id	sid	tid	token	lemma	pos
ap-2099	1	1	acta	acta	PROPN
ap-2099	1	2	polytechnica	polytechnica	PROPN
ap-2099	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2099	1	4	/	/	SYM
ap-2099	1	5	ap.2014.54.0149	ap.2014.54.0149	PROPN
ap-2099	1	6	acta	acta	PROPN
ap-2099	1	7	polytechnica	polytechnica	PROPN
ap-2099	1	8	54(2):149–155	54(2):149–155	PROPN
ap-2099	1	9	,	,	PUNCT
ap-2099	1	10	2014	2014	NUM
ap-2099	1	11	©	©	PROPN
ap-2099	1	12	czech	czech	PROPN
ap-2099	1	13	technical	technical	PROPN
ap-2099	1	14	university	university	PROPN
ap-2099	1	15	in	in	ADP
ap-2099	1	16	prague	prague	PROPN
ap-2099	1	17	,	,	PUNCT
ap-2099	1	18	2014	2014	NUM
ap-2099	1	19	available	available	ADJ
ap-2099	1	20	online	online	ADV
ap-2099	1	21	at	at	ADP
ap-2099	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2099	1	23	laplace	laplace	NOUN
ap-2099	1	24	-	-	PUNCT
ap-2099	1	25	runge	runge	NOUN
ap-2099	1	26	-	-	PUNCT
ap-2099	1	27	lenz	lenz	PROPN
ap-2099	1	28	vector	vector	NOUN
ap-2099	1	29	in	in	ADP
ap-2099	1	30	quantum	quantum	ADJ
ap-2099	1	31	mechanics	mechanic	NOUN
ap-2099	1	32	in	in	ADP
ap-2099	1	33	noncommutative	noncommutative	ADJ
ap-2099	1	34	space	space	NOUN
ap-2099	1	35	peter	peter	PROPN
ap-2099	1	36	prešnajder∗	prešnajder∗	VERB
ap-2099	1	37	,	,	PUNCT
ap-2099	1	38	veronika	veronika	PROPN
ap-2099	1	39	gáliková	gáliková	PROPN
ap-2099	1	40	,	,	PUNCT
ap-2099	1	41	samuel	samuel	PROPN
ap-2099	1	42	kováčik	kováčik	PROPN
ap-2099	1	43	commenius	commenius	PROPN
ap-2099	1	44	university	university	PROPN
ap-2099	1	45	bratislava	bratislava	NOUN
ap-2099	1	46	,	,	PUNCT
ap-2099	1	47	faculty	faculty	NOUN
ap-2099	1	48	of	of	ADP
ap-2099	1	49	mathematics	mathematic	NOUN
ap-2099	1	50	,	,	PUNCT
ap-2099	1	51	physics	physics	NOUN
ap-2099	1	52	and	and	CCONJ
ap-2099	1	53	informatics	informatics	PROPN
ap-2099	1	54	∗	∗	NOUN
ap-2099	1	55	corresponding	correspond	VERB
ap-2099	1	56	author	author	NOUN
ap-2099	1	57	:	:	PUNCT
ap-2099	1	58	presnajder.peter@gmail.com	presnajder.peter@gmail.com	X
ap-2099	1	59	abstract	abstract	ADJ
ap-2099	1	60	.	.	PUNCT
ap-2099	2	1	the	the	DET
ap-2099	2	2	object	object	NOUN
ap-2099	2	3	under	under	ADP
ap-2099	2	4	scrutiny	scrutiny	NOUN
ap-2099	2	5	is	be	AUX
ap-2099	2	6	the	the	DET
ap-2099	2	7	dynamical	dynamical	ADJ
ap-2099	2	8	symmetry	symmetry	NOUN
ap-2099	2	9	connected	connect	VERB
ap-2099	2	10	with	with	ADP
ap-2099	2	11	conservation	conservation	NOUN
ap-2099	2	12	of	of	ADP
ap-2099	2	13	the	the	DET
ap-2099	2	14	laplace	laplace	NOUN
ap-2099	2	15	-	-	PUNCT
ap-2099	2	16	runge	runge	NOUN
ap-2099	2	17	-	-	PUNCT
ap-2099	2	18	lenz	lenz	PROPN
ap-2099	2	19	vector	vector	PROPN
ap-2099	2	20	(	(	PUNCT
ap-2099	2	21	lrl	lrl	PROPN
ap-2099	2	22	)	)	PUNCT
ap-2099	2	23	in	in	ADP
ap-2099	2	24	the	the	DET
ap-2099	2	25	hydrogen	hydrogen	NOUN
ap-2099	2	26	atom	atom	NOUN
ap-2099	2	27	problem	problem	NOUN
ap-2099	2	28	solved	solve	VERB
ap-2099	2	29	by	by	ADP
ap-2099	2	30	means	mean	NOUN
ap-2099	2	31	of	of	ADP
ap-2099	2	32	noncommutative	noncommutative	ADJ
ap-2099	2	33	quantum	quantum	ADJ
ap-2099	2	34	mechanics	mechanic	NOUN
ap-2099	2	35	(	(	PUNCT
ap-2099	2	36	ncqm	ncqm	NOUN
ap-2099	2	37	)	)	PUNCT
ap-2099	2	38	.	.	PUNCT
ap-2099	3	1	the	the	DET
ap-2099	3	2	considered	consider	VERB
ap-2099	3	3	noncommutative	noncommutative	ADJ
ap-2099	3	4	configuration	configuration	NOUN
ap-2099	3	5	space	space	NOUN
ap-2099	3	6	has	have	VERB
ap-2099	3	7	such	such	DET
ap-2099	3	8	a	a	DET
ap-2099	3	9	“	"	PUNCT
ap-2099	3	10	fuzzy	fuzzy	ADJ
ap-2099	3	11	”	"	PUNCT
ap-2099	3	12	structure	structure	NOUN
ap-2099	3	13	that	that	PRON
ap-2099	3	14	the	the	DET
ap-2099	3	15	rotational	rotational	ADJ
ap-2099	3	16	invariance	invariance	NOUN
ap-2099	3	17	is	be	AUX
ap-2099	3	18	not	not	PART
ap-2099	3	19	spoilt	spoilt	ADJ
ap-2099	3	20	.	.	PUNCT
ap-2099	4	1	an	an	DET
ap-2099	4	2	analogy	analogy	NOUN
ap-2099	4	3	with	with	ADP
ap-2099	4	4	the	the	DET
ap-2099	4	5	lrl	lrl	PROPN
ap-2099	4	6	vector	vector	NOUN
ap-2099	4	7	in	in	ADP
ap-2099	4	8	the	the	DET
ap-2099	4	9	ncqm	ncqm	NOUN
ap-2099	4	10	is	be	AUX
ap-2099	4	11	brought	bring	VERB
ap-2099	4	12	to	to	PART
ap-2099	4	13	provide	provide	VERB
ap-2099	4	14	our	our	PRON
ap-2099	4	15	results	result	NOUN
ap-2099	4	16	and	and	CCONJ
ap-2099	4	17	also	also	ADV
ap-2099	4	18	a	a	DET
ap-2099	4	19	comparison	comparison	NOUN
ap-2099	4	20	with	with	ADP
ap-2099	4	21	the	the	DET
ap-2099	4	22	standard	standard	ADJ
ap-2099	4	23	qm	qm	PROPN
ap-2099	4	24	predictions	prediction	NOUN
ap-2099	4	25	.	.	PUNCT
ap-2099	5	1	keywords	keyword	NOUN
ap-2099	5	2	:	:	PUNCT
ap-2099	5	3	noncommutative	noncommutative	ADJ
ap-2099	5	4	space	space	NOUN
ap-2099	5	5	,	,	PUNCT
ap-2099	5	6	coulomb	coulomb	NOUN
ap-2099	5	7	-	-	PUNCT
ap-2099	5	8	kepler	kepler	PROPN
ap-2099	5	9	problem	problem	NOUN
ap-2099	5	10	,	,	PUNCT
ap-2099	5	11	symmetry	symmetry	NOUN
ap-2099	5	12	.	.	PUNCT
ap-2099	6	1	1	1	X
ap-2099	6	2	.	.	X
ap-2099	6	3	introduction	introduction	VERB
ap-2099	6	4	our	our	PRON
ap-2099	6	5	main	main	ADJ
ap-2099	6	6	goal	goal	NOUN
ap-2099	6	7	we	we	PRON
ap-2099	6	8	are	be	AUX
ap-2099	6	9	after	after	ADP
ap-2099	6	10	is	be	AUX
ap-2099	6	11	to	to	PART
ap-2099	6	12	investigate	investigate	VERB
ap-2099	6	13	the	the	DET
ap-2099	6	14	existence	existence	NOUN
ap-2099	6	15	of	of	ADP
ap-2099	6	16	dynamical	dynamical	ADJ
ap-2099	6	17	symmetry	symmetry	NOUN
ap-2099	6	18	of	of	ADP
ap-2099	6	19	the	the	DET
ap-2099	6	20	coulomb	coulomb	NOUN
ap-2099	6	21	-	-	PUNCT
ap-2099	6	22	kepler	kepler	NOUN
ap-2099	6	23	problem	problem	NOUN
ap-2099	6	24	in	in	ADP
ap-2099	6	25	the	the	DET
ap-2099	6	26	quantum	quantum	ADJ
ap-2099	6	27	mechanics	mechanic	NOUN
ap-2099	6	28	in	in	ADP
ap-2099	6	29	noncommutative	noncommutative	ADJ
ap-2099	6	30	space	space	NOUN
ap-2099	6	31	,	,	PUNCT
ap-2099	6	32	and	and	CCONJ
ap-2099	6	33	possibly	possibly	ADV
ap-2099	6	34	to	to	PART
ap-2099	6	35	find	find	VERB
ap-2099	6	36	the	the	DET
ap-2099	6	37	generalization	generalization	NOUN
ap-2099	6	38	of	of	ADP
ap-2099	6	39	the	the	DET
ap-2099	6	40	so	so	ADV
ap-2099	6	41	-	-	PUNCT
ap-2099	6	42	called	call	VERB
ap-2099	6	43	laplace	laplace	NOUN
ap-2099	6	44	-	-	PUNCT
ap-2099	6	45	runge	runge	NOUN
ap-2099	6	46	-	-	PUNCT
ap-2099	6	47	lenz	lenz	PROPN
ap-2099	6	48	(	(	PUNCT
ap-2099	6	49	lrl	lrl	PROPN
ap-2099	6	50	)	)	PUNCT
ap-2099	6	51	vector	vector	NOUN
ap-2099	6	52	for	for	ADP
ap-2099	6	53	this	this	DET
ap-2099	6	54	case	case	NOUN
ap-2099	6	55	.	.	PUNCT
ap-2099	7	1	before	before	ADP
ap-2099	7	2	actually	actually	ADV
ap-2099	7	3	starting	start	VERB
ap-2099	7	4	,	,	PUNCT
ap-2099	7	5	we	we	PRON
ap-2099	7	6	briefly	briefly	ADV
ap-2099	7	7	look	look	VERB
ap-2099	7	8	at	at	ADP
ap-2099	7	9	the	the	DET
ap-2099	7	10	history	history	NOUN
ap-2099	7	11	of	of	ADP
ap-2099	7	12	the	the	DET
ap-2099	7	13	lrl	lrl	PROPN
ap-2099	7	14	vector	vector	NOUN
ap-2099	7	15	.	.	PUNCT
ap-2099	8	1	we	we	PRON
ap-2099	8	2	call	call	VERB
ap-2099	8	3	this	this	DET
ap-2099	8	4	laplace	laplace	NOUN
ap-2099	8	5	-	-	PUNCT
ap-2099	8	6	runge	runge	NOUN
ap-2099	8	7	-	-	PUNCT
ap-2099	8	8	lenz	lenz	PROPN
ap-2099	8	9	vector	vector	PROPN
ap-2099	8	10	,	,	PUNCT
ap-2099	8	11	as	as	SCONJ
ap-2099	8	12	it	it	PRON
ap-2099	8	13	is	be	AUX
ap-2099	8	14	commonly	commonly	ADV
ap-2099	8	15	named	name	VERB
ap-2099	8	16	nowadays	nowadays	ADV
ap-2099	8	17	,	,	PUNCT
ap-2099	8	18	but	but	CCONJ
ap-2099	8	19	as	as	ADV
ap-2099	8	20	far	far	ADV
ap-2099	8	21	as	as	SCONJ
ap-2099	8	22	we	we	PRON
ap-2099	8	23	know	know	VERB
ap-2099	8	24	,	,	PUNCT
ap-2099	8	25	the	the	DET
ap-2099	8	26	first	first	ADJ
ap-2099	8	27	ones	one	NOUN
ap-2099	8	28	to	to	PART
ap-2099	8	29	make	make	VERB
ap-2099	8	30	a	a	DET
ap-2099	8	31	mention	mention	NOUN
ap-2099	8	32	of	of	ADP
ap-2099	8	33	it	it	PRON
ap-2099	8	34	were	be	AUX
ap-2099	8	35	jakob	jakob	PROPN
ap-2099	8	36	hermann	hermann	PROPN
ap-2099	8	37	and	and	CCONJ
ap-2099	8	38	johann	johann	PROPN
ap-2099	8	39	bernoulli	bernoulli	PROPN
ap-2099	8	40	in	in	ADP
ap-2099	8	41	the	the	DET
ap-2099	8	42	letters	letter	NOUN
ap-2099	8	43	they	they	PRON
ap-2099	8	44	exchanged	exchange	VERB
ap-2099	8	45	in	in	ADP
ap-2099	8	46	1710	1710	NUM
ap-2099	8	47	,	,	PUNCT
ap-2099	8	48	see	see	VERB
ap-2099	8	49	[	[	X
ap-2099	8	50	1	1	NUM
ap-2099	8	51	]	]	PUNCT
ap-2099	8	52	,	,	PUNCT
ap-2099	8	53	[	[	X
ap-2099	8	54	2	2	NUM
ap-2099	8	55	]	]	PUNCT
ap-2099	8	56	.	.	PUNCT
ap-2099	9	1	so	so	ADV
ap-2099	9	2	the	the	DET
ap-2099	9	3	name	name	NOUN
ap-2099	9	4	“	"	PUNCT
ap-2099	9	5	hermann	hermann	PROPN
ap-2099	9	6	-	-	PUNCT
ap-2099	9	7	bernoulli	bernoulli	PROPN
ap-2099	9	8	vector	vector	NOUN
ap-2099	9	9	”	"	PUNCT
ap-2099	9	10	would	would	AUX
ap-2099	9	11	be	be	AUX
ap-2099	9	12	more	more	ADV
ap-2099	9	13	proper	proper	ADJ
ap-2099	9	14	.	.	PUNCT
ap-2099	10	1	much	much	ADV
ap-2099	10	2	later	later	ADV
ap-2099	10	3	,	,	PUNCT
ap-2099	10	4	in	in	ADP
ap-2099	10	5	1799	1799	NUM
ap-2099	10	6	the	the	DET
ap-2099	10	7	vector	vector	NOUN
ap-2099	10	8	was	be	AUX
ap-2099	10	9	rediscovered	rediscover	VERB
ap-2099	10	10	by	by	ADP
ap-2099	10	11	laplace	laplace	NOUN
ap-2099	10	12	in	in	ADP
ap-2099	10	13	his	his	PRON
ap-2099	10	14	celestial	celestial	ADJ
ap-2099	10	15	mechanics	mechanic	NOUN
ap-2099	10	16	[	[	X
ap-2099	10	17	3	3	NUM
ap-2099	10	18	]	]	PUNCT
ap-2099	10	19	.	.	PUNCT
ap-2099	11	1	then	then	ADV
ap-2099	11	2	it	it	PRON
ap-2099	11	3	appeared	appear	VERB
ap-2099	11	4	in	in	ADP
ap-2099	11	5	a	a	DET
ap-2099	11	6	popular	popular	ADJ
ap-2099	11	7	german	german	ADJ
ap-2099	11	8	textbook	textbook	NOUN
ap-2099	11	9	on	on	ADP
ap-2099	11	10	vectors	vector	NOUN
ap-2099	11	11	by	by	ADP
ap-2099	11	12	c.	c.	PROPN
ap-2099	11	13	runge	runge	PROPN
ap-2099	11	14	[	[	X
ap-2099	11	15	4	4	NUM
ap-2099	11	16	]	]	PUNCT
ap-2099	11	17	,	,	PUNCT
ap-2099	11	18	which	which	PRON
ap-2099	11	19	was	be	AUX
ap-2099	11	20	referenced	reference	VERB
ap-2099	11	21	by	by	ADP
ap-2099	11	22	w.	w.	PROPN
ap-2099	11	23	lenz	lenz	PROPN
ap-2099	11	24	in	in	ADP
ap-2099	11	25	his	his	PRON
ap-2099	11	26	paper	paper	NOUN
ap-2099	11	27	on	on	ADP
ap-2099	11	28	the	the	DET
ap-2099	11	29	(	(	PUNCT
ap-2099	11	30	old	old	ADJ
ap-2099	11	31	)	)	PUNCT
ap-2099	11	32	quantum	quantum	ADJ
ap-2099	11	33	mechanical	mechanical	ADJ
ap-2099	11	34	treatment	treatment	NOUN
ap-2099	11	35	of	of	ADP
ap-2099	11	36	the	the	DET
ap-2099	11	37	kepler	kepler	NOUN
ap-2099	11	38	problem	problem	NOUN
ap-2099	11	39	or	or	CCONJ
ap-2099	11	40	hydrogen	hydrogen	NOUN
ap-2099	11	41	atom	atom	NOUN
ap-2099	11	42	[	[	X
ap-2099	11	43	5	5	NUM
ap-2099	11	44	]	]	PUNCT
ap-2099	11	45	.	.	PUNCT
ap-2099	12	1	now	now	ADV
ap-2099	12	2	back	back	ADV
ap-2099	12	3	to	to	ADP
ap-2099	12	4	physics	physics	NOUN
ap-2099	12	5	.	.	PUNCT
ap-2099	13	1	the	the	DET
ap-2099	13	2	coulomb	coulomb	NOUN
ap-2099	13	3	-	-	PUNCT
ap-2099	13	4	kepler	kepler	NOUN
ap-2099	13	5	problem	problem	NOUN
ap-2099	13	6	is	be	AUX
ap-2099	13	7	all	all	ADV
ap-2099	13	8	about	about	ADP
ap-2099	13	9	the	the	DET
ap-2099	13	10	motion	motion	NOUN
ap-2099	13	11	of	of	ADP
ap-2099	13	12	a	a	DET
ap-2099	13	13	particle	particle	NOUN
ap-2099	13	14	in	in	ADP
ap-2099	13	15	a	a	DET
ap-2099	13	16	field	field	NOUN
ap-2099	13	17	of	of	ADP
ap-2099	13	18	a	a	DET
ap-2099	13	19	central	central	ADJ
ap-2099	13	20	force	force	NOUN
ap-2099	13	21	proportional	proportional	ADJ
ap-2099	13	22	to	to	ADP
ap-2099	13	23	(	(	PUNCT
ap-2099	13	24	r−2	r−2	PROPN
ap-2099	13	25	)	)	PUNCT
ap-2099	13	26	.	.	PUNCT
ap-2099	14	1	the	the	DET
ap-2099	14	2	corresponding	correspond	VERB
ap-2099	14	3	newton	newton	PROPN
ap-2099	14	4	equation	equation	NOUN
ap-2099	14	5	for	for	ADP
ap-2099	14	6	a	a	DET
ap-2099	14	7	body	body	NOUN
ap-2099	14	8	of	of	ADP
ap-2099	14	9	mass	mass	NOUN
ap-2099	14	10	m	m	NOUN
ap-2099	14	11	reads	read	VERB
ap-2099	14	12	m~̇v	m~̇v	NOUN
ap-2099	14	13	=	=	PUNCT
ap-2099	15	1	−q	−q	ADJ
ap-2099	15	2	~r	~r	NUM
ap-2099	15	3	r3	r3	PROPN
ap-2099	15	4	.	.	PUNCT
ap-2099	16	1	(	(	PUNCT
ap-2099	16	2	1	1	X
ap-2099	16	3	)	)	PUNCT
ap-2099	16	4	here	here	ADV
ap-2099	16	5	q	q	PROPN
ap-2099	16	6	denotes	denote	VERB
ap-2099	16	7	a	a	DET
ap-2099	16	8	constant	constant	ADJ
ap-2099	16	9	which	which	PRON
ap-2099	16	10	specifies	specify	VERB
ap-2099	16	11	the	the	DET
ap-2099	16	12	magnitude	magnitude	NOUN
ap-2099	16	13	of	of	ADP
ap-2099	16	14	the	the	DET
ap-2099	16	15	force	force	NOUN
ap-2099	16	16	applied	apply	VERB
ap-2099	16	17	.	.	PUNCT
ap-2099	17	1	the	the	DET
ap-2099	17	2	system	system	NOUN
ap-2099	17	3	with	with	ADP
ap-2099	17	4	a	a	DET
ap-2099	17	5	central	central	ADJ
ap-2099	17	6	force	force	NOUN
ap-2099	17	7	definitely	definitely	ADV
ap-2099	17	8	is	be	AUX
ap-2099	17	9	rotationally	rotationally	ADV
ap-2099	17	10	symmetric	symmetric	ADJ
ap-2099	17	11	and	and	CCONJ
ap-2099	17	12	the	the	DET
ap-2099	17	13	orbital	orbital	ADJ
ap-2099	17	14	momentum	momentum	NOUN
ap-2099	17	15	,	,	PUNCT
ap-2099	17	16	~l	~l	PUNCT
ap-2099	17	17	=	=	PUNCT
ap-2099	17	18	m	m	PUNCT
ap-2099	17	19	~	~	PUNCT
ap-2099	17	20	r	r	NOUN
ap-2099	17	21	×	×	NOUN
ap-2099	17	22	~v	~v	PUNCT
ap-2099	17	23	,	,	PUNCT
ap-2099	17	24	(	(	PUNCT
ap-2099	17	25	2	2	X
ap-2099	17	26	)	)	PUNCT
ap-2099	17	27	is	be	AUX
ap-2099	17	28	conserved	conserve	VERB
ap-2099	17	29	in	in	ADP
ap-2099	17	30	any	any	DET
ap-2099	17	31	central	central	ADJ
ap-2099	17	32	field	field	NOUN
ap-2099	17	33	.	.	PUNCT
ap-2099	18	1	however	however	ADV
ap-2099	18	2	,	,	PUNCT
ap-2099	18	3	as	as	ADP
ap-2099	18	4	to	to	ADP
ap-2099	18	5	the	the	DET
ap-2099	18	6	symmetries	symmetry	NOUN
ap-2099	18	7	,	,	PUNCT
ap-2099	18	8	more	more	ADJ
ap-2099	18	9	has	have	VERB
ap-2099	18	10	to	to	PART
ap-2099	18	11	be	be	AUX
ap-2099	18	12	said	say	VERB
ap-2099	18	13	in	in	ADP
ap-2099	18	14	this	this	DET
ap-2099	18	15	case	case	NOUN
ap-2099	18	16	,	,	PUNCT
ap-2099	18	17	due	due	ADP
ap-2099	18	18	to	to	ADP
ap-2099	18	19	the	the	DET
ap-2099	18	20	fact	fact	NOUN
ap-2099	18	21	that	that	SCONJ
ap-2099	18	22	not	not	PART
ap-2099	18	23	only	only	ADV
ap-2099	18	24	is	be	AUX
ap-2099	18	25	the	the	DET
ap-2099	18	26	force	force	NOUN
ap-2099	18	27	central	central	ADJ
ap-2099	18	28	,	,	PUNCT
ap-2099	18	29	but	but	CCONJ
ap-2099	18	30	in	in	ADP
ap-2099	18	31	addition	addition	NOUN
ap-2099	18	32	it	it	PRON
ap-2099	18	33	has	have	VERB
ap-2099	18	34	the	the	DET
ap-2099	18	35	inverse	inverse	ADJ
ap-2099	18	36	square	square	ADJ
ap-2099	18	37	dependence	dependence	NOUN
ap-2099	18	38	of	of	ADP
ap-2099	18	39	the	the	DET
ap-2099	18	40	distance	distance	NOUN
ap-2099	18	41	.	.	PUNCT
ap-2099	19	1	besides	besides	SCONJ
ap-2099	19	2	the	the	DET
ap-2099	19	3	components	component	NOUN
ap-2099	19	4	of	of	ADP
ap-2099	19	5	~l	~l	NUM
ap-2099	19	6	,	,	PUNCT
ap-2099	19	7	the	the	DET
ap-2099	19	8	coulombkepler	coulombkepler	ADJ
ap-2099	19	9	problem	problem	NOUN
ap-2099	19	10	has	have	VERB
ap-2099	19	11	three	three	NUM
ap-2099	19	12	additional	additional	ADJ
ap-2099	19	13	integrals	integral	NOUN
ap-2099	19	14	of	of	ADP
ap-2099	19	15	motion	motion	NOUN
ap-2099	19	16	,	,	PUNCT
ap-2099	19	17	namely	namely	ADV
ap-2099	19	18	those	those	PRON
ap-2099	19	19	represented	represent	VERB
ap-2099	19	20	by	by	ADP
ap-2099	19	21	the	the	DET
ap-2099	19	22	conserved	conserve	VERB
ap-2099	19	23	lrl	lrl	PROPN
ap-2099	19	24	vector	vector	NOUN
ap-2099	19	25	,	,	PUNCT
ap-2099	19	26	~a	~a	PUNCT
ap-2099	19	27	=	=	SYM
ap-2099	19	28	~l×	~l×	NUM
ap-2099	19	29	~v	~v	PUNCT
ap-2099	19	30	+	+	PUNCT
ap-2099	19	31	q	q	SYM
ap-2099	19	32	~r	~r	PUNCT
ap-2099	19	33	r	r	NOUN
ap-2099	19	34	.	.	PUNCT
ap-2099	20	1	(	(	PUNCT
ap-2099	20	2	3	3	X
ap-2099	20	3	)	)	PUNCT
ap-2099	20	4	when	when	SCONJ
ap-2099	20	5	the	the	DET
ap-2099	20	6	motion	motion	NOUN
ap-2099	20	7	of	of	ADP
ap-2099	20	8	a	a	DET
ap-2099	20	9	planet	planet	NOUN
ap-2099	20	10	around	around	ADP
ap-2099	20	11	the	the	DET
ap-2099	20	12	sun	sun	NOUN
ap-2099	20	13	is	be	AUX
ap-2099	20	14	considered	consider	VERB
ap-2099	20	15	,	,	PUNCT
ap-2099	20	16	the	the	DET
ap-2099	20	17	conservation	conservation	NOUN
ap-2099	20	18	of	of	ADP
ap-2099	20	19	the	the	DET
ap-2099	20	20	given	give	VERB
ap-2099	20	21	quantity	quantity	NOUN
ap-2099	20	22	has	have	VERB
ap-2099	20	23	to	to	PART
ap-2099	20	24	do	do	VERB
ap-2099	20	25	with	with	ADP
ap-2099	20	26	the	the	DET
ap-2099	20	27	constant	constant	ADJ
ap-2099	20	28	eccentricity	eccentricity	NOUN
ap-2099	20	29	of	of	ADP
ap-2099	20	30	the	the	DET
ap-2099	20	31	orbit	orbit	NOUN
ap-2099	20	32	and	and	CCONJ
ap-2099	20	33	the	the	DET
ap-2099	20	34	position	position	NOUN
ap-2099	20	35	of	of	ADP
ap-2099	20	36	the	the	DET
ap-2099	20	37	perihelion	perihelion	NOUN
ap-2099	20	38	.	.	PUNCT
ap-2099	21	1	another	another	DET
ap-2099	21	2	well	well	ADV
ap-2099	21	3	-	-	PUNCT
ap-2099	21	4	known	know	VERB
ap-2099	21	5	system	system	NOUN
ap-2099	21	6	characterized	characterize	VERB
ap-2099	21	7	by	by	ADP
ap-2099	21	8	coulomb	coulomb	NOUN
ap-2099	21	9	potential	potential	NOUN
ap-2099	21	10	is	be	AUX
ap-2099	21	11	the	the	DET
ap-2099	21	12	hydrogen	hydrogen	NOUN
ap-2099	21	13	atom	atom	NOUN
ap-2099	21	14	.	.	PUNCT
ap-2099	22	1	obviously	obviously	ADV
ap-2099	22	2	a	a	DET
ap-2099	22	3	need	need	NOUN
ap-2099	22	4	for	for	ADP
ap-2099	22	5	the	the	DET
ap-2099	22	6	use	use	NOUN
ap-2099	22	7	of	of	ADP
ap-2099	22	8	quantum	quantum	ADJ
ap-2099	22	9	mechanics	mechanic	NOUN
ap-2099	22	10	arises	arise	VERB
ap-2099	22	11	here	here	ADV
ap-2099	22	12	.	.	PUNCT
ap-2099	23	1	there	there	PRON
ap-2099	23	2	are	be	VERB
ap-2099	23	3	,	,	PUNCT
ap-2099	23	4	however	however	ADV
ap-2099	23	5	,	,	PUNCT
ap-2099	23	6	several	several	ADJ
ap-2099	23	7	ways	way	NOUN
ap-2099	23	8	to	to	PART
ap-2099	23	9	address	address	VERB
ap-2099	23	10	the	the	DET
ap-2099	23	11	issue	issue	NOUN
ap-2099	23	12	.	.	PUNCT
ap-2099	24	1	in	in	ADP
ap-2099	24	2	1926	1926	NUM
ap-2099	24	3	wolfgang	wolfgang	PROPN
ap-2099	24	4	pauli	pauli	PROPN
ap-2099	24	5	published	publish	VERB
ap-2099	24	6	his	his	PRON
ap-2099	24	7	paper	paper	NOUN
ap-2099	24	8	on	on	ADP
ap-2099	24	9	the	the	DET
ap-2099	24	10	subject	subject	NOUN
ap-2099	24	11	[	[	X
ap-2099	24	12	6	6	NUM
ap-2099	24	13	]	]	PUNCT
ap-2099	24	14	.	.	PUNCT
ap-2099	25	1	he	he	PRON
ap-2099	25	2	used	use	VERB
ap-2099	25	3	the	the	DET
ap-2099	25	4	lrl	lrl	PROPN
ap-2099	25	5	vector	vector	NOUN
ap-2099	25	6	to	to	PART
ap-2099	25	7	find	find	VERB
ap-2099	25	8	the	the	DET
ap-2099	25	9	spectrum	spectrum	NOUN
ap-2099	25	10	of	of	ADP
ap-2099	25	11	a	a	DET
ap-2099	25	12	hydrogen	hydrogen	NOUN
ap-2099	25	13	atom	atom	NOUN
ap-2099	25	14	using	use	VERB
ap-2099	25	15	modern	modern	ADJ
ap-2099	25	16	quantum	quantum	ADJ
ap-2099	25	17	mechanics	mechanic	NOUN
ap-2099	25	18	and	and	CCONJ
ap-2099	25	19	the	the	DET
ap-2099	25	20	hidden	hide	VERB
ap-2099	25	21	dynamical	dynamical	ADJ
ap-2099	25	22	symmetry	symmetry	NOUN
ap-2099	25	23	of	of	ADP
ap-2099	25	24	the	the	DET
ap-2099	25	25	problem	problem	NOUN
ap-2099	25	26	,	,	PUNCT
ap-2099	25	27	without	without	ADP
ap-2099	25	28	knowledge	knowledge	NOUN
ap-2099	25	29	of	of	ADP
ap-2099	25	30	the	the	DET
ap-2099	25	31	explicit	explicit	ADJ
ap-2099	25	32	solution	solution	NOUN
ap-2099	25	33	of	of	ADP
ap-2099	25	34	the	the	DET
ap-2099	25	35	schrödinger	schrödinger	ADJ
ap-2099	25	36	equation	equation	NOUN
ap-2099	25	37	.	.	PUNCT
ap-2099	26	1	it	it	PRON
ap-2099	26	2	turned	turn	VERB
ap-2099	26	3	out	out	ADP
ap-2099	26	4	that	that	SCONJ
ap-2099	26	5	the	the	DET
ap-2099	26	6	lrl	lrl	PROPN
ap-2099	26	7	vector	vector	NOUN
ap-2099	26	8	can	can	AUX
ap-2099	26	9	be	be	AUX
ap-2099	26	10	found	find	VERB
ap-2099	26	11	among	among	ADP
ap-2099	26	12	the	the	DET
ap-2099	26	13	hermitian	hermitian	ADJ
ap-2099	26	14	operators	operator	NOUN
ap-2099	26	15	acting	act	VERB
ap-2099	26	16	in	in	ADP
ap-2099	26	17	the	the	DET
ap-2099	26	18	hilbert	hilbert	NOUN
ap-2099	26	19	space	space	NOUN
ap-2099	26	20	considered	consider	VERB
ap-2099	26	21	in	in	ADP
ap-2099	26	22	an	an	DET
ap-2099	26	23	almost	almost	ADV
ap-2099	26	24	complete	complete	ADJ
ap-2099	26	25	analogy	analogy	NOUN
ap-2099	26	26	with	with	ADP
ap-2099	26	27	the	the	DET
ap-2099	26	28	classical	classical	ADJ
ap-2099	26	29	case	case	NOUN
ap-2099	26	30	,	,	PUNCT
ap-2099	26	31	the	the	DET
ap-2099	26	32	only	only	ADJ
ap-2099	26	33	subtlety	subtlety	NOUN
ap-2099	26	34	to	to	PART
ap-2099	26	35	deal	deal	VERB
ap-2099	26	36	with	with	ADP
ap-2099	26	37	being	be	AUX
ap-2099	26	38	the	the	DET
ap-2099	26	39	fact	fact	NOUN
ap-2099	26	40	that	that	SCONJ
ap-2099	26	41	the	the	DET
ap-2099	26	42	cross	cross	NOUN
ap-2099	26	43	product	product	NOUN
ap-2099	26	44	needs	need	VERB
ap-2099	26	45	to	to	PART
ap-2099	26	46	be	be	AUX
ap-2099	26	47	properly	properly	ADV
ap-2099	26	48	symmetrized	symmetrize	VERB
ap-2099	26	49	,	,	PUNCT
ap-2099	26	50	resulting	result	VERB
ap-2099	26	51	in	in	ADP
ap-2099	26	52	aqmk	aqmk	PROPN
ap-2099	26	53	=	=	SYM
ap-2099	26	54	1	1	NUM
ap-2099	26	55	2εijk(livj	2εijk(livj	NUM
ap-2099	26	56	+	+	CCONJ
ap-2099	26	57	vjli	vjli	NOUN
ap-2099	26	58	)	)	PUNCT
ap-2099	27	1	+	+	CCONJ
ap-2099	27	2	q	q	PUNCT
ap-2099	27	3	xk	xk	PROPN
ap-2099	27	4	r	r	NOUN
ap-2099	27	5	,	,	PUNCT
ap-2099	27	6	(	(	PUNCT
ap-2099	27	7	4	4	NUM
ap-2099	27	8	)	)	PUNCT
ap-2099	27	9	where	where	SCONJ
ap-2099	27	10	vj	vj	ADP
ap-2099	27	11	=	=	PUNCT
ap-2099	27	12	−	−	PROPN
ap-2099	28	1	i	i	PRON
ap-2099	28	2	~	~	PUNCT
ap-2099	28	3	m∂j	m∂j	X
ap-2099	28	4	stands	stand	VERB
ap-2099	28	5	for	for	ADP
ap-2099	28	6	velocity	velocity	NOUN
ap-2099	28	7	operator	operator	NOUN
ap-2099	28	8	.	.	PUNCT
ap-2099	29	1	importantly	importantly	ADV
ap-2099	29	2	the	the	DET
ap-2099	29	3	operators	operator	NOUN
ap-2099	29	4	li	li	PROPN
ap-2099	29	5	and	and	CCONJ
ap-2099	29	6	ai	ai	PROPN
ap-2099	29	7	commute	commute	NOUN
ap-2099	29	8	with	with	ADP
ap-2099	29	9	the	the	DET
ap-2099	29	10	hamiltonian	hamiltonian	NOUN
ap-2099	29	11	,	,	PUNCT
ap-2099	29	12	i.e.	i.e.	X
ap-2099	29	13	are	be	AUX
ap-2099	29	14	conserved	conserve	VERB
ap-2099	29	15	with	with	ADP
ap-2099	29	16	respect	respect	NOUN
ap-2099	29	17	to	to	ADP
ap-2099	29	18	time	time	NOUN
ap-2099	29	19	evolution	evolution	NOUN
ap-2099	29	20	,	,	PUNCT
ap-2099	29	21	and	and	CCONJ
ap-2099	29	22	as	as	ADP
ap-2099	29	23	to	to	ADP
ap-2099	29	24	their	their	PRON
ap-2099	29	25	mutual	mutual	ADJ
ap-2099	29	26	commutation	commutation	NOUN
ap-2099	29	27	relations	relation	NOUN
ap-2099	29	28	,	,	PUNCT
ap-2099	29	29	there	there	PRON
ap-2099	29	30	would	would	AUX
ap-2099	29	31	be	be	AUX
ap-2099	29	32	pretty	pretty	ADV
ap-2099	29	33	good	good	ADJ
ap-2099	29	34	views	view	NOUN
ap-2099	29	35	of	of	ADP
ap-2099	29	36	them	they	PRON
ap-2099	29	37	forming	form	VERB
ap-2099	29	38	a	a	DET
ap-2099	29	39	closed	closed	ADJ
ap-2099	29	40	algebra	algebra	NOUN
ap-2099	29	41	so(4	so(4	NOUN
ap-2099	29	42	)	)	PUNCT
ap-2099	29	43	,	,	PUNCT
ap-2099	29	44	if	if	SCONJ
ap-2099	29	45	it	it	PRON
ap-2099	29	46	were	be	AUX
ap-2099	29	47	not	not	PART
ap-2099	29	48	for	for	ADP
ap-2099	29	49	the	the	DET
ap-2099	29	50	commutator	commutator	NOUN
ap-2099	30	1	[	[	X
ap-2099	30	2	ai	ai	VERB
ap-2099	30	3	,	,	PUNCT
ap-2099	30	4	aj	aj	PROPN
ap-2099	30	5	]	]	PUNCT
ap-2099	30	6	∝	∝	PROPN
ap-2099	30	7	lkh	lkh	PROPN
ap-2099	30	8	.	.	PUNCT
ap-2099	31	1	however	however	ADV
ap-2099	31	2	,	,	PUNCT
ap-2099	31	3	restricting	restrict	VERB
ap-2099	31	4	ourselves	ourselves	PRON
ap-2099	31	5	to	to	ADP
ap-2099	31	6	the	the	DET
ap-2099	31	7	subspace	subspace	NOUN
ap-2099	31	8	he	he	PRON
ap-2099	31	9	spanned	span	VERB
ap-2099	31	10	by	by	ADP
ap-2099	31	11	eigenvectors	eigenvector	NOUN
ap-2099	31	12	of	of	ADP
ap-2099	31	13	h	h	NOUN
ap-2099	31	14	corresponding	correspond	VERB
ap-2099	31	15	to	to	ADP
ap-2099	31	16	the	the	DET
ap-2099	31	17	eigenvalue	eigenvalue	PROPN
ap-2099	31	18	e	e	NOUN
ap-2099	31	19	,	,	PUNCT
ap-2099	31	20	h	h	PROPN
ap-2099	31	21	can	can	AUX
ap-2099	31	22	be	be	AUX
ap-2099	31	23	replaced	replace	VERB
ap-2099	31	24	by	by	ADP
ap-2099	31	25	its	its	PRON
ap-2099	31	26	eigenvalue	eigenvalue	NOUN
ap-2099	31	27	,	,	PUNCT
ap-2099	31	28	which	which	PRON
ap-2099	31	29	is	be	AUX
ap-2099	31	30	a	a	DET
ap-2099	31	31	c	c	NOUN
ap-2099	31	32	-	-	PUNCT
ap-2099	31	33	number	number	NOUN
ap-2099	31	34	.	.	PUNCT
ap-2099	32	1	besides	besides	SCONJ
ap-2099	32	2	enabling	enable	VERB
ap-2099	32	3	the	the	DET
ap-2099	32	4	algebra	algebra	NOUN
ap-2099	32	5	to	to	PART
ap-2099	32	6	close	close	VERB
ap-2099	32	7	,	,	PUNCT
ap-2099	32	8	we	we	PRON
ap-2099	32	9	have	have	AUX
ap-2099	32	10	also	also	ADV
ap-2099	32	11	dragged	drag	VERB
ap-2099	32	12	the	the	DET
ap-2099	32	13	energy	energy	NOUN
ap-2099	32	14	into	into	ADP
ap-2099	32	15	the	the	DET
ap-2099	32	16	very	very	ADJ
ap-2099	32	17	definition	definition	NOUN
ap-2099	32	18	of	of	ADP
ap-2099	32	19	the	the	DET
ap-2099	32	20	algebra	algebra	NOUN
ap-2099	32	21	generators	generator	NOUN
ap-2099	32	22	.	.	PUNCT
ap-2099	33	1	this	this	PRON
ap-2099	33	2	,	,	PUNCT
ap-2099	33	3	together	together	ADV
ap-2099	33	4	with	with	ADP
ap-2099	33	5	the	the	DET
ap-2099	33	6	theory	theory	NOUN
ap-2099	33	7	related	relate	VERB
ap-2099	33	8	to	to	ADP
ap-2099	33	9	the	the	DET
ap-2099	33	10	relevant	relevant	ADJ
ap-2099	33	11	casimir	casimir	NOUN
ap-2099	33	12	operators	operator	NOUN
ap-2099	33	13	,	,	PUNCT
ap-2099	33	14	has	have	VERB
ap-2099	33	15	a	a	DET
ap-2099	33	16	direct	direct	ADJ
ap-2099	33	17	impact	impact	NOUN
ap-2099	33	18	on	on	ADP
ap-2099	33	19	the	the	DET
ap-2099	33	20	h	h	NOUN
ap-2099	33	21	-	-	PUNCT
ap-2099	33	22	atom	atom	NOUN
ap-2099	33	23	energy	energy	NOUN
ap-2099	33	24	spectrum	spectrum	NOUN
ap-2099	33	25	.	.	PUNCT
ap-2099	34	1	in	in	ADP
ap-2099	34	2	this	this	DET
ap-2099	34	3	way	way	NOUN
ap-2099	34	4	pauli	pauli	PROPN
ap-2099	34	5	found	find	VERB
ap-2099	34	6	the	the	DET
ap-2099	34	7	correct	correct	ADJ
ap-2099	34	8	formulas	formula	NOUN
ap-2099	34	9	for	for	ADP
ap-2099	34	10	the	the	DET
ap-2099	34	11	hydrogen	hydrogen	NOUN
ap-2099	34	12	atom	atom	NOUN
ap-2099	34	13	spectrum	spectrum	NOUN
ap-2099	34	14	even	even	ADV
ap-2099	34	15	before	before	ADP
ap-2099	34	16	schrödinger	schrödinger	NOUN
ap-2099	34	17	.	.	PUNCT
ap-2099	35	1	now	now	ADV
ap-2099	35	2	the	the	DET
ap-2099	35	3	search	search	NOUN
ap-2099	35	4	for	for	ADP
ap-2099	35	5	the	the	DET
ap-2099	35	6	analogy	analogy	NOUN
ap-2099	35	7	in	in	ADP
ap-2099	35	8	noncommutative	noncommutative	ADJ
ap-2099	35	9	quantum	quantum	ADJ
ap-2099	35	10	mechanics	mechanic	NOUN
ap-2099	35	11	(	(	PUNCT
ap-2099	35	12	ncqm	ncqm	NOUN
ap-2099	35	13	)	)	PUNCT
ap-2099	35	14	begins	begin	VERB
ap-2099	35	15	.	.	PUNCT
ap-2099	36	1	the	the	DET
ap-2099	36	2	rest	rest	NOUN
ap-2099	36	3	of	of	ADP
ap-2099	36	4	this	this	DET
ap-2099	36	5	paper	paper	NOUN
ap-2099	36	6	is	be	AUX
ap-2099	36	7	organized	organize	VERB
ap-2099	36	8	in	in	ADP
ap-2099	36	9	the	the	DET
ap-2099	36	10	following	following	ADJ
ap-2099	36	11	way	way	NOUN
ap-2099	36	12	:	:	PUNCT
ap-2099	36	13	in	in	ADP
ap-2099	36	14	section	section	NOUN
ap-2099	36	15	2	2	NUM
ap-2099	36	16	149	149	NUM
ap-2099	36	17	http://dx.doi.org/10.14311/ap.2014.54.0149	http://dx.doi.org/10.14311/ap.2014.54.0149	ADP
ap-2099	36	18	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2099	36	19	p.	p.	NOUN
ap-2099	36	20	presnajder	presnajder	NOUN
ap-2099	36	21	,	,	PUNCT
ap-2099	36	22	v.	v.	PROPN
ap-2099	36	23	galikova	galikova	PROPN
ap-2099	36	24	,	,	PUNCT
ap-2099	36	25	s.	s.	PROPN
ap-2099	36	26	kovacik	kovacik	PROPN
ap-2099	36	27	acta	acta	PROPN
ap-2099	36	28	polytechnica	polytechnica	PROPN
ap-2099	36	29	we	we	PRON
ap-2099	36	30	give	give	VERB
ap-2099	36	31	a	a	DET
ap-2099	36	32	brief	brief	ADJ
ap-2099	36	33	introduction	introduction	NOUN
ap-2099	36	34	to	to	ADP
ap-2099	36	35	the	the	DET
ap-2099	36	36	quantum	quantum	ADJ
ap-2099	36	37	mechanics	mechanic	NOUN
ap-2099	36	38	in	in	ADP
ap-2099	36	39	a	a	DET
ap-2099	36	40	spherically	spherically	NOUN
ap-2099	36	41	symmetric	symmetric	ADJ
ap-2099	36	42	noncommutative	noncommutative	ADJ
ap-2099	36	43	space	space	NOUN
ap-2099	36	44	.	.	PUNCT
ap-2099	37	1	the	the	DET
ap-2099	37	2	hilbert	hilbert	PROPN
ap-2099	37	3	space	space	NOUN
ap-2099	37	4	of	of	ADP
ap-2099	37	5	wave	wave	NOUN
ap-2099	37	6	functions	function	NOUN
ap-2099	37	7	in	in	ADP
ap-2099	37	8	nc	nc	PROPN
ap-2099	37	9	space	space	NOUN
ap-2099	37	10	and	and	CCONJ
ap-2099	37	11	the	the	DET
ap-2099	37	12	nc	nc	PROPN
ap-2099	37	13	generalizations	generalization	NOUN
ap-2099	37	14	of	of	ADP
ap-2099	37	15	important	important	ADJ
ap-2099	37	16	operators	operator	NOUN
ap-2099	37	17	(	(	PUNCT
ap-2099	37	18	hamiltonian	hamiltonian	ADJ
ap-2099	37	19	,	,	PUNCT
ap-2099	37	20	angular	angular	ADJ
ap-2099	37	21	momentum	momentum	NOUN
ap-2099	37	22	,	,	PUNCT
ap-2099	37	23	coordinate	coordinate	NOUN
ap-2099	37	24	and	and	CCONJ
ap-2099	37	25	velocity	velocity	NOUN
ap-2099	37	26	)	)	PUNCT
ap-2099	37	27	are	be	AUX
ap-2099	37	28	introduced	introduce	VERB
ap-2099	37	29	.	.	PUNCT
ap-2099	38	1	when	when	SCONJ
ap-2099	38	2	we	we	PRON
ap-2099	38	3	use	use	VERB
ap-2099	38	4	these	these	PRON
ap-2099	38	5	,	,	PUNCT
ap-2099	38	6	a	a	DET
ap-2099	38	7	generalization	generalization	NOUN
ap-2099	38	8	of	of	ADP
ap-2099	38	9	the	the	DET
ap-2099	38	10	dynamical	dynamical	ADJ
ap-2099	38	11	symmetry	symmetry	NOUN
ap-2099	38	12	of	of	ADP
ap-2099	38	13	the	the	DET
ap-2099	38	14	coulomb	coulomb	NOUN
ap-2099	38	15	-	-	PUNCT
ap-2099	38	16	kepler	kepler	NOUN
ap-2099	38	17	problem	problem	NOUN
ap-2099	38	18	in	in	ADP
ap-2099	38	19	ncqm	ncqm	NOUN
ap-2099	38	20	is	be	AUX
ap-2099	38	21	presented	present	VERB
ap-2099	38	22	in	in	ADP
ap-2099	38	23	section	section	NOUN
ap-2099	38	24	3	3	NUM
ap-2099	38	25	.	.	PUNCT
ap-2099	38	26	section	section	NOUN
ap-2099	38	27	4	4	NUM
ap-2099	38	28	provides	provide	VERB
ap-2099	38	29	conclusions	conclusion	NOUN
ap-2099	38	30	.	.	PUNCT
ap-2099	39	1	we	we	PRON
ap-2099	39	2	skip	skip	VERB
ap-2099	39	3	all	all	DET
ap-2099	39	4	the	the	DET
ap-2099	39	5	detailed	detailed	ADJ
ap-2099	39	6	and	and	CCONJ
ap-2099	39	7	lengthy	lengthy	ADJ
ap-2099	39	8	calculations	calculation	NOUN
ap-2099	39	9	that	that	PRON
ap-2099	39	10	can	can	AUX
ap-2099	39	11	be	be	AUX
ap-2099	39	12	found	find	VERB
ap-2099	39	13	in	in	ADP
ap-2099	39	14	our	our	PRON
ap-2099	39	15	recently	recently	ADV
ap-2099	39	16	published	publish	VERB
ap-2099	39	17	paper	paper	NOUN
ap-2099	39	18	[	[	X
ap-2099	39	19	7	7	NUM
ap-2099	39	20	]	]	SYM
ap-2099	39	21	.	.	PUNCT
ap-2099	40	1	2	2	X
ap-2099	40	2	.	.	X
ap-2099	40	3	basics	basic	NOUN
ap-2099	40	4	of	of	ADP
ap-2099	40	5	noncommutative	noncommutative	ADJ
ap-2099	40	6	quantum	quantum	ADJ
ap-2099	40	7	mechanics	mechanic	NOUN
ap-2099	40	8	to	to	PART
ap-2099	40	9	begin	begin	VERB
ap-2099	40	10	,	,	PUNCT
ap-2099	40	11	it	it	PRON
ap-2099	40	12	should	should	AUX
ap-2099	40	13	be	be	AUX
ap-2099	40	14	made	make	VERB
ap-2099	40	15	clear	clear	ADJ
ap-2099	40	16	how	how	SCONJ
ap-2099	40	17	to	to	PART
ap-2099	40	18	introduce	introduce	VERB
ap-2099	40	19	some	some	DET
ap-2099	40	20	uncertainty	uncertainty	NOUN
ap-2099	40	21	principle	principle	NOUN
ap-2099	40	22	into	into	ADP
ap-2099	40	23	the	the	DET
ap-2099	40	24	configuration	configuration	NOUN
ap-2099	40	25	space	space	NOUN
ap-2099	40	26	for	for	ADP
ap-2099	40	27	the	the	DET
ap-2099	40	28	coulomb	coulomb	NOUN
ap-2099	40	29	problem	problem	NOUN
ap-2099	40	30	without	without	ADP
ap-2099	40	31	spoiling	spoil	VERB
ap-2099	40	32	the	the	DET
ap-2099	40	33	key	key	ADJ
ap-2099	40	34	feature	feature	NOUN
ap-2099	40	35	which	which	PRON
ap-2099	40	36	allows	allow	VERB
ap-2099	40	37	us	we	PRON
ap-2099	40	38	to	to	PART
ap-2099	40	39	find	find	VERB
ap-2099	40	40	the	the	DET
ap-2099	40	41	exact	exact	ADJ
ap-2099	40	42	solution	solution	NOUN
ap-2099	40	43	the	the	DET
ap-2099	40	44	rotational	rotational	ADJ
ap-2099	40	45	invariance	invariance	NOUN
ap-2099	40	46	.	.	PUNCT
ap-2099	41	1	the	the	DET
ap-2099	41	2	uncertainty	uncertainty	NOUN
ap-2099	41	3	is	be	AUX
ap-2099	41	4	expressed	express	VERB
ap-2099	41	5	as	as	ADP
ap-2099	41	6	nontrivial	nontrivial	ADJ
ap-2099	41	7	commutation	commutation	NOUN
ap-2099	41	8	relations	relation	NOUN
ap-2099	41	9	for	for	ADP
ap-2099	41	10	the	the	DET
ap-2099	41	11	nc	nc	PROPN
ap-2099	41	12	analogs	analogs	PROPN
ap-2099	41	13	of	of	ADP
ap-2099	41	14	the	the	DET
ap-2099	41	15	former	former	ADJ
ap-2099	41	16	cartesian	cartesian	ADJ
ap-2099	41	17	coordinates	coordinate	NOUN
ap-2099	41	18	(	(	PUNCT
ap-2099	41	19	obviously	obviously	ADV
ap-2099	41	20	we	we	PRON
ap-2099	41	21	have	have	AUX
ap-2099	41	22	to	to	PART
ap-2099	41	23	abandon	abandon	VERB
ap-2099	41	24	c	c	NOUN
ap-2099	41	25	-	-	PUNCT
ap-2099	41	26	numbers	number	NOUN
ap-2099	41	27	)	)	PUNCT
ap-2099	41	28	,	,	PUNCT
ap-2099	41	29	defined	define	VERB
ap-2099	41	30	in	in	ADP
ap-2099	41	31	a	a	DET
ap-2099	41	32	spherically	spherically	NOUN
ap-2099	41	33	symmetrical	symmetrical	ADJ
ap-2099	41	34	way	way	NOUN
ap-2099	41	35	.	.	PUNCT
ap-2099	42	1	the	the	DET
ap-2099	42	2	coordinates	coordinate	NOUN
ap-2099	42	3	in	in	ADP
ap-2099	42	4	the	the	DET
ap-2099	42	5	nc	nc	PROPN
ap-2099	42	6	configuration	configuration	PROPN
ap-2099	42	7	space	space	NOUN
ap-2099	42	8	r3	r3	PROPN
ap-2099	42	9	λ	λ	NOUN
ap-2099	42	10	are	be	AUX
ap-2099	42	11	realized	realize	VERB
ap-2099	42	12	in	in	ADP
ap-2099	42	13	terms	term	NOUN
ap-2099	42	14	of	of	ADP
ap-2099	42	15	2	2	NUM
ap-2099	42	16	pairs	pair	NOUN
ap-2099	42	17	of	of	ADP
ap-2099	42	18	boson	boson	NOUN
ap-2099	42	19	annihilation	annihilation	NOUN
ap-2099	42	20	and	and	CCONJ
ap-2099	42	21	creation	creation	NOUN
ap-2099	42	22	operators	operator	NOUN
ap-2099	42	23	aα	aα	PROPN
ap-2099	42	24	,	,	PUNCT
ap-2099	42	25	a+	a+	PUNCT
ap-2099	42	26	α	α	NOUN
ap-2099	42	27	,	,	PUNCT
ap-2099	42	28	α	α	NOUN
ap-2099	42	29	=	=	SYM
ap-2099	42	30	1	1	NUM
ap-2099	42	31	,	,	PUNCT
ap-2099	42	32	2	2	NUM
ap-2099	42	33	,	,	PUNCT
ap-2099	42	34	satisfying	satisfy	VERB
ap-2099	42	35	[	[	X
ap-2099	42	36	aα	aα	NOUN
ap-2099	42	37	,	,	PUNCT
ap-2099	42	38	a+	a+	PUNCT
ap-2099	43	1	β	β	X
ap-2099	43	2	]	]	PUNCT
ap-2099	43	3	=	=	PUNCT
ap-2099	43	4	δαβ	δαβ	NOUN
ap-2099	43	5	,	,	PUNCT
ap-2099	43	6	[	[	X
ap-2099	43	7	aα	aα	NOUN
ap-2099	43	8	,	,	PUNCT
ap-2099	43	9	aβ	aβ	NOUN
ap-2099	43	10	]	]	PUNCT
ap-2099	43	11	=	=	PUNCT
ap-2099	44	1	[	[	X
ap-2099	44	2	a+	a+	X
ap-2099	44	3	α	α	NOUN
ap-2099	44	4	,	,	PUNCT
ap-2099	44	5	a	a	DET
ap-2099	44	6	+	+	X
ap-2099	44	7	β	β	X
ap-2099	44	8	]	]	X
ap-2099	44	9	=	=	PUNCT
ap-2099	44	10	0	0	X
ap-2099	44	11	.	.	PUNCT
ap-2099	45	1	(	(	PUNCT
ap-2099	45	2	5	5	X
ap-2099	45	3	)	)	PUNCT
ap-2099	45	4	they	they	PRON
ap-2099	45	5	act	act	VERB
ap-2099	45	6	in	in	ADP
ap-2099	45	7	an	an	DET
ap-2099	45	8	auxiliary	auxiliary	ADJ
ap-2099	45	9	fock	fock	ADJ
ap-2099	45	10	space	space	NOUN
ap-2099	45	11	f	f	PROPN
ap-2099	45	12	spanned	span	VERB
ap-2099	45	13	by	by	ADP
ap-2099	45	14	the	the	DET
ap-2099	45	15	normalized	normalize	VERB
ap-2099	45	16	vectors	vector	NOUN
ap-2099	45	17	|n1	|n1	VERB
ap-2099	45	18	,	,	PUNCT
ap-2099	45	19	n2	n2	ADJ
ap-2099	45	20	〉	〉	NOUN
ap-2099	45	21	=	=	SYM
ap-2099	45	22	(	(	PUNCT
ap-2099	45	23	a+	a+	X
ap-2099	45	24	1	1	NUM
ap-2099	45	25	)	)	PUNCT
ap-2099	46	1	n1(a+	n1(a+	PROPN
ap-2099	46	2	2	2	NUM
ap-2099	46	3	)	)	PUNCT
ap-2099	46	4	n2	n2	ADJ
ap-2099	46	5	√	√	NOUN
ap-2099	46	6	n1!n2	n1!n2	PROPN
ap-2099	46	7	!	!	PUNCT
ap-2099	47	1	|0	|0	NUM
ap-2099	48	1	〉	〉	PROPN
ap-2099	48	2	.	.	PUNCT
ap-2099	49	1	(	(	PUNCT
ap-2099	49	2	6	6	NUM
ap-2099	49	3	)	)	PUNCT
ap-2099	49	4	the	the	DET
ap-2099	49	5	normalized	normalize	VERB
ap-2099	49	6	vacuum	vacuum	NOUN
ap-2099	49	7	state	state	NOUN
ap-2099	49	8	is	be	AUX
ap-2099	49	9	denoted	denote	VERB
ap-2099	49	10	as	as	ADP
ap-2099	49	11	|0	|0	NUM
ap-2099	49	12	〉	〉	PROPN
ap-2099	49	13	≡	≡	PROPN
ap-2099	49	14	|0	|0	NUM
ap-2099	49	15	,	,	PUNCT
ap-2099	49	16	0	0	NUM
ap-2099	49	17	〉	〉	NUM
ap-2099	49	18	.	.	PUNCT
ap-2099	50	1	the	the	DET
ap-2099	50	2	noncommutative	noncommutative	PROPN
ap-2099	50	3	coordinates	coordinate	NOUN
ap-2099	50	4	xj	xj	PROPN
ap-2099	50	5	,	,	PUNCT
ap-2099	50	6	j	j	PROPN
ap-2099	50	7	=	=	SYM
ap-2099	50	8	1	1	NUM
ap-2099	50	9	,	,	PUNCT
ap-2099	50	10	2	2	NUM
ap-2099	50	11	,	,	PUNCT
ap-2099	50	12	3	3	NUM
ap-2099	50	13	,	,	PUNCT
ap-2099	50	14	and	and	CCONJ
ap-2099	50	15	the	the	DET
ap-2099	50	16	nc	nc	PROPN
ap-2099	50	17	analog	analog	NOUN
ap-2099	50	18	of	of	ADP
ap-2099	50	19	the	the	DET
ap-2099	50	20	euclidean	euclidean	ADJ
ap-2099	50	21	distance	distance	NOUN
ap-2099	50	22	from	from	ADP
ap-2099	50	23	the	the	DET
ap-2099	50	24	origin	origin	NOUN
ap-2099	50	25	are	be	AUX
ap-2099	50	26	given	give	VERB
ap-2099	50	27	as	as	ADP
ap-2099	50	28	xj	xj	PROPN
ap-2099	50	29	=	=	SYM
ap-2099	50	30	λa+σja	λa+σja	PROPN
ap-2099	50	31	≡	≡	PROPN
ap-2099	50	32	λσjαβa	λσjαβa	PROPN
ap-2099	50	33	+	+	NUM
ap-2099	50	34	αaβ	αaβ	NOUN
ap-2099	50	35	,	,	PUNCT
ap-2099	50	36	r	r	NOUN
ap-2099	50	37	=	=	PUNCT
ap-2099	50	38	λ(n	λ(n	X
ap-2099	50	39	+	+	CCONJ
ap-2099	51	1	1	1	NUM
ap-2099	51	2	)	)	PUNCT
ap-2099	51	3	,	,	PUNCT
ap-2099	51	4	(	(	PUNCT
ap-2099	51	5	7	7	X
ap-2099	51	6	)	)	PUNCT
ap-2099	51	7	where	where	SCONJ
ap-2099	51	8	σj	σj	NOUN
ap-2099	51	9	are	be	AUX
ap-2099	51	10	the	the	DET
ap-2099	51	11	pauli	pauli	PROPN
ap-2099	51	12	matrices	matrix	NOUN
ap-2099	51	13	,	,	PUNCT
ap-2099	51	14	n	n	NOUN
ap-2099	51	15	=	=	PRON
ap-2099	51	16	a+	a+	PUNCT
ap-2099	51	17	αaα	αaα	ADV
ap-2099	51	18	is	be	AUX
ap-2099	51	19	the	the	DET
ap-2099	51	20	number	number	NOUN
ap-2099	51	21	operator	operator	NOUN
ap-2099	51	22	in	in	ADP
ap-2099	51	23	the	the	DET
ap-2099	51	24	fock	fock	ADJ
ap-2099	51	25	space	space	NOUN
ap-2099	51	26	,	,	PUNCT
ap-2099	51	27	and	and	CCONJ
ap-2099	51	28	λ	λ	PROPN
ap-2099	51	29	is	be	AUX
ap-2099	51	30	a	a	DET
ap-2099	51	31	length	length	NOUN
ap-2099	51	32	parameter	parameter	NOUN
ap-2099	51	33	.	.	PUNCT
ap-2099	52	1	its	its	PRON
ap-2099	52	2	magnitude	magnitude	NOUN
ap-2099	52	3	is	be	AUX
ap-2099	52	4	not	not	PART
ap-2099	52	5	fixed	fix	VERB
ap-2099	52	6	within	within	ADP
ap-2099	52	7	our	our	PRON
ap-2099	52	8	model	model	NOUN
ap-2099	52	9	.	.	PUNCT
ap-2099	53	1	naturally	naturally	ADV
ap-2099	53	2	it	it	PRON
ap-2099	53	3	has	have	VERB
ap-2099	53	4	a	a	DET
ap-2099	53	5	connection	connection	NOUN
ap-2099	53	6	with	with	ADP
ap-2099	53	7	the	the	DET
ap-2099	53	8	smallest	small	ADJ
ap-2099	53	9	distance	distance	NOUN
ap-2099	53	10	relevant	relevant	ADJ
ap-2099	53	11	in	in	ADP
ap-2099	53	12	the	the	DET
ap-2099	53	13	given	give	VERB
ap-2099	53	14	noncommutative	noncommutative	ADJ
ap-2099	53	15	configuration	configuration	NOUN
ap-2099	53	16	space	space	NOUN
ap-2099	53	17	denoted	denote	VERB
ap-2099	53	18	as	as	ADP
ap-2099	53	19	r3	r3	PROPN
ap-2099	53	20	λ	λ	PROPN
ap-2099	53	21	.	.	PUNCT
ap-2099	54	1	the	the	DET
ap-2099	54	2	key	key	ADJ
ap-2099	54	3	rotationally	rotationally	ADV
ap-2099	54	4	invariant	invariant	ADJ
ap-2099	54	5	relations	relation	NOUN
ap-2099	54	6	in	in	ADP
ap-2099	54	7	the	the	DET
ap-2099	54	8	theory	theory	NOUN
ap-2099	54	9	are	be	AUX
ap-2099	54	10	[	[	X
ap-2099	54	11	xi	xi	PROPN
ap-2099	54	12	,	,	PUNCT
ap-2099	54	13	xj	xj	X
ap-2099	54	14	]	]	PUNCT
ap-2099	54	15	=	=	PUNCT
ap-2099	55	1	2iλεijkxk	2iλεijkxk	NUM
ap-2099	55	2	,	,	PUNCT
ap-2099	55	3	[	[	X
ap-2099	55	4	xi	xi	X
ap-2099	55	5	,	,	PUNCT
ap-2099	55	6	r	r	X
ap-2099	55	7	]	]	X
ap-2099	55	8	=	=	SYM
ap-2099	55	9	0	0	NUM
ap-2099	55	10	,	,	PUNCT
ap-2099	55	11	r2−x2	r2−x2	NUM
ap-2099	55	12	j	j	NOUN
ap-2099	55	13	=	=	SYM
ap-2099	55	14	λ2	λ2	PROPN
ap-2099	55	15	.	.	PUNCT
ap-2099	56	1	(	(	PUNCT
ap-2099	56	2	8)	8)	NUM
ap-2099	56	3	the	the	DET
ap-2099	56	4	first	first	ADJ
ap-2099	56	5	equation	equation	NOUN
ap-2099	56	6	defines	define	VERB
ap-2099	56	7	a	a	DET
ap-2099	56	8	noncommutative	noncommutative	ADJ
ap-2099	56	9	or	or	CCONJ
ap-2099	56	10	fuzzy	fuzzy	ADJ
ap-2099	56	11	sphere	sphere	NOUN
ap-2099	56	12	that	that	PRON
ap-2099	56	13	appeared	appear	VERB
ap-2099	56	14	a	a	DET
ap-2099	56	15	long	long	ADJ
ap-2099	56	16	time	time	NOUN
ap-2099	56	17	ago	ago	ADV
ap-2099	56	18	in	in	ADP
ap-2099	56	19	various	various	ADJ
ap-2099	56	20	contexts	context	NOUN
ap-2099	56	21	[	[	X
ap-2099	56	22	8	8	NUM
ap-2099	56	23	]	]	PUNCT
ap-2099	56	24	,	,	PUNCT
ap-2099	56	25	e.g.	e.g.	ADV
ap-2099	56	26	,	,	PUNCT
ap-2099	56	27	quantization	quantization	NOUN
ap-2099	56	28	on	on	ADP
ap-2099	56	29	a	a	DET
ap-2099	56	30	sphere	sphere	NOUN
ap-2099	56	31	=	=	SYM
ap-2099	56	32	nonflat	nonflat	NOUN
ap-2099	56	33	phase	phase	NOUN
ap-2099	56	34	space	space	NOUN
ap-2099	56	35	,	,	PUNCT
ap-2099	56	36	a	a	DET
ap-2099	56	37	simple	simple	ADJ
ap-2099	56	38	model	model	NOUN
ap-2099	56	39	of	of	ADP
ap-2099	56	40	nc	nc	PROPN
ap-2099	56	41	manifolds	manifolds	PROPN
ap-2099	56	42	.	.	PUNCT
ap-2099	57	1	all	all	DET
ap-2099	57	2	these	these	DET
ap-2099	57	3	models	model	NOUN
ap-2099	57	4	considered	consider	VERB
ap-2099	57	5	a	a	DET
ap-2099	57	6	single	single	ADJ
ap-2099	57	7	fuzzy	fuzzy	ADJ
ap-2099	57	8	sphere	sphere	NOUN
ap-2099	57	9	.	.	PUNCT
ap-2099	58	1	here	here	ADV
ap-2099	58	2	we	we	PRON
ap-2099	58	3	deal	deal	VERB
ap-2099	58	4	with	with	ADP
ap-2099	58	5	an	an	DET
ap-2099	58	6	infinite	infinite	ADJ
ap-2099	58	7	sequence	sequence	NOUN
ap-2099	58	8	of	of	ADP
ap-2099	58	9	fuzzy	fuzzy	ADJ
ap-2099	58	10	spheres	sphere	NOUN
ap-2099	58	11	dynamically	dynamically	ADV
ap-2099	58	12	via	via	ADP
ap-2099	58	13	an	an	DET
ap-2099	58	14	nc	nc	PROPN
ap-2099	58	15	analog	analog	NOUN
ap-2099	58	16	of	of	ADP
ap-2099	58	17	the	the	DET
ap-2099	58	18	(	(	PUNCT
ap-2099	58	19	radial	radial	ADJ
ap-2099	58	20	)	)	PUNCT
ap-2099	58	21	schrödinger	schrödinger	ADJ
ap-2099	58	22	equation	equation	NOUN
ap-2099	58	23	that	that	PRON
ap-2099	58	24	is	be	AUX
ap-2099	58	25	introduced	introduce	VERB
ap-2099	58	26	below	below	ADV
ap-2099	58	27	.	.	PUNCT
ap-2099	59	1	we	we	PRON
ap-2099	59	2	remark	remark	VERB
ap-2099	59	3	that	that	SCONJ
ap-2099	59	4	while	while	SCONJ
ap-2099	59	5	the	the	DET
ap-2099	59	6	first	first	ADJ
ap-2099	59	7	equation	equation	NOUN
ap-2099	59	8	in	in	ADP
ap-2099	59	9	(	(	PUNCT
ap-2099	59	10	8)	8)	NUM
ap-2099	59	11	is	be	AUX
ap-2099	59	12	postulated	postulate	VERB
ap-2099	59	13	,	,	PUNCT
ap-2099	59	14	the	the	DET
ap-2099	59	15	other	other	ADJ
ap-2099	59	16	two	two	NUM
ap-2099	59	17	follow	follow	NOUN
ap-2099	59	18	from	from	ADP
ap-2099	59	19	the	the	DET
ap-2099	59	20	construction	construction	NOUN
ap-2099	59	21	of	of	ADP
ap-2099	59	22	r3	r3	PROPN
ap-2099	59	23	λ	λ	PROPN
ap-2099	59	24	.	.	PUNCT
ap-2099	60	1	while	while	SCONJ
ap-2099	60	2	constructing	construct	VERB
ap-2099	60	3	nc	nc	PROPN
ap-2099	60	4	quantum	quantum	ADJ
ap-2099	60	5	mechanics	mechanic	NOUN
ap-2099	60	6	,	,	PUNCT
ap-2099	60	7	firstly	firstly	ADV
ap-2099	60	8	we	we	PRON
ap-2099	60	9	have	have	VERB
ap-2099	60	10	to	to	PART
ap-2099	60	11	decide	decide	VERB
ap-2099	60	12	on	on	ADP
ap-2099	60	13	a	a	DET
ap-2099	60	14	hilbert	hilbert	NOUN
ap-2099	60	15	space	space	NOUN
ap-2099	60	16	hλ	hλ	NOUN
ap-2099	60	17	of	of	ADP
ap-2099	60	18	states	state	NOUN
ap-2099	60	19	(	(	PUNCT
ap-2099	60	20	see	see	VERB
ap-2099	60	21	also	also	ADV
ap-2099	60	22	[	[	X
ap-2099	60	23	9	9	NUM
ap-2099	60	24	]	]	NUM
ap-2099	60	25	)	)	PUNCT
ap-2099	60	26	.	.	PUNCT
ap-2099	61	1	the	the	DET
ap-2099	61	2	suitable	suitable	ADJ
ap-2099	61	3	choice	choice	NOUN
ap-2099	61	4	is	be	AUX
ap-2099	61	5	a	a	DET
ap-2099	61	6	linear	linear	ADJ
ap-2099	61	7	space	space	NOUN
ap-2099	61	8	of	of	ADP
ap-2099	61	9	normally	normally	ADV
ap-2099	61	10	-	-	PUNCT
ap-2099	61	11	ordered	order	VERB
ap-2099	61	12	analytic	analytic	ADJ
ap-2099	61	13	functions	function	NOUN
ap-2099	61	14	containing	contain	VERB
ap-2099	61	15	the	the	DET
ap-2099	61	16	same	same	ADJ
ap-2099	61	17	number	number	NOUN
ap-2099	61	18	of	of	ADP
ap-2099	61	19	creation	creation	NOUN
ap-2099	61	20	and	and	CCONJ
ap-2099	61	21	annihilation	annihilation	NOUN
ap-2099	61	22	operators	operator	NOUN
ap-2099	61	23	:	:	PUNCT
ap-2099	61	24	ψ	ψ	X
ap-2099	61	25	=	=	PUNCT
ap-2099	61	26	∑	∑	PROPN
ap-2099	61	27	cm1m2n1n2(a+	cm1m2n1n2(a+	NOUN
ap-2099	61	28	1	1	X
ap-2099	61	29	)	)	PUNCT
ap-2099	61	30	m1(a+	m1(a+	NOUN
ap-2099	61	31	2	2	NUM
ap-2099	61	32	)	)	PUNCT
ap-2099	61	33	m2an1	m2an1	ADJ
ap-2099	61	34	1	1	NUM
ap-2099	61	35	an2	an2	NUM
ap-2099	61	36	2	2	NUM
ap-2099	61	37	,	,	PUNCT
ap-2099	61	38	(	(	PUNCT
ap-2099	61	39	9	9	X
ap-2099	61	40	)	)	PUNCT
ap-2099	61	41	which	which	PRON
ap-2099	61	42	possess	possess	VERB
ap-2099	61	43	finite	finite	PROPN
ap-2099	61	44	weighted	weight	VERB
ap-2099	61	45	hilbert	hilbert	PROPN
ap-2099	61	46	-	-	PUNCT
ap-2099	61	47	schmidt	schmidt	ADJ
ap-2099	61	48	norm	norm	NOUN
ap-2099	61	49	‖ψ‖2	‖ψ‖2	PUNCT
ap-2099	61	50	=	=	SYM
ap-2099	61	51	4πλ2tr[rψ†ψ	4πλ2tr[rψ†ψ	PROPN
ap-2099	61	52	]	]	PUNCT
ap-2099	61	53	.	.	PUNCT
ap-2099	62	1	(	(	PUNCT
ap-2099	62	2	10	10	NUM
ap-2099	62	3	)	)	PUNCT
ap-2099	62	4	(	(	PUNCT
ap-2099	62	5	the	the	DET
ap-2099	62	6	summation	summation	NOUN
ap-2099	62	7	in	in	ADP
ap-2099	62	8	(	(	PUNCT
ap-2099	62	9	9	9	NUM
ap-2099	62	10	)	)	PUNCT
ap-2099	62	11	is	be	AUX
ap-2099	62	12	over	over	ADP
ap-2099	62	13	nonnegative	nonnegative	ADJ
ap-2099	62	14	integers	integer	NOUN
ap-2099	62	15	satisfying	satisfy	VERB
ap-2099	62	16	m1	m1	PROPN
ap-2099	62	17	+	+	PROPN
ap-2099	62	18	m2	m2	PROPN
ap-2099	62	19	=	=	SYM
ap-2099	62	20	n1	n1	PROPN
ap-2099	62	21	+	+	CCONJ
ap-2099	62	22	n2	n2	ADJ
ap-2099	62	23	.	.	PUNCT
ap-2099	62	24	)	)	PUNCT
ap-2099	63	1	our	our	PRON
ap-2099	63	2	nc	nc	PROPN
ap-2099	63	3	wave	wave	PROPN
ap-2099	63	4	functions	function	NOUN
ap-2099	63	5	ψ	ψ	NOUN
ap-2099	63	6	are	be	AUX
ap-2099	63	7	themselves	themselves	PRON
ap-2099	63	8	operators	operator	NOUN
ap-2099	63	9	on	on	ADP
ap-2099	63	10	the	the	DET
ap-2099	63	11	fock	fock	ADJ
ap-2099	63	12	space	space	NOUN
ap-2099	63	13	mentioned	mention	VERB
ap-2099	63	14	above	above	ADV
ap-2099	63	15	,	,	PUNCT
ap-2099	63	16	so	so	SCONJ
ap-2099	63	17	the	the	DET
ap-2099	63	18	relations	relation	NOUN
ap-2099	63	19	which	which	PRON
ap-2099	63	20	occur	occur	VERB
ap-2099	63	21	are	be	AUX
ap-2099	63	22	to	to	PART
ap-2099	63	23	be	be	AUX
ap-2099	63	24	looked	look	VERB
ap-2099	63	25	at	at	ADP
ap-2099	63	26	as	as	ADP
ap-2099	63	27	operator	operator	NOUN
ap-2099	63	28	equalities	equality	NOUN
ap-2099	63	29	(	(	PUNCT
ap-2099	63	30	we	we	PRON
ap-2099	63	31	could	could	AUX
ap-2099	63	32	put	put	VERB
ap-2099	63	33	|n1	|n1	NOUN
ap-2099	63	34	,	,	PUNCT
ap-2099	63	35	n2	n2	ADJ
ap-2099	63	36	〉	〉	NOUN
ap-2099	63	37	on	on	ADP
ap-2099	63	38	both	both	DET
ap-2099	63	39	sides	side	NOUN
ap-2099	63	40	of	of	ADP
ap-2099	63	41	every	every	DET
ap-2099	63	42	such	such	ADJ
ap-2099	63	43	equation	equation	NOUN
ap-2099	63	44	)	)	PUNCT
ap-2099	63	45	.	.	PUNCT
ap-2099	64	1	we	we	PRON
ap-2099	64	2	can	can	AUX
ap-2099	64	3	move	move	VERB
ap-2099	64	4	to	to	ADP
ap-2099	64	5	the	the	DET
ap-2099	64	6	definition	definition	NOUN
ap-2099	64	7	of	of	ADP
ap-2099	64	8	the	the	DET
ap-2099	64	9	operators	operator	NOUN
ap-2099	64	10	acting	act	VERB
ap-2099	64	11	on	on	ADP
ap-2099	64	12	nc	nc	PROPN
ap-2099	64	13	wave	wave	PROPN
ap-2099	64	14	functions	function	NOUN
ap-2099	64	15	ψ	ψ	ADP
ap-2099	64	16	∈	∈	NOUN
ap-2099	64	17	hλ	hλ	NOUN
ap-2099	64	18	.	.	PUNCT
ap-2099	65	1	to	to	PART
ap-2099	65	2	avoid	avoid	VERB
ap-2099	65	3	potential	potential	ADJ
ap-2099	65	4	confusion	confusion	NOUN
ap-2099	65	5	,	,	PUNCT
ap-2099	65	6	we	we	PRON
ap-2099	65	7	have	have	AUX
ap-2099	65	8	decided	decide	VERB
ap-2099	65	9	to	to	PART
ap-2099	65	10	leave	leave	VERB
ap-2099	65	11	the	the	DET
ap-2099	65	12	nc	nc	PROPN
ap-2099	65	13	coordinates	coordinate	NOUN
ap-2099	65	14	and	and	CCONJ
ap-2099	65	15	the	the	DET
ap-2099	65	16	nc	nc	PROPN
ap-2099	65	17	wave	wave	PROPN
ap-2099	65	18	functions	function	NOUN
ap-2099	65	19	ψ	ψ	X
ap-2099	65	20	(	(	PUNCT
ap-2099	65	21	operators	operator	NOUN
ap-2099	65	22	on	on	ADP
ap-2099	65	23	the	the	DET
ap-2099	65	24	fock	fock	ADJ
ap-2099	65	25	space	space	NOUN
ap-2099	65	26	)	)	PUNCT
ap-2099	65	27	as	as	SCONJ
ap-2099	65	28	they	they	PRON
ap-2099	65	29	are	be	AUX
ap-2099	65	30	,	,	PUNCT
ap-2099	65	31	and	and	CCONJ
ap-2099	65	32	to	to	PART
ap-2099	65	33	denote	denote	VERB
ap-2099	65	34	the	the	DET
ap-2099	65	35	operators	operator	NOUN
ap-2099	65	36	acting	act	VERB
ap-2099	65	37	on	on	ADP
ap-2099	65	38	ψ	ψ	PRON
ap-2099	65	39	with	with	ADP
ap-2099	65	40	a	a	DET
ap-2099	65	41	hat	hat	NOUN
ap-2099	65	42	from	from	ADP
ap-2099	65	43	now	now	ADV
ap-2099	65	44	on	on	ADV
ap-2099	65	45	.	.	PUNCT
ap-2099	66	1	the	the	DET
ap-2099	66	2	generators	generator	NOUN
ap-2099	66	3	of	of	ADP
ap-2099	66	4	rotations	rotation	NOUN
ap-2099	66	5	in	in	ADP
ap-2099	66	6	hλ	hλ	ADP
ap-2099	66	7	,	,	PUNCT
ap-2099	66	8	orbital	orbital	ADJ
ap-2099	66	9	momentum	momentum	NOUN
ap-2099	66	10	operators	operator	NOUN
ap-2099	66	11	,	,	PUNCT
ap-2099	66	12	are	be	AUX
ap-2099	66	13	defined	define	VERB
ap-2099	66	14	as	as	ADP
ap-2099	66	15	l̂jψ	l̂jψ	NOUN
ap-2099	66	16	=	=	SYM
ap-2099	66	17	1	1	NUM
ap-2099	66	18	2λ	2λ	NOUN
ap-2099	66	19	(	(	PUNCT
ap-2099	66	20	xjψ−ψxj	xjψ−ψxj	PROPN
ap-2099	66	21	)	)	PUNCT
ap-2099	66	22	,	,	PUNCT
ap-2099	66	23	j	j	X
ap-2099	67	1	=	=	SYM
ap-2099	67	2	1	1	NUM
ap-2099	67	3	,	,	PUNCT
ap-2099	67	4	2	2	NUM
ap-2099	67	5	,	,	PUNCT
ap-2099	67	6	3	3	NUM
ap-2099	67	7	.	.	PUNCT
ap-2099	68	1	(	(	PUNCT
ap-2099	68	2	11	11	NUM
ap-2099	68	3	)	)	PUNCT
ap-2099	68	4	they	they	PRON
ap-2099	68	5	are	be	AUX
ap-2099	68	6	hermitian	hermitian	ADJ
ap-2099	68	7	and	and	CCONJ
ap-2099	68	8	obey	obey	VERB
ap-2099	68	9	the	the	DET
ap-2099	68	10	usual	usual	ADJ
ap-2099	68	11	commutation	commutation	NOUN
ap-2099	68	12	relations	relation	NOUN
ap-2099	68	13	[	[	X
ap-2099	68	14	l̂i	l̂i	NOUN
ap-2099	68	15	,	,	PUNCT
ap-2099	68	16	l̂j	l̂j	VERB
ap-2099	68	17	]	]	X
ap-2099	68	18	ψ	ψ	X
ap-2099	68	19	≡	≡	PROPN
ap-2099	68	20	(	(	PUNCT
ap-2099	68	21	l̂il̂j	l̂il̂j	NOUN
ap-2099	68	22	−	−	PROPN
ap-2099	68	23	l̂jl̂i)ψ	l̂jl̂i)ψ	NOUN
ap-2099	68	24	=	=	SYM
ap-2099	68	25	iεijkl̂kψ	iεijkl̂kψ	PROPN
ap-2099	68	26	.	.	PUNCT
ap-2099	69	1	(	(	PUNCT
ap-2099	69	2	12	12	NUM
ap-2099	69	3	)	)	PUNCT
ap-2099	69	4	the	the	DET
ap-2099	69	5	standard	standard	ADJ
ap-2099	69	6	eigenfunctions	eigenfunction	NOUN
ap-2099	69	7	ψjm	ψjm	NOUN
ap-2099	69	8	,	,	PUNCT
ap-2099	69	9	j	j	PROPN
ap-2099	69	10	=	=	SYM
ap-2099	69	11	0	0	NUM
ap-2099	69	12	,	,	PUNCT
ap-2099	69	13	1	1	NUM
ap-2099	69	14	,	,	PUNCT
ap-2099	69	15	2	2	NUM
ap-2099	69	16	,	,	PUNCT
ap-2099	69	17	.	.	PUNCT
ap-2099	69	18	.	.	PUNCT
ap-2099	69	19	.	.	PUNCT
ap-2099	70	1	,	,	PUNCT
ap-2099	70	2	m	m	VERB
ap-2099	70	3	=	=	ADJ
ap-2099	70	4	−j	−j	NOUN
ap-2099	70	5	,	,	PUNCT
ap-2099	70	6	.	.	PUNCT
ap-2099	70	7	.	.	PUNCT
ap-2099	70	8	.	.	PUNCT
ap-2099	71	1	,	,	PUNCT
ap-2099	71	2	+	+	PROPN
ap-2099	71	3	j	j	NOUN
ap-2099	71	4	,	,	PUNCT
ap-2099	71	5	satisfying	satisfy	VERB
ap-2099	71	6	l̂2	l̂2	VERB
ap-2099	71	7	iψjm	iψjm	NOUN
ap-2099	71	8	=	=	SYM
ap-2099	71	9	j(j	j(j	PROPN
ap-2099	71	10	+	+	CCONJ
ap-2099	71	11	1)ψjm	1)ψjm	NUM
ap-2099	71	12	,	,	PUNCT
ap-2099	71	13	l̂3ψjm	l̂3ψjm	ADP
ap-2099	71	14	=	=	SYM
ap-2099	71	15	mψjm	mψjm	NOUN
ap-2099	71	16	,	,	PUNCT
ap-2099	71	17	(	(	PUNCT
ap-2099	71	18	13	13	NUM
ap-2099	71	19	)	)	PUNCT
ap-2099	71	20	are	be	AUX
ap-2099	71	21	given	give	VERB
ap-2099	71	22	by	by	ADP
ap-2099	71	23	ψjm	ψjm	NOUN
ap-2099	71	24	=	=	SYM
ap-2099	71	25	∑	∑	PUNCT
ap-2099	71	26	(	(	PUNCT
ap-2099	71	27	jm	jm	NOUN
ap-2099	71	28	)	)	PUNCT
ap-2099	71	29	(	(	PUNCT
ap-2099	71	30	a+	a+	X
ap-2099	71	31	1	1	NUM
ap-2099	71	32	)	)	PUNCT
ap-2099	71	33	m1(a+	m1(a+	NOUN
ap-2099	71	34	2	2	NUM
ap-2099	71	35	)	)	PUNCT
ap-2099	71	36	m2	m2	PROPN
ap-2099	71	37	m1!m2	m1!m2	PROPN
ap-2099	71	38	!	!	PUNCT
ap-2099	71	39	rj(r	rj(r	PUNCT
ap-2099	71	40	)	)	PUNCT
ap-2099	72	1	an1	an1	NOUN
ap-2099	72	2	1	1	NUM
ap-2099	72	3	(	(	PUNCT
ap-2099	72	4	−a2)n2	−a2)n2	VERB
ap-2099	72	5	n1!n2	n1!n2	ADJ
ap-2099	72	6	!	!	PUNCT
ap-2099	72	7	.	.	PUNCT
ap-2099	73	1	(	(	PUNCT
ap-2099	73	2	14	14	NUM
ap-2099	73	3	)	)	PUNCT
ap-2099	73	4	the	the	DET
ap-2099	73	5	summation	summation	NOUN
ap-2099	73	6	goes	go	VERB
ap-2099	73	7	over	over	ADP
ap-2099	73	8	all	all	DET
ap-2099	73	9	nonnegative	nonnegative	ADJ
ap-2099	73	10	integers	integer	NOUN
ap-2099	73	11	that	that	PRON
ap-2099	73	12	satisfy	satisfy	VERB
ap-2099	73	13	m1	m1	PROPN
ap-2099	74	1	+	+	PROPN
ap-2099	74	2	m2	m2	PROPN
ap-2099	74	3	=	=	SYM
ap-2099	74	4	n1	n1	PROPN
ap-2099	74	5	+	+	CCONJ
ap-2099	74	6	n2	n2	ADJ
ap-2099	74	7	=	=	SYM
ap-2099	74	8	j	j	PROPN
ap-2099	74	9	,	,	PUNCT
ap-2099	74	10	m1	m1	PROPN
ap-2099	74	11	−m2	−m2	NOUN
ap-2099	74	12	−	−	PROPN
ap-2099	74	13	n1	n1	PROPN
ap-2099	74	14	+	+	CCONJ
ap-2099	74	15	n2	n2	ADJ
ap-2099	74	16	=	=	SYM
ap-2099	74	17	2	2	NUM
ap-2099	74	18	m.	m.	NOUN
ap-2099	74	19	for	for	ADP
ap-2099	74	20	any	any	DET
ap-2099	74	21	fixed	fix	VERB
ap-2099	74	22	rj(r	rj(r	NOUN
ap-2099	74	23	)	)	PUNCT
ap-2099	74	24	equation	equation	NOUN
ap-2099	74	25	(	(	PUNCT
ap-2099	74	26	14	14	NUM
ap-2099	74	27	)	)	PUNCT
ap-2099	74	28	defines	define	VERB
ap-2099	74	29	a	a	DET
ap-2099	74	30	representation	representation	NOUN
ap-2099	74	31	space	space	NOUN
ap-2099	74	32	for	for	ADP
ap-2099	74	33	a	a	DET
ap-2099	74	34	unitary	unitary	ADJ
ap-2099	74	35	irreducible	irreducible	ADJ
ap-2099	74	36	representation	representation	NOUN
ap-2099	74	37	with	with	ADP
ap-2099	74	38	spin	spin	NOUN
ap-2099	74	39	j.	j.	PROPN
ap-2099	74	40	the	the	DET
ap-2099	74	41	nc	nc	PROPN
ap-2099	74	42	analog	analog	PROPN
ap-2099	74	43	of	of	ADP
ap-2099	74	44	the	the	DET
ap-2099	74	45	usual	usual	ADJ
ap-2099	74	46	laplace	laplace	NOUN
ap-2099	74	47	operator	operator	NOUN
ap-2099	74	48	is	be	AUX
ap-2099	74	49	∆̂λψ	∆̂λψ	NOUN
ap-2099	74	50	=	=	SYM
ap-2099	74	51	−	−	PROPN
ap-2099	74	52	1	1	NUM
ap-2099	74	53	λr	λr	NOUN
ap-2099	75	1	[	[	X
ap-2099	75	2	â+	â+	ADJ
ap-2099	75	3	α	α	NOUN
ap-2099	75	4	,	,	PUNCT
ap-2099	75	5	[	[	X
ap-2099	75	6	âα	âα	X
ap-2099	75	7	,	,	PUNCT
ap-2099	75	8	ψ	ψ	X
ap-2099	75	9	]	]	X
ap-2099	75	10	]	]	X
ap-2099	75	11	=	=	PUNCT
ap-2099	76	1	−	−	PROPN
ap-2099	76	2	1	1	NUM
ap-2099	76	3	λ2(n	λ2(n	X
ap-2099	76	4	+	+	NOUN
ap-2099	76	5	1	1	NUM
ap-2099	76	6	)	)	PUNCT
ap-2099	77	1	[	[	X
ap-2099	77	2	â+	â+	ADP
ap-2099	77	3	α	α	NOUN
ap-2099	77	4	,	,	PUNCT
ap-2099	77	5	[	[	X
ap-2099	77	6	âα	âα	X
ap-2099	77	7	,	,	PUNCT
ap-2099	77	8	ψ	ψ	X
ap-2099	77	9	]	]	X
ap-2099	77	10	]	]	PUNCT
ap-2099	77	11	.	.	PUNCT
ap-2099	78	1	(	(	PUNCT
ap-2099	78	2	15	15	NUM
ap-2099	78	3	)	)	PUNCT
ap-2099	78	4	150	150	NUM
ap-2099	78	5	vol	vol	NOUN
ap-2099	78	6	.	.	PUNCT
ap-2099	79	1	54	54	NUM
ap-2099	79	2	no	no	NOUN
ap-2099	79	3	.	.	PUNCT
ap-2099	80	1	2/2014	2/2014	NUM
ap-2099	80	2	lrl	lrl	PROPN
ap-2099	80	3	vector	vector	NOUN
ap-2099	80	4	in	in	ADP
ap-2099	80	5	quantum	quantum	ADJ
ap-2099	80	6	mechanics	mechanic	NOUN
ap-2099	80	7	in	in	ADP
ap-2099	80	8	noncommutative	noncommutative	ADJ
ap-2099	80	9	space	space	NOUN
ap-2099	80	10	as	as	ADP
ap-2099	80	11	to	to	ADP
ap-2099	80	12	the	the	DET
ap-2099	80	13	operator	operator	NOUN
ap-2099	80	14	û	û	NUM
ap-2099	80	15	,	,	PUNCT
ap-2099	80	16	the	the	DET
ap-2099	80	17	nc	nc	PROPN
ap-2099	80	18	analog	analog	NOUN
ap-2099	80	19	of	of	ADP
ap-2099	80	20	the	the	DET
ap-2099	80	21	central	central	ADJ
ap-2099	80	22	potential	potential	NOUN
ap-2099	80	23	,	,	PUNCT
ap-2099	80	24	it	it	PRON
ap-2099	80	25	is	be	AUX
ap-2099	80	26	defined	define	VERB
ap-2099	80	27	simply	simply	ADV
ap-2099	80	28	as	as	ADP
ap-2099	80	29	the	the	DET
ap-2099	80	30	multiplication	multiplication	NOUN
ap-2099	80	31	of	of	ADP
ap-2099	80	32	the	the	DET
ap-2099	80	33	nc	nc	PROPN
ap-2099	80	34	wave	wave	PROPN
ap-2099	80	35	function	function	NOUN
ap-2099	80	36	by	by	ADP
ap-2099	80	37	u(r	u(r	PROPN
ap-2099	80	38	):	):	PUNCT
ap-2099	80	39	(	(	PUNCT
ap-2099	80	40	ûψ)(r	ûψ)(r	NOUN
ap-2099	80	41	)	)	PUNCT
ap-2099	80	42	=	=	NOUN
ap-2099	80	43	u(r)ψ	u(r)ψ	X
ap-2099	80	44	=	=	PRON
ap-2099	80	45	ψu(r	ψu(r	PRON
ap-2099	80	46	)	)	PUNCT
ap-2099	80	47	.	.	PUNCT
ap-2099	81	1	(	(	PUNCT
ap-2099	81	2	16	16	NUM
ap-2099	81	3	)	)	PUNCT
ap-2099	81	4	since	since	SCONJ
ap-2099	81	5	any	any	DET
ap-2099	81	6	term	term	NOUN
ap-2099	81	7	of	of	ADP
ap-2099	81	8	ψ	ψ	X
ap-2099	81	9	∈	∈	NOUN
ap-2099	81	10	hλ	hλ	NOUN
ap-2099	81	11	consists	consist	VERB
ap-2099	81	12	of	of	ADP
ap-2099	81	13	the	the	DET
ap-2099	81	14	same	same	ADJ
ap-2099	81	15	number	number	NOUN
ap-2099	81	16	of	of	ADP
ap-2099	81	17	creation	creation	NOUN
ap-2099	81	18	and	and	CCONJ
ap-2099	81	19	annihilation	annihilation	NOUN
ap-2099	81	20	operators	operator	NOUN
ap-2099	81	21	(	(	PUNCT
ap-2099	81	22	any	any	DET
ap-2099	81	23	commutator	commutator	NOUN
ap-2099	81	24	of	of	ADP
ap-2099	81	25	such	such	DET
ap-2099	81	26	a	a	DET
ap-2099	81	27	term	term	NOUN
ap-2099	81	28	with	with	ADP
ap-2099	81	29	r	r	NOUN
ap-2099	81	30	is	be	AUX
ap-2099	81	31	zero	zero	NUM
ap-2099	81	32	)	)	PUNCT
ap-2099	81	33	,	,	PUNCT
ap-2099	81	34	there	there	PRON
ap-2099	81	35	is	be	VERB
ap-2099	81	36	no	no	DET
ap-2099	81	37	difference	difference	NOUN
ap-2099	81	38	between	between	ADP
ap-2099	81	39	left	left	ADJ
ap-2099	81	40	and	and	CCONJ
ap-2099	81	41	right	right	ADJ
ap-2099	81	42	multiplication	multiplication	NOUN
ap-2099	81	43	by	by	ADP
ap-2099	81	44	u(r	u(r	NOUN
ap-2099	81	45	)	)	PUNCT
ap-2099	81	46	.	.	PUNCT
ap-2099	82	1	so	so	ADV
ap-2099	82	2	finally	finally	ADV
ap-2099	82	3	here	here	ADV
ap-2099	82	4	is	be	AUX
ap-2099	82	5	the	the	DET
ap-2099	82	6	definition	definition	NOUN
ap-2099	82	7	of	of	ADP
ap-2099	82	8	our	our	PRON
ap-2099	82	9	nc	nc	PROPN
ap-2099	82	10	hamiltonian	hamiltonian	PROPN
ap-2099	82	11	:	:	PUNCT
ap-2099	82	12	ĥψ	ĥψ	X
ap-2099	82	13	=	=	SYM
ap-2099	82	14	~2	~2	NOUN
ap-2099	82	15	2mλr	2mλr	NUM
ap-2099	83	1	[	[	X
ap-2099	83	2	â+	â+	NOUN
ap-2099	83	3	α	α	NOUN
ap-2099	83	4	,	,	PUNCT
ap-2099	83	5	[	[	X
ap-2099	83	6	âα	âα	X
ap-2099	83	7	,	,	PUNCT
ap-2099	83	8	ψ]]−	ψ]]−	NOUN
ap-2099	83	9	q	q	NOUN
ap-2099	83	10	r	r	NOUN
ap-2099	83	11	ψ	ψ	NOUN
ap-2099	83	12	.	.	PUNCT
ap-2099	84	1	(	(	PUNCT
ap-2099	84	2	17	17	NUM
ap-2099	84	3	)	)	PUNCT
ap-2099	84	4	the	the	DET
ap-2099	84	5	coordinate	coordinate	NOUN
ap-2099	84	6	operator	operator	NOUN
ap-2099	84	7	x̂j	x̂j	PRON
ap-2099	84	8	acts	act	VERB
ap-2099	84	9	on	on	ADP
ap-2099	84	10	ψ	ψ	SYM
ap-2099	84	11	symmetrically	symmetrically	ADV
ap-2099	84	12	as	as	ADP
ap-2099	84	13	x̂jψ	x̂jψ	PROPN
ap-2099	84	14	=	=	NOUN
ap-2099	84	15	1	1	NUM
ap-2099	84	16	2(xjψ	2(xjψ	NUM
ap-2099	84	17	+	+	CCONJ
ap-2099	84	18	ψxj	ψxj	NOUN
ap-2099	84	19	)	)	PUNCT
ap-2099	84	20	.	.	PUNCT
ap-2099	85	1	(	(	PUNCT
ap-2099	85	2	18	18	NUM
ap-2099	85	3	)	)	PUNCT
ap-2099	85	4	as	as	ADP
ap-2099	85	5	to	to	ADP
ap-2099	85	6	the	the	DET
ap-2099	85	7	velocity	velocity	NOUN
ap-2099	85	8	operator	operator	NOUN
ap-2099	85	9	,	,	PUNCT
ap-2099	85	10	clearly	clearly	ADV
ap-2099	85	11	it	it	PRON
ap-2099	85	12	should	should	AUX
ap-2099	85	13	be	be	AUX
ap-2099	85	14	in	in	ADP
ap-2099	85	15	some	some	DET
ap-2099	85	16	relation	relation	NOUN
ap-2099	85	17	with	with	ADP
ap-2099	85	18	the	the	DET
ap-2099	85	19	evolution	evolution	NOUN
ap-2099	85	20	of	of	ADP
ap-2099	85	21	the	the	DET
ap-2099	85	22	coordinate	coordinate	NOUN
ap-2099	85	23	operator	operator	NOUN
ap-2099	85	24	.	.	PUNCT
ap-2099	86	1	the	the	DET
ap-2099	86	2	nc	nc	PROPN
ap-2099	86	3	analog	analog	NOUN
ap-2099	86	4	of	of	ADP
ap-2099	86	5	the	the	DET
ap-2099	86	6	time	time	NOUN
ap-2099	86	7	derivative	derivative	NOUN
ap-2099	86	8	is	be	AUX
ap-2099	86	9	proportional	proportional	ADJ
ap-2099	86	10	to	to	ADP
ap-2099	86	11	the	the	DET
ap-2099	86	12	commutator	commutator	NOUN
ap-2099	86	13	of	of	ADP
ap-2099	86	14	the	the	DET
ap-2099	86	15	quantity	quantity	NOUN
ap-2099	86	16	considered	consider	VERB
ap-2099	86	17	with	with	ADP
ap-2099	86	18	h	h	NOUN
ap-2099	86	19	;	;	PUNCT
ap-2099	86	20	so	so	SCONJ
ap-2099	86	21	the	the	DET
ap-2099	86	22	components	component	NOUN
ap-2099	86	23	of	of	ADP
ap-2099	86	24	the	the	DET
ap-2099	86	25	velocity	velocity	NOUN
ap-2099	86	26	operator	operator	NOUN
ap-2099	86	27	are	be	AUX
ap-2099	86	28	given	give	VERB
ap-2099	86	29	by	by	ADP
ap-2099	86	30	v̂jψ	v̂jψ	NOUN
ap-2099	86	31	=	=	SYM
ap-2099	86	32	−i[x̂j	−i[x̂j	PROPN
ap-2099	86	33	,	,	PUNCT
ap-2099	86	34	ĥ]ψ	ĥ]ψ	PROPN
ap-2099	86	35	.	.	PUNCT
ap-2099	87	1	(	(	PUNCT
ap-2099	87	2	19	19	NUM
ap-2099	87	3	)	)	PUNCT
ap-2099	87	4	both	both	DET
ap-2099	87	5	sets	set	NOUN
ap-2099	87	6	of	of	ADP
ap-2099	87	7	nc	nc	PROPN
ap-2099	87	8	observables	observable	NOUN
ap-2099	87	9	,	,	PUNCT
ap-2099	87	10	v̂j	v̂j	X
ap-2099	87	11	and	and	CCONJ
ap-2099	87	12	x̂j	x̂j	PROPN
ap-2099	87	13	,	,	PUNCT
ap-2099	87	14	have	have	AUX
ap-2099	87	15	been	be	AUX
ap-2099	87	16	introduced	introduce	VERB
ap-2099	87	17	in	in	ADP
ap-2099	87	18	[	[	X
ap-2099	87	19	10	10	NUM
ap-2099	87	20	]	]	PUNCT
ap-2099	87	21	.	.	PUNCT
ap-2099	88	1	as	as	SCONJ
ap-2099	88	2	we	we	PRON
ap-2099	88	3	see	see	VERB
ap-2099	88	4	below	below	ADV
ap-2099	88	5	,	,	PUNCT
ap-2099	88	6	they	they	PRON
ap-2099	88	7	are	be	AUX
ap-2099	88	8	well	well	ADV
ap-2099	88	9	adapted	adapt	VERB
ap-2099	88	10	to	to	ADP
ap-2099	88	11	the	the	DET
ap-2099	88	12	construction	construction	NOUN
ap-2099	88	13	of	of	ADP
ap-2099	88	14	the	the	DET
ap-2099	88	15	nc	nc	PROPN
ap-2099	88	16	analog	analog	PROPN
ap-2099	88	17	of	of	ADP
ap-2099	88	18	the	the	DET
ap-2099	88	19	lrl	lrl	PROPN
ap-2099	88	20	vector	vector	PROPN
ap-2099	88	21	.	.	PUNCT
ap-2099	89	1	based	base	VERB
ap-2099	89	2	on	on	ADP
ap-2099	89	3	what	what	PRON
ap-2099	89	4	has	have	AUX
ap-2099	89	5	been	be	AUX
ap-2099	89	6	briefly	briefly	ADV
ap-2099	89	7	summarized	summarize	VERB
ap-2099	89	8	above	above	ADV
ap-2099	89	9	,	,	PUNCT
ap-2099	89	10	thenc	thenc	PRON
ap-2099	89	11	analog	analog	NOUN
ap-2099	89	12	of	of	ADP
ap-2099	89	13	the	the	DET
ap-2099	89	14	schrödinger	schrödinger	ADJ
ap-2099	89	15	equation	equation	NOUN
ap-2099	89	16	with	with	ADP
ap-2099	89	17	the	the	DET
ap-2099	89	18	coulomb	coulomb	NOUN
ap-2099	89	19	potential	potential	NOUN
ap-2099	89	20	in	in	ADP
ap-2099	89	21	r3	r3	PROPN
ap-2099	89	22	λ	λ	PROPN
ap-2099	89	23	can	can	AUX
ap-2099	89	24	be	be	AUX
ap-2099	89	25	postulated	postulate	VERB
ap-2099	89	26	:	:	PUNCT
ap-2099	89	27	~2	~2	NOUN
ap-2099	89	28	2mλr	2mλr	NUM
ap-2099	90	1	[	[	X
ap-2099	90	2	â+	â+	NOUN
ap-2099	90	3	α	α	NOUN
ap-2099	90	4	,	,	PUNCT
ap-2099	90	5	[	[	X
ap-2099	90	6	âα	âα	X
ap-2099	90	7	,	,	PUNCT
ap-2099	90	8	ψ]]−	ψ]]−	NOUN
ap-2099	90	9	q	q	NOUN
ap-2099	90	10	r	r	NOUN
ap-2099	90	11	ψ	ψ	X
ap-2099	90	12	=	=	X
ap-2099	90	13	eψ	eψ	PROPN
ap-2099	90	14	.	.	PUNCT
ap-2099	91	1	(	(	PUNCT
ap-2099	91	2	20	20	NUM
ap-2099	91	3	)	)	PUNCT
ap-2099	91	4	to	to	PART
ap-2099	91	5	avoid	avoid	VERB
ap-2099	91	6	overloading	overload	VERB
ap-2099	91	7	the	the	DET
ap-2099	91	8	formulas	formula	NOUN
ap-2099	91	9	,	,	PUNCT
ap-2099	91	10	we	we	PRON
ap-2099	91	11	usually	usually	ADV
ap-2099	91	12	set	set	VERB
ap-2099	91	13	m	m	NOUN
ap-2099	91	14	=	=	NOUN
ap-2099	91	15	1	1	NUM
ap-2099	91	16	,	,	PUNCT
ap-2099	91	17	~	~	PUNCT
ap-2099	91	18	=	=	SYM
ap-2099	92	1	1	1	NUM
ap-2099	92	2	below	below	ADV
ap-2099	92	3	.	.	PUNCT
ap-2099	93	1	3	3	X
ap-2099	93	2	.	.	X
ap-2099	93	3	dynamical	dynamical	ADJ
ap-2099	93	4	symmetry	symmetry	NOUN
ap-2099	93	5	in	in	ADP
ap-2099	93	6	ncqm	ncqm	NOUN
ap-2099	93	7	it	it	PRON
ap-2099	93	8	is	be	AUX
ap-2099	93	9	time	time	NOUN
ap-2099	93	10	to	to	PART
ap-2099	93	11	address	address	VERB
ap-2099	93	12	the	the	DET
ap-2099	93	13	ncqm	ncqm	NOUN
ap-2099	93	14	version	version	NOUN
ap-2099	93	15	of	of	ADP
ap-2099	93	16	the	the	DET
ap-2099	93	17	coulomb	coulomb	NOUN
ap-2099	93	18	-	-	PUNCT
ap-2099	93	19	kepler	kepler	NOUN
ap-2099	93	20	problem	problem	NOUN
ap-2099	93	21	.	.	PUNCT
ap-2099	94	1	our	our	PRON
ap-2099	94	2	task	task	NOUN
ap-2099	94	3	is	be	AUX
ap-2099	94	4	to	to	PART
ap-2099	94	5	find	find	VERB
ap-2099	94	6	sensible	sensible	ADJ
ap-2099	94	7	analogs	analog	NOUN
ap-2099	94	8	of	of	ADP
ap-2099	94	9	the	the	DET
ap-2099	94	10	three	three	NUM
ap-2099	94	11	components	component	NOUN
ap-2099	94	12	ai	ai	VERB
ap-2099	94	13	of	of	ADP
ap-2099	94	14	the	the	DET
ap-2099	94	15	lrl	lrl	PROPN
ap-2099	94	16	vector	vector	NOUN
ap-2099	94	17	in	in	ADP
ap-2099	94	18	such	such	DET
ap-2099	94	19	a	a	DET
ap-2099	94	20	way	way	NOUN
ap-2099	94	21	that	that	PRON
ap-2099	94	22	all	all	DET
ap-2099	94	23	the	the	DET
ap-2099	94	24	requirements	requirement	NOUN
ap-2099	94	25	regarding	regard	VERB
ap-2099	94	26	commutation	commutation	NOUN
ap-2099	94	27	relations	relation	NOUN
ap-2099	94	28	are	be	AUX
ap-2099	94	29	met	meet	VERB
ap-2099	94	30	(	(	PUNCT
ap-2099	94	31	the	the	DET
ap-2099	94	32	commutator	commutator	NOUN
ap-2099	94	33	with	with	ADP
ap-2099	94	34	the	the	DET
ap-2099	94	35	hamiltonian	hamiltonian	NOUN
ap-2099	94	36	has	have	VERB
ap-2099	94	37	to	to	PART
ap-2099	94	38	be	be	AUX
ap-2099	94	39	zero	zero	NUM
ap-2099	94	40	because	because	SCONJ
ap-2099	94	41	of	of	ADP
ap-2099	94	42	the	the	DET
ap-2099	94	43	conservation	conservation	NOUN
ap-2099	94	44	law	law	NOUN
ap-2099	94	45	and	and	CCONJ
ap-2099	94	46	relations	relation	NOUN
ap-2099	94	47	among	among	ADP
ap-2099	94	48	all	all	DET
ap-2099	94	49	components	component	NOUN
ap-2099	94	50	of	of	ADP
ap-2099	94	51	~a	~a	NUM
ap-2099	94	52	and	and	CCONJ
ap-2099	94	53	~l	~l	NUM
ap-2099	94	54	are	be	AUX
ap-2099	94	55	supposed	suppose	VERB
ap-2099	94	56	to	to	PART
ap-2099	94	57	correspond	correspond	VERB
ap-2099	94	58	to	to	ADP
ap-2099	94	59	the	the	DET
ap-2099	94	60	relevant	relevant	ADJ
ap-2099	94	61	symmetry	symmetry	NOUN
ap-2099	94	62	)	)	PUNCT
ap-2099	94	63	.	.	PUNCT
ap-2099	95	1	recall	recall	VERB
ap-2099	95	2	the	the	DET
ap-2099	95	3	subtlety	subtlety	NOUN
ap-2099	95	4	which	which	PRON
ap-2099	95	5	had	have	VERB
ap-2099	95	6	to	to	PART
ap-2099	95	7	be	be	AUX
ap-2099	95	8	taken	take	VERB
ap-2099	95	9	into	into	ADP
ap-2099	95	10	account	account	NOUN
ap-2099	95	11	when	when	SCONJ
ap-2099	95	12	the	the	DET
ap-2099	95	13	standard	standard	ADJ
ap-2099	95	14	qm	qm	PROPN
ap-2099	95	15	version	version	NOUN
ap-2099	95	16	of	of	ADP
ap-2099	95	17	the	the	DET
ap-2099	95	18	lrl	lrl	PROPN
ap-2099	95	19	vector	vector	NOUN
ap-2099	95	20	had	have	AUX
ap-2099	95	21	been	be	AUX
ap-2099	95	22	built	build	VERB
ap-2099	95	23	based	base	VERB
ap-2099	95	24	on	on	ADP
ap-2099	95	25	the	the	DET
ap-2099	95	26	classical	classical	ADJ
ap-2099	95	27	model	model	NOUN
ap-2099	95	28	.	.	PUNCT
ap-2099	96	1	the	the	DET
ap-2099	96	2	cross	cross	NOUN
ap-2099	96	3	product	product	NOUN
ap-2099	96	4	of	of	ADP
ap-2099	96	5	velocity	velocity	NOUN
ap-2099	96	6	and	and	CCONJ
ap-2099	96	7	angular	angular	ADJ
ap-2099	96	8	momentum	momentum	NOUN
ap-2099	96	9	needed	need	VERB
ap-2099	96	10	symmetrization	symmetrization	NOUN
ap-2099	96	11	due	due	ADP
ap-2099	96	12	to	to	ADP
ap-2099	96	13	their	their	PRON
ap-2099	96	14	nonvanishing	nonvanishe	VERB
ap-2099	96	15	commutator	commutator	NOUN
ap-2099	96	16	.	.	PUNCT
ap-2099	97	1	the	the	DET
ap-2099	97	2	nc	nc	PROPN
ap-2099	97	3	operators	operators	PROPN
ap-2099	97	4	that	that	SCONJ
ap-2099	97	5	we	we	PRON
ap-2099	97	6	are	be	AUX
ap-2099	97	7	going	go	VERB
ap-2099	97	8	to	to	PART
ap-2099	97	9	use	use	VERB
ap-2099	97	10	when	when	SCONJ
ap-2099	97	11	constructing	construct	VERB
ap-2099	97	12	the	the	DET
ap-2099	97	13	analog	analog	NOUN
ap-2099	97	14	of	of	ADP
ap-2099	97	15	the	the	DET
ap-2099	97	16	cross	cross	NOUN
ap-2099	97	17	product	product	NOUN
ap-2099	97	18	part	part	NOUN
ap-2099	97	19	,	,	PUNCT
ap-2099	97	20	i.e.	i.e.	X
ap-2099	97	21	v̂i	v̂i	NUM
ap-2099	97	22	,	,	PUNCT
ap-2099	97	23	l̂i	l̂i	NOUN
ap-2099	97	24	,	,	PUNCT
ap-2099	97	25	do	do	AUX
ap-2099	97	26	not	not	PART
ap-2099	97	27	commute	commute	VERB
ap-2099	97	28	either	either	ADV
ap-2099	97	29	,	,	PUNCT
ap-2099	97	30	so	so	ADV
ap-2099	97	31	some	some	DET
ap-2099	97	32	adjustment	adjustment	NOUN
ap-2099	97	33	of	of	ADP
ap-2099	97	34	this	this	DET
ap-2099	97	35	sort	sort	NOUN
ap-2099	97	36	will	will	AUX
ap-2099	97	37	also	also	ADV
ap-2099	97	38	have	have	VERB
ap-2099	97	39	to	to	PART
ap-2099	97	40	be	be	AUX
ap-2099	97	41	made	make	VERB
ap-2099	97	42	.	.	PUNCT
ap-2099	98	1	however	however	ADV
ap-2099	98	2	,	,	PUNCT
ap-2099	98	3	there	there	PRON
ap-2099	98	4	is	be	VERB
ap-2099	98	5	also	also	ADV
ap-2099	98	6	another	another	PRON
ap-2099	98	7	,	,	PUNCT
ap-2099	98	8	“	"	PUNCT
ap-2099	98	9	potential	potential	ADJ
ap-2099	98	10	”	"	PUNCT
ap-2099	98	11	part	part	NOUN
ap-2099	98	12	of	of	ADP
ap-2099	98	13	the	the	DET
ap-2099	98	14	lrl	lrl	PROPN
ap-2099	98	15	vector	vector	PROPN
ap-2099	98	16	,	,	PUNCT
ap-2099	98	17	which	which	PRON
ap-2099	98	18	is	be	AUX
ap-2099	98	19	proportional	proportional	ADJ
ap-2099	98	20	to	to	ADP
ap-2099	98	21	~r	~r	NUM
ap-2099	98	22	/	/	SYM
ap-2099	98	23	r.	r.	NOUN
ap-2099	98	24	the	the	DET
ap-2099	98	25	corresponding	corresponding	PROPN
ap-2099	98	26	nc	nc	PROPN
ap-2099	98	27	analogs	analog	NOUN
ap-2099	98	28	of	of	ADP
ap-2099	98	29	xi	xi	PROPN
ap-2099	98	30	and	and	CCONJ
ap-2099	98	31	ψ	ψ	X
ap-2099	98	32	do	do	AUX
ap-2099	98	33	not	not	PART
ap-2099	98	34	commute	commute	VERB
ap-2099	98	35	either	either	ADV
ap-2099	98	36	,	,	PUNCT
ap-2099	98	37	so	so	ADV
ap-2099	98	38	we	we	PRON
ap-2099	98	39	resolve	resolve	VERB
ap-2099	98	40	the	the	DET
ap-2099	98	41	ordering	ordering	NOUN
ap-2099	98	42	in	in	ADP
ap-2099	98	43	a	a	DET
ap-2099	98	44	similar	similar	ADJ
ap-2099	98	45	way	way	NOUN
ap-2099	98	46	as	as	ADP
ap-2099	98	47	in	in	ADP
ap-2099	98	48	the	the	DET
ap-2099	98	49	cross	cross	NOUN
ap-2099	98	50	product	product	NOUN
ap-2099	98	51	case	case	NOUN
ap-2099	98	52	—	—	PUNCT
ap-2099	98	53	we	we	PRON
ap-2099	98	54	take	take	VERB
ap-2099	98	55	x̂k	x̂k	PROPN
ap-2099	98	56	instead	instead	ADV
ap-2099	98	57	of	of	ADP
ap-2099	98	58	xk	xk	NOUN
ap-2099	98	59	:	:	PUNCT
ap-2099	98	60	âk	âk	X
ap-2099	98	61	=	=	SYM
ap-2099	98	62	1	1	NUM
ap-2099	98	63	2εijk(l̂iv̂j	2εijk(l̂iv̂j	NUM
ap-2099	98	64	+	+	CCONJ
ap-2099	98	65	v̂jl̂i	v̂jl̂i	NOUN
ap-2099	98	66	)	)	PUNCT
ap-2099	99	1	+	+	NOUN
ap-2099	99	2	q	q	SYM
ap-2099	100	1	x̂k	x̂k	NOUN
ap-2099	100	2	r	r	NOUN
ap-2099	100	3	.	.	PUNCT
ap-2099	101	1	(	(	PUNCT
ap-2099	101	2	21	21	NUM
ap-2099	101	3	)	)	PUNCT
ap-2099	101	4	it	it	PRON
ap-2099	101	5	has	have	AUX
ap-2099	101	6	turned	turn	VERB
ap-2099	101	7	out	out	ADP
ap-2099	101	8	that	that	SCONJ
ap-2099	101	9	besides	besides	SCONJ
ap-2099	101	10	coping	cope	VERB
ap-2099	101	11	with	with	ADP
ap-2099	101	12	the	the	DET
ap-2099	101	13	ordering	ordering	NOUN
ap-2099	101	14	dilemma	dilemma	NOUN
ap-2099	101	15	,	,	PUNCT
ap-2099	101	16	nothing	nothing	PRON
ap-2099	101	17	more	more	ADJ
ap-2099	101	18	needs	need	VERB
ap-2099	101	19	to	to	PART
ap-2099	101	20	be	be	AUX
ap-2099	101	21	done	do	VERB
ap-2099	101	22	that	that	PRON
ap-2099	101	23	is	be	AUX
ap-2099	101	24	,	,	PUNCT
ap-2099	101	25	except	except	SCONJ
ap-2099	101	26	for	for	ADP
ap-2099	101	27	doing	do	VERB
ap-2099	101	28	the	the	DET
ap-2099	101	29	calculations	calculation	NOUN
ap-2099	101	30	to	to	PART
ap-2099	101	31	show	show	VERB
ap-2099	101	32	that	that	SCONJ
ap-2099	101	33	our	our	PRON
ap-2099	101	34	definition	definition	NOUN
ap-2099	101	35	of	of	ADP
ap-2099	101	36	âk	âk	PROPN
ap-2099	101	37	has	have	AUX
ap-2099	101	38	been	be	AUX
ap-2099	101	39	a	a	DET
ap-2099	101	40	good	good	ADJ
ap-2099	101	41	choice	choice	NOUN
ap-2099	101	42	.	.	PUNCT
ap-2099	102	1	so	so	ADV
ap-2099	102	2	now	now	ADV
ap-2099	102	3	we	we	PRON
ap-2099	102	4	are	be	AUX
ap-2099	102	5	going	go	VERB
ap-2099	102	6	to	to	PART
ap-2099	102	7	take	take	VERB
ap-2099	102	8	the	the	DET
ap-2099	102	9	nc	nc	PROPN
ap-2099	102	10	analogs	analog	NOUN
ap-2099	102	11	of	of	ADP
ap-2099	102	12	the	the	DET
ap-2099	102	13	hamiltonian	hamiltonian	ADJ
ap-2099	102	14	,	,	PUNCT
ap-2099	102	15	velocity	velocity	NOUN
ap-2099	102	16	,	,	PUNCT
ap-2099	102	17	angular	angular	ADJ
ap-2099	102	18	momentum	momentum	NOUN
ap-2099	102	19	and	and	CCONJ
ap-2099	102	20	position	position	NOUN
ap-2099	102	21	operators	operator	NOUN
ap-2099	102	22	,	,	PUNCT
ap-2099	102	23	and	and	CCONJ
ap-2099	102	24	build	build	VERB
ap-2099	102	25	the	the	DET
ap-2099	102	26	nc	nc	PROPN
ap-2099	102	27	lrl	lrl	PROPN
ap-2099	102	28	vector	vector	PROPN
ap-2099	102	29	according	accord	VERB
ap-2099	102	30	to	to	ADP
ap-2099	102	31	(	(	PUNCT
ap-2099	102	32	21	21	NUM
ap-2099	102	33	)	)	PUNCT
ap-2099	102	34	.	.	PUNCT
ap-2099	103	1	then	then	ADV
ap-2099	103	2	we	we	PRON
ap-2099	103	3	have	have	VERB
ap-2099	103	4	to	to	PART
ap-2099	103	5	move	move	VERB
ap-2099	103	6	to	to	ADP
ap-2099	103	7	the	the	DET
ap-2099	103	8	next	next	ADJ
ap-2099	103	9	task	task	NOUN
ap-2099	103	10	evaluate	evaluate	VERB
ap-2099	103	11	the	the	DET
ap-2099	103	12	commutator	commutator	NOUN
ap-2099	103	13	[	[	X
ap-2099	103	14	âi	âi	NOUN
ap-2099	103	15	,	,	PUNCT
ap-2099	103	16	ĥ	ĥ	X
ap-2099	103	17	]	]	PUNCT
ap-2099	103	18	,	,	PUNCT
ap-2099	103	19	examine	examine	VERB
ap-2099	103	20	the	the	DET
ap-2099	103	21	commutation	commutation	NOUN
ap-2099	103	22	relations	relation	NOUN
ap-2099	103	23	between	between	ADP
ap-2099	103	24	âk	âk	PROPN
ap-2099	103	25	and	and	CCONJ
ap-2099	103	26	l̂k	l̂k	PROPN
ap-2099	103	27	,	,	PUNCT
ap-2099	103	28	searching	search	VERB
ap-2099	103	29	for	for	ADP
ap-2099	103	30	the	the	DET
ap-2099	103	31	signs	sign	NOUN
ap-2099	103	32	of	of	ADP
ap-2099	103	33	a	a	DET
ap-2099	103	34	higher	high	ADJ
ap-2099	103	35	dynamical	dynamical	ADJ
ap-2099	103	36	symmetry	symmetry	NOUN
ap-2099	103	37	.	.	PUNCT
ap-2099	104	1	as	as	ADV
ap-2099	104	2	soon	soon	ADV
ap-2099	104	3	as	as	SCONJ
ap-2099	104	4	the	the	DET
ap-2099	104	5	symmetry	symmetry	NOUN
ap-2099	104	6	group	group	NOUN
ap-2099	104	7	is	be	AUX
ap-2099	104	8	recognized	recognize	VERB
ap-2099	104	9	,	,	PUNCT
ap-2099	104	10	we	we	PRON
ap-2099	104	11	can	can	AUX
ap-2099	104	12	construct	construct	VERB
ap-2099	104	13	the	the	DET
ap-2099	104	14	corresponding	correspond	VERB
ap-2099	104	15	casimir	casimir	NOUN
ap-2099	104	16	operators	operator	NOUN
ap-2099	104	17	.	.	PUNCT
ap-2099	105	1	all	all	DET
ap-2099	105	2	these	these	DET
ap-2099	105	3	crucial	crucial	ADJ
ap-2099	105	4	operators	operator	NOUN
ap-2099	105	5	:	:	PUNCT
ap-2099	105	6	the	the	DET
ap-2099	105	7	hamiltonian	hamiltonian	ADJ
ap-2099	105	8	,	,	PUNCT
ap-2099	105	9	velocity	velocity	NOUN
ap-2099	105	10	,	,	PUNCT
ap-2099	105	11	angular	angular	ADJ
ap-2099	105	12	momentum	momentum	NOUN
ap-2099	105	13	and	and	CCONJ
ap-2099	105	14	position	position	NOUN
ap-2099	105	15	operators	operator	NOUN
ap-2099	105	16	,	,	PUNCT
ap-2099	105	17	have	have	AUX
ap-2099	105	18	been	be	AUX
ap-2099	105	19	defined	define	VERB
ap-2099	105	20	already	already	ADV
ap-2099	105	21	in	in	ADP
ap-2099	105	22	terms	term	NOUN
ap-2099	105	23	of	of	ADP
ap-2099	105	24	creation	creation	NOUN
ap-2099	105	25	and	and	CCONJ
ap-2099	105	26	annihilation	annihilation	NOUN
ap-2099	105	27	operators	operator	NOUN
ap-2099	105	28	a+	a+	PUNCT
ap-2099	105	29	α	α	NOUN
ap-2099	105	30	,	,	PUNCT
ap-2099	105	31	aα	aα	PROPN
ap-2099	105	32	;	;	PUNCT
ap-2099	105	33	knowing	know	VERB
ap-2099	105	34	the	the	DET
ap-2099	105	35	commutation	commutation	NOUN
ap-2099	105	36	relations	relation	NOUN
ap-2099	105	37	for	for	ADP
ap-2099	105	38	these	these	PRON
ap-2099	105	39	,	,	PUNCT
ap-2099	105	40	one	one	PRON
ap-2099	105	41	can	can	AUX
ap-2099	105	42	calculate	calculate	VERB
ap-2099	105	43	all	all	PRON
ap-2099	105	44	that	that	PRON
ap-2099	105	45	is	be	AUX
ap-2099	105	46	required	require	VERB
ap-2099	105	47	.	.	PUNCT
ap-2099	106	1	however	however	ADV
ap-2099	106	2	,	,	PUNCT
ap-2099	106	3	after	after	ADP
ap-2099	106	4	writing	write	VERB
ap-2099	106	5	it	it	PRON
ap-2099	106	6	all	all	PRON
ap-2099	106	7	down	down	ADV
ap-2099	106	8	and	and	CCONJ
ap-2099	106	9	trying	try	VERB
ap-2099	106	10	to	to	PART
ap-2099	106	11	make	make	VERB
ap-2099	106	12	heads	head	NOUN
ap-2099	106	13	and	and	CCONJ
ap-2099	106	14	tails	tail	NOUN
ap-2099	106	15	of	of	ADP
ap-2099	106	16	it	it	PRON
ap-2099	106	17	,	,	PUNCT
ap-2099	106	18	we	we	PRON
ap-2099	106	19	soon	soon	ADV
ap-2099	106	20	realize	realize	VERB
ap-2099	106	21	that	that	SCONJ
ap-2099	106	22	the	the	DET
ap-2099	106	23	problem	problem	NOUN
ap-2099	106	24	is	be	AUX
ap-2099	106	25	not	not	PART
ap-2099	106	26	assigned	assign	VERB
ap-2099	106	27	in	in	ADP
ap-2099	106	28	the	the	DET
ap-2099	106	29	most	most	ADV
ap-2099	106	30	friendly	friendly	ADJ
ap-2099	106	31	way	way	NOUN
ap-2099	106	32	.	.	PUNCT
ap-2099	107	1	this	this	PRON
ap-2099	107	2	definitely	definitely	ADV
ap-2099	107	3	seems	seem	VERB
ap-2099	107	4	to	to	PART
ap-2099	107	5	be	be	AUX
ap-2099	107	6	a	a	DET
ap-2099	107	7	case	case	NOUN
ap-2099	107	8	in	in	ADP
ap-2099	107	9	which	which	PRON
ap-2099	107	10	introducing	introduce	VERB
ap-2099	107	11	some	some	DET
ap-2099	107	12	auxiliary	auxiliary	ADJ
ap-2099	107	13	quantities	quantity	NOUN
ap-2099	107	14	may	may	AUX
ap-2099	107	15	help	help	VERB
ap-2099	107	16	.	.	PUNCT
ap-2099	108	1	there	there	PRON
ap-2099	108	2	are	be	VERB
ap-2099	108	3	certain	certain	ADJ
ap-2099	108	4	combinations	combination	NOUN
ap-2099	108	5	of	of	ADP
ap-2099	108	6	a+	a+	PRON
ap-2099	108	7	α	α	NOUN
ap-2099	108	8	,	,	PUNCT
ap-2099	108	9	aα	aα	NOUN
ap-2099	108	10	that	that	PRON
ap-2099	108	11	occur	occur	VERB
ap-2099	108	12	often	often	ADV
ap-2099	108	13	in	in	ADP
ap-2099	108	14	our	our	PRON
ap-2099	108	15	expressions	expression	NOUN
ap-2099	108	16	,	,	PUNCT
ap-2099	108	17	and	and	CCONJ
ap-2099	108	18	separating	separate	VERB
ap-2099	108	19	them	they	PRON
ap-2099	108	20	the	the	DET
ap-2099	108	21	right	right	ADJ
ap-2099	108	22	way	way	NOUN
ap-2099	108	23	makes	make	VERB
ap-2099	108	24	the	the	DET
ap-2099	108	25	calculations	calculation	NOUN
ap-2099	108	26	more	more	ADV
ap-2099	108	27	manageable	manageable	ADJ
ap-2099	108	28	.	.	PUNCT
ap-2099	109	1	3.1	3.1	NUM
ap-2099	109	2	.	.	PUNCT
ap-2099	109	3	auxiliary	auxiliary	ADJ
ap-2099	109	4	operators	operator	NOUN
ap-2099	109	5	we	we	PRON
ap-2099	109	6	have	have	VERB
ap-2099	109	7	to	to	PART
ap-2099	109	8	examine	examine	VERB
ap-2099	109	9	how	how	SCONJ
ap-2099	109	10	the	the	DET
ap-2099	109	11	operators	operator	NOUN
ap-2099	109	12	considered	consider	VERB
ap-2099	109	13	here	here	ADV
ap-2099	109	14	act	act	VERB
ap-2099	109	15	on	on	ADP
ap-2099	109	16	the	the	DET
ap-2099	109	17	wave	wave	NOUN
ap-2099	109	18	function	function	NOUN
ap-2099	109	19	ψ	ψ	NOUN
ap-2099	109	20	.	.	PUNCT
ap-2099	110	1	they	they	PRON
ap-2099	110	2	are	be	AUX
ap-2099	110	3	expressed	express	VERB
ap-2099	110	4	in	in	ADP
ap-2099	110	5	terms	term	NOUN
ap-2099	110	6	of	of	ADP
ap-2099	110	7	â+	â+	PROPN
ap-2099	110	8	α	α	NOUN
ap-2099	110	9	,	,	PUNCT
ap-2099	110	10	âα	âα	PROPN
ap-2099	110	11	.	.	PUNCT
ap-2099	111	1	in	in	ADP
ap-2099	111	2	general	general	ADJ
ap-2099	111	3	it	it	PRON
ap-2099	111	4	makes	make	VERB
ap-2099	111	5	a	a	DET
ap-2099	111	6	difference	difference	NOUN
ap-2099	111	7	whether	whether	SCONJ
ap-2099	111	8	the	the	DET
ap-2099	111	9	creation	creation	NOUN
ap-2099	111	10	and	and	CCONJ
ap-2099	111	11	annihilation	annihilation	NOUN
ap-2099	111	12	operators	operator	NOUN
ap-2099	111	13	act	act	VERB
ap-2099	111	14	from	from	ADP
ap-2099	111	15	the	the	DET
ap-2099	111	16	right	right	NOUN
ap-2099	111	17	or	or	CCONJ
ap-2099	111	18	the	the	DET
ap-2099	111	19	left	left	NOUN
ap-2099	111	20	and	and	CCONJ
ap-2099	111	21	the	the	DET
ap-2099	111	22	following	follow	VERB
ap-2099	111	23	notation	notation	NOUN
ap-2099	111	24	seems	seem	VERB
ap-2099	111	25	to	to	PART
ap-2099	111	26	be	be	AUX
ap-2099	111	27	useful	useful	ADJ
ap-2099	111	28	to	to	PART
ap-2099	111	29	keep	keep	VERB
ap-2099	111	30	track	track	NOUN
ap-2099	111	31	of	of	ADP
ap-2099	111	32	it	it	PRON
ap-2099	111	33	:	:	PUNCT
ap-2099	111	34	âαψ	âαψ	NOUN
ap-2099	111	35	=	=	SYM
ap-2099	111	36	aαψ	aαψ	NOUN
ap-2099	111	37	,	,	PUNCT
ap-2099	111	38	b̂αψ	b̂αψ	PROPN
ap-2099	111	39	=	=	SYM
ap-2099	111	40	ψaα	ψaα	PROPN
ap-2099	111	41	,	,	PUNCT
ap-2099	111	42	(	(	PUNCT
ap-2099	111	43	22	22	NUM
ap-2099	111	44	)	)	PUNCT
ap-2099	112	1	â+	â+	NUM
ap-2099	112	2	αψ	αψ	NOUN
ap-2099	112	3	=	=	SYM
ap-2099	112	4	a+	a+	PUNCT
ap-2099	112	5	αψ	αψ	PROPN
ap-2099	112	6	,	,	PUNCT
ap-2099	112	7	b̂+	b̂+	NUM
ap-2099	112	8	αψ	αψ	X
ap-2099	113	1	=	=	PUNCT
ap-2099	113	2	ψa+	ψa+	PROPN
ap-2099	113	3	α	α	X
ap-2099	113	4	.	.	PUNCT
ap-2099	114	1	(	(	PUNCT
ap-2099	114	2	23	23	NUM
ap-2099	114	3	)	)	PUNCT
ap-2099	114	4	an	an	DET
ap-2099	114	5	advantage	advantage	NOUN
ap-2099	114	6	of	of	ADP
ap-2099	114	7	this	this	DET
ap-2099	114	8	notation	notation	NOUN
ap-2099	114	9	is	be	AUX
ap-2099	114	10	the	the	DET
ap-2099	114	11	fact	fact	NOUN
ap-2099	114	12	that	that	SCONJ
ap-2099	114	13	now	now	ADV
ap-2099	114	14	we	we	PRON
ap-2099	114	15	do	do	AUX
ap-2099	114	16	not	not	PART
ap-2099	114	17	have	have	AUX
ap-2099	114	18	to	to	PART
ap-2099	114	19	drag	drag	VERB
ap-2099	114	20	ψ	ψ	NOUN
ap-2099	114	21	into	into	ADP
ap-2099	114	22	the	the	DET
ap-2099	114	23	formulas	formula	NOUN
ap-2099	114	24	just	just	ADV
ap-2099	114	25	to	to	PART
ap-2099	114	26	make	make	VERB
ap-2099	114	27	clear	clear	ADJ
ap-2099	114	28	which	which	DET
ap-2099	114	29	side	side	NOUN
ap-2099	114	30	the	the	DET
ap-2099	114	31	operators	operator	NOUN
ap-2099	114	32	act	act	VERB
ap-2099	114	33	from	from	ADP
ap-2099	114	34	.	.	PUNCT
ap-2099	115	1	the	the	DET
ap-2099	115	2	relevant	relevant	ADJ
ap-2099	115	3	commutation	commutation	NOUN
ap-2099	115	4	relations	relation	NOUN
ap-2099	115	5	are	be	AUX
ap-2099	115	6	(	(	PUNCT
ap-2099	115	7	see	see	VERB
ap-2099	115	8	(	(	PUNCT
ap-2099	115	9	5	5	NUM
ap-2099	115	10	)	)	PUNCT
ap-2099	115	11	)	)	PUNCT
ap-2099	116	1	[	[	X
ap-2099	116	2	âα	âα	X
ap-2099	116	3	,	,	PUNCT
ap-2099	116	4	â+	â+	NUM
ap-2099	116	5	β	β	X
ap-2099	116	6	]	]	PUNCT
ap-2099	116	7	=	=	PUNCT
ap-2099	116	8	δαβ	δαβ	NOUN
ap-2099	116	9	,	,	PUNCT
ap-2099	116	10	[	[	X
ap-2099	116	11	b̂α	b̂α	NOUN
ap-2099	116	12	,	,	PUNCT
ap-2099	116	13	b̂+	b̂+	X
ap-2099	116	14	β	β	X
ap-2099	116	15	]	]	PUNCT
ap-2099	116	16	=	=	X
ap-2099	116	17	−δαβ	−δαβ	NOUN
ap-2099	116	18	.	.	PUNCT
ap-2099	117	1	(	(	PUNCT
ap-2099	117	2	24	24	NUM
ap-2099	117	3	)	)	PUNCT
ap-2099	117	4	the	the	DET
ap-2099	117	5	other	other	ADJ
ap-2099	117	6	commutators	commutator	NOUN
ap-2099	117	7	are	be	AUX
ap-2099	117	8	zero	zero	NUM
ap-2099	117	9	.	.	PUNCT
ap-2099	118	1	this	this	PRON
ap-2099	118	2	,	,	PUNCT
ap-2099	118	3	when	when	SCONJ
ap-2099	118	4	kept	keep	VERB
ap-2099	118	5	in	in	ADP
ap-2099	118	6	mind	mind	NOUN
ap-2099	118	7	,	,	PUNCT
ap-2099	118	8	spares	spare	VERB
ap-2099	118	9	a	a	DET
ap-2099	118	10	lot	lot	NOUN
ap-2099	118	11	of	of	ADP
ap-2099	118	12	paper	paper	NOUN
ap-2099	118	13	during	during	ADP
ap-2099	118	14	the	the	DET
ap-2099	118	15	calculations	calculation	NOUN
ap-2099	118	16	.	.	PUNCT
ap-2099	119	1	151	151	NUM
ap-2099	119	2	p.	p.	NOUN
ap-2099	119	3	presnajder	presnajder	NOUN
ap-2099	119	4	,	,	PUNCT
ap-2099	119	5	v.	v.	PROPN
ap-2099	119	6	galikova	galikova	PROPN
ap-2099	119	7	,	,	PUNCT
ap-2099	119	8	s.	s.	PROPN
ap-2099	119	9	kovacik	kovacik	PROPN
ap-2099	119	10	acta	acta	PROPN
ap-2099	119	11	polytechnica	polytechnica	PROPN
ap-2099	119	12	as	as	SCONJ
ap-2099	119	13	it	it	PRON
ap-2099	119	14	was	be	AUX
ap-2099	119	15	already	already	ADV
ap-2099	119	16	mentioned	mention	VERB
ap-2099	119	17	,	,	PUNCT
ap-2099	119	18	we	we	PRON
ap-2099	119	19	use	use	VERB
ap-2099	119	20	the	the	DET
ap-2099	119	21	position	position	NOUN
ap-2099	119	22	operator	operator	NOUN
ap-2099	119	23	in	in	ADP
ap-2099	119	24	the	the	DET
ap-2099	119	25	form	form	NOUN
ap-2099	119	26	x̂iψ	x̂iψ	PROPN
ap-2099	119	27	=	=	SYM
ap-2099	119	28	1	1	NUM
ap-2099	119	29	2(xiψ	2(xiψ	NUM
ap-2099	119	30	+	+	CCONJ
ap-2099	119	31	ψxi	ψxi	NOUN
ap-2099	119	32	)	)	PUNCT
ap-2099	119	33	=	=	PUNCT
ap-2099	120	1	λ	λ	NOUN
ap-2099	120	2	2σ	2σ	NOUN
ap-2099	121	1	i	i	PRON
ap-2099	121	2	αβ(â+	αβ(â+	VERB
ap-2099	121	3	α	α	X
ap-2099	121	4	âβ	âβ	X
ap-2099	121	5	+	+	CCONJ
ap-2099	121	6	b̂β	b̂β	NOUN
ap-2099	121	7	b̂	b̂	NOUN
ap-2099	121	8	+	+	CCONJ
ap-2099	121	9	α	α	NOUN
ap-2099	121	10	)	)	PUNCT
ap-2099	121	11	ψ	ψ	NOUN
ap-2099	121	12	,	,	PUNCT
ap-2099	121	13	r̂ψ	r̂ψ	PROPN
ap-2099	121	14	=	=	NOUN
ap-2099	121	15	1	1	NUM
ap-2099	121	16	2(rψ	2(rψ	NUM
ap-2099	121	17	+	+	CCONJ
ap-2099	121	18	ψr	ψr	ADJ
ap-2099	121	19	)	)	PUNCT
ap-2099	121	20	=	=	SYM
ap-2099	121	21	λ	λ	NOUN
ap-2099	121	22	2	2	NUM
ap-2099	121	23	(	(	PUNCT
ap-2099	121	24	(	(	PUNCT
ap-2099	121	25	â+	â+	ADP
ap-2099	121	26	α	α	NOUN
ap-2099	121	27	âα	âα	X
ap-2099	121	28	+	+	NOUN
ap-2099	121	29	1	1	NUM
ap-2099	121	30	)	)	PUNCT
ap-2099	121	31	+	+	CCONJ
ap-2099	121	32	(	(	PUNCT
ap-2099	121	33	b̂αb̂+	b̂αb̂+	NOUN
ap-2099	121	34	α	α	X
ap-2099	121	35	+	+	X
ap-2099	122	1	1))ψ	1))ψ	NUM
ap-2099	122	2	.	.	PUNCT
ap-2099	123	1	(	(	PUNCT
ap-2099	123	2	25	25	NUM
ap-2099	123	3	)	)	PUNCT
ap-2099	123	4	the	the	DET
ap-2099	123	5	following	follow	VERB
ap-2099	123	6	sequences	sequence	NOUN
ap-2099	123	7	of	of	ADP
ap-2099	123	8	operators	operator	NOUN
ap-2099	123	9	appear	appear	VERB
ap-2099	123	10	often	often	ADV
ap-2099	123	11	and	and	CCONJ
ap-2099	123	12	their	their	PRON
ap-2099	123	13	role	role	NOUN
ap-2099	123	14	is	be	AUX
ap-2099	123	15	important	important	ADJ
ap-2099	123	16	enough	enough	ADV
ap-2099	123	17	to	to	PART
ap-2099	123	18	admit	admit	VERB
ap-2099	123	19	that	that	SCONJ
ap-2099	123	20	they	they	PRON
ap-2099	123	21	deserve	deserve	VERB
ap-2099	123	22	some	some	DET
ap-2099	123	23	notation	notation	NOUN
ap-2099	123	24	on	on	ADP
ap-2099	123	25	their	their	PRON
ap-2099	123	26	own	own	ADJ
ap-2099	123	27	:	:	PUNCT
ap-2099	123	28	ŵk	ŵk	X
ap-2099	123	29	=	=	SYM
ap-2099	123	30	σkαβ(â+	σkαβ(â+	PROPN
ap-2099	123	31	α	α	PROPN
ap-2099	123	32	âβ	âβ	NOUN
ap-2099	123	33	−	−	PROPN
ap-2099	123	34	â+	â+	PROPN
ap-2099	123	35	α	α	PROPN
ap-2099	123	36	b̂β	b̂β	NOUN
ap-2099	123	37	−	−	X
ap-2099	123	38	âβ	âβ	X
ap-2099	123	39	b̂+	b̂+	ADJ
ap-2099	124	1	α	α	PROPN
ap-2099	125	1	+	+	X
ap-2099	125	2	b̂+	b̂+	PROPN
ap-2099	125	3	α	α	NUM
ap-2099	125	4	b̂β	b̂β	NOUN
ap-2099	125	5	)	)	PUNCT
ap-2099	125	6	,	,	PUNCT
ap-2099	125	7	ŵ	ŵ	X
ap-2099	125	8	=	=	SYM
ap-2099	126	1	â+	â+	PROPN
ap-2099	126	2	α	α	PROPN
ap-2099	126	3	âα	âα	X
ap-2099	126	4	−	−	PROPN
ap-2099	126	5	â+	â+	PROPN
ap-2099	126	6	α	α	NOUN
ap-2099	126	7	b̂α	b̂α	NOUN
ap-2099	126	8	−	−	PROPN
ap-2099	127	1	b̂+	b̂+	ADV
ap-2099	127	2	α	α	PROPN
ap-2099	127	3	âα	âα	X
ap-2099	128	1	+	+	CCONJ
ap-2099	128	2	b̂+	b̂+	PROPN
ap-2099	128	3	α	α	NUM
ap-2099	128	4	b̂α	b̂α	NOUN
ap-2099	128	5	,	,	PUNCT
ap-2099	128	6	ŵ	ŵ	X
ap-2099	128	7	′k	′k	NOUN
ap-2099	128	8	=	=	PUNCT
ap-2099	128	9	ŵk	ŵk	NUM
ap-2099	128	10	−	−	NOUN
ap-2099	128	11	2λex̂k	2λex̂k	NOUN
ap-2099	128	12	,	,	PUNCT
ap-2099	128	13	ŵ	ŵ	X
ap-2099	128	14	′	′	NUM
ap-2099	129	1	=	=	SYM
ap-2099	129	2	ŵ	ŵ	X
ap-2099	130	1	−	−	NOUN
ap-2099	130	2	2λer̂	2λer̂	NUM
ap-2099	130	3	,	,	PUNCT
ap-2099	130	4	(	(	PUNCT
ap-2099	130	5	26	26	NUM
ap-2099	130	6	)	)	PUNCT
ap-2099	130	7	where	where	SCONJ
ap-2099	130	8	e	e	NOUN
ap-2099	130	9	is	be	AUX
ap-2099	130	10	energy	energy	NOUN
ap-2099	130	11	and	and	CCONJ
ap-2099	130	12	λ	λ	PROPN
ap-2099	130	13	is	be	AUX
ap-2099	130	14	the	the	DET
ap-2099	130	15	nc	nc	PROPN
ap-2099	130	16	parameter	parameter	PROPN
ap-2099	130	17	already	already	ADV
ap-2099	130	18	mentioned	mention	VERB
ap-2099	130	19	.	.	PUNCT
ap-2099	131	1	note	note	VERB
ap-2099	131	2	that	that	SCONJ
ap-2099	131	3	the	the	DET
ap-2099	131	4	only	only	ADJ
ap-2099	131	5	difference	difference	NOUN
ap-2099	131	6	between	between	ADP
ap-2099	131	7	ŵ	ŵ	X
ap-2099	131	8	′k	′k	NOUN
ap-2099	131	9	and	and	CCONJ
ap-2099	131	10	ŵk	ŵk	NOUN
ap-2099	131	11	is	be	AUX
ap-2099	131	12	the	the	DET
ap-2099	131	13	constant	constant	ADJ
ap-2099	131	14	multiplying	multiply	VERB
ap-2099	131	15	one	one	NUM
ap-2099	131	16	of	of	ADP
ap-2099	131	17	their	their	PRON
ap-2099	131	18	terms	term	NOUN
ap-2099	131	19	.	.	PUNCT
ap-2099	132	1	ŵ	ŵ	X
ap-2099	133	1	′	′	NUM
ap-2099	133	2	and	and	CCONJ
ap-2099	133	3	ŵ	ŵ	PROPN
ap-2099	133	4	are	be	AUX
ap-2099	133	5	related	relate	VERB
ap-2099	133	6	similarly	similarly	ADV
ap-2099	133	7	.	.	PUNCT
ap-2099	134	1	3.2	3.2	NUM
ap-2099	134	2	.	.	PUNCT
ap-2099	134	3	nc	nc	PROPN
ap-2099	134	4	operators	operators	PROPN
ap-2099	134	5	revisited	revisit	VERB
ap-2099	134	6	now	now	ADV
ap-2099	134	7	we	we	PRON
ap-2099	134	8	rewrite	rewrite	VERB
ap-2099	134	9	the	the	DET
ap-2099	134	10	hamiltonian	hamiltonian	NOUN
ap-2099	134	11	,	,	PUNCT
ap-2099	134	12	the	the	DET
ap-2099	134	13	velocity	velocity	NOUN
ap-2099	134	14	operator	operator	NOUN
ap-2099	134	15	and	and	CCONJ
ap-2099	134	16	the	the	DET
ap-2099	134	17	nc	nc	PROPN
ap-2099	134	18	lrl	lrl	PROPN
ap-2099	134	19	vector	vector	NOUN
ap-2099	134	20	in	in	ADP
ap-2099	134	21	terms	term	NOUN
ap-2099	134	22	of	of	ADP
ap-2099	134	23	the	the	DET
ap-2099	134	24	new	new	ADJ
ap-2099	134	25	auxiliary	auxiliary	ADJ
ap-2099	134	26	operators	operator	NOUN
ap-2099	134	27	which	which	PRON
ap-2099	134	28	have	have	AUX
ap-2099	134	29	been	be	AUX
ap-2099	134	30	introduced	introduce	VERB
ap-2099	134	31	.	.	PUNCT
ap-2099	135	1	ĥ	ĥ	X
ap-2099	135	2	=	=	PUNCT
ap-2099	136	1	1	1	NUM
ap-2099	136	2	2λr̂	2λr̂	NUM
ap-2099	136	3	(	(	PUNCT
ap-2099	136	4	â+	â+	PROPN
ap-2099	136	5	α	α	NOUN
ap-2099	136	6	âα	âα	X
ap-2099	136	7	+	+	SYM
ap-2099	136	8	b̂+	b̂+	PROPN
ap-2099	136	9	α	α	NUM
ap-2099	136	10	b̂α	b̂α	NOUN
ap-2099	136	11	−	−	PROPN
ap-2099	136	12	â+	â+	NUM
ap-2099	136	13	α	α	NOUN
ap-2099	136	14	b̂α	b̂α	ADV
ap-2099	136	15	−	−	PROPN
ap-2099	136	16	âαb̂+	âαb̂+	ADJ
ap-2099	136	17	α	α	NOUN
ap-2099	136	18	)	)	PUNCT
ap-2099	136	19	−	−	PROPN
ap-2099	136	20	q	q	PUNCT
ap-2099	136	21	r̂	r̂	NOUN
ap-2099	136	22	=	=	NOUN
ap-2099	136	23	1	1	NUM
ap-2099	136	24	2λr̂	2λr̂	NUM
ap-2099	136	25	ŵ	ŵ	NUM
ap-2099	136	26	−	−	PROPN
ap-2099	136	27	q	q	NOUN
ap-2099	136	28	r̂	r̂	NOUN
ap-2099	136	29	,	,	PUNCT
ap-2099	136	30	(	(	PUNCT
ap-2099	136	31	27	27	NUM
ap-2099	136	32	)	)	PUNCT
ap-2099	136	33	v̂i	v̂i	NOUN
ap-2099	136	34	=	=	SYM
ap-2099	136	35	−i[x̂i	−i[x̂i	PROPN
ap-2099	136	36	,	,	PUNCT
ap-2099	136	37	ĥ	ĥ	X
ap-2099	136	38	]	]	PUNCT
ap-2099	136	39	=	=	SYM
ap-2099	137	1	i	i	PRON
ap-2099	137	2	2r̂	2r̂	PROPN
ap-2099	137	3	σ	σ	NOUN
ap-2099	138	1	i	i	PRON
ap-2099	138	2	αβ(â+	αβ(â+	VERB
ap-2099	138	3	α	α	NOUN
ap-2099	138	4	b̂β	b̂β	NOUN
ap-2099	139	1	−	−	PROPN
ap-2099	140	1	âβ	âβ	X
ap-2099	140	2	b̂+	b̂+	ADV
ap-2099	140	3	α	α	PROPN
ap-2099	140	4	)	)	PUNCT
ap-2099	140	5	(	(	PUNCT
ap-2099	140	6	28	28	NUM
ap-2099	140	7	)	)	PUNCT
ap-2099	140	8	âk	âk	PART
ap-2099	141	1	=	=	SYM
ap-2099	141	2	1	1	NUM
ap-2099	141	3	2εijk(l̂iv̂j	2εijk(l̂iv̂j	NUM
ap-2099	141	4	+	+	CCONJ
ap-2099	141	5	v̂jl̂i	v̂jl̂i	NOUN
ap-2099	141	6	)	)	PUNCT
ap-2099	141	7	+	+	NOUN
ap-2099	141	8	q	q	PUNCT
ap-2099	141	9	x̂k	x̂k	NUM
ap-2099	141	10	r̂	r̂	NOUN
ap-2099	141	11	=	=	SYM
ap-2099	141	12	1	1	NUM
ap-2099	141	13	2r̂λ	2r̂λ	NUM
ap-2099	141	14	(	(	PUNCT
ap-2099	141	15	r̂ŵ	r̂ŵ	X
ap-2099	141	16	′k	′k	ADV
ap-2099	141	17	−	−	PROPN
ap-2099	141	18	x̂k(ŵ	x̂k(ŵ	NOUN
ap-2099	142	1	′	′	NUM
ap-2099	143	1	−	−	PROPN
ap-2099	143	2	2λq	2λq	NOUN
ap-2099	143	3	)	)	PUNCT
ap-2099	143	4	)	)	PUNCT
ap-2099	143	5	.	.	PUNCT
ap-2099	144	1	(	(	PUNCT
ap-2099	144	2	29	29	X
ap-2099	144	3	)	)	PUNCT
ap-2099	144	4	deriving	derive	VERB
ap-2099	144	5	equations	equation	NOUN
ap-2099	144	6	(	(	PUNCT
ap-2099	144	7	28	28	NUM
ap-2099	144	8	)	)	PUNCT
ap-2099	144	9	and	and	CCONJ
ap-2099	144	10	(	(	PUNCT
ap-2099	144	11	29	29	NUM
ap-2099	144	12	)	)	PUNCT
ap-2099	144	13	involves	involve	VERB
ap-2099	144	14	somewhat	somewhat	ADV
ap-2099	144	15	laborious	laborious	ADJ
ap-2099	144	16	calculations	calculation	NOUN
ap-2099	144	17	.	.	PUNCT
ap-2099	145	1	the	the	DET
ap-2099	145	2	details	detail	NOUN
ap-2099	145	3	can	can	AUX
ap-2099	145	4	be	be	AUX
ap-2099	145	5	found	find	VERB
ap-2099	145	6	in	in	ADP
ap-2099	145	7	[	[	X
ap-2099	145	8	7	7	NUM
ap-2099	145	9	]	]	PUNCT
ap-2099	145	10	.	.	PUNCT
ap-2099	146	1	this	this	PRON
ap-2099	146	2	gives	give	VERB
ap-2099	146	3	us	we	PRON
ap-2099	146	4	an	an	DET
ap-2099	146	5	opportunity	opportunity	NOUN
ap-2099	146	6	to	to	PART
ap-2099	146	7	write	write	VERB
ap-2099	146	8	the	the	DET
ap-2099	146	9	nc	nc	PROPN
ap-2099	146	10	schrödinger	schrödinger	PROPN
ap-2099	146	11	equation	equation	NOUN
ap-2099	146	12	in	in	ADP
ap-2099	146	13	the	the	DET
ap-2099	146	14	following	following	ADJ
ap-2099	146	15	way	way	NOUN
ap-2099	146	16	:	:	PUNCT
ap-2099	146	17	(	(	PUNCT
ap-2099	146	18	1	1	NUM
ap-2099	146	19	2λr̂	2λr̂	NUM
ap-2099	146	20	ŵ−	ŵ−	PROPN
ap-2099	146	21	q	q	PUNCT
ap-2099	146	22	r̂	r̂	NOUN
ap-2099	146	23	−e	−e	NOUN
ap-2099	146	24	)	)	PUNCT
ap-2099	146	25	ψe	ψe	NOUN
ap-2099	146	26	=	=	SYM
ap-2099	146	27	1	1	NUM
ap-2099	146	28	2λr̂	2λr̂	NUM
ap-2099	146	29	(	(	PUNCT
ap-2099	146	30	ŵ	ŵ	X
ap-2099	146	31	′−2λq)ψe	′−2λq)ψe	PROPN
ap-2099	146	32	=	=	SYM
ap-2099	146	33	0	0	PROPN
ap-2099	146	34	.	.	PUNCT
ap-2099	147	1	(	(	PUNCT
ap-2099	147	2	30	30	NUM
ap-2099	147	3	)	)	PUNCT
ap-2099	147	4	ψe	ψe	NOUN
ap-2099	147	5	belongs	belong	VERB
ap-2099	147	6	to	to	ADP
ap-2099	147	7	heλ	heλ	PROPN
ap-2099	147	8	,	,	PUNCT
ap-2099	147	9	i.e.	i.e.	X
ap-2099	147	10	to	to	ADP
ap-2099	147	11	the	the	DET
ap-2099	147	12	subspace	subspace	NOUN
ap-2099	147	13	spanned	span	VERB
ap-2099	147	14	by	by	ADP
ap-2099	147	15	the	the	DET
ap-2099	147	16	eigenvectors	eigenvector	NOUN
ap-2099	147	17	of	of	ADP
ap-2099	147	18	the	the	DET
ap-2099	147	19	hamiltonian	hamiltonian	NOUN
ap-2099	147	20	.	.	PUNCT
ap-2099	148	1	the	the	DET
ap-2099	148	2	important	important	ADJ
ap-2099	148	3	quantity	quantity	NOUN
ap-2099	148	4	for	for	ADP
ap-2099	148	5	us	we	PRON
ap-2099	148	6	is	be	AUX
ap-2099	148	7	âk|he	âk|he	ADJ
ap-2099	148	8	λ	λ	NOUN
ap-2099	148	9	,	,	PUNCT
ap-2099	148	10	the	the	DET
ap-2099	148	11	lrl	lrl	PROPN
ap-2099	148	12	vector	vector	NOUN
ap-2099	148	13	as	as	SCONJ
ap-2099	148	14	it	it	PRON
ap-2099	148	15	acts	act	VERB
ap-2099	148	16	on	on	ADP
ap-2099	148	17	the	the	DET
ap-2099	148	18	solutions	solution	NOUN
ap-2099	148	19	of	of	ADP
ap-2099	148	20	the	the	DET
ap-2099	148	21	schrödinger	schrödinger	ADJ
ap-2099	148	22	equation	equation	NOUN
ap-2099	148	23	:	:	PUNCT
ap-2099	148	24	âk|he	âk|he	PROPN
ap-2099	148	25	λ	λ	X
ap-2099	148	26	=	=	SYM
ap-2099	148	27	1	1	NUM
ap-2099	148	28	2r̂λ	2r̂λ	NUM
ap-2099	148	29	(	(	PUNCT
ap-2099	148	30	r̂ŵ	r̂ŵ	PROPN
ap-2099	148	31	′k−	′k−	PROPN
ap-2099	148	32	x̂k	x̂k	PROPN
ap-2099	149	1	(	(	PUNCT
ap-2099	149	2	ŵ	ŵ	X
ap-2099	149	3	′	′	NUM
ap-2099	150	1	−	−	PROPN
ap-2099	150	2	2λq)︸	2λq)︸	NUM
ap-2099	150	3	︷︷	︷︷	PROPN
ap-2099	150	4	︸	︸	X
ap-2099	150	5	see	see	VERB
ap-2099	150	6	eq	eq	NOUN
ap-2099	150	7	.	.	PUNCT
ap-2099	151	1	(	(	PUNCT
ap-2099	151	2	30	30	NUM
ap-2099	151	3	)	)	PUNCT
ap-2099	151	4	)	)	PUNCT
ap-2099	152	1	=	=	SYM
ap-2099	152	2	1	1	NUM
ap-2099	152	3	2λŵ	2λŵ	NUM
ap-2099	152	4	′	′	NUM
ap-2099	152	5	k.	k.	NOUN
ap-2099	153	1	(	(	PUNCT
ap-2099	153	2	31	31	NUM
ap-2099	153	3	)	)	PUNCT
ap-2099	153	4	when	when	SCONJ
ap-2099	153	5	dealing	deal	VERB
ap-2099	153	6	with	with	ADP
ap-2099	153	7	calculations	calculation	NOUN
ap-2099	153	8	related	relate	VERB
ap-2099	153	9	to	to	ADP
ap-2099	153	10	the	the	DET
ap-2099	153	11	conservation	conservation	NOUN
ap-2099	153	12	of	of	ADP
ap-2099	153	13	âk	âk	PROPN
ap-2099	153	14	,	,	PUNCT
ap-2099	153	15	we	we	PRON
ap-2099	153	16	just	just	ADV
ap-2099	153	17	need	need	VERB
ap-2099	153	18	to	to	PART
ap-2099	153	19	ascertain	ascertain	VERB
ap-2099	153	20	whether	whether	SCONJ
ap-2099	153	21	the	the	DET
ap-2099	153	22	following	follow	VERB
ap-2099	153	23	commutator	commutator	NOUN
ap-2099	153	24	with	with	ADP
ap-2099	153	25	the	the	DET
ap-2099	153	26	hamiltonian	hamiltonian	NOUN
ap-2099	153	27	vanishes	vanish	VERB
ap-2099	153	28	:	:	PUNCT
ap-2099	153	29	˙̂	˙̂	PROPN
ap-2099	154	1	w	w	NOUN
ap-2099	154	2	′k	′k	ADV
ap-2099	155	1	=	=	PUNCT
ap-2099	155	2	i	i	PRON
ap-2099	155	3	[	[	PUNCT
ap-2099	155	4	ĥ0	ĥ0	NOUN
ap-2099	155	5	−	−	NOUN
ap-2099	155	6	q	q	NOUN
ap-2099	155	7	r̂	r̂	NOUN
ap-2099	155	8	,	,	PUNCT
ap-2099	155	9	ŵ	ŵ	X
ap-2099	155	10	′k	′k	NOUN
ap-2099	155	11	]	]	PUNCT
ap-2099	156	1	=	=	PUNCT
ap-2099	156	2	i	i	PRON
ap-2099	156	3	[	[	PUNCT
ap-2099	156	4	1	1	NUM
ap-2099	156	5	2r̂λŵ	2r̂λŵ	NUM
ap-2099	156	6	′	′	NOUN
ap-2099	156	7	−	−	ADP
ap-2099	156	8	q	q	PUNCT
ap-2099	156	9	r̂	r̂	NOUN
ap-2099	156	10	,	,	PUNCT
ap-2099	156	11	ŵ	ŵ	X
ap-2099	156	12	′k	′k	NOUN
ap-2099	156	13	]	]	PUNCT
ap-2099	157	1	=	=	PUNCT
ap-2099	157	2	i	i	PRON
ap-2099	157	3	2r̂λ	2r̂λ	PROPN
ap-2099	157	4	[	[	PUNCT
ap-2099	157	5	ŵ	ŵ	NUM
ap-2099	157	6	′	′	NUM
ap-2099	157	7	,	,	PUNCT
ap-2099	157	8	ŵ	ŵ	PUNCT
ap-2099	157	9	′k	′k	NOUN
ap-2099	157	10	]	]	PUNCT
ap-2099	158	1	+	+	CCONJ
ap-2099	158	2	i	i	PRON
ap-2099	158	3	[	[	X
ap-2099	158	4	1	1	NUM
ap-2099	158	5	r̂	r̂	NOUN
ap-2099	158	6	,	,	PUNCT
ap-2099	158	7	ŵ	ŵ	X
ap-2099	158	8	′k	′k	NOUN
ap-2099	158	9	]	]	X
ap-2099	158	10	(	(	PUNCT
ap-2099	158	11	ŵ	ŵ	X
ap-2099	158	12	′	′	NUM
ap-2099	158	13	2λ	2λ	NUM
ap-2099	159	1	−	−	NOUN
ap-2099	159	2	q	q	NOUN
ap-2099	159	3	)	)	PUNCT
ap-2099	160	1	=	=	SYM
ap-2099	160	2	0	0	X
ap-2099	160	3	.	.	PUNCT
ap-2099	161	1	(	(	PUNCT
ap-2099	161	2	32	32	NUM
ap-2099	161	3	)	)	PUNCT
ap-2099	161	4	the	the	DET
ap-2099	161	5	second	second	ADJ
ap-2099	161	6	term	term	NOUN
ap-2099	161	7	in	in	ADP
ap-2099	161	8	the	the	DET
ap-2099	161	9	second	second	ADJ
ap-2099	161	10	-	-	PUNCT
ap-2099	161	11	to	to	ADP
ap-2099	161	12	-	-	PUNCT
ap-2099	161	13	last	last	ADJ
ap-2099	161	14	line	line	NOUN
ap-2099	161	15	vanishes	vanish	VERB
ap-2099	161	16	when	when	SCONJ
ap-2099	161	17	acting	act	VERB
ap-2099	161	18	on	on	ADP
ap-2099	161	19	vectors	vector	NOUN
ap-2099	161	20	from	from	ADP
ap-2099	161	21	heλ	heλ	PROPN
ap-2099	161	22	(	(	PUNCT
ap-2099	161	23	and	and	CCONJ
ap-2099	161	24	we	we	PRON
ap-2099	161	25	are	be	AUX
ap-2099	161	26	not	not	PART
ap-2099	161	27	so	so	ADV
ap-2099	161	28	interested	interested	ADJ
ap-2099	161	29	in	in	ADP
ap-2099	161	30	the	the	DET
ap-2099	161	31	rest	rest	NOUN
ap-2099	161	32	of	of	ADP
ap-2099	161	33	hλ	hλ	NOUN
ap-2099	161	34	)	)	PUNCT
ap-2099	161	35	.	.	PUNCT
ap-2099	162	1	the	the	DET
ap-2099	162	2	first	first	ADJ
ap-2099	162	3	term	term	NOUN
ap-2099	162	4	proportional	proportional	ADJ
ap-2099	162	5	to	to	ADP
ap-2099	162	6	[	[	X
ap-2099	162	7	ŵ	ŵ	PROPN
ap-2099	162	8	′	′	NUM
ap-2099	162	9	,	,	PUNCT
ap-2099	162	10	ŵ	ŵ	X
ap-2099	162	11	′k	′k	NOUN
ap-2099	162	12	]	]	PUNCT
ap-2099	162	13	does	do	AUX
ap-2099	162	14	not	not	PART
ap-2099	162	15	contribute	contribute	VERB
ap-2099	162	16	either	either	ADV
ap-2099	162	17	.	.	PUNCT
ap-2099	163	1	the	the	DET
ap-2099	163	2	calculations	calculation	NOUN
ap-2099	163	3	proving	prove	VERB
ap-2099	163	4	this	this	PRON
ap-2099	163	5	involve	involve	VERB
ap-2099	163	6	more	more	ADJ
ap-2099	163	7	steps	step	NOUN
ap-2099	163	8	and	and	CCONJ
ap-2099	163	9	can	can	AUX
ap-2099	163	10	be	be	AUX
ap-2099	163	11	found	find	VERB
ap-2099	163	12	in	in	ADP
ap-2099	163	13	[	[	X
ap-2099	163	14	7	7	NUM
ap-2099	163	15	]	]	PUNCT
ap-2099	163	16	.	.	PUNCT
ap-2099	164	1	the	the	DET
ap-2099	164	2	equation	equation	NOUN
ap-2099	164	3	above	above	ADP
ap-2099	164	4	encourages	encourage	VERB
ap-2099	164	5	one	one	NUM
ap-2099	164	6	to	to	PART
ap-2099	164	7	search	search	VERB
ap-2099	164	8	for	for	ADP
ap-2099	164	9	the	the	DET
ap-2099	164	10	underlying	underlying	ADJ
ap-2099	164	11	so(4	so(4	PROPN
ap-2099	164	12	)	)	PUNCT
ap-2099	164	13	symmetry	symmetry	NOUN
ap-2099	164	14	,	,	PUNCT
ap-2099	164	15	since	since	SCONJ
ap-2099	164	16	the	the	DET
ap-2099	164	17	lrl	lrl	PROPN
ap-2099	164	18	vector	vector	NOUN
ap-2099	164	19	conservation	conservation	NOUN
ap-2099	164	20	makes	make	VERB
ap-2099	164	21	its	its	PRON
ap-2099	164	22	components	component	NOUN
ap-2099	164	23	suitable	suitable	ADJ
ap-2099	164	24	candidates	candidate	NOUN
ap-2099	164	25	for	for	ADP
ap-2099	164	26	half	half	NOUN
ap-2099	164	27	of	of	ADP
ap-2099	164	28	its	its	PRON
ap-2099	164	29	generators	generator	NOUN
ap-2099	164	30	,	,	PUNCT
ap-2099	164	31	the	the	DET
ap-2099	164	32	remaining	remain	VERB
ap-2099	164	33	three	three	NUM
ap-2099	164	34	consisting	consisting	NOUN
ap-2099	164	35	of	of	ADP
ap-2099	164	36	the	the	DET
ap-2099	164	37	components	component	NOUN
ap-2099	164	38	of	of	ADP
ap-2099	164	39	the	the	DET
ap-2099	164	40	angular	angular	ADJ
ap-2099	164	41	momentum	momentum	NOUN
ap-2099	164	42	.	.	PUNCT
ap-2099	165	1	once	once	ADV
ap-2099	165	2	again	again	ADV
ap-2099	165	3	we	we	PRON
ap-2099	165	4	have	have	VERB
ap-2099	165	5	to	to	PART
ap-2099	165	6	ask	ask	VERB
ap-2099	165	7	the	the	DET
ap-2099	165	8	reader	reader	NOUN
ap-2099	165	9	either	either	CCONJ
ap-2099	165	10	to	to	PART
ap-2099	165	11	check	check	VERB
ap-2099	165	12	[	[	X
ap-2099	165	13	7	7	X
ap-2099	165	14	]	]	PUNCT
ap-2099	165	15	for	for	ADP
ap-2099	165	16	details	detail	NOUN
ap-2099	165	17	or	or	CCONJ
ap-2099	165	18	simply	simply	ADV
ap-2099	165	19	to	to	PART
ap-2099	165	20	believe	believe	VERB
ap-2099	165	21	that	that	SCONJ
ap-2099	165	22	the	the	DET
ap-2099	165	23	following	follow	VERB
ap-2099	165	24	holds	hold	VERB
ap-2099	165	25	:	:	PUNCT
ap-2099	166	1	[	[	X
ap-2099	166	2	âi	âi	ADP
ap-2099	166	3	,	,	PUNCT
ap-2099	166	4	âj	âj	NOUN
ap-2099	166	5	]	]	PUNCT
ap-2099	166	6	=	=	PUNCT
ap-2099	166	7	iεijk(−2e	iεijk(−2e	PROPN
ap-2099	166	8	+	+	CCONJ
ap-2099	166	9	λ2e2)l̂k	λ2e2)l̂k	PROPN
ap-2099	166	10	(	(	PUNCT
ap-2099	166	11	33	33	NUM
ap-2099	166	12	)	)	PUNCT
ap-2099	166	13	there	there	PRON
ap-2099	166	14	is	be	VERB
ap-2099	166	15	nothing	nothing	PRON
ap-2099	166	16	but	but	SCONJ
ap-2099	166	17	a	a	DET
ap-2099	166	18	constant	constant	ADJ
ap-2099	166	19	in	in	ADP
ap-2099	166	20	the	the	DET
ap-2099	166	21	way	way	NOUN
ap-2099	166	22	,	,	PUNCT
ap-2099	166	23	as	as	ADV
ap-2099	166	24	long	long	ADV
ap-2099	166	25	as	as	SCONJ
ap-2099	166	26	we	we	PRON
ap-2099	166	27	let	let	VERB
ap-2099	166	28	the	the	DET
ap-2099	166	29	operator	operator	NOUN
ap-2099	166	30	[	[	X
ap-2099	166	31	âi	âi	NOUN
ap-2099	166	32	,	,	PUNCT
ap-2099	166	33	âj	âj	NOUN
ap-2099	166	34	]	]	PUNCT
ap-2099	166	35	act	act	VERB
ap-2099	166	36	upon	upon	SCONJ
ap-2099	166	37	the	the	DET
ap-2099	166	38	vectors	vector	NOUN
ap-2099	166	39	from	from	ADP
ap-2099	166	40	heλ	heλ	NOUN
ap-2099	166	41	with	with	ADP
ap-2099	166	42	the	the	DET
ap-2099	166	43	energy	energy	NOUN
ap-2099	166	44	fixed	fix	VERB
ap-2099	166	45	.	.	PUNCT
ap-2099	167	1	eq	eq	X
ap-2099	167	2	.	.	PUNCT
ap-2099	168	1	(	(	PUNCT
ap-2099	168	2	33	33	NUM
ap-2099	168	3	)	)	PUNCT
ap-2099	168	4	and	and	CCONJ
ap-2099	168	5	[	[	X
ap-2099	168	6	l̂i	l̂i	NOUN
ap-2099	168	7	,	,	PUNCT
ap-2099	168	8	l̂j	l̂j	X
ap-2099	168	9	]	]	PUNCT
ap-2099	168	10	=	=	PUNCT
ap-2099	168	11	iεijkl̂k	iεijkl̂k	ADJ
ap-2099	168	12	,	,	PUNCT
ap-2099	168	13	[	[	X
ap-2099	168	14	l̂i	l̂i	NOUN
ap-2099	168	15	,	,	PUNCT
ap-2099	168	16	âj	âj	NOUN
ap-2099	168	17	]	]	X
ap-2099	168	18	=	=	SYM
ap-2099	168	19	iεijkâk	iεijkâk	X
ap-2099	168	20	(	(	PUNCT
ap-2099	168	21	34	34	NUM
ap-2099	168	22	)	)	PUNCT
ap-2099	168	23	define	define	VERB
ap-2099	168	24	lie	lie	NOUN
ap-2099	168	25	algebra	algebra	NOUN
ap-2099	168	26	relations	relation	NOUN
ap-2099	168	27	corresponding	correspond	VERB
ap-2099	168	28	to	to	ADP
ap-2099	168	29	a	a	DET
ap-2099	168	30	particular	particular	ADJ
ap-2099	168	31	symmetry	symmetry	NOUN
ap-2099	168	32	group	group	NOUN
ap-2099	168	33	,	,	PUNCT
ap-2099	168	34	the	the	DET
ap-2099	168	35	actual	actual	ADJ
ap-2099	168	36	form	form	NOUN
ap-2099	168	37	of	of	ADP
ap-2099	168	38	which	which	PRON
ap-2099	168	39	depends	depend	VERB
ap-2099	168	40	on	on	ADP
ap-2099	168	41	the	the	DET
ap-2099	168	42	sign	sign	NOUN
ap-2099	168	43	of	of	ADP
ap-2099	168	44	the	the	DET
ap-2099	168	45	e	e	NOUN
ap-2099	168	46	-	-	ADJ
ap-2099	168	47	dependent	dependent	ADJ
ap-2099	168	48	factor	factor	NOUN
ap-2099	168	49	in	in	ADP
ap-2099	168	50	(	(	PUNCT
ap-2099	168	51	33	33	NUM
ap-2099	168	52	)	)	PUNCT
ap-2099	168	53	.	.	PUNCT
ap-2099	169	1	the	the	DET
ap-2099	169	2	relevant	relevant	ADJ
ap-2099	169	3	relations	relation	NOUN
ap-2099	169	4	for	for	ADP
ap-2099	169	5	l̂i	l̂i	NOUN
ap-2099	169	6	have	have	AUX
ap-2099	169	7	already	already	ADV
ap-2099	169	8	been	be	AUX
ap-2099	169	9	mentioned	mention	VERB
ap-2099	169	10	,	,	PUNCT
ap-2099	169	11	the	the	DET
ap-2099	169	12	formula	formula	NOUN
ap-2099	169	13	for	for	ADP
ap-2099	169	14	the	the	DET
ap-2099	169	15	mixed	mixed	ADJ
ap-2099	169	16	commutator	commutator	NOUN
ap-2099	170	1	[	[	X
ap-2099	170	2	l̂i	l̂i	NOUN
ap-2099	170	3	,	,	PUNCT
ap-2099	170	4	âj	âj	PROPN
ap-2099	170	5	]	]	PUNCT
ap-2099	170	6	follows	follow	VERB
ap-2099	170	7	from	from	ADP
ap-2099	170	8	the	the	DET
ap-2099	170	9	fact	fact	NOUN
ap-2099	170	10	that	that	SCONJ
ap-2099	170	11	âj	âj	NOUN
ap-2099	170	12	,	,	PUNCT
ap-2099	170	13	j	j	PROPN
ap-2099	170	14	=	=	SYM
ap-2099	170	15	1	1	NUM
ap-2099	170	16	,	,	PUNCT
ap-2099	170	17	2	2	NUM
ap-2099	170	18	,	,	PUNCT
ap-2099	170	19	3	3	NUM
ap-2099	170	20	,	,	PUNCT
ap-2099	170	21	are	be	AUX
ap-2099	170	22	components	component	NOUN
ap-2099	170	23	of	of	ADP
ap-2099	170	24	a	a	DET
ap-2099	170	25	vector	vector	NOUN
ap-2099	170	26	.	.	PUNCT
ap-2099	171	1	there	there	PRON
ap-2099	171	2	are	be	VERB
ap-2099	171	3	three	three	NUM
ap-2099	171	4	independent	independent	ADJ
ap-2099	171	5	cases	case	NOUN
ap-2099	171	6	:	:	PUNCT
ap-2099	171	7	•	•	NUM
ap-2099	171	8	so(4	so(4	NOUN
ap-2099	171	9	)	)	PUNCT
ap-2099	171	10	symmetry	symmetry	NOUN
ap-2099	171	11	:	:	PUNCT
ap-2099	171	12	−2e	−2e	PROPN
ap-2099	171	13	+	+	CCONJ
ap-2099	171	14	λ2e2	λ2e2	PROPN
ap-2099	171	15	>	>	X
ap-2099	171	16	0	0	PUNCT
ap-2099	171	17	⇐	⇐	ADJ
ap-2099	171	18	⇒	⇒	NOUN
ap-2099	171	19	e	e	X
ap-2099	171	20	<	<	X
ap-2099	171	21	0	0	NUM
ap-2099	171	22	or	or	CCONJ
ap-2099	171	23	e	e	X
ap-2099	171	24	>	>	X
ap-2099	171	25	2	2	NUM
ap-2099	171	26	/	/	SYM
ap-2099	171	27	λ2	λ2	NOUN
ap-2099	171	28	;	;	PUNCT
ap-2099	171	29	•	•	NUM
ap-2099	171	30	so(3	so(3	NOUN
ap-2099	171	31	,	,	PUNCT
ap-2099	171	32	1	1	NUM
ap-2099	171	33	)	)	PUNCT
ap-2099	171	34	symmetry	symmetry	NOUN
ap-2099	171	35	:	:	PUNCT
ap-2099	171	36	−2e	−2e	PROPN
ap-2099	171	37	+	+	CCONJ
ap-2099	171	38	λ2e2	λ2e2	X
ap-2099	171	39	<	<	X
ap-2099	171	40	0	0	NUM
ap-2099	171	41	⇐	⇐	ADJ
ap-2099	171	42	⇒	⇒	NOUN
ap-2099	171	43	0	0	PUNCT
ap-2099	171	44	<	<	X
ap-2099	171	45	e	e	X
ap-2099	171	46	<	<	X
ap-2099	171	47	2	2	NUM
ap-2099	171	48	/	/	SYM
ap-2099	171	49	λ2	λ2	NOUN
ap-2099	171	50	;	;	PUNCT
ap-2099	171	51	•	•	NUM
ap-2099	171	52	e(3	e(3	PROPN
ap-2099	171	53	)	)	PUNCT
ap-2099	171	54	euclidean	euclidean	ADJ
ap-2099	171	55	group	group	NOUN
ap-2099	171	56	:	:	PUNCT
ap-2099	171	57	−2e	−2e	PROPN
ap-2099	171	58	+	+	CCONJ
ap-2099	171	59	λ2e2	λ2e2	SYM
ap-2099	172	1	=	=	SYM
ap-2099	172	2	0	0	NUM
ap-2099	172	3	⇐	⇐	ADJ
ap-2099	172	4	⇒	⇒	NOUN
ap-2099	172	5	e	e	X
ap-2099	172	6	=	=	SYM
ap-2099	172	7	0	0	NUM
ap-2099	172	8	or	or	CCONJ
ap-2099	172	9	e	e	X
ap-2099	172	10	=	=	SYM
ap-2099	172	11	2	2	NUM
ap-2099	172	12	/	/	SYM
ap-2099	172	13	λ2	λ2	NOUN
ap-2099	172	14	.	.	PUNCT
ap-2099	173	1	the	the	DET
ap-2099	173	2	admissible	admissible	ADJ
ap-2099	173	3	values	value	NOUN
ap-2099	173	4	of	of	ADP
ap-2099	173	5	e	e	PRON
ap-2099	173	6	should	should	AUX
ap-2099	173	7	correspond	correspond	VERB
ap-2099	173	8	to	to	ADP
ap-2099	173	9	the	the	DET
ap-2099	173	10	unitary	unitary	ADJ
ap-2099	173	11	representations	representation	NOUN
ap-2099	173	12	of	of	ADP
ap-2099	173	13	the	the	DET
ap-2099	173	14	symmetry	symmetry	NOUN
ap-2099	173	15	in	in	ADP
ap-2099	173	16	question	question	NOUN
ap-2099	173	17	.	.	PUNCT
ap-2099	174	1	this	this	DET
ap-2099	174	2	requirement	requirement	NOUN
ap-2099	174	3	guarantees	guarantee	VERB
ap-2099	174	4	that	that	SCONJ
ap-2099	174	5	the	the	DET
ap-2099	174	6	generators	generator	NOUN
ap-2099	174	7	l̂j	l̂j	NOUN
ap-2099	174	8	and	and	CCONJ
ap-2099	174	9	âj	âj	NOUN
ap-2099	174	10	are	be	AUX
ap-2099	174	11	realized	realize	VERB
ap-2099	174	12	as	as	ADP
ap-2099	174	13	hermitian	hermitian	ADJ
ap-2099	174	14	operators	operator	NOUN
ap-2099	174	15	,	,	PUNCT
ap-2099	174	16	and	and	CCONJ
ap-2099	174	17	consequently	consequently	ADV
ap-2099	174	18	correspond	correspond	VERB
ap-2099	174	19	to	to	ADP
ap-2099	174	20	physical	physical	ADJ
ap-2099	174	21	observables	observable	NOUN
ap-2099	174	22	.	.	PUNCT
ap-2099	175	1	the	the	DET
ap-2099	175	2	casimir	casimir	PROPN
ap-2099	175	3	operators	operator	NOUN
ap-2099	175	4	in	in	ADP
ap-2099	175	5	the	the	DET
ap-2099	175	6	mentioned	mention	VERB
ap-2099	175	7	cases	case	NOUN
ap-2099	175	8	are	be	AUX
ap-2099	175	9	ĉ	ĉ	ADV
ap-2099	175	10	′1	′1	X
ap-2099	175	11	=	=	SYM
ap-2099	175	12	l̂jâj	l̂jâj	PROPN
ap-2099	175	13	,	,	PUNCT
ap-2099	175	14	ĉ	ĉ	ADV
ap-2099	175	15	′2	′2	X
ap-2099	175	16	=	=	SYM
ap-2099	175	17	âiâi	âiâi	PROPN
ap-2099	175	18	+	+	CCONJ
ap-2099	175	19	(	(	PUNCT
ap-2099	175	20	−2e	−2e	PROPN
ap-2099	175	21	+	+	CCONJ
ap-2099	175	22	λ2e2)(l̂il̂i	λ2e2)(l̂il̂i	X
ap-2099	175	23	+	+	NOUN
ap-2099	175	24	1	1	NUM
ap-2099	175	25	)	)	PUNCT
ap-2099	175	26	.	.	PUNCT
ap-2099	176	1	(	(	PUNCT
ap-2099	176	2	35	35	NUM
ap-2099	176	3	)	)	PUNCT
ap-2099	176	4	152	152	NUM
ap-2099	176	5	vol	vol	NOUN
ap-2099	176	6	.	.	PUNCT
ap-2099	177	1	54	54	NUM
ap-2099	177	2	no	no	NOUN
ap-2099	177	3	.	.	PUNCT
ap-2099	178	1	2/2014	2/2014	NUM
ap-2099	178	2	lrl	lrl	PROPN
ap-2099	178	3	vector	vector	NOUN
ap-2099	178	4	in	in	ADP
ap-2099	178	5	quantum	quantum	ADJ
ap-2099	178	6	mechanics	mechanic	NOUN
ap-2099	178	7	in	in	ADP
ap-2099	178	8	noncommutative	noncommutative	ADJ
ap-2099	178	9	space	space	NOUN
ap-2099	178	10	the	the	DET
ap-2099	178	11	prime	prime	NOUN
ap-2099	178	12	indicates	indicate	VERB
ap-2099	178	13	that	that	SCONJ
ap-2099	178	14	we	we	PRON
ap-2099	178	15	are	be	AUX
ap-2099	178	16	not	not	PART
ap-2099	178	17	using	use	VERB
ap-2099	178	18	the	the	DET
ap-2099	178	19	standard	standard	ADJ
ap-2099	178	20	normalization	normalization	NOUN
ap-2099	178	21	of	of	ADP
ap-2099	178	22	casimir	casimir	NOUN
ap-2099	178	23	operators	operator	NOUN
ap-2099	178	24	.	.	PUNCT
ap-2099	179	1	now	now	ADV
ap-2099	179	2	,	,	PUNCT
ap-2099	179	3	we	we	PRON
ap-2099	179	4	need	need	VERB
ap-2099	179	5	to	to	PART
ap-2099	179	6	calculate	calculate	VERB
ap-2099	179	7	their	their	PRON
ap-2099	179	8	values	value	NOUN
ap-2099	179	9	in	in	ADP
ap-2099	179	10	heλ	heλ	PROPN
ap-2099	179	11	.	.	PUNCT
ap-2099	180	1	the	the	DET
ap-2099	180	2	first	first	ADJ
ap-2099	180	3	casimir	casimir	NOUN
ap-2099	180	4	vanishes	vanish	VERB
ap-2099	180	5	in	in	ADP
ap-2099	180	6	all	all	DET
ap-2099	180	7	cases	case	NOUN
ap-2099	180	8	due	due	ADP
ap-2099	180	9	to	to	ADP
ap-2099	180	10	the	the	DET
ap-2099	180	11	fact	fact	NOUN
ap-2099	180	12	that	that	SCONJ
ap-2099	180	13	ĉ	ĉ	ADV
ap-2099	180	14	′1ψe	′1ψe	ADV
ap-2099	180	15	∼	∼	VERB
ap-2099	180	16	rψe	rψe	NOUN
ap-2099	180	17	−ψer	−ψer	NOUN
ap-2099	180	18	=	=	NOUN
ap-2099	181	1	0	0	X
ap-2099	181	2	.	.	PUNCT
ap-2099	182	1	the	the	DET
ap-2099	182	2	second	second	ADJ
ap-2099	182	3	casimir	casimir	NOUN
ap-2099	182	4	operator	operator	NOUN
ap-2099	182	5	is	be	AUX
ap-2099	182	6	somewhat	somewhat	ADV
ap-2099	182	7	more	more	ADV
ap-2099	182	8	demanding	demanding	ADJ
ap-2099	182	9	.	.	PUNCT
ap-2099	183	1	according	accord	VERB
ap-2099	183	2	to	to	ADP
ap-2099	183	3	(	(	PUNCT
ap-2099	183	4	31	31	NUM
ap-2099	183	5	)	)	PUNCT
ap-2099	183	6	we	we	PRON
ap-2099	183	7	have	have	VERB
ap-2099	183	8	ĉ	ĉ	X
ap-2099	183	9	′2ψe	′2ψe	PROPN
ap-2099	183	10	=	=	SYM
ap-2099	183	11	(	(	PUNCT
ap-2099	183	12	ŵ	ŵ	X
ap-2099	183	13	′iŵ	′iŵ	NOUN
ap-2099	183	14	′i	′i	NOUN
ap-2099	183	15	4λ2	4λ2	NUM
ap-2099	183	16	+	+	CCONJ
ap-2099	183	17	(	(	PUNCT
ap-2099	183	18	−2e	−2e	PROPN
ap-2099	183	19	+	+	CCONJ
ap-2099	183	20	λ2e2)(l̂il̂i	λ2e2)(l̂il̂i	X
ap-2099	183	21	+	+	NOUN
ap-2099	183	22	1	1	NUM
ap-2099	183	23	)	)	PUNCT
ap-2099	183	24	)	)	PUNCT
ap-2099	183	25	ψe	ψe	NOUN
ap-2099	183	26	=	=	SYM
ap-2099	183	27	1	1	NUM
ap-2099	183	28	4λ2	4λ2	NUM
ap-2099	183	29	ŵ	ŵ	X
ap-2099	183	30	′ŵ	′ŵ	PUNCT
ap-2099	183	31	′ψe	′ψe	NOUN
ap-2099	183	32	,	,	PUNCT
ap-2099	183	33	(	(	PUNCT
ap-2099	183	34	36	36	NUM
ap-2099	183	35	)	)	PUNCT
ap-2099	183	36	where	where	SCONJ
ap-2099	183	37	we	we	PRON
ap-2099	183	38	used	use	VERB
ap-2099	183	39	the	the	DET
ap-2099	183	40	quadratic	quadratic	ADJ
ap-2099	183	41	identity	identity	NOUN
ap-2099	183	42	ŵ	ŵ	PUNCT
ap-2099	183	43	′iŵ	′iŵ	NOUN
ap-2099	184	1	′	′	NUM
ap-2099	185	1	i	i	PRON
ap-2099	185	2	+	+	PUNCT
ap-2099	185	3	4λ2(−2e	4λ2(−2e	NUM
ap-2099	186	1	+	+	CCONJ
ap-2099	186	2	λ2e2)(l̂il̂i	λ2e2)(l̂il̂i	X
ap-2099	186	3	+	+	NOUN
ap-2099	186	4	1	1	X
ap-2099	186	5	)	)	PUNCT
ap-2099	186	6	=	=	NOUN
ap-2099	186	7	ŵ	ŵ	X
ap-2099	186	8	′2	′2	NOUN
ap-2099	186	9	.	.	PUNCT
ap-2099	187	1	(	(	PUNCT
ap-2099	187	2	37	37	NUM
ap-2099	187	3	)	)	PUNCT
ap-2099	187	4	according	accord	VERB
ap-2099	187	5	to	to	ADP
ap-2099	187	6	the	the	DET
ap-2099	187	7	schrödinger	schrödinger	ADJ
ap-2099	187	8	equation	equation	NOUN
ap-2099	187	9	,	,	PUNCT
ap-2099	187	10	(	(	PUNCT
ap-2099	187	11	ŵ	ŵ	X
ap-2099	187	12	′)2ψe	′)2ψe	NOUN
ap-2099	187	13	=	=	SYM
ap-2099	187	14	4λ2q2ψe	4λ2q2ψe	PROPN
ap-2099	187	15	,	,	PUNCT
ap-2099	187	16	and	and	CCONJ
ap-2099	187	17	we	we	PRON
ap-2099	187	18	are	be	AUX
ap-2099	187	19	left	leave	VERB
ap-2099	187	20	with	with	ADP
ap-2099	187	21	ĉ	ĉ	X
ap-2099	187	22	′2ψe	′2ψe	PROPN
ap-2099	187	23	=	=	PRON
ap-2099	187	24	q2ψe	q2ψe	PUNCT
ap-2099	187	25	.	.	PUNCT
ap-2099	188	1	(	(	PUNCT
ap-2099	188	2	38	38	NUM
ap-2099	188	3	)	)	PUNCT
ap-2099	188	4	since	since	SCONJ
ap-2099	188	5	both	both	DET
ap-2099	188	6	casimir	casimir	NOUN
ap-2099	188	7	operators	operator	NOUN
ap-2099	188	8	take	take	VERB
ap-2099	188	9	constant	constant	ADJ
ap-2099	188	10	values	value	NOUN
ap-2099	188	11	ĉ	ĉ	ADV
ap-2099	188	12	′1	′1	X
ap-2099	188	13	=	=	SYM
ap-2099	188	14	0	0	NUM
ap-2099	188	15	and	and	CCONJ
ap-2099	188	16	ĉ	ĉ	ADV
ap-2099	188	17	′2	′2	X
ap-2099	188	18	=	=	SYM
ap-2099	188	19	q2	q2	NOUN
ap-2099	188	20	in	in	ADP
ap-2099	188	21	heλ	heλ	PROPN
ap-2099	188	22	,	,	PUNCT
ap-2099	188	23	we	we	PRON
ap-2099	188	24	are	be	AUX
ap-2099	188	25	dealing	deal	VERB
ap-2099	188	26	with	with	ADP
ap-2099	188	27	irreducible	irreducible	ADJ
ap-2099	188	28	representations	representation	NOUN
ap-2099	188	29	of	of	ADP
ap-2099	188	30	the	the	DET
ap-2099	188	31	dynamical	dynamical	ADJ
ap-2099	188	32	symmetry	symmetry	NOUN
ap-2099	188	33	group	group	NOUN
ap-2099	188	34	g	g	PROPN
ap-2099	188	35	that	that	PRON
ap-2099	188	36	are	be	AUX
ap-2099	188	37	unitary	unitary	ADJ
ap-2099	188	38	for	for	ADP
ap-2099	188	39	particular	particular	ADJ
ap-2099	188	40	values	value	NOUN
ap-2099	188	41	of	of	ADP
ap-2099	188	42	energy	energy	NOUN
ap-2099	188	43	.	.	PUNCT
ap-2099	189	1	in	in	ADP
ap-2099	189	2	all	all	DET
ap-2099	189	3	the	the	DET
ap-2099	189	4	cases	case	NOUN
ap-2099	189	5	considered	consider	VERB
ap-2099	189	6	,	,	PUNCT
ap-2099	189	7	g	g	PROPN
ap-2099	189	8	=	=	PUNCT
ap-2099	189	9	so(4),so(3	so(4),so(3	PROPN
ap-2099	189	10	,	,	PUNCT
ap-2099	189	11	1	1	NUM
ap-2099	189	12	)	)	PUNCT
ap-2099	189	13	,	,	PUNCT
ap-2099	189	14	e(3	e(3	PROPN
ap-2099	189	15	)	)	PUNCT
ap-2099	189	16	,	,	PUNCT
ap-2099	189	17	the	the	DET
ap-2099	189	18	unitary	unitary	ADJ
ap-2099	189	19	irreducible	irreducible	ADJ
ap-2099	189	20	representations	representation	NOUN
ap-2099	189	21	are	be	AUX
ap-2099	189	22	well	well	ADV
ap-2099	189	23	known	know	VERB
ap-2099	189	24	.	.	PUNCT
ap-2099	190	1	the	the	DET
ap-2099	190	2	corresponding	correspond	VERB
ap-2099	190	3	systems	system	NOUN
ap-2099	190	4	of	of	ADP
ap-2099	190	5	eigenfunctions	eigenfunction	NOUN
ap-2099	190	6	that	that	PRON
ap-2099	190	7	span	span	VERB
ap-2099	190	8	the	the	DET
ap-2099	190	9	representation	representation	NOUN
ap-2099	190	10	space	space	NOUN
ap-2099	190	11	have	have	AUX
ap-2099	190	12	been	be	AUX
ap-2099	190	13	found	find	VERB
ap-2099	190	14	in	in	ADP
ap-2099	190	15	[	[	X
ap-2099	190	16	9	9	NUM
ap-2099	190	17	]	]	PUNCT
ap-2099	190	18	.	.	PUNCT
ap-2099	191	1	here	here	ADV
ap-2099	191	2	we	we	PRON
ap-2099	191	3	do	do	AUX
ap-2099	191	4	not	not	PART
ap-2099	191	5	repeat	repeat	VERB
ap-2099	191	6	their	their	PRON
ap-2099	191	7	construction	construction	NOUN
ap-2099	191	8	,	,	PUNCT
ap-2099	191	9	but	but	CCONJ
ap-2099	191	10	we	we	PRON
ap-2099	191	11	restrict	restrict	VERB
ap-2099	191	12	ourselves	ourselves	PRON
ap-2099	191	13	to	to	PART
ap-2099	191	14	brief	brief	ADJ
ap-2099	191	15	comments	comment	NOUN
ap-2099	191	16	pointing	point	VERB
ap-2099	191	17	out	out	ADP
ap-2099	191	18	some	some	DET
ap-2099	191	19	interesting	interesting	ADJ
ap-2099	191	20	aspects	aspect	NOUN
ap-2099	191	21	.	.	PUNCT
ap-2099	192	1	3.3	3.3	NUM
ap-2099	192	2	.	.	PUNCT
ap-2099	193	1	bound	bind	VERB
ap-2099	193	2	states	state	NOUN
ap-2099	193	3	–	–	PUNCT
ap-2099	193	4	the	the	DET
ap-2099	193	5	case	case	NOUN
ap-2099	193	6	of	of	ADP
ap-2099	193	7	so(4	so(4	NOUN
ap-2099	193	8	)	)	PUNCT
ap-2099	193	9	symmetry	symmetry	NOUN
ap-2099	193	10	−2e	−2e	PROPN
ap-2099	193	11	+	+	CCONJ
ap-2099	193	12	λ2e2	λ2e2	PROPN
ap-2099	193	13	>	>	X
ap-2099	193	14	0	0	PUNCT
ap-2099	194	1	in	in	ADP
ap-2099	194	2	this	this	DET
ap-2099	194	3	case	case	NOUN
ap-2099	194	4	we	we	PRON
ap-2099	194	5	rescale	rescale	VERB
ap-2099	194	6	the	the	DET
ap-2099	194	7	lrl	lrl	PROPN
ap-2099	194	8	vector	vector	NOUN
ap-2099	194	9	as	as	ADP
ap-2099	194	10	k̂j	k̂j	X
ap-2099	194	11	=	=	PUNCT
ap-2099	194	12	âj√	âj√	NOUN
ap-2099	194	13	−2e	−2e	PROPN
ap-2099	194	14	+	+	CCONJ
ap-2099	194	15	λ2e2	λ2e2	PROPN
ap-2099	194	16	=	=	SYM
ap-2099	194	17	ŵ	ŵ	X
ap-2099	194	18	′j	′j	ADJ
ap-2099	194	19	2λ	2λ	NOUN
ap-2099	194	20	√	√	ADP
ap-2099	194	21	−2e	−2e	PROPN
ap-2099	194	22	+	+	NOUN
ap-2099	194	23	λ2e2	λ2e2	PROPN
ap-2099	194	24	.	.	PUNCT
ap-2099	195	1	(	(	PUNCT
ap-2099	195	2	39	39	NUM
ap-2099	195	3	)	)	PUNCT
ap-2099	195	4	after	after	ADP
ap-2099	195	5	this	this	DET
ap-2099	195	6	step	step	NOUN
ap-2099	195	7	eqs	eqs	X
ap-2099	195	8	.	.	PUNCT
ap-2099	196	1	(	(	PUNCT
ap-2099	196	2	33	33	NUM
ap-2099	196	3	)	)	PUNCT
ap-2099	196	4	,	,	PUNCT
ap-2099	196	5	(	(	PUNCT
ap-2099	196	6	34	34	NUM
ap-2099	196	7	)	)	PUNCT
ap-2099	196	8	turn	turn	VERB
ap-2099	196	9	into	into	ADP
ap-2099	196	10	the	the	DET
ap-2099	196	11	following	follow	VERB
ap-2099	196	12	relations	relation	NOUN
ap-2099	196	13	:	:	PUNCT
ap-2099	197	1	[	[	X
ap-2099	197	2	l̂i	l̂i	NOUN
ap-2099	197	3	,	,	PUNCT
ap-2099	197	4	l̂j	l̂j	X
ap-2099	197	5	]	]	PUNCT
ap-2099	197	6	=	=	PUNCT
ap-2099	197	7	iεijkl̂k	iεijkl̂k	ADJ
ap-2099	197	8	,	,	PUNCT
ap-2099	197	9	[	[	X
ap-2099	197	10	l̂i	l̂i	NOUN
ap-2099	197	11	,	,	PUNCT
ap-2099	197	12	k̂j	k̂j	X
ap-2099	197	13	]	]	PUNCT
ap-2099	197	14	=	=	SYM
ap-2099	197	15	iεijkk̂k	iεijkk̂k	NOUN
ap-2099	197	16	,	,	PUNCT
ap-2099	197	17	[	[	X
ap-2099	197	18	k̂i	k̂i	NOUN
ap-2099	197	19	,	,	PUNCT
ap-2099	197	20	k̂j	k̂j	X
ap-2099	197	21	]	]	PUNCT
ap-2099	197	22	=	=	PUNCT
ap-2099	197	23	iεijkl̂k	iεijkl̂k	NOUN
ap-2099	197	24	.	.	PUNCT
ap-2099	198	1	(	(	PUNCT
ap-2099	198	2	40	40	NUM
ap-2099	198	3	)	)	PUNCT
ap-2099	198	4	thus	thus	ADV
ap-2099	198	5	we	we	PRON
ap-2099	198	6	have	have	AUX
ap-2099	198	7	got	get	VERB
ap-2099	198	8	the	the	DET
ap-2099	198	9	representation	representation	NOUN
ap-2099	198	10	of	of	ADP
ap-2099	198	11	the	the	DET
ap-2099	198	12	so(4	so(4	PROPN
ap-2099	198	13	)	)	PUNCT
ap-2099	198	14	algebra	algebra	NOUN
ap-2099	198	15	.	.	PUNCT
ap-2099	199	1	the	the	DET
ap-2099	199	2	relevant	relevant	ADJ
ap-2099	199	3	normalized	normalize	VERB
ap-2099	199	4	casimir	casimir	NOUN
ap-2099	199	5	operators	operator	NOUN
ap-2099	199	6	are	be	AUX
ap-2099	199	7	ĉ1	ĉ1	X
ap-2099	200	1	=	=	SYM
ap-2099	200	2	l̂jk̂j	l̂jk̂j	INTJ
ap-2099	200	3	,	,	PUNCT
ap-2099	200	4	ĉ2	ĉ2	PROPN
ap-2099	200	5	=	=	PUNCT
ap-2099	201	1	k̂ik̂i	k̂ik̂i	PROPN
ap-2099	201	2	+	+	NUM
ap-2099	201	3	l̂il̂i	l̂il̂i	PROPN
ap-2099	201	4	+	+	NOUN
ap-2099	201	5	1	1	X
ap-2099	201	6	.	.	PUNCT
ap-2099	201	7	(	(	PUNCT
ap-2099	201	8	41	41	NUM
ap-2099	201	9	)	)	PUNCT
ap-2099	201	10	as	as	SCONJ
ap-2099	201	11	we	we	PRON
ap-2099	201	12	have	have	AUX
ap-2099	201	13	stated	state	VERB
ap-2099	201	14	already	already	ADV
ap-2099	201	15	,	,	PUNCT
ap-2099	201	16	the	the	DET
ap-2099	201	17	ĉ1	ĉ1	NOUN
ap-2099	201	18	acting	act	VERB
ap-2099	201	19	on	on	ADP
ap-2099	201	20	an	an	DET
ap-2099	201	21	eigenfunction	eigenfunction	NOUN
ap-2099	201	22	of	of	ADP
ap-2099	201	23	the	the	DET
ap-2099	201	24	hamiltonian	hamiltonian	ADJ
ap-2099	201	25	returns	return	NOUN
ap-2099	201	26	zero	zero	NUM
ap-2099	201	27	.	.	PUNCT
ap-2099	202	1	as	as	ADP
ap-2099	202	2	to	to	ADP
ap-2099	202	3	ĉ2	ĉ2	PROPN
ap-2099	202	4	,	,	PUNCT
ap-2099	202	5	we	we	PRON
ap-2099	202	6	know	know	VERB
ap-2099	202	7	that	that	PRON
ap-2099	202	8	for	for	ADP
ap-2099	202	9	so(4	so(4	NOUN
ap-2099	202	10	)	)	PUNCT
ap-2099	202	11	,	,	PUNCT
ap-2099	202	12	under	under	ADP
ap-2099	202	13	the	the	DET
ap-2099	202	14	condition	condition	NOUN
ap-2099	202	15	that	that	SCONJ
ap-2099	202	16	the	the	DET
ap-2099	202	17	first	first	ADJ
ap-2099	202	18	casimir	casimir	NOUN
ap-2099	202	19	is	be	AUX
ap-2099	202	20	zero	zero	NUM
ap-2099	202	21	,	,	PUNCT
ap-2099	202	22	the	the	DET
ap-2099	202	23	second	second	ADJ
ap-2099	202	24	casimir	casimir	NOUN
ap-2099	202	25	has	have	VERB
ap-2099	202	26	to	to	PART
ap-2099	202	27	be	be	AUX
ap-2099	202	28	equal	equal	ADJ
ap-2099	202	29	to	to	ADP
ap-2099	202	30	n2	n2	VERB
ap-2099	202	31	for	for	ADP
ap-2099	202	32	some	some	DET
ap-2099	202	33	integer	integer	NOUN
ap-2099	202	34	n	n	NOUN
ap-2099	202	35	=	=	NUM
ap-2099	202	36	j+	j+	NUM
ap-2099	202	37	1	1	NUM
ap-2099	202	38	,	,	PUNCT
ap-2099	202	39	j+	j+	NUM
ap-2099	202	40	2	2	NUM
ap-2099	202	41	,	,	PUNCT
ap-2099	202	42	.	.	PUNCT
ap-2099	202	43	.	.	PUNCT
ap-2099	202	44	.	.	PUNCT
ap-2099	203	1	(	(	PUNCT
ap-2099	203	2	with	with	ADP
ap-2099	203	3	j(j	j(j	PROPN
ap-2099	203	4	+	+	CCONJ
ap-2099	203	5	1	1	X
ap-2099	203	6	)	)	PUNCT
ap-2099	203	7	corresponding	correspond	VERB
ap-2099	203	8	to	to	ADP
ap-2099	203	9	the	the	DET
ap-2099	203	10	square	square	NOUN
ap-2099	203	11	of	of	ADP
ap-2099	203	12	the	the	DET
ap-2099	203	13	angular	angular	ADJ
ap-2099	203	14	momentum	momentum	NOUN
ap-2099	203	15	)	)	PUNCT
ap-2099	203	16	.	.	PUNCT
ap-2099	204	1	at	at	ADP
ap-2099	204	2	the	the	DET
ap-2099	204	3	same	same	ADJ
ap-2099	204	4	time	time	NOUN
ap-2099	204	5	,	,	PUNCT
ap-2099	204	6	according	accord	VERB
ap-2099	204	7	to	to	ADP
ap-2099	204	8	(	(	PUNCT
ap-2099	204	9	38	38	NUM
ap-2099	204	10	)	)	PUNCT
ap-2099	204	11	it	it	PRON
ap-2099	204	12	is	be	AUX
ap-2099	204	13	related	relate	VERB
ap-2099	204	14	to	to	ADP
ap-2099	204	15	the	the	DET
ap-2099	204	16	energy	energy	NOUN
ap-2099	204	17	:	:	PUNCT
ap-2099	204	18	k̂ik̂i	k̂ik̂i	PROPN
ap-2099	204	19	+	+	NUM
ap-2099	204	20	l̂il̂i	l̂il̂i	NOUN
ap-2099	204	21	+	+	CCONJ
ap-2099	204	22	1	1	NUM
ap-2099	204	23	=	=	SYM
ap-2099	204	24	q2	q2	PROPN
ap-2099	204	25	λ2e2	λ2e2	PROPN
ap-2099	205	1	−	−	PROPN
ap-2099	205	2	2e	2e	PROPN
ap-2099	205	3	=	=	SYM
ap-2099	205	4	n2	n2	PROPN
ap-2099	205	5	.	.	PUNCT
ap-2099	206	1	(	(	PUNCT
ap-2099	206	2	42	42	NUM
ap-2099	206	3	)	)	PUNCT
ap-2099	206	4	now	now	ADV
ap-2099	206	5	solving	solve	VERB
ap-2099	206	6	the	the	DET
ap-2099	206	7	quadratic	quadratic	ADJ
ap-2099	206	8	equation	equation	NOUN
ap-2099	206	9	for	for	ADP
ap-2099	206	10	energy	energy	NOUN
ap-2099	206	11	we	we	PRON
ap-2099	206	12	obtain	obtain	VERB
ap-2099	206	13	two	two	NUM
ap-2099	206	14	discrete	discrete	ADJ
ap-2099	206	15	sets	set	NOUN
ap-2099	206	16	of	of	ADP
ap-2099	206	17	solutions	solution	NOUN
ap-2099	206	18	depending	depend	VERB
ap-2099	206	19	on	on	ADP
ap-2099	206	20	n	n	CCONJ
ap-2099	206	21	:	:	PUNCT
ap-2099	206	22	e	e	NOUN
ap-2099	206	23	=	=	SYM
ap-2099	206	24	1	1	NUM
ap-2099	206	25	λ2	λ2	NOUN
ap-2099	206	26	∓	∓	NOUN
ap-2099	206	27	1	1	NUM
ap-2099	206	28	λ2	λ2	NOUN
ap-2099	206	29	√	√	NUM
ap-2099	206	30	1	1	NUM
ap-2099	206	31	+	+	NUM
ap-2099	206	32	κ2	κ2	NOUN
ap-2099	206	33	n	n	CCONJ
ap-2099	206	34	,	,	PUNCT
ap-2099	206	35	κn	κn	NOUN
ap-2099	206	36	=	=	PUNCT
ap-2099	206	37	qλ	qλ	PROPN
ap-2099	206	38	n	n	PROPN
ap-2099	206	39	.	.	PUNCT
ap-2099	207	1	(	(	PUNCT
ap-2099	207	2	43	43	NUM
ap-2099	207	3	)	)	PUNCT
ap-2099	207	4	the	the	DET
ap-2099	207	5	first	first	ADJ
ap-2099	207	6	set	set	NOUN
ap-2099	207	7	of	of	ADP
ap-2099	207	8	eigenfunctions	eigenfunction	NOUN
ap-2099	207	9	of	of	ADP
ap-2099	207	10	the	the	DET
ap-2099	207	11	hamiltonian	hamiltonian	NOUN
ap-2099	207	12	in	in	ADP
ap-2099	207	13	(	(	PUNCT
ap-2099	207	14	17	17	NUM
ap-2099	207	15	)	)	PUNCT
ap-2099	207	16	for	for	ADP
ap-2099	207	17	energies	energy	NOUN
ap-2099	207	18	e	e	X
ap-2099	207	19	<	<	X
ap-2099	207	20	0	0	PUNCT
ap-2099	207	21	(	(	PUNCT
ap-2099	207	22	i.e.	i.e.	X
ap-2099	207	23	negative	negative	ADJ
ap-2099	207	24	sign	sign	NOUN
ap-2099	207	25	in	in	ADP
ap-2099	207	26	front	front	NOUN
ap-2099	207	27	of	of	ADP
ap-2099	207	28	the	the	DET
ap-2099	207	29	square	square	ADJ
ap-2099	207	30	root	root	NOUN
ap-2099	207	31	in	in	ADP
ap-2099	207	32	(	(	PUNCT
ap-2099	207	33	43	43	NUM
ap-2099	207	34	)	)	PUNCT
ap-2099	207	35	)	)	PUNCT
ap-2099	207	36	has	have	AUX
ap-2099	207	37	been	be	AUX
ap-2099	207	38	found	find	VERB
ap-2099	207	39	for	for	ADP
ap-2099	207	40	coulomb	coulomb	NOUN
ap-2099	207	41	attractive	attractive	ADJ
ap-2099	207	42	potential	potential	NOUN
ap-2099	207	43	,	,	PUNCT
ap-2099	207	44	i.e.	i.e.	X
ap-2099	207	45	q	q	X
ap-2099	207	46	>	>	X
ap-2099	207	47	0	0	PUNCT
ap-2099	208	1	in	in	ADP
ap-2099	208	2	(	(	PUNCT
ap-2099	208	3	17	17	NUM
ap-2099	208	4	):	):	PUNCT
ap-2099	208	5	eiλn	eiλn	NOUN
ap-2099	208	6	=	=	SYM
ap-2099	208	7	1	1	NUM
ap-2099	208	8	λ2	λ2	NOUN
ap-2099	208	9	−	−	NOUN
ap-2099	208	10	1	1	NUM
ap-2099	208	11	λ2	λ2	NOUN
ap-2099	208	12	√	√	NUM
ap-2099	208	13	1	1	NUM
ap-2099	208	14	+	+	NUM
ap-2099	208	15	κ2	κ2	NOUN
ap-2099	208	16	n.	n.	NOUN
ap-2099	208	17	(	(	PUNCT
ap-2099	208	18	44	44	NUM
ap-2099	208	19	)	)	PUNCT
ap-2099	208	20	these	these	PRON
ap-2099	208	21	eigenvalues	eigenvalue	VERB
ap-2099	208	22	possess	possess	VERB
ap-2099	208	23	a	a	DET
ap-2099	208	24	smooth	smooth	ADJ
ap-2099	208	25	standard	standard	ADJ
ap-2099	208	26	limit	limit	NOUN
ap-2099	208	27	for	for	ADP
ap-2099	208	28	λ→	λ→	PROPN
ap-2099	208	29	0	0	NUM
ap-2099	208	30	eiλn	eiλn	NOUN
ap-2099	208	31	=	=	SYM
ap-2099	208	32	1	1	NUM
ap-2099	208	33	λ2	λ2	NOUN
ap-2099	208	34	−	−	NOUN
ap-2099	208	35	1	1	NUM
ap-2099	208	36	λ2	λ2	NOUN
ap-2099	208	37	(	(	PUNCT
ap-2099	208	38	1	1	NUM
ap-2099	209	1	+	+	SYM
ap-2099	209	2	1	1	NUM
ap-2099	209	3	2κ	2κ	NOUN
ap-2099	209	4	2	2	NUM
ap-2099	209	5	n	n	CCONJ
ap-2099	209	6	−	−	NUM
ap-2099	209	7	1	1	NUM
ap-2099	209	8	24κ	24κ	SYM
ap-2099	209	9	4	4	NUM
ap-2099	209	10	n	n	NOUN
ap-2099	209	11	+	+	NUM
ap-2099	209	12	·	·	PUNCT
ap-2099	209	13	·	·	PUNCT
ap-2099	209	14	·	·	PUNCT
ap-2099	209	15	)	)	PUNCT
ap-2099	209	16	→	→	PUNCT
ap-2099	209	17	−	−	NUM
ap-2099	209	18	q2	q2	NOUN
ap-2099	209	19	2n2	2n2	NUM
ap-2099	209	20	=	=	SYM
ap-2099	209	21	−	−	PROPN
ap-2099	209	22	q2	q2	NOUN
ap-2099	209	23	m	m	PROPN
ap-2099	209	24	2n2~2	2n2~2	NUM
ap-2099	209	25	.	.	PUNCT
ap-2099	210	1	(	(	PUNCT
ap-2099	210	2	45	45	NUM
ap-2099	210	3	)	)	PUNCT
ap-2099	210	4	this	this	DET
ap-2099	210	5	spectrum	spectrum	NOUN
ap-2099	210	6	coincides	coincide	VERB
ap-2099	210	7	(	(	PUNCT
ap-2099	210	8	in	in	ADP
ap-2099	210	9	the	the	DET
ap-2099	210	10	commutative	commutative	ADJ
ap-2099	210	11	limit	limit	NOUN
ap-2099	210	12	λ→	λ→	NOUN
ap-2099	210	13	0	0	NUM
ap-2099	210	14	)	)	PUNCT
ap-2099	210	15	with	with	ADP
ap-2099	210	16	the	the	DET
ap-2099	210	17	spectrum	spectrum	NOUN
ap-2099	210	18	for	for	ADP
ap-2099	210	19	coulomb	coulomb	NOUN
ap-2099	210	20	attractive	attractive	ADJ
ap-2099	210	21	potential	potential	NOUN
ap-2099	210	22	,	,	PUNCT
ap-2099	210	23	q	q	X
ap-2099	210	24	>	>	X
ap-2099	210	25	0	0	NUM
ap-2099	210	26	,	,	PUNCT
ap-2099	210	27	that	that	PRON
ap-2099	210	28	was	be	AUX
ap-2099	210	29	found	find	VERB
ap-2099	210	30	by	by	ADP
ap-2099	210	31	pauli	pauli	PROPN
ap-2099	210	32	using	use	VERB
ap-2099	210	33	algebraic	algebraic	ADJ
ap-2099	210	34	methods	method	NOUN
ap-2099	210	35	prior	prior	ADV
ap-2099	210	36	to	to	ADP
ap-2099	210	37	solving	solve	VERB
ap-2099	210	38	schrödinger	schrödinger	ADJ
ap-2099	210	39	equation	equation	NOUN
ap-2099	210	40	for	for	ADP
ap-2099	210	41	the	the	DET
ap-2099	210	42	hydrogen	hydrogen	NOUN
ap-2099	210	43	atom	atom	NOUN
ap-2099	210	44	.	.	PUNCT
ap-2099	211	1	the	the	DET
ap-2099	211	2	full	full	ADJ
ap-2099	211	3	set	set	NOUN
ap-2099	211	4	of	of	ADP
ap-2099	211	5	eigenfunctions	eigenfunction	NOUN
ap-2099	211	6	of	of	ADP
ap-2099	211	7	(	(	PUNCT
ap-2099	211	8	17	17	NUM
ap-2099	211	9	)	)	PUNCT
ap-2099	211	10	for	for	ADP
ap-2099	211	11	energies	energy	NOUN
ap-2099	211	12	e	e	X
ap-2099	211	13	<	<	X
ap-2099	211	14	0	0	NUM
ap-2099	211	15	was	be	AUX
ap-2099	211	16	constructed	construct	VERB
ap-2099	211	17	in	in	ADP
ap-2099	211	18	[	[	X
ap-2099	211	19	9	9	NUM
ap-2099	211	20	]	]	PUNCT
ap-2099	211	21	by	by	ADP
ap-2099	211	22	explicitly	explicitly	ADV
ap-2099	211	23	solving	solve	VERB
ap-2099	211	24	the	the	DET
ap-2099	211	25	nc	nc	PROPN
ap-2099	211	26	schrödinger	schrödinger	PROPN
ap-2099	211	27	equation	equation	NOUN
ap-2099	211	28	.	.	PUNCT
ap-2099	212	1	the	the	DET
ap-2099	212	2	radial	radial	ADJ
ap-2099	212	3	nc	nc	PROPN
ap-2099	212	4	wave	wave	PROPN
ap-2099	212	5	functions	function	NOUN
ap-2099	212	6	defined	define	VERB
ap-2099	212	7	in	in	ADP
ap-2099	212	8	(	(	PUNCT
ap-2099	212	9	14	14	NUM
ap-2099	212	10	)	)	PUNCT
ap-2099	212	11	are	be	AUX
ap-2099	212	12	given	give	VERB
ap-2099	212	13	in	in	ADP
ap-2099	212	14	terms	term	NOUN
ap-2099	212	15	of	of	ADP
ap-2099	212	16	the	the	DET
ap-2099	212	17	hypergeometric	hypergeometric	ADJ
ap-2099	212	18	function	function	NOUN
ap-2099	212	19	riλn	riλn	NOUN
ap-2099	212	20	=	=	SYM
ap-2099	212	21	(	(	PUNCT
ap-2099	212	22	ωn)nf	ωn)nf	PUNCT
ap-2099	212	23	(	(	PUNCT
ap-2099	212	24	−n,−n	−n,−n	ADV
ap-2099	212	25	,	,	PUNCT
ap-2099	212	26	2j	2j	X
ap-2099	212	27	+	+	CCONJ
ap-2099	212	28	2,−2κnω−1	2,−2κnω−1	NUM
ap-2099	212	29	n	n	NUM
ap-2099	212	30	)	)	PUNCT
ap-2099	212	31	,	,	PUNCT
ap-2099	212	32	ωn	ωn	PROPN
ap-2099	212	33	=	=	PUNCT
ap-2099	212	34	κn	κn	NOUN
ap-2099	212	35	−	−	PROPN
ap-2099	212	36	√	√	NOUN
ap-2099	212	37	1	1	NUM
ap-2099	212	38	+	+	NUM
ap-2099	212	39	κ2	κ2	NOUN
ap-2099	212	40	n	n	PROPN
ap-2099	212	41	+	+	CCONJ
ap-2099	212	42	1	1	NUM
ap-2099	212	43	κn	κn	NOUN
ap-2099	212	44	+	+	CCONJ
ap-2099	212	45	√	√	NUM
ap-2099	212	46	1	1	NUM
ap-2099	212	47	+	+	NUM
ap-2099	212	48	κ2	κ2	NOUN
ap-2099	212	49	n	n	CCONJ
ap-2099	212	50	−	−	PROPN
ap-2099	212	51	1	1	NUM
ap-2099	212	52	,	,	PUNCT
ap-2099	212	53	(	(	PUNCT
ap-2099	212	54	46	46	NUM
ap-2099	212	55	)	)	PUNCT
ap-2099	212	56	where	where	SCONJ
ap-2099	212	57	n	n	NOUN
ap-2099	212	58	=	=	PRON
ap-2099	212	59	a+	a+	PUNCT
ap-2099	212	60	αaα	αaα	ADV
ap-2099	212	61	controls	control	VERB
ap-2099	212	62	the	the	DET
ap-2099	212	63	radial	radial	ADJ
ap-2099	212	64	nc	nc	PROPN
ap-2099	212	65	variable	variable	NOUN
ap-2099	212	66	.	.	PUNCT
ap-2099	213	1	the	the	DET
ap-2099	213	2	second	second	ADJ
ap-2099	213	3	set	set	NOUN
ap-2099	213	4	of	of	ADP
ap-2099	213	5	very	very	ADV
ap-2099	213	6	unexpected	unexpected	ADJ
ap-2099	213	7	solutions	solution	NOUN
ap-2099	213	8	corresponds	correspond	VERB
ap-2099	213	9	to	to	ADP
ap-2099	213	10	energies	energy	NOUN
ap-2099	213	11	(	(	PUNCT
ap-2099	213	12	43	43	NUM
ap-2099	213	13	)	)	PUNCT
ap-2099	213	14	with	with	ADP
ap-2099	213	15	positive	positive	ADJ
ap-2099	213	16	sign	sign	NOUN
ap-2099	213	17	eiiλn	eiiλn	NOUN
ap-2099	213	18	=	=	SYM
ap-2099	213	19	1	1	NUM
ap-2099	213	20	λ2	λ2	NOUN
ap-2099	213	21	+	+	CCONJ
ap-2099	213	22	1	1	NUM
ap-2099	213	23	λ2	λ2	NOUN
ap-2099	213	24	√	√	NUM
ap-2099	213	25	1	1	NUM
ap-2099	213	26	+	+	NUM
ap-2099	213	27	κ2	κ2	NOUN
ap-2099	213	28	n	n	CCONJ
ap-2099	213	29	>	>	X
ap-2099	213	30	2	2	NUM
ap-2099	213	31	λ2	λ2	NOUN
ap-2099	213	32	.	.	PUNCT
ap-2099	214	1	(	(	PUNCT
ap-2099	214	2	47	47	NUM
ap-2099	214	3	)	)	PUNCT
ap-2099	214	4	the	the	DET
ap-2099	214	5	corresponding	correspond	VERB
ap-2099	214	6	radial	radial	PROPN
ap-2099	214	7	nc	nc	PROPN
ap-2099	214	8	wave	wave	PROPN
ap-2099	214	9	functions	function	NOUN
ap-2099	214	10	have	have	AUX
ap-2099	214	11	been	be	AUX
ap-2099	214	12	found	find	VERB
ap-2099	214	13	in	in	ADP
ap-2099	214	14	[	[	X
ap-2099	214	15	9	9	NUM
ap-2099	214	16	]	]	PUNCT
ap-2099	214	17	solving	solve	VERB
ap-2099	214	18	nc	nc	PROPN
ap-2099	214	19	schrödinger	schrödinger	ADJ
ap-2099	214	20	equation	equation	NOUN
ap-2099	214	21	for	for	ADP
ap-2099	214	22	a	a	DET
ap-2099	214	23	coulomb	coulomb	NOUN
ap-2099	214	24	repulsive	repulsive	ADJ
ap-2099	214	25	potential	potential	NOUN
ap-2099	214	26	,	,	PUNCT
ap-2099	214	27	q	q	X
ap-2099	214	28	<	<	X
ap-2099	214	29	0	0	PUNCT
ap-2099	214	30	in	in	ADP
ap-2099	214	31	(	(	PUNCT
ap-2099	214	32	17	17	NUM
ap-2099	214	33	)	)	PUNCT
ap-2099	214	34	.	.	PUNCT
ap-2099	215	1	these	these	DET
ap-2099	215	2	radial	radial	PROPN
ap-2099	215	3	nc	nc	PROPN
ap-2099	215	4	wave	wave	PROPN
ap-2099	215	5	functions	function	NOUN
ap-2099	215	6	are	be	AUX
ap-2099	215	7	closely	closely	ADV
ap-2099	215	8	related	relate	VERB
ap-2099	215	9	to	to	ADP
ap-2099	215	10	those	those	PRON
ap-2099	215	11	given	give	VERB
ap-2099	215	12	above	above	ADP
ap-2099	215	13	riiλn	riiλn	NOUN
ap-2099	215	14	=	=	SYM
ap-2099	215	15	(	(	PUNCT
ap-2099	215	16	−ωn)nf	−ωn)nf	NOUN
ap-2099	215	17	(	(	PUNCT
ap-2099	215	18	−n,−n	−n,−n	ADV
ap-2099	215	19	,	,	PUNCT
ap-2099	215	20	2j	2j	X
ap-2099	216	1	+	+	CCONJ
ap-2099	216	2	2	2	NUM
ap-2099	216	3	,	,	PUNCT
ap-2099	216	4	2κnω−1	2κnω−1	NUM
ap-2099	216	5	n	n	CCONJ
ap-2099	216	6	)	)	PUNCT
ap-2099	216	7	.	.	PUNCT
ap-2099	217	1	(	(	PUNCT
ap-2099	217	2	48	48	NUM
ap-2099	217	3	)	)	PUNCT
ap-2099	217	4	both	both	DET
ap-2099	217	5	so(4	so(4	NOUN
ap-2099	217	6	)	)	PUNCT
ap-2099	217	7	representations	representation	NOUN
ap-2099	217	8	,	,	PUNCT
ap-2099	217	9	the	the	DET
ap-2099	217	10	representation	representation	NOUN
ap-2099	217	11	for	for	ADP
ap-2099	217	12	coulomb	coulomb	NOUN
ap-2099	217	13	attractive	attractive	ADJ
ap-2099	217	14	potential	potential	NOUN
ap-2099	217	15	with	with	ADP
ap-2099	217	16	eiλn	eiλn	NOUN
ap-2099	217	17	<	<	X
ap-2099	217	18	0	0	PUNCT
ap-2099	218	1	and	and	CCONJ
ap-2099	218	2	that	that	SCONJ
ap-2099	218	3	for	for	ADP
ap-2099	218	4	ultra	ultra	ADJ
ap-2099	218	5	-	-	ADJ
ap-2099	218	6	high	high	ADJ
ap-2099	218	7	energies	energy	NOUN
ap-2099	218	8	eiiλn	eiiλn	VERB
ap-2099	218	9	>	>	X
ap-2099	218	10	2	2	NUM
ap-2099	218	11	/	/	SYM
ap-2099	218	12	λ2	λ2	NOUN
ap-2099	218	13	for	for	ADP
ap-2099	218	14	coulomb	coulomb	NOUN
ap-2099	218	15	repulsive	repulsive	ADJ
ap-2099	218	16	potential	potential	NOUN
ap-2099	218	17	,	,	PUNCT
ap-2099	218	18	are	be	AUX
ap-2099	218	19	unitary	unitary	ADJ
ap-2099	218	20	equivalent	equivalent	ADJ
ap-2099	218	21	as	as	ADP
ap-2099	218	22	in	in	ADP
ap-2099	218	23	both	both	DET
ap-2099	218	24	representations	representation	NOUN
ap-2099	218	25	the	the	DET
ap-2099	218	26	casimir	casimir	NOUN
ap-2099	218	27	operators	operator	NOUN
ap-2099	218	28	take	take	VERB
ap-2099	218	29	the	the	DET
ap-2099	218	30	same	same	ADJ
ap-2099	218	31	values	value	NOUN
ap-2099	218	32	,	,	PUNCT
ap-2099	218	33	ĉ1	ĉ1	NOUN
ap-2099	218	34	=	=	SYM
ap-2099	218	35	0	0	NUM
ap-2099	218	36	and	and	CCONJ
ap-2099	218	37	ĉ1	ĉ1	NOUN
ap-2099	218	38	=	=	SYM
ap-2099	218	39	n2	n2	NOUN
ap-2099	218	40	.	.	PUNCT
ap-2099	219	1	however	however	ADV
ap-2099	219	2	,	,	PUNCT
ap-2099	219	3	physically	physically	ADV
ap-2099	219	4	they	they	PRON
ap-2099	219	5	are	be	AUX
ap-2099	219	6	quite	quite	ADV
ap-2099	219	7	distinct	distinct	ADJ
ap-2099	219	8	:	:	PUNCT
ap-2099	219	9	in	in	ADP
ap-2099	219	10	the	the	DET
ap-2099	219	11	commutative	commutative	ADJ
ap-2099	219	12	limit	limit	NOUN
ap-2099	219	13	λ	λ	X
ap-2099	219	14	→	→	SYM
ap-2099	219	15	0	0	NUM
ap-2099	219	16	the	the	DET
ap-2099	219	17	first	first	ADJ
ap-2099	219	18	bound	bind	VERB
ap-2099	219	19	states	state	NOUN
ap-2099	219	20	persist	persist	VERB
ap-2099	219	21	and	and	CCONJ
ap-2099	219	22	reduce	reduce	VERB
ap-2099	219	23	to	to	ADP
ap-2099	219	24	the	the	DET
ap-2099	219	25	standard	standard	ADJ
ap-2099	219	26	ones	one	NOUN
ap-2099	219	27	,	,	PUNCT
ap-2099	219	28	while	while	SCONJ
ap-2099	219	29	the	the	DET
ap-2099	219	30	extraordinary	extraordinary	ADJ
ap-2099	219	31	bound	bind	VERB
ap-2099	219	32	states	state	NOUN
ap-2099	219	33	at	at	ADP
ap-2099	219	34	ultra	ultra	ADJ
ap-2099	219	35	-	-	ADJ
ap-2099	219	36	high	high	ADJ
ap-2099	219	37	energies	energy	NOUN
ap-2099	219	38	disappear	disappear	VERB
ap-2099	219	39	from	from	ADP
ap-2099	219	40	the	the	DET
ap-2099	219	41	hilbert	hilbert	NOUN
ap-2099	219	42	space	space	NOUN
ap-2099	219	43	.	.	PUNCT
ap-2099	220	1	153	153	NUM
ap-2099	220	2	p.	p.	NOUN
ap-2099	220	3	presnajder	presnajder	NOUN
ap-2099	220	4	,	,	PUNCT
ap-2099	220	5	v.	v.	PROPN
ap-2099	220	6	galikova	galikova	PROPN
ap-2099	220	7	,	,	PUNCT
ap-2099	220	8	s.	s.	PROPN
ap-2099	220	9	kovacik	kovacik	PROPN
ap-2099	220	10	acta	acta	PROPN
ap-2099	220	11	polytechnica	polytechnica	PROPN
ap-2099	220	12	3.4	3.4	NUM
ap-2099	220	13	.	.	PUNCT
ap-2099	220	14	coulomb	coulomb	NOUN
ap-2099	220	15	scattering	scattering	NOUN
ap-2099	220	16	–	–	PUNCT
ap-2099	220	17	the	the	DET
ap-2099	220	18	case	case	NOUN
ap-2099	220	19	2e	2e	NUM
ap-2099	220	20	−	−	PROPN
ap-2099	220	21	λ2e2	λ2e2	PROPN
ap-2099	220	22	>	>	X
ap-2099	220	23	0	0	PUNCT
ap-2099	221	1	in	in	ADP
ap-2099	221	2	this	this	DET
ap-2099	221	3	case	case	NOUN
ap-2099	221	4	we	we	PRON
ap-2099	221	5	rescale	rescale	VERB
ap-2099	221	6	the	the	DET
ap-2099	221	7	lrl	lrl	PROPN
ap-2099	221	8	vector	vector	NOUN
ap-2099	221	9	as	as	ADP
ap-2099	221	10	k̂j	k̂j	X
ap-2099	221	11	=	=	PUNCT
ap-2099	221	12	âj√	âj√	NOUN
ap-2099	221	13	2e	2e	NOUN
ap-2099	221	14	−	−	NOUN
ap-2099	221	15	λ2e2	λ2e2	PROPN
ap-2099	221	16	=	=	SYM
ap-2099	221	17	ŵ	ŵ	X
ap-2099	221	18	′j	′j	ADJ
ap-2099	221	19	2λ	2λ	NUM
ap-2099	221	20	√	√	ADP
ap-2099	221	21	2e	2e	NUM
ap-2099	221	22	−	−	PROPN
ap-2099	221	23	λ2e2	λ2e2	PROPN
ap-2099	221	24	.	.	PUNCT
ap-2099	222	1	(	(	PUNCT
ap-2099	222	2	49	49	NUM
ap-2099	222	3	)	)	PUNCT
ap-2099	222	4	after	after	ADP
ap-2099	222	5	this	this	DET
ap-2099	222	6	step	step	NOUN
ap-2099	222	7	we	we	PRON
ap-2099	222	8	obtain	obtain	VERB
ap-2099	222	9	equations	equation	NOUN
ap-2099	223	1	[	[	X
ap-2099	223	2	l̂i	l̂i	NOUN
ap-2099	223	3	,	,	PUNCT
ap-2099	223	4	l̂j	l̂j	X
ap-2099	223	5	]	]	PUNCT
ap-2099	223	6	=	=	PUNCT
ap-2099	223	7	iεijkl̂k	iεijkl̂k	ADJ
ap-2099	223	8	,	,	PUNCT
ap-2099	223	9	[	[	X
ap-2099	223	10	l̂i	l̂i	NOUN
ap-2099	223	11	,	,	PUNCT
ap-2099	223	12	k̂j	k̂j	X
ap-2099	223	13	]	]	PUNCT
ap-2099	223	14	=	=	SYM
ap-2099	223	15	iεijkk̂k	iεijkk̂k	NOUN
ap-2099	223	16	,	,	PUNCT
ap-2099	223	17	[	[	X
ap-2099	223	18	k̂i	k̂i	NOUN
ap-2099	223	19	,	,	PUNCT
ap-2099	223	20	k̂j	k̂j	X
ap-2099	223	21	]	]	PUNCT
ap-2099	223	22	=	=	SYM
ap-2099	223	23	−iεijkl̂k	−iεijkl̂k	NOUN
ap-2099	223	24	.	.	PUNCT
ap-2099	224	1	(	(	PUNCT
ap-2099	224	2	50	50	NUM
ap-2099	224	3	)	)	PUNCT
ap-2099	224	4	so	so	ADV
ap-2099	224	5	this	this	DET
ap-2099	224	6	time	time	NOUN
ap-2099	224	7	we	we	PRON
ap-2099	224	8	have	have	AUX
ap-2099	224	9	obtained	obtain	VERB
ap-2099	224	10	the	the	DET
ap-2099	224	11	representation	representation	NOUN
ap-2099	224	12	of	of	ADP
ap-2099	224	13	the	the	DET
ap-2099	224	14	so(3	so(3	NOUN
ap-2099	224	15	,	,	PUNCT
ap-2099	224	16	1	1	X
ap-2099	224	17	)	)	PUNCT
ap-2099	224	18	algebra	algebra	NOUN
ap-2099	224	19	.	.	PUNCT
ap-2099	225	1	the	the	DET
ap-2099	225	2	relevant	relevant	ADJ
ap-2099	225	3	normalized	normalize	VERB
ap-2099	225	4	casimir	casimir	NOUN
ap-2099	225	5	operators	operator	NOUN
ap-2099	225	6	are	be	AUX
ap-2099	225	7	ĉ1	ĉ1	X
ap-2099	226	1	=	=	SYM
ap-2099	226	2	l̂jk̂j	l̂jk̂j	INTJ
ap-2099	226	3	,	,	PUNCT
ap-2099	226	4	ĉ2	ĉ2	PROPN
ap-2099	226	5	=	=	PUNCT
ap-2099	227	1	k̂ik̂i	k̂ik̂i	PROPN
ap-2099	227	2	−	−	PROPN
ap-2099	227	3	l̂il̂i	l̂il̂i	PROPN
ap-2099	227	4	.	.	PUNCT
ap-2099	228	1	(	(	PUNCT
ap-2099	228	2	51	51	NUM
ap-2099	228	3	)	)	PUNCT
ap-2099	228	4	in	in	ADP
ap-2099	228	5	our	our	PRON
ap-2099	228	6	case	case	NOUN
ap-2099	228	7	ĉ1	ĉ1	NOUN
ap-2099	228	8	=	=	SYM
ap-2099	228	9	0	0	NUM
ap-2099	228	10	,	,	PUNCT
ap-2099	228	11	so	so	SCONJ
ap-2099	228	12	we	we	PRON
ap-2099	228	13	are	be	AUX
ap-2099	228	14	dealing	deal	VERB
ap-2099	228	15	with	with	ADP
ap-2099	228	16	so(3	so(3	NOUN
ap-2099	228	17	,	,	PUNCT
ap-2099	228	18	1	1	NUM
ap-2099	228	19	)	)	PUNCT
ap-2099	228	20	unitary	unitary	ADJ
ap-2099	228	21	representations	representation	NOUN
ap-2099	228	22	that	that	PRON
ap-2099	228	23	are	be	AUX
ap-2099	228	24	labeled	label	VERB
ap-2099	228	25	by	by	ADP
ap-2099	228	26	the	the	DET
ap-2099	228	27	value	value	NOUN
ap-2099	228	28	of	of	ADP
ap-2099	228	29	second	second	ADJ
ap-2099	228	30	casimir	casimir	NOUN
ap-2099	228	31	operator	operator	NOUN
ap-2099	228	32	ĉ2	ĉ2	PROPN
ap-2099	228	33	.	.	PUNCT
ap-2099	229	1	rewriting	rewrite	VERB
ap-2099	229	2	(	(	PUNCT
ap-2099	229	3	38	38	NUM
ap-2099	229	4	)	)	PUNCT
ap-2099	229	5	in	in	ADP
ap-2099	229	6	terms	term	NOUN
ap-2099	229	7	of	of	ADP
ap-2099	229	8	k̂j	k̂j	PRON
ap-2099	229	9	we	we	PRON
ap-2099	229	10	obtain	obtain	VERB
ap-2099	229	11	relation	relation	NOUN
ap-2099	229	12	between	between	ADP
ap-2099	229	13	energy	energy	NOUN
ap-2099	229	14	e	e	NOUN
ap-2099	229	15	and	and	CCONJ
ap-2099	229	16	the	the	DET
ap-2099	229	17	eigenvalue	eigenvalue	PROPN
ap-2099	229	18	τ	τ	PROPN
ap-2099	229	19	of	of	ADP
ap-2099	229	20	ĉ2	ĉ2	PROPN
ap-2099	229	21	:	:	PUNCT
ap-2099	230	1	k̂ik̂i	k̂ik̂i	PROPN
ap-2099	230	2	−	−	PROPN
ap-2099	230	3	l̂il̂i	l̂il̂i	PROPN
ap-2099	230	4	=	=	SYM
ap-2099	230	5	1	1	NUM
ap-2099	230	6	+	+	NUM
ap-2099	230	7	q2	q2	NOUN
ap-2099	230	8	2e	2e	NOUN
ap-2099	230	9	−	−	PROPN
ap-2099	231	1	λ2e2	λ2e2	PROPN
ap-2099	232	1	=	=	SYM
ap-2099	233	1	τ	τ	X
ap-2099	234	1	>	>	X
ap-2099	235	1	1	1	NUM
ap-2099	235	2	.	.	PUNCT
ap-2099	235	3	(	(	PUNCT
ap-2099	235	4	52	52	NUM
ap-2099	235	5	)	)	PUNCT
ap-2099	235	6	thus	thus	ADV
ap-2099	235	7	we	we	PRON
ap-2099	235	8	are	be	AUX
ap-2099	235	9	dealing	deal	VERB
ap-2099	235	10	with	with	ADP
ap-2099	235	11	the	the	DET
ap-2099	235	12	spherical	spherical	ADJ
ap-2099	235	13	principal	principal	ADJ
ap-2099	235	14	series	series	NOUN
ap-2099	235	15	of	of	ADP
ap-2099	235	16	so(3	so(3	PROPN
ap-2099	235	17	,	,	PUNCT
ap-2099	235	18	1	1	NUM
ap-2099	235	19	)	)	PUNCT
ap-2099	235	20	unitary	unitary	ADJ
ap-2099	235	21	representations	representation	NOUN
ap-2099	235	22	,	,	PUNCT
ap-2099	235	23	see	see	VERB
ap-2099	235	24	e.g	e.g	PROPN
ap-2099	236	1	[	[	X
ap-2099	236	2	11	11	NUM
ap-2099	236	3	]	]	PUNCT
ap-2099	236	4	.	.	PUNCT
ap-2099	237	1	the	the	DET
ap-2099	237	2	scattering	scatter	VERB
ap-2099	237	3	nc	nc	PROPN
ap-2099	237	4	wave	wave	PROPN
ap-2099	237	5	functions	function	NOUN
ap-2099	237	6	have	have	AUX
ap-2099	237	7	been	be	AUX
ap-2099	237	8	constructed	construct	VERB
ap-2099	237	9	in	in	ADP
ap-2099	237	10	[	[	X
ap-2099	237	11	9	9	NUM
ap-2099	237	12	]	]	PUNCT
ap-2099	237	13	for	for	ADP
ap-2099	237	14	any	any	DET
ap-2099	237	15	admissible	admissible	ADJ
ap-2099	237	16	energy	energy	NOUN
ap-2099	237	17	e	e	NOUN
ap-2099	237	18	∈	∈	PROPN
ap-2099	237	19	(	(	PUNCT
ap-2099	237	20	0	0	NUM
ap-2099	237	21	,	,	PUNCT
ap-2099	237	22	2	2	NUM
ap-2099	237	23	/	/	SYM
ap-2099	237	24	λ2	λ2	NOUN
ap-2099	237	25	)	)	PUNCT
ap-2099	237	26	,	,	PUNCT
ap-2099	237	27	and	and	CCONJ
ap-2099	237	28	from	from	ADP
ap-2099	237	29	their	their	PRON
ap-2099	237	30	asymptotic	asymptotic	ADJ
ap-2099	237	31	behavior	behavior	NOUN
ap-2099	237	32	the	the	DET
ap-2099	237	33	partial	partial	ADJ
ap-2099	237	34	wave	wave	NOUN
ap-2099	237	35	s	s	NOUN
ap-2099	237	36	-	-	NOUN
ap-2099	237	37	matrix	matrix	NOUN
ap-2099	237	38	has	have	AUX
ap-2099	237	39	been	be	AUX
ap-2099	237	40	derived	derive	VERB
ap-2099	237	41	sλj	sλj	NOUN
ap-2099	237	42	(	(	PUNCT
ap-2099	237	43	e	e	NOUN
ap-2099	237	44	)	)	PUNCT
ap-2099	237	45	=	=	NOUN
ap-2099	238	1	γ(j	γ(j	NOUN
ap-2099	238	2	+	+	CCONJ
ap-2099	238	3	1−	1−	NUM
ap-2099	238	4	i	i	PRON
ap-2099	238	5	qp	qp	ADV
ap-2099	238	6	)	)	PUNCT
ap-2099	239	1	γ(j	γ(j	NOUN
ap-2099	239	2	+	+	CCONJ
ap-2099	239	3	1	1	NUM
ap-2099	239	4	+	+	NUM
ap-2099	239	5	i	i	PRON
ap-2099	239	6	qp	qp	ADV
ap-2099	239	7	)	)	PUNCT
ap-2099	239	8	,	,	PUNCT
ap-2099	239	9	p	p	NOUN
ap-2099	239	10	=	=	NOUN
ap-2099	239	11	√	√	PROPN
ap-2099	239	12	2e	2e	NUM
ap-2099	239	13	−	−	PROPN
ap-2099	239	14	λ2e2	λ2e2	PROPN
ap-2099	239	15	.	.	PUNCT
ap-2099	240	1	(	(	PUNCT
ap-2099	240	2	53	53	NUM
ap-2099	240	3	)	)	PUNCT
ap-2099	240	4	it	it	PRON
ap-2099	240	5	can	can	AUX
ap-2099	240	6	be	be	AUX
ap-2099	240	7	easily	easily	ADV
ap-2099	240	8	seen	see	VERB
ap-2099	240	9	that	that	SCONJ
ap-2099	240	10	such	such	ADJ
ap-2099	240	11	s	s	NOUN
ap-2099	240	12	-	-	PUNCT
ap-2099	240	13	matrix	matrix	NOUN
ap-2099	240	14	possesses	possesse	NOUN
ap-2099	240	15	poles	pole	NOUN
ap-2099	240	16	at	at	ADP
ap-2099	240	17	energies	energy	NOUN
ap-2099	240	18	e	e	X
ap-2099	240	19	=	=	PUNCT
ap-2099	240	20	eiλn	eiλn	PROPN
ap-2099	240	21	for	for	ADP
ap-2099	240	22	coulomb	coulomb	NOUN
ap-2099	240	23	attractive	attractive	ADJ
ap-2099	240	24	potential	potential	NOUN
ap-2099	240	25	and	and	CCONJ
ap-2099	240	26	poles	pole	NOUN
ap-2099	240	27	at	at	ADP
ap-2099	240	28	energies	energy	NOUN
ap-2099	240	29	e	e	NOUN
ap-2099	240	30	=	=	SYM
ap-2099	240	31	eiiλn	eiiλn	PROPN
ap-2099	240	32	for	for	ADP
ap-2099	240	33	coulomb	coulomb	NOUN
ap-2099	240	34	repulsive	repulsive	ADJ
ap-2099	240	35	potential	potential	NOUN
ap-2099	240	36	,	,	PUNCT
ap-2099	240	37	where	where	SCONJ
ap-2099	240	38	both	both	DET
ap-2099	240	39	eiλn	eiλn	NOUN
ap-2099	240	40	and	and	CCONJ
ap-2099	240	41	eiiλn	eiiλn	PROPN
ap-2099	240	42	coincide	coincide	NOUN
ap-2099	240	43	with	with	ADP
ap-2099	240	44	(	(	PUNCT
ap-2099	240	45	44	44	NUM
ap-2099	240	46	)	)	PUNCT
ap-2099	240	47	and	and	CCONJ
ap-2099	240	48	(	(	PUNCT
ap-2099	240	49	47	47	NUM
ap-2099	240	50	)	)	PUNCT
ap-2099	240	51	given	give	VERB
ap-2099	240	52	above	above	ADV
ap-2099	240	53	.	.	PUNCT
ap-2099	241	1	as	as	ADP
ap-2099	241	2	for	for	ADP
ap-2099	241	3	energies	energy	NOUN
ap-2099	241	4	eλ∓	eλ∓	ADJ
ap-2099	241	5	=	=	SYM
ap-2099	241	6	1	1	NUM
ap-2099	241	7	λ2	λ2	NOUN
ap-2099	241	8	(	(	PUNCT
ap-2099	241	9	1∓	1∓	NOUN
ap-2099	241	10	√	√	ADP
ap-2099	241	11	1−	1−	NUM
ap-2099	241	12	λ2q2	λ2q2	NOUN
ap-2099	241	13	τ	τ	PROPN
ap-2099	241	14	−	−	PROPN
ap-2099	241	15	1	1	NUM
ap-2099	241	16	)	)	PUNCT
ap-2099	241	17	(	(	PUNCT
ap-2099	241	18	54	54	NUM
ap-2099	241	19	)	)	PUNCT
ap-2099	241	20	the	the	DET
ap-2099	241	21	casimir	casimir	NOUN
ap-2099	241	22	operator	operator	NOUN
ap-2099	241	23	values	value	NOUN
ap-2099	241	24	coincide	coincide	NOUN
ap-2099	241	25	,	,	PUNCT
ap-2099	241	26	the	the	DET
ap-2099	241	27	corresponding	corresponding	ADJ
ap-2099	241	28	representations	representation	NOUN
ap-2099	241	29	are	be	AUX
ap-2099	241	30	unitarily	unitarily	ADV
ap-2099	241	31	equivalent	equivalent	ADJ
ap-2099	241	32	.	.	PUNCT
ap-2099	242	1	this	this	PRON
ap-2099	242	2	relates	relate	VERB
ap-2099	242	3	the	the	DET
ap-2099	242	4	scattering	scattering	NOUN
ap-2099	242	5	for	for	ADP
ap-2099	242	6	low	low	ADJ
ap-2099	242	7	energies	energy	NOUN
ap-2099	242	8	0	0	PUNCT
ap-2099	242	9	<	<	X
ap-2099	242	10	e	e	X
ap-2099	242	11	<	<	X
ap-2099	242	12	1	1	NUM
ap-2099	242	13	/	/	SYM
ap-2099	242	14	λ2	λ2	NOUN
ap-2099	242	15	to	to	ADP
ap-2099	242	16	that	that	PRON
ap-2099	242	17	at	at	ADP
ap-2099	242	18	high	high	ADJ
ap-2099	242	19	energies	energy	NOUN
ap-2099	242	20	1	1	NUM
ap-2099	242	21	/	/	SYM
ap-2099	242	22	λ2	λ2	NOUN
ap-2099	242	23	<	<	X
ap-2099	242	24	e	e	X
ap-2099	242	25	<	<	X
ap-2099	242	26	2	2	NUM
ap-2099	242	27	/	/	SYM
ap-2099	242	28	λ2	λ2	NOUN
ap-2099	242	29	.	.	PUNCT
ap-2099	243	1	we	we	PRON
ap-2099	243	2	skip	skip	VERB
ap-2099	243	3	the	the	DET
ap-2099	243	4	limiting	limit	VERB
ap-2099	243	5	cases	case	NOUN
ap-2099	243	6	of	of	ADP
ap-2099	243	7	the	the	DET
ap-2099	243	8	scattering	scattering	NOUN
ap-2099	243	9	at	at	ADP
ap-2099	243	10	the	the	DET
ap-2099	243	11	edges	edge	NOUN
ap-2099	243	12	e	e	NOUN
ap-2099	243	13	=	=	SYM
ap-2099	243	14	0	0	PUNCT
ap-2099	243	15	and	and	CCONJ
ap-2099	243	16	e	e	X
ap-2099	243	17	=	=	SYM
ap-2099	243	18	2	2	NUM
ap-2099	243	19	/	/	SYM
ap-2099	243	20	λ2	λ2	NOUN
ap-2099	243	21	of	of	ADP
ap-2099	243	22	the	the	DET
ap-2099	243	23	admissible	admissible	ADJ
ap-2099	243	24	interval	interval	NOUN
ap-2099	243	25	of	of	ADP
ap-2099	243	26	energies	energy	NOUN
ap-2099	243	27	,	,	PUNCT
ap-2099	243	28	where	where	SCONJ
ap-2099	243	29	the	the	DET
ap-2099	243	30	so(3	so(3	NOUN
ap-2099	243	31	,	,	PUNCT
ap-2099	243	32	1	1	NUM
ap-2099	243	33	)	)	PUNCT
ap-2099	243	34	group	group	NOUN
ap-2099	243	35	contracts	contract	NOUN
ap-2099	243	36	to	to	ADP
ap-2099	243	37	the	the	DET
ap-2099	243	38	euclidean	euclidean	ADJ
ap-2099	243	39	group	group	NOUN
ap-2099	243	40	e(3	e(3	PROPN
ap-2099	243	41	)	)	PUNCT
ap-2099	244	1	=	=	SYM
ap-2099	244	2	so(3	so(3	NOUN
ap-2099	244	3	)	)	PUNCT
ap-2099	244	4	.	.	PUNCT
ap-2099	245	1	t	t	PROPN
ap-2099	245	2	(	(	PUNCT
ap-2099	245	3	3	3	NUM
ap-2099	245	4	)	)	PUNCT
ap-2099	245	5	of	of	ADP
ap-2099	245	6	isometries	isometry	NOUN
ap-2099	245	7	of	of	ADP
ap-2099	245	8	3d	3d	NUM
ap-2099	245	9	space	space	NOUN
ap-2099	245	10	.	.	PUNCT
ap-2099	246	1	the	the	DET
ap-2099	246	2	corresponding	corresponding	PROPN
ap-2099	246	3	nc	nc	PROPN
ap-2099	246	4	hamiltonian	hamiltonian	PROPN
ap-2099	246	5	eigenstates	eigenstate	NOUN
ap-2099	246	6	are	be	AUX
ap-2099	246	7	given	give	VERB
ap-2099	246	8	in	in	ADP
ap-2099	246	9	[	[	PUNCT
ap-2099	246	10	9	9	NUM
ap-2099	246	11	]	]	SYM
ap-2099	246	12	.	.	PUNCT
ap-2099	247	1	4	4	X
ap-2099	247	2	.	.	X
ap-2099	247	3	conclusions	conclusion	NOUN
ap-2099	247	4	this	this	DET
ap-2099	247	5	paper	paper	NOUN
ap-2099	247	6	deals	deal	NOUN
ap-2099	247	7	with	with	ADP
ap-2099	247	8	the	the	DET
ap-2099	247	9	coulomb	coulomb	NOUN
ap-2099	247	10	-	-	PUNCT
ap-2099	247	11	kepler	kepler	NOUN
ap-2099	247	12	problem	problem	NOUN
ap-2099	247	13	in	in	ADP
ap-2099	247	14	noncommutative	noncommutative	ADJ
ap-2099	247	15	space	space	NOUN
ap-2099	247	16	.	.	PUNCT
ap-2099	248	1	we	we	PRON
ap-2099	248	2	have	have	AUX
ap-2099	248	3	found	find	VERB
ap-2099	248	4	the	the	DET
ap-2099	248	5	nc	nc	PROPN
ap-2099	248	6	analog	analog	NOUN
ap-2099	248	7	of	of	ADP
ap-2099	248	8	the	the	DET
ap-2099	248	9	lrl	lrl	PROPN
ap-2099	248	10	vector	vector	NOUN
ap-2099	248	11	;	;	PUNCT
ap-2099	248	12	its	its	PRON
ap-2099	248	13	components	component	NOUN
ap-2099	248	14	,	,	PUNCT
ap-2099	248	15	together	together	ADV
ap-2099	248	16	with	with	ADP
ap-2099	248	17	those	those	PRON
ap-2099	248	18	of	of	ADP
ap-2099	248	19	the	the	DET
ap-2099	248	20	nc	nc	PROPN
ap-2099	248	21	angular	angular	ADJ
ap-2099	248	22	momentum	momentum	NOUN
ap-2099	248	23	operator	operator	NOUN
ap-2099	248	24	,	,	PUNCT
ap-2099	248	25	supply	supply	VERB
ap-2099	248	26	the	the	DET
ap-2099	248	27	algebra	algebra	NOUN
ap-2099	248	28	of	of	ADP
ap-2099	248	29	generators	generator	NOUN
ap-2099	248	30	of	of	ADP
ap-2099	248	31	a	a	DET
ap-2099	248	32	symmetry	symmetry	NOUN
ap-2099	248	33	group	group	NOUN
ap-2099	248	34	.	.	PUNCT
ap-2099	249	1	it	it	PRON
ap-2099	249	2	is	be	AUX
ap-2099	249	3	interesting	interesting	ADJ
ap-2099	249	4	that	that	SCONJ
ap-2099	249	5	the	the	DET
ap-2099	249	6	formula	formula	NOUN
ap-2099	249	7	for	for	ADP
ap-2099	249	8	the	the	DET
ap-2099	249	9	nc	nc	PROPN
ap-2099	249	10	version	version	PROPN
ap-2099	249	11	of	of	ADP
ap-2099	249	12	the	the	DET
ap-2099	249	13	lrl	lrl	PROPN
ap-2099	249	14	vector	vector	NOUN
ap-2099	249	15	looks	look	VERB
ap-2099	249	16	very	very	ADV
ap-2099	249	17	much	much	ADV
ap-2099	249	18	like	like	ADP
ap-2099	249	19	the	the	DET
ap-2099	249	20	one	one	NOUN
ap-2099	249	21	from	from	ADP
ap-2099	249	22	standard	standard	PROPN
ap-2099	249	23	qm	qm	PROPN
ap-2099	249	24	,	,	PUNCT
ap-2099	249	25	that	that	ADV
ap-2099	249	26	is	is	ADV
ap-2099	249	27	,	,	PUNCT
ap-2099	249	28	when	when	SCONJ
ap-2099	249	29	written	write	VERB
ap-2099	249	30	in	in	ADP
ap-2099	249	31	terms	term	NOUN
ap-2099	249	32	of	of	ADP
ap-2099	249	33	the	the	DET
ap-2099	249	34	proper	proper	ADJ
ap-2099	249	35	nc	nc	PROPN
ap-2099	249	36	observables	observable	NOUN
ap-2099	249	37	:	:	PUNCT
ap-2099	249	38	nc	nc	PROPN
ap-2099	249	39	angular	angular	PROPN
ap-2099	249	40	momentum	momentum	PROPN
ap-2099	249	41	,	,	PUNCT
ap-2099	249	42	nc	nc	PROPN
ap-2099	249	43	velocity	velocity	PROPN
ap-2099	249	44	,	,	PUNCT
ap-2099	249	45	symmetrized	symmetrize	VERB
ap-2099	249	46	nc	nc	PROPN
ap-2099	249	47	coordinate	coordinate	PROPN
ap-2099	249	48	and	and	CCONJ
ap-2099	249	49	nc	nc	PROPN
ap-2099	249	50	radial	radial	ADJ
ap-2099	249	51	distance	distance	NOUN
ap-2099	249	52	.	.	PUNCT
ap-2099	250	1	it	it	PRON
ap-2099	250	2	is	be	AUX
ap-2099	250	3	quite	quite	ADV
ap-2099	250	4	remarkable	remarkable	ADJ
ap-2099	250	5	that	that	SCONJ
ap-2099	250	6	the	the	DET
ap-2099	250	7	so(4	so(4	PROPN
ap-2099	250	8	)	)	PUNCT
ap-2099	250	9	symmetry	symmetry	NOUN
ap-2099	250	10	has	have	AUX
ap-2099	250	11	appeared	appear	VERB
ap-2099	250	12	twice	twice	ADV
ap-2099	250	13	:	:	PUNCT
ap-2099	250	14	firstly	firstly	ADV
ap-2099	250	15	,	,	PUNCT
ap-2099	250	16	not	not	PART
ap-2099	250	17	so	so	ADV
ap-2099	250	18	surprisingly	surprisingly	ADV
ap-2099	250	19	,	,	PUNCT
ap-2099	250	20	when	when	SCONJ
ap-2099	250	21	addressing	address	VERB
ap-2099	250	22	the	the	DET
ap-2099	250	23	problem	problem	NOUN
ap-2099	250	24	of	of	ADP
ap-2099	250	25	the	the	DET
ap-2099	250	26	bound	bind	VERB
ap-2099	250	27	states	state	NOUN
ap-2099	250	28	for	for	ADP
ap-2099	250	29	negative	negative	ADJ
ap-2099	250	30	energies	energy	NOUN
ap-2099	250	31	in	in	ADP
ap-2099	250	32	the	the	DET
ap-2099	250	33	case	case	NOUN
ap-2099	250	34	of	of	ADP
ap-2099	250	35	the	the	DET
ap-2099	250	36	attractive	attractive	ADJ
ap-2099	250	37	coulomb	coulomb	NOUN
ap-2099	250	38	potential	potential	NOUN
ap-2099	250	39	.	.	PUNCT
ap-2099	251	1	these	these	PRON
ap-2099	251	2	have	have	VERB
ap-2099	251	3	an	an	DET
ap-2099	251	4	analog	analog	NOUN
ap-2099	251	5	in	in	ADP
ap-2099	251	6	standard	standard	ADJ
ap-2099	251	7	quantum	quantum	ADJ
ap-2099	251	8	mechanics	mechanic	NOUN
ap-2099	251	9	,	,	PUNCT
ap-2099	251	10	and	and	CCONJ
ap-2099	251	11	our	our	PRON
ap-2099	251	12	result	result	NOUN
ap-2099	251	13	for	for	ADP
ap-2099	251	14	negative	negative	ADJ
ap-2099	251	15	energy	energy	NOUN
ap-2099	251	16	bound	bind	VERB
ap-2099	251	17	states	state	NOUN
ap-2099	251	18	indeed	indeed	ADV
ap-2099	251	19	coincides	coincide	VERB
ap-2099	251	20	with	with	ADP
ap-2099	251	21	the	the	DET
ap-2099	251	22	well	well	ADV
ap-2099	251	23	known	know	VERB
ap-2099	251	24	qm	qm	PROPN
ap-2099	251	25	prediction	prediction	NOUN
ap-2099	251	26	if	if	SCONJ
ap-2099	251	27	the	the	DET
ap-2099	251	28	commutative	commutative	ADJ
ap-2099	251	29	limit	limit	NOUN
ap-2099	251	30	λ→	λ→	PUNCT
ap-2099	251	31	0	0	NUM
ap-2099	251	32	is	be	AUX
ap-2099	251	33	applied	apply	VERB
ap-2099	251	34	.	.	PUNCT
ap-2099	252	1	the	the	DET
ap-2099	252	2	second	second	ADJ
ap-2099	252	3	appearance	appearance	NOUN
ap-2099	252	4	of	of	ADP
ap-2099	252	5	the	the	DET
ap-2099	252	6	so(4	so(4	PROPN
ap-2099	252	7	)	)	PUNCT
ap-2099	252	8	symmetry	symmetry	NOUN
ap-2099	252	9	is	be	AUX
ap-2099	252	10	probably	probably	ADV
ap-2099	252	11	not	not	PART
ap-2099	252	12	so	so	ADV
ap-2099	252	13	expected	expect	VERB
ap-2099	252	14	,	,	PUNCT
ap-2099	252	15	for	for	SCONJ
ap-2099	252	16	we	we	PRON
ap-2099	252	17	have	have	AUX
ap-2099	252	18	found	find	VERB
ap-2099	252	19	a	a	DET
ap-2099	252	20	set	set	NOUN
ap-2099	252	21	of	of	ADP
ap-2099	252	22	bound	bind	VERB
ap-2099	252	23	states	state	NOUN
ap-2099	252	24	for	for	ADP
ap-2099	252	25	positive	positive	ADJ
ap-2099	252	26	energies	energy	NOUN
ap-2099	252	27	above	above	ADP
ap-2099	252	28	a	a	DET
ap-2099	252	29	certain	certain	ADJ
ap-2099	252	30	ultra	ultra	ADJ
ap-2099	252	31	-	-	ADJ
ap-2099	252	32	high	high	ADJ
ap-2099	252	33	value	value	NOUN
ap-2099	252	34	in	in	ADP
ap-2099	252	35	the	the	DET
ap-2099	252	36	case	case	NOUN
ap-2099	252	37	that	that	SCONJ
ap-2099	252	38	the	the	DET
ap-2099	252	39	potential	potential	NOUN
ap-2099	252	40	is	be	AUX
ap-2099	252	41	repulsive	repulsive	ADJ
ap-2099	252	42	.	.	PUNCT
ap-2099	253	1	however	however	ADV
ap-2099	253	2	,	,	PUNCT
ap-2099	253	3	there	there	PRON
ap-2099	253	4	is	be	VERB
ap-2099	253	5	again	again	ADV
ap-2099	253	6	no	no	DET
ap-2099	253	7	discrepancy	discrepancy	NOUN
ap-2099	253	8	between	between	ADP
ap-2099	253	9	qm	qm	PROPN
ap-2099	253	10	and	and	CCONJ
ap-2099	253	11	ncqm	ncqm	VERB
ap-2099	253	12	,	,	PUNCT
ap-2099	253	13	since	since	SCONJ
ap-2099	253	14	the	the	DET
ap-2099	253	15	unexpected	unexpected	ADJ
ap-2099	253	16	ultra	ultra	ADJ
ap-2099	253	17	-	-	ADJ
ap-2099	253	18	high	high	ADJ
ap-2099	253	19	energy	energy	NOUN
ap-2099	253	20	bound	bind	VERB
ap-2099	253	21	states	state	NOUN
ap-2099	253	22	disappear	disappear	VERB
ap-2099	253	23	from	from	ADP
ap-2099	253	24	the	the	DET
ap-2099	253	25	hilbert	hilbert	NOUN
ap-2099	253	26	space	space	NOUN
ap-2099	253	27	in	in	ADP
ap-2099	253	28	the	the	DET
ap-2099	253	29	above	above	ADJ
ap-2099	253	30	mentioned	mention	VERB
ap-2099	253	31	commutative	commutative	ADJ
ap-2099	253	32	limit	limit	NOUN
ap-2099	253	33	.	.	PUNCT
ap-2099	254	1	when	when	SCONJ
ap-2099	254	2	examining	examine	VERB
ap-2099	254	3	the	the	DET
ap-2099	254	4	scattering	scattering	NOUN
ap-2099	254	5	(	(	PUNCT
ap-2099	254	6	relevant	relevant	ADJ
ap-2099	254	7	for	for	ADP
ap-2099	254	8	the	the	DET
ap-2099	254	9	interval	interval	NOUN
ap-2099	254	10	of	of	ADP
ap-2099	254	11	energies	energy	NOUN
ap-2099	254	12	between	between	ADP
ap-2099	254	13	zero	zero	NUM
ap-2099	254	14	and	and	CCONJ
ap-2099	254	15	the	the	DET
ap-2099	254	16	mentioned	mention	VERB
ap-2099	254	17	critical	critical	ADJ
ap-2099	254	18	ultra	ultra	ADJ
ap-2099	254	19	-	-	ADJ
ap-2099	254	20	high	high	ADJ
ap-2099	254	21	value	value	NOUN
ap-2099	254	22	)	)	PUNCT
ap-2099	254	23	,	,	PUNCT
ap-2099	254	24	so(3	so(3	NOUN
ap-2099	254	25	,	,	PUNCT
ap-2099	254	26	1	1	NUM
ap-2099	254	27	)	)	PUNCT
ap-2099	254	28	is	be	AUX
ap-2099	254	29	the	the	DET
ap-2099	254	30	symmetry	symmetry	NOUN
ap-2099	254	31	to	to	PART
ap-2099	254	32	be	be	AUX
ap-2099	254	33	considered	consider	VERB
ap-2099	254	34	.	.	PUNCT
ap-2099	255	1	the	the	DET
ap-2099	255	2	scattering	scattering	NOUN
ap-2099	255	3	is	be	AUX
ap-2099	255	4	usually	usually	ADV
ap-2099	255	5	characterized	characterize	VERB
ap-2099	255	6	by	by	ADP
ap-2099	255	7	the	the	DET
ap-2099	255	8	s	s	NOUN
ap-2099	255	9	-	-	NOUN
ap-2099	255	10	matrix	matrix	NOUN
ap-2099	255	11	.	.	PUNCT
ap-2099	256	1	in	in	ADP
ap-2099	256	2	the	the	DET
ap-2099	256	3	nc	nc	PROPN
ap-2099	256	4	version	version	NOUN
ap-2099	256	5	of	of	ADP
ap-2099	256	6	the	the	DET
ap-2099	256	7	problem	problem	NOUN
ap-2099	256	8	this	this	DET
ap-2099	256	9	object	object	NOUN
ap-2099	256	10	has	have	VERB
ap-2099	256	11	exactly	exactly	ADV
ap-2099	256	12	those	those	DET
ap-2099	256	13	poles	pole	NOUN
ap-2099	256	14	in	in	ADP
ap-2099	256	15	complex	complex	ADJ
ap-2099	256	16	energy	energy	NOUN
ap-2099	256	17	plane	plane	NOUN
ap-2099	256	18	which	which	PRON
ap-2099	256	19	correspond	correspond	VERB
ap-2099	256	20	to	to	ADP
ap-2099	256	21	the	the	DET
ap-2099	256	22	bound	bind	VERB
ap-2099	256	23	states	state	NOUN
ap-2099	256	24	(	(	PUNCT
ap-2099	256	25	of	of	ADP
ap-2099	256	26	both	both	DET
ap-2099	256	27	kinds	kind	NOUN
ap-2099	256	28	)	)	PUNCT
ap-2099	256	29	mentioned	mention	VERB
ap-2099	256	30	above	above	ADV
ap-2099	256	31	.	.	PUNCT
ap-2099	257	1	this	this	PRON
ap-2099	257	2	goes	go	VERB
ap-2099	257	3	,	,	PUNCT
ap-2099	257	4	however	however	ADV
ap-2099	257	5	,	,	PUNCT
ap-2099	257	6	beyond	beyond	ADP
ap-2099	257	7	the	the	DET
ap-2099	257	8	scope	scope	NOUN
ap-2099	257	9	of	of	ADP
ap-2099	257	10	this	this	DET
ap-2099	257	11	paper	paper	NOUN
ap-2099	257	12	.	.	PUNCT
ap-2099	258	1	to	to	PART
ap-2099	258	2	summarize	summarize	VERB
ap-2099	258	3	,	,	PUNCT
ap-2099	258	4	there	there	PRON
ap-2099	258	5	are	be	VERB
ap-2099	258	6	basically	basically	ADV
ap-2099	258	7	two	two	NUM
ap-2099	258	8	ways	way	NOUN
ap-2099	258	9	of	of	ADP
ap-2099	258	10	examining	examine	VERB
ap-2099	258	11	the	the	DET
ap-2099	258	12	hydrogen	hydrogen	NOUN
ap-2099	258	13	energy	energy	NOUN
ap-2099	258	14	spectrum	spectrum	NOUN
ap-2099	258	15	:	:	PUNCT
ap-2099	258	16	by	by	ADP
ap-2099	258	17	solving	solve	VERB
ap-2099	258	18	some	some	DET
ap-2099	258	19	differential	differential	ADJ
ap-2099	258	20	equation	equation	NOUN
ap-2099	258	21	in	in	ADP
ap-2099	258	22	schrödinger	schrödinger	ADJ
ap-2099	258	23	fashion	fashion	NOUN
ap-2099	258	24	or	or	CCONJ
ap-2099	258	25	by	by	ADP
ap-2099	258	26	looking	look	VERB
ap-2099	258	27	for	for	ADP
ap-2099	258	28	an	an	DET
ap-2099	258	29	underlying	underlie	VERB
ap-2099	258	30	symmetry	symmetry	NOUN
ap-2099	258	31	and	and	CCONJ
ap-2099	258	32	using	use	VERB
ap-2099	258	33	an	an	DET
ap-2099	258	34	algebraic	algebraic	ADJ
ap-2099	258	35	approach	approach	NOUN
ap-2099	258	36	à	à	X
ap-2099	258	37	la	la	PROPN
ap-2099	258	38	pauli	pauli	PROPN
ap-2099	258	39	.	.	PUNCT
ap-2099	259	1	both	both	DET
ap-2099	259	2	possibilities	possibility	NOUN
ap-2099	259	3	were	be	AUX
ap-2099	259	4	tried	try	VERB
ap-2099	259	5	in	in	ADP
ap-2099	259	6	ncqm	ncqm	NOUN
ap-2099	259	7	(	(	PUNCT
ap-2099	259	8	the	the	DET
ap-2099	259	9	aim	aim	NOUN
ap-2099	259	10	of	of	ADP
ap-2099	259	11	this	this	DET
ap-2099	259	12	paper	paper	NOUN
ap-2099	259	13	has	have	AUX
ap-2099	259	14	been	be	AUX
ap-2099	259	15	mainly	mainly	ADV
ap-2099	259	16	to	to	PART
ap-2099	259	17	provide	provide	VERB
ap-2099	259	18	some	some	DET
ap-2099	259	19	outline	outline	NOUN
ap-2099	259	20	of	of	ADP
ap-2099	259	21	the	the	DET
ap-2099	259	22	latter	latter	ADJ
ap-2099	259	23	option	option	NOUN
ap-2099	259	24	)	)	PUNCT
ap-2099	259	25	,	,	PUNCT
ap-2099	259	26	for	for	SCONJ
ap-2099	259	27	details	detail	NOUN
ap-2099	259	28	see	see	VERB
ap-2099	259	29	[	[	X
ap-2099	259	30	7	7	NUM
ap-2099	259	31	]	]	PUNCT
ap-2099	259	32	,	,	PUNCT
ap-2099	260	1	[	[	X
ap-2099	260	2	9	9	NUM
ap-2099	260	3	]	]	PUNCT
ap-2099	260	4	.	.	PUNCT
ap-2099	261	1	we	we	PRON
ap-2099	261	2	are	be	AUX
ap-2099	261	3	glad	glad	ADJ
ap-2099	261	4	to	to	PART
ap-2099	261	5	find	find	VERB
ap-2099	261	6	out	out	ADP
ap-2099	261	7	that	that	SCONJ
ap-2099	261	8	both	both	DET
ap-2099	261	9	approaches	approach	NOUN
ap-2099	261	10	(	(	PUNCT
ap-2099	261	11	agreeing	agree	VERB
ap-2099	261	12	in	in	ADP
ap-2099	261	13	standard	standard	PROPN
ap-2099	261	14	qm	qm	PROPN
ap-2099	261	15	)	)	PUNCT
ap-2099	261	16	lead	lead	VERB
ap-2099	261	17	to	to	ADP
ap-2099	261	18	the	the	DET
ap-2099	261	19	same	same	ADJ
ap-2099	261	20	outcomes	outcome	NOUN
ap-2099	261	21	also	also	ADV
ap-2099	261	22	in	in	ADP
ap-2099	261	23	ncqm	ncqm	NOUN
ap-2099	261	24	.	.	PUNCT
ap-2099	262	1	acknowledgements	acknowledgement	VERB
ap-2099	262	2	the	the	DET
ap-2099	262	3	author	author	NOUN
ap-2099	262	4	v.	v.	ADP
ap-2099	262	5	g.	g.	PROPN
ap-2099	262	6	is	be	AUX
ap-2099	262	7	indebted	indebte	VERB
ap-2099	262	8	to	to	ADP
ap-2099	262	9	comenius	comenius	VERB
ap-2099	262	10	university	university	NOUN
ap-2099	262	11	for	for	ADP
ap-2099	262	12	support	support	NOUN
ap-2099	262	13	received	receive	VERB
ap-2099	262	14	from	from	ADP
ap-2099	262	15	grant	grant	NOUN
ap-2099	262	16	no	no	NOUN
ap-2099	262	17	.	.	PUNCT
ap-2099	263	1	uk/545/2013	uk/545/2013	PROPN
ap-2099	263	2	.	.	PROPN
ap-2099	263	3	references	reference	NOUN
ap-2099	264	1	[	[	X
ap-2099	264	2	1	1	NUM
ap-2099	264	3	]	]	PUNCT
ap-2099	264	4	jakob	jakob	PROPN
ap-2099	264	5	hermann	hermann	PROPN
ap-2099	264	6	,	,	PUNCT
ap-2099	264	7	giornale	giornale	PROPN
ap-2099	264	8	de	de	X
ap-2099	264	9	letterati	letterati	PROPN
ap-2099	264	10	d’italia	d’italia	PROPN
ap-2099	264	11	2	2	NUM
ap-2099	264	12	(	(	PUNCT
ap-2099	264	13	1710	1710	NUM
ap-2099	264	14	)	)	PUNCT
ap-2099	264	15	447	447	NUM
ap-2099	264	16	;	;	PUNCT
ap-2099	264	17	jakob	jakob	PROPN
ap-2099	264	18	hermann	hermann	PROPN
ap-2099	264	19	,	,	PUNCT
ap-2099	264	20	extrait	extrait	NOUN
ap-2099	264	21	d’une	d’une	NUM
ap-2099	264	22	lettre	lettre	PROPN
ap-2099	264	23	de	de	PROPN
ap-2099	264	24	m.	m.	PROPN
ap-2099	264	25	herman	herman	PROPN
ap-2099	264	26	à	à	PROPN
ap-2099	264	27	m.	m.	PROPN
ap-2099	264	28	bernoulli	bernoulli	PROPN
ap-2099	264	29	datée	datée	PROPN
ap-2099	264	30	de	de	PROPN
ap-2099	264	31	padoüe	padoüe	PROPN
ap-2099	264	32	le	le	PROPN
ap-2099	264	33	12	12	NUM
ap-2099	264	34	.	.	PUNCT
ap-2099	265	1	juillet	juillet	PROPN
ap-2099	265	2	1710	1710	NUM
ap-2099	265	3	,	,	PUNCT
ap-2099	265	4	histoire	histoire	PROPN
ap-2099	265	5	de	de	X
ap-2099	265	6	l’academie	l’academie	VERB
ap-2099	265	7	royale	royale	PROPN
ap-2099	265	8	des	des	PROPN
ap-2099	265	9	sciences	sciences	PROPN
ap-2099	265	10	(	(	PUNCT
ap-2099	265	11	paris	paris	PROPN
ap-2099	265	12	)	)	PUNCT
ap-2099	265	13	1732	1732	NUM
ap-2099	265	14	:	:	PUNCT
ap-2099	265	15	519	519	NUM
ap-2099	265	16	;	;	PUNCT
ap-2099	265	17	154	154	NUM
ap-2099	265	18	vol	vol	NOUN
ap-2099	265	19	.	.	PUNCT
ap-2099	266	1	54	54	NUM
ap-2099	266	2	no	no	NOUN
ap-2099	266	3	.	.	PUNCT
ap-2099	267	1	2/2014	2/2014	NUM
ap-2099	267	2	lrl	lrl	PROPN
ap-2099	267	3	vector	vector	NOUN
ap-2099	267	4	in	in	ADP
ap-2099	267	5	quantum	quantum	ADJ
ap-2099	267	6	mechanics	mechanic	NOUN
ap-2099	267	7	in	in	ADP
ap-2099	267	8	noncommutative	noncommutative	ADJ
ap-2099	267	9	space	space	NOUN
ap-2099	267	10	[	[	X
ap-2099	267	11	2	2	NUM
ap-2099	267	12	]	]	X
ap-2099	267	13	johann	johann	PROPN
ap-2099	267	14	bernoulli	bernoulli	PROPN
ap-2099	267	15	,	,	PUNCT
ap-2099	267	16	extrait	extrait	NOUN
ap-2099	267	17	de	de	X
ap-2099	267	18	la	la	X
ap-2099	267	19	réponse	réponse	PROPN
ap-2099	267	20	de	de	PROPN
ap-2099	267	21	m.	m.	PROPN
ap-2099	267	22	bernoulli	bernoulli	PROPN
ap-2099	267	23	à	à	X
ap-2099	268	1	m.	m.	PROPN
ap-2099	268	2	herman	herman	PROPN
ap-2099	268	3	datée	datée	PROPN
ap-2099	268	4	de	de	PROPN
ap-2099	268	5	basle	basle	PROPN
ap-2099	268	6	le	le	PROPN
ap-2099	268	7	7	7	X
ap-2099	268	8	.	.	PUNCT
ap-2099	268	9	octobre	octobre	PROPN
ap-2099	268	10	1710	1710	NUM
ap-2099	268	11	,	,	PUNCT
ap-2099	268	12	histoire	histoire	PROPN
ap-2099	268	13	de	de	X
ap-2099	268	14	l’academie	l’academie	VERB
ap-2099	268	15	royale	royale	PROPN
ap-2099	268	16	des	des	PROPN
ap-2099	268	17	sciences	sciences	PROPN
ap-2099	268	18	(	(	PUNCT
ap-2099	268	19	paris	paris	PROPN
ap-2099	268	20	)	)	PUNCT
ap-2099	268	21	1732	1732	NUM
ap-2099	268	22	:	:	PUNCT
ap-2099	268	23	521	521	NUM
ap-2099	268	24	.	.	PUNCT
ap-2099	269	1	[	[	X
ap-2099	269	2	3	3	X
ap-2099	269	3	]	]	PUNCT
ap-2099	269	4	p.	p.	NOUN
ap-2099	269	5	s.	s.	PROPN
ap-2099	269	6	laplace	laplace	PROPN
ap-2099	269	7	,	,	PUNCT
ap-2099	269	8	traité	traité	X
ap-2099	269	9	de	de	X
ap-2099	269	10	mécanique	mécanique	PROPN
ap-2099	269	11	céleste	céleste	PROPN
ap-2099	269	12	,	,	PUNCT
ap-2099	269	13	tome	tome	NOUN
ap-2099	269	14	i	i	PRON
ap-2099	269	15	(	(	PUNCT
ap-2099	269	16	1799	1799	NUM
ap-2099	269	17	)	)	PUNCT
ap-2099	269	18	,	,	PUNCT
ap-2099	269	19	premiere	premiere	ADJ
ap-2099	269	20	partie	partie	NOUN
ap-2099	269	21	,	,	PUNCT
ap-2099	269	22	livre	livre	PROPN
ap-2099	269	23	ii	ii	PROPN
ap-2099	269	24	,	,	PUNCT
ap-2099	269	25	pp.165ff	pp.165ff	NOUN
ap-2099	269	26	.	.	PUNCT
ap-2099	270	1	[	[	X
ap-2099	270	2	4	4	NUM
ap-2099	270	3	]	]	X
ap-2099	270	4	c.	c.	NOUN
ap-2099	270	5	runge	runge	PROPN
ap-2099	270	6	,	,	PUNCT
ap-2099	270	7	vektoranalysis	vektoranalysis	NOUN
ap-2099	270	8	,	,	PUNCT
ap-2099	270	9	volume	volume	NOUN
ap-2099	270	10	i	i	PROPN
ap-2099	270	11	,	,	PUNCT
ap-2099	270	12	leipzig	leipzig	PROPN
ap-2099	270	13	hirzel	hirzel	PROPN
ap-2099	270	14	(	(	PUNCT
ap-2099	270	15	1919	1919	NUM
ap-2099	270	16	)	)	PUNCT
ap-2099	270	17	.	.	PUNCT
ap-2099	271	1	[	[	X
ap-2099	271	2	5	5	X
ap-2099	271	3	]	]	PUNCT
ap-2099	271	4	w.	w.	PROPN
ap-2099	271	5	lenz	lenz	PROPN
ap-2099	271	6	,	,	PUNCT
ap-2099	271	7	zeitschrift	zeitschrift	PROPN
ap-2099	271	8	für	für	PROPN
ap-2099	271	9	physik	physik	PROPN
ap-2099	271	10	24	24	NUM
ap-2099	271	11	(	(	PUNCT
ap-2099	271	12	1924	1924	NUM
ap-2099	271	13	)	)	PUNCT
ap-2099	271	14	197	197	NUM
ap-2099	271	15	,	,	PUNCT
ap-2099	271	16	über	über	PROPN
ap-2099	271	17	den	den	PROPN
ap-2099	271	18	bewegungsverlauf	bewegungsverlauf	PROPN
ap-2099	271	19	und	und	NOUN
ap-2099	271	20	quantenzustände	quantenzustände	ADJ
ap-2099	271	21	der	der	NOUN
ap-2099	271	22	gestörten	gestörten	PROPN
ap-2099	271	23	keplerbewegung	keplerbewegung	PROPN
ap-2099	271	24	.	.	PUNCT
ap-2099	272	1	[	[	X
ap-2099	272	2	6	6	NUM
ap-2099	272	3	]	]	PUNCT
ap-2099	272	4	w.	w.	PROPN
ap-2099	272	5	pauli	pauli	PROPN
ap-2099	272	6	,	,	PUNCT
ap-2099	272	7	zeitschrift	zeitschrift	PROPN
ap-2099	272	8	für	für	PROPN
ap-2099	272	9	physik	physik	PROPN
ap-2099	272	10	36	36	NUM
ap-2099	272	11	(	(	PUNCT
ap-2099	272	12	1926	1926	NUM
ap-2099	272	13	)	)	PUNCT
ap-2099	272	14	336	336	NUM
ap-2099	272	15	,	,	PUNCT
ap-2099	272	16	über	über	PROPN
ap-2099	272	17	das	das	PROPN
ap-2099	272	18	wasserstoffspektrum	wasserstoffspektrum	PROPN
ap-2099	272	19	vom	vom	PROPN
ap-2099	272	20	standpunkt	standpunkt	PROPN
ap-2099	272	21	der	der	PROPN
ap-2099	272	22	neuen	neuen	NOUN
ap-2099	272	23	quantenmechanik	quantenmechanik	X
ap-2099	272	24	.	.	PUNCT
ap-2099	273	1	[	[	X
ap-2099	273	2	7	7	X
ap-2099	273	3	]	]	X
ap-2099	273	4	veronika	veronika	X
ap-2099	273	5	gáliková	gáliková	PROPN
ap-2099	273	6	,	,	PUNCT
ap-2099	273	7	s.	s.	PROPN
ap-2099	273	8	kováčik	kováčik	PROPN
ap-2099	273	9	and	and	CCONJ
ap-2099	273	10	p.	p.	PROPN
ap-2099	273	11	prešnajder	prešnajder	NOUN
ap-2099	273	12	,	,	PUNCT
ap-2099	273	13	laplace	laplace	NOUN
ap-2099	273	14	-	-	PUNCT
ap-2099	273	15	rung	rung	NOUN
ap-2099	273	16	-	-	PUNCT
ap-2099	273	17	lenz	lenz	PROPN
ap-2099	273	18	vector	vector	NOUN
ap-2099	273	19	in	in	ADP
ap-2099	273	20	quantum	quantum	ADJ
ap-2099	273	21	mechanics	mechanic	NOUN
ap-2099	273	22	in	in	ADP
ap-2099	273	23	noncommutative	noncommutative	ADJ
ap-2099	273	24	space	space	NOUN
ap-2099	273	25	j.	j.	PROPN
ap-2099	273	26	math	math	PROPN
ap-2099	273	27	.	.	PUNCT
ap-2099	274	1	phys	phy	NOUN
ap-2099	274	2	.	.	PUNCT
ap-2099	275	1	54	54	NUM
ap-2099	275	2	,	,	PUNCT
ap-2099	275	3	122106	122106	NUM
ap-2099	275	4	(	(	PUNCT
ap-2099	275	5	2013	2013	NUM
ap-2099	275	6	)	)	PUNCT
ap-2099	275	7	doi	doi	NOUN
ap-2099	275	8	:	:	PUNCT
ap-2099	275	9	10.1063/1.4835615	10.1063/1.4835615	NUM
ap-2099	275	10	[	[	NOUN
ap-2099	275	11	8	8	NUM
ap-2099	275	12	]	]	X
ap-2099	275	13	f.	f.	PROPN
ap-2099	275	14	a.	a.	PROPN
ap-2099	275	15	berezin	berezin	PROPN
ap-2099	275	16	,	,	PUNCT
ap-2099	275	17	commun	commun	PROPN
ap-2099	275	18	.	.	PUNCT
ap-2099	275	19	math	math	NOUN
ap-2099	275	20	.	.	PUNCT
ap-2099	276	1	phys	phy	NOUN
ap-2099	276	2	.	.	PUNCT
ap-2099	277	1	40	40	NUM
ap-2099	277	2	(	(	PUNCT
ap-2099	277	3	1975	1975	NUM
ap-2099	277	4	)	)	PUNCT
ap-2099	277	5	153	153	NUM
ap-2099	277	6	doi	doi	NOUN
ap-2099	277	7	:	:	PUNCT
ap-2099	277	8	1007	1007	NUM
ap-2099	277	9	/	/	SYM
ap-2099	277	10	bf01609397	bf01609397	PROPN
ap-2099	277	11	;	;	PUNCT
ap-2099	277	12	j.	j.	PROPN
ap-2099	277	13	hoppe	hoppe	PROPN
ap-2099	277	14	,	,	PUNCT
ap-2099	277	15	elem	elem	NOUN
ap-2099	277	16	.	.	PUNCT
ap-2099	278	1	part	part	NOUN
ap-2099	278	2	.	.	PUNCT
ap-2099	279	1	res	re	NOUN
ap-2099	279	2	.	.	PUNCT
ap-2099	280	1	j.	j.	PROPN
ap-2099	280	2	80	80	NUM
ap-2099	280	3	(	(	PUNCT
ap-2099	280	4	1989	1989	NUM
ap-2099	280	5	)	)	PUNCT
ap-2099	280	6	145	145	NUM
ap-2099	280	7	;	;	PUNCT
ap-2099	280	8	j.	j.	PROPN
ap-2099	280	9	madore	madore	PROPN
ap-2099	280	10	,	,	PUNCT
ap-2099	280	11	journ	journ	NOUN
ap-2099	280	12	.	.	PUNCT
ap-2099	281	1	math	math	NOUN
ap-2099	281	2	.	.	PUNCT
ap-2099	282	1	phys	phy	NOUN
ap-2099	282	2	.	.	PUNCT
ap-2099	283	1	32	32	NUM
ap-2099	283	2	(	(	PUNCT
ap-2099	283	3	1991	1991	NUM
ap-2099	283	4	)	)	PUNCT
ap-2099	283	5	332	332	NUM
ap-2099	283	6	doi	doi	NOUN
ap-2099	283	7	:	:	PUNCT
ap-2099	283	8	10.1063/1.529418	10.1063/1.529418	NUM
ap-2099	283	9	;	;	PUNCT
ap-2099	283	10	h.	h.	PROPN
ap-2099	283	11	grosse	grosse	PROPN
ap-2099	283	12	and	and	CCONJ
ap-2099	283	13	p.	p.	NOUN
ap-2099	283	14	prešnajder	prešnajder	NOUN
ap-2099	283	15	,	,	PUNCT
ap-2099	283	16	lett	lett	PROPN
ap-2099	283	17	.	.	PUNCT
ap-2099	283	18	math	math	NOUN
ap-2099	283	19	.	.	PUNCT
ap-2099	284	1	phys	phy	NOUN
ap-2099	284	2	.	.	PUNCT
ap-2099	285	1	28	28	NUM
ap-2099	285	2	(	(	PUNCT
ap-2099	285	3	1993	1993	NUM
ap-2099	285	4	)	)	PUNCT
ap-2099	285	5	239	239	NUM
ap-2099	285	6	doi	doi	NOUN
ap-2099	285	7	:	:	PUNCT
ap-2099	285	8	10.1007	10.1007	NUM
ap-2099	285	9	/	/	SYM
ap-2099	285	10	bf00745155	bf00745155	PROPN
ap-2099	285	11	;	;	PUNCT
ap-2099	285	12	h.	h.	PROPN
ap-2099	285	13	grosse	grosse	PROPN
ap-2099	285	14	,	,	PUNCT
ap-2099	285	15	c.	c.	NOUN
ap-2099	285	16	klimčík	klimčík	PROPN
ap-2099	285	17	and	and	CCONJ
ap-2099	285	18	p.	p.	NOUN
ap-2099	285	19	prešnajder	prešnajder	NOUN
ap-2099	285	20	,	,	PUNCT
ap-2099	285	21	int	int	NOUN
ap-2099	285	22	.	.	PUNCT
ap-2099	286	1	j.	j.	PROPN
ap-2099	286	2	theor	theor	PROPN
ap-2099	286	3	.	.	PUNCT
ap-2099	287	1	phys	phy	NOUN
ap-2099	287	2	.	.	PUNCT
ap-2099	288	1	35	35	NUM
ap-2099	288	2	(	(	PUNCT
ap-2099	288	3	1996	1996	NUM
ap-2099	288	4	)	)	PUNCT
ap-2099	288	5	231	231	NUM
ap-2099	288	6	doi	doi	NOUN
ap-2099	288	7	:	:	PUNCT
ap-2099	288	8	10.1007	10.1007	NUM
ap-2099	288	9	/	/	SYM
ap-2099	288	10	bf02083810	bf02083810	NOUN
ap-2099	288	11	.	.	PUNCT
ap-2099	289	1	[	[	X
ap-2099	289	2	9	9	NUM
ap-2099	289	3	]	]	X
ap-2099	289	4	veronika	veronika	X
ap-2099	289	5	gáliková	gáliková	PROPN
ap-2099	289	6	and	and	CCONJ
ap-2099	289	7	peter	peter	PROPN
ap-2099	289	8	prešnajder	prešnajder	NOUN
ap-2099	289	9	,	,	PUNCT
ap-2099	289	10	coulomb	coulomb	NOUN
ap-2099	289	11	problem	problem	NOUN
ap-2099	289	12	in	in	ADP
ap-2099	289	13	non	non	ADJ
ap-2099	289	14	-	-	ADJ
ap-2099	289	15	commutative	commutative	ADJ
ap-2099	289	16	quantum	quantum	ADJ
ap-2099	289	17	mechanics	mechanic	NOUN
ap-2099	289	18	j.	j.	PROPN
ap-2099	289	19	math	math	PROPN
ap-2099	289	20	.	.	PUNCT
ap-2099	290	1	phys	phy	NOUN
ap-2099	290	2	.	.	PUNCT
ap-2099	291	1	54	54	NUM
ap-2099	291	2	,	,	PUNCT
ap-2099	291	3	052102	052102	NUM
ap-2099	291	4	(	(	PUNCT
ap-2099	291	5	2013	2013	NUM
ap-2099	291	6	)	)	PUNCT
ap-2099	291	7	doi	doi	NOUN
ap-2099	291	8	:	:	PUNCT
ap-2099	291	9	10.1063/4803457	10.1063/4803457	NUM
ap-2099	291	10	;	;	PUNCT
ap-2099	292	1	[	[	X
ap-2099	292	2	10	10	NUM
ap-2099	292	3	]	]	X
ap-2099	292	4	s.	s.	PROPN
ap-2099	292	5	kováčik	kováčik	PROPN
ap-2099	292	6	and	and	CCONJ
ap-2099	292	7	p.	p.	PROPN
ap-2099	292	8	prešnajder	prešnajder	NOUN
ap-2099	292	9	,	,	PUNCT
ap-2099	292	10	the	the	DET
ap-2099	292	11	velocity	velocity	NOUN
ap-2099	292	12	operator	operator	NOUN
ap-2099	292	13	in	in	ADP
ap-2099	292	14	quantum	quantum	ADJ
ap-2099	292	15	mechanics	mechanic	NOUN
ap-2099	292	16	in	in	ADP
ap-2099	292	17	noncommutative	noncommutative	ADJ
ap-2099	292	18	space	space	NOUN
ap-2099	292	19	,	,	PUNCT
ap-2099	292	20	j.	j.	PROPN
ap-2099	292	21	math	math	PROPN
ap-2099	292	22	.	.	PUNCT
ap-2099	293	1	phys	phy	NOUN
ap-2099	293	2	.	.	PUNCT
ap-2099	294	1	54	54	NUM
ap-2099	294	2	,	,	PUNCT
ap-2099	294	3	102103	102103	NUM
ap-2099	294	4	(	(	PUNCT
ap-2099	294	5	2013	2013	NUM
ap-2099	294	6	)	)	PUNCT
ap-2099	294	7	doi	doi	NOUN
ap-2099	294	8	:	:	PUNCT
ap-2099	294	9	1063/1.4826355	1063/1.4826355	NUM
ap-2099	294	10	;	;	PUNCT
ap-2099	294	11	[	[	X
ap-2099	294	12	11	11	NUM
ap-2099	294	13	]	]	PUNCT
ap-2099	294	14	a.	a.	NOUN
ap-2099	294	15	o.	o.	NOUN
ap-2099	294	16	barut	barut	PROPN
ap-2099	294	17	and	and	CCONJ
ap-2099	294	18	r.	r.	PROPN
ap-2099	294	19	raçzka	raçzka	PROPN
ap-2099	294	20	,	,	PUNCT
ap-2099	294	21	theory	theory	NOUN
ap-2099	294	22	of	of	ADP
ap-2099	294	23	group	group	NOUN
ap-2099	294	24	representations	representation	NOUN
ap-2099	294	25	and	and	CCONJ
ap-2099	294	26	applications	application	NOUN
ap-2099	294	27	,	,	PUNCT
ap-2099	294	28	polish	polish	ADJ
ap-2099	294	29	scientific	scientific	ADJ
ap-2099	294	30	publishers	publisher	NOUN
ap-2099	294	31	,	,	PUNCT
ap-2099	294	32	1977	1977	NUM
ap-2099	294	33	.	.	PUNCT
ap-2099	295	1	155	155	NUM
ap-2099	295	2	http://dx.doi.org/10.1063/1.4835615	http://dx.doi.org/10.1063/1.4835615	NOUN
ap-2099	295	3	http://dx.doi.org/1007/bf01609397	http://dx.doi.org/1007/bf01609397	ADJ
ap-2099	295	4	http://dx.doi.org/10.1063/1.529418	http://dx.doi.org/10.1063/1.529418	NOUN
ap-2099	295	5	http://dx.doi.org/10.1007/bf00745155	http://dx.doi.org/10.1007/bf00745155	PROPN
ap-2099	295	6	http://dx.doi.org/10.1007/bf02083810	http://dx.doi.org/10.1007/bf02083810	PROPN
ap-2099	295	7	http://dx.doi.org/10.1063/4803457	http://dx.doi.org/10.1063/4803457	PROPN
ap-2099	295	8	http://dx.doi.org/1063/1.4826355	http://dx.doi.org/1063/1.4826355	PROPN
ap-2099	295	9	acta	acta	PROPN
ap-2099	295	10	polytechnica	polytechnica	PROPN
ap-2099	295	11	54(2):149–155	54(2):149–155	PROPN
ap-2099	295	12	,	,	PUNCT
ap-2099	295	13	2014	2014	NUM
ap-2099	295	14	1	1	NUM
ap-2099	295	15	introduction	introduction	NOUN
ap-2099	295	16	2	2	NUM
ap-2099	295	17	basics	basic	NOUN
ap-2099	295	18	of	of	ADP
ap-2099	295	19	noncommutative	noncommutative	ADJ
ap-2099	295	20	quantum	quantum	ADJ
ap-2099	295	21	mechanics	mechanic	NOUN
ap-2099	295	22	3	3	NUM
ap-2099	295	23	dynamical	dynamical	ADJ
ap-2099	295	24	symmetry	symmetry	NOUN
ap-2099	295	25	in	in	ADP
ap-2099	295	26	ncqm	ncqm	PROPN
ap-2099	295	27	3.1	3.1	NUM
ap-2099	295	28	auxiliary	auxiliary	ADJ
ap-2099	295	29	operators	operator	NOUN
ap-2099	295	30	3.2	3.2	NUM
ap-2099	295	31	nc	nc	PROPN
ap-2099	295	32	operators	operator	NOUN
ap-2099	295	33	revisited	revisit	VERB
ap-2099	295	34	3.3	3.3	NUM
ap-2099	295	35	bound	bind	VERB
ap-2099	295	36	states	state	NOUN
ap-2099	295	37	3.4	3.4	NUM
ap-2099	295	38	coulomb	coulomb	NOUN
ap-2099	295	39	scattering	scatter	VERB
ap-2099	295	40	4	4	NUM
ap-2099	295	41	conclusions	conclusion	NOUN
ap-2099	295	42	acknowledgements	acknowledgement	NOUN
ap-2099	295	43	references	reference	NOUN