−	−	PROPN
ap-10691	609	7	2mkm	2mkm	NUM
ap-10691	609	8	f(x	f(x	PROPN
ap-10691	609	9	)	)	PUNCT
ap-10691	610	1	+	+	CCONJ
ap-10691	610	2	k2(hy	k2(hy	PROPN
ap-10691	610	3	−	−	PROPN
ap-10691	610	4	e′	e′	PROPN
ap-10691	610	5	)	)	PUNCT
ap-10691	610	6	f(x	f(x	PROPN
ap-10691	610	7	)	)	PUNCT
ap-10691	610	8	,	,	PUNCT
ap-10691	610	9	(	(	PUNCT
ap-10691	610	10	127	127	NUM
ap-10691	610	11	)	)	PUNCT
ap-10691	610	12	since	since	SCONJ
ap-10691	610	13	hx	hx	PROPN
ap-10691	610	14	+	+	CCONJ
ap-10691	610	15	(	(	PUNCT
ap-10691	610	16	mk	mk	X
ap-10691	610	17	+	+	ADJ
ap-10691	610	18	m)2	m)2	PROPN
ap-10691	610	19	/	/	SYM
ap-10691	610	20	f(x	f(x	PROPN
ap-10691	610	21	)	)	PUNCT
ap-10691	610	22	=	=	SYM
ap-10691	610	23	hx	hx	PROPN
ap-10691	610	24	mk+m	mk+m	PROPN
ap-10691	610	25	.	.	PUNCT
ap-10691	611	1	applying	apply	VERB
ap-10691	611	2	the	the	DET
ap-10691	611	3	hamiltonian	hamiltonian	ADJ
ap-10691	611	4	hk	hk	PROPN
ap-10691	611	5	(	(	PUNCT
ap-10691	611	6	equation	equation	NOUN
ap-10691	611	7	(	(	PUNCT
ap-10691	611	8	127	127	NUM
ap-10691	611	9	)	)	PUNCT
ap-10691	611	10	)	)	PUNCT
ap-10691	611	11	to	to	ADP
ap-10691	611	12	the	the	DET
ap-10691	611	13	function	function	NOUN
ap-10691	611	14	ψβ+nφmk+m	ψβ+nφmk+m	NOUN
ap-10691	611	15	(	(	PUNCT
ap-10691	611	16	equation	equation	NOUN
ap-10691	611	17	(	(	PUNCT
ap-10691	611	18	126	126	NUM
ap-10691	611	19	)	)	PUNCT
ap-10691	611	20	)	)	PUNCT
ap-10691	612	1	we	we	PRON
ap-10691	612	2	find	find	VERB
ap-10691	612	3	that	that	SCONJ
ap-10691	612	4	:	:	PUNCT
ap-10691	612	5	hkφmk+mψβ+n	hkφmk+mψβ+n	NOUN
ap-10691	612	6	=	=	SYM
ap-10691	612	7	(	(	PUNCT
ap-10691	612	8	e	e	X
ap-10691	612	9	+	+	CCONJ
ap-10691	612	10	−m2	−m2	NOUN
ap-10691	612	11	−	−	PROPN
ap-10691	612	12	2mkm	2mkm	NUM
ap-10691	612	13	f(x	f(x	PROPN
ap-10691	612	14	)	)	PUNCT
ap-10691	613	1	+	+	CCONJ
ap-10691	613	2	k2(e′	k2(e′	ADJ
ap-10691	613	3	+	+	CCONJ
ap-10691	613	4	2βn+	2βn+	NUM
ap-10691	613	5	n2	n2	NOUN
ap-10691	613	6	−	−	PROPN
ap-10691	613	7	e′	e′	PROPN
ap-10691	613	8	)	)	PUNCT
ap-10691	613	9	f(x	f(x	PROPN
ap-10691	613	10	)	)	PUNCT
ap-10691	613	11	)	)	PUNCT
ap-10691	614	1	φmk+mψβ+n	φmk+mψβ+n	NOUN
ap-10691	614	2	.	.	PUNCT
ap-10691	615	1	(	(	PUNCT
ap-10691	615	2	128	128	NUM
ap-10691	615	3	)	)	PUNCT
ap-10691	615	4	for	for	SCONJ
ap-10691	615	5	the	the	DET
ap-10691	615	6	commutator	commutator	NOUN
ap-10691	615	7	in	in	ADP
ap-10691	615	8	equation	equation	NOUN
ap-10691	615	9	(	(	PUNCT
ap-10691	615	10	125	125	NUM
ap-10691	615	11	)	)	PUNCT
ap-10691	615	12	to	to	PART
ap-10691	615	13	vanish	vanish	VERB
ap-10691	615	14	,	,	PUNCT
ap-10691	615	15	it	it	PRON
ap-10691	615	16	is	be	AUX
ap-10691	615	17	sufficient	sufficient	ADJ
ap-10691	615	18	that	that	SCONJ
ap-10691	615	19	the	the	DET
ap-10691	615	20	additional	additional	ADJ
ap-10691	615	21	term	term	NOUN
ap-10691	615	22	on	on	ADP
ap-10691	615	23	the	the	DET
ap-10691	615	24	right	right	ADJ
ap-10691	615	25	-	-	PUNCT
ap-10691	615	26	hand	hand	NOUN
ap-10691	615	27	side	side	NOUN
ap-10691	615	28	of	of	ADP
ap-10691	615	29	equation	equation	NOUN
ap-10691	615	30	(	(	PUNCT
ap-10691	615	31	128	128	NUM
ap-10691	615	32	)	)	PUNCT
ap-10691	615	33	vanishes	vanish	VERB
ap-10691	615	34	,	,	PUNCT
ap-10691	615	35	namely	namely	ADV
ap-10691	615	36	:	:	PUNCT
ap-10691	615	37	−m2	−m2	NOUN
ap-10691	615	38	−	−	NOUN
ap-10691	615	39	2mkm+	2mkm+	NUM
ap-10691	615	40	k2(2βn+	k2(2βn+	PROPN
ap-10691	615	41	n2	n2	NOUN
ap-10691	615	42	)	)	PUNCT
ap-10691	615	43	,	,	PUNCT
ap-10691	615	44	(	(	PUNCT
ap-10691	615	45	129	129	NUM
ap-10691	615	46	)	)	PUNCT
ap-10691	615	47	which	which	PRON
ap-10691	615	48	can	can	AUX
ap-10691	615	49	be	be	AUX
ap-10691	615	50	rearranged	rearrange	VERB
ap-10691	615	51	as	as	ADP
ap-10691	615	52	:	:	PUNCT
ap-10691	615	53	−(mk	−(mk	NOUN
ap-10691	616	1	+	+	NOUN
ap-10691	616	2	m)2	m)2	PROPN
ap-10691	616	3	+	+	CCONJ
ap-10691	616	4	(	(	PUNCT
ap-10691	616	5	mk	mk	X
ap-10691	616	6	+	+	CCONJ
ap-10691	616	7	kn)2	kn)2	NOUN
ap-10691	616	8	=	=	SYM
ap-10691	616	9	0	0	NUM
ap-10691	616	10	,	,	PUNCT
ap-10691	616	11	(	(	PUNCT
ap-10691	616	12	130	130	NUM
ap-10691	616	13	)	)	PUNCT
ap-10691	616	14	recalling	recall	VERB
ap-10691	616	15	that	that	SCONJ
ap-10691	616	16	kβ	kβ	PROPN
ap-10691	616	17	=	=	SYM
ap-10691	616	18	mk	mk	PROPN
ap-10691	616	19	.	.	PUNCT
ap-10691	616	20	equation	equation	NOUN
ap-10691	616	21	(	(	PUNCT
ap-10691	616	22	130	130	NUM
ap-10691	616	23	)	)	PUNCT
ap-10691	616	24	admits	admit	VERB
ap-10691	616	25	two	two	NUM
ap-10691	616	26	possible	possible	ADJ
ap-10691	616	27	solutions	solution	NOUN
ap-10691	616	28	:	:	PUNCT
ap-10691	616	29	mk	mk	PROPN
ap-10691	617	1	+	+	NOUN
ap-10691	617	2	m	m	VERB
ap-10691	617	3	=	=	ADJ
ap-10691	617	4	mk	mk	PROPN
ap-10691	617	5	+	+	CCONJ
ap-10691	617	6	kn	kn	PROPN
ap-10691	617	7	,	,	PUNCT
ap-10691	617	8	(	(	PUNCT
ap-10691	617	9	131	131	X
ap-10691	617	10	)	)	PUNCT
ap-10691	617	11	mk	mk	NOUN
ap-10691	618	1	+	+	NOUN
ap-10691	618	2	m	m	PROPN
ap-10691	618	3	=	=	ADJ
ap-10691	618	4	−mk	−mk	PROPN
ap-10691	618	5	−	−	PROPN
ap-10691	619	1	kn	kn	PROPN
ap-10691	619	2	.	.	PUNCT
ap-10691	620	1	(	(	PUNCT
ap-10691	620	2	132	132	NUM
ap-10691	620	3	)	)	PUNCT
ap-10691	620	4	the	the	DET
ap-10691	620	5	second	second	ADJ
ap-10691	620	6	solution	solution	NOUN
ap-10691	620	7	(	(	PUNCT
ap-10691	620	8	equation	equation	NOUN
ap-10691	620	9	(	(	PUNCT
ap-10691	620	10	132	132	NUM
ap-10691	620	11	)	)	PUNCT
ap-10691	620	12	)	)	PUNCT
ap-10691	620	13	is	be	AUX
ap-10691	620	14	valid	valid	ADJ
ap-10691	620	15	only	only	ADV
ap-10691	620	16	for	for	ADP
ap-10691	620	17	specific	specific	ADJ
ap-10691	620	18	values	value	NOUN
ap-10691	620	19	of	of	ADP
ap-10691	620	20	ψβ	ψβ	PROPN
ap-10691	620	21	and	and	CCONJ
ap-10691	620	22	mk	mk	PROPN
ap-10691	620	23	,	,	PUNCT
ap-10691	620	24	and	and	CCONJ
ap-10691	620	25	not	not	PART
ap-10691	620	26	in	in	ADP
ap-10691	620	27	general	general	ADJ
ap-10691	620	28	.	.	PUNCT
ap-10691	621	1	therefore	therefore	ADV
ap-10691	621	2	,	,	PUNCT
ap-10691	621	3	the	the	DET
ap-10691	621	4	appropriate	appropriate	ADJ
ap-10691	621	5	and	and	CCONJ
ap-10691	621	6	general	general	ADJ
ap-10691	621	7	solution	solution	NOUN
ap-10691	621	8	is	be	AUX
ap-10691	621	9	the	the	DET
ap-10691	621	10	first	first	ADJ
ap-10691	621	11	one	one	NUM
ap-10691	621	12	,	,	PUNCT
ap-10691	621	13	equation	equation	NOUN
ap-10691	621	14	(	(	PUNCT
ap-10691	621	15	131	131	NUM
ap-10691	621	16	)	)	PUNCT
ap-10691	621	17	,	,	PUNCT
ap-10691	621	18	which	which	PRON
ap-10691	621	19	leads	lead	VERB
ap-10691	621	20	to	to	ADP
ap-10691	621	21	the	the	DET
ap-10691	621	22	condition	condition	NOUN
ap-10691	621	23	:	:	PUNCT
ap-10691	621	24	k	k	X
ap-10691	621	25	=	=	PUNCT
ap-10691	621	26	m	m	VERB
ap-10691	621	27	n	n	ADJ
ap-10691	621	28	.	.	PUNCT
ap-10691	622	1	(	(	PUNCT
ap-10691	622	2	133	133	NUM
ap-10691	622	3	)	)	PUNCT
ap-10691	622	4	this	this	DET
ap-10691	622	5	result	result	NOUN
ap-10691	622	6	shows	show	VERB
ap-10691	622	7	that	that	SCONJ
ap-10691	622	8	we	we	PRON
ap-10691	622	9	must	must	AUX
ap-10691	622	10	construct	construct	VERB
ap-10691	622	11	ladder	ladder	NOUN
ap-10691	622	12	operators	operator	NOUN
ap-10691	622	13	ly	ly	ADP
ap-10691	622	14	n	n	ADV
ap-10691	622	15	and	and	CCONJ
ap-10691	622	16	shift	shift	VERB
ap-10691	622	17	operators	operator	NOUN
ap-10691	622	18	sx	sx	PROPN
ap-10691	622	19	m	m	PROPN
ap-10691	622	20	such	such	ADJ
ap-10691	622	21	that	that	SCONJ
ap-10691	622	22	they	they	PRON
ap-10691	622	23	preserve	preserve	VERB
ap-10691	622	24	the	the	DET
ap-10691	622	25	quantity	quantity	NOUN
ap-10691	622	26	mk	mk	NOUN
ap-10691	622	27	.	.	PUNCT
ap-10691	623	1	in	in	ADP
ap-10691	623	2	our	our	PRON
ap-10691	623	3	two	two	NUM
ap-10691	623	4	systems	system	NOUN
ap-10691	623	5	,	,	PUNCT
ap-10691	623	6	as	as	SCONJ
ap-10691	623	7	previously	previously	ADV
ap-10691	623	8	observed	observe	VERB
ap-10691	623	9	,	,	PUNCT
ap-10691	623	10	both	both	DET
ap-10691	623	11	m	m	VERB
ap-10691	623	12	and	and	CCONJ
ap-10691	623	13	n	n	PRON
ap-10691	623	14	must	must	AUX
ap-10691	623	15	be	be	AUX
ap-10691	623	16	even	even	ADV
ap-10691	623	17	integers	integer	NOUN
ap-10691	623	18	.	.	PUNCT
ap-10691	624	1	moreover	moreover	ADV
ap-10691	624	2	,	,	PUNCT
ap-10691	624	3	since	since	SCONJ
ap-10691	624	4	both	both	DET
ap-10691	624	5	operators	operator	NOUN
ap-10691	624	6	depends	depend	VERB
ap-10691	624	7	of	of	ADP
ap-10691	624	8	different	different	ADJ
ap-10691	624	9	variables	variable	NOUN
ap-10691	624	10	,	,	PUNCT
ap-10691	624	11	they	they	PRON
ap-10691	624	12	commute	commute	VERB
ap-10691	624	13	.	.	PUNCT
ap-10691	625	1	533	533	NUM
ap-10691	625	2	acta	acta	PROPN
ap-10691	625	3	polytechnica	polytechnica	PROPN
ap-10691	625	4	65(5):520–533	65(5):520–533	PROPN
ap-10691	625	5	,	,	PUNCT
ap-10691	625	6	2025	2025	NUM
ap-10691	625	7	1	1	NUM
ap-10691	625	8	introduction	introduction	NOUN
ap-10691	625	9	2	2	NUM
ap-10691	625	10	ttw	ttw	NOUN
ap-10691	625	11	so(3)-hamiltonian	so(3)-hamiltonian	NOUN
ap-10691	625	12	2.1	2.1	NUM
ap-10691	625	13	hamiltonian	hamiltonian	ADJ
ap-10691	625	14	factorisation	factorisation	NOUN
ap-10691	625	15	2.2	2.2	NUM
ap-10691	625	16	higher	high	ADJ
ap-10691	625	17	rank	rank	NOUN
ap-10691	625	18	ladder	ladder	NOUN
ap-10691	625	19	/	/	SYM
ap-10691	625	20	shift	shift	NOUN
ap-10691	625	21	operators	operator	NOUN
ap-10691	625	22	2.3	2.3	NUM
ap-10691	625	23	superintegrability	superintegrability	NOUN
ap-10691	625	24	of	of	ADP
ap-10691	625	25	the	the	DET
ap-10691	625	26	ttw	ttw	PROPN
ap-10691	625	27	so(3)-hamiltonian	so(3)-hamiltonian	NOUN
ap-10691	625	28	3	3	NUM
ap-10691	625	29	analysis	analysis	NOUN
ap-10691	625	30	of	of	ADP
ap-10691	625	31	the	the	DET
ap-10691	625	32	ttw	ttw	PROPN
ap-10691	625	33	so(3)-hamiltonian	so(3)-hamiltonian	NOUN
ap-10691	625	34	3.1	3.1	NUM
ap-10691	625	35	factorisation	factorisation	NOUN
ap-10691	625	36	of	of	ADP
ap-10691	625	37	h	h	NOUN
ap-10691	625	38	3.2	3.2	NUM
ap-10691	625	39	factorisation	factorisation	NOUN
ap-10691	625	40	of	of	ADP
ap-10691	625	41	hmk	hmk	NOUN
ap-10691	625	42	3.3	3.3	NUM
ap-10691	625	43	factorisation	factorisation	NOUN
ap-10691	625	44	of	of	ADP
ap-10691	625	45	multi	multi	ADJ
ap-10691	625	46	-	-	ADJ
ap-10691	625	47	parametric	parametric	ADJ
ap-10691	625	48	hamiltonian	hamiltonian	NOUN
ap-10691	625	49	3.4	3.4	NUM
ap-10691	625	50	on	on	ADP
ap-10691	625	51	the	the	DET
ap-10691	625	52	factorisation	factorisation	NOUN
ap-10691	625	53	of	of	ADP
ap-10691	625	54	the	the	DET
ap-10691	625	55	multi	multi	ADJ
ap-10691	625	56	-	-	ADJ
ap-10691	625	57	indexed	indexed	ADJ
ap-10691	625	58	hamiltonian	hamiltonian	ADJ
ap-10691	625	59	hmk	hmk	NOUN
ap-10691	625	60	4	4	NUM
ap-10691	625	61	associated	associate	VERB
ap-10691	625	62	classical	classical	ADJ
ap-10691	625	63	system	system	NOUN
ap-10691	625	64	4.1	4.1	NUM
ap-10691	625	65	superintegrability	superintegrability	NOUN
ap-10691	625	66	4.2	4.2	NUM
ap-10691	625	67	classical	classical	ADJ
ap-10691	625	68	trajectories	trajectory	NOUN
ap-10691	625	69	5	5	NUM
ap-10691	625	70	hyperbolic	hyperbolic	ADJ
ap-10691	625	71	ttw	ttw	NOUN
ap-10691	625	72	so(2,1)-hamiltonian	so(2,1)-hamiltonian	ADJ
ap-10691	625	73	5.1	5.1	NUM
ap-10691	625	74	factorisation	factorisation	NOUN
ap-10691	625	75	of	of	ADP
ap-10691	625	76	hmk	hmk	NOUN
ap-10691	625	77	5.2	5.2	NUM
ap-10691	625	78	associated	associate	VERB
ap-10691	625	79	classical	classical	ADJ
ap-10691	625	80	hamiltonian	hamiltonian	NOUN
ap-10691	625	81	6	6	NUM
ap-10691	625	82	conclusions	conclusion	NOUN
ap-10691	625	83	acknowledgements	acknowledgement	NOUN
ap-10691	625	84	references	reference	VERB
ap-10691	625	85	a	a	DET
ap-10691	625	86	generalisation	generalisation	NOUN
ap-10691	625	87	of	of	ADP
ap-10691	625	88	theorem	theorem	NOUN
ap-10691	625	89	1	1	NUM