id	sid	tid	token	lemma	pos
ap-9818	1	1	acta	acta	PROPN
ap-9818	1	2	polytechnica	polytechnica	PROPN
ap-9818	1	3	https://doi.org/10.14311/ap.2025.65.0222	https://doi.org/10.14311/ap.2025.65.0222	PROPN
ap-9818	1	4	acta	acta	PROPN
ap-9818	1	5	polytechnica	polytechnica	PROPN
ap-9818	1	6	65(2):222–236	65(2):222–236	PROPN
ap-9818	1	7	,	,	PUNCT
ap-9818	1	8	2025	2025	NUM
ap-9818	1	9	©	©	ADP
ap-9818	1	10	2025	2025	NUM
ap-9818	1	11	the	the	DET
ap-9818	1	12	author(s	author(s	NOUN
ap-9818	1	13	)	)	PUNCT
ap-9818	1	14	.	.	PUNCT
ap-9818	2	1	licensed	license	VERB
ap-9818	2	2	under	under	ADP
ap-9818	2	3	a	a	DET
ap-9818	2	4	cc	cc	NOUN
ap-9818	2	5	-	-	PUNCT
ap-9818	2	6	by	by	ADP
ap-9818	2	7	4.0	4.0	NUM
ap-9818	2	8	licence	licence	NOUN
ap-9818	2	9	published	publish	VERB
ap-9818	2	10	by	by	ADP
ap-9818	2	11	the	the	DET
ap-9818	2	12	czech	czech	PROPN
ap-9818	2	13	technical	technical	PROPN
ap-9818	2	14	university	university	PROPN
ap-9818	2	15	in	in	ADP
ap-9818	2	16	prague	prague	PROPN
ap-9818	2	17	persistence	persistence	NOUN
ap-9818	2	18	of	of	ADP
ap-9818	2	19	solvability	solvability	NOUN
ap-9818	2	20	in	in	ADP
ap-9818	2	21	quantum	quantum	NOUN
ap-9818	2	22	systems	system	NOUN
ap-9818	2	23	deformed	deform	VERB
ap-9818	2	24	by	by	ADP
ap-9818	2	25	dunkl	dunkl	NOUN
ap-9818	2	26	operators	operator	NOUN
ap-9818	2	27	axel	axel	VERB
ap-9818	2	28	schulze	schulze	PROPN
ap-9818	2	29	-	-	PUNCT
ap-9818	2	30	halberg	halberg	PROPN
ap-9818	2	31	indiana	indiana	PROPN
ap-9818	2	32	university	university	PROPN
ap-9818	2	33	northwest	northwest	NOUN
ap-9818	2	34	,	,	PUNCT
ap-9818	2	35	department	department	NOUN
ap-9818	2	36	of	of	ADP
ap-9818	2	37	mathematics	mathematic	NOUN
ap-9818	2	38	and	and	CCONJ
ap-9818	2	39	actuarial	actuarial	ADJ
ap-9818	2	40	science	science	NOUN
ap-9818	2	41	,	,	PUNCT
ap-9818	2	42	and	and	CCONJ
ap-9818	2	43	department	department	NOUN
ap-9818	2	44	of	of	ADP
ap-9818	2	45	physics	physics	PROPN
ap-9818	2	46	,	,	PUNCT
ap-9818	2	47	3400	3400	NUM
ap-9818	2	48	broadway	broadway	NOUN
ap-9818	2	49	,	,	PUNCT
ap-9818	2	50	gary	gary	PROPN
ap-9818	2	51	in	in	ADP
ap-9818	2	52	46408	46408	NUM
ap-9818	2	53	,	,	PUNCT
ap-9818	2	54	united	united	PROPN
ap-9818	2	55	states	states	PROPN
ap-9818	2	56	of	of	ADP
ap-9818	2	57	america	america	PROPN
ap-9818	2	58	correspondence	correspondence	NOUN
ap-9818	2	59	:	:	PUNCT
ap-9818	2	60	axgeschu@iu.edu	axgeschu@iu.edu	X
ap-9818	2	61	abstract	abstract	ADJ
ap-9818	2	62	.	.	PUNCT
ap-9818	3	1	we	we	PRON
ap-9818	3	2	study	study	VERB
ap-9818	3	3	persistence	persistence	NOUN
ap-9818	3	4	of	of	ADP
ap-9818	3	5	solvability	solvability	NOUN
ap-9818	3	6	in	in	ADP
ap-9818	3	7	nonrelativistic	nonrelativistic	ADJ
ap-9818	3	8	quantum	quantum	NOUN
ap-9818	3	9	systems	system	NOUN
ap-9818	3	10	with	with	ADP
ap-9818	3	11	positiondependent	positiondependent	ADJ
ap-9818	3	12	mass	mass	NOUN
ap-9818	3	13	upon	upon	SCONJ
ap-9818	3	14	introduction	introduction	NOUN
ap-9818	3	15	of	of	ADP
ap-9818	3	16	a	a	DET
ap-9818	3	17	deformation	deformation	NOUN
ap-9818	3	18	by	by	ADP
ap-9818	3	19	dunkl	dunkl	NOUN
ap-9818	3	20	operators	operator	NOUN
ap-9818	3	21	.	.	PUNCT
ap-9818	4	1	conditions	condition	NOUN
ap-9818	4	2	are	be	AUX
ap-9818	4	3	derived	derive	VERB
ap-9818	4	4	for	for	ADP
ap-9818	4	5	the	the	DET
ap-9818	4	6	governing	govern	VERB
ap-9818	4	7	schrödinger	schrödinger	ADJ
ap-9818	4	8	equation	equation	NOUN
ap-9818	4	9	of	of	ADP
ap-9818	4	10	the	the	DET
ap-9818	4	11	conventional	conventional	ADJ
ap-9818	4	12	system	system	NOUN
ap-9818	4	13	to	to	PART
ap-9818	4	14	admit	admit	VERB
ap-9818	4	15	the	the	DET
ap-9818	4	16	same	same	ADJ
ap-9818	4	17	solutions	solution	NOUN
ap-9818	4	18	as	as	ADP
ap-9818	4	19	in	in	ADP
ap-9818	4	20	the	the	DET
ap-9818	4	21	deformed	deform	VERB
ap-9818	4	22	case	case	NOUN
ap-9818	4	23	,	,	PUNCT
ap-9818	4	24	up	up	ADP
ap-9818	4	25	to	to	ADP
ap-9818	4	26	a	a	DET
ap-9818	4	27	reparametrisation	reparametrisation	NOUN
ap-9818	4	28	of	of	ADP
ap-9818	4	29	coupling	coupling	NOUN
ap-9818	4	30	constants	constant	NOUN
ap-9818	4	31	.	.	PUNCT
ap-9818	5	1	these	these	DET
ap-9818	5	2	conditions	condition	NOUN
ap-9818	5	3	require	require	VERB
ap-9818	5	4	the	the	DET
ap-9818	5	5	positiondependent	positiondependent	ADJ
ap-9818	5	6	mass	mass	NOUN
ap-9818	5	7	or	or	CCONJ
ap-9818	5	8	the	the	DET
ap-9818	5	9	potential	potential	NOUN
ap-9818	5	10	of	of	ADP
ap-9818	5	11	the	the	DET
ap-9818	5	12	system	system	NOUN
ap-9818	5	13	to	to	PART
ap-9818	5	14	have	have	VERB
ap-9818	5	15	a	a	DET
ap-9818	5	16	specific	specific	ADJ
ap-9818	5	17	form	form	NOUN
ap-9818	5	18	.	.	PUNCT
ap-9818	6	1	if	if	SCONJ
ap-9818	6	2	this	this	PRON
ap-9818	6	3	is	be	AUX
ap-9818	6	4	the	the	DET
ap-9818	6	5	case	case	NOUN
ap-9818	6	6	for	for	ADP
ap-9818	6	7	a	a	DET
ap-9818	6	8	particular	particular	ADJ
ap-9818	6	9	system	system	NOUN
ap-9818	6	10	,	,	PUNCT
ap-9818	6	11	then	then	ADV
ap-9818	6	12	the	the	DET
ap-9818	6	13	schrödinger	schrödinger	ADJ
ap-9818	6	14	equations	equation	NOUN
ap-9818	6	15	for	for	ADP
ap-9818	6	16	its	its	PRON
ap-9818	6	17	conventional	conventional	ADJ
ap-9818	6	18	version	version	NOUN
ap-9818	6	19	and	and	CCONJ
ap-9818	6	20	for	for	ADP
ap-9818	6	21	the	the	DET
ap-9818	6	22	dunkl	dunkl	NOUN
ap-9818	6	23	-	-	PUNCT
ap-9818	6	24	deformed	deform	VERB
ap-9818	6	25	partner	partner	NOUN
ap-9818	6	26	share	share	NOUN
ap-9818	6	27	solutions	solution	NOUN
ap-9818	6	28	in	in	ADP
ap-9818	6	29	the	the	DET
ap-9818	6	30	same	same	ADJ
ap-9818	6	31	functional	functional	ADJ
ap-9818	6	32	form	form	NOUN
ap-9818	6	33	.	.	PUNCT
ap-9818	7	1	keywords	keyword	NOUN
ap-9818	7	2	:	:	PUNCT
ap-9818	7	3	schrödinger	schrödinger	ADJ
ap-9818	7	4	equation	equation	NOUN
ap-9818	7	5	,	,	PUNCT
ap-9818	7	6	dunkl	dunkl	NOUN
ap-9818	7	7	operator	operator	NOUN
ap-9818	7	8	,	,	PUNCT
ap-9818	7	9	bound	bind	VERB
ap-9818	7	10	states	state	NOUN
ap-9818	7	11	,	,	PUNCT
ap-9818	7	12	position	position	NOUN
ap-9818	7	13	-	-	PUNCT
ap-9818	7	14	dependent	dependent	ADJ
ap-9818	7	15	mass	mass	NOUN
ap-9818	7	16	.	.	PUNCT
ap-9818	8	1	1	1	X
ap-9818	8	2	.	.	X
ap-9818	8	3	introduction	introduction	NOUN
ap-9818	8	4	in	in	ADP
ap-9818	8	5	1950	1950	NUM
ap-9818	8	6	,	,	PUNCT
ap-9818	8	7	it	it	PRON
ap-9818	8	8	was	be	AUX
ap-9818	8	9	found	find	VERB
ap-9818	8	10	that	that	SCONJ
ap-9818	8	11	the	the	DET
ap-9818	8	12	fundamental	fundamental	ADJ
ap-9818	8	13	quantum	quantum	ADJ
ap-9818	8	14	-	-	ADJ
ap-9818	8	15	mechanical	mechanical	ADJ
ap-9818	8	16	commutation	commutation	NOUN
ap-9818	8	17	relations	relation	NOUN
ap-9818	8	18	are	be	AUX
ap-9818	8	19	not	not	PART
ap-9818	8	20	uniquely	uniquely	ADV
ap-9818	8	21	determined	determine	VERB
ap-9818	8	22	by	by	ADP
ap-9818	8	23	the	the	DET
ap-9818	8	24	equations	equation	NOUN
ap-9818	8	25	of	of	ADP
ap-9818	8	26	motion	motion	NOUN
ap-9818	8	27	[	[	X
ap-9818	8	28	1	1	NUM
ap-9818	8	29	]	]	PUNCT
ap-9818	8	30	.	.	PUNCT
ap-9818	9	1	this	this	DET
ap-9818	9	2	result	result	NOUN
ap-9818	9	3	,	,	PUNCT
ap-9818	9	4	obtained	obtain	VERB
ap-9818	9	5	for	for	ADP
ap-9818	9	6	the	the	DET
ap-9818	9	7	harmonic	harmonic	ADJ
ap-9818	9	8	oscillator	oscillator	NOUN
ap-9818	9	9	system	system	NOUN
ap-9818	9	10	,	,	PUNCT
ap-9818	9	11	allowed	allow	VERB
ap-9818	9	12	for	for	ADP
ap-9818	9	13	a	a	DET
ap-9818	9	14	generalised	generalised	ADJ
ap-9818	9	15	definition	definition	NOUN
ap-9818	9	16	of	of	ADP
ap-9818	9	17	the	the	DET
ap-9818	9	18	momentum	momentum	NOUN
ap-9818	9	19	operator	operator	NOUN
ap-9818	9	20	involving	involve	VERB
ap-9818	9	21	space	space	NOUN
ap-9818	9	22	reflections	reflection	NOUN
ap-9818	9	23	[	[	X
ap-9818	9	24	2	2	NUM
ap-9818	9	25	]	]	PUNCT
ap-9818	9	26	.	.	PUNCT
ap-9818	10	1	further	further	ADJ
ap-9818	10	2	extensions	extension	NOUN
ap-9818	10	3	of	of	ADP
ap-9818	10	4	these	these	DET
ap-9818	10	5	findings	finding	NOUN
ap-9818	10	6	concern	concern	NOUN
ap-9818	10	7	the	the	DET
ap-9818	10	8	introduction	introduction	NOUN
ap-9818	10	9	of	of	ADP
ap-9818	10	10	parafield	parafield	ADJ
ap-9818	10	11	quantisation	quantisation	NOUN
ap-9818	10	12	[	[	X
ap-9818	10	13	3	3	NUM
ap-9818	10	14	,	,	PUNCT
ap-9818	10	15	4	4	NUM
ap-9818	10	16	]	]	PUNCT
ap-9818	10	17	and	and	CCONJ
ap-9818	10	18	related	related	ADJ
ap-9818	10	19	applications	application	NOUN
ap-9818	10	20	,	,	PUNCT
ap-9818	10	21	see	see	VERB
ap-9818	10	22	,	,	PUNCT
ap-9818	10	23	for	for	ADP
ap-9818	10	24	example	example	NOUN
ap-9818	10	25	,	,	PUNCT
ap-9818	10	26	[	[	X
ap-9818	10	27	5–7	5–7	X
ap-9818	10	28	]	]	PUNCT
ap-9818	10	29	and	and	CCONJ
ap-9818	10	30	references	reference	NOUN
ap-9818	10	31	within	within	ADP
ap-9818	10	32	.	.	PUNCT
ap-9818	11	1	independent	independent	ADJ
ap-9818	11	2	of	of	ADP
ap-9818	11	3	these	these	DET
ap-9818	11	4	studies	study	NOUN
ap-9818	11	5	that	that	PRON
ap-9818	11	6	go	go	VERB
ap-9818	11	7	back	back	ADV
ap-9818	11	8	to	to	ADP
ap-9818	11	9	the	the	DET
ap-9818	11	10	initial	initial	ADJ
ap-9818	11	11	work	work	NOUN
ap-9818	11	12	[	[	X
ap-9818	11	13	1	1	NUM
ap-9818	11	14	]	]	PUNCT
ap-9818	11	15	,	,	PUNCT
ap-9818	11	16	in	in	ADP
ap-9818	11	17	1989	1989	NUM
ap-9818	11	18	the	the	DET
ap-9818	11	19	concept	concept	NOUN
ap-9818	11	20	of	of	ADP
ap-9818	11	21	dunkl	dunkl	PROPN
ap-9818	11	22	operators	operator	NOUN
ap-9818	11	23	was	be	AUX
ap-9818	11	24	introduced	introduce	VERB
ap-9818	11	25	[	[	X
ap-9818	11	26	8	8	NUM
ap-9818	11	27	]	]	PUNCT
ap-9818	11	28	.	.	PUNCT
ap-9818	12	1	these	these	DET
ap-9818	12	2	operators	operator	NOUN
ap-9818	12	3	are	be	AUX
ap-9818	12	4	parametrised	parametrise	VERB
ap-9818	12	5	generalisations	generalisation	NOUN
ap-9818	12	6	of	of	ADP
ap-9818	12	7	directional	directional	ADJ
ap-9818	12	8	derivatives	derivative	NOUN
ap-9818	12	9	that	that	PRON
ap-9818	12	10	involve	involve	VERB
ap-9818	12	11	reflection	reflection	NOUN
ap-9818	12	12	operators	operator	NOUN
ap-9818	12	13	.	.	PUNCT
ap-9818	13	1	it	it	PRON
ap-9818	13	2	turned	turn	VERB
ap-9818	13	3	out	out	ADP
ap-9818	13	4	that	that	SCONJ
ap-9818	13	5	dunkl	dunkl	PROPN
ap-9818	13	6	operators	operator	NOUN
ap-9818	13	7	have	have	VERB
ap-9818	13	8	a	a	DET
ap-9818	13	9	large	large	ADJ
ap-9818	13	10	amount	amount	NOUN
ap-9818	13	11	of	of	ADP
ap-9818	13	12	applications	application	NOUN
ap-9818	13	13	,	,	PUNCT
ap-9818	13	14	such	such	ADJ
ap-9818	13	15	as	as	ADP
ap-9818	13	16	in	in	ADP
ap-9818	13	17	quantum	quantum	NOUN
ap-9818	13	18	-	-	PUNCT
ap-9818	13	19	integrable	integrable	ADJ
ap-9818	13	20	calogero	calogero	PROPN
ap-9818	13	21	-	-	PUNCT
ap-9818	13	22	moser	moser	PROPN
ap-9818	13	23	-	-	PUNCT
ap-9818	13	24	sutherland	sutherland	PROPN
ap-9818	13	25	systems	system	NOUN
ap-9818	14	1	[	[	X
ap-9818	14	2	9	9	NUM
ap-9818	14	3	]	]	PUNCT
ap-9818	14	4	,	,	PUNCT
ap-9818	14	5	the	the	DET
ap-9818	14	6	higher	higher	ADV
ap-9818	14	7	-	-	PUNCT
ap-9818	14	8	dimensional	dimensional	ADJ
ap-9818	14	9	schrödinger	schrödinger	ADJ
ap-9818	14	10	case	case	NOUN
ap-9818	14	11	[	[	X
ap-9818	14	12	10	10	NUM
ap-9818	14	13	]	]	PUNCT
ap-9818	14	14	,	,	PUNCT
ap-9818	14	15	time	time	NOUN
ap-9818	14	16	-	-	PUNCT
ap-9818	14	17	dependent	dependent	ADJ
ap-9818	14	18	problems	problem	NOUN
ap-9818	15	1	[	[	X
ap-9818	15	2	11	11	NUM
ap-9818	15	3	]	]	PUNCT
ap-9818	15	4	,	,	PUNCT
ap-9818	15	5	the	the	DET
ap-9818	15	6	path	path	NOUN
ap-9818	15	7	integral	integral	ADJ
ap-9818	15	8	formalism	formalism	NOUN
ap-9818	15	9	for	for	ADP
ap-9818	15	10	time	time	NOUN
ap-9818	15	11	-	-	PUNCT
ap-9818	15	12	dependent	dependent	ADJ
ap-9818	15	13	systems	system	NOUN
ap-9818	16	1	[	[	X
ap-9818	16	2	12	12	NUM
ap-9818	16	3	]	]	PUNCT
ap-9818	16	4	,	,	PUNCT
ap-9818	16	5	vacuum	vacuum	NOUN
ap-9818	16	6	pair	pair	NOUN
ap-9818	16	7	creation	creation	NOUN
ap-9818	16	8	[	[	X
ap-9818	16	9	13	13	NUM
ap-9818	16	10	]	]	PUNCT
ap-9818	16	11	,	,	PUNCT
ap-9818	16	12	and	and	CCONJ
ap-9818	16	13	bose	bose	NOUN
ap-9818	16	14	-	-	PUNCT
ap-9818	16	15	einstein	einstein	NOUN
ap-9818	16	16	condensation	condensation	NOUN
ap-9818	16	17	[	[	X
ap-9818	16	18	14	14	NUM
ap-9818	16	19	]	]	PUNCT
ap-9818	16	20	.	.	PUNCT
ap-9818	17	1	in	in	ADP
ap-9818	17	2	1994	1994	NUM
ap-9818	17	3	it	it	PRON
ap-9818	17	4	was	be	AUX
ap-9818	17	5	pointed	point	VERB
ap-9818	17	6	out	out	ADP
ap-9818	17	7	[	[	X
ap-9818	17	8	15	15	NUM
ap-9818	17	9	]	]	PUNCT
ap-9818	17	10	that	that	SCONJ
ap-9818	17	11	the	the	DET
ap-9818	17	12	two	two	NUM
ap-9818	17	13	concepts	concept	NOUN
ap-9818	17	14	studied	study	VERB
ap-9818	17	15	in	in	ADP
ap-9818	17	16	[	[	X
ap-9818	17	17	1	1	NUM
ap-9818	17	18	]	]	PUNCT
ap-9818	17	19	and	and	CCONJ
ap-9818	17	20	[	[	X
ap-9818	17	21	8	8	NUM
ap-9818	17	22	]	]	PUNCT
ap-9818	17	23	are	be	AUX
ap-9818	17	24	very	very	ADV
ap-9818	17	25	closely	closely	ADV
ap-9818	17	26	related	relate	VERB
ap-9818	17	27	,	,	PUNCT
ap-9818	17	28	that	that	ADV
ap-9818	17	29	is	is	ADV
ap-9818	17	30	,	,	PUNCT
ap-9818	17	31	the	the	DET
ap-9818	17	32	generalised	generalised	ADJ
ap-9818	17	33	definition	definition	NOUN
ap-9818	17	34	of	of	ADP
ap-9818	17	35	the	the	DET
ap-9818	17	36	momentum	momentum	NOUN
ap-9818	17	37	operator	operator	NOUN
ap-9818	17	38	provided	provide	VERB
ap-9818	17	39	in	in	ADP
ap-9818	17	40	[	[	X
ap-9818	17	41	2	2	NUM
ap-9818	17	42	]	]	PUNCT
ap-9818	17	43	can	can	AUX
ap-9818	17	44	be	be	AUX
ap-9818	17	45	written	write	VERB
ap-9818	17	46	in	in	ADP
ap-9818	17	47	terms	term	NOUN
ap-9818	17	48	of	of	ADP
ap-9818	17	49	dunkl	dunkl	NOUN
ap-9818	17	50	operators	operator	NOUN
ap-9818	17	51	.	.	PUNCT
ap-9818	18	1	as	as	ADP
ap-9818	18	2	such	such	ADJ
ap-9818	18	3	,	,	PUNCT
ap-9818	18	4	these	these	DET
ap-9818	18	5	operators	operator	NOUN
ap-9818	18	6	have	have	AUX
ap-9818	18	7	been	be	AUX
ap-9818	18	8	used	use	VERB
ap-9818	18	9	to	to	PART
ap-9818	18	10	construct	construct	VERB
ap-9818	18	11	deformations	deformation	NOUN
ap-9818	18	12	of	of	ADP
ap-9818	18	13	quantum	quantum	ADJ
ap-9818	18	14	mechanics	mechanic	NOUN
ap-9818	18	15	,	,	PUNCT
ap-9818	18	16	in	in	ADP
ap-9818	18	17	which	which	PRON
ap-9818	18	18	the	the	DET
ap-9818	18	19	standard	standard	ADJ
ap-9818	18	20	momentum	momentum	NOUN
ap-9818	18	21	operators	operator	NOUN
ap-9818	18	22	are	be	AUX
ap-9818	18	23	replaced	replace	VERB
ap-9818	18	24	by	by	ADP
ap-9818	18	25	generalised	generalise	VERB
ap-9818	18	26	versions	version	NOUN
ap-9818	18	27	that	that	PRON
ap-9818	18	28	involve	involve	VERB
ap-9818	18	29	dunkl	dunkl	NOUN
ap-9818	18	30	operators	operator	NOUN
ap-9818	18	31	.	.	PUNCT
ap-9818	19	1	there	there	PRON
ap-9818	19	2	is	be	VERB
ap-9818	19	3	a	a	DET
ap-9818	19	4	vast	vast	ADJ
ap-9818	19	5	amount	amount	NOUN
ap-9818	19	6	on	on	ADP
ap-9818	19	7	literature	literature	NOUN
ap-9818	19	8	about	about	ADP
ap-9818	19	9	specific	specific	ADJ
ap-9818	19	10	quantum	quantum	NOUN
ap-9818	19	11	systems	system	NOUN
ap-9818	19	12	that	that	PRON
ap-9818	19	13	were	be	AUX
ap-9818	19	14	studied	study	VERB
ap-9818	19	15	within	within	ADP
ap-9818	19	16	the	the	DET
ap-9818	19	17	dunkl	dunkl	NOUN
ap-9818	19	18	formalism	formalism	NOUN
ap-9818	19	19	.	.	PUNCT
ap-9818	20	1	recent	recent	ADJ
ap-9818	20	2	examples	example	NOUN
ap-9818	20	3	include	include	VERB
ap-9818	20	4	the	the	DET
ap-9818	20	5	massless	massless	ADJ
ap-9818	20	6	dirac	dirac	NOUN
ap-9818	20	7	equation	equation	NOUN
ap-9818	20	8	in	in	ADP
ap-9818	20	9	the	the	DET
ap-9818	20	10	graphene	graphene	NOUN
ap-9818	20	11	setting	set	VERB
ap-9818	20	12	[	[	X
ap-9818	20	13	16	16	NUM
ap-9818	20	14	]	]	PUNCT
ap-9818	20	15	,	,	PUNCT
ap-9818	20	16	rational	rational	ADJ
ap-9818	20	17	extensions	extension	NOUN
ap-9818	20	18	of	of	ADP
ap-9818	20	19	the	the	DET
ap-9818	20	20	harmonic	harmonic	ADJ
ap-9818	20	21	oscillator	oscillator	NOUN
ap-9818	20	22	system	system	NOUN
ap-9818	20	23	[	[	X
ap-9818	20	24	17	17	NUM
ap-9818	20	25	]	]	PUNCT
ap-9818	20	26	,	,	PUNCT
ap-9818	20	27	and	and	CCONJ
ap-9818	20	28	the	the	DET
ap-9818	20	29	klein	klein	PROPN
ap-9818	20	30	-	-	PUNCT
ap-9818	20	31	gordon	gordon	PROPN
ap-9818	20	32	equation	equation	NOUN
ap-9818	20	33	in	in	ADP
ap-9818	20	34	three	three	NUM
ap-9818	20	35	dimensions	dimension	NOUN
ap-9818	20	36	[	[	X
ap-9818	20	37	18	18	NUM
ap-9818	20	38	]	]	PUNCT
ap-9818	20	39	.	.	PUNCT
ap-9818	21	1	further	further	ADJ
ap-9818	21	2	applications	application	NOUN
ap-9818	21	3	of	of	ADP
ap-9818	21	4	the	the	DET
ap-9818	21	5	dunkl	dunkl	NOUN
ap-9818	21	6	formalism	formalism	NOUN
ap-9818	21	7	to	to	ADP
ap-9818	21	8	quantum	quantum	ADJ
ap-9818	21	9	systems	system	NOUN
ap-9818	21	10	are	be	AUX
ap-9818	21	11	given	give	VERB
ap-9818	21	12	by	by	ADP
ap-9818	21	13	the	the	DET
ap-9818	21	14	path	path	NOUN
ap-9818	21	15	integral	integral	ADJ
ap-9818	21	16	formulation	formulation	NOUN
ap-9818	21	17	[	[	X
ap-9818	21	18	19	19	NUM
ap-9818	21	19	]	]	PUNCT
ap-9818	21	20	,	,	PUNCT
ap-9818	21	21	the	the	DET
ap-9818	21	22	dunkl	dunkl	NOUN
ap-9818	21	23	-	-	PUNCT
ap-9818	21	24	fokker	fokker	NOUN
ap-9818	21	25	-	-	PUNCT
ap-9818	21	26	planck	planck	NOUN
ap-9818	21	27	equation	equation	NOUN
ap-9818	21	28	[	[	X
ap-9818	21	29	20	20	NUM
ap-9818	21	30	]	]	PUNCT
ap-9818	21	31	,	,	PUNCT
ap-9818	21	32	the	the	DET
ap-9818	21	33	pauli	pauli	PROPN
ap-9818	21	34	equation	equation	NOUN
ap-9818	21	35	in	in	ADP
ap-9818	21	36	the	the	DET
ap-9818	21	37	presence	presence	NOUN
ap-9818	21	38	of	of	ADP
ap-9818	21	39	a	a	DET
ap-9818	21	40	magnetic	magnetic	ADJ
ap-9818	21	41	field	field	NOUN
ap-9818	21	42	[	[	X
ap-9818	21	43	21	21	NUM
ap-9818	21	44	]	]	X
ap-9818	21	45	,	,	PUNCT
ap-9818	21	46	a	a	DET
ap-9818	21	47	two	two	NUM
ap-9818	21	48	-	-	PUNCT
ap-9818	21	49	parameter	parameter	NOUN
ap-9818	21	50	version	version	NOUN
ap-9818	21	51	of	of	ADP
ap-9818	21	52	the	the	DET
ap-9818	21	53	dunkl	dunkl	NOUN
ap-9818	21	54	operator	operator	NOUN
ap-9818	21	55	applied	apply	VERB
ap-9818	21	56	to	to	ADP
ap-9818	21	57	two	two	NUM
ap-9818	21	58	-	-	PUNCT
ap-9818	21	59	dimensional	dimensional	ADJ
ap-9818	21	60	schrödinger	schrödinger	ADJ
ap-9818	21	61	equations	equation	NOUN
ap-9818	22	1	[	[	X
ap-9818	22	2	22	22	NUM
ap-9818	22	3	]	]	PUNCT
ap-9818	22	4	,	,	PUNCT
ap-9818	22	5	and	and	CCONJ
ap-9818	22	6	closed	closed	ADJ
ap-9818	22	7	-	-	PUNCT
ap-9818	22	8	form	form	NOUN
ap-9818	22	9	solutions	solution	NOUN
ap-9818	22	10	of	of	ADP
ap-9818	22	11	specific	specific	ADJ
ap-9818	22	12	systems	system	NOUN
ap-9818	22	13	[	[	X
ap-9818	22	14	23	23	NUM
ap-9818	22	15	,	,	PUNCT
ap-9818	22	16	24	24	NUM
ap-9818	22	17	]	]	PUNCT
ap-9818	22	18	.	.	PUNCT
ap-9818	23	1	in	in	ADP
ap-9818	23	2	many	many	ADJ
ap-9818	23	3	of	of	ADP
ap-9818	23	4	the	the	DET
ap-9818	23	5	previous	previous	ADJ
ap-9818	23	6	applications	application	NOUN
ap-9818	23	7	to	to	ADP
ap-9818	23	8	specific	specific	ADJ
ap-9818	23	9	quantum	quantum	NOUN
ap-9818	23	10	systems	system	NOUN
ap-9818	23	11	,	,	PUNCT
ap-9818	23	12	it	it	PRON
ap-9818	23	13	was	be	AUX
ap-9818	23	14	observed	observe	VERB
ap-9818	23	15	that	that	SCONJ
ap-9818	23	16	the	the	DET
ap-9818	23	17	schrödinger	schrödinger	ADJ
ap-9818	23	18	equation	equation	NOUN
ap-9818	23	19	remains	remain	VERB
ap-9818	23	20	solvable	solvable	ADJ
ap-9818	23	21	for	for	ADP
ap-9818	23	22	both	both	CCONJ
ap-9818	23	23	the	the	DET
ap-9818	23	24	conventional	conventional	ADJ
ap-9818	23	25	system	system	NOUN
ap-9818	23	26	as	as	ADV
ap-9818	23	27	well	well	ADV
ap-9818	23	28	as	as	ADP
ap-9818	23	29	for	for	ADP
ap-9818	23	30	its	its	PRON
ap-9818	23	31	associated	associated	ADJ
ap-9818	23	32	partner	partner	NOUN
ap-9818	23	33	within	within	ADP
ap-9818	23	34	the	the	DET
ap-9818	23	35	dunkl	dunkl	NOUN
ap-9818	23	36	formalism	formalism	NOUN
ap-9818	23	37	.	.	PUNCT
ap-9818	24	1	this	this	PRON
ap-9818	24	2	is	be	AUX
ap-9818	24	3	remarkable	remarkable	ADJ
ap-9818	24	4	because	because	SCONJ
ap-9818	24	5	the	the	DET
ap-9818	24	6	latter	latter	ADJ
ap-9818	24	7	formalism	formalism	NOUN
ap-9818	24	8	introduces	introduce	VERB
ap-9818	24	9	additional	additional	ADJ
ap-9818	24	10	terms	term	NOUN
ap-9818	24	11	in	in	ADP
ap-9818	24	12	the	the	DET
ap-9818	24	13	schrödinger	schrödinger	ADJ
ap-9818	24	14	equation	equation	NOUN
ap-9818	24	15	that	that	PRON
ap-9818	24	16	can	can	AUX
ap-9818	24	17	lead	lead	VERB
ap-9818	24	18	to	to	ADP
ap-9818	24	19	a	a	DET
ap-9818	24	20	loss	loss	NOUN
ap-9818	24	21	of	of	ADP
ap-9818	24	22	solvability	solvability	NOUN
ap-9818	24	23	.	.	PUNCT
ap-9818	25	1	therefore	therefore	ADV
ap-9818	25	2	,	,	PUNCT
ap-9818	25	3	the	the	DET
ap-9818	25	4	purpose	purpose	NOUN
ap-9818	25	5	of	of	ADP
ap-9818	25	6	the	the	DET
ap-9818	25	7	present	present	ADJ
ap-9818	25	8	work	work	NOUN
ap-9818	25	9	is	be	AUX
ap-9818	25	10	to	to	PART
ap-9818	25	11	investigate	investigate	VERB
ap-9818	25	12	under	under	ADP
ap-9818	25	13	which	which	PRON
ap-9818	25	14	conditions	condition	NOUN
ap-9818	25	15	solvability	solvability	NOUN
ap-9818	25	16	of	of	ADP
ap-9818	25	17	a	a	DET
ap-9818	25	18	conventional	conventional	ADJ
ap-9818	25	19	schrödinger	schrödinger	ADJ
ap-9818	25	20	equation	equation	NOUN
ap-9818	25	21	is	be	AUX
ap-9818	25	22	preserved	preserve	VERB
ap-9818	25	23	in	in	ADP
ap-9818	25	24	its	its	PRON
ap-9818	25	25	dunkl	dunkl	NOUN
ap-9818	25	26	partner	partner	NOUN
ap-9818	25	27	equation	equation	NOUN
ap-9818	25	28	.	.	PUNCT
ap-9818	26	1	for	for	ADP
ap-9818	26	2	the	the	DET
ap-9818	26	3	sake	sake	NOUN
ap-9818	26	4	of	of	ADP
ap-9818	26	5	generality	generality	NOUN
ap-9818	26	6	we	we	PRON
ap-9818	26	7	will	will	AUX
ap-9818	26	8	consider	consider	VERB
ap-9818	26	9	systems	system	NOUN
ap-9818	26	10	that	that	PRON
ap-9818	26	11	include	include	VERB
ap-9818	26	12	a	a	DET
ap-9818	26	13	position	position	NOUN
ap-9818	26	14	-	-	PUNCT
ap-9818	26	15	dependent	dependent	ADJ
ap-9818	26	16	mass	mass	NOUN
ap-9818	26	17	.	.	PUNCT
ap-9818	27	1	such	such	ADJ
ap-9818	27	2	masses	masse	NOUN
ap-9818	27	3	appear	appear	VERB
ap-9818	27	4	in	in	ADP
ap-9818	27	5	the	the	DET
ap-9818	27	6	context	context	NOUN
ap-9818	27	7	of	of	ADP
ap-9818	27	8	transport	transport	NOUN
ap-9818	27	9	phenomena	phenomenon	NOUN
ap-9818	27	10	in	in	ADP
ap-9818	27	11	crystals	crystal	NOUN
ap-9818	27	12	(	(	PUNCT
ap-9818	27	13	e.g.	e.g.	ADV
ap-9818	27	14	semiconductors	semiconductor	NOUN
ap-9818	27	15	)	)	PUNCT
ap-9818	27	16	,	,	PUNCT
ap-9818	27	17	where	where	SCONJ
ap-9818	27	18	the	the	DET
ap-9818	27	19	electrons	electron	NOUN
ap-9818	27	20	interact	interact	VERB
ap-9818	27	21	with	with	ADP
ap-9818	27	22	the	the	DET
ap-9818	27	23	lattice	lattice	PROPN
ap-9818	27	24	potential	potential	NOUN
ap-9818	27	25	,	,	PUNCT
ap-9818	27	26	rather	rather	ADV
ap-9818	27	27	than	than	ADP
ap-9818	27	28	being	be	AUX
ap-9818	27	29	completely	completely	ADV
ap-9818	27	30	free	free	ADJ
ap-9818	27	31	.	.	PUNCT
ap-9818	28	1	the	the	DET
ap-9818	28	2	dynamics	dynamic	NOUN
ap-9818	28	3	of	of	ADP
ap-9818	28	4	such	such	ADJ
ap-9818	28	5	electrons	electron	NOUN
ap-9818	28	6	can	can	AUX
ap-9818	28	7	be	be	AUX
ap-9818	28	8	described	describe	VERB
ap-9818	28	9	by	by	ADP
ap-9818	28	10	introducing	introduce	VERB
ap-9818	28	11	a	a	DET
ap-9818	28	12	position	position	NOUN
ap-9818	28	13	-	-	PUNCT
ap-9818	28	14	dependent	dependent	ADJ
ap-9818	28	15	mass	mass	NOUN
ap-9818	28	16	,	,	PUNCT
ap-9818	28	17	the	the	DET
ap-9818	28	18	behaviour	behaviour	NOUN
ap-9818	28	19	of	of	ADP
ap-9818	28	20	which	which	PRON
ap-9818	28	21	is	be	AUX
ap-9818	28	22	determined	determine	VERB
ap-9818	28	23	by	by	ADP
ap-9818	28	24	the	the	DET
ap-9818	28	25	band	band	NOUN
ap-9818	28	26	curvature	curvature	NOUN
ap-9818	29	1	[	[	X
ap-9818	29	2	25–29	25–29	NOUN
ap-9818	29	3	]	]	X
ap-9818	29	4	.	.	PUNCT
ap-9818	30	1	for	for	ADP
ap-9818	30	2	more	more	ADJ
ap-9818	30	3	details	detail	NOUN
ap-9818	30	4	and	and	CCONJ
ap-9818	30	5	further	further	ADJ
ap-9818	30	6	applications	application	NOUN
ap-9818	30	7	of	of	ADP
ap-9818	30	8	position	position	NOUN
ap-9818	30	9	-	-	PUNCT
ap-9818	30	10	dependent	dependent	ADJ
ap-9818	30	11	masses	masse	NOUN
ap-9818	30	12	,	,	PUNCT
ap-9818	30	13	the	the	DET
ap-9818	30	14	reader	reader	NOUN
ap-9818	30	15	is	be	AUX
ap-9818	30	16	referred	refer	VERB
ap-9818	30	17	to	to	ADP
ap-9818	30	18	[	[	X
ap-9818	30	19	30	30	NUM
ap-9818	30	20	]	]	PUNCT
ap-9818	30	21	and	and	CCONJ
ap-9818	30	22	[	[	X
ap-9818	30	23	31	31	NUM
ap-9818	30	24	]	]	PUNCT
ap-9818	30	25	.	.	PUNCT
ap-9818	31	1	the	the	DET
ap-9818	31	2	remainder	remainder	NOUN
ap-9818	31	3	of	of	ADP
ap-9818	31	4	this	this	DET
ap-9818	31	5	work	work	NOUN
ap-9818	31	6	is	be	AUX
ap-9818	31	7	organized	organize	VERB
ap-9818	31	8	as	as	SCONJ
ap-9818	31	9	follows	follow	VERB
ap-9818	31	10	:	:	PUNCT
ap-9818	31	11	in	in	ADP
ap-9818	31	12	section	section	NOUN
ap-9818	31	13	2	2	NUM
ap-9818	31	14	we	we	PRON
ap-9818	31	15	will	will	AUX
ap-9818	31	16	introduce	introduce	VERB
ap-9818	31	17	the	the	DET
ap-9818	31	18	position	position	NOUN
ap-9818	31	19	-	-	PUNCT
ap-9818	31	20	dependent	dependent	ADJ
ap-9818	31	21	mass	mass	NOUN
ap-9818	31	22	dunkl	dunkl	NOUN
ap-9818	31	23	-	-	PUNCT
ap-9818	31	24	hamiltonian	hamiltonian	NOUN
ap-9818	31	25	,	,	PUNCT
ap-9818	31	26	along	along	ADP
ap-9818	31	27	with	with	ADP
ap-9818	31	28	the	the	DET
ap-9818	31	29	corresponding	correspond	VERB
ap-9818	31	30	dunkl	dunkl	NOUN
ap-9818	31	31	-	-	PUNCT
ap-9818	31	32	schrödinger	schrödinger	NOUN
ap-9818	31	33	equation	equation	NOUN
ap-9818	31	34	.	.	PUNCT
ap-9818	32	1	section	section	NOUN
ap-9818	32	2	3	3	NUM
ap-9818	32	3	is	be	AUX
ap-9818	32	4	devoted	devote	VERB
ap-9818	32	5	to	to	ADP
ap-9818	32	6	the	the	DET
ap-9818	32	7	construction	construction	NOUN
ap-9818	32	8	of	of	ADP
ap-9818	32	9	conditions	condition	NOUN
ap-9818	32	10	for	for	ADP
ap-9818	32	11	solvability	solvability	NOUN
ap-9818	32	12	of	of	ADP
ap-9818	32	13	both	both	CCONJ
ap-9818	32	14	the	the	DET
ap-9818	32	15	conventional	conventional	ADJ
ap-9818	32	16	equation	equation	NOUN
ap-9818	32	17	and	and	CCONJ
ap-9818	32	18	its	its	PRON
ap-9818	32	19	dunkl	dunkl	NOUN
ap-9818	32	20	partner	partner	NOUN
ap-9818	32	21	.	.	PUNCT
ap-9818	33	1	several	several	ADJ
ap-9818	33	2	applications	application	NOUN
ap-9818	33	3	of	of	ADP
ap-9818	33	4	our	our	PRON
ap-9818	33	5	method	method	NOUN
ap-9818	33	6	are	be	AUX
ap-9818	33	7	presented	present	VERB
ap-9818	33	8	in	in	ADP
ap-9818	33	9	section	section	NOUN
ap-9818	33	10	4	4	NUM
ap-9818	33	11	.	.	NOUN
ap-9818	34	1	222	222	NUM
ap-9818	34	2	https://doi.org/10.14311/ap.2025.65.0222	https://doi.org/10.14311/ap.2025.65.0222	NOUN
ap-9818	34	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-9818	34	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-9818	34	5	vol	vol	NOUN
ap-9818	34	6	.	.	PROPN
ap-9818	35	1	65	65	NUM
ap-9818	35	2	no	no	NOUN
ap-9818	35	3	.	.	PUNCT
ap-9818	36	1	2/2025	2/2025	NUM
ap-9818	36	2	persistence	persistence	NOUN
ap-9818	36	3	of	of	ADP
ap-9818	36	4	solvability	solvability	NOUN
ap-9818	36	5	in	in	ADP
ap-9818	36	6	quantum	quantum	NOUN
ap-9818	36	7	systems	system	NOUN
ap-9818	36	8	deformed	deform	VERB
ap-9818	36	9	by	by	ADP
ap-9818	36	10	dunkl	dunkl	PROPN
ap-9818	36	11	.	.	PUNCT
ap-9818	36	12	.	.	PUNCT
ap-9818	36	13	.	.	PUNCT
ap-9818	37	1	2	2	X
ap-9818	37	2	.	.	X
ap-9818	37	3	dunkl	dunkl	NOUN
ap-9818	37	4	-	-	PUNCT
ap-9818	37	5	hamiltonian	hamiltonian	PROPN
ap-9818	37	6	and	and	CCONJ
ap-9818	37	7	schrödinger	schrödinger	ADJ
ap-9818	37	8	equation	equation	NOUN
ap-9818	37	9	nonrelativistic	nonrelativistic	ADJ
ap-9818	37	10	quantum	quantum	NOUN
ap-9818	37	11	systems	system	NOUN
ap-9818	37	12	featuring	feature	VERB
ap-9818	37	13	a	a	DET
ap-9818	37	14	position	position	NOUN
ap-9818	37	15	-	-	PUNCT
ap-9818	37	16	dependent	dependent	ADJ
ap-9818	37	17	mass	mass	NOUN
ap-9818	37	18	,	,	PUNCT
ap-9818	37	19	are	be	AUX
ap-9818	37	20	governed	govern	VERB
ap-9818	37	21	by	by	ADP
ap-9818	37	22	a	a	DET
ap-9818	37	23	symmetrised	symmetrise	VERB
ap-9818	37	24	hamiltonian	hamiltonian	NOUN
ap-9818	37	25	.	.	PUNCT
ap-9818	38	1	in	in	ADP
ap-9818	38	2	its	its	PRON
ap-9818	38	3	most	most	ADV
ap-9818	38	4	general	general	ADJ
ap-9818	38	5	hermitian	hermitian	ADJ
ap-9818	38	6	form	form	NOUN
ap-9818	38	7	,	,	PUNCT
ap-9818	38	8	this	this	DET
ap-9818	38	9	hamiltonian	hamiltonian	ADJ
ap-9818	38	10	h0	h0	NOUN
ap-9818	38	11	can	can	AUX
ap-9818	38	12	be	be	AUX
ap-9818	38	13	written	write	VERB
ap-9818	38	14	as	as	ADP
ap-9818	38	15	[	[	X
ap-9818	38	16	29	29	NUM
ap-9818	38	17	,	,	PUNCT
ap-9818	38	18	30	30	NUM
ap-9818	38	19	]	]	PUNCT
ap-9818	38	20	:	:	PUNCT
ap-9818	38	21	h0	h0	NOUN
ap-9818	38	22	=	=	NOUN
ap-9818	38	23	1	1	NUM
ap-9818	38	24	2	2	NUM
ap-9818	38	25	[	[	PUNCT
ap-9818	38	26	m(x)α	m(x)α	NOUN
ap-9818	38	27	p0	p0	NOUN
ap-9818	38	28	m(x)−1−α−γ	m(x)−1−α−γ	PROPN
ap-9818	38	29	p0	p0	NOUN
ap-9818	38	30	m(x)γ	m(x)γ	NOUN
ap-9818	38	31	+	+	SYM
ap-9818	38	32	m(x)γ	m(x)γ	NOUN
ap-9818	38	33	p0	p0	NOUN
ap-9818	38	34	m(x)−1−α−γ	m(x)−1−α−γ	NOUN
ap-9818	38	35	p0	p0	NOUN
ap-9818	38	36	m(x)α	m(x)α	NOUN
ap-9818	38	37	]	]	PUNCT
ap-9818	39	1	+	+	CCONJ
ap-9818	39	2	v	v	X
ap-9818	39	3	(	(	PUNCT
ap-9818	39	4	x	x	NOUN
ap-9818	39	5	)	)	PUNCT
ap-9818	39	6	,	,	PUNCT
ap-9818	39	7	(	(	PUNCT
ap-9818	39	8	1	1	X
ap-9818	39	9	)	)	PUNCT
ap-9818	39	10	where	where	SCONJ
ap-9818	39	11	p0	p0	NOUN
ap-9818	39	12	stands	stand	VERB
ap-9818	39	13	for	for	ADP
ap-9818	39	14	the	the	DET
ap-9818	39	15	momentum	momentum	NOUN
ap-9818	39	16	operator	operator	NOUN
ap-9818	39	17	,	,	PUNCT
ap-9818	39	18	and	and	CCONJ
ap-9818	39	19	α	α	X
ap-9818	39	20	,	,	PUNCT
ap-9818	39	21	γ	γ	PRON
ap-9818	39	22	represent	represent	VERB
ap-9818	39	23	real	real	ADJ
ap-9818	39	24	constants	constant	NOUN
ap-9818	39	25	.	.	PUNCT
ap-9818	40	1	furthermore	furthermore	ADV
ap-9818	40	2	,	,	PUNCT
ap-9818	40	3	the	the	DET
ap-9818	40	4	positiondependent	positiondependent	ADJ
ap-9818	40	5	mass	mass	PROPN
ap-9818	40	6	m	m	PROPN
ap-9818	40	7	≥	≥	NOUN
ap-9818	40	8	0	0	NUM
ap-9818	40	9	,	,	PUNCT
ap-9818	40	10	and	and	CCONJ
ap-9818	40	11	the	the	DET
ap-9818	40	12	potential	potential	ADJ
ap-9818	40	13	v	v	NOUN
ap-9818	40	14	are	be	AUX
ap-9818	40	15	continuous	continuous	ADJ
ap-9818	40	16	functions	function	NOUN
ap-9818	40	17	,	,	PUNCT
ap-9818	40	18	except	except	SCONJ
ap-9818	40	19	possibly	possibly	ADV
ap-9818	40	20	at	at	ADP
ap-9818	40	21	a	a	DET
ap-9818	40	22	finite	finite	ADJ
ap-9818	40	23	number	number	NOUN
ap-9818	40	24	of	of	ADP
ap-9818	40	25	singular	singular	ADJ
ap-9818	40	26	points	point	NOUN
ap-9818	40	27	that	that	SCONJ
ap-9818	40	28	the	the	DET
ap-9818	40	29	mass	mass	NOUN
ap-9818	40	30	or	or	CCONJ
ap-9818	40	31	the	the	DET
ap-9818	40	32	potential	potential	ADJ
ap-9818	40	33	exhibit	exhibit	NOUN
ap-9818	40	34	.	.	PUNCT
ap-9818	41	1	while	while	SCONJ
ap-9818	41	2	a	a	DET
ap-9818	41	3	point	point	NOUN
ap-9818	41	4	singularity	singularity	NOUN
ap-9818	41	5	is	be	AUX
ap-9818	41	6	nothing	nothing	PRON
ap-9818	41	7	unusual	unusual	ADJ
ap-9818	41	8	for	for	ADP
ap-9818	41	9	a	a	DET
ap-9818	41	10	potential	potential	NOUN
ap-9818	41	11	(	(	PUNCT
ap-9818	41	12	a	a	DET
ap-9818	41	13	famous	famous	ADJ
ap-9818	41	14	example	example	NOUN
ap-9818	41	15	is	be	AUX
ap-9818	41	16	the	the	DET
ap-9818	41	17	coulomb	coulomb	NOUN
ap-9818	41	18	interaction	interaction	NOUN
ap-9818	41	19	)	)	PUNCT
ap-9818	41	20	,	,	PUNCT
ap-9818	41	21	it	it	PRON
ap-9818	41	22	is	be	AUX
ap-9818	41	23	much	much	ADV
ap-9818	41	24	less	less	ADV
ap-9818	41	25	common	common	ADJ
ap-9818	41	26	in	in	ADP
ap-9818	41	27	position	position	NOUN
ap-9818	41	28	-	-	PUNCT
ap-9818	41	29	dependent	dependent	ADJ
ap-9818	41	30	masses	masse	NOUN
ap-9818	41	31	due	due	ADP
ap-9818	41	32	to	to	ADP
ap-9818	41	33	their	their	PRON
ap-9818	41	34	physical	physical	ADJ
ap-9818	41	35	meaning	meaning	NOUN
ap-9818	41	36	.	.	PUNCT
ap-9818	42	1	however	however	ADV
ap-9818	42	2	,	,	PUNCT
ap-9818	42	3	such	such	ADJ
ap-9818	42	4	singular	singular	ADJ
ap-9818	42	5	mass	mass	NOUN
ap-9818	42	6	functions	function	NOUN
ap-9818	42	7	are	be	AUX
ap-9818	42	8	used	use	VERB
ap-9818	42	9	in	in	ADP
ap-9818	42	10	lienard	lienard	ADJ
ap-9818	42	11	oscillator	oscillator	NOUN
ap-9818	42	12	systems	system	NOUN
ap-9818	42	13	,	,	PUNCT
ap-9818	42	14	which	which	PRON
ap-9818	42	15	we	we	PRON
ap-9818	42	16	will	will	AUX
ap-9818	42	17	comment	comment	VERB
ap-9818	42	18	on	on	ADP
ap-9818	42	19	in	in	ADP
ap-9818	42	20	our	our	PRON
ap-9818	42	21	example	example	NOUN
ap-9818	42	22	,	,	PUNCT
ap-9818	42	23	section	section	NOUN
ap-9818	42	24	4	4	NUM
ap-9818	42	25	.	.	PUNCT
ap-9818	42	26	note	note	VERB
ap-9818	42	27	that	that	SCONJ
ap-9818	42	28	the	the	DET
ap-9818	42	29	constants	constant	NOUN
ap-9818	42	30	α	α	PRON
ap-9818	42	31	and	and	CCONJ
ap-9818	42	32	γ	γ	PROPN
ap-9818	42	33	arise	arise	VERB
ap-9818	42	34	from	from	ADP
ap-9818	42	35	an	an	DET
ap-9818	42	36	ordering	ordering	NOUN
ap-9818	42	37	ambiguity	ambiguity	NOUN
ap-9818	42	38	of	of	ADP
ap-9818	42	39	momentum	momentum	NOUN
ap-9818	42	40	operators	operator	NOUN
ap-9818	42	41	and	and	CCONJ
ap-9818	42	42	position	position	NOUN
ap-9818	42	43	-	-	PUNCT
ap-9818	42	44	dependent	dependent	ADJ
ap-9818	42	45	mass	mass	NOUN
ap-9818	42	46	functions	function	NOUN
ap-9818	42	47	.	.	PUNCT
ap-9818	43	1	this	this	DET
ap-9818	43	2	ambiguity	ambiguity	NOUN
ap-9818	43	3	is	be	AUX
ap-9818	43	4	inherent	inherent	ADJ
ap-9818	43	5	to	to	ADP
ap-9818	43	6	a	a	DET
ap-9818	43	7	position	position	NOUN
ap-9818	43	8	-	-	PUNCT
ap-9818	43	9	dependent	dependent	ADJ
ap-9818	43	10	mass	mass	NOUN
ap-9818	43	11	hamiltonian	hamiltonian	NOUN
ap-9818	43	12	.	.	PUNCT
ap-9818	44	1	in	in	ADP
ap-9818	44	2	order	order	NOUN
ap-9818	44	3	to	to	PART
ap-9818	44	4	obtain	obtain	VERB
ap-9818	44	5	the	the	DET
ap-9818	44	6	latter	latter	ADJ
ap-9818	44	7	operator	operator	NOUN
ap-9818	44	8	in	in	ADP
ap-9818	44	9	a	a	DET
ap-9818	44	10	hermitian	hermitian	ADJ
ap-9818	44	11	form	form	NOUN
ap-9818	44	12	,	,	PUNCT
ap-9818	44	13	there	there	PRON
ap-9818	44	14	are	be	VERB
ap-9818	44	15	infinitely	infinitely	ADV
ap-9818	44	16	many	many	ADJ
ap-9818	44	17	choices	choice	NOUN
ap-9818	44	18	for	for	ADP
ap-9818	44	19	the	the	DET
ap-9818	44	20	values	value	NOUN
ap-9818	44	21	of	of	ADP
ap-9818	44	22	α	α	NOUN
ap-9818	44	23	and	and	CCONJ
ap-9818	44	24	β	β	NOUN
ap-9818	44	25	.	.	PUNCT
ap-9818	45	1	while	while	SCONJ
ap-9818	45	2	all	all	PRON
ap-9818	45	3	of	of	ADP
ap-9818	45	4	these	these	DET
ap-9818	45	5	values	value	NOUN
ap-9818	45	6	render	render	VERB
ap-9818	45	7	(	(	PUNCT
ap-9818	45	8	1	1	NUM
ap-9818	45	9	)	)	PUNCT
ap-9818	45	10	hermitian	hermitian	NOUN
ap-9818	45	11	,	,	PUNCT
ap-9818	45	12	they	they	PRON
ap-9818	45	13	affect	affect	VERB
ap-9818	45	14	the	the	DET
ap-9818	45	15	resulting	result	VERB
ap-9818	45	16	schrödinger	schrödinger	ADJ
ap-9818	45	17	equation	equation	NOUN
ap-9818	45	18	,	,	PUNCT
ap-9818	45	19	as	as	SCONJ
ap-9818	45	20	will	will	AUX
ap-9818	45	21	be	be	AUX
ap-9818	45	22	shown	show	VERB
ap-9818	45	23	in	in	ADP
ap-9818	45	24	section	section	NOUN
ap-9818	45	25	4	4	NUM
ap-9818	45	26	.	.	PUNCT
ap-9818	46	1	now	now	ADV
ap-9818	46	2	,	,	PUNCT
ap-9818	46	3	the	the	DET
ap-9818	46	4	momentum	momentum	NOUN
ap-9818	46	5	operator	operator	NOUN
ap-9818	46	6	p0	p0	NOUN
ap-9818	46	7	in	in	ADP
ap-9818	46	8	(	(	PUNCT
ap-9818	46	9	1	1	X
ap-9818	46	10	)	)	PUNCT
ap-9818	46	11	can	can	AUX
ap-9818	46	12	be	be	AUX
ap-9818	46	13	written	write	VERB
ap-9818	46	14	in	in	ADP
ap-9818	46	15	the	the	DET
ap-9818	46	16	usual	usual	ADJ
ap-9818	46	17	form	form	NOUN
ap-9818	46	18	:	:	PUNCT
ap-9818	46	19	p0	p0	NOUN
ap-9818	46	20	=	=	PUNCT
ap-9818	47	1	−i	−i	PROPN
ap-9818	48	1	d	d	X
ap-9818	48	2	dx	dx	PROPN
ap-9818	48	3	.	.	PUNCT
ap-9818	49	1	(	(	PUNCT
ap-9818	49	2	2	2	X
ap-9818	49	3	)	)	PUNCT
ap-9818	49	4	we	we	PRON
ap-9818	49	5	can	can	AUX
ap-9818	49	6	generalise	generalise	VERB
ap-9818	49	7	the	the	DET
ap-9818	49	8	hamiltonian	hamiltonian	NOUN
ap-9818	49	9	(	(	PUNCT
ap-9818	49	10	1	1	NUM
ap-9818	49	11	)	)	PUNCT
ap-9818	49	12	by	by	ADP
ap-9818	49	13	replacing	replace	VERB
ap-9818	49	14	the	the	DET
ap-9818	49	15	standard	standard	ADJ
ap-9818	49	16	derivatives	derivative	NOUN
ap-9818	49	17	through	through	ADP
ap-9818	49	18	the	the	DET
ap-9818	49	19	dunkl	dunkl	NOUN
ap-9818	49	20	operator	operator	NOUN
ap-9818	49	21	.	.	PUNCT
ap-9818	50	1	this	this	DET
ap-9818	50	2	operator	operator	NOUN
ap-9818	50	3	can	can	AUX
ap-9818	50	4	be	be	AUX
ap-9818	50	5	written	write	VERB
ap-9818	50	6	as	as	ADP
ap-9818	50	7	:	:	PUNCT
ap-9818	50	8	dν	dν	PROPN
ap-9818	50	9	=	=	SYM
ap-9818	50	10	d	d	X
ap-9818	50	11	dx	dx	PROPN
ap-9818	50	12	+	+	CCONJ
ap-9818	50	13	ν	ν	X
ap-9818	50	14	x	x	X
ap-9818	50	15	−	−	PROPN
ap-9818	51	1	ν	ν	X
ap-9818	51	2	x	x	SYM
ap-9818	51	3	r	r	NOUN
ap-9818	51	4	,	,	PUNCT
ap-9818	51	5	(	(	PUNCT
ap-9818	51	6	3	3	X
ap-9818	51	7	)	)	PUNCT
ap-9818	51	8	where	where	SCONJ
ap-9818	51	9	ν	ν	X
ap-9818	51	10	>	>	X
ap-9818	51	11	−	−	PROPN
ap-9818	51	12	1	1	NUM
ap-9818	51	13	2	2	NUM
ap-9818	51	14	is	be	AUX
ap-9818	51	15	a	a	DET
ap-9818	51	16	real	real	ADJ
ap-9818	51	17	number	number	NOUN
ap-9818	51	18	,	,	PUNCT
ap-9818	51	19	and	and	CCONJ
ap-9818	51	20	r	r	NOUN
ap-9818	51	21	stands	stand	VERB
ap-9818	51	22	for	for	ADP
ap-9818	51	23	the	the	DET
ap-9818	51	24	reflection	reflection	NOUN
ap-9818	51	25	or	or	CCONJ
ap-9818	51	26	parity	parity	NOUN
ap-9818	51	27	operator	operator	NOUN
ap-9818	51	28	that	that	PRON
ap-9818	51	29	acts	act	VERB
ap-9818	51	30	on	on	ADP
ap-9818	51	31	an	an	DET
ap-9818	51	32	admissible	admissible	ADJ
ap-9818	51	33	function	function	NOUN
ap-9818	51	34	ψ	ψ	NOUN
ap-9818	51	35	in	in	ADP
ap-9818	51	36	the	the	DET
ap-9818	51	37	way	way	NOUN
ap-9818	51	38	rψ(x	rψ(x	NOUN
ap-9818	51	39	)	)	PUNCT
ap-9818	51	40	=	=	SYM
ap-9818	51	41	ψ(−x	ψ(−x	NOUN
ap-9818	51	42	)	)	PUNCT
ap-9818	51	43	.	.	PUNCT
ap-9818	52	1	we	we	PRON
ap-9818	52	2	will	will	AUX
ap-9818	52	3	now	now	ADV
ap-9818	52	4	use	use	VERB
ap-9818	52	5	(	(	PUNCT
ap-9818	52	6	3	3	NUM
ap-9818	52	7	)	)	PUNCT
ap-9818	52	8	to	to	PART
ap-9818	52	9	generalise	generalise	VERB
ap-9818	52	10	the	the	DET
ap-9818	52	11	momentum	momentum	NOUN
ap-9818	52	12	operator	operator	NOUN
ap-9818	52	13	(	(	PUNCT
ap-9818	52	14	2	2	NUM
ap-9818	52	15	)	)	PUNCT
ap-9818	52	16	as	as	SCONJ
ap-9818	52	17	follows	follow	VERB
ap-9818	52	18	:	:	PUNCT
ap-9818	52	19	pν	pν	PROPN
ap-9818	52	20	=	=	PUNCT
ap-9818	52	21	−i	−i	NOUN
ap-9818	52	22	dν	dν	VERB
ap-9818	52	23	.	.	PUNCT
ap-9818	53	1	(	(	PUNCT
ap-9818	53	2	4	4	X
ap-9818	53	3	)	)	PUNCT
ap-9818	53	4	let	let	VERB
ap-9818	53	5	us	we	PRON
ap-9818	53	6	emphasize	emphasize	VERB
ap-9818	53	7	here	here	ADV
ap-9818	53	8	that	that	SCONJ
ap-9818	53	9	the	the	DET
ap-9818	53	10	definitions	definition	NOUN
ap-9818	53	11	(	(	PUNCT
ap-9818	53	12	3	3	NUM
ap-9818	53	13	)	)	PUNCT
ap-9818	53	14	and	and	CCONJ
ap-9818	53	15	(	(	PUNCT
ap-9818	53	16	4	4	X
ap-9818	53	17	)	)	PUNCT
ap-9818	53	18	generate	generate	VERB
ap-9818	53	19	a	a	DET
ap-9818	53	20	deformation	deformation	NOUN
ap-9818	53	21	of	of	ADP
ap-9818	53	22	the	the	DET
ap-9818	53	23	conventional	conventional	ADJ
ap-9818	53	24	quantum	quantum	NOUN
ap-9818	53	25	theory	theory	NOUN
ap-9818	53	26	.	.	PUNCT
ap-9818	54	1	more	more	ADV
ap-9818	54	2	precisely	precisely	ADV
ap-9818	54	3	,	,	PUNCT
ap-9818	54	4	it	it	PRON
ap-9818	54	5	will	will	AUX
ap-9818	54	6	turn	turn	VERB
ap-9818	54	7	out	out	ADP
ap-9818	54	8	that	that	SCONJ
ap-9818	54	9	substituting	substitute	VERB
ap-9818	54	10	the	the	DET
ap-9818	54	11	generalised	generalise	VERB
ap-9818	54	12	momentum	momentum	NOUN
ap-9818	54	13	operator	operator	NOUN
ap-9818	54	14	into	into	ADP
ap-9818	54	15	our	our	PRON
ap-9818	54	16	hamiltonian	hamiltonian	NOUN
ap-9818	54	17	affects	affect	VERB
ap-9818	54	18	the	the	DET
ap-9818	54	19	hilbert	hilbert	NOUN
ap-9818	54	20	space	space	NOUN
ap-9818	54	21	that	that	PRON
ap-9818	54	22	normalisable	normalisable	ADJ
ap-9818	54	23	eigenfunctions	eigenfunction	NOUN
ap-9818	54	24	are	be	AUX
ap-9818	54	25	located	locate	VERB
ap-9818	54	26	in	in	ADP
ap-9818	54	27	.	.	PUNCT
ap-9818	55	1	the	the	DET
ap-9818	55	2	deformation	deformation	NOUN
ap-9818	55	3	of	of	ADP
ap-9818	55	4	the	the	DET
ap-9818	55	5	conventional	conventional	ADJ
ap-9818	55	6	quantum	quantum	NOUN
ap-9818	55	7	theory	theory	NOUN
ap-9818	55	8	can	can	AUX
ap-9818	55	9	be	be	AUX
ap-9818	55	10	controlled	control	VERB
ap-9818	55	11	by	by	ADP
ap-9818	55	12	the	the	DET
ap-9818	55	13	parameter	parameter	NOUN
ap-9818	55	14	ν	ν	NOUN
ap-9818	55	15	:	:	PUNCT
ap-9818	55	16	inspection	inspection	NOUN
ap-9818	55	17	of	of	ADP
ap-9818	55	18	(	(	PUNCT
ap-9818	55	19	3	3	X
ap-9818	55	20	)	)	PUNCT
ap-9818	55	21	reveals	reveal	VERB
ap-9818	55	22	that	that	SCONJ
ap-9818	55	23	the	the	DET
ap-9818	55	24	setting	set	VERB
ap-9818	55	25	ν	ν	X
ap-9818	55	26	=	=	SYM
ap-9818	55	27	0	0	NUM
ap-9818	55	28	yields	yield	VERB
ap-9818	55	29	the	the	DET
ap-9818	55	30	standard	standard	ADJ
ap-9818	55	31	momentum	momentum	NOUN
ap-9818	55	32	operator	operator	NOUN
ap-9818	55	33	(	(	PUNCT
ap-9818	55	34	2	2	NUM
ap-9818	55	35	)	)	PUNCT
ap-9818	55	36	,	,	PUNCT
ap-9818	55	37	thus	thus	ADV
ap-9818	55	38	removing	remove	VERB
ap-9818	55	39	the	the	DET
ap-9818	55	40	deformation	deformation	NOUN
ap-9818	55	41	.	.	PUNCT
ap-9818	56	1	in	in	ADP
ap-9818	56	2	the	the	DET
ap-9818	56	3	next	next	ADJ
ap-9818	56	4	step	step	NOUN
ap-9818	56	5	,	,	PUNCT
ap-9818	56	6	we	we	PRON
ap-9818	56	7	rewrite	rewrite	VERB
ap-9818	56	8	our	our	PRON
ap-9818	56	9	hamiltonian	hamiltonian	NOUN
ap-9818	56	10	(	(	PUNCT
ap-9818	56	11	1	1	NUM
ap-9818	56	12	)	)	PUNCT
ap-9818	56	13	by	by	ADP
ap-9818	56	14	replacing	replace	VERB
ap-9818	56	15	the	the	DET
ap-9818	56	16	momentum	momentum	NOUN
ap-9818	56	17	operators	operator	NOUN
ap-9818	56	18	by	by	ADP
ap-9818	56	19	their	their	PRON
ap-9818	56	20	dunkl	dunkl	PROPN
ap-9818	56	21	counterparts	counterpart	NOUN
ap-9818	56	22	(	(	PUNCT
ap-9818	56	23	4	4	NUM
ap-9818	56	24	)	)	PUNCT
ap-9818	56	25	.	.	PUNCT
ap-9818	57	1	upon	upon	SCONJ
ap-9818	57	2	substitution	substitution	NOUN
ap-9818	57	3	of	of	ADP
ap-9818	57	4	(	(	PUNCT
ap-9818	57	5	4	4	NUM
ap-9818	57	6	)	)	PUNCT
ap-9818	57	7	,	,	PUNCT
ap-9818	57	8	we	we	PRON
ap-9818	57	9	obtain	obtain	VERB
ap-9818	57	10	our	our	PRON
ap-9818	57	11	dunkl	dunkl	NOUN
ap-9818	57	12	-	-	PUNCT
ap-9818	57	13	hamiltonian	hamiltonian	NOUN
ap-9818	57	14	in	in	ADP
ap-9818	57	15	the	the	DET
ap-9818	57	16	form	form	NOUN
ap-9818	57	17	:	:	PUNCT
ap-9818	57	18	hν	hν	NOUN
ap-9818	57	19	=	=	SYM
ap-9818	57	20	1	1	NUM
ap-9818	57	21	2	2	NUM
ap-9818	57	22	[	[	PUNCT
ap-9818	57	23	m(x)α	m(x)α	NOUN
ap-9818	57	24	pν	pν	ADP
ap-9818	57	25	m(x)−1−α−γ	m(x)−1−α−γ	NOUN
ap-9818	57	26	pν	pν	ADP
ap-9818	57	27	m(x)γ	m(x)γ	NOUN
ap-9818	57	28	+	+	CCONJ
ap-9818	57	29	m(x)γ	m(x)γ	NOUN
ap-9818	57	30	pν	pν	ADP
ap-9818	57	31	m(x)−1−α−γ	m(x)−1−α−γ	NOUN
ap-9818	57	32	pν	pν	ADP
ap-9818	57	33	m(x)α	m(x)α	NOUN
ap-9818	57	34	]	]	PUNCT
ap-9818	58	1	+	+	CCONJ
ap-9818	58	2	v	v	X
ap-9818	58	3	(	(	PUNCT
ap-9818	58	4	x	x	NOUN
ap-9818	58	5	)	)	PUNCT
ap-9818	58	6	.	.	PUNCT
ap-9818	59	1	(	(	PUNCT
ap-9818	59	2	5	5	X
ap-9818	59	3	)	)	PUNCT
ap-9818	59	4	this	this	DET
ap-9818	59	5	hamiltonian	hamiltonian	NOUN
ap-9818	59	6	generates	generate	VERB
ap-9818	59	7	its	its	PRON
ap-9818	59	8	associated	associated	ADJ
ap-9818	59	9	dunkl	dunkl	NOUN
ap-9818	59	10	-	-	PUNCT
ap-9818	59	11	schrödinger	schrödinger	NOUN
ap-9818	59	12	equation	equation	NOUN
ap-9818	59	13	by	by	ADP
ap-9818	59	14	means	mean	NOUN
ap-9818	59	15	of	of	ADP
ap-9818	59	16	(	(	PUNCT
ap-9818	59	17	hν	hν	NOUN
ap-9818	59	18	−	−	NOUN
ap-9818	59	19	e)ψ	e)ψ	ADV
ap-9818	59	20	=	=	SYM
ap-9818	59	21	0	0	NUM
ap-9818	59	22	,	,	PUNCT
ap-9818	59	23	where	where	SCONJ
ap-9818	59	24	ψ	ψ	NOUN
ap-9818	59	25	stands	stand	VERB
ap-9818	59	26	for	for	ADP
ap-9818	59	27	the	the	DET
ap-9818	59	28	solution	solution	NOUN
ap-9818	59	29	and	and	CCONJ
ap-9818	59	30	e	e	NOUN
ap-9818	59	31	represents	represent	VERB
ap-9818	59	32	the	the	DET
ap-9818	59	33	real	real	ADV
ap-9818	59	34	-	-	PUNCT
ap-9818	59	35	valued	value	VERB
ap-9818	59	36	stationary	stationary	ADJ
ap-9818	59	37	energy	energy	NOUN
ap-9818	59	38	of	of	ADP
ap-9818	59	39	the	the	DET
ap-9818	59	40	system	system	NOUN
ap-9818	59	41	.	.	PUNCT
ap-9818	60	1	in	in	ADP
ap-9818	60	2	explicit	explicit	ADJ
ap-9818	60	3	form	form	NOUN
ap-9818	60	4	,	,	PUNCT
ap-9818	60	5	this	this	DET
ap-9818	60	6	dunkl	dunkl	NOUN
ap-9818	60	7	-	-	PUNCT
ap-9818	60	8	schrödinger	schrödinger	NOUN
ap-9818	60	9	equation	equation	NOUN
ap-9818	60	10	reads	read	VERB
ap-9818	60	11	:	:	PUNCT
ap-9818	60	12	ψ′′	ψ′′	PROPN
ap-9818	60	13	ν(x	ν(x	PROPN
ap-9818	60	14	)	)	PUNCT
ap-9818	61	1	+	+	CCONJ
ap-9818	61	2	[	[	PUNCT
ap-9818	61	3	2	2	NUM
ap-9818	61	4	ν	ν	NOUN
ap-9818	61	5	x	x	X
ap-9818	61	6	−	−	PROPN
ap-9818	61	7	m′(x	m′(x	NOUN
ap-9818	61	8	)	)	PUNCT
ap-9818	61	9	m(x	m(x	PROPN
ap-9818	61	10	)	)	PUNCT
ap-9818	61	11	]	]	PUNCT
ap-9818	61	12	ψ′	ψ′	PUNCT
ap-9818	61	13	ν(x	ν(x	PROPN
ap-9818	61	14	)	)	PUNCT
ap-9818	62	1	+	+	CCONJ
ap-9818	62	2	{	{	PUNCT
ap-9818	62	3	δ	δ	NOUN
ap-9818	62	4	ν	ν	NOUN
ap-9818	62	5	−	−	NOUN
ap-9818	62	6	ν	ν	X
ap-9818	62	7	x2	x2	PROPN
ap-9818	63	1	+	+	CCONJ
ap-9818	63	2	[	[	X
ap-9818	63	3	−ν	−ν	ADJ
ap-9818	63	4	+	+	CCONJ
ap-9818	63	5	δ	δ	NOUN
ap-9818	63	6	ν	ν	NOUN
ap-9818	63	7	+	+	CCONJ
ap-9818	63	8	(	(	PUNCT
ap-9818	63	9	α	α	NOUN
ap-9818	63	10	+	+	CCONJ
ap-9818	63	11	γ	γ	X
ap-9818	63	12	)	)	PUNCT
ap-9818	63	13	δ	δ	NOUN
ap-9818	63	14	ν	ν	X
ap-9818	63	15	]	]	X
ap-9818	63	16	m′(x	m′(x	NOUN
ap-9818	63	17	)	)	PUNCT
ap-9818	63	18	x	x	SYM
ap-9818	63	19	m(x	m(x	PROPN
ap-9818	63	20	)	)	PUNCT
ap-9818	63	21	−(α	−(α	NOUN
ap-9818	64	1	+	+	CCONJ
ap-9818	64	2	γ	γ	X
ap-9818	64	3	+	+	X
ap-9818	64	4	α	α	PROPN
ap-9818	64	5	γ	γ	NOUN
ap-9818	64	6	)	)	PUNCT
ap-9818	64	7	[	[	PUNCT
ap-9818	64	8	m′(x	m′(x	NOUN
ap-9818	64	9	)	)	PUNCT
ap-9818	64	10	m(x	m(x	PROPN
ap-9818	64	11	)	)	PUNCT
ap-9818	64	12	]	]	PUNCT
ap-9818	64	13	2	2	X
ap-9818	64	14	+	+	CCONJ
ap-9818	64	15	(	(	PUNCT
ap-9818	64	16	α	α	NOUN
ap-9818	64	17	+	+	CCONJ
ap-9818	64	18	γ	γ	NOUN
ap-9818	64	19	)	)	PUNCT
ap-9818	64	20	m′′(x	m′′(x	NOUN
ap-9818	64	21	)	)	PUNCT
ap-9818	64	22	2	2	NUM
ap-9818	64	23	m(x	m(x	PROPN
ap-9818	64	24	)	)	PUNCT
ap-9818	64	25	+	+	CCONJ
ap-9818	65	1	e	e	X
ap-9818	65	2	−	−	PROPN
ap-9818	65	3	v	v	X
ap-9818	65	4	(	(	PUNCT
ap-9818	65	5	x	x	NOUN
ap-9818	65	6	)	)	PUNCT
ap-9818	65	7	}	}	PUNCT
ap-9818	65	8	ψν(x	ψν(x	PUNCT
ap-9818	65	9	)	)	PUNCT
ap-9818	65	10	=	=	SYM
ap-9818	65	11	0	0	X
ap-9818	65	12	.	.	PUNCT
ap-9818	66	1	(	(	PUNCT
ap-9818	66	2	6	6	NUM
ap-9818	66	3	)	)	PUNCT
ap-9818	66	4	as	as	SCONJ
ap-9818	66	5	mentioned	mention	VERB
ap-9818	66	6	above	above	ADV
ap-9818	66	7	,	,	PUNCT
ap-9818	66	8	the	the	DET
ap-9818	66	9	setting	set	VERB
ap-9818	66	10	ν	ν	X
ap-9818	66	11	=	=	SYM
ap-9818	66	12	0	0	NUM
ap-9818	66	13	removes	remove	VERB
ap-9818	66	14	the	the	DET
ap-9818	66	15	dunkl	dunkl	PROPN
ap-9818	66	16	scenario	scenario	NOUN
ap-9818	66	17	,	,	PUNCT
ap-9818	66	18	such	such	ADJ
ap-9818	66	19	that	that	SCONJ
ap-9818	66	20	the	the	DET
ap-9818	66	21	conventional	conventional	ADJ
ap-9818	66	22	schrödinger	schrödinger	ADJ
ap-9818	66	23	equation	equation	NOUN
ap-9818	66	24	for	for	ADP
ap-9818	66	25	the	the	DET
ap-9818	66	26	hamiltonian	hamiltonian	NOUN
ap-9818	66	27	(	(	PUNCT
ap-9818	66	28	1	1	X
ap-9818	66	29	)	)	PUNCT
ap-9818	66	30	is	be	AUX
ap-9818	66	31	recovered	recover	VERB
ap-9818	66	32	.	.	PUNCT
ap-9818	67	1	we	we	PRON
ap-9818	67	2	find	find	VERB
ap-9818	67	3	:	:	PUNCT
ap-9818	67	4	ψ′′	ψ′′	NOUN
ap-9818	67	5	0(x	0(x	NOUN
ap-9818	67	6	)	)	PUNCT
ap-9818	67	7	−	−	NUM
ap-9818	68	1	m′(x	m′(x	SYM
ap-9818	68	2	)	)	PUNCT
ap-9818	68	3	m(x	m(x	PROPN
ap-9818	68	4	)	)	PUNCT
ap-9818	68	5	ψ′	ψ′	PART
ap-9818	68	6	0(x	0(x	NOUN
ap-9818	68	7	)	)	PUNCT
ap-9818	69	1	+	+	CCONJ
ap-9818	69	2	{	{	PUNCT
ap-9818	69	3	−(α	−(α	NOUN
ap-9818	69	4	+	+	CCONJ
ap-9818	69	5	γ	γ	X
ap-9818	69	6	+	+	X
ap-9818	69	7	α	α	PROPN
ap-9818	69	8	γ	γ	NOUN
ap-9818	69	9	)	)	PUNCT
ap-9818	69	10	[	[	PUNCT
ap-9818	69	11	m′(x	m′(x	NOUN
ap-9818	69	12	)	)	PUNCT
ap-9818	69	13	m(x	m(x	PROPN
ap-9818	69	14	)	)	PUNCT
ap-9818	69	15	]	]	PUNCT
ap-9818	69	16	2	2	X
ap-9818	69	17	+	+	CCONJ
ap-9818	69	18	(	(	PUNCT
ap-9818	69	19	α	α	NOUN
ap-9818	69	20	+	+	CCONJ
ap-9818	69	21	γ	γ	NOUN
ap-9818	69	22	)	)	PUNCT
ap-9818	69	23	m′′(x	m′′(x	NOUN
ap-9818	69	24	)	)	PUNCT
ap-9818	69	25	2	2	NUM
ap-9818	69	26	m(x	m(x	PROPN
ap-9818	69	27	)	)	PUNCT
ap-9818	69	28	+	+	CCONJ
ap-9818	69	29	e	e	X
ap-9818	69	30	−	−	PROPN
ap-9818	69	31	v	v	X
ap-9818	69	32	(	(	PUNCT
ap-9818	69	33	x	x	NOUN
ap-9818	69	34	)	)	PUNCT
ap-9818	69	35	}	}	PUNCT
ap-9818	69	36	×	×	NOUN
ap-9818	69	37	ψ0(x	ψ0(x	SYM
ap-9818	69	38	)	)	PUNCT
ap-9818	69	39	=	=	SYM
ap-9818	69	40	0	0	X
ap-9818	69	41	.	.	PUNCT
ap-9818	70	1	(	(	PUNCT
ap-9818	70	2	7	7	X
ap-9818	70	3	)	)	PUNCT
ap-9818	70	4	this	this	DET
ap-9818	70	5	form	form	NOUN
ap-9818	70	6	coincides	coincide	VERB
ap-9818	70	7	with	with	ADP
ap-9818	70	8	the	the	DET
ap-9818	70	9	result	result	NOUN
ap-9818	70	10	found	find	VERB
ap-9818	70	11	in	in	ADP
ap-9818	70	12	[	[	X
ap-9818	70	13	30	30	NUM
ap-9818	70	14	]	]	PUNCT
ap-9818	70	15	.	.	PUNCT
ap-9818	71	1	in	in	ADP
ap-9818	71	2	order	order	NOUN
ap-9818	71	3	for	for	ADP
ap-9818	71	4	a	a	DET
ap-9818	71	5	solution	solution	NOUN
ap-9818	71	6	of	of	ADP
ap-9818	71	7	(	(	PUNCT
ap-9818	71	8	6	6	NUM
ap-9818	71	9	)	)	PUNCT
ap-9818	71	10	to	to	PART
ap-9818	71	11	be	be	AUX
ap-9818	71	12	normalisable	normalisable	ADJ
ap-9818	71	13	,	,	PUNCT
ap-9818	71	14	it	it	PRON
ap-9818	71	15	must	must	AUX
ap-9818	71	16	be	be	AUX
ap-9818	71	17	an	an	DET
ap-9818	71	18	element	element	NOUN
ap-9818	71	19	of	of	ADP
ap-9818	71	20	the	the	DET
ap-9818	71	21	weighted	weight	VERB
ap-9818	71	22	hilbert	hilbert	PROPN
ap-9818	71	23	space	space	NOUN
ap-9818	71	24	l2	l2	NOUN
ap-9818	71	25	w(r	w(r	PROPN
ap-9818	71	26	)	)	PUNCT
ap-9818	71	27	with	with	ADP
ap-9818	71	28	weight	weight	NOUN
ap-9818	71	29	function	function	NOUN
ap-9818	71	30	:	:	PUNCT
ap-9818	71	31	w(x	w(x	X
ap-9818	71	32	)	)	PUNCT
ap-9818	71	33	=	=	SYM
ap-9818	71	34	|x|2ν	|x|2ν	NOUN
ap-9818	71	35	.	.	PUNCT
ap-9818	72	1	(	(	PUNCT
ap-9818	72	2	8)	8)	NUM
ap-9818	72	3	223	223	NUM
ap-9818	72	4	axel	axel	PROPN
ap-9818	72	5	schulze	schulze	NOUN
ap-9818	72	6	-	-	PUNCT
ap-9818	72	7	halberg	halberg	PROPN
ap-9818	72	8	acta	acta	PROPN
ap-9818	72	9	polytechnica	polytechnica	PROPN
ap-9818	72	10	the	the	DET
ap-9818	72	11	associated	associated	ADJ
ap-9818	72	12	norm	norm	NOUN
ap-9818	72	13	of	of	ADP
ap-9818	72	14	a	a	DET
ap-9818	72	15	function	function	NOUN
ap-9818	72	16	ψν	ψν	NOUN
ap-9818	72	17	in	in	ADP
ap-9818	72	18	l2	l2	PROPN
ap-9818	72	19	w(r	w(r	PROPN
ap-9818	72	20	)	)	PUNCT
ap-9818	72	21	is	be	AUX
ap-9818	72	22	then	then	ADV
ap-9818	72	23	given	give	VERB
ap-9818	72	24	by	by	ADP
ap-9818	72	25	:	:	PUNCT
ap-9818	72	26	∥ψν(x)∥	∥ψν(x)∥	NOUN
ap-9818	72	27	=	=	PUNCT
ap-9818	72	28	∫	∫	NOUN
ap-9818	72	29	r	r	NOUN
ap-9818	72	30	ψν(x)∗ψν(x	ψν(x)∗ψν(x	NOUN
ap-9818	72	31	)	)	PUNCT
ap-9818	72	32	|x|2ν	|x|2ν	NOUN
ap-9818	72	33	dx	dx	VERB
ap-9818	72	34			NOUN
ap-9818	72	35	1	1	NUM
ap-9818	72	36	2	2	NUM
ap-9818	72	37	.	.	PUNCT
ap-9818	73	1	(	(	PUNCT
ap-9818	73	2	9	9	X
ap-9818	73	3	)	)	PUNCT
ap-9818	73	4	let	let	VERB
ap-9818	73	5	us	we	PRON
ap-9818	73	6	now	now	ADV
ap-9818	73	7	simplify	simplify	VERB
ap-9818	73	8	the	the	DET
ap-9818	73	9	form	form	NOUN
ap-9818	73	10	of	of	ADP
ap-9818	73	11	our	our	PRON
ap-9818	73	12	dunkl	dunkl	NOUN
ap-9818	73	13	-	-	PUNCT
ap-9818	73	14	schrödinger	schrödinger	NOUN
ap-9818	73	15	equation	equation	NOUN
ap-9818	73	16	(	(	PUNCT
ap-9818	73	17	6	6	NUM
ap-9818	73	18	)	)	PUNCT
ap-9818	73	19	by	by	ADP
ap-9818	73	20	removing	remove	VERB
ap-9818	73	21	the	the	DET
ap-9818	73	22	first	first	ADJ
ap-9818	73	23	-	-	PUNCT
ap-9818	73	24	order	order	NOUN
ap-9818	73	25	derivative	derivative	ADJ
ap-9818	73	26	term	term	NOUN
ap-9818	73	27	∼	∼	NOUN
ap-9818	73	28	ψ′	ψ′	NOUN
ap-9818	73	29	ν	ν	NOUN
ap-9818	73	30	.	.	PUNCT
ap-9818	74	1	to	to	ADP
ap-9818	74	2	this	this	DET
ap-9818	74	3	end	end	NOUN
ap-9818	74	4	,	,	PUNCT
ap-9818	74	5	we	we	PRON
ap-9818	74	6	apply	apply	VERB
ap-9818	74	7	the	the	DET
ap-9818	74	8	point	point	NOUN
ap-9818	74	9	transformation	transformation	NOUN
ap-9818	74	10	:	:	PUNCT
ap-9818	74	11	ψν(x	ψν(x	X
ap-9818	74	12	)	)	PUNCT
ap-9818	74	13	=	=	SYM
ap-9818	75	1	√	√	NUM
ap-9818	75	2	m(x	m(x	NOUN
ap-9818	75	3	)	)	PUNCT
ap-9818	75	4	xν	xν	NOUN
ap-9818	75	5	ξν(x	ξν(x	NUM
ap-9818	75	6	)	)	PUNCT
ap-9818	75	7	,	,	PUNCT
ap-9818	75	8	(	(	PUNCT
ap-9818	75	9	10	10	NUM
ap-9818	75	10	)	)	PUNCT
ap-9818	75	11	such	such	ADJ
ap-9818	75	12	that	that	SCONJ
ap-9818	75	13	the	the	DET
ap-9818	75	14	new	new	ADJ
ap-9818	75	15	function	function	NOUN
ap-9818	75	16	ξν	ξν	ADV
ap-9818	75	17	becomes	become	VERB
ap-9818	75	18	a	a	DET
ap-9818	75	19	solution	solution	NOUN
ap-9818	75	20	of	of	ADP
ap-9818	75	21	the	the	DET
ap-9818	75	22	following	follow	VERB
ap-9818	75	23	equation	equation	NOUN
ap-9818	75	24	:	:	PUNCT
ap-9818	75	25	ξ′′	ξ′′	PROPN
ap-9818	75	26	ν	ν	X
ap-9818	75	27	(	(	PUNCT
ap-9818	75	28	x	x	X
ap-9818	75	29	)	)	PUNCT
ap-9818	75	30	+	+	NUM
ap-9818	75	31	uν(x	uν(x	NOUN
ap-9818	75	32	)	)	PUNCT
ap-9818	75	33	ξν(x	ξν(x	PUNCT
ap-9818	75	34	)	)	PUNCT
ap-9818	76	1	=	=	SYM
ap-9818	76	2	0	0	NUM
ap-9818	76	3	,	,	PUNCT
ap-9818	76	4	(	(	PUNCT
ap-9818	76	5	11	11	NUM
ap-9818	76	6	)	)	PUNCT
ap-9818	76	7	where	where	SCONJ
ap-9818	76	8	the	the	DET
ap-9818	76	9	effective	effective	ADJ
ap-9818	76	10	potential	potential	NOUN
ap-9818	76	11	uν	uν	PROPN
ap-9818	76	12	is	be	AUX
ap-9818	76	13	given	give	VERB
ap-9818	76	14	by	by	ADP
ap-9818	76	15	:	:	PUNCT
ap-9818	76	16	uν(x	uν(x	NUM
ap-9818	76	17	)	)	PUNCT
ap-9818	76	18	=	=	PUNCT
ap-9818	77	1	[	[	X
ap-9818	77	2	e	e	X
ap-9818	77	3	−	−	PROPN
ap-9818	77	4	v	v	PART
ap-9818	77	5	(	(	PUNCT
ap-9818	77	6	x	x	NOUN
ap-9818	77	7	)	)	PUNCT
ap-9818	77	8	]	]	PUNCT
ap-9818	77	9	m(x	m(x	PROPN
ap-9818	77	10	)	)	PUNCT
ap-9818	77	11	−	−	PROPN
ap-9818	77	12	(	(	PUNCT
ap-9818	77	13	3	3	NUM
ap-9818	77	14	4	4	NUM
ap-9818	77	15	+	+	NUM
ap-9818	77	16	α	α	NOUN
ap-9818	77	17	+	+	X
ap-9818	77	18	γ	γ	X
ap-9818	77	19	+	+	X
ap-9818	77	20	α	α	PROPN
ap-9818	77	21	γ	γ	NOUN
ap-9818	77	22	)	)	PUNCT
ap-9818	77	23	[	[	PUNCT
ap-9818	77	24	m′(x	m′(x	NOUN
ap-9818	77	25	)	)	PUNCT
ap-9818	77	26	m(x	m(x	PROPN
ap-9818	77	27	)	)	PUNCT
ap-9818	77	28	]	]	PUNCT
ap-9818	77	29	2	2	NUM
ap-9818	77	30	+	+	CCONJ
ap-9818	77	31	(	(	PUNCT
ap-9818	77	32	1	1	NUM
ap-9818	77	33	+	+	NUM
ap-9818	77	34	α	α	NOUN
ap-9818	77	35	+	+	CCONJ
ap-9818	77	36	γ	γ	X
ap-9818	77	37	)	)	PUNCT
ap-9818	77	38	m′′(x	m′′(x	NOUN
ap-9818	77	39	)	)	PUNCT
ap-9818	77	40	2	2	NUM
ap-9818	77	41	m(x	m(x	PROPN
ap-9818	77	42	)	)	PUNCT
ap-9818	78	1	+	+	NUM
ap-9818	78	2	ν	ν	X
ap-9818	78	3	[	[	PUNCT
ap-9818	78	4	δ	δ	X
ap-9818	78	5	x2	x2	PROPN
ap-9818	79	1	+	+	CCONJ
ap-9818	79	2	(	(	PUNCT
ap-9818	79	3	δ	δ	PROPN
ap-9818	79	4	+	+	CCONJ
ap-9818	79	5	α	α	PROPN
ap-9818	79	6	δ	δ	PROPN
ap-9818	79	7	+	+	CCONJ
ap-9818	79	8	γ	γ	PROPN
ap-9818	79	9	δ	δ	PROPN
ap-9818	79	10	)	)	PUNCT
ap-9818	79	11	m′(x	m′(x	PROPN
ap-9818	79	12	)	)	PUNCT
ap-9818	79	13	x	x	SYM
ap-9818	79	14	m(x	m(x	PROPN
ap-9818	79	15	)	)	PUNCT
ap-9818	79	16	]	]	PUNCT
ap-9818	80	1	−	−	PROPN
ap-9818	80	2	ν2	ν2	NOUN
ap-9818	80	3	x2	x2	INTJ
ap-9818	80	4	.	.	PUNCT
ap-9818	81	1	(	(	PUNCT
ap-9818	81	2	12	12	NUM
ap-9818	81	3	)	)	PUNCT
ap-9818	81	4	note	note	NOUN
ap-9818	81	5	that	that	SCONJ
ap-9818	81	6	we	we	PRON
ap-9818	81	7	collected	collect	VERB
ap-9818	81	8	terms	term	NOUN
ap-9818	81	9	arising	arise	VERB
ap-9818	81	10	from	from	ADP
ap-9818	81	11	the	the	DET
ap-9818	81	12	dunkl	dunkl	NOUN
ap-9818	81	13	formalism	formalism	NOUN
ap-9818	81	14	by	by	ADP
ap-9818	81	15	means	mean	NOUN
ap-9818	81	16	of	of	ADP
ap-9818	81	17	the	the	DET
ap-9818	81	18	parameter	parameter	NOUN
ap-9818	81	19	ν	ν	PROPN
ap-9818	81	20	.	.	PUNCT
ap-9818	82	1	according	accord	VERB
ap-9818	82	2	to	to	ADP
ap-9818	82	3	the	the	DET
ap-9818	82	4	effective	effective	ADJ
ap-9818	82	5	potential	potential	NOUN
ap-9818	82	6	(	(	PUNCT
ap-9818	82	7	12	12	NUM
ap-9818	82	8	)	)	PUNCT
ap-9818	82	9	,	,	PUNCT
ap-9818	82	10	the	the	DET
ap-9818	82	11	latter	latter	ADJ
ap-9818	82	12	formalism	formalism	NOUN
ap-9818	82	13	contributes	contribute	VERB
ap-9818	82	14	an	an	DET
ap-9818	82	15	inverse	inverse	ADJ
ap-9818	82	16	square	square	ADJ
ap-9818	82	17	singularity	singularity	NOUN
ap-9818	82	18	at	at	ADP
ap-9818	82	19	the	the	DET
ap-9818	82	20	origin	origin	NOUN
ap-9818	82	21	,	,	PUNCT
ap-9818	82	22	as	as	ADV
ap-9818	82	23	well	well	ADV
ap-9818	82	24	as	as	ADP
ap-9818	82	25	possible	possible	ADJ
ap-9818	82	26	singularities	singularity	NOUN
ap-9818	82	27	in	in	ADP
ap-9818	82	28	the	the	DET
ap-9818	82	29	term	term	NOUN
ap-9818	82	30	∼	∼	VERB
ap-9818	82	31	m′	m′	NOUN
ap-9818	82	32	xm	xm	PROPN
ap-9818	82	33	.	.	PUNCT
ap-9818	83	1	as	as	ADP
ap-9818	83	2	such	such	ADJ
ap-9818	83	3	,	,	PUNCT
ap-9818	83	4	the	the	DET
ap-9818	83	5	parameters	parameter	NOUN
ap-9818	83	6	ν	ν	NOUN
ap-9818	83	7	and	and	CCONJ
ap-9818	83	8	δ	δ	PROPN
ap-9818	83	9	can	can	AUX
ap-9818	83	10	be	be	AUX
ap-9818	83	11	used	use	VERB
ap-9818	83	12	to	to	PART
ap-9818	83	13	remove	remove	VERB
ap-9818	83	14	singularities	singularity	NOUN
ap-9818	83	15	that	that	SCONJ
ap-9818	83	16	the	the	DET
ap-9818	83	17	potential	potential	NOUN
ap-9818	83	18	or	or	CCONJ
ap-9818	83	19	the	the	DET
ap-9818	83	20	position	position	NOUN
ap-9818	83	21	-	-	PUNCT
ap-9818	83	22	dependent	dependent	ADJ
ap-9818	83	23	mass	mass	NOUN
ap-9818	83	24	contain	contain	NOUN
ap-9818	83	25	.	.	PUNCT
ap-9818	84	1	we	we	PRON
ap-9818	84	2	will	will	AUX
ap-9818	84	3	discuss	discuss	VERB
ap-9818	84	4	examples	example	NOUN
ap-9818	84	5	in	in	ADP
ap-9818	84	6	section	section	NOUN
ap-9818	84	7	4	4	NUM
ap-9818	84	8	.	.	PUNCT
ap-9818	85	1	next	next	ADV
ap-9818	85	2	,	,	PUNCT
ap-9818	85	3	let	let	VERB
ap-9818	85	4	us	we	PRON
ap-9818	85	5	point	point	VERB
ap-9818	85	6	out	out	ADP
ap-9818	85	7	that	that	SCONJ
ap-9818	85	8	the	the	DET
ap-9818	85	9	particular	particular	ADJ
ap-9818	85	10	parameter	parameter	NOUN
ap-9818	85	11	setting	set	VERB
ap-9818	85	12	α	α	X
ap-9818	85	13	=	=	SYM
ap-9818	85	14	γ	γ	X
ap-9818	85	15	=	=	SYM
ap-9818	85	16	−	−	PROPN
ap-9818	85	17	1	1	NUM
ap-9818	85	18	2	2	NUM
ap-9818	85	19	renders	render	VERB
ap-9818	85	20	the	the	DET
ap-9818	85	21	function	function	NOUN
ap-9818	85	22	(	(	PUNCT
ap-9818	85	23	12	12	NUM
ap-9818	85	24	)	)	PUNCT
ap-9818	85	25	in	in	ADP
ap-9818	85	26	a	a	DET
ap-9818	85	27	particularly	particularly	ADV
ap-9818	85	28	simple	simple	ADJ
ap-9818	85	29	form	form	NOUN
ap-9818	85	30	.	.	PUNCT
ap-9818	86	1	we	we	PRON
ap-9818	86	2	find	find	VERB
ap-9818	86	3	:	:	PUNCT
ap-9818	86	4	uν(x	uν(x	X
ap-9818	86	5	)	)	PUNCT
ap-9818	86	6	=	=	PUNCT
ap-9818	87	1	[	[	X
ap-9818	87	2	e	e	X
ap-9818	87	3	−	−	PROPN
ap-9818	87	4	v	v	PART
ap-9818	87	5	(	(	PUNCT
ap-9818	87	6	x	x	NOUN
ap-9818	87	7	)	)	PUNCT
ap-9818	87	8	]	]	PUNCT
ap-9818	87	9	m(x	m(x	PROPN
ap-9818	87	10	)	)	PUNCT
ap-9818	88	1	+	+	CCONJ
ap-9818	88	2	ν	ν	X
ap-9818	88	3	δ	δ	NOUN
ap-9818	88	4	−	−	PROPN
ap-9818	88	5	ν2	ν2	PROPN
ap-9818	89	1	x2	x2	INTJ
ap-9818	89	2	.	.	PUNCT
ap-9818	90	1	(	(	PUNCT
ap-9818	90	2	13	13	NUM
ap-9818	90	3	)	)	PUNCT
ap-9818	90	4	if	if	SCONJ
ap-9818	90	5	we	we	PRON
ap-9818	90	6	set	set	VERB
ap-9818	90	7	ν	ν	NOUN
ap-9818	90	8	=	=	SYM
ap-9818	90	9	0	0	PROPN
ap-9818	90	10	,	,	PUNCT
ap-9818	90	11	the	the	DET
ap-9818	90	12	dunkl	dunkl	NOUN
ap-9818	90	13	formalism	formalism	NOUN
ap-9818	90	14	is	be	AUX
ap-9818	90	15	removed	remove	VERB
ap-9818	90	16	,	,	PUNCT
ap-9818	90	17	such	such	ADJ
ap-9818	90	18	that	that	SCONJ
ap-9818	90	19	our	our	PRON
ap-9818	90	20	equation	equation	NOUN
ap-9818	90	21	(	(	PUNCT
ap-9818	90	22	11	11	NUM
ap-9818	90	23	)	)	PUNCT
ap-9818	90	24	takes	take	VERB
ap-9818	90	25	the	the	DET
ap-9818	90	26	form	form	NOUN
ap-9818	90	27	:	:	PUNCT
ap-9818	90	28	ξ′′	ξ′′	NOUN
ap-9818	90	29	0	0	PUNCT
ap-9818	90	30	(	(	PUNCT
ap-9818	90	31	x	x	X
ap-9818	90	32	)	)	PUNCT
ap-9818	90	33	+	+	X
ap-9818	90	34	u0(x	u0(x	X
ap-9818	90	35	)	)	PUNCT
ap-9818	90	36	ξ0(x	ξ0(x	NOUN
ap-9818	90	37	)	)	PUNCT
ap-9818	90	38	=	=	NOUN
ap-9818	91	1	0	0	X
ap-9818	91	2	.	.	PUNCT
ap-9818	92	1	(	(	PUNCT
ap-9818	92	2	14	14	NUM
ap-9818	92	3	)	)	PUNCT
ap-9818	92	4	here	here	ADV
ap-9818	92	5	,	,	PUNCT
ap-9818	92	6	the	the	DET
ap-9818	92	7	effective	effective	ADJ
ap-9818	92	8	potential	potential	ADJ
ap-9818	92	9	u0	u0	NOUN
ap-9818	92	10	is	be	AUX
ap-9818	92	11	a	a	DET
ap-9818	92	12	special	special	ADJ
ap-9818	92	13	case	case	NOUN
ap-9818	92	14	of	of	ADP
ap-9818	92	15	(	(	PUNCT
ap-9818	92	16	12	12	NUM
ap-9818	92	17	)	)	PUNCT
ap-9818	92	18	that	that	PRON
ap-9818	92	19	reads	read	VERB
ap-9818	92	20	:	:	PUNCT
ap-9818	92	21	u0(x	u0(x	NUM
ap-9818	92	22	)	)	PUNCT
ap-9818	92	23	=	=	PUNCT
ap-9818	93	1	[	[	X
ap-9818	93	2	e	e	X
ap-9818	93	3	−	−	PROPN
ap-9818	93	4	v	v	PART
ap-9818	93	5	(	(	PUNCT
ap-9818	93	6	x	x	NOUN
ap-9818	93	7	)	)	PUNCT
ap-9818	93	8	]	]	PUNCT
ap-9818	93	9	m(x	m(x	PROPN
ap-9818	93	10	)	)	PUNCT
ap-9818	93	11	−	−	PROPN
ap-9818	94	1	(	(	PUNCT
ap-9818	94	2	3	3	NUM
ap-9818	94	3	4	4	NUM
ap-9818	94	4	+	+	NUM
ap-9818	94	5	α	α	NOUN
ap-9818	94	6	+	+	X
ap-9818	94	7	γ	γ	X
ap-9818	94	8	+	+	X
ap-9818	94	9	α	α	PROPN
ap-9818	94	10	γ	γ	NOUN
ap-9818	94	11	)	)	PUNCT
ap-9818	94	12	[	[	PUNCT
ap-9818	94	13	m′(x	m′(x	NOUN
ap-9818	94	14	)	)	PUNCT
ap-9818	94	15	m(x	m(x	PROPN
ap-9818	94	16	)	)	PUNCT
ap-9818	94	17	]	]	PUNCT
ap-9818	94	18	2	2	NUM
ap-9818	94	19	+	+	CCONJ
ap-9818	94	20	(	(	PUNCT
ap-9818	94	21	1	1	NUM
ap-9818	94	22	+	+	NUM
ap-9818	94	23	α	α	NOUN
ap-9818	94	24	+	+	CCONJ
ap-9818	94	25	γ	γ	X
ap-9818	94	26	)	)	PUNCT
ap-9818	94	27	m′′(x	m′′(x	NOUN
ap-9818	94	28	)	)	PUNCT
ap-9818	94	29	2	2	NUM
ap-9818	94	30	m(x	m(x	PROPN
ap-9818	94	31	)	)	PUNCT
ap-9818	94	32	.	.	PUNCT
ap-9818	95	1	(	(	PUNCT
ap-9818	95	2	15	15	X
ap-9818	95	3	)	)	PUNCT
ap-9818	95	4	our	our	PRON
ap-9818	95	5	next	next	ADJ
ap-9818	95	6	goal	goal	NOUN
ap-9818	95	7	is	be	AUX
ap-9818	95	8	to	to	PART
ap-9818	95	9	determine	determine	VERB
ap-9818	95	10	conditions	condition	NOUN
ap-9818	95	11	,	,	PUNCT
ap-9818	95	12	under	under	ADP
ap-9818	95	13	which	which	PRON
ap-9818	95	14	the	the	DET
ap-9818	95	15	effective	effective	ADJ
ap-9818	95	16	potentials	potential	NOUN
ap-9818	95	17	(	(	PUNCT
ap-9818	95	18	12	12	NUM
ap-9818	95	19	)	)	PUNCT
ap-9818	95	20	and	and	CCONJ
ap-9818	95	21	(	(	PUNCT
ap-9818	95	22	15	15	X
ap-9818	95	23	)	)	PUNCT
ap-9818	95	24	have	have	VERB
ap-9818	95	25	the	the	DET
ap-9818	95	26	same	same	ADJ
ap-9818	95	27	functional	functional	ADJ
ap-9818	95	28	form	form	NOUN
ap-9818	95	29	,	,	PUNCT
ap-9818	95	30	such	such	ADJ
ap-9818	95	31	that	that	SCONJ
ap-9818	95	32	their	their	PRON
ap-9818	95	33	associated	associated	ADJ
ap-9818	95	34	equations	equation	NOUN
ap-9818	95	35	have	have	VERB
ap-9818	95	36	the	the	DET
ap-9818	95	37	same	same	ADJ
ap-9818	95	38	solutions	solution	NOUN
ap-9818	95	39	,	,	PUNCT
ap-9818	95	40	up	up	ADP
ap-9818	95	41	to	to	ADP
ap-9818	95	42	a	a	DET
ap-9818	95	43	redefinition	redefinition	NOUN
ap-9818	95	44	of	of	ADP
ap-9818	95	45	parameters	parameter	NOUN
ap-9818	95	46	.	.	PUNCT
ap-9818	96	1	3	3	X
ap-9818	96	2	.	.	X
ap-9818	96	3	solvability	solvability	NOUN
ap-9818	96	4	conditions	condition	NOUN
ap-9818	96	5	we	we	PRON
ap-9818	96	6	will	will	AUX
ap-9818	96	7	now	now	ADV
ap-9818	96	8	compare	compare	VERB
ap-9818	96	9	the	the	DET
ap-9818	96	10	forms	form	NOUN
ap-9818	96	11	of	of	ADP
ap-9818	96	12	the	the	DET
ap-9818	96	13	reduced	reduce	VERB
ap-9818	96	14	dunkl	dunkl	NOUN
ap-9818	96	15	-	-	PUNCT
ap-9818	96	16	schrödinger	schrödinger	NOUN
ap-9818	96	17	equation	equation	NOUN
ap-9818	96	18	(	(	PUNCT
ap-9818	96	19	11	11	NUM
ap-9818	96	20	)	)	PUNCT
ap-9818	96	21	and	and	CCONJ
ap-9818	96	22	its	its	PRON
ap-9818	96	23	conventional	conventional	ADJ
ap-9818	96	24	counterpart	counterpart	NOUN
ap-9818	96	25	(	(	PUNCT
ap-9818	96	26	14	14	NUM
ap-9818	96	27	)	)	PUNCT
ap-9818	96	28	.	.	PUNCT
ap-9818	97	1	more	more	ADV
ap-9818	97	2	precisely	precisely	ADV
ap-9818	97	3	,	,	PUNCT
ap-9818	97	4	we	we	PRON
ap-9818	97	5	will	will	AUX
ap-9818	97	6	focus	focus	VERB
ap-9818	97	7	on	on	ADP
ap-9818	97	8	their	their	PRON
ap-9818	97	9	effective	effective	ADJ
ap-9818	97	10	potentials	potential	NOUN
ap-9818	97	11	uν	uν	ADP
ap-9818	97	12	and	and	CCONJ
ap-9818	97	13	u0	u0	ADJ
ap-9818	97	14	,	,	PUNCT
ap-9818	97	15	as	as	SCONJ
ap-9818	97	16	given	give	VERB
ap-9818	97	17	in	in	ADP
ap-9818	97	18	(	(	PUNCT
ap-9818	97	19	12	12	NUM
ap-9818	97	20	)	)	PUNCT
ap-9818	97	21	and	and	CCONJ
ap-9818	97	22	(	(	PUNCT
ap-9818	97	23	15	15	NUM
ap-9818	97	24	)	)	PUNCT
ap-9818	97	25	,	,	PUNCT
ap-9818	97	26	respectively	respectively	ADV
ap-9818	97	27	.	.	PUNCT
ap-9818	98	1	if	if	SCONJ
ap-9818	98	2	these	these	DET
ap-9818	98	3	two	two	NUM
ap-9818	98	4	potentials	potential	NOUN
ap-9818	98	5	have	have	VERB
ap-9818	98	6	the	the	DET
ap-9818	98	7	same	same	ADJ
ap-9818	98	8	functional	functional	ADJ
ap-9818	98	9	form	form	NOUN
ap-9818	98	10	,	,	PUNCT
ap-9818	98	11	but	but	CCONJ
ap-9818	98	12	differ	differ	VERB
ap-9818	98	13	merely	merely	ADV
ap-9818	98	14	in	in	ADP
ap-9818	98	15	numerical	numerical	ADJ
ap-9818	98	16	parameters	parameter	NOUN
ap-9818	98	17	,	,	PUNCT
ap-9818	98	18	then	then	ADV
ap-9818	98	19	the	the	DET
ap-9818	98	20	same	same	ADJ
ap-9818	98	21	is	be	AUX
ap-9818	98	22	true	true	ADJ
ap-9818	98	23	for	for	ADP
ap-9818	98	24	solutions	solution	NOUN
ap-9818	98	25	to	to	ADP
ap-9818	98	26	the	the	DET
ap-9818	98	27	corresponding	correspond	VERB
ap-9818	98	28	schrödinger	schrödinger	ADJ
ap-9818	98	29	equations	equation	NOUN
ap-9818	98	30	.	.	PUNCT
ap-9818	99	1	in	in	ADP
ap-9818	99	2	other	other	ADJ
ap-9818	99	3	words	word	NOUN
ap-9818	99	4	,	,	PUNCT
ap-9818	99	5	if	if	SCONJ
ap-9818	99	6	a	a	DET
ap-9818	99	7	solution	solution	NOUN
ap-9818	99	8	to	to	ADP
ap-9818	99	9	the	the	DET
ap-9818	99	10	conventional	conventional	ADJ
ap-9818	99	11	equation	equation	NOUN
ap-9818	99	12	is	be	AUX
ap-9818	99	13	known	know	VERB
ap-9818	99	14	,	,	PUNCT
ap-9818	99	15	then	then	ADV
ap-9818	99	16	it	it	PRON
ap-9818	99	17	can	can	AUX
ap-9818	99	18	be	be	AUX
ap-9818	99	19	mapped	map	VERB
ap-9818	99	20	onto	onto	ADP
ap-9818	99	21	a	a	DET
ap-9818	99	22	solution	solution	NOUN
ap-9818	99	23	of	of	ADP
ap-9818	99	24	the	the	DET
ap-9818	99	25	equation	equation	NOUN
ap-9818	99	26	within	within	ADP
ap-9818	99	27	the	the	DET
ap-9818	99	28	dunkl	dunkl	PROPN
ap-9818	99	29	scenario	scenario	NOUN
ap-9818	99	30	by	by	ADP
ap-9818	99	31	a	a	DET
ap-9818	99	32	change	change	NOUN
ap-9818	99	33	of	of	ADP
ap-9818	99	34	numerical	numerical	ADJ
ap-9818	99	35	parameters	parameter	NOUN
ap-9818	99	36	.	.	PUNCT
ap-9818	100	1	the	the	DET
ap-9818	100	2	functional	functional	ADJ
ap-9818	100	3	form	form	NOUN
ap-9818	100	4	of	of	ADP
ap-9818	100	5	the	the	DET
ap-9818	100	6	two	two	NUM
ap-9818	100	7	effective	effective	ADJ
ap-9818	100	8	potentials	potential	NOUN
ap-9818	100	9	(	(	PUNCT
ap-9818	100	10	12	12	NUM
ap-9818	100	11	)	)	PUNCT
ap-9818	100	12	and	and	CCONJ
ap-9818	100	13	(	(	PUNCT
ap-9818	100	14	15	15	NUM
ap-9818	100	15	)	)	PUNCT
ap-9818	100	16	is	be	AUX
ap-9818	100	17	,	,	PUNCT
ap-9818	100	18	in	in	ADP
ap-9818	100	19	general	general	ADJ
ap-9818	100	20	,	,	PUNCT
ap-9818	100	21	different	different	ADJ
ap-9818	100	22	due	due	ADP
ap-9818	100	23	to	to	ADP
ap-9818	100	24	two	two	NUM
ap-9818	100	25	terms	term	NOUN
ap-9818	100	26	that	that	PRON
ap-9818	100	27	are	be	AUX
ap-9818	100	28	contributed	contribute	VERB
ap-9818	100	29	by	by	ADP
ap-9818	100	30	the	the	DET
ap-9818	100	31	dunkl	dunkl	NOUN
ap-9818	100	32	formalism	formalism	NOUN
ap-9818	100	33	in	in	ADP
ap-9818	100	34	(	(	PUNCT
ap-9818	100	35	12	12	NUM
ap-9818	100	36	):	):	PUNCT
ap-9818	100	37	one	one	NUM
ap-9818	100	38	of	of	ADP
ap-9818	100	39	these	these	DET
ap-9818	100	40	terms	term	NOUN
ap-9818	100	41	is	be	AUX
ap-9818	100	42	proportional	proportional	ADJ
ap-9818	100	43	to	to	ADP
ap-9818	100	44	m′/xm	m′/xm	VERB
ap-9818	100	45	,	,	PUNCT
ap-9818	100	46	while	while	SCONJ
ap-9818	100	47	the	the	DET
ap-9818	100	48	other	other	ADJ
ap-9818	100	49	term	term	NOUN
ap-9818	100	50	is	be	AUX
ap-9818	100	51	inverse	inverse	ADJ
ap-9818	100	52	quadratic	quadratic	NOUN
ap-9818	100	53	.	.	PUNCT
ap-9818	101	1	we	we	PRON
ap-9818	101	2	will	will	AUX
ap-9818	101	3	now	now	ADV
ap-9818	101	4	set	set	VERB
ap-9818	101	5	up	up	ADP
ap-9818	101	6	conditions	condition	NOUN
ap-9818	101	7	on	on	ADP
ap-9818	101	8	the	the	DET
ap-9818	101	9	position	position	NOUN
ap-9818	101	10	-	-	PUNCT
ap-9818	101	11	dependent	dependent	ADJ
ap-9818	101	12	mass	mass	NOUN
ap-9818	101	13	and	and	CCONJ
ap-9818	101	14	the	the	DET
ap-9818	101	15	potential	potential	NOUN
ap-9818	101	16	,	,	PUNCT
ap-9818	101	17	such	such	ADJ
ap-9818	101	18	that	that	SCONJ
ap-9818	101	19	the	the	DET
ap-9818	101	20	latter	latter	ADJ
ap-9818	101	21	two	two	NUM
ap-9818	101	22	terms	term	NOUN
ap-9818	101	23	appear	appear	VERB
ap-9818	101	24	in	in	ADP
ap-9818	101	25	both	both	CCONJ
ap-9818	101	26	effective	effective	ADJ
ap-9818	101	27	potentials	potential	NOUN
ap-9818	101	28	(	(	PUNCT
ap-9818	101	29	12	12	NUM
ap-9818	101	30	)	)	PUNCT
ap-9818	101	31	and	and	CCONJ
ap-9818	101	32	(	(	PUNCT
ap-9818	101	33	15	15	NUM
ap-9818	101	34	)	)	PUNCT
ap-9818	101	35	.	.	PUNCT
ap-9818	102	1	first	first	ADJ
ap-9818	102	2	condition	condition	NOUN
ap-9818	102	3	.	.	PUNCT
ap-9818	103	1	let	let	VERB
ap-9818	103	2	us	we	PRON
ap-9818	103	3	focus	focus	VERB
ap-9818	103	4	on	on	ADP
ap-9818	103	5	the	the	DET
ap-9818	103	6	term	term	NOUN
ap-9818	103	7	proportional	proportional	ADJ
ap-9818	103	8	to	to	ADP
ap-9818	103	9	m′/xm	m′/xm	NOUN
ap-9818	103	10	that	that	PRON
ap-9818	103	11	appears	appear	VERB
ap-9818	103	12	in	in	ADP
ap-9818	103	13	the	the	DET
ap-9818	103	14	effective	effective	ADJ
ap-9818	103	15	potential	potential	NOUN
ap-9818	103	16	(	(	PUNCT
ap-9818	103	17	12	12	NUM
ap-9818	103	18	)	)	PUNCT
ap-9818	103	19	.	.	PUNCT
ap-9818	104	1	we	we	PRON
ap-9818	104	2	will	will	AUX
ap-9818	104	3	now	now	ADV
ap-9818	104	4	set	set	VERB
ap-9818	104	5	up	up	ADP
ap-9818	104	6	a	a	DET
ap-9818	104	7	condition	condition	NOUN
ap-9818	104	8	for	for	ADP
ap-9818	104	9	the	the	DET
ap-9818	104	10	position	position	NOUN
ap-9818	104	11	-	-	PUNCT
ap-9818	104	12	dependent	dependent	ADJ
ap-9818	104	13	mass	mass	NOUN
ap-9818	104	14	,	,	PUNCT
ap-9818	104	15	such	such	ADJ
ap-9818	104	16	that	that	SCONJ
ap-9818	104	17	the	the	DET
ap-9818	104	18	latter	latter	ADJ
ap-9818	104	19	term	term	NOUN
ap-9818	104	20	can	can	AUX
ap-9818	104	21	be	be	AUX
ap-9818	104	22	written	write	VERB
ap-9818	104	23	as	as	ADP
ap-9818	104	24	a	a	DET
ap-9818	104	25	linear	linear	ADJ
ap-9818	104	26	combination	combination	NOUN
ap-9818	104	27	of	of	ADP
ap-9818	104	28	existing	exist	VERB
ap-9818	104	29	terms	term	NOUN
ap-9818	104	30	in	in	ADP
ap-9818	104	31	(	(	PUNCT
ap-9818	104	32	15	15	NUM
ap-9818	104	33	)	)	PUNCT
ap-9818	104	34	.	.	PUNCT
ap-9818	105	1	this	this	DET
ap-9818	105	2	condition	condition	NOUN
ap-9818	105	3	reads	read	VERB
ap-9818	105	4	:	:	PUNCT
ap-9818	105	5	m′(x	m′(x	X
ap-9818	105	6	)	)	PUNCT
ap-9818	105	7	x	x	SYM
ap-9818	105	8	m(x	m(x	PROPN
ap-9818	105	9	)	)	PUNCT
ap-9818	105	10	=	=	NOUN
ap-9818	105	11	a	a	DET
ap-9818	105	12	m′′(x	m′′(x	NOUN
ap-9818	105	13	)	)	PUNCT
ap-9818	105	14	m(x	m(x	NOUN
ap-9818	105	15	)	)	PUNCT
ap-9818	106	1	+	+	CCONJ
ap-9818	106	2	b	b	X
ap-9818	106	3	[	[	PUNCT
ap-9818	106	4	m′(x	m′(x	NOUN
ap-9818	106	5	)	)	PUNCT
ap-9818	106	6	m(x	m(x	PROPN
ap-9818	106	7	)	)	PUNCT
ap-9818	106	8	]	]	PUNCT
ap-9818	106	9	2	2	NUM
ap-9818	106	10	,	,	PUNCT
ap-9818	106	11	(	(	PUNCT
ap-9818	106	12	16	16	NUM
ap-9818	106	13	)	)	PUNCT
ap-9818	106	14	224	224	NUM
ap-9818	106	15	vol	vol	NOUN
ap-9818	106	16	.	.	PUNCT
ap-9818	107	1	65	65	NUM
ap-9818	107	2	no	no	NOUN
ap-9818	107	3	.	.	PUNCT
ap-9818	108	1	2/2025	2/2025	NUM
ap-9818	108	2	persistence	persistence	NOUN
ap-9818	108	3	of	of	ADP
ap-9818	108	4	solvability	solvability	NOUN
ap-9818	108	5	in	in	ADP
ap-9818	108	6	quantum	quantum	NOUN
ap-9818	108	7	systems	system	NOUN
ap-9818	108	8	deformed	deform	VERB
ap-9818	108	9	by	by	ADP
ap-9818	108	10	dunkl	dunkl	PROPN
ap-9818	108	11	.	.	PUNCT
ap-9818	108	12	.	.	PUNCT
ap-9818	108	13	.	.	PUNCT
ap-9818	109	1	where	where	SCONJ
ap-9818	109	2	a	a	PRON
ap-9818	109	3	and	and	CCONJ
ap-9818	109	4	b	b	NOUN
ap-9818	109	5	are	be	AUX
ap-9818	109	6	arbitrary	arbitrary	ADJ
ap-9818	109	7	constants	constant	NOUN
ap-9818	109	8	.	.	PUNCT
ap-9818	110	1	the	the	DET
ap-9818	110	2	condition	condition	NOUN
ap-9818	110	3	can	can	AUX
ap-9818	110	4	be	be	AUX
ap-9818	110	5	solved	solve	VERB
ap-9818	110	6	in	in	ADP
ap-9818	110	7	closed	closed	ADJ
ap-9818	110	8	form	form	NOUN
ap-9818	110	9	for	for	ADP
ap-9818	110	10	the	the	DET
ap-9818	110	11	position	position	NOUN
ap-9818	110	12	-	-	PUNCT
ap-9818	110	13	dependent	dependent	ADJ
ap-9818	110	14	mass	mass	NOUN
ap-9818	110	15	.	.	PUNCT
ap-9818	111	1	the	the	DET
ap-9818	111	2	general	general	ADJ
ap-9818	111	3	solution	solution	NOUN
ap-9818	111	4	reads	read	VERB
ap-9818	111	5	:	:	PUNCT
ap-9818	111	6	m(x	m(x	X
ap-9818	111	7	)	)	PUNCT
ap-9818	112	1	=	=	SYM
ap-9818	112	2	c2	c2	PROPN
ap-9818	112	3	[	[	PUNCT
ap-9818	112	4	c1	c1	PROPN
ap-9818	112	5	(	(	PUNCT
ap-9818	112	6	a	a	DET
ap-9818	112	7	+	+	NOUN
ap-9818	112	8	1	1	NUM
ap-9818	112	9	)	)	PUNCT
ap-9818	112	10	+	+	CCONJ
ap-9818	112	11	(	(	PUNCT
ap-9818	112	12	a	a	DET
ap-9818	112	13	+	+	NOUN
ap-9818	112	14	b	b	NOUN
ap-9818	112	15	)	)	PUNCT
ap-9818	112	16	x1	x1	PROPN
ap-9818	113	1	+	+	ADP
ap-9818	113	2	1	1	NUM
ap-9818	113	3	a	a	PRON
ap-9818	113	4	]	]	X
ap-9818	113	5	a	a	DET
ap-9818	113	6	a+b	a+b	PROPN
ap-9818	113	7	,	,	PUNCT
ap-9818	113	8	(	(	PUNCT
ap-9818	113	9	17	17	X
ap-9818	113	10	)	)	PUNCT
ap-9818	113	11	introducing	introduce	VERB
ap-9818	113	12	arbitrary	arbitrary	ADJ
ap-9818	113	13	parameters	parameter	NOUN
ap-9818	113	14	c1	c1	PROPN
ap-9818	113	15	and	and	CCONJ
ap-9818	113	16	c2	c2	PROPN
ap-9818	113	17	.	.	PUNCT
ap-9818	114	1	special	special	ADJ
ap-9818	114	2	cases	case	NOUN
ap-9818	114	3	of	of	ADP
ap-9818	114	4	the	the	DET
ap-9818	114	5	function	function	NOUN
ap-9818	114	6	(	(	PUNCT
ap-9818	114	7	17	17	NUM
ap-9818	114	8	)	)	PUNCT
ap-9818	114	9	include	include	VERB
ap-9818	114	10	,	,	PUNCT
ap-9818	114	11	but	but	CCONJ
ap-9818	114	12	are	be	AUX
ap-9818	114	13	not	not	PART
ap-9818	114	14	limited	limit	VERB
ap-9818	114	15	to	to	ADP
ap-9818	114	16	,	,	PUNCT
ap-9818	114	17	the	the	DET
ap-9818	114	18	following	follow	VERB
ap-9818	114	19	:	:	PUNCT
ap-9818	114	20	m(x	m(x	X
ap-9818	114	21	)	)	PUNCT
ap-9818	114	22	=	=	SYM
ap-9818	114	23	xλ	xλ	PROPN
ap-9818	114	24	m(x	m(x	PROPN
ap-9818	114	25	)	)	PUNCT
ap-9818	114	26	=	=	SYM
ap-9818	114	27	1	1	NUM
ap-9818	114	28	x2	x2	NOUN
ap-9818	114	29	±	±	NUM
ap-9818	114	30	λ	λ	NOUN
ap-9818	114	31	m(x	m(x	PROPN
ap-9818	114	32	)	)	PUNCT
ap-9818	114	33	=	=	SYM
ap-9818	115	1	x2	x2	PROPN
ap-9818	116	1	+	+	CCONJ
ap-9818	116	2	1	1	NUM
ap-9818	116	3	m(x	m(x	NOUN
ap-9818	116	4	)	)	PUNCT
ap-9818	116	5	=	=	SYM
ap-9818	117	1	1	1	NUM
ap-9818	117	2	(	(	PUNCT
ap-9818	117	3	x2	x2	NOUN
ap-9818	117	4	±	±	NOUN
ap-9818	117	5	λ)2	λ)2	NOUN
ap-9818	117	6	m(x	m(x	PROPN
ap-9818	117	7	)	)	PUNCT
ap-9818	117	8	=	=	SYM
ap-9818	118	1	x4	x4	PROPN
ap-9818	118	2	(	(	PUNCT
ap-9818	118	3	x2	x2	NOUN
ap-9818	118	4	±	±	NUM
ap-9818	118	5	λ)2	λ)2	NOUN
ap-9818	118	6	,	,	PUNCT
ap-9818	118	7	where	where	SCONJ
ap-9818	118	8	λ	λ	PROPN
ap-9818	118	9	represents	represent	VERB
ap-9818	118	10	a	a	DET
ap-9818	118	11	constant	constant	ADJ
ap-9818	118	12	.	.	PUNCT
ap-9818	119	1	now	now	ADV
ap-9818	119	2	,	,	PUNCT
ap-9818	119	3	substitution	substitution	NOUN
ap-9818	119	4	of	of	ADP
ap-9818	119	5	(	(	PUNCT
ap-9818	119	6	16	16	NUM
ap-9818	119	7	)	)	PUNCT
ap-9818	119	8	into	into	ADP
ap-9818	119	9	the	the	DET
ap-9818	119	10	effective	effective	ADJ
ap-9818	119	11	potential	potential	NOUN
ap-9818	119	12	(	(	PUNCT
ap-9818	119	13	12	12	NUM
ap-9818	119	14	)	)	PUNCT
ap-9818	119	15	gives	give	VERB
ap-9818	119	16	:	:	PUNCT
ap-9818	119	17	uν(x	uν(x	NUM
ap-9818	119	18	)	)	PUNCT
ap-9818	119	19	=	=	PUNCT
ap-9818	120	1	[	[	X
ap-9818	120	2	e	e	X
ap-9818	120	3	−	−	PROPN
ap-9818	120	4	v	v	PART
ap-9818	120	5	(	(	PUNCT
ap-9818	120	6	x	x	NOUN
ap-9818	120	7	)	)	PUNCT
ap-9818	120	8	]	]	PUNCT
ap-9818	120	9	m(x	m(x	PROPN
ap-9818	120	10	)	)	PUNCT
ap-9818	120	11	−	−	PROPN
ap-9818	121	1	[	[	PUNCT
ap-9818	121	2	3	3	NUM
ap-9818	121	3	4	4	NUM
ap-9818	121	4	+	+	SYM
ap-9818	121	5	α	α	NOUN
ap-9818	121	6	+	+	X
ap-9818	121	7	γ	γ	X
ap-9818	121	8	+	+	X
ap-9818	121	9	α	α	PROPN
ap-9818	121	10	γ	γ	NOUN
ap-9818	121	11	−	−	PROPN
ap-9818	121	12	b	b	PROPN
ap-9818	121	13	ν	ν	X
ap-9818	121	14	(	(	PUNCT
ap-9818	121	15	δ	δ	PROPN
ap-9818	121	16	+	+	CCONJ
ap-9818	121	17	α	α	PROPN
ap-9818	121	18	δ	δ	PROPN
ap-9818	121	19	+	+	CCONJ
ap-9818	121	20	γ	γ	PROPN
ap-9818	121	21	δ	δ	PROPN
ap-9818	121	22	)	)	PUNCT
ap-9818	121	23	]	]	PUNCT
ap-9818	121	24	[	[	PUNCT
ap-9818	121	25	m′(x	m′(x	NOUN
ap-9818	121	26	)	)	PUNCT
ap-9818	121	27	m(x	m(x	PROPN
ap-9818	121	28	)	)	PUNCT
ap-9818	121	29	]	]	PUNCT
ap-9818	121	30	2	2	X
ap-9818	122	1	+	+	CCONJ
ap-9818	122	2	[	[	PUNCT
ap-9818	122	3	1	1	NUM
ap-9818	122	4	+	+	NUM
ap-9818	122	5	α	α	NOUN
ap-9818	122	6	+	+	X
ap-9818	122	7	γ	γ	X
ap-9818	122	8	+	+	PROPN
ap-9818	122	9	2	2	NUM
ap-9818	122	10	a	a	DET
ap-9818	122	11	ν	ν	X
ap-9818	122	12	(	(	PUNCT
ap-9818	122	13	δ	δ	PROPN
ap-9818	122	14	+	+	CCONJ
ap-9818	122	15	α	α	PROPN
ap-9818	122	16	δ	δ	PROPN
ap-9818	122	17	+	+	CCONJ
ap-9818	122	18	γ	γ	PROPN
ap-9818	122	19	δ	δ	PROPN
ap-9818	122	20	)	)	PUNCT
ap-9818	122	21	]	]	PUNCT
ap-9818	122	22	m′′(x	m′′(x	NOUN
ap-9818	122	23	)	)	PUNCT
ap-9818	122	24	2	2	NUM
ap-9818	122	25	m(x	m(x	PROPN
ap-9818	122	26	)	)	PUNCT
ap-9818	123	1	+	+	CCONJ
ap-9818	123	2	δ	δ	PROPN
ap-9818	123	3	ν	ν	NOUN
ap-9818	123	4	−	−	PROPN
ap-9818	123	5	ν2	ν2	NOUN
ap-9818	123	6	x2	x2	INTJ
ap-9818	123	7	,	,	PUNCT
ap-9818	123	8	(	(	PUNCT
ap-9818	123	9	18	18	NUM
ap-9818	123	10	)	)	PUNCT
ap-9818	123	11	note	note	NOUN
ap-9818	123	12	that	that	SCONJ
ap-9818	123	13	we	we	PRON
ap-9818	123	14	omit	omit	VERB
ap-9818	123	15	to	to	PART
ap-9818	123	16	insert	insert	VERB
ap-9818	123	17	the	the	DET
ap-9818	123	18	explicit	explicit	ADJ
ap-9818	123	19	form	form	NOUN
ap-9818	123	20	of	of	ADP
ap-9818	123	21	the	the	DET
ap-9818	123	22	mass	mass	NOUN
ap-9818	123	23	(	(	PUNCT
ap-9818	123	24	17	17	NUM
ap-9818	123	25	)	)	PUNCT
ap-9818	123	26	in	in	ADP
ap-9818	123	27	order	order	NOUN
ap-9818	123	28	to	to	PART
ap-9818	123	29	avoid	avoid	VERB
ap-9818	123	30	large	large	ADJ
ap-9818	123	31	expressions	expression	NOUN
ap-9818	123	32	.	.	PUNCT
ap-9818	124	1	comparison	comparison	NOUN
ap-9818	124	2	of	of	ADP
ap-9818	124	3	(	(	PUNCT
ap-9818	124	4	18	18	NUM
ap-9818	124	5	)	)	PUNCT
ap-9818	124	6	with	with	ADP
ap-9818	124	7	its	its	PRON
ap-9818	124	8	counterpart	counterpart	NOUN
ap-9818	124	9	(	(	PUNCT
ap-9818	124	10	15	15	NUM
ap-9818	124	11	)	)	PUNCT
ap-9818	124	12	shows	show	VERB
ap-9818	124	13	that	that	SCONJ
ap-9818	124	14	now	now	ADV
ap-9818	124	15	both	both	PRON
ap-9818	124	16	have	have	VERB
ap-9818	124	17	the	the	DET
ap-9818	124	18	same	same	ADJ
ap-9818	124	19	functional	functional	ADJ
ap-9818	124	20	form	form	NOUN
ap-9818	124	21	except	except	SCONJ
ap-9818	124	22	for	for	ADP
ap-9818	124	23	numerical	numerical	ADJ
ap-9818	124	24	parameters	parameter	NOUN
ap-9818	124	25	,	,	PUNCT
ap-9818	124	26	and	and	CCONJ
ap-9818	124	27	for	for	ADP
ap-9818	124	28	the	the	DET
ap-9818	124	29	inverse	inverse	ADJ
ap-9818	124	30	quadratic	quadratic	ADJ
ap-9818	124	31	term	term	NOUN
ap-9818	124	32	.	.	PUNCT
ap-9818	125	1	before	before	SCONJ
ap-9818	125	2	we	we	PRON
ap-9818	125	3	conclude	conclude	VERB
ap-9818	125	4	this	this	DET
ap-9818	125	5	paragraph	paragraph	NOUN
ap-9818	125	6	,	,	PUNCT
ap-9818	125	7	let	let	VERB
ap-9818	125	8	us	we	PRON
ap-9818	125	9	point	point	VERB
ap-9818	125	10	out	out	ADP
ap-9818	125	11	that	that	SCONJ
ap-9818	125	12	further	further	ADJ
ap-9818	125	13	simplification	simplification	NOUN
ap-9818	125	14	of	of	ADP
ap-9818	125	15	(	(	PUNCT
ap-9818	125	16	18	18	NUM
ap-9818	125	17	)	)	PUNCT
ap-9818	125	18	can	can	AUX
ap-9818	125	19	be	be	AUX
ap-9818	125	20	reached	reach	VERB
ap-9818	125	21	by	by	ADP
ap-9818	125	22	means	mean	NOUN
ap-9818	125	23	of	of	ADP
ap-9818	125	24	the	the	DET
ap-9818	125	25	parameter	parameter	NOUN
ap-9818	125	26	ν	ν	NOUN
ap-9818	125	27	from	from	ADP
ap-9818	125	28	the	the	DET
ap-9818	125	29	dunkl	dunkl	NOUN
ap-9818	125	30	operator	operator	NOUN
ap-9818	125	31	(	(	PUNCT
ap-9818	125	32	3	3	NUM
ap-9818	125	33	)	)	PUNCT
ap-9818	125	34	.	.	PUNCT
ap-9818	126	1	while	while	SCONJ
ap-9818	126	2	,	,	PUNCT
ap-9818	126	3	in	in	ADP
ap-9818	126	4	general	general	ADJ
ap-9818	126	5	,	,	PUNCT
ap-9818	126	6	we	we	PRON
ap-9818	126	7	keep	keep	VERB
ap-9818	126	8	this	this	DET
ap-9818	126	9	parameter	parameter	NOUN
ap-9818	126	10	undetermined	undetermined	ADJ
ap-9818	126	11	,	,	PUNCT
ap-9818	126	12	it	it	PRON
ap-9818	126	13	is	be	AUX
ap-9818	126	14	possible	possible	ADJ
ap-9818	126	15	to	to	PART
ap-9818	126	16	assign	assign	VERB
ap-9818	126	17	it	it	PRON
ap-9818	126	18	specific	specific	ADJ
ap-9818	126	19	values	value	NOUN
ap-9818	126	20	.	.	PUNCT
ap-9818	127	1	for	for	ADP
ap-9818	127	2	example	example	NOUN
ap-9818	127	3	,	,	PUNCT
ap-9818	127	4	the	the	DET
ap-9818	127	5	coefficient	coefficient	NOUN
ap-9818	127	6	terms	term	NOUN
ap-9818	127	7	of	of	ADP
ap-9818	127	8	the	the	DET
ap-9818	127	9	mass	mass	NOUN
ap-9818	127	10	functions	function	NOUN
ap-9818	127	11	in	in	ADP
ap-9818	127	12	(	(	PUNCT
ap-9818	127	13	18	18	NUM
ap-9818	127	14	)	)	PUNCT
ap-9818	127	15	vanish	vanish	VERB
ap-9818	127	16	if	if	SCONJ
ap-9818	127	17	the	the	DET
ap-9818	127	18	value	value	NOUN
ap-9818	127	19	for	for	ADP
ap-9818	127	20	ν	ν	NOUN
ap-9818	127	21	is	be	AUX
ap-9818	127	22	chosen	choose	VERB
ap-9818	127	23	suitably	suitably	ADV
ap-9818	127	24	,	,	PUNCT
ap-9818	127	25	thus	thus	ADV
ap-9818	127	26	rendering	render	VERB
ap-9818	127	27	the	the	DET
ap-9818	127	28	function	function	NOUN
ap-9818	127	29	uν	uν	INTJ
ap-9818	127	30	in	in	ADP
ap-9818	127	31	simpler	simple	ADJ
ap-9818	127	32	form	form	NOUN
ap-9818	127	33	.	.	PUNCT
ap-9818	128	1	a	a	DET
ap-9818	128	2	further	further	ADJ
ap-9818	128	3	example	example	NOUN
ap-9818	128	4	for	for	ADP
ap-9818	128	5	assigning	assign	VERB
ap-9818	128	6	specific	specific	ADJ
ap-9818	128	7	values	value	NOUN
ap-9818	128	8	to	to	ADP
ap-9818	128	9	the	the	DET
ap-9818	128	10	parameter	parameter	NOUN
ap-9818	128	11	ν	ν	NOUN
ap-9818	128	12	is	be	AUX
ap-9818	128	13	to	to	PART
ap-9818	128	14	establish	establish	VERB
ap-9818	128	15	parity	parity	NOUN
ap-9818	128	16	of	of	ADP
ap-9818	128	17	solutions	solution	NOUN
ap-9818	128	18	to	to	ADP
ap-9818	128	19	the	the	DET
ap-9818	128	20	dunkl	dunkl	NOUN
ap-9818	128	21	-	-	PUNCT
ap-9818	128	22	schrödinger	schrödinger	NOUN
ap-9818	128	23	equation	equation	NOUN
ap-9818	128	24	.	.	PUNCT
ap-9818	129	1	this	this	PRON
ap-9818	129	2	will	will	AUX
ap-9818	129	3	be	be	AUX
ap-9818	129	4	further	far	ADV
ap-9818	129	5	discussed	discuss	VERB
ap-9818	129	6	in	in	ADP
ap-9818	129	7	section	section	NOUN
ap-9818	129	8	4	4	NUM
ap-9818	129	9	.	.	PUNCT
ap-9818	129	10	second	second	ADJ
ap-9818	129	11	condition	condition	NOUN
ap-9818	129	12	.	.	PUNCT
ap-9818	130	1	since	since	SCONJ
ap-9818	130	2	the	the	DET
ap-9818	130	3	effective	effective	ADJ
ap-9818	130	4	potential	potential	NOUN
ap-9818	130	5	(	(	PUNCT
ap-9818	130	6	15	15	NUM
ap-9818	130	7	)	)	PUNCT
ap-9818	130	8	does	do	AUX
ap-9818	130	9	not	not	PART
ap-9818	130	10	contain	contain	VERB
ap-9818	130	11	an	an	DET
ap-9818	130	12	inverse	inverse	ADJ
ap-9818	130	13	quadratic	quadratic	ADJ
ap-9818	130	14	term	term	NOUN
ap-9818	130	15	,	,	PUNCT
ap-9818	130	16	we	we	PRON
ap-9818	130	17	must	must	AUX
ap-9818	130	18	generate	generate	VERB
ap-9818	130	19	it	it	PRON
ap-9818	130	20	by	by	ADP
ap-9818	130	21	means	mean	NOUN
ap-9818	130	22	of	of	ADP
ap-9818	130	23	choosing	choose	VERB
ap-9818	130	24	the	the	DET
ap-9818	130	25	potential	potential	ADJ
ap-9818	130	26	v	v	NOUN
ap-9818	130	27	in	in	ADP
ap-9818	130	28	a	a	DET
ap-9818	130	29	suitable	suitable	ADJ
ap-9818	130	30	form	form	NOUN
ap-9818	130	31	,	,	PUNCT
ap-9818	130	32	or	or	CCONJ
ap-9818	130	33	by	by	ADP
ap-9818	130	34	constraining	constrain	VERB
ap-9818	130	35	the	the	DET
ap-9818	130	36	position	position	NOUN
ap-9818	130	37	-	-	PUNCT
ap-9818	130	38	dependent	dependent	ADJ
ap-9818	130	39	mass	mass	NOUN
ap-9818	130	40	(	(	PUNCT
ap-9818	130	41	17	17	NUM
ap-9818	130	42	)	)	PUNCT
ap-9818	130	43	.	.	PUNCT
ap-9818	131	1	this	this	DET
ap-9818	131	2	way	way	NOUN
ap-9818	131	3	we	we	PRON
ap-9818	131	4	obtain	obtain	VERB
ap-9818	131	5	three	three	NUM
ap-9818	131	6	different	different	ADJ
ap-9818	131	7	conditions	condition	NOUN
ap-9818	131	8	that	that	PRON
ap-9818	131	9	will	will	AUX
ap-9818	131	10	be	be	AUX
ap-9818	131	11	distinguished	distinguish	VERB
ap-9818	131	12	now	now	ADV
ap-9818	131	13	.	.	PUNCT
ap-9818	132	1	•	•	NOUN
ap-9818	132	2	the	the	DET
ap-9818	132	3	first	first	ADJ
ap-9818	132	4	option	option	NOUN
ap-9818	132	5	to	to	PART
ap-9818	132	6	include	include	VERB
ap-9818	132	7	an	an	DET
ap-9818	132	8	inverse	inverse	ADJ
ap-9818	132	9	quadratic	quadratic	ADJ
ap-9818	132	10	term	term	NOUN
ap-9818	132	11	is	be	AUX
ap-9818	132	12	to	to	PART
ap-9818	132	13	constrain	constrain	VERB
ap-9818	132	14	the	the	DET
ap-9818	132	15	form	form	NOUN
ap-9818	132	16	of	of	ADP
ap-9818	132	17	the	the	DET
ap-9818	132	18	potential	potential	ADJ
ap-9818	132	19	v	v	NOUN
ap-9818	132	20	.	.	PUNCT
ap-9818	133	1	the	the	DET
ap-9818	133	2	corresponding	corresponding	ADJ
ap-9818	133	3	condition	condition	NOUN
ap-9818	133	4	takes	take	VERB
ap-9818	133	5	the	the	DET
ap-9818	133	6	form	form	NOUN
ap-9818	133	7	:	:	PUNCT
ap-9818	133	8	v	v	X
ap-9818	133	9	(	(	PUNCT
ap-9818	133	10	x	x	NOUN
ap-9818	133	11	)	)	PUNCT
ap-9818	133	12	=	=	SYM
ap-9818	133	13	c	c	X
ap-9818	133	14	x2	x2	PROPN
ap-9818	133	15	m(x	m(x	PROPN
ap-9818	133	16	)	)	PUNCT
ap-9818	134	1	+	+	CCONJ
ap-9818	134	2	w	w	X
ap-9818	134	3	(	(	PUNCT
ap-9818	134	4	x	x	NOUN
ap-9818	134	5	)	)	PUNCT
ap-9818	134	6	,	,	PUNCT
ap-9818	134	7	(	(	PUNCT
ap-9818	134	8	19	19	NUM
ap-9818	134	9	)	)	PUNCT
ap-9818	134	10	where	where	SCONJ
ap-9818	134	11	c	c	NOUN
ap-9818	134	12	is	be	AUX
ap-9818	134	13	an	an	DET
ap-9818	134	14	arbitrary	arbitrary	ADJ
ap-9818	134	15	constant	constant	ADJ
ap-9818	134	16	,	,	PUNCT
ap-9818	134	17	and	and	CCONJ
ap-9818	134	18	w	w	NOUN
ap-9818	134	19	contains	contain	VERB
ap-9818	134	20	the	the	DET
ap-9818	134	21	remaining	remain	VERB
ap-9818	134	22	terms	term	NOUN
ap-9818	134	23	of	of	ADP
ap-9818	134	24	the	the	DET
ap-9818	134	25	potential	potential	NOUN
ap-9818	134	26	,	,	PUNCT
ap-9818	134	27	if	if	SCONJ
ap-9818	134	28	any	any	PRON
ap-9818	134	29	.	.	PUNCT
ap-9818	135	1	note	note	VERB
ap-9818	135	2	that	that	SCONJ
ap-9818	135	3	w	w	NOUN
ap-9818	135	4	is	be	AUX
ap-9818	135	5	not	not	PART
ap-9818	135	6	allowed	allow	VERB
ap-9818	135	7	to	to	PART
ap-9818	135	8	contain	contain	VERB
ap-9818	135	9	any	any	DET
ap-9818	135	10	term	term	NOUN
ap-9818	135	11	of	of	ADP
ap-9818	135	12	the	the	DET
ap-9818	135	13	form	form	NOUN
ap-9818	135	14	∼	∼	NOUN
ap-9818	136	1	[	[	X
ap-9818	136	2	x2m]−1	x2m]−1	PROPN
ap-9818	136	3	.	.	PUNCT
ap-9818	137	1	in	in	ADP
ap-9818	137	2	order	order	NOUN
ap-9818	137	3	to	to	PART
ap-9818	137	4	compare	compare	VERB
ap-9818	137	5	the	the	DET
ap-9818	137	6	two	two	NUM
ap-9818	137	7	effective	effective	ADJ
ap-9818	137	8	potentials	potential	NOUN
ap-9818	137	9	for	for	ADP
ap-9818	137	10	the	the	DET
ap-9818	137	11	dunkl	dunkl	NOUN
ap-9818	137	12	context	context	NOUN
ap-9818	137	13	and	and	CCONJ
ap-9818	137	14	the	the	DET
ap-9818	137	15	conventional	conventional	ADJ
ap-9818	137	16	scenario	scenario	NOUN
ap-9818	137	17	,	,	PUNCT
ap-9818	137	18	let	let	VERB
ap-9818	137	19	us	we	PRON
ap-9818	137	20	now	now	ADV
ap-9818	137	21	substitute	substitute	VERB
ap-9818	137	22	(	(	PUNCT
ap-9818	137	23	19	19	NUM
ap-9818	137	24	)	)	PUNCT
ap-9818	137	25	into	into	ADP
ap-9818	137	26	(	(	PUNCT
ap-9818	137	27	18	18	NUM
ap-9818	137	28	)	)	PUNCT
ap-9818	137	29	and	and	CCONJ
ap-9818	137	30	(	(	PUNCT
ap-9818	137	31	15	15	NUM
ap-9818	137	32	)	)	PUNCT
ap-9818	137	33	.	.	PUNCT
ap-9818	138	1	the	the	DET
ap-9818	138	2	first	first	ADJ
ap-9818	138	3	potential	potential	NOUN
ap-9818	138	4	takes	take	VERB
ap-9818	138	5	the	the	DET
ap-9818	138	6	form	form	NOUN
ap-9818	138	7	:	:	PUNCT
ap-9818	138	8	uν(x	uν(x	NUM
ap-9818	138	9	)	)	PUNCT
ap-9818	138	10	=	=	PUNCT
ap-9818	139	1	[	[	X
ap-9818	139	2	e	e	X
ap-9818	139	3	−	−	PROPN
ap-9818	139	4	w	w	PROPN
ap-9818	139	5	(	(	PUNCT
ap-9818	139	6	x	x	NOUN
ap-9818	139	7	)	)	PUNCT
ap-9818	139	8	]	]	PUNCT
ap-9818	139	9	m(x	m(x	PROPN
ap-9818	139	10	)	)	PUNCT
ap-9818	139	11	−	−	PROPN
ap-9818	140	1	[	[	PUNCT
ap-9818	140	2	3	3	NUM
ap-9818	140	3	4	4	NUM
ap-9818	140	4	+	+	SYM
ap-9818	140	5	α	α	NOUN
ap-9818	140	6	+	+	X
ap-9818	140	7	γ	γ	X
ap-9818	140	8	+	+	X
ap-9818	140	9	α	α	PROPN
ap-9818	140	10	γ	γ	NOUN
ap-9818	140	11	−	−	PROPN
ap-9818	140	12	b	b	PROPN
ap-9818	140	13	ν	ν	X
ap-9818	140	14	(	(	PUNCT
ap-9818	140	15	δ	δ	PROPN
ap-9818	140	16	+	+	CCONJ
ap-9818	140	17	α	α	PROPN
ap-9818	140	18	δ	δ	PROPN
ap-9818	140	19	+	+	CCONJ
ap-9818	140	20	γ	γ	PROPN
ap-9818	140	21	δ	δ	PROPN
ap-9818	140	22	)	)	PUNCT
ap-9818	140	23	]	]	PUNCT
ap-9818	140	24	[	[	PUNCT
ap-9818	140	25	m′(x	m′(x	NOUN
ap-9818	140	26	)	)	PUNCT
ap-9818	140	27	m(x	m(x	PROPN
ap-9818	140	28	)	)	PUNCT
ap-9818	140	29	]	]	PUNCT
ap-9818	140	30	2	2	X
ap-9818	141	1	+	+	CCONJ
ap-9818	141	2	[	[	PUNCT
ap-9818	141	3	1	1	NUM
ap-9818	141	4	+	+	NUM
ap-9818	141	5	α	α	NOUN
ap-9818	141	6	+	+	X
ap-9818	141	7	γ	γ	X
ap-9818	141	8	+	+	PROPN
ap-9818	141	9	2	2	NUM
ap-9818	141	10	a	a	DET
ap-9818	141	11	ν	ν	X
ap-9818	141	12	(	(	PUNCT
ap-9818	141	13	δ	δ	PROPN
ap-9818	141	14	+	+	CCONJ
ap-9818	141	15	α	α	PROPN
ap-9818	141	16	δ	δ	PROPN
ap-9818	141	17	+	+	CCONJ
ap-9818	141	18	γ	γ	PROPN
ap-9818	141	19	δ	δ	PROPN
ap-9818	141	20	)	)	PUNCT
ap-9818	141	21	]	]	PUNCT
ap-9818	141	22	m′′(x	m′′(x	NOUN
ap-9818	141	23	)	)	PUNCT
ap-9818	141	24	2	2	NUM
ap-9818	141	25	m(x	m(x	PROPN
ap-9818	141	26	)	)	PUNCT
ap-9818	142	1	+	+	CCONJ
ap-9818	143	1	δ	δ	PROPN
ap-9818	143	2	ν	ν	NOUN
ap-9818	143	3	−	−	PROPN
ap-9818	143	4	ν2	ν2	NOUN
ap-9818	143	5	−	−	PROPN
ap-9818	143	6	c	c	NOUN
ap-9818	144	1	x2	x2	INTJ
ap-9818	144	2	,	,	PUNCT
ap-9818	144	3	(	(	PUNCT
ap-9818	144	4	20	20	NUM
ap-9818	144	5	)	)	PUNCT
ap-9818	144	6	while	while	SCONJ
ap-9818	144	7	the	the	DET
ap-9818	144	8	second	second	ADJ
ap-9818	144	9	potential	potential	ADJ
ap-9818	144	10	reads	read	NOUN
ap-9818	144	11	:	:	PUNCT
ap-9818	144	12	u0(x	u0(x	NUM
ap-9818	144	13	)	)	PUNCT
ap-9818	144	14	=	=	PUNCT
ap-9818	145	1	[	[	X
ap-9818	145	2	e	e	X
ap-9818	145	3	−	−	PROPN
ap-9818	145	4	w	w	PROPN
ap-9818	145	5	(	(	PUNCT
ap-9818	145	6	x	x	NOUN
ap-9818	145	7	)	)	PUNCT
ap-9818	145	8	]	]	PUNCT
ap-9818	145	9	m(x	m(x	PROPN
ap-9818	145	10	)	)	PUNCT
ap-9818	145	11	−	−	PROPN
ap-9818	146	1	(	(	PUNCT
ap-9818	146	2	3	3	NUM
ap-9818	146	3	4	4	NUM
ap-9818	146	4	+	+	NUM
ap-9818	146	5	α	α	NOUN
ap-9818	146	6	+	+	X
ap-9818	146	7	γ	γ	X
ap-9818	146	8	+	+	X
ap-9818	146	9	α	α	PROPN
ap-9818	146	10	γ	γ	NOUN
ap-9818	146	11	)	)	PUNCT
ap-9818	146	12	[	[	PUNCT
ap-9818	146	13	m′(x	m′(x	NOUN
ap-9818	146	14	)	)	PUNCT
ap-9818	146	15	m(x	m(x	PROPN
ap-9818	146	16	)	)	PUNCT
ap-9818	146	17	]	]	PUNCT
ap-9818	146	18	2	2	NUM
ap-9818	146	19	+	+	CCONJ
ap-9818	146	20	(	(	PUNCT
ap-9818	146	21	1	1	NUM
ap-9818	146	22	+	+	NUM
ap-9818	146	23	α	α	NOUN
ap-9818	146	24	+	+	CCONJ
ap-9818	146	25	γ	γ	X
ap-9818	146	26	)	)	PUNCT
ap-9818	146	27	m′′(x	m′′(x	NOUN
ap-9818	146	28	)	)	PUNCT
ap-9818	146	29	2	2	NUM
ap-9818	146	30	m(x	m(x	NOUN
ap-9818	146	31	)	)	PUNCT
ap-9818	146	32	−	−	PROPN
ap-9818	147	1	c	c	NOUN
ap-9818	147	2	x2	x2	INTJ
ap-9818	147	3	.	.	PUNCT
ap-9818	148	1	(	(	PUNCT
ap-9818	148	2	21	21	NUM
ap-9818	148	3	)	)	PUNCT
ap-9818	148	4	we	we	PRON
ap-9818	148	5	observe	observe	VERB
ap-9818	148	6	that	that	SCONJ
ap-9818	148	7	the	the	DET
ap-9818	148	8	two	two	NUM
ap-9818	148	9	effective	effective	ADJ
ap-9818	148	10	potentials	potential	NOUN
ap-9818	148	11	have	have	VERB
ap-9818	148	12	the	the	DET
ap-9818	148	13	same	same	ADJ
ap-9818	148	14	functional	functional	ADJ
ap-9818	148	15	form	form	NOUN
ap-9818	148	16	.	.	PUNCT
ap-9818	149	1	recall	recall	VERB
ap-9818	149	2	that	that	SCONJ
ap-9818	149	3	the	the	DET
ap-9818	149	4	two	two	NUM
ap-9818	149	5	conditions	condition	NOUN
ap-9818	149	6	for	for	ADP
ap-9818	149	7	this	this	PRON
ap-9818	149	8	are	be	AUX
ap-9818	149	9	given	give	VERB
ap-9818	149	10	by	by	ADP
ap-9818	149	11	(	(	PUNCT
ap-9818	149	12	17	17	NUM
ap-9818	149	13	)	)	PUNCT
ap-9818	149	14	and	and	CCONJ
ap-9818	149	15	(	(	PUNCT
ap-9818	149	16	19	19	NUM
ap-9818	149	17	)	)	PUNCT
ap-9818	149	18	.	.	PUNCT
ap-9818	150	1	225	225	NUM
ap-9818	150	2	axel	axel	PROPN
ap-9818	150	3	schulze	schulze	NOUN
ap-9818	150	4	-	-	PUNCT
ap-9818	150	5	halberg	halberg	PROPN
ap-9818	150	6	acta	acta	PROPN
ap-9818	150	7	polytechnica	polytechnica	PROPN
ap-9818	150	8	•	•	ADP
ap-9818	150	9	instead	instead	ADV
ap-9818	150	10	of	of	ADP
ap-9818	150	11	constraining	constrain	VERB
ap-9818	150	12	the	the	DET
ap-9818	150	13	potential	potential	ADJ
ap-9818	150	14	v	v	NOUN
ap-9818	150	15	,	,	PUNCT
ap-9818	150	16	we	we	PRON
ap-9818	150	17	can	can	AUX
ap-9818	150	18	also	also	ADV
ap-9818	150	19	use	use	VERB
ap-9818	150	20	the	the	DET
ap-9818	150	21	position	position	NOUN
ap-9818	150	22	-	-	PUNCT
ap-9818	150	23	dependent	dependent	ADJ
ap-9818	150	24	mass	mass	NOUN
ap-9818	150	25	to	to	PART
ap-9818	150	26	generate	generate	VERB
ap-9818	150	27	an	an	DET
ap-9818	150	28	inverse	inverse	ADJ
ap-9818	150	29	quadratic	quadratic	ADJ
ap-9818	150	30	term	term	NOUN
ap-9818	150	31	in	in	ADP
ap-9818	150	32	(	(	PUNCT
ap-9818	150	33	15	15	NUM
ap-9818	150	34	)	)	PUNCT
ap-9818	150	35	.	.	PUNCT
ap-9818	151	1	note	note	VERB
ap-9818	151	2	that	that	SCONJ
ap-9818	151	3	this	this	PRON
ap-9818	151	4	will	will	AUX
ap-9818	151	5	result	result	VERB
ap-9818	151	6	in	in	ADP
ap-9818	151	7	a	a	DET
ap-9818	151	8	compatibility	compatibility	NOUN
ap-9818	151	9	condition	condition	NOUN
ap-9818	151	10	for	for	ADP
ap-9818	151	11	the	the	DET
ap-9818	151	12	expression	expression	NOUN
ap-9818	151	13	(	(	PUNCT
ap-9818	151	14	17	17	NUM
ap-9818	151	15	)	)	PUNCT
ap-9818	151	16	.	.	PUNCT
ap-9818	152	1	starting	start	VERB
ap-9818	152	2	out	out	ADP
ap-9818	152	3	with	with	ADP
ap-9818	152	4	the	the	DET
ap-9818	152	5	term	term	NOUN
ap-9818	152	6	∼	∼	NOUN
ap-9818	152	7	m′′	m′′	NOUN
ap-9818	152	8	m	m	PROPN
ap-9818	152	9	,	,	PUNCT
ap-9818	152	10	we	we	PRON
ap-9818	152	11	must	must	AUX
ap-9818	152	12	satisfy	satisfy	VERB
ap-9818	152	13	:	:	PUNCT
ap-9818	152	14	m′′(x	m′′(x	NOUN
ap-9818	152	15	)	)	PUNCT
ap-9818	152	16	m(x	m(x	NOUN
ap-9818	152	17	)	)	PUNCT
ap-9818	153	1	=	=	PUNCT
ap-9818	154	1	c	c	NOUN
ap-9818	154	2	x2	x2	NOUN
ap-9818	154	3	⇝	⇝	NOUN
ap-9818	154	4	m(x	m(x	PROPN
ap-9818	154	5	)	)	PUNCT
ap-9818	155	1	=	=	PUNCT
ap-9818	155	2	c3	c3	NOUN
ap-9818	155	3	x	x	SYM
ap-9818	155	4	1	1	NUM
ap-9818	155	5	2	2	NUM
ap-9818	155	6	±	±	NUM
ap-9818	155	7	1	1	NUM
ap-9818	155	8	2	2	NUM
ap-9818	155	9	√	√	NUM
ap-9818	155	10	1	1	NUM
ap-9818	155	11	+	+	NOUN
ap-9818	155	12	4c	4c	NOUN
ap-9818	155	13	,	,	PUNCT
ap-9818	155	14	(	(	PUNCT
ap-9818	155	15	22	22	X
ap-9818	155	16	)	)	PUNCT
ap-9818	155	17	introducing	introduce	VERB
ap-9818	155	18	arbitrary	arbitrary	ADJ
ap-9818	155	19	constants	constant	NOUN
ap-9818	155	20	c3	c3	PROPN
ap-9818	155	21	and	and	CCONJ
ap-9818	155	22	c.	c.	NOUN
ap-9818	155	23	since	since	SCONJ
ap-9818	155	24	this	this	DET
ap-9818	155	25	condition	condition	NOUN
ap-9818	155	26	as	as	ADV
ap-9818	155	27	well	well	ADV
ap-9818	155	28	as	as	ADP
ap-9818	155	29	(	(	PUNCT
ap-9818	155	30	17	17	NUM
ap-9818	155	31	)	)	PUNCT
ap-9818	155	32	are	be	AUX
ap-9818	155	33	imposed	impose	VERB
ap-9818	155	34	on	on	ADP
ap-9818	155	35	the	the	DET
ap-9818	155	36	positiondependent	positiondependent	ADJ
ap-9818	155	37	mass	mass	NOUN
ap-9818	155	38	function	function	NOUN
ap-9818	155	39	simultaneously	simultaneously	ADV
ap-9818	155	40	,	,	PUNCT
ap-9818	155	41	both	both	DET
ap-9818	155	42	conditions	condition	NOUN
ap-9818	155	43	must	must	AUX
ap-9818	155	44	be	be	AUX
ap-9818	155	45	compatible	compatible	ADJ
ap-9818	155	46	.	.	PUNCT
ap-9818	156	1	this	this	PRON
ap-9818	156	2	can	can	AUX
ap-9818	156	3	be	be	AUX
ap-9818	156	4	achieved	achieve	VERB
ap-9818	156	5	by	by	ADP
ap-9818	156	6	setting	set	VERB
ap-9818	156	7	the	the	DET
ap-9818	156	8	parameters	parameter	NOUN
ap-9818	156	9	in	in	ADP
ap-9818	156	10	(	(	PUNCT
ap-9818	156	11	17	17	NUM
ap-9818	156	12	)	)	PUNCT
ap-9818	156	13	as	as	SCONJ
ap-9818	156	14	follows	follow	VERB
ap-9818	156	15	:	:	PUNCT
ap-9818	156	16	c1	c1	NOUN
ap-9818	156	17	=	=	PUNCT
ap-9818	156	18	0	0	PROPN
ap-9818	156	19	,	,	PUNCT
ap-9818	156	20	c2	c2	PROPN
ap-9818	156	21	=	=	SYM
ap-9818	156	22	c3	c3	PROPN
ap-9818	156	23	(	(	PUNCT
ap-9818	156	24	−1	−1	NOUN
ap-9818	156	25	±	±	NOUN
ap-9818	156	26	√	√	NOUN
ap-9818	156	27	1	1	NUM
ap-9818	157	1	+	+	CCONJ
ap-9818	157	2	4	4	NUM
ap-9818	157	3	c	c	NOUN
ap-9818	157	4	)	)	PUNCT
ap-9818	157	5	2	2	NUM
ap-9818	157	6	,	,	PUNCT
ap-9818	157	7	a	a	DET
ap-9818	157	8	=	=	SYM
ap-9818	157	9	2	2	NUM
ap-9818	157	10	−1	−1	NOUN
ap-9818	157	11	±	±	NOUN
ap-9818	157	12	√	√	NOUN
ap-9818	157	13	1	1	NUM
ap-9818	158	1	+	+	CCONJ
ap-9818	158	2	4	4	NUM
ap-9818	158	3	c	c	NOUN
ap-9818	158	4	,	,	PUNCT
ap-9818	158	5	b	b	X
ap-9818	158	6	=	=	SYM
ap-9818	158	7	0	0	PROPN
ap-9818	158	8	.	.	PUNCT
ap-9818	159	1	(	(	PUNCT
ap-9818	159	2	23	23	NUM
ap-9818	159	3	)	)	PUNCT
ap-9818	159	4	substitution	substitution	NOUN
ap-9818	159	5	of	of	ADP
ap-9818	159	6	these	these	DET
ap-9818	159	7	settings	setting	NOUN
ap-9818	159	8	into	into	ADP
ap-9818	159	9	the	the	DET
ap-9818	159	10	function	function	NOUN
ap-9818	159	11	uν	uν	INTJ
ap-9818	159	12	,	,	PUNCT
ap-9818	159	13	as	as	SCONJ
ap-9818	159	14	given	give	VERB
ap-9818	159	15	in	in	ADP
ap-9818	159	16	(	(	PUNCT
ap-9818	159	17	18	18	NUM
ap-9818	159	18	)	)	PUNCT
ap-9818	159	19	,	,	PUNCT
ap-9818	159	20	gives	give	VERB
ap-9818	159	21	the	the	DET
ap-9818	159	22	result	result	NOUN
ap-9818	159	23	:	:	PUNCT
ap-9818	159	24	uν(x	uν(x	X
ap-9818	159	25	)	)	PUNCT
ap-9818	159	26	=	=	SYM
ap-9818	160	1	c3	c3	NOUN
ap-9818	160	2	x	x	SYM
ap-9818	160	3	1	1	NUM
ap-9818	160	4	2	2	NUM
ap-9818	160	5	±	±	NUM
ap-9818	160	6	1	1	NUM
ap-9818	160	7	2	2	NUM
ap-9818	160	8	√	√	NUM
ap-9818	160	9	1	1	NUM
ap-9818	160	10	+	+	NUM
ap-9818	160	11	4c	4c	NOUN
ap-9818	160	12	[	[	X
ap-9818	160	13	e	e	X
ap-9818	160	14	−	−	PROPN
ap-9818	160	15	v	v	PART
ap-9818	160	16	(	(	PUNCT
ap-9818	160	17	x	x	NOUN
ap-9818	160	18	)	)	PUNCT
ap-9818	160	19	]	]	PUNCT
ap-9818	161	1	−	−	PROPN
ap-9818	161	2	1	1	NUM
ap-9818	161	3	8	8	NUM
ap-9818	161	4	x2	x2	NOUN
ap-9818	161	5	[	[	PUNCT
ap-9818	161	6	3	3	NUM
ap-9818	161	7	+	+	SYM
ap-9818	161	8	4	4	NUM
ap-9818	161	9	α	α	NOUN
ap-9818	161	10	+	+	ADP
ap-9818	161	11	4	4	NUM
ap-9818	161	12	γ	γ	NOUN
ap-9818	161	13	+	+	ADP
ap-9818	161	14	4	4	NUM
ap-9818	161	15	α	α	NUM
ap-9818	161	16	γ	γ	NOUN
ap-9818	161	17	+	+	ADP
ap-9818	161	18	2	2	NUM
ap-9818	161	19	c	c	NOUN
ap-9818	161	20	(	(	PUNCT
ap-9818	161	21	1	1	NUM
ap-9818	161	22	+	+	SYM
ap-9818	161	23	2	2	NUM
ap-9818	161	24	α	α	NOUN
ap-9818	161	25	)	)	PUNCT
ap-9818	161	26	(	(	PUNCT
ap-9818	161	27	1	1	NUM
ap-9818	161	28	+	+	SYM
ap-9818	161	29	2	2	NUM
ap-9818	161	30	γ	γ	NOUN
ap-9818	161	31	)	)	PUNCT
ap-9818	161	32	−	−	PROPN
ap-9818	161	33	4	4	NUM
ap-9818	161	34	δ	δ	NOUN
ap-9818	161	35	ν	ν	X
ap-9818	161	36	(	(	PUNCT
ap-9818	161	37	3	3	NUM
ap-9818	161	38	+	+	NUM
ap-9818	161	39	α	α	NOUN
ap-9818	161	40	+	+	X
ap-9818	161	41	γ	γ	X
ap-9818	161	42	)	)	PUNCT
ap-9818	161	43	+	+	NUM
ap-9818	161	44	8	8	NUM
ap-9818	161	45	ν2	ν2	NOUN
ap-9818	161	46	±	±	NUM
ap-9818	161	47	√	√	ADV
ap-9818	161	48	1	1	NUM
ap-9818	161	49	+	+	CCONJ
ap-9818	161	50	4	4	NUM
ap-9818	161	51	c	c	NOUN
ap-9818	161	52	(	(	PUNCT
ap-9818	161	53	3	3	NUM
ap-9818	161	54	+	+	SYM
ap-9818	161	55	4	4	NUM
ap-9818	161	56	α	α	NOUN
ap-9818	161	57	+	+	ADP
ap-9818	161	58	4	4	NUM
ap-9818	161	59	γ	γ	NOUN
ap-9818	161	60	+	+	ADP
ap-9818	161	61	4	4	NUM
ap-9818	161	62	α	α	NUM
ap-9818	161	63	γ	γ	NOUN
ap-9818	161	64	−	−	PROPN
ap-9818	161	65	4	4	NUM
ap-9818	161	66	δ	δ	NOUN
ap-9818	161	67	ν	ν	NOUN
ap-9818	161	68	−	−	PROPN
ap-9818	161	69	4	4	NUM
ap-9818	161	70	α	α	NOUN
ap-9818	161	71	δ	δ	NOUN
ap-9818	161	72	ν	ν	ADP
ap-9818	161	73	−	−	PROPN
ap-9818	161	74	4	4	NUM
ap-9818	161	75	γ	γ	PROPN
ap-9818	161	76	δ	δ	PROPN
ap-9818	161	77	ν	ν	PROPN
ap-9818	161	78	)	)	PUNCT
ap-9818	161	79	]	]	PUNCT
ap-9818	161	80	.	.	PUNCT
ap-9818	162	1	(	(	PUNCT
ap-9818	162	2	24	24	NUM
ap-9818	162	3	)	)	PUNCT
ap-9818	162	4	the	the	DET
ap-9818	162	5	settings	setting	NOUN
ap-9818	162	6	(	(	PUNCT
ap-9818	162	7	23	23	X
ap-9818	162	8	)	)	PUNCT
ap-9818	162	9	render	render	VERB
ap-9818	162	10	the	the	DET
ap-9818	162	11	remaining	remain	VERB
ap-9818	162	12	effective	effective	ADJ
ap-9818	162	13	potential	potential	ADJ
ap-9818	162	14	u0	u0	NOUN
ap-9818	162	15	in	in	ADP
ap-9818	162	16	the	the	DET
ap-9818	162	17	form	form	NOUN
ap-9818	162	18	:	:	PUNCT
ap-9818	162	19	u0(x	u0(x	NUM
ap-9818	162	20	)	)	PUNCT
ap-9818	162	21	=	=	PUNCT
ap-9818	163	1	c3	c3	NOUN
ap-9818	163	2	x	x	SYM
ap-9818	163	3	1	1	NUM
ap-9818	163	4	2	2	NUM
ap-9818	163	5	±	±	NUM
ap-9818	163	6	1	1	NUM
ap-9818	163	7	2	2	NUM
ap-9818	163	8	√	√	NUM
ap-9818	163	9	1	1	NUM
ap-9818	163	10	+	+	NUM
ap-9818	163	11	4c	4c	NOUN
ap-9818	163	12	[	[	X
ap-9818	163	13	e	e	X
ap-9818	163	14	−	−	PROPN
ap-9818	163	15	v	v	PART
ap-9818	163	16	(	(	PUNCT
ap-9818	163	17	x	x	NOUN
ap-9818	163	18	)	)	PUNCT
ap-9818	163	19	]	]	PUNCT
ap-9818	164	1	−	−	PROPN
ap-9818	164	2	1	1	NUM
ap-9818	164	3	8	8	NUM
ap-9818	164	4	x2	x2	NOUN
ap-9818	164	5	[	[	PUNCT
ap-9818	164	6	3	3	NUM
ap-9818	164	7	+	+	SYM
ap-9818	164	8	4	4	NUM
ap-9818	164	9	α	α	NOUN
ap-9818	164	10	+	+	ADP
ap-9818	164	11	4	4	NUM
ap-9818	164	12	γ	γ	NOUN
ap-9818	164	13	+	+	ADP
ap-9818	164	14	4	4	NUM
ap-9818	164	15	α	α	NUM
ap-9818	164	16	γ	γ	NOUN
ap-9818	164	17	+	+	ADP
ap-9818	164	18	2	2	NUM
ap-9818	164	19	c	c	NOUN
ap-9818	164	20	(	(	PUNCT
ap-9818	164	21	1	1	NUM
ap-9818	164	22	+	+	SYM
ap-9818	164	23	2	2	NUM
ap-9818	164	24	α	α	NOUN
ap-9818	164	25	)	)	PUNCT
ap-9818	164	26	(	(	PUNCT
ap-9818	164	27	1	1	NUM
ap-9818	164	28	+	+	SYM
ap-9818	164	29	2	2	NUM
ap-9818	164	30	γ	γ	NOUN
ap-9818	164	31	)	)	PUNCT
ap-9818	164	32	±	±	NOUN
ap-9818	164	33	√	√	ADV
ap-9818	164	34	1	1	NUM
ap-9818	164	35	+	+	CCONJ
ap-9818	164	36	4	4	NUM
ap-9818	164	37	c	c	NOUN
ap-9818	164	38	(	(	PUNCT
ap-9818	164	39	3	3	NUM
ap-9818	164	40	+	+	SYM
ap-9818	164	41	4	4	NUM
ap-9818	164	42	α	α	NOUN
ap-9818	164	43	+	+	ADP
ap-9818	164	44	4	4	NUM
ap-9818	164	45	γ	γ	NOUN
ap-9818	164	46	+	+	ADP
ap-9818	164	47	4	4	NUM
ap-9818	164	48	α	α	PRON
ap-9818	164	49	γ	γ	NOUN
ap-9818	164	50	)	)	PUNCT
ap-9818	164	51	]	]	PUNCT
ap-9818	164	52	.	.	PUNCT
ap-9818	165	1	(	(	PUNCT
ap-9818	165	2	25	25	NUM
ap-9818	165	3	)	)	PUNCT
ap-9818	165	4	in	in	ADP
ap-9818	165	5	summary	summary	NOUN
ap-9818	165	6	,	,	PUNCT
ap-9818	165	7	if	if	SCONJ
ap-9818	165	8	the	the	DET
ap-9818	165	9	conditions	condition	NOUN
ap-9818	165	10	(	(	PUNCT
ap-9818	165	11	17	17	NUM
ap-9818	165	12	)	)	PUNCT
ap-9818	165	13	and	and	CCONJ
ap-9818	165	14	(	(	PUNCT
ap-9818	165	15	22	22	NUM
ap-9818	165	16	)	)	PUNCT
ap-9818	165	17	with	with	ADP
ap-9818	165	18	(	(	PUNCT
ap-9818	165	19	23	23	NUM
ap-9818	165	20	)	)	PUNCT
ap-9818	165	21	are	be	AUX
ap-9818	165	22	met	meet	VERB
ap-9818	165	23	,	,	PUNCT
ap-9818	165	24	then	then	ADV
ap-9818	165	25	the	the	DET
ap-9818	165	26	two	two	NUM
ap-9818	165	27	functions	function	NOUN
ap-9818	165	28	(	(	PUNCT
ap-9818	165	29	24	24	NUM
ap-9818	165	30	)	)	PUNCT
ap-9818	165	31	and	and	CCONJ
ap-9818	165	32	(	(	PUNCT
ap-9818	165	33	25	25	NUM
ap-9818	165	34	)	)	PUNCT
ap-9818	165	35	have	have	VERB
ap-9818	165	36	the	the	DET
ap-9818	165	37	same	same	ADJ
ap-9818	165	38	functional	functional	ADJ
ap-9818	165	39	form	form	NOUN
ap-9818	165	40	.	.	PUNCT
ap-9818	166	1	•	•	NOUN
ap-9818	166	2	the	the	DET
ap-9818	166	3	last	last	ADJ
ap-9818	166	4	option	option	NOUN
ap-9818	166	5	to	to	PART
ap-9818	166	6	produce	produce	VERB
ap-9818	166	7	an	an	DET
ap-9818	166	8	inverse	inverse	ADJ
ap-9818	166	9	quadratic	quadratic	ADJ
ap-9818	166	10	term	term	NOUN
ap-9818	166	11	in	in	ADP
ap-9818	166	12	the	the	DET
ap-9818	166	13	effective	effective	ADJ
ap-9818	166	14	potential	potential	NOUN
ap-9818	166	15	(	(	PUNCT
ap-9818	166	16	15	15	NUM
ap-9818	166	17	)	)	PUNCT
ap-9818	166	18	is	be	AUX
ap-9818	166	19	to	to	PART
ap-9818	166	20	use	use	VERB
ap-9818	166	21	the	the	DET
ap-9818	166	22	positiondependent	positiondependent	ADJ
ap-9818	166	23	mass	mass	NOUN
ap-9818	166	24	by	by	ADP
ap-9818	166	25	means	mean	NOUN
ap-9818	166	26	of	of	ADP
ap-9818	166	27	the	the	DET
ap-9818	166	28	term	term	NOUN
ap-9818	166	29	(	(	PUNCT
ap-9818	166	30	m′/m)2	m′/m)2	NOUN
ap-9818	166	31	that	that	PRON
ap-9818	166	32	appears	appear	VERB
ap-9818	166	33	in	in	ADP
ap-9818	166	34	(	(	PUNCT
ap-9818	166	35	15	15	NUM
ap-9818	166	36	)	)	PUNCT
ap-9818	166	37	.	.	PUNCT
ap-9818	167	1	the	the	DET
ap-9818	167	2	corresponding	corresponding	ADJ
ap-9818	167	3	condition	condition	NOUN
ap-9818	167	4	is	be	AUX
ap-9818	167	5	given	give	VERB
ap-9818	167	6	by	by	ADP
ap-9818	167	7	:	:	PUNCT
ap-9818	167	8	[	[	PUNCT
ap-9818	167	9	m′(x	m′(x	NOUN
ap-9818	167	10	)	)	PUNCT
ap-9818	167	11	m(x	m(x	PROPN
ap-9818	167	12	)	)	PUNCT
ap-9818	168	1	]	]	PUNCT
ap-9818	168	2	2	2	X
ap-9818	168	3	=	=	SYM
ap-9818	168	4	c	c	NOUN
ap-9818	168	5	x2	x2	NOUN
ap-9818	168	6	⇝	⇝	NOUN
ap-9818	168	7	m(x	m(x	PROPN
ap-9818	168	8	)	)	PUNCT
ap-9818	169	1	=	=	PUNCT
ap-9818	169	2	c3	c3	PROPN
ap-9818	169	3	x±	x±	PROPN
ap-9818	170	1	√	√	NUM
ap-9818	170	2	c	c	NOUN
ap-9818	170	3	.	.	PUNCT
ap-9818	171	1	(	(	PUNCT
ap-9818	171	2	26	26	NUM
ap-9818	171	3	)	)	PUNCT
ap-9818	171	4	this	this	PRON
ap-9818	171	5	is	be	AUX
ap-9818	171	6	a	a	DET
ap-9818	171	7	particular	particular	ADJ
ap-9818	171	8	case	case	NOUN
ap-9818	171	9	of	of	ADP
ap-9818	171	10	our	our	PRON
ap-9818	171	11	previous	previous	ADJ
ap-9818	171	12	condition	condition	NOUN
ap-9818	171	13	(	(	PUNCT
ap-9818	171	14	22	22	NUM
ap-9818	171	15	)	)	PUNCT
ap-9818	171	16	,	,	PUNCT
ap-9818	171	17	such	such	ADJ
ap-9818	171	18	that	that	SCONJ
ap-9818	171	19	we	we	PRON
ap-9818	171	20	do	do	AUX
ap-9818	171	21	not	not	PART
ap-9818	171	22	need	need	VERB
ap-9818	171	23	to	to	PART
ap-9818	171	24	discuss	discuss	VERB
ap-9818	171	25	it	it	PRON
ap-9818	171	26	further	far	ADV
ap-9818	171	27	.	.	PUNCT
ap-9818	172	1	there	there	PRON
ap-9818	172	2	are	be	VERB
ap-9818	172	3	more	more	ADJ
ap-9818	172	4	possibilities	possibility	NOUN
ap-9818	172	5	for	for	ADP
ap-9818	172	6	setting	set	VERB
ap-9818	172	7	up	up	ADP
ap-9818	172	8	conditions	condition	NOUN
ap-9818	172	9	leading	lead	VERB
ap-9818	172	10	to	to	ADP
ap-9818	172	11	an	an	DET
ap-9818	172	12	inverse	inverse	ADJ
ap-9818	172	13	quadratic	quadratic	ADJ
ap-9818	172	14	term	term	NOUN
ap-9818	172	15	in	in	ADP
ap-9818	172	16	(	(	PUNCT
ap-9818	172	17	18	18	NUM
ap-9818	172	18	)	)	PUNCT
ap-9818	172	19	,	,	PUNCT
ap-9818	172	20	such	such	ADJ
ap-9818	172	21	as	as	ADP
ap-9818	172	22	a	a	DET
ap-9818	172	23	linear	linear	ADJ
ap-9818	172	24	combination	combination	NOUN
ap-9818	172	25	of	of	ADP
ap-9818	172	26	(	(	PUNCT
ap-9818	172	27	19	19	NUM
ap-9818	172	28	)	)	PUNCT
ap-9818	172	29	and	and	CCONJ
ap-9818	172	30	(	(	PUNCT
ap-9818	172	31	22	22	NUM
ap-9818	172	32	)	)	PUNCT
ap-9818	172	33	.	.	PUNCT
ap-9818	173	1	however	however	ADV
ap-9818	173	2	,	,	PUNCT
ap-9818	173	3	in	in	ADP
ap-9818	173	4	any	any	DET
ap-9818	173	5	case	case	NOUN
ap-9818	173	6	,	,	PUNCT
ap-9818	173	7	the	the	DET
ap-9818	173	8	compatibility	compatibility	NOUN
ap-9818	173	9	with	with	ADP
ap-9818	173	10	the	the	DET
ap-9818	173	11	position	position	NOUN
ap-9818	173	12	-	-	PUNCT
ap-9818	173	13	dependent	dependent	ADJ
ap-9818	173	14	mass	mass	NOUN
ap-9818	173	15	given	give	VERB
ap-9818	173	16	in	in	ADP
ap-9818	173	17	(	(	PUNCT
ap-9818	173	18	17	17	NUM
ap-9818	173	19	)	)	PUNCT
ap-9818	173	20	must	must	AUX
ap-9818	173	21	be	be	AUX
ap-9818	173	22	established	establish	VERB
ap-9818	173	23	.	.	PUNCT
ap-9818	174	1	summary	summary	NOUN
ap-9818	174	2	.	.	PUNCT
ap-9818	175	1	in	in	ADP
ap-9818	175	2	conclusion	conclusion	NOUN
ap-9818	175	3	,	,	PUNCT
ap-9818	175	4	the	the	DET
ap-9818	175	5	effective	effective	ADJ
ap-9818	175	6	potentials	potential	NOUN
ap-9818	175	7	for	for	ADP
ap-9818	175	8	the	the	DET
ap-9818	175	9	dunkl	dunkl	NOUN
ap-9818	175	10	case	case	NOUN
ap-9818	175	11	and	and	CCONJ
ap-9818	175	12	for	for	ADP
ap-9818	175	13	the	the	DET
ap-9818	175	14	conventional	conventional	ADJ
ap-9818	175	15	scenario	scenario	NOUN
ap-9818	175	16	have	have	VERB
ap-9818	175	17	the	the	DET
ap-9818	175	18	same	same	ADJ
ap-9818	175	19	functional	functional	ADJ
ap-9818	175	20	form	form	NOUN
ap-9818	175	21	,	,	PUNCT
ap-9818	175	22	if	if	SCONJ
ap-9818	175	23	the	the	DET
ap-9818	175	24	condition	condition	NOUN
ap-9818	175	25	(	(	PUNCT
ap-9818	175	26	17	17	NUM
ap-9818	175	27	)	)	PUNCT
ap-9818	175	28	,	,	PUNCT
ap-9818	175	29	and	and	CCONJ
ap-9818	175	30	one	one	NUM
ap-9818	175	31	of	of	ADP
ap-9818	175	32	the	the	DET
ap-9818	175	33	conditions	condition	NOUN
ap-9818	175	34	,	,	PUNCT
ap-9818	175	35	(	(	PUNCT
ap-9818	175	36	19	19	NUM
ap-9818	175	37	)	)	PUNCT
ap-9818	175	38	,	,	PUNCT
ap-9818	175	39	(	(	PUNCT
ap-9818	175	40	22	22	NUM
ap-9818	175	41	)	)	PUNCT
ap-9818	175	42	,	,	PUNCT
ap-9818	175	43	are	be	AUX
ap-9818	175	44	fulfilled	fulfil	VERB
ap-9818	175	45	.	.	PUNCT
ap-9818	176	1	in	in	ADP
ap-9818	176	2	this	this	DET
ap-9818	176	3	case	case	NOUN
ap-9818	176	4	,	,	PUNCT
ap-9818	176	5	the	the	DET
ap-9818	176	6	dunkl	dunkl	NOUN
ap-9818	176	7	-	-	PUNCT
ap-9818	176	8	schrödinger	schrödinger	NOUN
ap-9818	176	9	equation	equation	NOUN
ap-9818	176	10	(	(	PUNCT
ap-9818	176	11	6	6	NUM
ap-9818	176	12	)	)	PUNCT
ap-9818	176	13	and	and	CCONJ
ap-9818	176	14	its	its	PRON
ap-9818	176	15	conventional	conventional	ADJ
ap-9818	176	16	partner	partner	NOUN
ap-9818	176	17	(	(	PUNCT
ap-9818	176	18	7	7	X
ap-9818	176	19	)	)	PUNCT
ap-9818	176	20	share	share	VERB
ap-9818	176	21	the	the	DET
ap-9818	176	22	same	same	ADJ
ap-9818	176	23	solutions	solution	NOUN
ap-9818	176	24	,	,	PUNCT
ap-9818	176	25	up	up	ADP
ap-9818	176	26	to	to	ADP
ap-9818	176	27	a	a	DET
ap-9818	176	28	change	change	NOUN
ap-9818	176	29	of	of	ADP
ap-9818	176	30	numerical	numerical	ADJ
ap-9818	176	31	parameters	parameter	NOUN
ap-9818	176	32	.	.	PUNCT
ap-9818	177	1	let	let	VERB
ap-9818	177	2	us	we	PRON
ap-9818	177	3	now	now	ADV
ap-9818	177	4	summarise	summarise	VERB
ap-9818	177	5	the	the	DET
ap-9818	177	6	two	two	NUM
ap-9818	177	7	main	main	ADJ
ap-9818	177	8	routes	route	NOUN
ap-9818	177	9	for	for	ADP
ap-9818	177	10	fulfilling	fulfil	VERB
ap-9818	177	11	the	the	DET
ap-9818	177	12	solvability	solvability	NOUN
ap-9818	177	13	conditions	condition	NOUN
ap-9818	177	14	.	.	PUNCT
ap-9818	178	1	•	•	INTJ
ap-9818	178	2	we	we	PRON
ap-9818	178	3	impose	impose	VERB
ap-9818	178	4	the	the	DET
ap-9818	178	5	two	two	NUM
ap-9818	178	6	constraints	constraint	NOUN
ap-9818	178	7	(	(	PUNCT
ap-9818	178	8	17	17	NUM
ap-9818	178	9	)	)	PUNCT
ap-9818	178	10	and	and	CCONJ
ap-9818	178	11	(	(	PUNCT
ap-9818	178	12	19	19	NUM
ap-9818	178	13	):	):	PUNCT
ap-9818	178	14	m(x	m(x	X
ap-9818	178	15	)	)	PUNCT
ap-9818	179	1	=	=	SYM
ap-9818	179	2	c2	c2	PROPN
ap-9818	179	3	[	[	PUNCT
ap-9818	179	4	c1	c1	PROPN
ap-9818	179	5	(	(	PUNCT
ap-9818	179	6	a	a	DET
ap-9818	179	7	+	+	NOUN
ap-9818	179	8	1	1	NUM
ap-9818	179	9	)	)	PUNCT
ap-9818	179	10	+	+	CCONJ
ap-9818	179	11	(	(	PUNCT
ap-9818	179	12	a	a	DET
ap-9818	179	13	+	+	NOUN
ap-9818	179	14	b	b	NOUN
ap-9818	179	15	)	)	PUNCT
ap-9818	179	16	x1	x1	PROPN
ap-9818	180	1	+	+	ADP
ap-9818	180	2	1	1	NUM
ap-9818	180	3	a	a	PRON
ap-9818	180	4	]	]	X
ap-9818	180	5	a	a	PRON
ap-9818	180	6	a+b	a+b	NUM
ap-9818	180	7	,	,	PUNCT
ap-9818	180	8	v	v	NOUN
ap-9818	180	9	(	(	PUNCT
ap-9818	180	10	x	x	NOUN
ap-9818	180	11	)	)	PUNCT
ap-9818	180	12	=	=	SYM
ap-9818	181	1	c	c	X
ap-9818	181	2	x2	x2	PROPN
ap-9818	181	3	m(x	m(x	PROPN
ap-9818	181	4	)	)	PUNCT
ap-9818	182	1	+	+	CCONJ
ap-9818	182	2	w	w	X
ap-9818	182	3	(	(	PUNCT
ap-9818	182	4	x	x	NOUN
ap-9818	182	5	)	)	PUNCT
ap-9818	182	6	.	.	PUNCT
ap-9818	183	1	(	(	PUNCT
ap-9818	183	2	27	27	NUM
ap-9818	183	3	)	)	PUNCT
ap-9818	183	4	the	the	DET
ap-9818	183	5	resulting	result	VERB
ap-9818	183	6	effective	effective	ADJ
ap-9818	183	7	potential	potential	NOUN
ap-9818	183	8	of	of	ADP
ap-9818	183	9	the	the	DET
ap-9818	183	10	reduced	reduce	VERB
ap-9818	183	11	equation	equation	NOUN
ap-9818	183	12	(	(	PUNCT
ap-9818	183	13	11	11	NUM
ap-9818	183	14	)	)	PUNCT
ap-9818	183	15	takes	take	VERB
ap-9818	183	16	the	the	DET
ap-9818	183	17	form	form	NOUN
ap-9818	183	18	(	(	PUNCT
ap-9818	183	19	20	20	NUM
ap-9818	183	20	):	):	PUNCT
ap-9818	183	21	uν(x	uν(x	X
ap-9818	183	22	)	)	PUNCT
ap-9818	183	23	=	=	PUNCT
ap-9818	184	1	[	[	X
ap-9818	184	2	e	e	X
ap-9818	184	3	−	−	PROPN
ap-9818	184	4	w	w	PROPN
ap-9818	184	5	(	(	PUNCT
ap-9818	184	6	x	x	NOUN
ap-9818	184	7	)	)	PUNCT
ap-9818	184	8	]	]	PUNCT
ap-9818	184	9	m(x	m(x	PROPN
ap-9818	184	10	)	)	PUNCT
ap-9818	184	11	−	−	PROPN
ap-9818	185	1	[	[	PUNCT
ap-9818	185	2	3	3	NUM
ap-9818	185	3	4	4	NUM
ap-9818	185	4	+	+	SYM
ap-9818	185	5	α	α	NOUN
ap-9818	185	6	+	+	X
ap-9818	185	7	γ	γ	X
ap-9818	185	8	+	+	X
ap-9818	185	9	α	α	PROPN
ap-9818	185	10	γ	γ	NOUN
ap-9818	185	11	−	−	PROPN
ap-9818	185	12	b	b	PROPN
ap-9818	185	13	ν	ν	X
ap-9818	185	14	(	(	PUNCT
ap-9818	185	15	δ	δ	PROPN
ap-9818	185	16	+	+	CCONJ
ap-9818	185	17	α	α	PROPN
ap-9818	185	18	δ	δ	PROPN
ap-9818	185	19	+	+	CCONJ
ap-9818	185	20	γ	γ	PROPN
ap-9818	185	21	δ	δ	PROPN
ap-9818	185	22	)	)	PUNCT
ap-9818	185	23	]	]	PUNCT
ap-9818	185	24	[	[	PUNCT
ap-9818	185	25	m′(x	m′(x	NOUN
ap-9818	185	26	)	)	PUNCT
ap-9818	185	27	m(x	m(x	PROPN
ap-9818	185	28	)	)	PUNCT
ap-9818	185	29	]	]	PUNCT
ap-9818	185	30	2	2	X
ap-9818	186	1	+	+	CCONJ
ap-9818	186	2	[	[	PUNCT
ap-9818	186	3	1	1	NUM
ap-9818	186	4	+	+	NUM
ap-9818	186	5	α	α	NOUN
ap-9818	186	6	+	+	X
ap-9818	186	7	γ	γ	X
ap-9818	186	8	+	+	PROPN
ap-9818	186	9	2	2	NUM
ap-9818	186	10	a	a	DET
ap-9818	186	11	ν	ν	X
ap-9818	186	12	(	(	PUNCT
ap-9818	186	13	δ	δ	PROPN
ap-9818	186	14	+	+	CCONJ
ap-9818	186	15	α	α	PROPN
ap-9818	186	16	δ	δ	PROPN
ap-9818	186	17	+	+	CCONJ
ap-9818	186	18	γ	γ	PROPN
ap-9818	186	19	δ	δ	PROPN
ap-9818	186	20	)	)	PUNCT
ap-9818	186	21	]	]	PUNCT
ap-9818	186	22	m′′(x	m′′(x	NOUN
ap-9818	186	23	)	)	PUNCT
ap-9818	186	24	2	2	NUM
ap-9818	186	25	m(x	m(x	PROPN
ap-9818	186	26	)	)	PUNCT
ap-9818	187	1	+	+	CCONJ
ap-9818	187	2	δ	δ	PROPN
ap-9818	187	3	ν	ν	NOUN
ap-9818	187	4	−	−	PROPN
ap-9818	187	5	ν2	ν2	NOUN
ap-9818	187	6	−	−	PROPN
ap-9818	187	7	c	c	NOUN
ap-9818	187	8	x2	x2	PROPN
ap-9818	187	9	.	.	PUNCT
ap-9818	188	1	(	(	PUNCT
ap-9818	188	2	28	28	NUM
ap-9818	188	3	)	)	PUNCT
ap-9818	188	4	226	226	NUM
ap-9818	188	5	vol	vol	NOUN
ap-9818	188	6	.	.	PUNCT
ap-9818	189	1	65	65	NUM
ap-9818	189	2	no	no	NOUN
ap-9818	189	3	.	.	PUNCT
ap-9818	190	1	2/2025	2/2025	NUM
ap-9818	190	2	persistence	persistence	NOUN
ap-9818	190	3	of	of	ADP
ap-9818	190	4	solvability	solvability	NOUN
ap-9818	190	5	in	in	ADP
ap-9818	190	6	quantum	quantum	NOUN
ap-9818	190	7	systems	system	NOUN
ap-9818	190	8	deformed	deform	VERB
ap-9818	190	9	by	by	ADP
ap-9818	190	10	dunkl	dunkl	PROPN
ap-9818	190	11	.	.	PUNCT
ap-9818	190	12	.	.	PUNCT
ap-9818	191	1	.	.	PUNCT
ap-9818	192	1	•	•	INTJ
ap-9818	192	2	we	we	PRON
ap-9818	192	3	impose	impose	VERB
ap-9818	192	4	the	the	DET
ap-9818	192	5	constraint	constraint	NOUN
ap-9818	192	6	(	(	PUNCT
ap-9818	192	7	22	22	NUM
ap-9818	192	8	)	)	PUNCT
ap-9818	192	9	along	along	ADP
ap-9818	192	10	with	with	ADP
ap-9818	192	11	(	(	PUNCT
ap-9818	192	12	23	23	NUM
ap-9818	192	13	):	):	PUNCT
ap-9818	192	14	m(x	m(x	X
ap-9818	192	15	)	)	PUNCT
ap-9818	193	1	=	=	PUNCT
ap-9818	193	2	c3	c3	NOUN
ap-9818	193	3	x	x	SYM
ap-9818	193	4	1	1	NUM
ap-9818	193	5	2	2	NUM
ap-9818	193	6	±	±	NUM
ap-9818	193	7	1	1	NUM
ap-9818	193	8	2	2	NUM
ap-9818	193	9	√	√	NUM
ap-9818	193	10	1	1	NUM
ap-9818	193	11	+	+	NOUN
ap-9818	193	12	4c	4c	NOUN
ap-9818	193	13	.	.	PUNCT
ap-9818	194	1	(	(	PUNCT
ap-9818	194	2	29	29	NUM
ap-9818	194	3	)	)	PUNCT
ap-9818	194	4	the	the	DET
ap-9818	194	5	resulting	result	VERB
ap-9818	194	6	effective	effective	ADJ
ap-9818	194	7	potential	potential	NOUN
ap-9818	194	8	of	of	ADP
ap-9818	194	9	the	the	DET
ap-9818	194	10	reduced	reduce	VERB
ap-9818	194	11	equation	equation	NOUN
ap-9818	194	12	(	(	PUNCT
ap-9818	194	13	11	11	NUM
ap-9818	194	14	)	)	PUNCT
ap-9818	194	15	takes	take	VERB
ap-9818	194	16	the	the	DET
ap-9818	194	17	form	form	NOUN
ap-9818	194	18	(	(	PUNCT
ap-9818	194	19	24	24	NUM
ap-9818	194	20	):	):	PUNCT
ap-9818	194	21	uν(x	uν(x	X
ap-9818	194	22	)	)	PUNCT
ap-9818	194	23	=	=	SYM
ap-9818	195	1	c3	c3	NOUN
ap-9818	195	2	x	x	SYM
ap-9818	195	3	1	1	NUM
ap-9818	195	4	2	2	NUM
ap-9818	195	5	±	±	NUM
ap-9818	195	6	1	1	NUM
ap-9818	195	7	2	2	NUM
ap-9818	195	8	√	√	NUM
ap-9818	195	9	1	1	NUM
ap-9818	195	10	+	+	NUM
ap-9818	195	11	4c	4c	NOUN
ap-9818	195	12	[	[	X
ap-9818	195	13	e	e	X
ap-9818	195	14	−	−	PROPN
ap-9818	195	15	v	v	PART
ap-9818	195	16	(	(	PUNCT
ap-9818	195	17	x	x	NOUN
ap-9818	195	18	)	)	PUNCT
ap-9818	195	19	]	]	PUNCT
ap-9818	196	1	−	−	PROPN
ap-9818	196	2	1	1	NUM
ap-9818	196	3	8	8	NUM
ap-9818	196	4	x2	x2	NOUN
ap-9818	196	5	[	[	PUNCT
ap-9818	196	6	3	3	NUM
ap-9818	196	7	+	+	SYM
ap-9818	196	8	4	4	NUM
ap-9818	196	9	α	α	NOUN
ap-9818	196	10	+	+	ADP
ap-9818	196	11	4	4	NUM
ap-9818	196	12	γ	γ	NOUN
ap-9818	196	13	+	+	ADP
ap-9818	196	14	4	4	NUM
ap-9818	196	15	α	α	NUM
ap-9818	196	16	γ	γ	NOUN
ap-9818	196	17	+	+	ADP
ap-9818	196	18	2	2	NUM
ap-9818	196	19	c	c	NOUN
ap-9818	196	20	(	(	PUNCT
ap-9818	196	21	1	1	NUM
ap-9818	196	22	+	+	SYM
ap-9818	196	23	2	2	NUM
ap-9818	196	24	α	α	NOUN
ap-9818	196	25	)	)	PUNCT
ap-9818	196	26	(	(	PUNCT
ap-9818	196	27	1	1	NUM
ap-9818	196	28	+	+	SYM
ap-9818	196	29	2	2	NUM
ap-9818	196	30	γ	γ	NOUN
ap-9818	196	31	)	)	PUNCT
ap-9818	196	32	−	−	PROPN
ap-9818	196	33	4	4	NUM
ap-9818	196	34	δ	δ	NOUN
ap-9818	196	35	ν	ν	X
ap-9818	196	36	(	(	PUNCT
ap-9818	196	37	3	3	NUM
ap-9818	196	38	+	+	NUM
ap-9818	196	39	α	α	NOUN
ap-9818	196	40	+	+	X
ap-9818	196	41	γ	γ	X
ap-9818	196	42	)	)	PUNCT
ap-9818	196	43	+	+	NUM
ap-9818	196	44	8	8	NUM
ap-9818	196	45	ν2	ν2	NOUN
ap-9818	196	46	±	±	NUM
ap-9818	196	47	√	√	ADV
ap-9818	196	48	1	1	NUM
ap-9818	196	49	+	+	CCONJ
ap-9818	196	50	4	4	NUM
ap-9818	196	51	c	c	NOUN
ap-9818	196	52	(	(	PUNCT
ap-9818	196	53	3	3	NUM
ap-9818	196	54	+	+	SYM
ap-9818	196	55	4	4	NUM
ap-9818	196	56	α	α	NOUN
ap-9818	196	57	+	+	ADP
ap-9818	196	58	4	4	NUM
ap-9818	196	59	γ	γ	NOUN
ap-9818	196	60	+	+	ADP
ap-9818	196	61	4	4	NUM
ap-9818	196	62	α	α	NUM
ap-9818	196	63	γ	γ	NOUN
ap-9818	196	64	−	−	PROPN
ap-9818	196	65	4	4	NUM
ap-9818	196	66	δ	δ	NOUN
ap-9818	196	67	ν	ν	NOUN
ap-9818	196	68	−	−	PROPN
ap-9818	196	69	4	4	NUM
ap-9818	196	70	α	α	NOUN
ap-9818	196	71	δ	δ	NOUN
ap-9818	196	72	ν	ν	ADP
ap-9818	196	73	−	−	PROPN
ap-9818	196	74	4	4	NUM
ap-9818	196	75	γ	γ	PROPN
ap-9818	196	76	δ	δ	PROPN
ap-9818	196	77	ν	ν	PROPN
ap-9818	196	78	)	)	PUNCT
ap-9818	196	79	]	]	PUNCT
ap-9818	196	80	.	.	PUNCT
ap-9818	197	1	(	(	PUNCT
ap-9818	197	2	30	30	NUM
ap-9818	197	3	)	)	SYM
ap-9818	197	4	4	4	NUM
ap-9818	197	5	.	.	PUNCT
ap-9818	197	6	applications	application	NOUN
ap-9818	197	7	we	we	PRON
ap-9818	197	8	will	will	AUX
ap-9818	197	9	now	now	ADV
ap-9818	197	10	present	present	VERB
ap-9818	197	11	several	several	ADJ
ap-9818	197	12	examples	example	NOUN
ap-9818	197	13	for	for	ADP
ap-9818	197	14	quantum	quantum	NOUN
ap-9818	197	15	systems	system	NOUN
ap-9818	197	16	,	,	PUNCT
ap-9818	197	17	where	where	SCONJ
ap-9818	197	18	solutions	solution	NOUN
ap-9818	197	19	of	of	ADP
ap-9818	197	20	the	the	DET
ap-9818	197	21	governing	govern	VERB
ap-9818	197	22	dunkl	dunkl	NOUN
ap-9818	197	23	-	-	PUNCT
ap-9818	197	24	schrödinger	schrödinger	NOUN
ap-9818	197	25	equation	equation	NOUN
ap-9818	197	26	can	can	AUX
ap-9818	197	27	be	be	AUX
ap-9818	197	28	derived	derive	VERB
ap-9818	197	29	directly	directly	ADV
ap-9818	197	30	from	from	ADP
ap-9818	197	31	the	the	DET
ap-9818	197	32	conventional	conventional	ADJ
ap-9818	197	33	context	context	NOUN
ap-9818	197	34	.	.	PUNCT
ap-9818	198	1	in	in	ADP
ap-9818	198	2	each	each	DET
ap-9818	198	3	example	example	NOUN
ap-9818	198	4	,	,	PUNCT
ap-9818	198	5	we	we	PRON
ap-9818	198	6	verify	verify	VERB
ap-9818	198	7	that	that	SCONJ
ap-9818	198	8	our	our	PRON
ap-9818	198	9	solvability	solvability	NOUN
ap-9818	198	10	conditions	condition	NOUN
ap-9818	198	11	are	be	AUX
ap-9818	198	12	satisfied	satisfied	ADJ
ap-9818	198	13	,	,	PUNCT
ap-9818	198	14	and	and	CCONJ
ap-9818	198	15	afterwards	afterwards	ADV
ap-9818	198	16	construct	construct	VERB
ap-9818	198	17	bound	bind	VERB
ap-9818	198	18	state	state	NOUN
ap-9818	198	19	solutions	solution	NOUN
ap-9818	198	20	for	for	ADP
ap-9818	198	21	the	the	DET
ap-9818	198	22	dunkl	dunkl	NOUN
ap-9818	198	23	-	-	PUNCT
ap-9818	198	24	schrödinger	schrödinger	NOUN
ap-9818	198	25	equation	equation	NOUN
ap-9818	198	26	from	from	ADP
ap-9818	198	27	the	the	DET
ap-9818	198	28	conventional	conventional	ADJ
ap-9818	198	29	system	system	NOUN
ap-9818	198	30	.	.	PUNCT
ap-9818	199	1	in	in	ADP
ap-9818	199	2	each	each	PRON
ap-9818	199	3	of	of	ADP
ap-9818	199	4	the	the	DET
ap-9818	199	5	following	follow	VERB
ap-9818	199	6	examples	example	NOUN
ap-9818	199	7	,	,	PUNCT
ap-9818	199	8	we	we	PRON
ap-9818	199	9	will	will	AUX
ap-9818	199	10	point	point	VERB
ap-9818	199	11	out	out	ADP
ap-9818	199	12	existing	exist	VERB
ap-9818	199	13	applications	application	NOUN
ap-9818	199	14	for	for	ADP
ap-9818	199	15	the	the	DET
ap-9818	199	16	respective	respective	ADJ
ap-9818	199	17	potential	potential	NOUN
ap-9818	199	18	and	and	CCONJ
ap-9818	199	19	the	the	DET
ap-9818	199	20	position	position	NOUN
ap-9818	199	21	-	-	PUNCT
ap-9818	199	22	dependent	dependent	ADJ
ap-9818	199	23	mass	mass	NOUN
ap-9818	199	24	in	in	ADP
ap-9818	199	25	conventional	conventional	ADJ
ap-9818	199	26	quantum	quantum	NOUN
ap-9818	199	27	systems	system	NOUN
ap-9818	199	28	.	.	PUNCT
ap-9818	200	1	the	the	DET
ap-9818	200	2	study	study	NOUN
ap-9818	200	3	of	of	ADP
ap-9818	200	4	the	the	DET
ap-9818	200	5	systems	system	NOUN
ap-9818	200	6	within	within	ADP
ap-9818	200	7	the	the	DET
ap-9818	200	8	dunkl	dunkl	NOUN
ap-9818	200	9	formalism	formalism	NOUN
ap-9818	200	10	is	be	AUX
ap-9818	200	11	motivated	motivate	VERB
ap-9818	200	12	by	by	ADP
ap-9818	200	13	the	the	DET
ap-9818	200	14	interest	interest	NOUN
ap-9818	200	15	in	in	ADP
ap-9818	200	16	deformed	deform	VERB
ap-9818	200	17	quantum	quantum	ADJ
ap-9818	200	18	theories	theory	NOUN
ap-9818	200	19	rather	rather	ADV
ap-9818	200	20	than	than	ADP
ap-9818	200	21	in	in	ADP
ap-9818	200	22	experimental	experimental	ADJ
ap-9818	200	23	realisability	realisability	NOUN
ap-9818	200	24	.	.	PUNCT
ap-9818	201	1	for	for	ADP
ap-9818	201	2	this	this	DET
ap-9818	201	3	reason	reason	NOUN
ap-9818	201	4	,	,	PUNCT
ap-9818	201	5	we	we	PRON
ap-9818	201	6	can	can	AUX
ap-9818	201	7	not	not	PART
ap-9818	201	8	give	give	VERB
ap-9818	201	9	a	a	DET
ap-9818	201	10	physical	physical	ADJ
ap-9818	201	11	or	or	CCONJ
ap-9818	201	12	experimental	experimental	ADJ
ap-9818	201	13	realisation	realisation	NOUN
ap-9818	201	14	of	of	ADP
ap-9818	201	15	the	the	DET
ap-9818	201	16	latter	latter	ADJ
ap-9818	201	17	systems	system	NOUN
ap-9818	201	18	.	.	PUNCT
ap-9818	202	1	4.1	4.1	NUM
ap-9818	202	2	.	.	PUNCT
ap-9818	202	3	inverse	inverse	NOUN
ap-9818	202	4	-	-	PUNCT
ap-9818	202	5	quadratic	quadratic	ADJ
ap-9818	202	6	potential	potential	NOUN
ap-9818	202	7	with	with	ADP
ap-9818	202	8	confinement	confinement	NOUN
ap-9818	202	9	in	in	ADP
ap-9818	202	10	the	the	DET
ap-9818	202	11	first	first	ADJ
ap-9818	202	12	example	example	NOUN
ap-9818	202	13	we	we	PRON
ap-9818	202	14	will	will	AUX
ap-9818	202	15	consider	consider	VERB
ap-9818	202	16	a	a	DET
ap-9818	202	17	system	system	NOUN
ap-9818	202	18	constrained	constrain	VERB
ap-9818	202	19	onto	onto	ADP
ap-9818	202	20	the	the	DET
ap-9818	202	21	finite	finite	ADJ
ap-9818	202	22	interval	interval	NOUN
ap-9818	202	23	given	give	VERB
ap-9818	202	24	by	by	ADP
ap-9818	202	25	|x|	|x|	PROPN
ap-9818	202	26	<	<	X
ap-9818	202	27	1	1	NUM
ap-9818	202	28	.	.	PUNCT
ap-9818	202	29	after	after	ADP
ap-9818	202	30	verifying	verify	VERB
ap-9818	202	31	our	our	PRON
ap-9818	202	32	solvability	solvability	NOUN
ap-9818	202	33	conditions	condition	NOUN
ap-9818	202	34	,	,	PUNCT
ap-9818	202	35	we	we	PRON
ap-9818	202	36	find	find	VERB
ap-9818	202	37	the	the	DET
ap-9818	202	38	general	general	ADJ
ap-9818	202	39	solution	solution	NOUN
ap-9818	202	40	to	to	ADP
ap-9818	202	41	the	the	DET
ap-9818	202	42	conventioanl	conventioanl	ADJ
ap-9818	202	43	schrödinger	schrödinger	ADJ
ap-9818	202	44	equation	equation	NOUN
ap-9818	202	45	.	.	PUNCT
ap-9818	203	1	afterwards	afterwards	ADV
ap-9818	203	2	,	,	PUNCT
ap-9818	203	3	we	we	PRON
ap-9818	203	4	construct	construct	VERB
ap-9818	203	5	the	the	DET
ap-9818	203	6	general	general	ADJ
ap-9818	203	7	solution	solution	NOUN
ap-9818	203	8	of	of	ADP
ap-9818	203	9	the	the	DET
ap-9818	203	10	associated	associated	ADJ
ap-9818	203	11	dunkl	dunkl	NOUN
ap-9818	203	12	-	-	PUNCT
ap-9818	203	13	schrödinger	schrödinger	NOUN
ap-9818	203	14	equation	equation	NOUN
ap-9818	203	15	by	by	ADP
ap-9818	203	16	means	mean	NOUN
ap-9818	203	17	of	of	ADP
ap-9818	203	18	reparametrisation	reparametrisation	NOUN
ap-9818	203	19	.	.	PUNCT
ap-9818	204	1	the	the	DET
ap-9818	204	2	dunkl	dunkl	PROPN
ap-9818	204	3	quantum	quantum	PROPN
ap-9818	204	4	model	model	NOUN
ap-9818	204	5	.	.	PUNCT
ap-9818	205	1	our	our	PRON
ap-9818	205	2	system	system	NOUN
ap-9818	205	3	is	be	AUX
ap-9818	205	4	governed	govern	VERB
ap-9818	205	5	by	by	ADP
ap-9818	205	6	the	the	DET
ap-9818	205	7	dunkl	dunkl	NOUN
ap-9818	205	8	-	-	PUNCT
ap-9818	205	9	schrödinger	schrödinger	NOUN
ap-9818	205	10	equation	equation	NOUN
ap-9818	205	11	(	(	PUNCT
ap-9818	205	12	6	6	NUM
ap-9818	205	13	)	)	PUNCT
ap-9818	205	14	for	for	ADP
ap-9818	205	15	the	the	DET
ap-9818	205	16	following	follow	VERB
ap-9818	205	17	position	position	NOUN
ap-9818	205	18	-	-	PUNCT
ap-9818	205	19	dependent	dependent	ADJ
ap-9818	205	20	mass	mass	NOUN
ap-9818	205	21	m	m	NOUN
ap-9818	205	22	and	and	CCONJ
ap-9818	205	23	potential	potential	ADJ
ap-9818	205	24	v	v	NOUN
ap-9818	205	25	:	:	PUNCT
ap-9818	205	26	m(x	m(x	X
ap-9818	205	27	)	)	PUNCT
ap-9818	205	28	=	=	SYM
ap-9818	206	1	1	1	NUM
ap-9818	206	2	1	1	NUM
ap-9818	206	3	−	−	NOUN
ap-9818	207	1	x2	x2	INTJ
ap-9818	207	2	,	,	PUNCT
ap-9818	207	3	v	v	PROPN
ap-9818	207	4	(	(	PUNCT
ap-9818	207	5	x	x	NOUN
ap-9818	207	6	)	)	PUNCT
ap-9818	207	7	=	=	SYM
ap-9818	207	8	v1	v1	PROPN
ap-9818	207	9	x2	x2	NOUN
ap-9818	207	10	,	,	PUNCT
ap-9818	207	11	(	(	PUNCT
ap-9818	207	12	31	31	NUM
ap-9818	207	13	)	)	PUNCT
ap-9818	207	14	where	where	SCONJ
ap-9818	207	15	v1	v1	NOUN
ap-9818	207	16	is	be	AUX
ap-9818	207	17	a	a	DET
ap-9818	207	18	real	real	ADV
ap-9818	207	19	constant	constant	ADJ
ap-9818	207	20	.	.	PUNCT
ap-9818	208	1	we	we	PRON
ap-9818	208	2	observe	observe	VERB
ap-9818	208	3	that	that	SCONJ
ap-9818	208	4	the	the	DET
ap-9818	208	5	mass	mass	NOUN
ap-9818	208	6	is	be	AUX
ap-9818	208	7	singular	singular	ADJ
ap-9818	208	8	at	at	ADP
ap-9818	208	9	the	the	DET
ap-9818	208	10	endpoints	endpoint	NOUN
ap-9818	208	11	of	of	ADP
ap-9818	208	12	the	the	DET
ap-9818	208	13	domain	domain	NOUN
ap-9818	208	14	,	,	PUNCT
ap-9818	208	15	while	while	SCONJ
ap-9818	208	16	the	the	DET
ap-9818	208	17	potential	potential	NOUN
ap-9818	208	18	is	be	AUX
ap-9818	208	19	singular	singular	ADJ
ap-9818	208	20	at	at	ADP
ap-9818	208	21	the	the	DET
ap-9818	208	22	origin	origin	NOUN
ap-9818	208	23	.	.	PUNCT
ap-9818	209	1	the	the	DET
ap-9818	209	2	specific	specific	ADJ
ap-9818	209	3	combination	combination	NOUN
ap-9818	209	4	of	of	ADP
ap-9818	209	5	potential	potential	ADJ
ap-9818	209	6	and	and	CCONJ
ap-9818	209	7	mass	mass	NOUN
ap-9818	209	8	given	give	VERB
ap-9818	209	9	in	in	ADP
ap-9818	209	10	(	(	PUNCT
ap-9818	209	11	31	31	NUM
ap-9818	209	12	)	)	PUNCT
ap-9818	209	13	,	,	PUNCT
ap-9818	209	14	appears	appear	VERB
ap-9818	209	15	,	,	PUNCT
ap-9818	209	16	for	for	ADP
ap-9818	209	17	example	example	NOUN
ap-9818	209	18	,	,	PUNCT
ap-9818	209	19	in	in	ADP
ap-9818	209	20	isotonic	isotonic	ADJ
ap-9818	209	21	oscillator	oscillator	NOUN
ap-9818	209	22	models	model	NOUN
ap-9818	209	23	[	[	X
ap-9818	209	24	32	32	NUM
ap-9818	209	25	]	]	PUNCT
ap-9818	209	26	.	.	PUNCT
ap-9818	210	1	more	more	ADV
ap-9818	210	2	generally	generally	ADV
ap-9818	210	3	,	,	PUNCT
ap-9818	210	4	position	position	NOUN
ap-9818	210	5	-	-	PUNCT
ap-9818	210	6	dependent	dependent	ADJ
ap-9818	210	7	masses	masse	NOUN
ap-9818	210	8	,	,	PUNCT
ap-9818	210	9	as	as	ADP
ap-9818	210	10	in	in	ADP
ap-9818	210	11	(	(	PUNCT
ap-9818	210	12	31	31	NUM
ap-9818	210	13	)	)	PUNCT
ap-9818	210	14	,	,	PUNCT
ap-9818	210	15	have	have	VERB
ap-9818	210	16	applications	application	NOUN
ap-9818	210	17	in	in	ADP
ap-9818	210	18	quantum	quantum	ADJ
ap-9818	210	19	versions	version	NOUN
ap-9818	210	20	of	of	ADP
ap-9818	210	21	the	the	DET
ap-9818	210	22	mathews	mathews	NOUN
ap-9818	210	23	-	-	PUNCT
ap-9818	210	24	lakshmanan	lakshmanan	ADJ
ap-9818	210	25	oscillator	oscillator	NOUN
ap-9818	210	26	system	system	NOUN
ap-9818	210	27	[	[	X
ap-9818	210	28	33	33	NUM
ap-9818	210	29	,	,	PUNCT
ap-9818	210	30	34	34	NUM
ap-9818	210	31	]	]	PUNCT
ap-9818	210	32	,	,	PUNCT
ap-9818	210	33	see	see	VERB
ap-9818	210	34	also	also	ADV
ap-9818	210	35	[	[	X
ap-9818	210	36	35	35	NUM
ap-9818	210	37	]	]	PUNCT
ap-9818	210	38	.	.	PUNCT
ap-9818	211	1	solvability	solvability	NOUN
ap-9818	211	2	conditions	condition	NOUN
ap-9818	211	3	and	and	CCONJ
ap-9818	211	4	effective	effective	ADJ
ap-9818	211	5	potentials	potential	NOUN
ap-9818	211	6	.	.	PUNCT
ap-9818	212	1	in	in	ADP
ap-9818	212	2	order	order	NOUN
ap-9818	212	3	to	to	PART
ap-9818	212	4	determine	determine	VERB
ap-9818	212	5	if	if	SCONJ
ap-9818	212	6	solutions	solution	NOUN
ap-9818	212	7	of	of	ADP
ap-9818	212	8	the	the	DET
ap-9818	212	9	dunkl	dunkl	NOUN
ap-9818	212	10	-	-	PUNCT
ap-9818	212	11	schrödinger	schrödinger	ADJ
ap-9818	212	12	equation	equation	NOUN
ap-9818	212	13	for	for	ADP
ap-9818	212	14	the	the	DET
ap-9818	212	15	settings	setting	NOUN
ap-9818	212	16	(	(	PUNCT
ap-9818	212	17	31	31	NUM
ap-9818	212	18	)	)	PUNCT
ap-9818	212	19	can	can	AUX
ap-9818	212	20	be	be	AUX
ap-9818	212	21	found	find	VERB
ap-9818	212	22	from	from	ADP
ap-9818	212	23	the	the	DET
ap-9818	212	24	conventional	conventional	ADJ
ap-9818	212	25	system	system	NOUN
ap-9818	212	26	,	,	PUNCT
ap-9818	212	27	we	we	PRON
ap-9818	212	28	will	will	AUX
ap-9818	212	29	verify	verify	VERB
ap-9818	212	30	the	the	DET
ap-9818	212	31	solvability	solvability	NOUN
ap-9818	212	32	conditions	condition	NOUN
ap-9818	212	33	(	(	PUNCT
ap-9818	212	34	17	17	NUM
ap-9818	212	35	)	)	PUNCT
ap-9818	212	36	and	and	CCONJ
ap-9818	212	37	(	(	PUNCT
ap-9818	212	38	19	19	NUM
ap-9818	212	39	)	)	PUNCT
ap-9818	212	40	.	.	PUNCT
ap-9818	213	1	as	as	ADV
ap-9818	213	2	far	far	ADV
ap-9818	213	3	as	as	SCONJ
ap-9818	213	4	the	the	DET
ap-9818	213	5	first	first	ADJ
ap-9818	213	6	condition	condition	NOUN
ap-9818	213	7	is	be	AUX
ap-9818	213	8	concerned	concern	VERB
ap-9818	213	9	,	,	PUNCT
ap-9818	213	10	we	we	PRON
ap-9818	213	11	compare	compare	VERB
ap-9818	213	12	the	the	DET
ap-9818	213	13	position	position	NOUN
ap-9818	213	14	-	-	PUNCT
ap-9818	213	15	dependent	dependent	ADJ
ap-9818	213	16	mass	mass	NOUN
ap-9818	213	17	in	in	ADP
ap-9818	213	18	(	(	PUNCT
ap-9818	213	19	31	31	NUM
ap-9818	213	20	)	)	PUNCT
ap-9818	213	21	with	with	ADP
ap-9818	213	22	the	the	DET
ap-9818	213	23	general	general	ADJ
ap-9818	213	24	form	form	NOUN
ap-9818	213	25	(	(	PUNCT
ap-9818	213	26	17	17	NUM
ap-9818	213	27	)	)	PUNCT
ap-9818	213	28	.	.	PUNCT
ap-9818	214	1	both	both	PRON
ap-9818	214	2	of	of	ADP
ap-9818	214	3	these	these	DET
ap-9818	214	4	functions	function	NOUN
ap-9818	214	5	coincide	coincide	VERB
ap-9818	214	6	if	if	SCONJ
ap-9818	214	7	the	the	DET
ap-9818	214	8	following	follow	VERB
ap-9818	214	9	settings	setting	NOUN
ap-9818	214	10	are	be	AUX
ap-9818	214	11	in	in	ADP
ap-9818	214	12	effect	effect	NOUN
ap-9818	214	13	:	:	PUNCT
ap-9818	214	14	c1	c1	NOUN
ap-9818	214	15	=	=	NOUN
ap-9818	214	16	1	1	NUM
ap-9818	214	17	2	2	NUM
ap-9818	214	18	,	,	PUNCT
ap-9818	214	19	c2	c2	PROPN
ap-9818	214	20	=	=	SYM
ap-9818	214	21	−1	−1	PROPN
ap-9818	214	22	,	,	PUNCT
ap-9818	214	23	a	a	PRON
ap-9818	214	24	=	=	SYM
ap-9818	214	25	1	1	NUM
ap-9818	214	26	,	,	PUNCT
ap-9818	214	27	b	b	NOUN
ap-9818	214	28	=	=	SYM
ap-9818	214	29	−2	−2	PROPN
ap-9818	214	30	.	.	PUNCT
ap-9818	215	1	(	(	PUNCT
ap-9818	215	2	32	32	NUM
ap-9818	215	3	)	)	PUNCT
ap-9818	215	4	we	we	PRON
ap-9818	215	5	proceed	proceed	VERB
ap-9818	215	6	by	by	ADP
ap-9818	215	7	verifying	verify	VERB
ap-9818	215	8	our	our	PRON
ap-9818	215	9	second	second	ADJ
ap-9818	215	10	solvability	solvability	NOUN
ap-9818	215	11	condition	condition	NOUN
ap-9818	215	12	(	(	PUNCT
ap-9818	215	13	19	19	NUM
ap-9818	215	14	)	)	PUNCT
ap-9818	215	15	.	.	PUNCT
ap-9818	216	1	substituting	substitute	VERB
ap-9818	216	2	(	(	PUNCT
ap-9818	216	3	31	31	NUM
ap-9818	216	4	)	)	PUNCT
ap-9818	216	5	leads	lead	VERB
ap-9818	216	6	to	to	ADP
ap-9818	216	7	:	:	PUNCT
ap-9818	216	8	v1	v1	VERB
ap-9818	216	9	x2	x2	NOUN
ap-9818	217	1	=	=	PUNCT
ap-9818	217	2	c	c	X
ap-9818	217	3	(	(	PUNCT
ap-9818	217	4	1	1	NUM
ap-9818	217	5	−	−	PROPN
ap-9818	217	6	x2	x2	PROPN
ap-9818	217	7	)	)	PUNCT
ap-9818	217	8	x2	x2	PROPN
ap-9818	218	1	+	+	CCONJ
ap-9818	218	2	w	w	PROPN
ap-9818	218	3	(	(	PUNCT
ap-9818	218	4	x	x	NOUN
ap-9818	218	5	)	)	PUNCT
ap-9818	218	6	=	=	PUNCT
ap-9818	219	1	c	c	NOUN
ap-9818	219	2	x2	x2	INTJ
ap-9818	220	1	−	−	PROPN
ap-9818	220	2	c	c	X
ap-9818	221	1	+	+	CCONJ
ap-9818	221	2	w	w	PROPN
ap-9818	221	3	(	(	PUNCT
ap-9818	221	4	x	x	NOUN
ap-9818	221	5	)	)	PUNCT
ap-9818	221	6	.	.	PUNCT
ap-9818	222	1	(	(	PUNCT
ap-9818	222	2	33	33	NUM
ap-9818	222	3	)	)	PUNCT
ap-9818	222	4	it	it	PRON
ap-9818	222	5	is	be	AUX
ap-9818	222	6	straightforward	straightforward	ADJ
ap-9818	222	7	to	to	PART
ap-9818	222	8	see	see	VERB
ap-9818	222	9	that	that	SCONJ
ap-9818	222	10	the	the	DET
ap-9818	222	11	left	left	NOUN
ap-9818	222	12	and	and	CCONJ
ap-9818	222	13	the	the	DET
ap-9818	222	14	right	right	ADJ
ap-9818	222	15	side	side	NOUN
ap-9818	222	16	become	become	VERB
ap-9818	222	17	equal	equal	ADJ
ap-9818	222	18	,	,	PUNCT
ap-9818	222	19	provided	provide	VERB
ap-9818	222	20	we	we	PRON
ap-9818	222	21	set	set	VERB
ap-9818	222	22	w	w	NOUN
ap-9818	222	23	=	=	PUNCT
ap-9818	222	24	c	c	NOUN
ap-9818	222	25	=	=	SYM
ap-9818	222	26	v1	v1	PROPN
ap-9818	222	27	.	.	PUNCT
ap-9818	223	1	since	since	SCONJ
ap-9818	223	2	our	our	PRON
ap-9818	223	3	two	two	NUM
ap-9818	223	4	conditions	condition	NOUN
ap-9818	223	5	(	(	PUNCT
ap-9818	223	6	17	17	NUM
ap-9818	223	7	)	)	PUNCT
ap-9818	223	8	and	and	CCONJ
ap-9818	223	9	(	(	PUNCT
ap-9818	223	10	19	19	NUM
ap-9818	223	11	)	)	PUNCT
ap-9818	223	12	are	be	AUX
ap-9818	223	13	satisfied	satisfied	ADJ
ap-9818	223	14	,	,	PUNCT
ap-9818	223	15	the	the	DET
ap-9818	223	16	potentials	potential	NOUN
ap-9818	223	17	uν	uν	INTJ
ap-9818	223	18	in	in	ADP
ap-9818	223	19	(	(	PUNCT
ap-9818	223	20	20	20	NUM
ap-9818	223	21	)	)	PUNCT
ap-9818	223	22	and	and	CCONJ
ap-9818	223	23	u0	u0	ADJ
ap-9818	223	24	in	in	ADP
ap-9818	223	25	(	(	PUNCT
ap-9818	223	26	15	15	NUM
ap-9818	223	27	)	)	PUNCT
ap-9818	223	28	with	with	ADP
ap-9818	223	29	our	our	PRON
ap-9818	223	30	settings	setting	NOUN
ap-9818	223	31	(	(	PUNCT
ap-9818	223	32	31	31	NUM
ap-9818	223	33	)	)	PUNCT
ap-9818	223	34	must	must	AUX
ap-9818	223	35	have	have	VERB
ap-9818	223	36	the	the	DET
ap-9818	223	37	same	same	ADJ
ap-9818	223	38	functional	functional	ADJ
ap-9818	223	39	form	form	NOUN
ap-9818	223	40	except	except	SCONJ
ap-9818	223	41	for	for	ADP
ap-9818	223	42	constant	constant	ADJ
ap-9818	223	43	parameters	parameter	NOUN
ap-9818	223	44	.	.	PUNCT
ap-9818	224	1	we	we	PRON
ap-9818	224	2	verify	verify	VERB
ap-9818	224	3	this	this	PRON
ap-9818	224	4	by	by	ADP
ap-9818	224	5	substituting	substitute	VERB
ap-9818	224	6	the	the	DET
ap-9818	224	7	latter	latter	ADJ
ap-9818	224	8	settings	setting	NOUN
ap-9818	224	9	into	into	ADP
ap-9818	224	10	(	(	PUNCT
ap-9818	224	11	20	20	NUM
ap-9818	224	12	)	)	PUNCT
ap-9818	224	13	,	,	PUNCT
ap-9818	224	14	which	which	PRON
ap-9818	224	15	gives	give	VERB
ap-9818	224	16	the	the	DET
ap-9818	224	17	result	result	NOUN
ap-9818	224	18	:	:	PUNCT
ap-9818	224	19	uν(x	uν(x	X
ap-9818	224	20	)	)	PUNCT
ap-9818	224	21	=	=	SYM
ap-9818	225	1	1	1	NUM
ap-9818	225	2	x2	x2	NOUN
ap-9818	225	3	(	(	PUNCT
ap-9818	225	4	x2	x2	INTJ
ap-9818	225	5	−	−	PROPN
ap-9818	225	6	1)2	1)2	NUM
ap-9818	225	7	{	{	PUNCT
ap-9818	225	8	v1	v1	PROPN
ap-9818	225	9	+	+	CCONJ
ap-9818	225	10	δ	δ	PROPN
ap-9818	225	11	ν	ν	NOUN
ap-9818	225	12	−	−	NOUN
ap-9818	225	13	ν2	ν2	NOUN
ap-9818	225	14	+	+	CCONJ
ap-9818	225	15	x2	x2	X
ap-9818	226	1	[	[	X
ap-9818	226	2	1	1	NUM
ap-9818	226	3	−	−	NOUN
ap-9818	226	4	e	e	NOUN
ap-9818	226	5	−	−	PROPN
ap-9818	226	6	v1	v1	NOUN
ap-9818	226	7	+	+	CCONJ
ap-9818	226	8	α	α	NOUN
ap-9818	226	9	+	+	X
ap-9818	226	10	γ	γ	PROPN
ap-9818	226	11	−	−	PROPN
ap-9818	226	12	δ	δ	PROPN
ap-9818	226	13	ν	ν	X
ap-9818	226	14	+	+	CCONJ
ap-9818	226	15	δ	δ	PROPN
ap-9818	226	16	ν	ν	NOUN
ap-9818	226	17	(	(	PUNCT
ap-9818	226	18	1	1	NUM
ap-9818	226	19	+	+	SYM
ap-9818	226	20	2	2	NUM
ap-9818	226	21	α	α	NOUN
ap-9818	226	22	+	+	NOUN
ap-9818	226	23	2	2	NUM
ap-9818	226	24	γ	γ	NOUN
ap-9818	226	25	)	)	PUNCT
ap-9818	226	26	+	+	CCONJ
ap-9818	226	27	2	2	NUM
ap-9818	226	28	ν2	ν2	NOUN
ap-9818	226	29	]	]	PUNCT
ap-9818	226	30	+	+	CCONJ
ap-9818	226	31	x4	x4	PROPN
ap-9818	227	1	[	[	X
ap-9818	227	2	e	e	X
ap-9818	227	3	−	−	PROPN
ap-9818	227	4	α	α	NOUN
ap-9818	227	5	−	−	NOUN
ap-9818	227	6	γ	γ	NOUN
ap-9818	227	7	−	−	PROPN
ap-9818	227	8	4	4	NUM
ap-9818	227	9	α	α	PROPN
ap-9818	227	10	γ	γ	X
ap-9818	227	11	−	−	PROPN
ap-9818	227	12	δ	δ	PROPN
ap-9818	227	13	ν	ν	X
ap-9818	227	14	(	(	PUNCT
ap-9818	227	15	1	1	NUM
ap-9818	227	16	+	+	SYM
ap-9818	227	17	2	2	NUM
ap-9818	227	18	α	α	NOUN
ap-9818	227	19	+	+	NOUN
ap-9818	227	20	2	2	NUM
ap-9818	227	21	γ	γ	NOUN
ap-9818	227	22	)	)	PUNCT
ap-9818	227	23	−	−	NOUN
ap-9818	227	24	ν2	ν2	NOUN
ap-9818	227	25	]	]	PUNCT
ap-9818	227	26	}	}	PUNCT
ap-9818	227	27	.	.	PUNCT
ap-9818	228	1	(	(	PUNCT
ap-9818	228	2	34	34	NUM
ap-9818	228	3	)	)	SYM
ap-9818	228	4	227	227	NUM
ap-9818	228	5	axel	axel	PROPN
ap-9818	228	6	schulze	schulze	NOUN
ap-9818	228	7	-	-	PUNCT
ap-9818	228	8	halberg	halberg	PROPN
ap-9818	228	9	acta	acta	PROPN
ap-9818	228	10	polytechnica	polytechnica	PROPN
ap-9818	228	11	in	in	ADP
ap-9818	228	12	the	the	DET
ap-9818	228	13	next	next	ADJ
ap-9818	228	14	step	step	NOUN
ap-9818	228	15	,	,	PUNCT
ap-9818	228	16	we	we	PRON
ap-9818	228	17	obtain	obtain	VERB
ap-9818	228	18	the	the	DET
ap-9818	228	19	counterpart	counterpart	NOUN
ap-9818	228	20	u0	u0	NOUN
ap-9818	228	21	either	either	CCONJ
ap-9818	228	22	by	by	ADP
ap-9818	228	23	inserting	insert	VERB
ap-9818	228	24	the	the	DET
ap-9818	228	25	settings	setting	NOUN
ap-9818	228	26	(	(	PUNCT
ap-9818	228	27	31	31	NUM
ap-9818	228	28	)	)	PUNCT
ap-9818	228	29	into	into	ADP
ap-9818	228	30	(	(	PUNCT
ap-9818	228	31	15	15	NUM
ap-9818	228	32	)	)	PUNCT
ap-9818	228	33	,	,	PUNCT
ap-9818	228	34	or	or	CCONJ
ap-9818	228	35	by	by	ADP
ap-9818	228	36	setting	set	VERB
ap-9818	228	37	ν	ν	NOUN
ap-9818	228	38	=	=	SYM
ap-9818	228	39	0	0	NUM
ap-9818	228	40	in	in	ADP
ap-9818	228	41	(	(	PUNCT
ap-9818	228	42	34	34	NUM
ap-9818	228	43	)	)	PUNCT
ap-9818	228	44	.	.	PUNCT
ap-9818	229	1	we	we	PRON
ap-9818	229	2	obtain	obtain	VERB
ap-9818	229	3	:	:	PUNCT
ap-9818	229	4	u0(x	u0(x	NUM
ap-9818	229	5	)	)	PUNCT
ap-9818	229	6	=	=	SYM
ap-9818	230	1	1	1	NUM
ap-9818	230	2	x2	x2	NOUN
ap-9818	230	3	(	(	PUNCT
ap-9818	230	4	x2	x2	INTJ
ap-9818	230	5	−	−	PROPN
ap-9818	230	6	1)2	1)2	NUM
ap-9818	230	7	{	{	PUNCT
ap-9818	230	8	v1	v1	PROPN
ap-9818	230	9	+	+	CCONJ
ap-9818	230	10	x2	x2	PROPN
ap-9818	231	1	[	[	X
ap-9818	231	2	1	1	NUM
ap-9818	231	3	−	−	NOUN
ap-9818	231	4	e	e	NOUN
ap-9818	231	5	−	−	PROPN
ap-9818	231	6	v1	v1	NOUN
ap-9818	231	7	+	+	CCONJ
ap-9818	231	8	α	α	NOUN
ap-9818	231	9	+	+	X
ap-9818	231	10	γ	γ	X
ap-9818	231	11	]	]	X
ap-9818	231	12	+	+	CCONJ
ap-9818	231	13	x4	x4	PROPN
ap-9818	232	1	[	[	X
ap-9818	232	2	e	e	X
ap-9818	232	3	−	−	PROPN
ap-9818	232	4	α	α	NOUN
ap-9818	232	5	−	−	NOUN
ap-9818	232	6	γ	γ	NOUN
ap-9818	232	7	−	−	PROPN
ap-9818	232	8	4	4	NUM
ap-9818	232	9	α	α	PROPN
ap-9818	232	10	γ	γ	X
ap-9818	232	11	]	]	X
ap-9818	232	12	}	}	PUNCT
ap-9818	232	13	.	.	PUNCT
ap-9818	233	1	(	(	PUNCT
ap-9818	233	2	35	35	NUM
ap-9818	233	3	)	)	PUNCT
ap-9818	233	4	comparison	comparison	NOUN
ap-9818	233	5	with	with	ADP
ap-9818	233	6	(	(	PUNCT
ap-9818	233	7	34	34	NUM
ap-9818	233	8	)	)	PUNCT
ap-9818	233	9	shows	show	VERB
ap-9818	233	10	that	that	SCONJ
ap-9818	233	11	the	the	DET
ap-9818	233	12	functions	function	NOUN
ap-9818	233	13	have	have	VERB
ap-9818	233	14	the	the	DET
ap-9818	233	15	same	same	ADJ
ap-9818	233	16	functional	functional	ADJ
ap-9818	233	17	form	form	NOUN
ap-9818	233	18	,	,	PUNCT
ap-9818	233	19	such	such	ADJ
ap-9818	233	20	that	that	SCONJ
ap-9818	233	21	the	the	DET
ap-9818	233	22	reduced	reduced	ADJ
ap-9818	233	23	schrödinger	schrödinger	ADJ
ap-9818	233	24	equations	equation	NOUN
ap-9818	233	25	(	(	PUNCT
ap-9818	233	26	11	11	NUM
ap-9818	233	27	)	)	PUNCT
ap-9818	233	28	and	and	CCONJ
ap-9818	233	29	(	(	PUNCT
ap-9818	233	30	14	14	NUM
ap-9818	233	31	)	)	PUNCT
ap-9818	233	32	have	have	VERB
ap-9818	233	33	the	the	DET
ap-9818	233	34	same	same	ADJ
ap-9818	233	35	solutions	solution	NOUN
ap-9818	233	36	,	,	PUNCT
ap-9818	233	37	up	up	ADP
ap-9818	233	38	to	to	ADP
ap-9818	233	39	a	a	DET
ap-9818	233	40	redefinition	redefinition	NOUN
ap-9818	233	41	of	of	ADP
ap-9818	233	42	numerical	numerical	ADJ
ap-9818	233	43	parameters	parameter	NOUN
ap-9818	233	44	.	.	PUNCT
ap-9818	234	1	reduced	reduce	VERB
ap-9818	234	2	equations	equation	NOUN
ap-9818	234	3	and	and	CCONJ
ap-9818	234	4	general	general	ADJ
ap-9818	234	5	solutions	solution	NOUN
ap-9818	234	6	.	.	PUNCT
ap-9818	235	1	before	before	SCONJ
ap-9818	235	2	we	we	PRON
ap-9818	235	3	state	state	VERB
ap-9818	235	4	these	these	DET
ap-9818	235	5	solutions	solution	NOUN
ap-9818	235	6	,	,	PUNCT
ap-9818	235	7	let	let	VERB
ap-9818	235	8	us	we	PRON
ap-9818	235	9	simplify	simplify	VERB
ap-9818	235	10	subsequent	subsequent	ADJ
ap-9818	235	11	calculations	calculation	NOUN
ap-9818	235	12	by	by	ADP
ap-9818	235	13	setting	set	VERB
ap-9818	235	14	α	α	NOUN
ap-9818	235	15	=	=	SYM
ap-9818	235	16	γ	γ	X
ap-9818	235	17	=	=	SYM
ap-9818	235	18	−	−	PROPN
ap-9818	235	19	1	1	NUM
ap-9818	235	20	2	2	NUM
ap-9818	235	21	.	.	PUNCT
ap-9818	236	1	upon	upon	SCONJ
ap-9818	236	2	substituting	substitute	VERB
ap-9818	236	3	these	these	DET
ap-9818	236	4	values	value	NOUN
ap-9818	236	5	into	into	ADP
ap-9818	236	6	(	(	PUNCT
ap-9818	236	7	34	34	NUM
ap-9818	236	8	)	)	PUNCT
ap-9818	236	9	and	and	CCONJ
ap-9818	236	10	(	(	PUNCT
ap-9818	236	11	35	35	NUM
ap-9818	236	12	)	)	PUNCT
ap-9818	236	13	,	,	PUNCT
ap-9818	236	14	the	the	DET
ap-9818	236	15	associated	associate	VERB
ap-9818	236	16	reduced	reduce	VERB
ap-9818	236	17	schrödinger	schrödinger	ADJ
ap-9818	236	18	equations	equation	NOUN
ap-9818	236	19	take	take	VERB
ap-9818	236	20	the	the	DET
ap-9818	236	21	form	form	NOUN
ap-9818	236	22	:	:	PUNCT
ap-9818	236	23	ξ′′	ξ′′	PROPN
ap-9818	236	24	ν	ν	X
ap-9818	236	25	(	(	PUNCT
ap-9818	236	26	x	x	X
ap-9818	236	27	)	)	PUNCT
ap-9818	237	1	+	+	CCONJ
ap-9818	237	2	(	(	PUNCT
ap-9818	237	3	e	e	X
ap-9818	237	4	−	−	PROPN
ap-9818	237	5	v1	v1	PROPN
ap-9818	237	6	x2	x2	NOUN
ap-9818	237	7	−	−	NOUN
ap-9818	237	8	1	1	NUM
ap-9818	237	9	+	+	NUM
ap-9818	237	10	δ	δ	PROPN
ap-9818	237	11	ν	ν	NOUN
ap-9818	237	12	−	−	PROPN
ap-9818	237	13	ν2	ν2	NOUN
ap-9818	237	14	+	+	CCONJ
ap-9818	237	15	v1	v1	PROPN
ap-9818	237	16	x2	x2	PROPN
ap-9818	237	17	)	)	PUNCT
ap-9818	237	18	ξν(x	ξν(x	NUM
ap-9818	237	19	)	)	PUNCT
ap-9818	238	1	=	=	SYM
ap-9818	238	2	0	0	NUM
ap-9818	238	3	,	,	PUNCT
ap-9818	238	4	(	(	PUNCT
ap-9818	238	5	36	36	NUM
ap-9818	238	6	)	)	PUNCT
ap-9818	238	7	ξ′′	ξ′′	NOUN
ap-9818	238	8	0	0	PUNCT
ap-9818	238	9	(	(	PUNCT
ap-9818	238	10	x	x	X
ap-9818	238	11	)	)	PUNCT
ap-9818	238	12	+	+	CCONJ
ap-9818	238	13	(	(	PUNCT
ap-9818	238	14	e	e	X
ap-9818	238	15	−	−	PROPN
ap-9818	238	16	v1	v1	PROPN
ap-9818	238	17	x2	x2	NOUN
ap-9818	238	18	−	−	PROPN
ap-9818	238	19	1	1	NUM
ap-9818	238	20	+	+	NUM
ap-9818	238	21	v1	v1	PROPN
ap-9818	238	22	x2	x2	PROPN
ap-9818	238	23	)	)	PUNCT
ap-9818	238	24	ξ0(x	ξ0(x	PROPN
ap-9818	238	25	)	)	PUNCT
ap-9818	238	26	=	=	NOUN
ap-9818	238	27	0	0	X
ap-9818	238	28	.	.	PUNCT
ap-9818	239	1	(	(	PUNCT
ap-9818	239	2	37	37	NUM
ap-9818	239	3	)	)	PUNCT
ap-9818	239	4	we	we	PRON
ap-9818	239	5	observe	observe	VERB
ap-9818	239	6	that	that	SCONJ
ap-9818	239	7	in	in	ADP
ap-9818	239	8	(	(	PUNCT
ap-9818	239	9	36	36	NUM
ap-9818	239	10	)	)	PUNCT
ap-9818	239	11	the	the	DET
ap-9818	239	12	parameters	parameter	NOUN
ap-9818	239	13	ν	ν	PROPN
ap-9818	239	14	and	and	CCONJ
ap-9818	239	15	δ	δ	PROPN
ap-9818	239	16	from	from	ADP
ap-9818	239	17	the	the	DET
ap-9818	239	18	dunkl	dunkl	NOUN
ap-9818	239	19	operator	operator	NOUN
ap-9818	239	20	affect	affect	VERB
ap-9818	239	21	the	the	DET
ap-9818	239	22	singularity	singularity	NOUN
ap-9818	239	23	at	at	ADP
ap-9818	239	24	the	the	DET
ap-9818	239	25	origin	origin	NOUN
ap-9818	239	26	that	that	PRON
ap-9818	239	27	is	be	AUX
ap-9818	239	28	contributed	contribute	VERB
ap-9818	239	29	by	by	ADP
ap-9818	239	30	the	the	DET
ap-9818	239	31	potential	potential	NOUN
ap-9818	239	32	.	.	PUNCT
ap-9818	240	1	in	in	ADP
ap-9818	240	2	particular	particular	ADJ
ap-9818	240	3	,	,	PUNCT
ap-9818	240	4	the	the	DET
ap-9818	240	5	latter	latter	ADJ
ap-9818	240	6	parameters	parameter	NOUN
ap-9818	240	7	can	can	AUX
ap-9818	240	8	be	be	AUX
ap-9818	240	9	chosen	choose	VERB
ap-9818	240	10	such	such	ADJ
ap-9818	240	11	that	that	SCONJ
ap-9818	240	12	the	the	DET
ap-9818	240	13	singularity	singularity	NOUN
ap-9818	240	14	is	be	AUX
ap-9818	240	15	removed	remove	VERB
ap-9818	240	16	.	.	PUNCT
ap-9818	241	1	now	now	ADV
ap-9818	241	2	,	,	PUNCT
ap-9818	241	3	once	once	SCONJ
ap-9818	241	4	we	we	PRON
ap-9818	241	5	know	know	VERB
ap-9818	241	6	a	a	DET
ap-9818	241	7	solution	solution	NOUN
ap-9818	241	8	of	of	ADP
ap-9818	241	9	the	the	DET
ap-9818	241	10	conventional	conventional	ADJ
ap-9818	241	11	equation	equation	NOUN
ap-9818	241	12	(	(	PUNCT
ap-9818	241	13	37	37	NUM
ap-9818	241	14	)	)	PUNCT
ap-9818	241	15	,	,	PUNCT
ap-9818	241	16	we	we	PRON
ap-9818	241	17	can	can	AUX
ap-9818	241	18	generate	generate	VERB
ap-9818	241	19	a	a	DET
ap-9818	241	20	solution	solution	NOUN
ap-9818	241	21	to	to	ADP
ap-9818	241	22	the	the	DET
ap-9818	241	23	reduced	reduce	VERB
ap-9818	241	24	dunkl	dunkl	NOUN
ap-9818	241	25	-	-	PUNCT
ap-9818	241	26	schrödinger	schrödinger	NOUN
ap-9818	241	27	equation	equation	NOUN
ap-9818	241	28	(	(	PUNCT
ap-9818	241	29	36	36	NUM
ap-9818	241	30	)	)	PUNCT
ap-9818	241	31	by	by	ADP
ap-9818	241	32	a	a	DET
ap-9818	241	33	reparametrisation	reparametrisation	NOUN
ap-9818	241	34	of	of	ADP
ap-9818	241	35	the	the	DET
ap-9818	241	36	coefficients	coefficient	NOUN
ap-9818	241	37	to	to	ADP
ap-9818	241	38	the	the	DET
ap-9818	241	39	terms	term	NOUN
ap-9818	241	40	∼	∼	NOUN
ap-9818	241	41	(	(	PUNCT
ap-9818	241	42	x2	x2	NOUN
ap-9818	241	43	−	−	PROPN
ap-9818	241	44	1)−1	1)−1	NUM
ap-9818	241	45	and	and	CCONJ
ap-9818	241	46	∼	∼	NOUN
ap-9818	241	47	x−2	x−2	PROPN
ap-9818	241	48	.	.	PUNCT
ap-9818	242	1	we	we	PRON
ap-9818	242	2	observe	observe	VERB
ap-9818	242	3	that	that	SCONJ
ap-9818	242	4	the	the	DET
ap-9818	242	5	parameters	parameter	NOUN
ap-9818	242	6	ν	ν	NOUN
ap-9818	242	7	and	and	CCONJ
ap-9818	242	8	δ	δ	PROPN
ap-9818	242	9	from	from	ADP
ap-9818	242	10	the	the	DET
ap-9818	242	11	dunkl	dunkl	NOUN
ap-9818	242	12	operator	operator	NOUN
ap-9818	242	13	(	(	PUNCT
ap-9818	242	14	3	3	X
ap-9818	242	15	)	)	PUNCT
ap-9818	242	16	affect	affect	VERB
ap-9818	242	17	the	the	DET
ap-9818	242	18	behaviour	behaviour	NOUN
ap-9818	242	19	of	of	ADP
ap-9818	242	20	the	the	DET
ap-9818	242	21	effective	effective	ADJ
ap-9818	242	22	potential	potential	NOUN
ap-9818	242	23	in	in	ADP
ap-9818	242	24	equation	equation	NOUN
ap-9818	242	25	(	(	PUNCT
ap-9818	242	26	36	36	NUM
ap-9818	242	27	)	)	PUNCT
ap-9818	242	28	.	.	PUNCT
ap-9818	243	1	in	in	ADP
ap-9818	243	2	particular	particular	ADJ
ap-9818	243	3	,	,	PUNCT
ap-9818	243	4	for	for	ADP
ap-9818	243	5	obtaining	obtain	VERB
ap-9818	243	6	bound	bind	VERB
ap-9818	243	7	states	state	NOUN
ap-9818	243	8	of	of	ADP
ap-9818	243	9	our	our	PRON
ap-9818	243	10	system	system	NOUN
ap-9818	243	11	,	,	PUNCT
ap-9818	243	12	the	the	DET
ap-9818	243	13	singularity	singularity	NOUN
ap-9818	243	14	at	at	ADP
ap-9818	243	15	the	the	DET
ap-9818	243	16	origin	origin	NOUN
ap-9818	243	17	should	should	AUX
ap-9818	243	18	be	be	AUX
ap-9818	243	19	attractive	attractive	ADJ
ap-9818	243	20	,	,	PUNCT
ap-9818	243	21	meaning	mean	VERB
ap-9818	243	22	that	that	SCONJ
ap-9818	243	23	:	:	PUNCT
ap-9818	243	24	δ	δ	X
ap-9818	243	25	ν	ν	ADP
ap-9818	243	26	−	−	PROPN
ap-9818	243	27	ν2	ν2	NOUN
ap-9818	243	28	+	+	CCONJ
ap-9818	243	29	v1	v1	VERB
ap-9818	243	30	<	<	X
ap-9818	243	31	0	0	NUM
ap-9818	243	32	.	.	PUNCT
ap-9818	244	1	(	(	PUNCT
ap-9818	244	2	38	38	NUM
ap-9818	244	3	)	)	PUNCT
ap-9818	244	4	this	this	DET
ap-9818	244	5	condition	condition	NOUN
ap-9818	244	6	can	can	AUX
ap-9818	244	7	be	be	AUX
ap-9818	244	8	satisfied	satisfied	ADJ
ap-9818	244	9	by	by	ADP
ap-9818	244	10	making	make	VERB
ap-9818	244	11	v1	v1	NOUN
ap-9818	244	12	negative	negative	ADJ
ap-9818	244	13	with	with	ADP
ap-9818	244	14	sufficiently	sufficiently	ADV
ap-9818	244	15	large	large	ADJ
ap-9818	244	16	value	value	NOUN
ap-9818	244	17	in	in	ADP
ap-9818	244	18	modulus	modulus	NOUN
ap-9818	244	19	.	.	PUNCT
ap-9818	245	1	we	we	PRON
ap-9818	245	2	will	will	AUX
ap-9818	245	3	comment	comment	VERB
ap-9818	245	4	on	on	ADP
ap-9818	245	5	this	this	DET
ap-9818	245	6	further	far	ADV
ap-9818	245	7	below	below	ADV
ap-9818	245	8	when	when	SCONJ
ap-9818	245	9	determining	determine	VERB
ap-9818	245	10	the	the	DET
ap-9818	245	11	stationary	stationary	ADJ
ap-9818	245	12	energies	energy	NOUN
ap-9818	245	13	.	.	PUNCT
ap-9818	246	1	now	now	ADV
ap-9818	246	2	,	,	PUNCT
ap-9818	246	3	the	the	DET
ap-9818	246	4	general	general	ADJ
ap-9818	246	5	solution	solution	NOUN
ap-9818	246	6	of	of	ADP
ap-9818	246	7	(	(	PUNCT
ap-9818	246	8	37	37	NUM
ap-9818	246	9	)	)	PUNCT
ap-9818	246	10	is	be	AUX
ap-9818	246	11	known	know	VERB
ap-9818	246	12	and	and	CCONJ
ap-9818	246	13	can	can	AUX
ap-9818	246	14	be	be	AUX
ap-9818	246	15	written	write	VERB
ap-9818	246	16	in	in	ADP
ap-9818	246	17	the	the	DET
ap-9818	246	18	form	form	NOUN
ap-9818	246	19	:	:	PUNCT
ap-9818	246	20	ξ0,gen(x	ξ0,gen(x	NUM
ap-9818	246	21	)	)	PUNCT
ap-9818	247	1	=	=	SYM
ap-9818	247	2	c1	c1	NOUN
ap-9818	247	3	x	x	NOUN
ap-9818	247	4	1	1	NUM
ap-9818	247	5	2	2	NUM
ap-9818	247	6	−	−	PROPN
ap-9818	247	7	g2	g2	PROPN
ap-9818	247	8	2	2	NUM
ap-9818	247	9	2f1	2f1	NUM
ap-9818	247	10	(	(	PUNCT
ap-9818	247	11	−g1	−g1	VERB
ap-9818	247	12	4	4	NUM
ap-9818	247	13	−	−	PROPN
ap-9818	247	14	g2	g2	PROPN
ap-9818	247	15	4	4	NUM
ap-9818	247	16	,	,	PUNCT
ap-9818	247	17	g1	g1	VERB
ap-9818	247	18	4	4	NUM
ap-9818	247	19	−	−	NOUN
ap-9818	247	20	g2	g2	PROPN
ap-9818	247	21	4	4	NUM
ap-9818	247	22	,	,	PUNCT
ap-9818	247	23	1	1	NUM
ap-9818	247	24	−	−	PROPN
ap-9818	247	25	g2	g2	PROPN
ap-9818	247	26	2	2	NUM
ap-9818	247	27	,	,	PUNCT
ap-9818	247	28	x2	x2	PROPN
ap-9818	247	29	)	)	PUNCT
ap-9818	248	1	+	+	CCONJ
ap-9818	248	2	c2	c2	PROPN
ap-9818	248	3	x	x	SYM
ap-9818	248	4	1	1	NUM
ap-9818	248	5	2	2	NUM
ap-9818	248	6	+	+	CCONJ
ap-9818	248	7	g2	g2	PROPN
ap-9818	248	8	2	2	NUM
ap-9818	248	9	2f1	2f1	NUM
ap-9818	248	10	(	(	PUNCT
ap-9818	248	11	−g1	−g1	VERB
ap-9818	248	12	4	4	NUM
ap-9818	248	13	+	+	CCONJ
ap-9818	248	14	g2	g2	PROPN
ap-9818	248	15	4	4	NUM
ap-9818	248	16	,	,	PUNCT
ap-9818	248	17	g1	g1	VERB
ap-9818	248	18	4	4	NUM
ap-9818	249	1	+	+	NUM
ap-9818	249	2	g2	g2	PROPN
ap-9818	249	3	4	4	NUM
ap-9818	249	4	,	,	PUNCT
ap-9818	249	5	1	1	NUM
ap-9818	249	6	+	+	CCONJ
ap-9818	249	7	g2	g2	PROPN
ap-9818	249	8	2	2	NUM
ap-9818	249	9	,	,	PUNCT
ap-9818	249	10	x2	x2	PROPN
ap-9818	249	11	)	)	PUNCT
ap-9818	249	12	,	,	PUNCT
ap-9818	249	13	(	(	PUNCT
ap-9818	249	14	39	39	NUM
ap-9818	249	15	)	)	PUNCT
ap-9818	249	16	where	where	SCONJ
ap-9818	249	17	the	the	DET
ap-9818	249	18	following	follow	VERB
ap-9818	249	19	abbreviations	abbreviation	NOUN
ap-9818	249	20	are	be	AUX
ap-9818	249	21	in	in	ADP
ap-9818	249	22	use	use	NOUN
ap-9818	249	23	:	:	PUNCT
ap-9818	249	24	g1	g1	PROPN
ap-9818	249	25	=	=	SYM
ap-9818	249	26	√	√	ADV
ap-9818	249	27	1	1	NUM
ap-9818	249	28	−	−	PROPN
ap-9818	249	29	4	4	NUM
ap-9818	249	30	e	e	NOUN
ap-9818	249	31	,	,	PUNCT
ap-9818	249	32	g2	g2	PROPN
ap-9818	249	33	=	=	PUNCT
ap-9818	250	1	√	√	ADV
ap-9818	250	2	1	1	NUM
ap-9818	250	3	−	−	PROPN
ap-9818	250	4	4	4	NUM
ap-9818	250	5	v1	v1	NOUN
ap-9818	250	6	.	.	PUNCT
ap-9818	251	1	(	(	PUNCT
ap-9818	251	2	40	40	NUM
ap-9818	251	3	)	)	PUNCT
ap-9818	251	4	since	since	SCONJ
ap-9818	251	5	the	the	DET
ap-9818	251	6	effective	effective	ADJ
ap-9818	251	7	potentials	potential	NOUN
ap-9818	251	8	(	(	PUNCT
ap-9818	251	9	34	34	NUM
ap-9818	251	10	)	)	PUNCT
ap-9818	251	11	and	and	CCONJ
ap-9818	251	12	(	(	PUNCT
ap-9818	251	13	35	35	NUM
ap-9818	251	14	)	)	PUNCT
ap-9818	251	15	have	have	VERB
ap-9818	251	16	the	the	DET
ap-9818	251	17	same	same	ADJ
ap-9818	251	18	functional	functional	ADJ
ap-9818	251	19	form	form	NOUN
ap-9818	251	20	,	,	PUNCT
ap-9818	251	21	we	we	PRON
ap-9818	251	22	can	can	AUX
ap-9818	251	23	now	now	ADV
ap-9818	251	24	construct	construct	VERB
ap-9818	251	25	the	the	DET
ap-9818	251	26	general	general	ADJ
ap-9818	251	27	solution	solution	NOUN
ap-9818	251	28	of	of	ADP
ap-9818	251	29	the	the	DET
ap-9818	251	30	reduced	reduce	VERB
ap-9818	251	31	dunkl	dunkl	NOUN
ap-9818	251	32	-	-	PUNCT
ap-9818	251	33	schrödinger	schrödinger	NOUN
ap-9818	251	34	equation	equation	NOUN
ap-9818	251	35	(	(	PUNCT
ap-9818	251	36	36	36	NUM
ap-9818	251	37	)	)	PUNCT
ap-9818	251	38	.	.	PUNCT
ap-9818	252	1	after	after	ADP
ap-9818	252	2	a	a	DET
ap-9818	252	3	reparametrisation	reparametrisation	NOUN
ap-9818	252	4	,	,	PUNCT
ap-9818	252	5	we	we	PRON
ap-9818	252	6	find	find	VERB
ap-9818	252	7	:	:	PUNCT
ap-9818	252	8	ξν	ξν	ADV
ap-9818	252	9	,	,	PUNCT
ap-9818	252	10	gen(x	gen(x	NOUN
ap-9818	252	11	)	)	PUNCT
ap-9818	252	12	=	=	SYM
ap-9818	252	13	c1	c1	NOUN
ap-9818	252	14	x	x	NOUN
ap-9818	252	15	1	1	NUM
ap-9818	252	16	2	2	NUM
ap-9818	252	17	−	−	NOUN
ap-9818	252	18	f2	f2	PROPN
ap-9818	252	19	2	2	NUM
ap-9818	252	20	2f1	2f1	NUM
ap-9818	252	21	(	(	PUNCT
ap-9818	252	22	−f1	−f1	PROPN
ap-9818	252	23	4	4	NUM
ap-9818	252	24	−	−	NOUN
ap-9818	252	25	f2	f2	PROPN
ap-9818	252	26	4	4	NUM
ap-9818	252	27	,	,	PUNCT
ap-9818	252	28	f1	f1	NOUN
ap-9818	252	29	4	4	NUM
ap-9818	252	30	−	−	NOUN
ap-9818	252	31	f2	f2	PROPN
ap-9818	252	32	4	4	NUM
ap-9818	252	33	,	,	PUNCT
ap-9818	252	34	1	1	NUM
ap-9818	252	35	−	−	NOUN
ap-9818	252	36	f2	f2	PROPN
ap-9818	252	37	2	2	NUM
ap-9818	252	38	,	,	PUNCT
ap-9818	252	39	x2	x2	PROPN
ap-9818	252	40	)	)	PUNCT
ap-9818	253	1	+	+	CCONJ
ap-9818	253	2	c2	c2	PROPN
ap-9818	253	3	x	x	SYM
ap-9818	253	4	1	1	NUM
ap-9818	253	5	2	2	NUM
ap-9818	253	6	+	+	SYM
ap-9818	253	7	f2	f2	PROPN
ap-9818	253	8	2	2	NUM
ap-9818	253	9	2f1	2f1	NUM
ap-9818	253	10	(	(	PUNCT
ap-9818	253	11	−f1	−f1	PROPN
ap-9818	253	12	4	4	NUM
ap-9818	253	13	+	+	CCONJ
ap-9818	253	14	f2	f2	PROPN
ap-9818	253	15	4	4	NUM
ap-9818	253	16	,	,	PUNCT
ap-9818	253	17	f1	f1	NOUN
ap-9818	253	18	4	4	NUM
ap-9818	253	19	+	+	SYM
ap-9818	253	20	f2	f2	PROPN
ap-9818	253	21	4	4	NUM
ap-9818	253	22	,	,	PUNCT
ap-9818	253	23	1	1	NUM
ap-9818	253	24	+	+	CCONJ
ap-9818	253	25	f2	f2	PROPN
ap-9818	253	26	2	2	NUM
ap-9818	253	27	,	,	PUNCT
ap-9818	253	28	x2	x2	PROPN
ap-9818	253	29	)	)	PUNCT
ap-9818	253	30	,	,	PUNCT
ap-9818	253	31	(	(	PUNCT
ap-9818	253	32	41	41	NUM
ap-9818	253	33	)	)	PUNCT
ap-9818	253	34	where	where	SCONJ
ap-9818	253	35	2f1	2f1	NUM
ap-9818	253	36	denotes	denote	VERB
ap-9818	253	37	the	the	DET
ap-9818	253	38	hypergeometric	hypergeometric	ADJ
ap-9818	253	39	function	function	NOUN
ap-9818	253	40	[	[	X
ap-9818	253	41	36	36	NUM
ap-9818	253	42	]	]	PUNCT
ap-9818	253	43	,	,	PUNCT
ap-9818	253	44	and	and	CCONJ
ap-9818	253	45	c1	c1	NOUN
ap-9818	253	46	,	,	PUNCT
ap-9818	253	47	c2	c2	PROPN
ap-9818	253	48	stand	stand	VERB
ap-9818	253	49	for	for	ADP
ap-9818	253	50	arbitrary	arbitrary	ADJ
ap-9818	253	51	constants	constant	NOUN
ap-9818	253	52	.	.	PUNCT
ap-9818	254	1	furthermore	furthermore	ADV
ap-9818	254	2	,	,	PUNCT
ap-9818	254	3	the	the	DET
ap-9818	254	4	parameters	parameter	NOUN
ap-9818	254	5	f1	f1	NOUN
ap-9818	254	6	,	,	PUNCT
ap-9818	254	7	f2	f2	PROPN
ap-9818	254	8	are	be	AUX
ap-9818	254	9	defined	define	VERB
ap-9818	254	10	as	as	ADP
ap-9818	254	11	:	:	PUNCT
ap-9818	254	12	f1	f1	NOUN
ap-9818	254	13	=	=	SYM
ap-9818	254	14	√	√	ADP
ap-9818	254	15	1	1	NUM
ap-9818	254	16	−	−	PROPN
ap-9818	254	17	4	4	NUM
ap-9818	254	18	e	e	NOUN
ap-9818	254	19	+	+	CCONJ
ap-9818	254	20	4	4	NUM
ap-9818	254	21	ν	ν	NOUN
ap-9818	254	22	(	(	PUNCT
ap-9818	254	23	ν	ν	X
ap-9818	254	24	−	−	PROPN
ap-9818	254	25	δ	δ	PROPN
ap-9818	254	26	)	)	PUNCT
ap-9818	254	27	,	,	PUNCT
ap-9818	254	28	f2	f2	PROPN
ap-9818	254	29	=	=	NOUN
ap-9818	254	30	√	√	ADP
ap-9818	254	31	1	1	NUM
ap-9818	254	32	−	−	PROPN
ap-9818	254	33	4	4	NUM
ap-9818	254	34	v1	v1	NOUN
ap-9818	254	35	+	+	CCONJ
ap-9818	254	36	4	4	NUM
ap-9818	254	37	ν	ν	NOUN
ap-9818	254	38	(	(	PUNCT
ap-9818	254	39	ν	ν	X
ap-9818	254	40	−	−	PROPN
ap-9818	254	41	δ	δ	PROPN
ap-9818	254	42	)	)	PUNCT
ap-9818	254	43	.	.	PUNCT
ap-9818	255	1	(	(	PUNCT
ap-9818	255	2	42	42	X
ap-9818	255	3	)	)	PUNCT
ap-9818	255	4	recall	recall	NOUN
ap-9818	255	5	that	that	SCONJ
ap-9818	255	6	we	we	PRON
ap-9818	255	7	are	be	AUX
ap-9818	255	8	interested	interested	ADJ
ap-9818	255	9	in	in	ADP
ap-9818	255	10	the	the	DET
ap-9818	255	11	solution	solution	NOUN
ap-9818	255	12	of	of	ADP
ap-9818	255	13	the	the	DET
ap-9818	255	14	actual	actual	ADJ
ap-9818	255	15	dunkl	dunkl	NOUN
ap-9818	255	16	-	-	PUNCT
ap-9818	255	17	schrödinger	schrödinger	NOUN
ap-9818	255	18	equation	equation	NOUN
ap-9818	255	19	(	(	PUNCT
ap-9818	255	20	6	6	NUM
ap-9818	255	21	)	)	PUNCT
ap-9818	255	22	,	,	PUNCT
ap-9818	255	23	the	the	DET
ap-9818	255	24	general	general	ADJ
ap-9818	255	25	solution	solution	NOUN
ap-9818	255	26	ψν	ψν	NOUN
ap-9818	255	27	,	,	PUNCT
ap-9818	255	28	gen	gen	PROPN
ap-9818	255	29	of	of	ADP
ap-9818	255	30	which	which	PRON
ap-9818	255	31	is	be	AUX
ap-9818	255	32	obtained	obtain	VERB
ap-9818	255	33	from	from	ADP
ap-9818	255	34	(	(	PUNCT
ap-9818	255	35	41	41	NUM
ap-9818	255	36	)	)	PUNCT
ap-9818	255	37	by	by	ADP
ap-9818	255	38	means	mean	NOUN
ap-9818	255	39	of	of	ADP
ap-9818	255	40	point	point	NOUN
ap-9818	255	41	transformation	transformation	NOUN
ap-9818	255	42	(	(	PUNCT
ap-9818	255	43	10	10	NUM
ap-9818	255	44	)	)	PUNCT
ap-9818	255	45	.	.	PUNCT
ap-9818	256	1	insertion	insertion	NOUN
ap-9818	256	2	of	of	ADP
ap-9818	256	3	the	the	DET
ap-9818	256	4	position	position	NOUN
ap-9818	256	5	-	-	PUNCT
ap-9818	256	6	dependent	dependent	ADJ
ap-9818	256	7	mass	mass	NOUN
ap-9818	256	8	from	from	ADP
ap-9818	256	9	(	(	PUNCT
ap-9818	256	10	31	31	NUM
ap-9818	256	11	)	)	PUNCT
ap-9818	256	12	gives	give	VERB
ap-9818	256	13	the	the	DET
ap-9818	256	14	relationship	relationship	NOUN
ap-9818	256	15	:	:	PUNCT
ap-9818	256	16	ψν	ψν	NOUN
ap-9818	256	17	,	,	PUNCT
ap-9818	256	18	gen(x	gen(x	NOUN
ap-9818	256	19	)	)	PUNCT
ap-9818	257	1	=	=	SYM
ap-9818	257	2	1√	1√	NUM
ap-9818	257	3	x2	x2	NOUN
ap-9818	258	1	+	+	CCONJ
ap-9818	258	2	1	1	NUM
ap-9818	258	3	xν	xν	NOUN
ap-9818	258	4	ξν	ξν	ADV
ap-9818	258	5	,	,	PUNCT
ap-9818	258	6	gen(x	gen(x	NOUN
ap-9818	258	7	)	)	PUNCT
ap-9818	258	8	.	.	PUNCT
ap-9818	259	1	(	(	PUNCT
ap-9818	259	2	43	43	NUM
ap-9818	259	3	)	)	PUNCT
ap-9818	259	4	rather	rather	ADV
ap-9818	259	5	than	than	ADP
ap-9818	259	6	considering	consider	VERB
ap-9818	259	7	the	the	DET
ap-9818	259	8	general	general	ADJ
ap-9818	259	9	solution	solution	NOUN
ap-9818	259	10	of	of	ADP
ap-9818	259	11	our	our	PRON
ap-9818	259	12	problem	problem	NOUN
ap-9818	259	13	,	,	PUNCT
ap-9818	259	14	let	let	VERB
ap-9818	259	15	us	we	PRON
ap-9818	259	16	now	now	ADV
ap-9818	259	17	restrict	restrict	VERB
ap-9818	259	18	ourselves	ourselves	PRON
ap-9818	259	19	to	to	ADP
ap-9818	259	20	the	the	DET
ap-9818	259	21	case	case	NOUN
ap-9818	259	22	of	of	ADP
ap-9818	259	23	bound	bind	VERB
ap-9818	259	24	states	state	NOUN
ap-9818	259	25	.	.	PUNCT
ap-9818	260	1	228	228	NUM
ap-9818	260	2	vol	vol	NOUN
ap-9818	260	3	.	.	PUNCT
ap-9818	261	1	65	65	NUM
ap-9818	261	2	no	no	NOUN
ap-9818	261	3	.	.	PUNCT
ap-9818	262	1	2/2025	2/2025	NUM
ap-9818	262	2	persistence	persistence	NOUN
ap-9818	262	3	of	of	ADP
ap-9818	262	4	solvability	solvability	NOUN
ap-9818	262	5	in	in	ADP
ap-9818	262	6	quantum	quantum	NOUN
ap-9818	262	7	systems	system	NOUN
ap-9818	262	8	deformed	deform	VERB
ap-9818	262	9	by	by	ADP
ap-9818	262	10	dunkl	dunkl	PROPN
ap-9818	262	11	.	.	PUNCT
ap-9818	262	12	.	.	PUNCT
ap-9818	263	1	.	.	PUNCT
ap-9818	264	1	bound	bind	VERB
ap-9818	264	2	states	state	NOUN
ap-9818	264	3	of	of	ADP
ap-9818	264	4	the	the	DET
ap-9818	264	5	dunkl	dunkl	NOUN
ap-9818	264	6	-	-	PUNCT
ap-9818	264	7	schrödinger	schrödinger	NOUN
ap-9818	264	8	equation	equation	NOUN
ap-9818	264	9	.	.	PUNCT
ap-9818	265	1	solutions	solution	NOUN
ap-9818	265	2	of	of	ADP
ap-9818	265	3	bound	bind	VERB
ap-9818	265	4	state	state	NOUN
ap-9818	265	5	type	type	NOUN
ap-9818	265	6	can	can	AUX
ap-9818	265	7	be	be	AUX
ap-9818	265	8	extracted	extract	VERB
ap-9818	265	9	from	from	ADP
ap-9818	265	10	(	(	PUNCT
ap-9818	265	11	41	41	NUM
ap-9818	265	12	)	)	PUNCT
ap-9818	265	13	by	by	ADP
ap-9818	265	14	setting	set	VERB
ap-9818	265	15	c1	c1	NOUN
ap-9818	265	16	=	=	PUNCT
ap-9818	265	17	0	0	NUM
ap-9818	266	1	in	in	ADP
ap-9818	266	2	order	order	NOUN
ap-9818	266	3	to	to	PART
ap-9818	266	4	remove	remove	VERB
ap-9818	266	5	singular	singular	ADJ
ap-9818	266	6	terms	term	NOUN
ap-9818	266	7	,	,	PUNCT
ap-9818	266	8	and	and	CCONJ
ap-9818	266	9	by	by	ADP
ap-9818	266	10	requiring	require	VERB
ap-9818	266	11	the	the	DET
ap-9818	266	12	first	first	ADJ
ap-9818	266	13	argument	argument	NOUN
ap-9818	266	14	of	of	ADP
ap-9818	266	15	the	the	DET
ap-9818	266	16	remaining	remain	VERB
ap-9818	266	17	hypergeometric	hypergeometric	ADJ
ap-9818	266	18	function	function	NOUN
ap-9818	266	19	to	to	PART
ap-9818	266	20	equal	equal	VERB
ap-9818	266	21	a	a	DET
ap-9818	266	22	nonpositive	nonpositive	ADJ
ap-9818	266	23	integer	integer	NOUN
ap-9818	266	24	,	,	PUNCT
ap-9818	266	25	recall	recall	VERB
ap-9818	266	26	that	that	SCONJ
ap-9818	266	27	this	this	PRON
ap-9818	266	28	will	will	AUX
ap-9818	266	29	make	make	VERB
ap-9818	266	30	the	the	DET
ap-9818	266	31	latter	latter	ADJ
ap-9818	266	32	function	function	NOUN
ap-9818	266	33	degenerate	degenerate	ADJ
ap-9818	266	34	to	to	ADP
ap-9818	266	35	a	a	DET
ap-9818	266	36	polynomial	polynomial	NOUN
ap-9818	266	37	.	.	PUNCT
ap-9818	267	1	the	the	DET
ap-9818	267	2	condition	condition	NOUN
ap-9818	267	3	reads	read	VERB
ap-9818	267	4	:	:	PUNCT
ap-9818	267	5	−f1	−f1	NOUN
ap-9818	267	6	4	4	NUM
ap-9818	267	7	+	+	CCONJ
ap-9818	267	8	f2	f2	PROPN
ap-9818	267	9	4	4	NUM
ap-9818	267	10	=	=	SYM
ap-9818	267	11	−n	−n	NOUN
ap-9818	267	12	.	.	PUNCT
ap-9818	268	1	(	(	PUNCT
ap-9818	268	2	44	44	NUM
ap-9818	268	3	)	)	PUNCT
ap-9818	268	4	upon	upon	SCONJ
ap-9818	268	5	substituting	substitute	VERB
ap-9818	268	6	the	the	DET
ap-9818	268	7	abbreviations	abbreviation	NOUN
ap-9818	268	8	(	(	PUNCT
ap-9818	268	9	42	42	NUM
ap-9818	268	10	)	)	PUNCT
ap-9818	268	11	,	,	PUNCT
ap-9818	268	12	we	we	PRON
ap-9818	268	13	can	can	AUX
ap-9818	268	14	solve	solve	VERB
ap-9818	268	15	this	this	DET
ap-9818	268	16	condition	condition	NOUN
ap-9818	268	17	with	with	ADP
ap-9818	268	18	respect	respect	NOUN
ap-9818	268	19	to	to	ADP
ap-9818	268	20	the	the	DET
ap-9818	268	21	stationary	stationary	ADJ
ap-9818	268	22	energy	energy	NOUN
ap-9818	268	23	e	e	NOUN
ap-9818	268	24	=	=	SYM
ap-9818	268	25	eν	eν	PROPN
ap-9818	268	26	,	,	PUNCT
ap-9818	268	27	n.	n.	NOUN
ap-9818	268	28	this	this	DET
ap-9818	268	29	yields	yield	NOUN
ap-9818	268	30	:	:	PUNCT
ap-9818	268	31	eν	eν	NOUN
ap-9818	268	32	,	,	PUNCT
ap-9818	268	33	n	n	NOUN
ap-9818	268	34	=	=	SYM
ap-9818	268	35	−4	−4	X
ap-9818	268	36	n2	n2	NOUN
ap-9818	268	37	+	+	CCONJ
ap-9818	268	38	v1	v1	NOUN
ap-9818	268	39	−	−	PROPN
ap-9818	268	40	2	2	NUM
ap-9818	268	41	n	n	NOUN
ap-9818	268	42	f2	f2	NOUN
ap-9818	268	43	=	=	SYM
ap-9818	268	44	−4	−4	X
ap-9818	268	45	n2	n2	NOUN
ap-9818	268	46	+	+	CCONJ
ap-9818	268	47	v1	v1	NOUN
ap-9818	268	48	−	−	PROPN
ap-9818	268	49	2	2	NUM
ap-9818	268	50	n	n	NOUN
ap-9818	268	51	√	√	ADV
ap-9818	268	52	1	1	NUM
ap-9818	268	53	−	−	PROPN
ap-9818	268	54	4	4	NUM
ap-9818	268	55	v1	v1	NOUN
ap-9818	268	56	+	+	CCONJ
ap-9818	268	57	4	4	NUM
ap-9818	268	58	ν	ν	NOUN
ap-9818	268	59	(	(	PUNCT
ap-9818	268	60	ν	ν	X
ap-9818	268	61	−	−	PROPN
ap-9818	268	62	δ	δ	PROPN
ap-9818	268	63	)	)	PUNCT
ap-9818	268	64	.	.	PUNCT
ap-9818	269	1	(	(	PUNCT
ap-9818	269	2	45	45	NUM
ap-9818	269	3	)	)	PUNCT
ap-9818	269	4	we	we	PRON
ap-9818	269	5	observe	observe	VERB
ap-9818	269	6	that	that	SCONJ
ap-9818	269	7	the	the	DET
ap-9818	269	8	root	root	NOUN
ap-9818	269	9	on	on	ADP
ap-9818	269	10	the	the	DET
ap-9818	269	11	right	right	ADJ
ap-9818	269	12	side	side	NOUN
ap-9818	269	13	contains	contain	VERB
ap-9818	269	14	a	a	DET
ap-9818	269	15	term	term	NOUN
ap-9818	269	16	that	that	PRON
ap-9818	269	17	appears	appear	VERB
ap-9818	269	18	in	in	ADP
ap-9818	269	19	(	(	PUNCT
ap-9818	269	20	38	38	NUM
ap-9818	269	21	)	)	PUNCT
ap-9818	269	22	.	.	PUNCT
ap-9818	270	1	if	if	SCONJ
ap-9818	270	2	the	the	DET
ap-9818	270	3	latter	latter	ADJ
ap-9818	270	4	condition	condition	NOUN
ap-9818	270	5	is	be	AUX
ap-9818	270	6	fulfilled	fulfil	VERB
ap-9818	270	7	,	,	PUNCT
ap-9818	270	8	then	then	ADV
ap-9818	270	9	the	the	DET
ap-9818	270	10	stationary	stationary	ADJ
ap-9818	270	11	energies	energy	NOUN
ap-9818	270	12	(	(	PUNCT
ap-9818	270	13	45	45	NUM
ap-9818	270	14	)	)	PUNCT
ap-9818	270	15	take	take	VERB
ap-9818	270	16	real	real	ADJ
ap-9818	270	17	values	value	NOUN
ap-9818	270	18	only	only	ADV
ap-9818	270	19	,	,	PUNCT
ap-9818	270	20	which	which	PRON
ap-9818	270	21	is	be	AUX
ap-9818	270	22	in	in	ADP
ap-9818	270	23	accordance	accordance	NOUN
ap-9818	270	24	with	with	ADP
ap-9818	270	25	bound	bind	VERB
ap-9818	270	26	state	state	NOUN
ap-9818	270	27	energies	energy	NOUN
ap-9818	270	28	.	.	PUNCT
ap-9818	271	1	however	however	ADV
ap-9818	271	2	,	,	PUNCT
ap-9818	271	3	if	if	SCONJ
ap-9818	271	4	v1	v1	NOUN
ap-9818	271	5	takes	take	VERB
ap-9818	271	6	positive	positive	ADJ
ap-9818	271	7	values	value	NOUN
ap-9818	271	8	,	,	PUNCT
ap-9818	271	9	then	then	ADV
ap-9818	271	10	(	(	PUNCT
ap-9818	271	11	45	45	NUM
ap-9818	271	12	)	)	PUNCT
ap-9818	271	13	can	can	AUX
ap-9818	271	14	become	become	VERB
ap-9818	271	15	complex	complex	ADV
ap-9818	271	16	-	-	PUNCT
ap-9818	271	17	valued	value	VERB
ap-9818	271	18	,	,	PUNCT
ap-9818	271	19	depending	depend	VERB
ap-9818	271	20	on	on	ADP
ap-9818	271	21	the	the	DET
ap-9818	271	22	parameters	parameter	NOUN
ap-9818	271	23	ν	ν	NOUN
ap-9818	271	24	and	and	CCONJ
ap-9818	271	25	δ	δ	PROPN
ap-9818	271	26	from	from	ADP
ap-9818	271	27	the	the	DET
ap-9818	271	28	dunkl	dunkl	NOUN
ap-9818	271	29	operator	operator	NOUN
ap-9818	271	30	(	(	PUNCT
ap-9818	271	31	3	3	NUM
ap-9818	271	32	)	)	PUNCT
ap-9818	271	33	.	.	PUNCT
ap-9818	272	1	now	now	ADV
ap-9818	272	2	we	we	PRON
ap-9818	272	3	insert	insert	VERB
ap-9818	272	4	this	this	DET
ap-9818	272	5	energy	energy	NOUN
ap-9818	272	6	,	,	PUNCT
ap-9818	272	7	and	and	CCONJ
ap-9818	272	8	the	the	DET
ap-9818	272	9	setting	set	VERB
ap-9818	272	10	c1	c1	NOUN
ap-9818	272	11	=	=	SYM
ap-9818	272	12	0	0	PROPN
ap-9818	272	13	,	,	PUNCT
ap-9818	272	14	c2	c2	PROPN
ap-9818	272	15	=	=	NOUN
ap-9818	272	16	1	1	NUM
ap-9818	272	17	into	into	ADP
ap-9818	272	18	(	(	PUNCT
ap-9818	272	19	41	41	NUM
ap-9818	272	20	)	)	PUNCT
ap-9818	272	21	.	.	PUNCT
ap-9818	273	1	combination	combination	NOUN
ap-9818	273	2	with	with	ADP
ap-9818	273	3	(	(	PUNCT
ap-9818	273	4	43	43	NUM
ap-9818	273	5	)	)	PUNCT
ap-9818	273	6	gives	give	VERB
ap-9818	273	7	the	the	DET
ap-9818	273	8	solutions	solution	NOUN
ap-9818	273	9	of	of	ADP
ap-9818	273	10	our	our	PRON
ap-9818	273	11	dunkl	dunkl	NOUN
ap-9818	273	12	-	-	PUNCT
ap-9818	273	13	schrödinger	schrödinger	NOUN
ap-9818	273	14	equation	equation	NOUN
ap-9818	273	15	(	(	PUNCT
ap-9818	273	16	6	6	NUM
ap-9818	273	17	)	)	PUNCT
ap-9818	273	18	in	in	ADP
ap-9818	273	19	the	the	DET
ap-9818	273	20	form	form	NOUN
ap-9818	273	21	:	:	PUNCT
ap-9818	273	22	ψν	ψν	NOUN
ap-9818	273	23	,	,	PUNCT
ap-9818	273	24	n(x	n(x	ADJ
ap-9818	273	25	)	)	PUNCT
ap-9818	274	1	=	=	SYM
ap-9818	274	2	1√	1√	NUM
ap-9818	274	3	x2	x2	PROPN
ap-9818	275	1	+	+	CCONJ
ap-9818	275	2	1	1	NUM
ap-9818	275	3	x−ν+	x−ν+	PROPN
ap-9818	275	4	1	1	NUM
ap-9818	275	5	2	2	NUM
ap-9818	275	6	+	+	SYM
ap-9818	275	7	f2	f2	PROPN
ap-9818	275	8	2	2	NUM
ap-9818	275	9	2f1	2f1	NUM
ap-9818	275	10	(	(	PUNCT
ap-9818	275	11	−n	−n	PROPN
ap-9818	275	12	,	,	PUNCT
ap-9818	275	13	f1	f1	NOUN
ap-9818	275	14	4	4	NUM
ap-9818	275	15	+	+	SYM
ap-9818	275	16	f2	f2	PROPN
ap-9818	275	17	4	4	NUM
ap-9818	275	18	,	,	PUNCT
ap-9818	275	19	1	1	NUM
ap-9818	275	20	+	+	CCONJ
ap-9818	275	21	f2	f2	PROPN
ap-9818	275	22	2	2	NUM
ap-9818	275	23	,	,	PUNCT
ap-9818	275	24	x2	x2	PROPN
ap-9818	275	25	)	)	PUNCT
ap-9818	275	26	.	.	PUNCT
ap-9818	276	1	(	(	PUNCT
ap-9818	276	2	46	46	X
ap-9818	276	3	)	)	PUNCT
ap-9818	276	4	these	these	DET
ap-9818	276	5	solutions	solution	NOUN
ap-9818	276	6	include	include	VERB
ap-9818	276	7	the	the	DET
ap-9818	276	8	standard	standard	ADJ
ap-9818	276	9	case	case	NOUN
ap-9818	276	10	(	(	PUNCT
ap-9818	276	11	without	without	ADP
ap-9818	276	12	dunkl	dunkl	NOUN
ap-9818	276	13	formalism	formalism	NOUN
ap-9818	276	14	)	)	PUNCT
ap-9818	276	15	,	,	PUNCT
ap-9818	276	16	that	that	SCONJ
ap-9818	276	17	we	we	PRON
ap-9818	276	18	obtain	obtain	VERB
ap-9818	276	19	by	by	ADP
ap-9818	276	20	setting	set	VERB
ap-9818	276	21	ν	ν	NOUN
ap-9818	276	22	=	=	SYM
ap-9818	276	23	0	0	NUM
ap-9818	276	24	in	in	ADP
ap-9818	276	25	(	(	PUNCT
ap-9818	276	26	46	46	NUM
ap-9818	276	27	)	)	PUNCT
ap-9818	276	28	.	.	PUNCT
ap-9818	277	1	note	note	VERB
ap-9818	277	2	that	that	SCONJ
ap-9818	277	3	the	the	DET
ap-9818	277	4	negative	negative	ADJ
ap-9818	277	5	power	power	NOUN
ap-9818	277	6	of	of	ADP
ap-9818	277	7	ν	ν	NOUN
ap-9818	277	8	in	in	ADP
ap-9818	277	9	the	the	DET
ap-9818	277	10	exponent	exponent	NOUN
ap-9818	277	11	on	on	ADP
ap-9818	277	12	the	the	DET
ap-9818	277	13	right	right	ADJ
ap-9818	277	14	side	side	NOUN
ap-9818	277	15	of	of	ADP
ap-9818	277	16	(	(	PUNCT
ap-9818	277	17	46	46	NUM
ap-9818	277	18	)	)	PUNCT
ap-9818	277	19	does	do	AUX
ap-9818	277	20	not	not	PART
ap-9818	277	21	create	create	VERB
ap-9818	277	22	a	a	DET
ap-9818	277	23	singularity	singularity	NOUN
ap-9818	277	24	at	at	ADP
ap-9818	277	25	the	the	DET
ap-9818	277	26	origin	origin	NOUN
ap-9818	277	27	,	,	PUNCT
ap-9818	277	28	as	as	ADV
ap-9818	277	29	long	long	ADV
ap-9818	277	30	as	as	SCONJ
ap-9818	277	31	v1	v1	NOUN
ap-9818	277	32	is	be	AUX
ap-9818	277	33	negative	negative	ADJ
ap-9818	277	34	.	.	PUNCT
ap-9818	278	1	this	this	PRON
ap-9818	278	2	is	be	AUX
ap-9818	278	3	due	due	ADJ
ap-9818	278	4	to	to	ADP
ap-9818	278	5	the	the	DET
ap-9818	278	6	occurrence	occurrence	NOUN
ap-9818	278	7	of	of	ADP
ap-9818	278	8	ν	ν	NOUN
ap-9818	278	9	in	in	ADP
ap-9818	278	10	the	the	DET
ap-9818	278	11	constant	constant	ADJ
ap-9818	278	12	f2	f2	PROPN
ap-9818	278	13	,	,	PUNCT
ap-9818	278	14	see	see	VERB
ap-9818	278	15	(	(	PUNCT
ap-9818	278	16	42	42	NUM
ap-9818	278	17	)	)	PUNCT
ap-9818	278	18	.	.	PUNCT
ap-9818	279	1	if	if	SCONJ
ap-9818	279	2	the	the	DET
ap-9818	279	3	dunkl	dunkl	NOUN
ap-9818	279	4	formalism	formalism	NOUN
ap-9818	279	5	is	be	AUX
ap-9818	279	6	present	present	ADJ
ap-9818	279	7	,	,	PUNCT
ap-9818	279	8	meaning	mean	VERB
ap-9818	279	9	ν	ν	X
ap-9818	279	10	̸=	̸=	PROPN
ap-9818	279	11	0	0	NUM
ap-9818	279	12	,	,	PUNCT
ap-9818	279	13	then	then	ADV
ap-9818	279	14	one	one	NUM
ap-9818	279	15	more	more	ADJ
ap-9818	279	16	detail	detail	NOUN
ap-9818	279	17	must	must	AUX
ap-9818	279	18	be	be	AUX
ap-9818	279	19	considered	consider	VERB
ap-9818	279	20	before	before	SCONJ
ap-9818	279	21	we	we	PRON
ap-9818	279	22	have	have	VERB
ap-9818	279	23	the	the	DET
ap-9818	279	24	solution	solution	NOUN
ap-9818	279	25	in	in	ADP
ap-9818	279	26	its	its	PRON
ap-9818	279	27	final	final	ADJ
ap-9818	279	28	form	form	NOUN
ap-9818	279	29	.	.	PUNCT
ap-9818	280	1	this	this	DET
ap-9818	280	2	detail	detail	NOUN
ap-9818	280	3	is	be	AUX
ap-9818	280	4	the	the	DET
ap-9818	280	5	solution	solution	NOUN
ap-9818	280	6	’s	’s	PART
ap-9818	280	7	parity	parity	NOUN
ap-9818	280	8	.	.	PUNCT
ap-9818	281	1	as	as	SCONJ
ap-9818	281	2	we	we	PRON
ap-9818	281	3	can	can	AUX
ap-9818	281	4	see	see	VERB
ap-9818	281	5	by	by	ADP
ap-9818	281	6	inspecting	inspect	VERB
ap-9818	281	7	the	the	DET
ap-9818	281	8	explicit	explicit	ADJ
ap-9818	281	9	form	form	NOUN
ap-9818	281	10	(	(	PUNCT
ap-9818	281	11	46	46	NUM
ap-9818	281	12	)	)	PUNCT
ap-9818	281	13	,	,	PUNCT
ap-9818	281	14	our	our	PRON
ap-9818	281	15	solution	solution	NOUN
ap-9818	281	16	does	do	AUX
ap-9818	281	17	not	not	PART
ap-9818	281	18	have	have	VERB
ap-9818	281	19	parity	parity	NOUN
ap-9818	281	20	due	due	ADP
ap-9818	281	21	to	to	ADP
ap-9818	281	22	the	the	DET
ap-9818	281	23	exponent	exponent	NOUN
ap-9818	281	24	of	of	ADP
ap-9818	281	25	the	the	DET
ap-9818	281	26	monomial	monomial	ADJ
ap-9818	281	27	term	term	NOUN
ap-9818	281	28	.	.	PUNCT
ap-9818	282	1	in	in	ADP
ap-9818	282	2	order	order	NOUN
ap-9818	282	3	for	for	ADP
ap-9818	282	4	the	the	DET
ap-9818	282	5	solution	solution	NOUN
ap-9818	282	6	to	to	PART
ap-9818	282	7	have	have	VERB
ap-9818	282	8	the	the	DET
ap-9818	282	9	correct	correct	ADJ
ap-9818	282	10	parity	parity	NOUN
ap-9818	282	11	,	,	PUNCT
ap-9818	282	12	this	this	DET
ap-9818	282	13	exponent	exponent	NOUN
ap-9818	282	14	must	must	AUX
ap-9818	282	15	be	be	AUX
ap-9818	282	16	an	an	DET
ap-9818	282	17	odd	odd	ADJ
ap-9818	282	18	integer	integer	NOUN
ap-9818	282	19	if	if	SCONJ
ap-9818	282	20	δ	δ	PROPN
ap-9818	282	21	=	=	VERB
ap-9818	282	22	−1	−1	NOUN
ap-9818	282	23	(	(	PUNCT
ap-9818	282	24	odd	odd	ADJ
ap-9818	282	25	parity	parity	NOUN
ap-9818	282	26	)	)	PUNCT
ap-9818	282	27	,	,	PUNCT
ap-9818	282	28	and	and	CCONJ
ap-9818	282	29	it	it	PRON
ap-9818	282	30	must	must	AUX
ap-9818	282	31	equal	equal	VERB
ap-9818	282	32	an	an	DET
ap-9818	282	33	even	even	ADV
ap-9818	282	34	integer	integer	NOUN
ap-9818	282	35	for	for	ADP
ap-9818	282	36	δ	δ	PROPN
ap-9818	282	37	=	=	SYM
ap-9818	282	38	1	1	NUM
ap-9818	282	39	(	(	PUNCT
ap-9818	282	40	even	even	ADV
ap-9818	282	41	parity	parity	NOUN
ap-9818	282	42	)	)	PUNCT
ap-9818	282	43	.	.	PUNCT
ap-9818	283	1	in	in	ADP
ap-9818	283	2	the	the	DET
ap-9818	283	3	first	first	ADJ
ap-9818	283	4	of	of	ADP
ap-9818	283	5	the	the	DET
ap-9818	283	6	two	two	NUM
ap-9818	283	7	cases	case	NOUN
ap-9818	283	8	the	the	DET
ap-9818	283	9	aforementioned	aforementioned	ADJ
ap-9818	283	10	condition	condition	NOUN
ap-9818	283	11	reads	read	VERB
ap-9818	283	12	:	:	PUNCT
ap-9818	283	13	−ν	−ν	ADJ
ap-9818	283	14	+	+	CCONJ
ap-9818	283	15	1	1	NUM
ap-9818	283	16	2	2	NUM
ap-9818	283	17	+	+	SYM
ap-9818	283	18	f2	f2	PROPN
ap-9818	283	19	2	2	NUM
ap-9818	283	20	=	=	SYM
ap-9818	283	21	2	2	NUM
ap-9818	283	22	k	k	NOUN
ap-9818	284	1	+	+	NOUN
ap-9818	284	2	1	1	NUM
ap-9818	284	3	⇝	⇝	NOUN
ap-9818	284	4	ν	ν	NOUN
ap-9818	284	5	=	=	SYM
ap-9818	284	6	−1	−1	NOUN
ap-9818	284	7	2	2	NUM
ap-9818	284	8	−	−	NOUN
ap-9818	284	9	k	k	NOUN
ap-9818	284	10	−	−	PROPN
ap-9818	284	11	v1	v1	PROPN
ap-9818	284	12	4	4	NUM
ap-9818	284	13	k	k	NOUN
ap-9818	284	14	,	,	PUNCT
ap-9818	284	15	(	(	PUNCT
ap-9818	284	16	47	47	NUM
ap-9818	284	17	)	)	PUNCT
ap-9818	284	18	where	where	SCONJ
ap-9818	284	19	k	k	PROPN
ap-9818	284	20	is	be	AUX
ap-9818	284	21	an	an	DET
ap-9818	284	22	arbitrary	arbitrary	ADJ
ap-9818	284	23	integer	integer	NOUN
ap-9818	284	24	.	.	PUNCT
ap-9818	285	1	in	in	ADP
ap-9818	285	2	the	the	DET
ap-9818	285	3	remaining	remain	VERB
ap-9818	285	4	case	case	NOUN
ap-9818	285	5	δ	δ	NOUN
ap-9818	285	6	=	=	SYM
ap-9818	285	7	1	1	NUM
ap-9818	285	8	we	we	PRON
ap-9818	285	9	must	must	AUX
ap-9818	285	10	have	have	VERB
ap-9818	285	11	:	:	PUNCT
ap-9818	285	12	ν	ν	X
ap-9818	285	13	+	+	NOUN
ap-9818	285	14	1	1	NUM
ap-9818	285	15	2	2	NUM
ap-9818	285	16	+	+	SYM
ap-9818	285	17	f2	f2	PROPN
ap-9818	285	18	2	2	NUM
ap-9818	285	19	=	=	SYM
ap-9818	285	20	2	2	NUM
ap-9818	285	21	k	k	NOUN
ap-9818	285	22	⇝	⇝	NOUN
ap-9818	285	23	ν	ν	X
ap-9818	285	24	=	=	SYM
ap-9818	285	25	1	1	NUM
ap-9818	285	26	2	2	NUM
ap-9818	285	27	−	−	NOUN
ap-9818	285	28	k	k	NOUN
ap-9818	285	29	−	−	PROPN
ap-9818	285	30	v1	v1	PROPN
ap-9818	285	31	4	4	NUM
ap-9818	285	32	k	k	NOUN
ap-9818	285	33	.	.	PUNCT
ap-9818	286	1	(	(	PUNCT
ap-9818	286	2	48	48	NUM
ap-9818	286	3	)	)	PUNCT
ap-9818	286	4	it	it	PRON
ap-9818	286	5	is	be	AUX
ap-9818	286	6	important	important	ADJ
ap-9818	286	7	to	to	PART
ap-9818	286	8	point	point	VERB
ap-9818	286	9	out	out	ADP
ap-9818	286	10	that	that	SCONJ
ap-9818	286	11	the	the	DET
ap-9818	286	12	value	value	NOUN
ap-9818	286	13	of	of	ADP
ap-9818	286	14	k	k	PROPN
ap-9818	286	15	does	do	AUX
ap-9818	286	16	not	not	PART
ap-9818	286	17	have	have	VERB
ap-9818	286	18	to	to	PART
ap-9818	286	19	be	be	AUX
ap-9818	286	20	the	the	DET
ap-9818	286	21	same	same	ADJ
ap-9818	286	22	for	for	ADP
ap-9818	286	23	odd	odd	ADJ
ap-9818	286	24	and	and	CCONJ
ap-9818	286	25	even	even	ADV
ap-9818	286	26	solutions	solution	NOUN
ap-9818	286	27	.	.	PUNCT
ap-9818	287	1	hence	hence	ADV
ap-9818	287	2	,	,	PUNCT
ap-9818	287	3	by	by	ADP
ap-9818	287	4	choosing	choose	VERB
ap-9818	287	5	different	different	ADJ
ap-9818	287	6	values	value	NOUN
ap-9818	287	7	of	of	ADP
ap-9818	287	8	k	k	PROPN
ap-9818	287	9	in	in	ADP
ap-9818	287	10	(	(	PUNCT
ap-9818	287	11	47	47	NUM
ap-9818	287	12	)	)	PUNCT
ap-9818	287	13	and	and	CCONJ
ap-9818	287	14	(	(	PUNCT
ap-9818	287	15	48	48	NUM
ap-9818	287	16	)	)	PUNCT
ap-9818	287	17	,	,	PUNCT
ap-9818	287	18	one	one	PRON
ap-9818	287	19	can	can	AUX
ap-9818	287	20	obtain	obtain	VERB
ap-9818	287	21	the	the	DET
ap-9818	287	22	same	same	ADJ
ap-9818	287	23	value	value	NOUN
ap-9818	287	24	of	of	ADP
ap-9818	287	25	ν	ν	NOUN
ap-9818	287	26	in	in	ADP
ap-9818	287	27	both	both	DET
ap-9818	287	28	cases	case	NOUN
ap-9818	287	29	.	.	PUNCT
ap-9818	288	1	in	in	ADP
ap-9818	288	2	summary	summary	NOUN
ap-9818	288	3	,	,	PUNCT
ap-9818	288	4	the	the	DET
ap-9818	288	5	function	function	NOUN
ap-9818	288	6	(	(	PUNCT
ap-9818	288	7	46	46	NUM
ap-9818	288	8	)	)	PUNCT
ap-9818	288	9	is	be	AUX
ap-9818	288	10	a	a	DET
ap-9818	288	11	solution	solution	NOUN
ap-9818	288	12	of	of	ADP
ap-9818	288	13	our	our	PRON
ap-9818	288	14	dunkl	dunkl	NOUN
ap-9818	288	15	-	-	PUNCT
ap-9818	288	16	schrödinger	schrödinger	NOUN
ap-9818	288	17	equation	equation	NOUN
ap-9818	288	18	(	(	PUNCT
ap-9818	288	19	6	6	NUM
ap-9818	288	20	)	)	PUNCT
ap-9818	288	21	for	for	ADP
ap-9818	288	22	ν	ν	X
ap-9818	288	23	̸=	̸=	PROPN
ap-9818	288	24	0	0	NUM
ap-9818	288	25	and	and	CCONJ
ap-9818	288	26	the	the	DET
ap-9818	288	27	present	present	ADJ
ap-9818	288	28	settings	setting	NOUN
ap-9818	288	29	(	(	PUNCT
ap-9818	288	30	31	31	NUM
ap-9818	288	31	)	)	PUNCT
ap-9818	288	32	,	,	PUNCT
ap-9818	288	33	provided	provide	VERB
ap-9818	288	34	the	the	DET
ap-9818	288	35	parameter	parameter	NOUN
ap-9818	288	36	ν	ν	PROPN
ap-9818	288	37	complies	complie	NOUN
ap-9818	288	38	with	with	ADP
ap-9818	288	39	(	(	PUNCT
ap-9818	288	40	47	47	NUM
ap-9818	288	41	)	)	PUNCT
ap-9818	288	42	for	for	ADP
ap-9818	288	43	δ	δ	PROPN
ap-9818	288	44	=	=	SYM
ap-9818	288	45	−1	−1	NOUN
ap-9818	288	46	,	,	PUNCT
ap-9818	288	47	and	and	CCONJ
ap-9818	288	48	it	it	PRON
ap-9818	288	49	complies	comply	VERB
ap-9818	288	50	with	with	ADP
ap-9818	288	51	(	(	PUNCT
ap-9818	288	52	48	48	NUM
ap-9818	288	53	)	)	PUNCT
ap-9818	288	54	for	for	ADP
ap-9818	288	55	δ	δ	PROPN
ap-9818	288	56	=	=	SYM
ap-9818	288	57	1	1	X
ap-9818	288	58	.	.	PUNCT
ap-9818	288	59	particular	particular	ADJ
ap-9818	288	60	cases	case	NOUN
ap-9818	288	61	of	of	ADP
ap-9818	288	62	our	our	PRON
ap-9818	288	63	solutions	solution	NOUN
ap-9818	288	64	are	be	AUX
ap-9818	288	65	shown	show	VERB
ap-9818	288	66	in	in	ADP
ap-9818	288	67	figures	figure	NOUN
ap-9818	288	68	1	1	NUM
ap-9818	288	69	and	and	CCONJ
ap-9818	288	70	2	2	NUM
ap-9818	288	71	.	.	X
ap-9818	289	1	we	we	PRON
ap-9818	289	2	omit	omit	VERB
ap-9818	289	3	to	to	PART
ap-9818	289	4	show	show	VERB
ap-9818	289	5	graphs	graph	NOUN
ap-9818	289	6	of	of	ADP
ap-9818	289	7	solutions	solution	NOUN
ap-9818	289	8	to	to	ADP
ap-9818	289	9	the	the	DET
ap-9818	289	10	standard	standard	ADJ
ap-9818	289	11	schrödinger	schrödinger	ADJ
ap-9818	289	12	equation	equation	NOUN
ap-9818	289	13	,	,	PUNCT
ap-9818	289	14	as	as	SCONJ
ap-9818	289	15	these	these	PRON
ap-9818	289	16	are	be	AUX
ap-9818	289	17	similar	similar	ADJ
ap-9818	289	18	to	to	ADP
ap-9818	289	19	the	the	DET
ap-9818	289	20	ones	one	NOUN
ap-9818	289	21	displayed	display	VERB
ap-9818	289	22	in	in	ADP
ap-9818	289	23	the	the	DET
ap-9818	289	24	above	above	ADJ
ap-9818	289	25	figures	figure	NOUN
ap-9818	289	26	.	.	PUNCT
ap-9818	290	1	4.2	4.2	NUM
ap-9818	290	2	.	.	PUNCT
ap-9818	290	3	inverse	inverse	NOUN
ap-9818	290	4	-	-	PUNCT
ap-9818	290	5	quadratic	quadratic	ADJ
ap-9818	290	6	potential	potential	NOUN
ap-9818	290	7	without	without	ADP
ap-9818	290	8	confinement	confinement	NOUN
ap-9818	290	9	in	in	ADP
ap-9818	290	10	our	our	PRON
ap-9818	290	11	next	next	ADJ
ap-9818	290	12	example	example	NOUN
ap-9818	290	13	,	,	PUNCT
ap-9818	290	14	we	we	PRON
ap-9818	290	15	will	will	AUX
ap-9818	290	16	focus	focus	VERB
ap-9818	290	17	on	on	ADP
ap-9818	290	18	a	a	DET
ap-9818	290	19	system	system	NOUN
ap-9818	290	20	that	that	PRON
ap-9818	290	21	is	be	AUX
ap-9818	290	22	closely	closely	ADV
ap-9818	290	23	related	relate	VERB
ap-9818	290	24	to	to	ADP
ap-9818	290	25	the	the	DET
ap-9818	290	26	previous	previous	ADJ
ap-9818	290	27	one	one	NUM
ap-9818	290	28	.	.	PUNCT
ap-9818	291	1	in	in	ADP
ap-9818	291	2	particular	particular	ADJ
ap-9818	291	3	,	,	PUNCT
ap-9818	291	4	we	we	PRON
ap-9818	291	5	will	will	AUX
ap-9818	291	6	use	use	VERB
ap-9818	291	7	the	the	DET
ap-9818	291	8	same	same	ADJ
ap-9818	291	9	potential	potential	NOUN
ap-9818	291	10	,	,	PUNCT
ap-9818	291	11	but	but	CCONJ
ap-9818	291	12	modify	modify	VERB
ap-9818	291	13	the	the	DET
ap-9818	291	14	position	position	NOUN
ap-9818	291	15	-	-	PUNCT
ap-9818	291	16	dependent	dependent	ADJ
ap-9818	291	17	mass	mass	NOUN
ap-9818	291	18	,	,	PUNCT
ap-9818	291	19	such	such	ADJ
ap-9818	291	20	that	that	SCONJ
ap-9818	291	21	our	our	PRON
ap-9818	291	22	system	system	NOUN
ap-9818	291	23	is	be	AUX
ap-9818	291	24	defined	define	VERB
ap-9818	291	25	on	on	ADP
ap-9818	291	26	the	the	DET
ap-9818	291	27	whole	whole	ADJ
ap-9818	291	28	real	real	ADJ
ap-9818	291	29	line	line	NOUN
ap-9818	291	30	.	.	PUNCT
ap-9818	292	1	since	since	SCONJ
ap-9818	292	2	the	the	DET
ap-9818	292	3	approach	approach	NOUN
ap-9818	292	4	to	to	ADP
ap-9818	292	5	the	the	DET
ap-9818	292	6	present	present	ADJ
ap-9818	292	7	example	example	NOUN
ap-9818	292	8	is	be	AUX
ap-9818	292	9	the	the	DET
ap-9818	292	10	same	same	ADJ
ap-9818	292	11	as	as	ADP
ap-9818	292	12	for	for	ADP
ap-9818	292	13	the	the	DET
ap-9818	292	14	last	last	ADJ
ap-9818	292	15	case	case	NOUN
ap-9818	292	16	,	,	PUNCT
ap-9818	292	17	we	we	PRON
ap-9818	292	18	will	will	AUX
ap-9818	292	19	omit	omit	VERB
ap-9818	292	20	details	detail	NOUN
ap-9818	292	21	.	.	PUNCT
ap-9818	293	1	our	our	PRON
ap-9818	293	2	starting	starting	NOUN
ap-9818	293	3	point	point	NOUN
ap-9818	293	4	is	be	AUX
ap-9818	293	5	the	the	DET
ap-9818	293	6	position	position	NOUN
ap-9818	293	7	-	-	PUNCT
ap-9818	293	8	dependent	dependent	ADJ
ap-9818	293	9	mass	mass	NOUN
ap-9818	293	10	and	and	CCONJ
ap-9818	293	11	the	the	DET
ap-9818	293	12	potential	potential	NOUN
ap-9818	293	13	that	that	PRON
ap-9818	293	14	define	define	VERB
ap-9818	293	15	our	our	PRON
ap-9818	293	16	system	system	NOUN
ap-9818	293	17	.	.	PUNCT
ap-9818	294	1	these	these	DET
ap-9818	294	2	functions	function	NOUN
ap-9818	294	3	are	be	AUX
ap-9818	294	4	given	give	VERB
ap-9818	294	5	by	by	ADP
ap-9818	294	6	:	:	PUNCT
ap-9818	294	7	m(x	m(x	PROPN
ap-9818	294	8	)	)	PUNCT
ap-9818	294	9	=	=	SYM
ap-9818	294	10	1	1	NUM
ap-9818	294	11	1	1	NUM
ap-9818	294	12	+	+	NUM
ap-9818	294	13	x2	x2	PROPN
ap-9818	294	14	,	,	PUNCT
ap-9818	294	15	v	v	NOUN
ap-9818	294	16	(	(	PUNCT
ap-9818	294	17	x	x	NOUN
ap-9818	294	18	)	)	PUNCT
ap-9818	294	19	=	=	SYM
ap-9818	294	20	v1	v1	PROPN
ap-9818	294	21	x2	x2	NOUN
ap-9818	294	22	,	,	PUNCT
ap-9818	294	23	(	(	PUNCT
ap-9818	294	24	49	49	NUM
ap-9818	294	25	)	)	PUNCT
ap-9818	294	26	where	where	SCONJ
ap-9818	294	27	v1	v1	NOUN
ap-9818	294	28	is	be	AUX
ap-9818	294	29	a	a	DET
ap-9818	294	30	real	real	ADV
ap-9818	294	31	-	-	PUNCT
ap-9818	294	32	valued	value	VERB
ap-9818	294	33	coupling	coupling	NOUN
ap-9818	294	34	constant	constant	ADJ
ap-9818	294	35	.	.	PUNCT
ap-9818	295	1	the	the	DET
ap-9818	295	2	mass	mass	ADJ
ap-9818	295	3	profile	profile	NOUN
ap-9818	295	4	given	give	VERB
ap-9818	295	5	in	in	ADP
ap-9818	295	6	(	(	PUNCT
ap-9818	295	7	49	49	NUM
ap-9818	295	8	)	)	PUNCT
ap-9818	295	9	can	can	AUX
ap-9818	295	10	be	be	AUX
ap-9818	295	11	defined	define	VERB
ap-9818	295	12	on	on	ADP
ap-9818	295	13	the	the	DET
ap-9818	295	14	real	real	ADJ
ap-9818	295	15	line	line	NOUN
ap-9818	295	16	,	,	PUNCT
ap-9818	295	17	and	and	CCONJ
ap-9818	295	18	it	it	PRON
ap-9818	295	19	has	have	AUX
ap-9818	295	20	been	be	AUX
ap-9818	295	21	used	use	VERB
ap-9818	295	22	in	in	ADP
ap-9818	295	23	the	the	DET
ap-9818	295	24	literature	literature	NOUN
ap-9818	295	25	,	,	PUNCT
ap-9818	295	26	see	see	VERB
ap-9818	295	27	,	,	PUNCT
ap-9818	295	28	for	for	ADP
ap-9818	295	29	example	example	NOUN
ap-9818	295	30	,	,	PUNCT
ap-9818	296	1	[	[	X
ap-9818	296	2	30	30	NUM
ap-9818	296	3	]	]	PUNCT
ap-9818	296	4	and	and	CCONJ
ap-9818	296	5	references	reference	NOUN
ap-9818	296	6	therein	therein	ADV
ap-9818	296	7	.	.	PUNCT
ap-9818	297	1	in	in	ADP
ap-9818	297	2	the	the	DET
ap-9818	297	3	next	next	ADJ
ap-9818	297	4	step	step	NOUN
ap-9818	297	5	,	,	PUNCT
ap-9818	297	6	we	we	PRON
ap-9818	297	7	verify	verify	VERB
ap-9818	297	8	that	that	SCONJ
ap-9818	297	9	our	our	PRON
ap-9818	297	10	solvability	solvability	NOUN
ap-9818	297	11	conditions	condition	NOUN
ap-9818	297	12	are	be	AUX
ap-9818	297	13	fulfilled	fulfil	VERB
ap-9818	297	14	.	.	PUNCT
ap-9818	298	1	the	the	DET
ap-9818	298	2	first	first	ADJ
ap-9818	298	3	condition	condition	NOUN
ap-9818	298	4	(	(	PUNCT
ap-9818	298	5	17	17	NUM
ap-9818	298	6	)	)	PUNCT
ap-9818	298	7	can	can	AUX
ap-9818	298	8	be	be	AUX
ap-9818	298	9	satisfied	satisfy	VERB
ap-9818	298	10	by	by	ADP
ap-9818	298	11	setting	set	VERB
ap-9818	298	12	:	:	PUNCT
ap-9818	298	13	c1	c1	NOUN
ap-9818	298	14	=	=	SYM
ap-9818	298	15	−1	−1	NOUN
ap-9818	298	16	2	2	NUM
ap-9818	298	17	,	,	PUNCT
ap-9818	298	18	c2	c2	PROPN
ap-9818	298	19	=	=	SYM
ap-9818	298	20	−1	−1	PROPN
ap-9818	298	21	,	,	PUNCT
ap-9818	298	22	a	a	DET
ap-9818	298	23	=	=	SYM
ap-9818	298	24	1	1	NUM
ap-9818	298	25	,	,	PUNCT
ap-9818	298	26	b	b	NOUN
ap-9818	298	27	=	=	SYM
ap-9818	298	28	−2	−2	NOUN
ap-9818	298	29	,	,	PUNCT
ap-9818	298	30	(	(	PUNCT
ap-9818	298	31	50	50	NUM
ap-9818	298	32	)	)	PUNCT
ap-9818	298	33	229	229	NUM
ap-9818	298	34	axel	axel	PROPN
ap-9818	298	35	schulze	schulze	NOUN
ap-9818	298	36	-	-	PUNCT
ap-9818	298	37	halberg	halberg	PROPN
ap-9818	298	38	acta	acta	PROPN
ap-9818	298	39	polytechnica	polytechnica	PROPN
ap-9818	299	1	1.0	1.0	NUM
ap-9818	299	2	0.5	0.5	NUM
ap-9818	299	3	0.5	0.5	NUM
ap-9818	299	4	1.0	1.0	NUM
ap-9818	299	5	x	x	SYM
ap-9818	299	6	20	20	NUM
ap-9818	299	7	10	10	NUM
ap-9818	299	8	10	10	NUM
ap-9818	299	9	20	20	NUM
ap-9818	299	10	,	,	PUNCT
ap-9818	299	11	n(x	n(x	X
ap-9818	299	12	)	)	PUNCT
ap-9818	299	13	figure	figure	NOUN
ap-9818	299	14	1	1	NUM
ap-9818	299	15	.	.	PUNCT
ap-9818	300	1	graphs	graph	NOUN
ap-9818	300	2	of	of	ADP
ap-9818	300	3	odd	odd	ADJ
ap-9818	300	4	-	-	PUNCT
ap-9818	300	5	parity	parity	NOUN
ap-9818	300	6	(	(	PUNCT
ap-9818	300	7	δ	δ	NOUN
ap-9818	300	8	=	=	SYM
ap-9818	300	9	−1	−1	NOUN
ap-9818	300	10	)	)	PUNCT
ap-9818	300	11	solutions	solution	NOUN
ap-9818	300	12	(	(	PUNCT
ap-9818	300	13	46	46	NUM
ap-9818	300	14	)	)	PUNCT
ap-9818	300	15	for	for	ADP
ap-9818	300	16	the	the	DET
ap-9818	300	17	settings	setting	NOUN
ap-9818	300	18	v1	v1	VERB
ap-9818	300	19	=	=	SYM
ap-9818	300	20	−1	−1	NOUN
ap-9818	300	21	and	and	CCONJ
ap-9818	300	22	k	k	PROPN
ap-9818	300	23	=	=	SYM
ap-9818	300	24	−1	−1	NOUN
ap-9818	300	25	,	,	PUNCT
ap-9818	300	26	corresponding	correspond	VERB
ap-9818	300	27	to	to	ADP
ap-9818	300	28	ν	ν	X
ap-9818	300	29	=	=	SYM
ap-9818	300	30	1	1	NUM
ap-9818	300	31	4	4	NUM
ap-9818	300	32	.	.	PUNCT
ap-9818	301	1	the	the	DET
ap-9818	301	2	solutions	solution	NOUN
ap-9818	301	3	are	be	AUX
ap-9818	301	4	given	give	VERB
ap-9818	301	5	for	for	ADP
ap-9818	301	6	n	n	NOUN
ap-9818	301	7	=	=	SYM
ap-9818	301	8	1	1	NUM
ap-9818	301	9	(	(	PUNCT
ap-9818	301	10	black	black	ADJ
ap-9818	301	11	solid	solid	ADJ
ap-9818	301	12	curve	curve	NOUN
ap-9818	301	13	)	)	PUNCT
ap-9818	301	14	,	,	PUNCT
ap-9818	301	15	n	n	NOUN
ap-9818	301	16	=	=	SYM
ap-9818	301	17	2	2	NUM
ap-9818	301	18	(	(	PUNCT
ap-9818	301	19	gray	gray	ADJ
ap-9818	301	20	curve	curve	NOUN
ap-9818	301	21	)	)	PUNCT
ap-9818	301	22	,	,	PUNCT
ap-9818	301	23	n	n	NOUN
ap-9818	301	24	=	=	SYM
ap-9818	301	25	3	3	NUM
ap-9818	301	26	(	(	PUNCT
ap-9818	301	27	dashed	dash	VERB
ap-9818	301	28	curve	curve	NOUN
ap-9818	301	29	)	)	PUNCT
ap-9818	301	30	.	.	PUNCT
ap-9818	302	1	1.0	1.0	NUM
ap-9818	302	2	0.5	0.5	NUM
ap-9818	302	3	0.5	0.5	NUM
ap-9818	302	4	1.0	1.0	NUM
ap-9818	302	5	x	x	SYM
ap-9818	302	6	10	10	NUM
ap-9818	302	7	5	5	NUM
ap-9818	302	8	5	5	NUM
ap-9818	302	9	10	10	NUM
ap-9818	302	10	15	15	NUM
ap-9818	302	11	,	,	PUNCT
ap-9818	302	12	n(x	n(x	NOUN
ap-9818	302	13	)	)	PUNCT
ap-9818	302	14	figure	figure	NOUN
ap-9818	302	15	2	2	NUM
ap-9818	302	16	.	.	PUNCT
ap-9818	302	17	graphs	graph	NOUN
ap-9818	302	18	of	of	ADP
ap-9818	302	19	even	even	ADJ
ap-9818	302	20	-	-	PUNCT
ap-9818	302	21	parity	parity	NOUN
ap-9818	302	22	(	(	PUNCT
ap-9818	302	23	δ	δ	NOUN
ap-9818	302	24	=	=	SYM
ap-9818	302	25	1	1	X
ap-9818	302	26	)	)	PUNCT
ap-9818	302	27	solutions	solution	NOUN
ap-9818	302	28	(	(	PUNCT
ap-9818	302	29	46	46	NUM
ap-9818	302	30	)	)	PUNCT
ap-9818	302	31	for	for	ADP
ap-9818	302	32	the	the	DET
ap-9818	302	33	settings	setting	NOUN
ap-9818	302	34	v1	v1	VERB
ap-9818	302	35	=	=	SYM
ap-9818	302	36	−1	−1	NOUN
ap-9818	302	37	and	and	CCONJ
ap-9818	302	38	k	k	NOUN
ap-9818	302	39	=	=	SYM
ap-9818	302	40	1	1	NUM
ap-9818	302	41	,	,	PUNCT
ap-9818	302	42	corresponding	correspond	VERB
ap-9818	302	43	to	to	ADP
ap-9818	302	44	ν	ν	X
ap-9818	302	45	=	=	PUNCT
ap-9818	302	46	−	−	PROPN
ap-9818	302	47	1	1	NUM
ap-9818	302	48	4	4	NUM
ap-9818	302	49	.	.	PUNCT
ap-9818	303	1	the	the	DET
ap-9818	303	2	solutions	solution	NOUN
ap-9818	303	3	are	be	AUX
ap-9818	303	4	given	give	VERB
ap-9818	303	5	for	for	ADP
ap-9818	303	6	n	n	NOUN
ap-9818	303	7	=	=	SYM
ap-9818	303	8	1	1	NUM
ap-9818	303	9	(	(	PUNCT
ap-9818	303	10	black	black	ADJ
ap-9818	303	11	solid	solid	ADJ
ap-9818	303	12	curve	curve	NOUN
ap-9818	303	13	)	)	PUNCT
ap-9818	303	14	,	,	PUNCT
ap-9818	303	15	n	n	NOUN
ap-9818	303	16	=	=	SYM
ap-9818	303	17	2	2	NUM
ap-9818	303	18	(	(	PUNCT
ap-9818	303	19	gray	gray	ADJ
ap-9818	303	20	curve	curve	NOUN
ap-9818	303	21	)	)	PUNCT
ap-9818	303	22	,	,	PUNCT
ap-9818	303	23	n	n	NOUN
ap-9818	303	24	=	=	SYM
ap-9818	303	25	3	3	NUM
ap-9818	303	26	(	(	PUNCT
ap-9818	303	27	dashed	dash	VERB
ap-9818	303	28	curve	curve	NOUN
ap-9818	303	29	)	)	PUNCT
ap-9818	303	30	.	.	PUNCT
ap-9818	304	1	while	while	SCONJ
ap-9818	304	2	the	the	DET
ap-9818	304	3	second	second	ADJ
ap-9818	304	4	condition	condition	NOUN
ap-9818	304	5	(	(	PUNCT
ap-9818	304	6	19	19	NUM
ap-9818	304	7	)	)	PUNCT
ap-9818	304	8	in	in	ADP
ap-9818	304	9	combination	combination	NOUN
ap-9818	304	10	with	with	ADP
ap-9818	304	11	(	(	PUNCT
ap-9818	304	12	49	49	NUM
ap-9818	304	13	)	)	PUNCT
ap-9818	304	14	takes	take	VERB
ap-9818	304	15	the	the	DET
ap-9818	304	16	form	form	NOUN
ap-9818	304	17	:	:	PUNCT
ap-9818	304	18	v1	v1	NOUN
ap-9818	304	19	x2	x2	NOUN
ap-9818	305	1	=	=	PUNCT
ap-9818	305	2	c	c	X
ap-9818	305	3	(	(	PUNCT
ap-9818	305	4	1	1	NUM
ap-9818	305	5	+	+	NUM
ap-9818	305	6	x2	x2	ADJ
ap-9818	305	7	)	)	PUNCT
ap-9818	306	1	x2	x2	PROPN
ap-9818	307	1	+	+	CCONJ
ap-9818	307	2	w	w	PROPN
ap-9818	307	3	(	(	PUNCT
ap-9818	307	4	x	x	NOUN
ap-9818	307	5	)	)	PUNCT
ap-9818	307	6	=	=	PUNCT
ap-9818	308	1	c	c	X
ap-9818	308	2	x2	x2	NOUN
ap-9818	309	1	+	+	NUM
ap-9818	309	2	c	c	PROPN
ap-9818	310	1	+	+	CCONJ
ap-9818	310	2	w	w	PROPN
ap-9818	310	3	(	(	PUNCT
ap-9818	310	4	x	x	NOUN
ap-9818	310	5	)	)	PUNCT
ap-9818	310	6	.	.	PUNCT
ap-9818	311	1	(	(	PUNCT
ap-9818	311	2	51	51	NUM
ap-9818	311	3	)	)	PUNCT
ap-9818	311	4	we	we	PRON
ap-9818	311	5	choose	choose	VERB
ap-9818	311	6	w	w	NOUN
ap-9818	311	7	=	=	NOUN
ap-9818	311	8	−c	−c	NOUN
ap-9818	311	9	and	and	CCONJ
ap-9818	311	10	c	c	NOUN
ap-9818	311	11	=	=	SYM
ap-9818	311	12	v1	v1	PROPN
ap-9818	311	13	to	to	PART
ap-9818	311	14	comply	comply	VERB
ap-9818	311	15	with	with	ADP
ap-9818	311	16	this	this	DET
ap-9818	311	17	condition	condition	NOUN
ap-9818	311	18	.	.	PUNCT
ap-9818	312	1	consequently	consequently	ADV
ap-9818	312	2	,	,	PUNCT
ap-9818	312	3	the	the	DET
ap-9818	312	4	effective	effective	ADJ
ap-9818	312	5	potentials	potential	NOUN
ap-9818	312	6	for	for	ADP
ap-9818	312	7	the	the	DET
ap-9818	312	8	dunkl	dunkl	PROPN
ap-9818	312	9	case	case	NOUN
ap-9818	312	10	(	(	PUNCT
ap-9818	312	11	20	20	NUM
ap-9818	312	12	)	)	PUNCT
ap-9818	312	13	,	,	PUNCT
ap-9818	312	14	and	and	CCONJ
ap-9818	312	15	for	for	ADP
ap-9818	312	16	the	the	DET
ap-9818	312	17	conventional	conventional	ADJ
ap-9818	312	18	scenario	scenario	NOUN
ap-9818	312	19	(	(	PUNCT
ap-9818	312	20	15	15	NUM
ap-9818	312	21	)	)	PUNCT
ap-9818	312	22	must	must	AUX
ap-9818	312	23	have	have	VERB
ap-9818	312	24	the	the	DET
ap-9818	312	25	same	same	ADJ
ap-9818	312	26	functional	functional	ADJ
ap-9818	312	27	form	form	NOUN
ap-9818	312	28	.	.	PUNCT
ap-9818	313	1	substituting	substitute	VERB
ap-9818	313	2	the	the	DET
ap-9818	313	3	present	present	ADJ
ap-9818	313	4	settings	setting	NOUN
ap-9818	313	5	(	(	PUNCT
ap-9818	313	6	49	49	NUM
ap-9818	313	7	)	)	PUNCT
ap-9818	313	8	for	for	ADP
ap-9818	313	9	(	(	PUNCT
ap-9818	313	10	20	20	NUM
ap-9818	313	11	):	):	PUNCT
ap-9818	313	12	uν(x	uν(x	NUM
ap-9818	313	13	)	)	PUNCT
ap-9818	313	14	=	=	SYM
ap-9818	313	15	1	1	NUM
ap-9818	313	16	x2	x2	NOUN
ap-9818	313	17	(	(	PUNCT
ap-9818	313	18	1	1	NUM
ap-9818	313	19	+	+	NUM
ap-9818	313	20	x2	x2	NOUN
ap-9818	313	21	)	)	PUNCT
ap-9818	313	22	{	{	PUNCT
ap-9818	313	23	−	−	PROPN
ap-9818	313	24	v1	v1	PROPN
ap-9818	313	25	+	+	CCONJ
ap-9818	313	26	δ	δ	NOUN
ap-9818	313	27	ν	ν	NOUN
ap-9818	313	28	−	−	NOUN
ap-9818	313	29	ν2	ν2	NOUN
ap-9818	313	30	+	+	CCONJ
ap-9818	313	31	x2	x2	NOUN
ap-9818	314	1	[	[	X
ap-9818	314	2	−1	−1	NOUN
ap-9818	314	3	+	+	NOUN
ap-9818	314	4	e	e	NOUN
ap-9818	314	5	−	−	PROPN
ap-9818	314	6	v1	v1	NOUN
ap-9818	314	7	−	−	PROPN
ap-9818	314	8	α	α	NOUN
ap-9818	314	9	−	−	NOUN
ap-9818	314	10	γ	γ	NOUN
ap-9818	314	11	−	−	PROPN
ap-9818	314	12	2	2	NUM
ap-9818	314	13	δ	δ	NOUN
ap-9818	314	14	ν	ν	X
ap-9818	314	15	(	(	PUNCT
ap-9818	314	16	α	α	NOUN
ap-9818	314	17	+	+	X
ap-9818	314	18	γ	γ	X
ap-9818	314	19	)	)	PUNCT
ap-9818	314	20	−	−	PROPN
ap-9818	314	21	2	2	NUM
ap-9818	314	22	ν2	ν2	NOUN
ap-9818	314	23	]	]	PUNCT
ap-9818	314	24	+	+	CCONJ
ap-9818	314	25	x4	x4	PROPN
ap-9818	315	1	[	[	X
ap-9818	315	2	e	e	X
ap-9818	315	3	−	−	PROPN
ap-9818	315	4	δ	δ	PROPN
ap-9818	315	5	ν	ν	NOUN
ap-9818	315	6	−	−	PROPN
ap-9818	315	7	ν2	ν2	NOUN
ap-9818	315	8	−	−	PROPN
ap-9818	315	9	γ	γ	X
ap-9818	315	10	(	(	PUNCT
ap-9818	315	11	1	1	NUM
ap-9818	315	12	+	+	SYM
ap-9818	315	13	2	2	NUM
ap-9818	315	14	δ	δ	PROPN
ap-9818	315	15	ν	ν	PROPN
ap-9818	315	16	)	)	PUNCT
ap-9818	315	17	−	−	PROPN
ap-9818	315	18	α	α	INTJ
ap-9818	315	19	(	(	PUNCT
ap-9818	315	20	1	1	NUM
ap-9818	315	21	+	+	SYM
ap-9818	315	22	4	4	NUM
ap-9818	315	23	γ	γ	NOUN
ap-9818	315	24	+	+	CCONJ
ap-9818	315	25	2	2	NUM
ap-9818	315	26	δ	δ	PROPN
ap-9818	315	27	ν	ν	PROPN
ap-9818	315	28	)	)	PUNCT
ap-9818	315	29	]	]	PUNCT
ap-9818	315	30	}	}	PUNCT
ap-9818	315	31	.	.	PUNCT
ap-9818	316	1	(	(	PUNCT
ap-9818	316	2	52	52	NUM
ap-9818	316	3	)	)	PUNCT
ap-9818	316	4	similarly	similarly	ADV
ap-9818	316	5	,	,	PUNCT
ap-9818	316	6	the	the	DET
ap-9818	316	7	effective	effective	ADJ
ap-9818	316	8	potential	potential	NOUN
ap-9818	316	9	for	for	ADP
ap-9818	316	10	the	the	DET
ap-9818	316	11	conventional	conventional	ADJ
ap-9818	316	12	case	case	NOUN
ap-9818	316	13	reads	read	VERB
ap-9818	316	14	:	:	PUNCT
ap-9818	316	15	u0(x	u0(x	NUM
ap-9818	316	16	)	)	PUNCT
ap-9818	316	17	=	=	SYM
ap-9818	316	18	1	1	NUM
ap-9818	316	19	x2	x2	NOUN
ap-9818	316	20	(	(	PUNCT
ap-9818	316	21	1	1	NUM
ap-9818	316	22	+	+	NUM
ap-9818	316	23	x2	x2	NOUN
ap-9818	316	24	)	)	PUNCT
ap-9818	316	25	{	{	PUNCT
ap-9818	316	26	−	−	PROPN
ap-9818	316	27	v1	v1	PROPN
ap-9818	316	28	+	+	CCONJ
ap-9818	316	29	x2	x2	PROPN
ap-9818	316	30	(	(	PUNCT
ap-9818	316	31	−1	−1	NOUN
ap-9818	316	32	+	+	CCONJ
ap-9818	316	33	e	e	NOUN
ap-9818	316	34	−	−	PROPN
ap-9818	316	35	v1	v1	NOUN
ap-9818	316	36	−	−	PROPN
ap-9818	316	37	α	α	NOUN
ap-9818	316	38	−	−	PROPN
ap-9818	316	39	γ	γ	X
ap-9818	316	40	)	)	PUNCT
ap-9818	316	41	+	+	CCONJ
ap-9818	316	42	x4	x4	PROPN
ap-9818	316	43	(	(	PUNCT
ap-9818	316	44	e	e	NOUN
ap-9818	316	45	−	−	PROPN
ap-9818	316	46	α	α	NOUN
ap-9818	316	47	−	−	NOUN
ap-9818	316	48	γ	γ	NOUN
ap-9818	316	49	−	−	PROPN
ap-9818	316	50	4	4	NUM
ap-9818	316	51	α	α	PROPN
ap-9818	316	52	γ	γ	NOUN
ap-9818	316	53	)	)	PUNCT
ap-9818	316	54	}	}	PUNCT
ap-9818	316	55	.	.	PUNCT
ap-9818	317	1	(	(	PUNCT
ap-9818	317	2	53	53	NUM
ap-9818	317	3	)	)	PUNCT
ap-9818	317	4	comparison	comparison	NOUN
ap-9818	317	5	of	of	ADP
ap-9818	317	6	the	the	DET
ap-9818	317	7	two	two	NUM
ap-9818	317	8	functions	function	NOUN
ap-9818	317	9	(	(	PUNCT
ap-9818	317	10	52	52	NUM
ap-9818	317	11	)	)	PUNCT
ap-9818	317	12	and	and	CCONJ
ap-9818	317	13	(	(	PUNCT
ap-9818	317	14	53	53	NUM
ap-9818	317	15	)	)	PUNCT
ap-9818	317	16	shows	show	VERB
ap-9818	317	17	that	that	SCONJ
ap-9818	317	18	they	they	PRON
ap-9818	317	19	have	have	VERB
ap-9818	317	20	the	the	DET
ap-9818	317	21	same	same	ADJ
ap-9818	317	22	functional	functional	ADJ
ap-9818	317	23	form	form	NOUN
ap-9818	317	24	.	.	PUNCT
ap-9818	318	1	for	for	ADP
ap-9818	318	2	the	the	DET
ap-9818	318	3	sake	sake	NOUN
ap-9818	318	4	of	of	ADP
ap-9818	318	5	simplicity	simplicity	NOUN
ap-9818	318	6	let	let	VERB
ap-9818	318	7	us	we	PRON
ap-9818	318	8	now	now	ADV
ap-9818	318	9	set	set	VERB
ap-9818	318	10	α	α	NOUN
ap-9818	318	11	=	=	SYM
ap-9818	318	12	γ	γ	X
ap-9818	318	13	=	=	SYM
ap-9818	318	14	−	−	PROPN
ap-9818	318	15	1	1	NUM
ap-9818	318	16	2	2	NUM
ap-9818	318	17	.	.	PUNCT
ap-9818	319	1	substitution	substitution	NOUN
ap-9818	319	2	of	of	ADP
ap-9818	319	3	the	the	DET
ap-9818	319	4	resulting	result	VERB
ap-9818	319	5	effective	effective	ADJ
ap-9818	319	6	potential	potential	NOUN
ap-9818	319	7	(	(	PUNCT
ap-9818	319	8	52	52	NUM
ap-9818	319	9	)	)	PUNCT
ap-9818	319	10	renders	render	VERB
ap-9818	319	11	the	the	DET
ap-9818	319	12	reduced	reduce	VERB
ap-9818	319	13	dunkl	dunkl	NOUN
ap-9818	319	14	-	-	PUNCT
ap-9818	319	15	schrödinger	schrödinger	NOUN
ap-9818	319	16	equation	equation	NOUN
ap-9818	319	17	(	(	PUNCT
ap-9818	319	18	36	36	NUM
ap-9818	319	19	)	)	PUNCT
ap-9818	319	20	in	in	ADP
ap-9818	319	21	the	the	DET
ap-9818	319	22	form	form	NOUN
ap-9818	319	23	:	:	PUNCT
ap-9818	319	24	ξ′′	ξ′′	PROPN
ap-9818	319	25	ν	ν	X
ap-9818	319	26	(	(	PUNCT
ap-9818	319	27	x	x	X
ap-9818	319	28	)	)	PUNCT
ap-9818	320	1	+	+	CCONJ
ap-9818	320	2	(	(	PUNCT
ap-9818	320	3	e	e	X
ap-9818	320	4	+	+	NOUN
ap-9818	320	5	v1	v1	VERB
ap-9818	320	6	x2	x2	NOUN
ap-9818	321	1	+	+	CCONJ
ap-9818	321	2	1	1	NUM
ap-9818	321	3	+	+	NUM
ap-9818	321	4	δ	δ	PROPN
ap-9818	321	5	ν	ν	NOUN
ap-9818	321	6	−	−	PROPN
ap-9818	321	7	ν2	ν2	NOUN
ap-9818	321	8	−	−	PROPN
ap-9818	321	9	v1	v1	PROPN
ap-9818	321	10	x2	x2	PROPN
ap-9818	321	11	)	)	PUNCT
ap-9818	321	12	ξν(x	ξν(x	NUM
ap-9818	321	13	)	)	PUNCT
ap-9818	322	1	=	=	SYM
ap-9818	322	2	0	0	NUM
ap-9818	322	3	,	,	PUNCT
ap-9818	322	4	(	(	PUNCT
ap-9818	322	5	54	54	NUM
ap-9818	322	6	)	)	PUNCT
ap-9818	322	7	230	230	NUM
ap-9818	322	8	vol	vol	NOUN
ap-9818	322	9	.	.	PUNCT
ap-9818	323	1	65	65	NUM
ap-9818	323	2	no	no	NOUN
ap-9818	323	3	.	.	PUNCT
ap-9818	324	1	2/2025	2/2025	NUM
ap-9818	324	2	persistence	persistence	NOUN
ap-9818	324	3	of	of	ADP
ap-9818	324	4	solvability	solvability	NOUN
ap-9818	324	5	in	in	ADP
ap-9818	324	6	quantum	quantum	NOUN
ap-9818	324	7	systems	system	NOUN
ap-9818	324	8	deformed	deform	VERB
ap-9818	324	9	by	by	ADP
ap-9818	324	10	dunkl	dunkl	PROPN
ap-9818	324	11	.	.	PUNCT
ap-9818	324	12	.	.	PUNCT
ap-9818	324	13	.	.	PUNCT
ap-9818	325	1	while	while	SCONJ
ap-9818	325	2	its	its	PRON
ap-9818	325	3	conventional	conventional	ADJ
ap-9818	325	4	partner	partner	NOUN
ap-9818	325	5	reads	read	VERB
ap-9818	325	6	:	:	PUNCT
ap-9818	325	7	ξ′′	ξ′′	NOUN
ap-9818	325	8	0	0	PUNCT
ap-9818	325	9	(	(	PUNCT
ap-9818	325	10	x	x	X
ap-9818	325	11	)	)	PUNCT
ap-9818	325	12	+	+	CCONJ
ap-9818	325	13	(	(	PUNCT
ap-9818	325	14	e	e	X
ap-9818	325	15	+	+	NOUN
ap-9818	325	16	v1	v1	VERB
ap-9818	325	17	x2	x2	NOUN
ap-9818	326	1	+	+	CCONJ
ap-9818	326	2	1	1	NUM
ap-9818	326	3	−	−	NOUN
ap-9818	326	4	v1	v1	PROPN
ap-9818	326	5	x2	x2	PROPN
ap-9818	326	6	)	)	PUNCT
ap-9818	326	7	ξ0(x	ξ0(x	PROPN
ap-9818	326	8	)	)	PUNCT
ap-9818	326	9	=	=	NOUN
ap-9818	326	10	0	0	X
ap-9818	326	11	.	.	PUNCT
ap-9818	327	1	(	(	PUNCT
ap-9818	327	2	55	55	NUM
ap-9818	327	3	)	)	PUNCT
ap-9818	327	4	upon	upon	SCONJ
ap-9818	327	5	comparing	compare	VERB
ap-9818	327	6	(	(	PUNCT
ap-9818	327	7	54	54	NUM
ap-9818	327	8	)	)	PUNCT
ap-9818	327	9	with	with	ADP
ap-9818	327	10	its	its	PRON
ap-9818	327	11	counterpart	counterpart	NOUN
ap-9818	327	12	from	from	ADP
ap-9818	327	13	the	the	DET
ap-9818	327	14	previous	previous	ADJ
ap-9818	327	15	example	example	NOUN
ap-9818	327	16	(	(	PUNCT
ap-9818	327	17	36	36	NUM
ap-9818	327	18	)	)	PUNCT
ap-9818	327	19	,	,	PUNCT
ap-9818	327	20	we	we	PRON
ap-9818	327	21	see	see	VERB
ap-9818	327	22	that	that	SCONJ
ap-9818	327	23	the	the	DET
ap-9818	327	24	sign	sign	NOUN
ap-9818	327	25	of	of	ADP
ap-9818	327	26	v1	v1	NOUN
ap-9818	327	27	in	in	ADP
ap-9818	327	28	the	the	DET
ap-9818	327	29	term	term	NOUN
ap-9818	327	30	∼	∼	NOUN
ap-9818	327	31	x−2	x−2	PROPN
ap-9818	327	32	has	have	AUX
ap-9818	327	33	changed	change	VERB
ap-9818	327	34	.	.	PUNCT
ap-9818	328	1	as	as	ADP
ap-9818	328	2	a	a	DET
ap-9818	328	3	consequence	consequence	NOUN
ap-9818	328	4	,	,	PUNCT
ap-9818	328	5	for	for	ADP
ap-9818	328	6	the	the	DET
ap-9818	328	7	existence	existence	NOUN
ap-9818	328	8	of	of	ADP
ap-9818	328	9	bound	bound	ADJ
ap-9818	328	10	states	state	NOUN
ap-9818	328	11	the	the	DET
ap-9818	328	12	condition	condition	NOUN
ap-9818	328	13	:	:	PUNCT
ap-9818	328	14	δ	δ	X
ap-9818	328	15	ν	ν	ADP
ap-9818	328	16	−	−	PROPN
ap-9818	328	17	ν2	ν2	NOUN
ap-9818	328	18	−	−	PROPN
ap-9818	328	19	v1	v1	PROPN
ap-9818	328	20	<	<	X
ap-9818	328	21	0	0	NUM
ap-9818	328	22	,	,	PUNCT
ap-9818	328	23	(	(	PUNCT
ap-9818	328	24	56	56	NUM
ap-9818	328	25	)	)	PUNCT
ap-9818	328	26	must	must	AUX
ap-9818	328	27	be	be	AUX
ap-9818	328	28	satisfied	satisfied	ADJ
ap-9818	328	29	.	.	PUNCT
ap-9818	329	1	while	while	SCONJ
ap-9818	329	2	in	in	ADP
ap-9818	329	3	the	the	DET
ap-9818	329	4	previous	previous	ADJ
ap-9818	329	5	example	example	NOUN
ap-9818	329	6	this	this	PRON
ap-9818	329	7	required	require	VERB
ap-9818	329	8	negative	negative	ADJ
ap-9818	329	9	values	value	NOUN
ap-9818	329	10	of	of	ADP
ap-9818	329	11	v1	v1	NOUN
ap-9818	329	12	,	,	PUNCT
ap-9818	329	13	in	in	ADP
ap-9818	329	14	the	the	DET
ap-9818	329	15	present	present	ADJ
ap-9818	329	16	case	case	NOUN
ap-9818	329	17	v1	v1	NOUN
ap-9818	329	18	must	must	AUX
ap-9818	329	19	be	be	AUX
ap-9818	329	20	positive	positive	ADJ
ap-9818	329	21	.	.	PUNCT
ap-9818	330	1	the	the	DET
ap-9818	330	2	general	general	ADJ
ap-9818	330	3	solution	solution	NOUN
ap-9818	330	4	of	of	ADP
ap-9818	330	5	(	(	PUNCT
ap-9818	330	6	55	55	NUM
ap-9818	330	7	)	)	PUNCT
ap-9818	330	8	is	be	AUX
ap-9818	330	9	very	very	ADV
ap-9818	330	10	similar	similar	ADJ
ap-9818	330	11	to	to	ADP
ap-9818	330	12	(	(	PUNCT
ap-9818	330	13	39	39	NUM
ap-9818	330	14	)	)	PUNCT
ap-9818	330	15	.	.	PUNCT
ap-9818	331	1	we	we	PRON
ap-9818	331	2	find	find	VERB
ap-9818	331	3	:	:	PUNCT
ap-9818	331	4	ξ0,gen(x	ξ0,gen(x	NUM
ap-9818	331	5	)	)	PUNCT
ap-9818	332	1	=	=	SYM
ap-9818	332	2	c1	c1	NOUN
ap-9818	332	3	x	x	NOUN
ap-9818	332	4	1	1	NUM
ap-9818	332	5	2	2	NUM
ap-9818	332	6	−	−	PROPN
ap-9818	332	7	g2	g2	PROPN
ap-9818	332	8	2	2	NUM
ap-9818	332	9	2f1	2f1	NUM
ap-9818	332	10	(	(	PUNCT
ap-9818	332	11	−g1	−g1	VERB
ap-9818	332	12	4	4	NUM
ap-9818	332	13	−	−	PROPN
ap-9818	332	14	g2	g2	PROPN
ap-9818	332	15	4	4	NUM
ap-9818	332	16	,	,	PUNCT
ap-9818	332	17	g1	g1	VERB
ap-9818	332	18	4	4	NUM
ap-9818	332	19	−	−	NOUN
ap-9818	332	20	g2	g2	PROPN
ap-9818	332	21	4	4	NUM
ap-9818	332	22	,	,	PUNCT
ap-9818	332	23	1	1	NUM
ap-9818	332	24	−	−	PROPN
ap-9818	332	25	g2	g2	PROPN
ap-9818	332	26	2	2	NUM
ap-9818	332	27	,	,	PUNCT
ap-9818	332	28	−x2	−x2	PROPN
ap-9818	332	29	)	)	PUNCT
ap-9818	333	1	+	+	CCONJ
ap-9818	333	2	c2	c2	PROPN
ap-9818	333	3	x	x	SYM
ap-9818	333	4	1	1	NUM
ap-9818	333	5	2	2	NUM
ap-9818	333	6	+	+	CCONJ
ap-9818	333	7	g2	g2	PROPN
ap-9818	333	8	2	2	NUM
ap-9818	333	9	2f1	2f1	NUM
ap-9818	333	10	(	(	PUNCT
ap-9818	333	11	−g1	−g1	VERB
ap-9818	333	12	4	4	NUM
ap-9818	333	13	+	+	CCONJ
ap-9818	333	14	g2	g2	PROPN
ap-9818	333	15	4	4	NUM
ap-9818	333	16	,	,	PUNCT
ap-9818	333	17	g1	g1	VERB
ap-9818	333	18	4	4	NUM
ap-9818	333	19	+	+	NUM
ap-9818	333	20	g2	g2	PROPN
ap-9818	333	21	4	4	NUM
ap-9818	333	22	,	,	PUNCT
ap-9818	333	23	1	1	NUM
ap-9818	333	24	+	+	CCONJ
ap-9818	333	25	g2	g2	PROPN
ap-9818	333	26	2	2	NUM
ap-9818	333	27	,	,	PUNCT
ap-9818	333	28	−x2	−x2	PROPN
ap-9818	333	29	)	)	PUNCT
ap-9818	333	30	,	,	PUNCT
ap-9818	333	31	(	(	PUNCT
ap-9818	333	32	57	57	NUM
ap-9818	333	33	)	)	PUNCT
ap-9818	333	34	where	where	SCONJ
ap-9818	333	35	the	the	DET
ap-9818	333	36	constants	constant	NOUN
ap-9818	333	37	g1	g1	PROPN
ap-9818	333	38	and	and	CCONJ
ap-9818	333	39	g2	g2	PROPN
ap-9818	333	40	stand	stand	VERB
ap-9818	333	41	for	for	ADP
ap-9818	333	42	:	:	PUNCT
ap-9818	333	43	g1	g1	PROPN
ap-9818	333	44	=	=	SYM
ap-9818	334	1	√	√	ADV
ap-9818	334	2	1	1	NUM
ap-9818	334	3	−	−	PROPN
ap-9818	334	4	4	4	NUM
ap-9818	334	5	e	e	NOUN
ap-9818	334	6	,	,	PUNCT
ap-9818	334	7	g2	g2	PROPN
ap-9818	334	8	=	=	PUNCT
ap-9818	335	1	√	√	ADV
ap-9818	335	2	1	1	NUM
ap-9818	336	1	+	+	CCONJ
ap-9818	336	2	4	4	NUM
ap-9818	336	3	v1	v1	NOUN
ap-9818	336	4	.	.	PUNCT
ap-9818	337	1	(	(	PUNCT
ap-9818	337	2	58	58	X
ap-9818	337	3	)	)	PUNCT
ap-9818	337	4	we	we	PRON
ap-9818	337	5	can	can	AUX
ap-9818	337	6	now	now	ADV
ap-9818	337	7	reparametrise	reparametrise	VERB
ap-9818	337	8	the	the	DET
ap-9818	337	9	effective	effective	ADJ
ap-9818	337	10	potential	potential	NOUN
ap-9818	337	11	in	in	ADP
ap-9818	337	12	equation	equation	NOUN
ap-9818	337	13	(	(	PUNCT
ap-9818	337	14	55	55	NUM
ap-9818	337	15	)	)	PUNCT
ap-9818	337	16	in	in	ADP
ap-9818	337	17	order	order	NOUN
ap-9818	337	18	to	to	PART
ap-9818	337	19	construct	construct	VERB
ap-9818	337	20	the	the	DET
ap-9818	337	21	general	general	ADJ
ap-9818	337	22	solution	solution	NOUN
ap-9818	337	23	of	of	ADP
ap-9818	337	24	(	(	PUNCT
ap-9818	337	25	54	54	NUM
ap-9818	337	26	)	)	PUNCT
ap-9818	337	27	.	.	PUNCT
ap-9818	338	1	this	this	PRON
ap-9818	338	2	gives	give	VERB
ap-9818	338	3	:	:	PUNCT
ap-9818	338	4	ξν	ξν	ADV
ap-9818	338	5	,	,	PUNCT
ap-9818	338	6	gen(x	gen(x	NOUN
ap-9818	338	7	)	)	PUNCT
ap-9818	338	8	=	=	SYM
ap-9818	338	9	c1	c1	NOUN
ap-9818	338	10	x	x	NOUN
ap-9818	338	11	1	1	NUM
ap-9818	338	12	2	2	NUM
ap-9818	338	13	−	−	NOUN
ap-9818	338	14	f2	f2	PROPN
ap-9818	338	15	2	2	NUM
ap-9818	338	16	2f1	2f1	NUM
ap-9818	338	17	(	(	PUNCT
ap-9818	338	18	−f1	−f1	PROPN
ap-9818	338	19	4	4	NUM
ap-9818	338	20	−	−	NOUN
ap-9818	338	21	f2	f2	PROPN
ap-9818	338	22	4	4	NUM
ap-9818	338	23	,	,	PUNCT
ap-9818	338	24	f1	f1	NOUN
ap-9818	338	25	4	4	NUM
ap-9818	338	26	−	−	NOUN
ap-9818	338	27	f2	f2	PROPN
ap-9818	338	28	4	4	NUM
ap-9818	338	29	,	,	PUNCT
ap-9818	338	30	1	1	NUM
ap-9818	338	31	−	−	NOUN
ap-9818	338	32	f2	f2	PROPN
ap-9818	338	33	2	2	NUM
ap-9818	338	34	,	,	PUNCT
ap-9818	338	35	−x2	−x2	PROPN
ap-9818	338	36	)	)	PUNCT
ap-9818	339	1	+	+	CCONJ
ap-9818	339	2	c2	c2	PROPN
ap-9818	339	3	x	x	SYM
ap-9818	339	4	1	1	NUM
ap-9818	339	5	2	2	NUM
ap-9818	339	6	+	+	SYM
ap-9818	339	7	f2	f2	PROPN
ap-9818	339	8	2	2	NUM
ap-9818	339	9	2f1	2f1	NUM
ap-9818	339	10	(	(	PUNCT
ap-9818	339	11	−f1	−f1	PROPN
ap-9818	339	12	4	4	NUM
ap-9818	339	13	+	+	CCONJ
ap-9818	339	14	f2	f2	PROPN
ap-9818	339	15	4	4	NUM
ap-9818	339	16	,	,	PUNCT
ap-9818	339	17	f1	f1	NOUN
ap-9818	339	18	4	4	NUM
ap-9818	339	19	+	+	SYM
ap-9818	339	20	f2	f2	PROPN
ap-9818	339	21	4	4	NUM
ap-9818	339	22	,	,	PUNCT
ap-9818	339	23	1	1	NUM
ap-9818	339	24	+	+	CCONJ
ap-9818	339	25	f2	f2	PROPN
ap-9818	339	26	2	2	NUM
ap-9818	339	27	,	,	PUNCT
ap-9818	339	28	−x2	−x2	PROPN
ap-9818	339	29	)	)	PUNCT
ap-9818	339	30	,	,	PUNCT
ap-9818	339	31	(	(	PUNCT
ap-9818	339	32	59	59	NUM
ap-9818	339	33	)	)	PUNCT
ap-9818	339	34	with	with	ADP
ap-9818	339	35	the	the	DET
ap-9818	339	36	abbreviations	abbreviation	NOUN
ap-9818	339	37	:	:	PUNCT
ap-9818	339	38	f1	f1	NOUN
ap-9818	339	39	=	=	SYM
ap-9818	339	40	√	√	ADP
ap-9818	339	41	1	1	NUM
ap-9818	339	42	−	−	PROPN
ap-9818	339	43	4	4	NUM
ap-9818	339	44	e	e	NOUN
ap-9818	339	45	+	+	CCONJ
ap-9818	339	46	4	4	NUM
ap-9818	339	47	ν	ν	NOUN
ap-9818	339	48	(	(	PUNCT
ap-9818	339	49	ν	ν	X
ap-9818	339	50	−	−	PROPN
ap-9818	339	51	δ	δ	PROPN
ap-9818	339	52	)	)	PUNCT
ap-9818	339	53	,	,	PUNCT
ap-9818	339	54	f2	f2	PROPN
ap-9818	339	55	=	=	NOUN
ap-9818	339	56	√	√	ADP
ap-9818	339	57	1	1	NUM
ap-9818	339	58	+	+	CCONJ
ap-9818	339	59	4	4	NUM
ap-9818	339	60	v1	v1	NOUN
ap-9818	339	61	+	+	CCONJ
ap-9818	339	62	4	4	NUM
ap-9818	339	63	ν	ν	NOUN
ap-9818	339	64	(	(	PUNCT
ap-9818	339	65	ν	ν	X
ap-9818	339	66	−	−	PROPN
ap-9818	339	67	δ	δ	PROPN
ap-9818	339	68	)	)	PUNCT
ap-9818	339	69	.	.	PUNCT
ap-9818	340	1	(	(	PUNCT
ap-9818	340	2	60	60	NUM
ap-9818	340	3	)	)	PUNCT
ap-9818	340	4	hence	hence	ADV
ap-9818	340	5	,	,	PUNCT
ap-9818	340	6	the	the	DET
ap-9818	340	7	general	general	ADJ
ap-9818	340	8	solution	solution	NOUN
ap-9818	340	9	of	of	ADP
ap-9818	340	10	the	the	DET
ap-9818	340	11	dunkl	dunkl	NOUN
ap-9818	340	12	-	-	PUNCT
ap-9818	340	13	schrödinger	schrödinger	NOUN
ap-9818	340	14	equation	equation	NOUN
ap-9818	340	15	(	(	PUNCT
ap-9818	340	16	6	6	NUM
ap-9818	340	17	)	)	PUNCT
ap-9818	340	18	can	can	AUX
ap-9818	340	19	be	be	AUX
ap-9818	340	20	determined	determine	VERB
ap-9818	340	21	by	by	ADP
ap-9818	340	22	means	mean	NOUN
ap-9818	340	23	of	of	ADP
ap-9818	340	24	(	(	PUNCT
ap-9818	340	25	59	59	NUM
ap-9818	340	26	)	)	PUNCT
ap-9818	340	27	,	,	PUNCT
ap-9818	340	28	in	in	ADP
ap-9818	340	29	combination	combination	NOUN
ap-9818	340	30	with	with	ADP
ap-9818	340	31	the	the	DET
ap-9818	340	32	point	point	NOUN
ap-9818	340	33	transformation	transformation	NOUN
ap-9818	340	34	(	(	PUNCT
ap-9818	340	35	10	10	NUM
ap-9818	340	36	)	)	PUNCT
ap-9818	340	37	,	,	PUNCT
ap-9818	340	38	and	and	CCONJ
ap-9818	340	39	our	our	PRON
ap-9818	340	40	settings	setting	NOUN
ap-9818	340	41	(	(	PUNCT
ap-9818	340	42	49	49	NUM
ap-9818	340	43	)	)	PUNCT
ap-9818	340	44	.	.	PUNCT
ap-9818	341	1	we	we	PRON
ap-9818	341	2	have	have	VERB
ap-9818	341	3	:	:	PUNCT
ap-9818	341	4	ψν	ψν	NOUN
ap-9818	341	5	,	,	PUNCT
ap-9818	341	6	gen(x	gen(x	NOUN
ap-9818	341	7	)	)	PUNCT
ap-9818	341	8	=	=	SYM
ap-9818	341	9	1√	1√	NUM
ap-9818	341	10	x2	x2	NOUN
ap-9818	342	1	+	+	CCONJ
ap-9818	342	2	1	1	NUM
ap-9818	342	3	xν	xν	NOUN
ap-9818	342	4	ξν	ξν	ADV
ap-9818	342	5	,	,	PUNCT
ap-9818	342	6	gen(x	gen(x	NOUN
ap-9818	342	7	)	)	PUNCT
ap-9818	342	8	.	.	PUNCT
ap-9818	343	1	(	(	PUNCT
ap-9818	343	2	61	61	NUM
ap-9818	343	3	)	)	PUNCT
ap-9818	343	4	bound	bind	VERB
ap-9818	343	5	states	state	NOUN
ap-9818	343	6	can	can	AUX
ap-9818	343	7	be	be	AUX
ap-9818	343	8	extracted	extract	VERB
ap-9818	343	9	from	from	ADP
ap-9818	343	10	this	this	DET
ap-9818	343	11	general	general	ADJ
ap-9818	343	12	solution	solution	NOUN
ap-9818	343	13	by	by	ADP
ap-9818	343	14	requiring	require	VERB
ap-9818	343	15	c1	c1	NOUN
ap-9818	343	16	=	=	SYM
ap-9818	343	17	0	0	PROPN
ap-9818	343	18	,	,	PUNCT
ap-9818	343	19	c2	c2	PROPN
ap-9818	343	20	=	=	SYM
ap-9818	343	21	1	1	NUM
ap-9818	343	22	,	,	PUNCT
ap-9818	343	23	and	and	CCONJ
ap-9818	343	24	:	:	PUNCT
ap-9818	343	25	f1	f1	NOUN
ap-9818	343	26	4	4	NUM
ap-9818	343	27	+	+	SYM
ap-9818	343	28	f2	f2	PROPN
ap-9818	343	29	4	4	NUM
ap-9818	343	30	=	=	SYM
ap-9818	343	31	−n	−n	NOUN
ap-9818	343	32	−	−	NOUN
ap-9818	343	33	1	1	NUM
ap-9818	343	34	,	,	PUNCT
ap-9818	343	35	(	(	PUNCT
ap-9818	343	36	62	62	X
ap-9818	343	37	)	)	PUNCT
ap-9818	343	38	introducing	introduce	VERB
ap-9818	343	39	a	a	DET
ap-9818	343	40	nonnegative	nonnegative	ADJ
ap-9818	343	41	integer	integer	NOUN
ap-9818	343	42	n.	n.	NOUN
ap-9818	343	43	after	after	ADP
ap-9818	343	44	solving	solve	VERB
ap-9818	343	45	this	this	DET
ap-9818	343	46	constraint	constraint	NOUN
ap-9818	343	47	for	for	ADP
ap-9818	343	48	the	the	DET
ap-9818	343	49	stationary	stationary	ADJ
ap-9818	343	50	energy	energy	NOUN
ap-9818	343	51	e	e	NOUN
ap-9818	343	52	=	=	SYM
ap-9818	343	53	eν	eν	PROPN
ap-9818	343	54	,	,	PUNCT
ap-9818	343	55	n	n	CCONJ
ap-9818	343	56	,	,	PUNCT
ap-9818	343	57	we	we	PRON
ap-9818	343	58	obtain	obtain	VERB
ap-9818	343	59	:	:	PUNCT
ap-9818	343	60	eν	eν	NOUN
ap-9818	343	61	,	,	PUNCT
ap-9818	343	62	n	n	NOUN
ap-9818	343	63	=	=	SYM
ap-9818	343	64	−4	−4	NOUN
ap-9818	343	65	n2	n2	NOUN
ap-9818	343	66	−	−	PROPN
ap-9818	343	67	8	8	NUM
ap-9818	343	68	n	n	CCONJ
ap-9818	343	69	−	−	NUM
ap-9818	343	70	2	2	NUM
ap-9818	343	71	n	n	NOUN
ap-9818	343	72	f2	f2	ADV
ap-9818	343	73	−	−	PROPN
ap-9818	343	74	v1	v1	NOUN
ap-9818	343	75	−	−	PROPN
ap-9818	343	76	4	4	NUM
ap-9818	343	77	−	−	NOUN
ap-9818	343	78	2	2	NUM
ap-9818	343	79	f2	f2	ADV
ap-9818	343	80	=	=	SYM
ap-9818	343	81	−4	−4	NOUN
ap-9818	343	82	n2	n2	NOUN
ap-9818	343	83	−	−	PROPN
ap-9818	343	84	8	8	NUM
ap-9818	343	85	n	n	ADV
ap-9818	343	86	−	−	PROPN
ap-9818	343	87	(	(	PUNCT
ap-9818	343	88	2	2	NUM
ap-9818	343	89	n	n	NOUN
ap-9818	343	90	+	+	NOUN
ap-9818	343	91	2	2	NUM
ap-9818	343	92	)	)	PUNCT
ap-9818	343	93	√	√	NOUN
ap-9818	343	94	1	1	NUM
ap-9818	343	95	+	+	SYM
ap-9818	343	96	4	4	NUM
ap-9818	343	97	v1	v1	NOUN
ap-9818	343	98	+	+	CCONJ
ap-9818	343	99	4	4	NUM
ap-9818	343	100	ν	ν	NOUN
ap-9818	343	101	(	(	PUNCT
ap-9818	343	102	ν	ν	PROPN
ap-9818	343	103	−	−	PROPN
ap-9818	343	104	δ	δ	PROPN
ap-9818	343	105	)	)	PUNCT
ap-9818	343	106	−	−	PROPN
ap-9818	343	107	v1	v1	NOUN
ap-9818	343	108	−	−	PROPN
ap-9818	343	109	4	4	NUM
ap-9818	343	110	.	.	PUNCT
ap-9818	344	1	(	(	PUNCT
ap-9818	344	2	63	63	NUM
ap-9818	344	3	)	)	PUNCT
ap-9818	344	4	these	these	DET
ap-9818	344	5	energies	energy	NOUN
ap-9818	344	6	are	be	AUX
ap-9818	344	7	real	real	ADV
ap-9818	344	8	-	-	PUNCT
ap-9818	344	9	valued	value	VERB
ap-9818	344	10	,	,	PUNCT
ap-9818	344	11	as	as	ADV
ap-9818	344	12	long	long	ADV
ap-9818	344	13	as	as	SCONJ
ap-9818	344	14	v1	v1	NOUN
ap-9818	344	15	takes	take	VERB
ap-9818	344	16	positive	positive	ADJ
ap-9818	344	17	values	value	NOUN
ap-9818	344	18	,	,	PUNCT
ap-9818	344	19	see	see	VERB
ap-9818	344	20	(	(	PUNCT
ap-9818	344	21	56	56	NUM
ap-9818	344	22	)	)	PUNCT
ap-9818	344	23	.	.	PUNCT
ap-9818	345	1	after	after	ADP
ap-9818	345	2	inserting	insert	VERB
ap-9818	345	3	this	this	DET
ap-9818	345	4	expression	expression	NOUN
ap-9818	345	5	into	into	ADP
ap-9818	345	6	the	the	DET
ap-9818	345	7	solution	solution	NOUN
ap-9818	345	8	(	(	PUNCT
ap-9818	345	9	61	61	NUM
ap-9818	345	10	)	)	PUNCT
ap-9818	345	11	,	,	PUNCT
ap-9818	345	12	and	and	CCONJ
ap-9818	345	13	applying	apply	VERB
ap-9818	345	14	the	the	DET
ap-9818	345	15	identity	identity	NOUN
ap-9818	345	16	[	[	X
ap-9818	345	17	37	37	NUM
ap-9818	345	18	]	]	PUNCT
ap-9818	345	19	,	,	PUNCT
ap-9818	345	20	our	our	PRON
ap-9818	345	21	bound	bound	ADJ
ap-9818	345	22	states	state	NOUN
ap-9818	345	23	can	can	AUX
ap-9818	345	24	be	be	AUX
ap-9818	345	25	written	write	VERB
ap-9818	345	26	in	in	ADP
ap-9818	345	27	the	the	DET
ap-9818	345	28	form	form	NOUN
ap-9818	345	29	:	:	PUNCT
ap-9818	345	30	ψν	ψν	NOUN
ap-9818	345	31	,	,	PUNCT
ap-9818	345	32	n(x	n(x	ADJ
ap-9818	345	33	)	)	PUNCT
ap-9818	345	34	=	=	SYM
ap-9818	345	35	1√	1√	NUM
ap-9818	345	36	x2	x2	PROPN
ap-9818	346	1	+	+	CCONJ
ap-9818	346	2	1	1	NUM
ap-9818	346	3	x−ν+	x−ν+	PROPN
ap-9818	346	4	f2	f2	PROPN
ap-9818	346	5	+	+	PROPN
ap-9818	346	6	1	1	NUM
ap-9818	346	7	2	2	NUM
ap-9818	346	8	(	(	PUNCT
ap-9818	346	9	x2	x2	PROPN
ap-9818	347	1	+	+	NUM
ap-9818	347	2	1)−1−	1)−1−	NUM
ap-9818	347	3	3f1	3f1	NUM
ap-9818	347	4	4	4	NUM
ap-9818	347	5	−	−	NOUN
ap-9818	347	6	f2	f2	PROPN
ap-9818	347	7	4	4	NUM
ap-9818	347	8	×	×	NOUN
ap-9818	347	9	2f1	2f1	NUM
ap-9818	347	10	(	(	PUNCT
ap-9818	347	11	−n	−n	ADV
ap-9818	347	12	,	,	PUNCT
ap-9818	347	13	3f1	3f1	NUM
ap-9818	347	14	4	4	NUM
ap-9818	347	15	+	+	SYM
ap-9818	347	16	f2	f2	PROPN
ap-9818	347	17	4	4	NUM
ap-9818	347	18	+	+	SYM
ap-9818	347	19	1	1	NUM
ap-9818	347	20	,	,	PUNCT
ap-9818	347	21	f2	f2	PROPN
ap-9818	347	22	2	2	NUM
ap-9818	347	23	+	+	SYM
ap-9818	347	24	1	1	NUM
ap-9818	347	25	,	,	PUNCT
ap-9818	347	26	x2	x2	PROPN
ap-9818	347	27	x2	x2	PROPN
ap-9818	348	1	+	+	CCONJ
ap-9818	348	2	1	1	NUM
ap-9818	348	3	)	)	PUNCT
ap-9818	348	4	.	.	PUNCT
ap-9818	349	1	(	(	PUNCT
ap-9818	349	2	64	64	NUM
ap-9818	349	3	)	)	PUNCT
ap-9818	349	4	note	note	VERB
ap-9818	349	5	that	that	SCONJ
ap-9818	349	6	the	the	DET
ap-9818	349	7	hypergeometric	hypergeometric	ADJ
ap-9818	349	8	function	function	NOUN
ap-9818	349	9	degenerates	degenerate	NOUN
ap-9818	349	10	to	to	ADP
ap-9818	349	11	a	a	DET
ap-9818	349	12	polynomial	polynomial	ADJ
ap-9818	349	13	,	,	PUNCT
ap-9818	349	14	since	since	SCONJ
ap-9818	349	15	n	n	PRON
ap-9818	349	16	is	be	AUX
ap-9818	349	17	a	a	DET
ap-9818	349	18	nonnegative	nonnegative	ADJ
ap-9818	349	19	integer	integer	NOUN
ap-9818	349	20	.	.	PUNCT
ap-9818	350	1	also	also	ADV
ap-9818	350	2	,	,	PUNCT
ap-9818	350	3	recall	recall	VERB
ap-9818	350	4	that	that	SCONJ
ap-9818	350	5	the	the	DET
ap-9818	350	6	negative	negative	ADJ
ap-9818	350	7	power	power	NOUN
ap-9818	350	8	of	of	ADP
ap-9818	350	9	ν	ν	NOUN
ap-9818	350	10	in	in	ADP
ap-9818	350	11	(	(	PUNCT
ap-9818	350	12	64	64	NUM
ap-9818	350	13	)	)	PUNCT
ap-9818	350	14	does	do	AUX
ap-9818	350	15	not	not	PART
ap-9818	350	16	create	create	VERB
ap-9818	350	17	a	a	DET
ap-9818	350	18	singularity	singularity	NOUN
ap-9818	350	19	at	at	ADP
ap-9818	350	20	the	the	DET
ap-9818	350	21	origin	origin	NOUN
ap-9818	350	22	,	,	PUNCT
ap-9818	350	23	as	as	ADV
ap-9818	350	24	long	long	ADV
ap-9818	350	25	as	as	SCONJ
ap-9818	350	26	v1	v1	NOUN
ap-9818	350	27	is	be	AUX
ap-9818	350	28	positive	positive	ADJ
ap-9818	350	29	.	.	PUNCT
ap-9818	351	1	the	the	DET
ap-9818	351	2	remaining	remain	VERB
ap-9818	351	3	task	task	NOUN
ap-9818	351	4	is	be	AUX
ap-9818	351	5	to	to	PART
ap-9818	351	6	establish	establish	VERB
ap-9818	351	7	parity	parity	NOUN
ap-9818	351	8	of	of	ADP
ap-9818	351	9	(	(	PUNCT
ap-9818	351	10	46	46	NUM
ap-9818	351	11	)	)	PUNCT
ap-9818	351	12	,	,	PUNCT
ap-9818	351	13	according	accord	VERB
ap-9818	351	14	to	to	ADP
ap-9818	351	15	the	the	DET
ap-9818	351	16	value	value	NOUN
ap-9818	351	17	of	of	ADP
ap-9818	351	18	the	the	DET
ap-9818	351	19	parameter	parameter	PROPN
ap-9818	351	20	δ	δ	PROPN
ap-9818	351	21	.	.	PUNCT
ap-9818	352	1	this	this	PRON
ap-9818	352	2	can	can	AUX
ap-9818	352	3	be	be	AUX
ap-9818	352	4	done	do	VERB
ap-9818	352	5	by	by	ADP
ap-9818	352	6	imposing	impose	VERB
ap-9818	352	7	suitable	suitable	ADJ
ap-9818	352	8	restrictions	restriction	NOUN
ap-9818	352	9	on	on	ADP
ap-9818	352	10	the	the	DET
ap-9818	352	11	exponent	exponent	NOUN
ap-9818	352	12	of	of	ADP
ap-9818	352	13	the	the	DET
ap-9818	352	14	monomial	monomial	ADJ
ap-9818	352	15	term	term	NOUN
ap-9818	352	16	in	in	ADP
ap-9818	352	17	our	our	PRON
ap-9818	352	18	solution	solution	NOUN
ap-9818	352	19	.	.	PUNCT
ap-9818	353	1	in	in	ADP
ap-9818	353	2	the	the	DET
ap-9818	353	3	case	case	NOUN
ap-9818	353	4	of	of	ADP
ap-9818	353	5	odd	odd	ADJ
ap-9818	353	6	parity	parity	NOUN
ap-9818	353	7	,	,	PUNCT
ap-9818	353	8	corresponding	correspond	VERB
ap-9818	353	9	to	to	ADP
ap-9818	353	10	δ	δ	PROPN
ap-9818	353	11	=	=	SYM
ap-9818	353	12	−1	−1	NOUN
ap-9818	353	13	,	,	PUNCT
ap-9818	353	14	the	the	DET
ap-9818	353	15	restriction	restriction	NOUN
ap-9818	353	16	reads	read	VERB
ap-9818	353	17	:	:	PUNCT
ap-9818	353	18	−ν	−ν	ADJ
ap-9818	353	19	+	+	CCONJ
ap-9818	353	20	1	1	NUM
ap-9818	353	21	2	2	NUM
ap-9818	353	22	+	+	SYM
ap-9818	353	23	f2	f2	PROPN
ap-9818	353	24	2	2	NUM
ap-9818	353	25	=	=	SYM
ap-9818	353	26	2	2	NUM
ap-9818	353	27	k	k	NOUN
ap-9818	354	1	+	+	NOUN
ap-9818	354	2	1	1	NUM
ap-9818	354	3	⇝	⇝	NOUN
ap-9818	354	4	ν	ν	NOUN
ap-9818	354	5	=	=	SYM
ap-9818	354	6	−1	−1	NOUN
ap-9818	354	7	2	2	NUM
ap-9818	354	8	−	−	PROPN
ap-9818	354	9	k	k	NOUN
ap-9818	354	10	+	+	PUNCT
ap-9818	354	11	v1	v1	PROPN
ap-9818	354	12	4	4	NUM
ap-9818	354	13	k	k	NOUN
ap-9818	354	14	,	,	PUNCT
ap-9818	354	15	(	(	PUNCT
ap-9818	354	16	65	65	NUM
ap-9818	354	17	)	)	SYM
ap-9818	354	18	231	231	NUM
ap-9818	354	19	axel	axel	PROPN
ap-9818	354	20	schulze	schulze	NOUN
ap-9818	354	21	-	-	PUNCT
ap-9818	354	22	halberg	halberg	PROPN
ap-9818	354	23	acta	acta	PROPN
ap-9818	354	24	polytechnica	polytechnica	PROPN
ap-9818	354	25	2	2	NUM
ap-9818	354	26	1	1	NUM
ap-9818	354	27	1	1	NUM
ap-9818	354	28	2	2	NUM
ap-9818	354	29	x	x	SYM
ap-9818	354	30	60	60	NUM
ap-9818	354	31	40	40	NUM
ap-9818	354	32	20	20	NUM
ap-9818	354	33	20	20	NUM
ap-9818	354	34	40	40	NUM
ap-9818	354	35	60	60	NUM
ap-9818	354	36	,	,	PUNCT
ap-9818	354	37	n(x	n(x	X
ap-9818	354	38	)	)	PUNCT
ap-9818	354	39	figure	figure	NOUN
ap-9818	354	40	3	3	NUM
ap-9818	354	41	.	.	PUNCT
ap-9818	354	42	graphs	graph	NOUN
ap-9818	354	43	of	of	ADP
ap-9818	354	44	odd	odd	ADJ
ap-9818	354	45	-	-	PUNCT
ap-9818	354	46	parity	parity	NOUN
ap-9818	354	47	(	(	PUNCT
ap-9818	354	48	δ	δ	NOUN
ap-9818	354	49	=	=	SYM
ap-9818	354	50	−1	−1	NOUN
ap-9818	354	51	)	)	PUNCT
ap-9818	354	52	solutions	solution	NOUN
ap-9818	354	53	(	(	PUNCT
ap-9818	354	54	64	64	NUM
ap-9818	354	55	)	)	PUNCT
ap-9818	354	56	for	for	ADP
ap-9818	354	57	the	the	DET
ap-9818	354	58	settings	setting	NOUN
ap-9818	354	59	v1	v1	VERB
ap-9818	354	60	=	=	SYM
ap-9818	354	61	1	1	NUM
ap-9818	354	62	and	and	CCONJ
ap-9818	354	63	k	k	NOUN
ap-9818	354	64	=	=	SYM
ap-9818	354	65	−1	−1	NOUN
ap-9818	354	66	,	,	PUNCT
ap-9818	354	67	corresponding	correspond	VERB
ap-9818	354	68	to	to	ADP
ap-9818	354	69	ν	ν	X
ap-9818	354	70	=	=	SYM
ap-9818	354	71	1	1	NUM
ap-9818	354	72	4	4	NUM
ap-9818	354	73	.	.	PUNCT
ap-9818	355	1	the	the	DET
ap-9818	355	2	solutions	solution	NOUN
ap-9818	355	3	are	be	AUX
ap-9818	355	4	given	give	VERB
ap-9818	355	5	for	for	ADP
ap-9818	355	6	n	n	NOUN
ap-9818	355	7	=	=	SYM
ap-9818	355	8	0	0	PUNCT
ap-9818	355	9	(	(	PUNCT
ap-9818	355	10	black	black	ADJ
ap-9818	355	11	solid	solid	ADJ
ap-9818	355	12	curve	curve	NOUN
ap-9818	355	13	)	)	PUNCT
ap-9818	355	14	,	,	PUNCT
ap-9818	355	15	n	n	NOUN
ap-9818	355	16	=	=	SYM
ap-9818	355	17	1	1	NUM
ap-9818	355	18	(	(	PUNCT
ap-9818	355	19	gray	gray	ADJ
ap-9818	355	20	curve	curve	NOUN
ap-9818	355	21	)	)	PUNCT
ap-9818	355	22	,	,	PUNCT
ap-9818	355	23	n	n	NOUN
ap-9818	355	24	=	=	SYM
ap-9818	355	25	2	2	NUM
ap-9818	355	26	(	(	PUNCT
ap-9818	355	27	dashed	dash	VERB
ap-9818	355	28	curve	curve	NOUN
ap-9818	355	29	)	)	PUNCT
ap-9818	355	30	.	.	PUNCT
ap-9818	356	1	2	2	NUM
ap-9818	356	2	1	1	NUM
ap-9818	356	3	1	1	NUM
ap-9818	356	4	2	2	NUM
ap-9818	356	5	x	x	SYM
ap-9818	356	6	10	10	NUM
ap-9818	356	7	10	10	NUM
ap-9818	356	8	20	20	NUM
ap-9818	356	9	30	30	NUM
ap-9818	356	10	,	,	PUNCT
ap-9818	356	11	n(x	n(x	X
ap-9818	356	12	)	)	PUNCT
ap-9818	356	13	figure	figure	NOUN
ap-9818	356	14	4	4	NUM
ap-9818	356	15	.	.	PUNCT
ap-9818	357	1	graphs	graph	NOUN
ap-9818	357	2	of	of	ADP
ap-9818	357	3	even	even	ADJ
ap-9818	357	4	-	-	PUNCT
ap-9818	357	5	parity	parity	NOUN
ap-9818	357	6	(	(	PUNCT
ap-9818	357	7	δ	δ	NOUN
ap-9818	357	8	=	=	SYM
ap-9818	357	9	1	1	X
ap-9818	357	10	)	)	PUNCT
ap-9818	357	11	solutions	solution	NOUN
ap-9818	357	12	(	(	PUNCT
ap-9818	357	13	64	64	NUM
ap-9818	357	14	)	)	PUNCT
ap-9818	357	15	for	for	ADP
ap-9818	357	16	the	the	DET
ap-9818	357	17	settings	setting	NOUN
ap-9818	357	18	v1	v1	VERB
ap-9818	357	19	=	=	SYM
ap-9818	357	20	1	1	NUM
ap-9818	357	21	and	and	CCONJ
ap-9818	357	22	k	k	NOUN
ap-9818	357	23	=	=	SYM
ap-9818	357	24	1	1	NUM
ap-9818	357	25	,	,	PUNCT
ap-9818	357	26	corresponding	correspond	VERB
ap-9818	357	27	to	to	ADP
ap-9818	357	28	ν	ν	X
ap-9818	357	29	=	=	PUNCT
ap-9818	357	30	−	−	PROPN
ap-9818	357	31	1	1	NUM
ap-9818	357	32	4	4	NUM
ap-9818	357	33	.	.	PUNCT
ap-9818	358	1	the	the	DET
ap-9818	358	2	solutions	solution	NOUN
ap-9818	358	3	are	be	AUX
ap-9818	358	4	given	give	VERB
ap-9818	358	5	for	for	ADP
ap-9818	358	6	n	n	NOUN
ap-9818	358	7	=	=	SYM
ap-9818	358	8	0	0	PUNCT
ap-9818	358	9	(	(	PUNCT
ap-9818	358	10	black	black	ADJ
ap-9818	358	11	solid	solid	ADJ
ap-9818	358	12	curve	curve	NOUN
ap-9818	358	13	)	)	PUNCT
ap-9818	358	14	,	,	PUNCT
ap-9818	358	15	n	n	NOUN
ap-9818	358	16	=	=	SYM
ap-9818	358	17	1	1	NUM
ap-9818	358	18	(	(	PUNCT
ap-9818	358	19	gray	gray	ADJ
ap-9818	358	20	curve	curve	NOUN
ap-9818	358	21	)	)	PUNCT
ap-9818	358	22	,	,	PUNCT
ap-9818	358	23	n	n	NOUN
ap-9818	358	24	=	=	SYM
ap-9818	358	25	2	2	NUM
ap-9818	358	26	(	(	PUNCT
ap-9818	358	27	dashed	dash	VERB
ap-9818	358	28	curve	curve	NOUN
ap-9818	358	29	)	)	PUNCT
ap-9818	358	30	.	.	PUNCT
ap-9818	359	1	where	where	SCONJ
ap-9818	359	2	k	k	PROPN
ap-9818	359	3	is	be	AUX
ap-9818	359	4	an	an	DET
ap-9818	359	5	integer	integer	NOUN
ap-9818	359	6	that	that	PRON
ap-9818	359	7	must	must	AUX
ap-9818	359	8	be	be	AUX
ap-9818	359	9	chosen	choose	VERB
ap-9818	360	1	such	such	ADJ
ap-9818	360	2	that	that	SCONJ
ap-9818	360	3	ν	ν	PROPN
ap-9818	360	4	>	>	X
ap-9818	360	5	−	−	PROPN
ap-9818	360	6	1	1	NUM
ap-9818	360	7	2	2	NUM
ap-9818	360	8	.	.	PUNCT
ap-9818	361	1	for	for	ADP
ap-9818	361	2	even	even	ADV
ap-9818	361	3	parity	parity	NOUN
ap-9818	361	4	of	of	ADP
ap-9818	361	5	our	our	PRON
ap-9818	361	6	solution	solution	NOUN
ap-9818	361	7	(	(	PUNCT
ap-9818	361	8	δ	δ	NOUN
ap-9818	361	9	=	=	SYM
ap-9818	361	10	1	1	NUM
ap-9818	361	11	)	)	PUNCT
ap-9818	361	12	,	,	PUNCT
ap-9818	361	13	we	we	PRON
ap-9818	361	14	must	must	AUX
ap-9818	361	15	have	have	VERB
ap-9818	361	16	:	:	PUNCT
ap-9818	361	17	−ν	−ν	VERB
ap-9818	361	18	+	+	CCONJ
ap-9818	361	19	1	1	NUM
ap-9818	361	20	2	2	NUM
ap-9818	361	21	+	+	SYM
ap-9818	361	22	f2	f2	PROPN
ap-9818	361	23	2	2	NUM
ap-9818	361	24	=	=	SYM
ap-9818	361	25	2	2	NUM
ap-9818	361	26	k	k	NOUN
ap-9818	361	27	⇝	⇝	NOUN
ap-9818	361	28	ν	ν	X
ap-9818	361	29	=	=	SYM
ap-9818	361	30	1	1	NUM
ap-9818	361	31	2	2	NUM
ap-9818	361	32	−	−	PROPN
ap-9818	362	1	k	k	NOUN
ap-9818	363	1	+	+	PUNCT
ap-9818	363	2	v1	v1	PROPN
ap-9818	363	3	4	4	NUM
ap-9818	363	4	k	k	NOUN
ap-9818	363	5	,	,	PUNCT
ap-9818	363	6	(	(	PUNCT
ap-9818	363	7	66	66	NUM
ap-9818	363	8	)	)	PUNCT
ap-9818	363	9	recall	recall	VERB
ap-9818	363	10	that	that	SCONJ
ap-9818	363	11	we	we	PRON
ap-9818	363	12	require	require	VERB
ap-9818	363	13	ν	ν	X
ap-9818	363	14	>	>	X
ap-9818	363	15	−	−	PROPN
ap-9818	363	16	1	1	NUM
ap-9818	363	17	2	2	NUM
ap-9818	363	18	.	.	PUNCT
ap-9818	364	1	figures	figure	NOUN
ap-9818	364	2	3	3	NUM
ap-9818	364	3	and	and	CCONJ
ap-9818	364	4	4	4	NUM
ap-9818	364	5	show	show	VERB
ap-9818	364	6	examples	example	NOUN
ap-9818	364	7	of	of	ADP
ap-9818	364	8	our	our	PRON
ap-9818	364	9	bound	bind	VERB
ap-9818	364	10	state	state	NOUN
ap-9818	364	11	solutions	solution	NOUN
ap-9818	364	12	(	(	PUNCT
ap-9818	364	13	64	64	NUM
ap-9818	364	14	)	)	PUNCT
ap-9818	364	15	for	for	ADP
ap-9818	364	16	particular	particular	ADJ
ap-9818	364	17	values	value	NOUN
ap-9818	364	18	of	of	ADP
ap-9818	364	19	the	the	DET
ap-9818	364	20	parameter	parameter	NOUN
ap-9818	364	21	ν	ν	PROPN
ap-9818	364	22	.	.	PROPN
ap-9818	364	23	4.3	4.3	NUM
ap-9818	364	24	.	.	PUNCT
ap-9818	364	25	lienard	lienard	ADJ
ap-9818	364	26	-	-	PUNCT
ap-9818	364	27	type	type	NOUN
ap-9818	364	28	oscillator	oscillator	NOUN
ap-9818	364	29	potential	potential	NOUN
ap-9818	364	30	with	with	ADP
ap-9818	364	31	spiked	spiked	ADJ
ap-9818	364	32	mass	mass	NOUN
ap-9818	364	33	our	our	PRON
ap-9818	364	34	next	next	ADJ
ap-9818	364	35	example	example	NOUN
ap-9818	364	36	focuses	focus	VERB
ap-9818	364	37	on	on	ADP
ap-9818	364	38	a	a	DET
ap-9818	364	39	quantum	quantum	ADJ
ap-9818	364	40	system	system	NOUN
ap-9818	364	41	that	that	PRON
ap-9818	364	42	was	be	AUX
ap-9818	364	43	first	first	ADV
ap-9818	364	44	studied	study	VERB
ap-9818	364	45	in	in	ADP
ap-9818	364	46	[	[	X
ap-9818	364	47	38	38	NUM
ap-9818	364	48	]	]	PUNCT
ap-9818	364	49	.	.	PUNCT
ap-9818	365	1	this	this	DET
ap-9818	365	2	system	system	NOUN
ap-9818	365	3	,	,	PUNCT
ap-9818	365	4	the	the	DET
ap-9818	365	5	classical	classical	ADJ
ap-9818	365	6	version	version	NOUN
ap-9818	365	7	of	of	ADP
ap-9818	365	8	which	which	PRON
ap-9818	365	9	is	be	AUX
ap-9818	365	10	a	a	DET
ap-9818	365	11	nonlinear	nonlinear	ADJ
ap-9818	365	12	oscillator	oscillator	NOUN
ap-9818	365	13	of	of	ADP
ap-9818	365	14	lienard	lienard	ADJ
ap-9818	365	15	type	type	NOUN
ap-9818	365	16	,	,	PUNCT
ap-9818	365	17	is	be	AUX
ap-9818	365	18	characterised	characterise	VERB
ap-9818	365	19	by	by	ADP
ap-9818	365	20	a	a	DET
ap-9818	365	21	spiked	spiked	ADJ
ap-9818	365	22	mass	mass	NOUN
ap-9818	365	23	function	function	NOUN
ap-9818	365	24	and	and	CCONJ
ap-9818	365	25	a	a	DET
ap-9818	365	26	harmonic	harmonic	ADJ
ap-9818	365	27	oscillator	oscillator	NOUN
ap-9818	365	28	potential	potential	NOUN
ap-9818	365	29	.	.	PUNCT
ap-9818	366	1	these	these	DET
ap-9818	366	2	functions	function	NOUN
ap-9818	366	3	are	be	AUX
ap-9818	366	4	given	give	VERB
ap-9818	366	5	by	by	ADP
ap-9818	366	6	:	:	PUNCT
ap-9818	366	7	m(x	m(x	PROPN
ap-9818	366	8	)	)	PUNCT
ap-9818	366	9	=	=	SYM
ap-9818	366	10	2	2	NUM
ap-9818	366	11	x4	x4	PROPN
ap-9818	366	12	,	,	PUNCT
ap-9818	366	13	v	v	X
ap-9818	366	14	(	(	PUNCT
ap-9818	366	15	x	x	NOUN
ap-9818	366	16	)	)	PUNCT
ap-9818	366	17	=	=	SYM
ap-9818	366	18	λ	λ	X
ap-9818	366	19	x2	x2	PROPN
ap-9818	366	20	,	,	PUNCT
ap-9818	366	21	(	(	PUNCT
ap-9818	366	22	67	67	X
ap-9818	366	23	)	)	PUNCT
ap-9818	366	24	introducing	introduce	VERB
ap-9818	366	25	a	a	DET
ap-9818	366	26	real	real	ADV
ap-9818	366	27	-	-	PUNCT
ap-9818	366	28	valued	value	VERB
ap-9818	366	29	constant	constant	ADJ
ap-9818	366	30	λ	λ	X
ap-9818	366	31	>	>	X
ap-9818	366	32	0	0	X
ap-9818	366	33	.	.	PUNCT
ap-9818	367	1	note	note	VERB
ap-9818	367	2	that	that	SCONJ
ap-9818	367	3	here	here	ADV
ap-9818	367	4	the	the	DET
ap-9818	367	5	mass	mass	NOUN
ap-9818	367	6	function	function	NOUN
ap-9818	367	7	does	do	AUX
ap-9818	367	8	not	not	PART
ap-9818	367	9	have	have	VERB
ap-9818	367	10	the	the	DET
ap-9818	367	11	same	same	ADJ
ap-9818	367	12	physical	physical	ADJ
ap-9818	367	13	meaning	meaning	NOUN
ap-9818	367	14	as	as	ADP
ap-9818	367	15	in	in	ADP
ap-9818	367	16	semiconductor	semiconductor	NOUN
ap-9818	367	17	applications	application	NOUN
ap-9818	367	18	that	that	PRON
ap-9818	367	19	were	be	AUX
ap-9818	367	20	mentioned	mention	VERB
ap-9818	367	21	in	in	ADP
ap-9818	367	22	the	the	DET
ap-9818	367	23	introduction	introduction	NOUN
ap-9818	367	24	,	,	PUNCT
ap-9818	367	25	but	but	CCONJ
ap-9818	367	26	rather	rather	ADV
ap-9818	367	27	appears	appear	VERB
ap-9818	367	28	as	as	ADP
ap-9818	367	29	a	a	DET
ap-9818	367	30	byproduct	byproduct	NOUN
ap-9818	367	31	when	when	SCONJ
ap-9818	367	32	converting	convert	VERB
ap-9818	367	33	the	the	DET
ap-9818	367	34	classical	classical	ADJ
ap-9818	367	35	hamiltonian	hamiltonian	ADJ
ap-9818	367	36	function	function	NOUN
ap-9818	367	37	of	of	ADP
ap-9818	367	38	the	the	DET
ap-9818	367	39	lienard	lienard	ADJ
ap-9818	367	40	oscillator	oscillator	NOUN
ap-9818	367	41	into	into	ADP
ap-9818	367	42	a	a	DET
ap-9818	367	43	quantum	quantum	ADJ
ap-9818	367	44	hamiltonian	hamiltonian	ADJ
ap-9818	367	45	operator	operator	NOUN
ap-9818	367	46	.	.	PUNCT
ap-9818	368	1	more	more	ADV
ap-9818	368	2	precisely	precisely	ADV
ap-9818	368	3	,	,	PUNCT
ap-9818	368	4	in	in	ADP
ap-9818	368	5	the	the	DET
ap-9818	368	6	course	course	NOUN
ap-9818	368	7	of	of	ADP
ap-9818	368	8	the	the	DET
ap-9818	368	9	latter	latter	ADJ
ap-9818	368	10	conversion	conversion	NOUN
ap-9818	368	11	,	,	PUNCT
ap-9818	368	12	a	a	DET
ap-9818	368	13	first	first	ADJ
ap-9818	368	14	-	-	PUNCT
ap-9818	368	15	derivative	derivative	ADJ
ap-9818	368	16	term	term	NOUN
ap-9818	368	17	is	be	AUX
ap-9818	368	18	generated	generate	VERB
ap-9818	368	19	in	in	ADP
ap-9818	368	20	the	the	DET
ap-9818	368	21	associated	associated	ADJ
ap-9818	368	22	schrödinger	schrödinger	ADJ
ap-9818	368	23	equation	equation	NOUN
ap-9818	368	24	,	,	PUNCT
ap-9818	368	25	the	the	DET
ap-9818	368	26	coefficient	coefficient	NOUN
ap-9818	368	27	of	of	ADP
ap-9818	368	28	which	which	PRON
ap-9818	368	29	can	can	AUX
ap-9818	368	30	be	be	AUX
ap-9818	368	31	interpreted	interpret	VERB
ap-9818	368	32	as	as	ADP
ap-9818	368	33	a	a	DET
ap-9818	368	34	position	position	NOUN
ap-9818	368	35	-	-	PUNCT
ap-9818	368	36	dependent	dependent	ADJ
ap-9818	368	37	mass	mass	NOUN
ap-9818	368	38	.	.	PUNCT
ap-9818	369	1	for	for	ADP
ap-9818	369	2	this	this	DET
ap-9818	369	3	reason	reason	NOUN
ap-9818	369	4	,	,	PUNCT
ap-9818	369	5	it	it	PRON
ap-9818	369	6	is	be	AUX
ap-9818	369	7	not	not	PART
ap-9818	369	8	problematic	problematic	ADJ
ap-9818	369	9	if	if	SCONJ
ap-9818	369	10	the	the	DET
ap-9818	369	11	position	position	NOUN
ap-9818	369	12	-	-	PUNCT
ap-9818	369	13	dependent	dependent	ADJ
ap-9818	369	14	mass	mass	NOUN
ap-9818	369	15	exhibits	exhibit	VERB
ap-9818	369	16	a	a	DET
ap-9818	369	17	singularity	singularity	NOUN
ap-9818	369	18	.	.	PUNCT
ap-9818	370	1	in	in	ADP
ap-9818	370	2	fact	fact	NOUN
ap-9818	370	3	,	,	PUNCT
ap-9818	370	4	as	as	ADP
ap-9818	370	5	232	232	NUM
ap-9818	370	6	vol	vol	NOUN
ap-9818	370	7	.	.	PUNCT
ap-9818	370	8	65	65	NUM
ap-9818	370	9	no	no	NOUN
ap-9818	370	10	.	.	PUNCT
ap-9818	371	1	2/2025	2/2025	NUM
ap-9818	371	2	persistence	persistence	NOUN
ap-9818	371	3	of	of	ADP
ap-9818	371	4	solvability	solvability	NOUN
ap-9818	371	5	in	in	ADP
ap-9818	371	6	quantum	quantum	NOUN
ap-9818	371	7	systems	system	NOUN
ap-9818	371	8	deformed	deform	VERB
ap-9818	371	9	by	by	ADP
ap-9818	371	10	dunkl	dunkl	PROPN
ap-9818	371	11	.	.	PUNCT
ap-9818	371	12	.	.	PUNCT
ap-9818	372	1	.	.	PUNCT
ap-9818	373	1	mentioned	mention	VERB
ap-9818	373	2	at	at	ADP
ap-9818	373	3	the	the	DET
ap-9818	373	4	beginning	beginning	NOUN
ap-9818	373	5	of	of	ADP
ap-9818	373	6	section	section	NOUN
ap-9818	373	7	2	2	NUM
ap-9818	373	8	,	,	PUNCT
ap-9818	373	9	a	a	DET
ap-9818	373	10	singular	singular	ADJ
ap-9818	373	11	mass	mass	NOUN
ap-9818	373	12	function	function	NOUN
ap-9818	373	13	is	be	AUX
ap-9818	373	14	common	common	ADJ
ap-9818	373	15	in	in	ADP
ap-9818	373	16	lienard	lienard	ADJ
ap-9818	373	17	oscillator	oscillator	NOUN
ap-9818	373	18	or	or	CCONJ
ap-9818	373	19	related	related	ADJ
ap-9818	373	20	systems	system	NOUN
ap-9818	373	21	.	.	PUNCT
ap-9818	374	1	we	we	PRON
ap-9818	374	2	will	will	AUX
ap-9818	374	3	now	now	ADV
ap-9818	374	4	determine	determine	VERB
ap-9818	374	5	if	if	SCONJ
ap-9818	374	6	we	we	PRON
ap-9818	374	7	can	can	AUX
ap-9818	374	8	construct	construct	VERB
ap-9818	374	9	solutions	solution	NOUN
ap-9818	374	10	of	of	ADP
ap-9818	374	11	the	the	DET
ap-9818	374	12	dunkl	dunkl	NOUN
ap-9818	374	13	-	-	PUNCT
ap-9818	374	14	schrödinger	schrödinger	NOUN
ap-9818	374	15	equation	equation	NOUN
ap-9818	374	16	(	(	PUNCT
ap-9818	374	17	6	6	NUM
ap-9818	374	18	)	)	PUNCT
ap-9818	374	19	with	with	ADP
ap-9818	374	20	(	(	PUNCT
ap-9818	374	21	67	67	NUM
ap-9818	374	22	)	)	PUNCT
ap-9818	374	23	,	,	PUNCT
ap-9818	374	24	from	from	ADP
ap-9818	374	25	the	the	DET
ap-9818	374	26	known	know	VERB
ap-9818	374	27	solutions	solution	NOUN
ap-9818	374	28	of	of	ADP
ap-9818	374	29	the	the	DET
ap-9818	374	30	conventional	conventional	ADJ
ap-9818	374	31	equation	equation	NOUN
ap-9818	374	32	(	(	PUNCT
ap-9818	374	33	7	7	NUM
ap-9818	374	34	)	)	PUNCT
ap-9818	374	35	.	.	PUNCT
ap-9818	375	1	to	to	ADP
ap-9818	375	2	this	this	DET
ap-9818	375	3	end	end	NOUN
ap-9818	375	4	,	,	PUNCT
ap-9818	375	5	let	let	VERB
ap-9818	375	6	us	we	PRON
ap-9818	375	7	verify	verify	VERB
ap-9818	375	8	that	that	SCONJ
ap-9818	375	9	the	the	DET
ap-9818	375	10	first	first	ADJ
ap-9818	375	11	solvability	solvability	NOUN
ap-9818	375	12	condition	condition	NOUN
ap-9818	375	13	(	(	PUNCT
ap-9818	375	14	17	17	NUM
ap-9818	375	15	)	)	PUNCT
ap-9818	375	16	is	be	AUX
ap-9818	375	17	true	true	ADJ
ap-9818	375	18	.	.	PUNCT
ap-9818	376	1	we	we	PRON
ap-9818	376	2	find	find	VERB
ap-9818	376	3	that	that	SCONJ
ap-9818	376	4	the	the	DET
ap-9818	376	5	setting	setting	NOUN
ap-9818	376	6	:	:	PUNCT
ap-9818	376	7	c1	c1	NOUN
ap-9818	376	8	=	=	PUNCT
ap-9818	376	9	0	0	PROPN
ap-9818	376	10	,	,	PUNCT
ap-9818	376	11	c2	c2	PROPN
ap-9818	376	12	=	=	SYM
ap-9818	376	13	1	1	NUM
ap-9818	376	14	2	2	NUM
ap-9818	376	15	,	,	PUNCT
ap-9818	376	16	a	a	PRON
ap-9818	376	17	=	=	SYM
ap-9818	376	18	0	0	NUM
ap-9818	376	19	,	,	PUNCT
ap-9818	376	20	b	b	X
ap-9818	376	21	=	=	NOUN
ap-9818	376	22	−3	−3	PROPN
ap-9818	376	23	2	2	NUM
ap-9818	376	24	,	,	PUNCT
ap-9818	376	25	(	(	PUNCT
ap-9818	376	26	68	68	NUM
ap-9818	376	27	)	)	PUNCT
ap-9818	376	28	makes	make	VERB
ap-9818	376	29	the	the	DET
ap-9818	376	30	position	position	NOUN
ap-9818	376	31	-	-	PUNCT
ap-9818	376	32	dependent	dependent	ADJ
ap-9818	376	33	masses	masse	NOUN
ap-9818	376	34	(	(	PUNCT
ap-9818	376	35	17	17	NUM
ap-9818	376	36	)	)	PUNCT
ap-9818	376	37	and	and	CCONJ
ap-9818	376	38	(	(	PUNCT
ap-9818	376	39	67	67	NUM
ap-9818	376	40	)	)	PUNCT
ap-9818	376	41	coincide	coincide	NOUN
ap-9818	376	42	,	,	PUNCT
ap-9818	376	43	as	as	SCONJ
ap-9818	376	44	desired	desire	VERB
ap-9818	376	45	.	.	PUNCT
ap-9818	377	1	in	in	ADP
ap-9818	377	2	the	the	DET
ap-9818	377	3	next	next	ADJ
ap-9818	377	4	step	step	NOUN
ap-9818	377	5	,	,	PUNCT
ap-9818	377	6	we	we	PRON
ap-9818	377	7	verify	verify	VERB
ap-9818	377	8	our	our	PRON
ap-9818	377	9	second	second	ADJ
ap-9818	377	10	solvability	solvability	NOUN
ap-9818	377	11	condition	condition	NOUN
ap-9818	377	12	(	(	PUNCT
ap-9818	377	13	19	19	NUM
ap-9818	377	14	)	)	PUNCT
ap-9818	377	15	by	by	ADP
ap-9818	377	16	substituting	substitute	VERB
ap-9818	377	17	,	,	PUNCT
ap-9818	377	18	mass	mass	ADJ
ap-9818	377	19	and	and	CCONJ
ap-9818	377	20	potential	potential	ADJ
ap-9818	377	21	from	from	ADP
ap-9818	377	22	(	(	PUNCT
ap-9818	377	23	67	67	NUM
ap-9818	377	24	)	)	PUNCT
ap-9818	377	25	.	.	PUNCT
ap-9818	378	1	we	we	PRON
ap-9818	378	2	obtain	obtain	VERB
ap-9818	378	3	:	:	PUNCT
ap-9818	379	1	λ	λ	X
ap-9818	379	2	x2	x2	NOUN
ap-9818	380	1	=	=	PUNCT
ap-9818	380	2	c	c	NOUN
ap-9818	380	3	x2	x2	NOUN
ap-9818	380	4	2	2	NUM
ap-9818	380	5	+	+	NUM
ap-9818	380	6	w	w	ADJ
ap-9818	380	7	(	(	PUNCT
ap-9818	380	8	x	x	NOUN
ap-9818	380	9	)	)	PUNCT
ap-9818	380	10	.	.	PUNCT
ap-9818	381	1	(	(	PUNCT
ap-9818	381	2	69	69	NUM
ap-9818	381	3	)	)	PUNCT
ap-9818	381	4	we	we	PRON
ap-9818	381	5	can	can	AUX
ap-9818	381	6	fulfill	fulfill	VERB
ap-9818	381	7	this	this	DET
ap-9818	381	8	condition	condition	NOUN
ap-9818	381	9	by	by	ADP
ap-9818	381	10	setting	set	VERB
ap-9818	381	11	c	c	NOUN
ap-9818	381	12	=	=	SYM
ap-9818	381	13	2λ	2λ	PROPN
ap-9818	381	14	and	and	CCONJ
ap-9818	381	15	w	w	NOUN
ap-9818	381	16	=	=	NOUN
ap-9818	381	17	0	0	NUM
ap-9818	381	18	.	.	PUNCT
ap-9818	382	1	as	as	ADP
ap-9818	382	2	such	such	ADJ
ap-9818	382	3	,	,	PUNCT
ap-9818	382	4	the	the	DET
ap-9818	382	5	effective	effective	ADJ
ap-9818	382	6	potential	potential	NOUN
ap-9818	382	7	uν	uν	X
ap-9818	382	8	in	in	ADP
ap-9818	382	9	(	(	PUNCT
ap-9818	382	10	20	20	NUM
ap-9818	382	11	)	)	PUNCT
ap-9818	382	12	and	and	CCONJ
ap-9818	382	13	its	its	PRON
ap-9818	382	14	counterpart	counterpart	NOUN
ap-9818	382	15	u0	u0	NOUN
ap-9818	382	16	in	in	ADP
ap-9818	382	17	(	(	PUNCT
ap-9818	382	18	15	15	NUM
ap-9818	382	19	)	)	PUNCT
ap-9818	382	20	with	with	ADP
ap-9818	382	21	the	the	DET
ap-9818	382	22	present	present	ADJ
ap-9818	382	23	settings	setting	NOUN
ap-9818	382	24	(	(	PUNCT
ap-9818	382	25	67	67	NUM
ap-9818	382	26	)	)	PUNCT
ap-9818	382	27	must	must	AUX
ap-9818	382	28	have	have	VERB
ap-9818	382	29	the	the	DET
ap-9818	382	30	same	same	ADJ
ap-9818	382	31	functional	functional	ADJ
ap-9818	382	32	form	form	NOUN
ap-9818	382	33	.	.	PUNCT
ap-9818	383	1	inserting	insert	VERB
ap-9818	383	2	the	the	DET
ap-9818	383	3	latter	latter	ADJ
ap-9818	383	4	settings	setting	NOUN
ap-9818	383	5	into	into	ADP
ap-9818	383	6	the	the	DET
ap-9818	383	7	explicit	explicit	ADJ
ap-9818	383	8	form	form	NOUN
ap-9818	383	9	of	of	ADP
ap-9818	383	10	the	the	DET
ap-9818	383	11	effective	effective	ADJ
ap-9818	383	12	potentials	potential	NOUN
ap-9818	383	13	shows	show	VERB
ap-9818	383	14	that	that	SCONJ
ap-9818	383	15	this	this	PRON
ap-9818	383	16	is	be	AUX
ap-9818	383	17	true	true	ADJ
ap-9818	383	18	.	.	PUNCT
ap-9818	384	1	we	we	PRON
ap-9818	384	2	have	have	VERB
ap-9818	384	3	:	:	PUNCT
ap-9818	384	4	uν(x	uν(x	X
ap-9818	384	5	)	)	PUNCT
ap-9818	384	6	=	=	SYM
ap-9818	384	7	2	2	NUM
ap-9818	384	8	e	e	X
ap-9818	384	9	x4	x4	PROPN
ap-9818	384	10	+	+	CCONJ
ap-9818	384	11	2	2	NUM
ap-9818	385	1	[	[	SYM
ap-9818	385	2	1	1	NUM
ap-9818	385	3	+	+	NUM
ap-9818	385	4	3	3	NUM
ap-9818	385	5	γ	γ	X
ap-9818	385	6	+	+	PROPN
ap-9818	385	7	α	α	PROPN
ap-9818	385	8	(	(	PUNCT
ap-9818	385	9	3	3	NUM
ap-9818	385	10	+	+	SYM
ap-9818	385	11	9	9	NUM
ap-9818	385	12	γ	γ	NOUN
ap-9818	385	13	)	)	PUNCT
ap-9818	385	14	+	+	SYM
ap-9818	385	15	λ	λ	X
ap-9818	385	16	]	]	X
ap-9818	385	17	+	+	NUM
ap-9818	385	18	δ	δ	PROPN
ap-9818	385	19	ν	ν	NOUN
ap-9818	385	20	(	(	PUNCT
ap-9818	385	21	3	3	NUM
ap-9818	385	22	+	+	SYM
ap-9818	385	23	4	4	NUM
ap-9818	385	24	α	α	NOUN
ap-9818	385	25	+	+	ADP
ap-9818	385	26	4	4	NUM
ap-9818	385	27	γ	γ	NOUN
ap-9818	385	28	)	)	PUNCT
ap-9818	385	29	+	+	CCONJ
ap-9818	385	30	ν2	ν2	NOUN
ap-9818	385	31	x2	x2	NOUN
ap-9818	385	32	,	,	PUNCT
ap-9818	385	33	u0(x	u0(x	NUM
ap-9818	385	34	)	)	PUNCT
ap-9818	385	35	=	=	SYM
ap-9818	385	36	2	2	NUM
ap-9818	385	37	e	e	X
ap-9818	385	38	x4	x4	PROPN
ap-9818	386	1	+	+	CCONJ
ap-9818	386	2	2	2	NUM
ap-9818	387	1	[	[	SYM
ap-9818	387	2	1	1	NUM
ap-9818	387	3	+	+	NUM
ap-9818	387	4	3	3	NUM
ap-9818	387	5	γ	γ	X
ap-9818	387	6	+	+	PROPN
ap-9818	387	7	α	α	PROPN
ap-9818	387	8	(	(	PUNCT
ap-9818	387	9	3	3	NUM
ap-9818	387	10	+	+	SYM
ap-9818	387	11	9	9	NUM
ap-9818	387	12	γ	γ	NOUN
ap-9818	387	13	)	)	PUNCT
ap-9818	387	14	+	+	SYM
ap-9818	387	15	λ	λ	X
ap-9818	387	16	]	]	X
ap-9818	387	17	x2	x2	X
ap-9818	387	18	.	.	PUNCT
ap-9818	388	1	(	(	PUNCT
ap-9818	388	2	70	70	NUM
ap-9818	388	3	)	)	PUNCT
ap-9818	388	4	consequently	consequently	ADV
ap-9818	388	5	,	,	PUNCT
ap-9818	388	6	the	the	DET
ap-9818	388	7	schrödinger	schrödinger	ADJ
ap-9818	388	8	equations	equation	NOUN
ap-9818	388	9	for	for	ADP
ap-9818	388	10	the	the	DET
ap-9818	388	11	dunkl	dunkl	NOUN
ap-9818	388	12	context	context	NOUN
ap-9818	388	13	(	(	PUNCT
ap-9818	388	14	6	6	NUM
ap-9818	388	15	)	)	PUNCT
ap-9818	388	16	and	and	CCONJ
ap-9818	388	17	without	without	ADP
ap-9818	388	18	it	it	PRON
ap-9818	388	19	have	have	VERB
ap-9818	388	20	the	the	DET
ap-9818	388	21	same	same	ADJ
ap-9818	388	22	solutions	solution	NOUN
ap-9818	388	23	,	,	PUNCT
ap-9818	388	24	up	up	ADP
ap-9818	388	25	to	to	ADP
ap-9818	388	26	a	a	DET
ap-9818	388	27	redefinition	redefinition	NOUN
ap-9818	388	28	of	of	ADP
ap-9818	388	29	numerical	numerical	ADJ
ap-9818	388	30	parameters	parameter	NOUN
ap-9818	388	31	.	.	PUNCT
ap-9818	389	1	since	since	SCONJ
ap-9818	389	2	these	these	DET
ap-9818	389	3	solutions	solution	NOUN
ap-9818	389	4	were	be	AUX
ap-9818	389	5	found	find	VERB
ap-9818	389	6	and	and	CCONJ
ap-9818	389	7	analyzed	analyze	VERB
ap-9818	389	8	in	in	ADP
ap-9818	389	9	[	[	X
ap-9818	389	10	24	24	NUM
ap-9818	389	11	,	,	PUNCT
ap-9818	389	12	38	38	NUM
ap-9818	389	13	]	]	PUNCT
ap-9818	389	14	,	,	PUNCT
ap-9818	389	15	we	we	PRON
ap-9818	389	16	do	do	AUX
ap-9818	389	17	not	not	PART
ap-9818	389	18	discuss	discuss	VERB
ap-9818	389	19	them	they	PRON
ap-9818	389	20	here	here	ADV
ap-9818	389	21	any	any	PRON
ap-9818	389	22	further	far	ADV
ap-9818	389	23	.	.	PUNCT
ap-9818	390	1	4.4	4.4	NUM
ap-9818	390	2	.	.	PUNCT
ap-9818	390	3	constant	constant	ADJ
ap-9818	390	4	mass	mass	NOUN
ap-9818	390	5	system	system	NOUN
ap-9818	390	6	in	in	ADP
ap-9818	390	7	our	our	PRON
ap-9818	390	8	final	final	ADJ
ap-9818	390	9	example	example	NOUN
ap-9818	390	10	we	we	PRON
ap-9818	390	11	consider	consider	VERB
ap-9818	390	12	the	the	DET
ap-9818	390	13	simplest	simple	ADJ
ap-9818	390	14	scenario	scenario	NOUN
ap-9818	390	15	of	of	ADP
ap-9818	390	16	a	a	DET
ap-9818	390	17	constant	constant	ADJ
ap-9818	390	18	mass	mass	NOUN
ap-9818	390	19	m	m	PROPN
ap-9818	390	20	,	,	PUNCT
ap-9818	390	21	that	that	SCONJ
ap-9818	390	22	without	without	ADP
ap-9818	390	23	restriction	restriction	NOUN
ap-9818	390	24	we	we	PRON
ap-9818	390	25	can	can	AUX
ap-9818	390	26	set	set	VERB
ap-9818	390	27	equal	equal	ADJ
ap-9818	390	28	to	to	ADP
ap-9818	390	29	one	one	NUM
ap-9818	390	30	,	,	PUNCT
ap-9818	390	31	meaning	mean	VERB
ap-9818	390	32	:	:	PUNCT
ap-9818	390	33	m(x	m(x	X
ap-9818	390	34	)	)	PUNCT
ap-9818	390	35	=	=	SYM
ap-9818	391	1	1	1	X
ap-9818	391	2	.	.	PUNCT
ap-9818	391	3	(	(	PUNCT
ap-9818	391	4	71	71	NUM
ap-9818	391	5	)	)	PUNCT
ap-9818	391	6	furthermore	furthermore	ADV
ap-9818	391	7	,	,	PUNCT
ap-9818	391	8	we	we	PRON
ap-9818	391	9	leave	leave	VERB
ap-9818	391	10	the	the	DET
ap-9818	391	11	potential	potential	ADJ
ap-9818	391	12	v	v	NOUN
ap-9818	391	13	of	of	ADP
ap-9818	391	14	our	our	PRON
ap-9818	391	15	system	system	NOUN
ap-9818	391	16	undetermined	undetermined	ADJ
ap-9818	391	17	except	except	SCONJ
ap-9818	391	18	for	for	ADP
ap-9818	391	19	requiring	require	VERB
ap-9818	391	20	the	the	DET
ap-9818	391	21	existence	existence	NOUN
ap-9818	391	22	of	of	ADP
ap-9818	391	23	an	an	DET
ap-9818	391	24	inverse	inverse	ADJ
ap-9818	391	25	quadratic	quadratic	ADJ
ap-9818	391	26	term	term	NOUN
ap-9818	391	27	.	.	PUNCT
ap-9818	392	1	we	we	PRON
ap-9818	392	2	write	write	VERB
ap-9818	392	3	:	:	PUNCT
ap-9818	392	4	v	v	NOUN
ap-9818	392	5	(	(	PUNCT
ap-9818	392	6	x	x	NOUN
ap-9818	392	7	)	)	PUNCT
ap-9818	392	8	=	=	PUNCT
ap-9818	393	1	c	c	X
ap-9818	393	2	x2	x2	PROPN
ap-9818	394	1	+	+	CCONJ
ap-9818	394	2	w	w	PROPN
ap-9818	394	3	(	(	PUNCT
ap-9818	394	4	x	x	NOUN
ap-9818	394	5	)	)	PUNCT
ap-9818	394	6	,	,	PUNCT
ap-9818	394	7	(	(	PUNCT
ap-9818	394	8	72	72	NUM
ap-9818	394	9	)	)	PUNCT
ap-9818	394	10	where	where	SCONJ
ap-9818	394	11	c	c	NOUN
ap-9818	394	12	is	be	AUX
ap-9818	394	13	a	a	DET
ap-9818	394	14	free	free	ADJ
ap-9818	394	15	constant	constant	ADJ
ap-9818	394	16	,	,	PUNCT
ap-9818	394	17	and	and	CCONJ
ap-9818	394	18	w	w	NOUN
ap-9818	394	19	stands	stand	VERB
ap-9818	394	20	for	for	ADP
ap-9818	394	21	an	an	DET
ap-9818	394	22	arbitrary	arbitrary	ADJ
ap-9818	394	23	function	function	NOUN
ap-9818	394	24	.	.	PUNCT
ap-9818	395	1	the	the	DET
ap-9818	395	2	combination	combination	NOUN
ap-9818	395	3	of	of	ADP
ap-9818	395	4	mass	mass	NOUN
ap-9818	395	5	(	(	PUNCT
ap-9818	395	6	71	71	NUM
ap-9818	395	7	)	)	PUNCT
ap-9818	395	8	and	and	CCONJ
ap-9818	395	9	potential	potential	ADJ
ap-9818	395	10	(	(	PUNCT
ap-9818	395	11	72	72	NUM
ap-9818	395	12	)	)	PUNCT
ap-9818	395	13	occurs	occur	VERB
ap-9818	395	14	in	in	ADP
ap-9818	395	15	radial	radial	ADJ
ap-9818	395	16	equations	equation	NOUN
ap-9818	395	17	that	that	PRON
ap-9818	395	18	result	result	VERB
ap-9818	395	19	from	from	ADP
ap-9818	395	20	a	a	DET
ap-9818	395	21	variable	variable	ADJ
ap-9818	395	22	separation	separation	NOUN
ap-9818	395	23	in	in	ADP
ap-9818	395	24	spherical	spherical	ADJ
ap-9818	395	25	coordinates	coordinate	NOUN
ap-9818	395	26	of	of	ADP
ap-9818	395	27	the	the	DET
ap-9818	395	28	three	three	NUM
ap-9818	395	29	-	-	PUNCT
ap-9818	395	30	dimensional	dimensional	ADJ
ap-9818	395	31	schrödinger	schrödinger	ADJ
ap-9818	395	32	equation	equation	NOUN
ap-9818	395	33	.	.	PUNCT
ap-9818	396	1	let	let	VERB
ap-9818	396	2	us	we	PRON
ap-9818	396	3	now	now	ADV
ap-9818	396	4	verify	verify	VERB
ap-9818	396	5	our	our	PRON
ap-9818	396	6	solvability	solvability	NOUN
ap-9818	396	7	conditions	condition	NOUN
ap-9818	396	8	(	(	PUNCT
ap-9818	396	9	17	17	NUM
ap-9818	396	10	)	)	PUNCT
ap-9818	396	11	and	and	CCONJ
ap-9818	396	12	(	(	PUNCT
ap-9818	396	13	19	19	NUM
ap-9818	396	14	)	)	PUNCT
ap-9818	396	15	.	.	PUNCT
ap-9818	397	1	it	it	PRON
ap-9818	397	2	is	be	AUX
ap-9818	397	3	straightforward	straightforward	ADJ
ap-9818	397	4	to	to	PART
ap-9818	397	5	see	see	VERB
ap-9818	397	6	that	that	SCONJ
ap-9818	397	7	the	the	DET
ap-9818	397	8	settings	setting	NOUN
ap-9818	397	9	:	:	PUNCT
ap-9818	397	10	c1	c1	PROPN
ap-9818	397	11	=	=	PUNCT
ap-9818	397	12	0	0	PROPN
ap-9818	397	13	,	,	PUNCT
ap-9818	397	14	c2	c2	PROPN
ap-9818	397	15	=	=	PUNCT
ap-9818	397	16	−m	−m	PROPN
ap-9818	397	17	,	,	PUNCT
ap-9818	397	18	a	a	DET
ap-9818	397	19	=	=	SYM
ap-9818	397	20	−1	−1	NOUN
ap-9818	397	21	,	,	PUNCT
ap-9818	397	22	b	b	NOUN
ap-9818	397	23	=	=	SYM
ap-9818	397	24	0	0	NUM
ap-9818	397	25	,	,	PUNCT
ap-9818	397	26	(	(	PUNCT
ap-9818	397	27	73	73	NUM
ap-9818	397	28	)	)	PUNCT
ap-9818	397	29	give	give	VERB
ap-9818	397	30	a	a	DET
ap-9818	397	31	constant	constant	ADJ
ap-9818	397	32	function	function	NOUN
ap-9818	397	33	,	,	PUNCT
ap-9818	397	34	such	such	ADJ
ap-9818	397	35	that	that	SCONJ
ap-9818	397	36	(	(	PUNCT
ap-9818	397	37	17	17	NUM
ap-9818	397	38	)	)	PUNCT
ap-9818	397	39	is	be	AUX
ap-9818	397	40	satisfied	satisfied	ADJ
ap-9818	397	41	.	.	PUNCT
ap-9818	398	1	the	the	DET
ap-9818	398	2	remaining	remain	VERB
ap-9818	398	3	condition	condition	NOUN
ap-9818	398	4	(	(	PUNCT
ap-9818	398	5	19	19	NUM
ap-9818	398	6	)	)	PUNCT
ap-9818	398	7	is	be	AUX
ap-9818	398	8	automatically	automatically	ADV
ap-9818	398	9	fulfilled	fulfil	VERB
ap-9818	398	10	after	after	ADP
ap-9818	398	11	inserting	insert	VERB
ap-9818	398	12	(	(	PUNCT
ap-9818	398	13	72	72	NUM
ap-9818	398	14	)	)	PUNCT
ap-9818	398	15	.	.	PUNCT
ap-9818	399	1	hence	hence	ADV
ap-9818	399	2	,	,	PUNCT
ap-9818	399	3	the	the	DET
ap-9818	399	4	effective	effective	ADJ
ap-9818	399	5	potentials	potential	NOUN
ap-9818	399	6	(	(	PUNCT
ap-9818	399	7	12	12	NUM
ap-9818	399	8	)	)	PUNCT
ap-9818	399	9	and	and	CCONJ
ap-9818	399	10	(	(	PUNCT
ap-9818	399	11	15	15	X
ap-9818	399	12	)	)	PUNCT
ap-9818	399	13	have	have	VERB
ap-9818	399	14	the	the	DET
ap-9818	399	15	same	same	ADJ
ap-9818	399	16	functional	functional	ADJ
ap-9818	399	17	form	form	NOUN
ap-9818	399	18	.	.	PUNCT
ap-9818	400	1	in	in	ADP
ap-9818	400	2	fact	fact	NOUN
ap-9818	400	3	,	,	PUNCT
ap-9818	400	4	their	their	PRON
ap-9818	400	5	explicit	explicit	ADJ
ap-9818	400	6	form	form	NOUN
ap-9818	400	7	reads	read	VERB
ap-9818	400	8	:	:	PUNCT
ap-9818	400	9	uν(x	uν(x	NUM
ap-9818	400	10	)	)	PUNCT
ap-9818	400	11	=	=	SYM
ap-9818	400	12	m	m	VERB
ap-9818	401	1	[	[	X
ap-9818	401	2	e	e	X
ap-9818	401	3	−	−	PROPN
ap-9818	401	4	w	w	PROPN
ap-9818	401	5	(	(	PUNCT
ap-9818	401	6	x	x	NOUN
ap-9818	401	7	)	)	PUNCT
ap-9818	401	8	]	]	PUNCT
ap-9818	402	1	+	+	CCONJ
ap-9818	402	2	δ	δ	PROPN
ap-9818	402	3	ν	ν	NOUN
ap-9818	402	4	−	−	PROPN
ap-9818	402	5	ν2	ν2	NOUN
ap-9818	402	6	−	−	PROPN
ap-9818	402	7	c	c	PROPN
ap-9818	402	8	x2	x2	PROPN
ap-9818	402	9	,	,	PUNCT
ap-9818	402	10	u0(x	u0(x	NUM
ap-9818	402	11	)	)	PUNCT
ap-9818	402	12	=	=	SYM
ap-9818	402	13	m	m	VERB
ap-9818	403	1	[	[	X
ap-9818	403	2	e	e	X
ap-9818	403	3	−	−	PROPN
ap-9818	403	4	w	w	PROPN
ap-9818	403	5	(	(	PUNCT
ap-9818	403	6	x	x	NOUN
ap-9818	403	7	)	)	PUNCT
ap-9818	403	8	]	]	PUNCT
ap-9818	404	1	−	−	PROPN
ap-9818	404	2	c	c	NOUN
ap-9818	404	3	x2	x2	INTJ
ap-9818	404	4	.	.	PUNCT
ap-9818	405	1	(	(	PUNCT
ap-9818	405	2	74	74	NUM
ap-9818	405	3	)	)	PUNCT
ap-9818	405	4	consequently	consequently	ADV
ap-9818	405	5	,	,	PUNCT
ap-9818	405	6	solvability	solvability	NOUN
ap-9818	405	7	of	of	ADP
ap-9818	405	8	the	the	DET
ap-9818	405	9	conventional	conventional	ADJ
ap-9818	405	10	equation	equation	NOUN
ap-9818	405	11	(	(	PUNCT
ap-9818	405	12	14	14	NUM
ap-9818	405	13	)	)	PUNCT
ap-9818	405	14	is	be	AUX
ap-9818	405	15	preserved	preserve	VERB
ap-9818	405	16	when	when	SCONJ
ap-9818	405	17	transitioning	transition	VERB
ap-9818	405	18	to	to	ADP
ap-9818	405	19	the	the	DET
ap-9818	405	20	dunkl	dunkl	PROPN
ap-9818	405	21	scenario	scenario	NOUN
ap-9818	405	22	(	(	PUNCT
ap-9818	405	23	11	11	NUM
ap-9818	405	24	)	)	PUNCT
ap-9818	405	25	.	.	PUNCT
ap-9818	406	1	5	5	X
ap-9818	406	2	.	.	X
ap-9818	406	3	concluding	conclude	VERB
ap-9818	406	4	remarks	remark	NOUN
ap-9818	406	5	we	we	PRON
ap-9818	406	6	will	will	AUX
ap-9818	406	7	now	now	ADV
ap-9818	406	8	make	make	VERB
ap-9818	406	9	several	several	ADJ
ap-9818	406	10	comments	comment	NOUN
ap-9818	406	11	on	on	ADP
ap-9818	406	12	the	the	DET
ap-9818	406	13	results	result	NOUN
ap-9818	406	14	found	find	VERB
ap-9818	406	15	in	in	ADP
ap-9818	406	16	this	this	DET
ap-9818	406	17	note	note	NOUN
ap-9818	406	18	,	,	PUNCT
ap-9818	406	19	discussing	discuss	VERB
ap-9818	406	20	its	its	PRON
ap-9818	406	21	properties	property	NOUN
ap-9818	406	22	,	,	PUNCT
ap-9818	406	23	and	and	CCONJ
ap-9818	406	24	possible	possible	ADJ
ap-9818	406	25	generalisations	generalisation	NOUN
ap-9818	406	26	.	.	PUNCT
ap-9818	407	1	•	•	NUM
ap-9818	407	2	upon	upon	SCONJ
ap-9818	407	3	introduction	introduction	NOUN
ap-9818	407	4	of	of	ADP
ap-9818	407	5	a	a	DET
ap-9818	407	6	deformed	deform	VERB
ap-9818	407	7	quantum	quantum	NOUN
ap-9818	407	8	theory	theory	NOUN
ap-9818	407	9	,	,	PUNCT
ap-9818	407	10	the	the	DET
ap-9818	407	11	associated	associated	ADJ
ap-9818	407	12	schrödinger	schrödinger	ADJ
ap-9818	407	13	equation	equation	NOUN
ap-9818	407	14	for	for	ADP
ap-9818	407	15	a	a	DET
ap-9818	407	16	specific	specific	ADJ
ap-9818	407	17	system	system	NOUN
ap-9818	407	18	can	can	AUX
ap-9818	407	19	change	change	VERB
ap-9818	407	20	its	its	PRON
ap-9818	407	21	solvability	solvability	NOUN
ap-9818	407	22	properties	property	NOUN
ap-9818	407	23	.	.	PUNCT
ap-9818	408	1	if	if	SCONJ
ap-9818	408	2	the	the	DET
ap-9818	408	3	deformation	deformation	NOUN
ap-9818	408	4	is	be	AUX
ap-9818	408	5	created	create	VERB
ap-9818	408	6	by	by	ADP
ap-9818	408	7	replacing	replace	VERB
ap-9818	408	8	the	the	DET
ap-9818	408	9	conventional	conventional	ADJ
ap-9818	408	10	derivative	derivative	NOUN
ap-9818	408	11	(	(	PUNCT
ap-9818	408	12	e.g.	e.g.	ADV
ap-9818	408	13	by	by	ADP
ap-9818	408	14	a	a	DET
ap-9818	408	15	dunkl	dunkl	NOUN
ap-9818	408	16	operator	operator	NOUN
ap-9818	408	17	)	)	PUNCT
ap-9818	408	18	,	,	PUNCT
ap-9818	408	19	then	then	ADV
ap-9818	408	20	the	the	DET
ap-9818	408	21	associated	associated	ADJ
ap-9818	408	22	schrödinger	schrödinger	ADJ
ap-9818	408	23	equation	equation	NOUN
ap-9818	408	24	can	can	AUX
ap-9818	408	25	have	have	VERB
ap-9818	408	26	a	a	DET
ap-9818	408	27	more	more	ADV
ap-9818	408	28	complicated	complicated	ADJ
ap-9818	408	29	structure	structure	NOUN
ap-9818	408	30	,	,	PUNCT
ap-9818	408	31	as	as	SCONJ
ap-9818	408	32	compared	compare	VERB
ap-9818	408	33	to	to	ADP
ap-9818	408	34	its	its	PRON
ap-9818	408	35	conventional	conventional	ADJ
ap-9818	408	36	(	(	PUNCT
ap-9818	408	37	non	non	ADJ
ap-9818	408	38	-	-	ADJ
ap-9818	408	39	deformed	deformed	ADJ
ap-9818	408	40	)	)	PUNCT
ap-9818	408	41	counterpart	counterpart	NOUN
ap-9818	408	42	.	.	PUNCT
ap-9818	409	1	if	if	SCONJ
ap-9818	409	2	the	the	DET
ap-9818	409	3	deformation	deformation	NOUN
ap-9818	409	4	is	be	AUX
ap-9818	409	5	due	due	ADJ
ap-9818	409	6	to	to	ADP
ap-9818	409	7	another	another	DET
ap-9818	409	8	mechanism	mechanism	NOUN
ap-9818	409	9	,	,	PUNCT
ap-9818	409	10	for	for	ADP
ap-9818	409	11	example	example	NOUN
ap-9818	409	12	the	the	DET
ap-9818	409	13	introduction	introduction	NOUN
ap-9818	409	14	of	of	ADP
ap-9818	409	15	energy	energy	NOUN
ap-9818	409	16	dependence	dependence	NOUN
ap-9818	409	17	in	in	ADP
ap-9818	409	18	the	the	DET
ap-9818	409	19	potential	potential	NOUN
ap-9818	409	20	,	,	PUNCT
ap-9818	409	21	the	the	DET
ap-9818	409	22	norm	norm	NOUN
ap-9818	409	23	takes	take	VERB
ap-9818	409	24	a	a	DET
ap-9818	409	25	non	non	ADJ
ap-9818	409	26	-	-	ADJ
ap-9818	409	27	conventional	conventional	ADJ
ap-9818	409	28	form	form	NOUN
ap-9818	409	29	[	[	X
ap-9818	409	30	27	27	NUM
ap-9818	409	31	]	]	PUNCT
ap-9818	409	32	.	.	PUNCT
ap-9818	410	1	in	in	ADP
ap-9818	410	2	both	both	DET
ap-9818	410	3	cases	case	NOUN
ap-9818	410	4	,	,	PUNCT
ap-9818	410	5	the	the	DET
ap-9818	410	6	solvability	solvability	NOUN
ap-9818	410	7	properties	property	NOUN
ap-9818	410	8	(	(	PUNCT
ap-9818	410	9	regarding	regard	VERB
ap-9818	410	10	physically	physically	ADV
ap-9818	410	11	meaningful	meaningful	ADJ
ap-9818	410	12	solutions	solution	NOUN
ap-9818	410	13	)	)	PUNCT
ap-9818	410	14	of	of	ADP
ap-9818	410	15	the	the	DET
ap-9818	410	16	governing	govern	VERB
ap-9818	410	17	equation	equation	NOUN
ap-9818	410	18	typically	typically	ADV
ap-9818	410	19	change	change	VERB
ap-9818	410	20	.	.	PUNCT
ap-9818	411	1	233	233	NUM
ap-9818	411	2	axel	axel	PROPN
ap-9818	411	3	schulze	schulze	NOUN
ap-9818	411	4	-	-	PUNCT
ap-9818	411	5	halberg	halberg	PROPN
ap-9818	411	6	acta	acta	PROPN
ap-9818	411	7	polytechnica	polytechnica	PROPN
ap-9818	411	8	•	•	SCONJ
ap-9818	411	9	there	there	PRON
ap-9818	411	10	is	be	VERB
ap-9818	411	11	no	no	DET
ap-9818	411	12	general	general	ADJ
ap-9818	411	13	method	method	NOUN
ap-9818	411	14	for	for	ADP
ap-9818	411	15	transitioning	transition	VERB
ap-9818	411	16	from	from	ADP
ap-9818	411	17	a	a	DET
ap-9818	411	18	conventional	conventional	ADJ
ap-9818	411	19	,	,	PUNCT
ap-9818	411	20	solvable	solvable	ADJ
ap-9818	411	21	schrödinger	schrödinger	ADJ
ap-9818	411	22	equation	equation	NOUN
ap-9818	411	23	to	to	ADP
ap-9818	411	24	its	its	PRON
ap-9818	411	25	deformed	deform	VERB
ap-9818	411	26	counterpart	counterpart	NOUN
ap-9818	411	27	.	.	PUNCT
ap-9818	412	1	in	in	ADP
ap-9818	412	2	order	order	NOUN
ap-9818	412	3	to	to	PART
ap-9818	412	4	construct	construct	VERB
ap-9818	412	5	such	such	DET
ap-9818	412	6	a	a	DET
ap-9818	412	7	transition	transition	NOUN
ap-9818	412	8	for	for	ADP
ap-9818	412	9	the	the	DET
ap-9818	412	10	solutions	solution	NOUN
ap-9818	412	11	,	,	PUNCT
ap-9818	412	12	the	the	DET
ap-9818	412	13	deformed	deform	VERB
ap-9818	412	14	schrödinger	schrödinger	ADJ
ap-9818	412	15	equation	equation	NOUN
ap-9818	412	16	must	must	AUX
ap-9818	412	17	be	be	AUX
ap-9818	412	18	compared	compare	VERB
ap-9818	412	19	with	with	ADP
ap-9818	412	20	its	its	PRON
ap-9818	412	21	conventional	conventional	ADJ
ap-9818	412	22	partner	partner	NOUN
ap-9818	412	23	,	,	PUNCT
ap-9818	412	24	such	such	ADJ
ap-9818	412	25	that	that	SCONJ
ap-9818	412	26	,	,	PUNCT
ap-9818	412	27	conditions	condition	NOUN
ap-9818	412	28	for	for	ADP
ap-9818	412	29	the	the	DET
ap-9818	412	30	persistence	persistence	NOUN
ap-9818	412	31	of	of	ADP
ap-9818	412	32	solvability	solvability	NOUN
ap-9818	412	33	can	can	AUX
ap-9818	412	34	be	be	AUX
ap-9818	412	35	derived	derive	VERB
ap-9818	412	36	.	.	PUNCT
ap-9818	413	1	this	this	PRON
ap-9818	413	2	leads	lead	VERB
ap-9818	413	3	to	to	ADP
ap-9818	413	4	constraints	constraint	NOUN
ap-9818	413	5	on	on	ADP
ap-9818	413	6	the	the	DET
ap-9818	413	7	parameters	parameter	NOUN
ap-9818	413	8	in	in	ADP
ap-9818	413	9	the	the	DET
ap-9818	413	10	equation	equation	NOUN
ap-9818	413	11	,	,	PUNCT
ap-9818	413	12	such	such	ADJ
ap-9818	413	13	as	as	ADP
ap-9818	413	14	the	the	DET
ap-9818	413	15	potential	potential	NOUN
ap-9818	413	16	or	or	CCONJ
ap-9818	413	17	,	,	PUNCT
ap-9818	413	18	as	as	ADP
ap-9818	413	19	in	in	ADP
ap-9818	413	20	the	the	DET
ap-9818	413	21	present	present	ADJ
ap-9818	413	22	case	case	NOUN
ap-9818	413	23	,	,	PUNCT
ap-9818	413	24	the	the	DET
ap-9818	413	25	position	position	NOUN
ap-9818	413	26	-	-	PUNCT
ap-9818	413	27	dependent	dependent	ADJ
ap-9818	413	28	mass	mass	NOUN
ap-9818	413	29	.	.	PUNCT
ap-9818	414	1	•	•	NUM
ap-9818	414	2	our	our	PRON
ap-9818	414	3	solvability	solvability	NOUN
ap-9818	414	4	conditions	condition	NOUN
ap-9818	414	5	derived	derive	VERB
ap-9818	414	6	in	in	ADP
ap-9818	414	7	section	section	NOUN
ap-9818	414	8	3	3	NUM
ap-9818	414	9	open	open	VERB
ap-9818	414	10	the	the	DET
ap-9818	414	11	possibility	possibility	NOUN
ap-9818	414	12	of	of	ADP
ap-9818	414	13	constructing	construct	VERB
ap-9818	414	14	solutions	solution	NOUN
ap-9818	414	15	to	to	ADP
ap-9818	414	16	the	the	DET
ap-9818	414	17	governing	govern	VERB
ap-9818	414	18	equations	equation	NOUN
ap-9818	414	19	in	in	ADP
ap-9818	414	20	dunkl	dunkl	NOUN
ap-9818	414	21	-	-	PUNCT
ap-9818	414	22	schrödinger	schrödinger	NOUN
ap-9818	414	23	systems	system	NOUN
ap-9818	414	24	from	from	ADP
ap-9818	414	25	their	their	PRON
ap-9818	414	26	conventional	conventional	ADJ
ap-9818	414	27	counterparts	counterpart	NOUN
ap-9818	414	28	.	.	PUNCT
ap-9818	415	1	in	in	ADP
ap-9818	415	2	addition	addition	NOUN
ap-9818	415	3	,	,	PUNCT
ap-9818	415	4	our	our	PRON
ap-9818	415	5	method	method	NOUN
ap-9818	415	6	provides	provide	VERB
ap-9818	415	7	an	an	DET
ap-9818	415	8	explanation	explanation	NOUN
ap-9818	415	9	for	for	ADP
ap-9818	415	10	the	the	DET
ap-9818	415	11	solvability	solvability	NOUN
ap-9818	415	12	of	of	ADP
ap-9818	415	13	systems	system	NOUN
ap-9818	415	14	within	within	ADP
ap-9818	415	15	the	the	DET
ap-9818	415	16	dunkl	dunkl	NOUN
ap-9818	415	17	formalism	formalism	NOUN
ap-9818	415	18	that	that	PRON
ap-9818	415	19	were	be	AUX
ap-9818	415	20	recently	recently	ADV
ap-9818	415	21	studied	study	VERB
ap-9818	415	22	in	in	ADP
ap-9818	415	23	the	the	DET
ap-9818	415	24	literature	literature	NOUN
ap-9818	415	25	.	.	PUNCT
ap-9818	416	1	•	•	NUM
ap-9818	416	2	a	a	DET
ap-9818	416	3	restriction	restriction	NOUN
ap-9818	416	4	to	to	ADP
ap-9818	416	5	the	the	DET
ap-9818	416	6	approach	approach	NOUN
ap-9818	416	7	we	we	PRON
ap-9818	416	8	are	be	AUX
ap-9818	416	9	taking	take	VERB
ap-9818	416	10	in	in	ADP
ap-9818	416	11	this	this	DET
ap-9818	416	12	work	work	NOUN
ap-9818	416	13	lies	lie	VERB
ap-9818	416	14	in	in	ADP
ap-9818	416	15	the	the	DET
ap-9818	416	16	particular	particular	ADJ
ap-9818	416	17	shape	shape	NOUN
ap-9818	416	18	of	of	ADP
ap-9818	416	19	the	the	DET
ap-9818	416	20	position	position	NOUN
ap-9818	416	21	-	-	PUNCT
ap-9818	416	22	dependent	dependent	ADJ
ap-9818	416	23	mass	mass	NOUN
ap-9818	416	24	that	that	PRON
ap-9818	416	25	must	must	AUX
ap-9818	416	26	comply	comply	VERB
ap-9818	416	27	with	with	ADP
ap-9818	416	28	the	the	DET
ap-9818	416	29	four	four	NUM
ap-9818	416	30	-	-	PUNCT
ap-9818	416	31	parameter	parameter	NOUN
ap-9818	416	32	class	class	NOUN
ap-9818	416	33	(	(	PUNCT
ap-9818	416	34	17	17	NUM
ap-9818	416	35	)	)	PUNCT
ap-9818	416	36	.	.	PUNCT
ap-9818	417	1	even	even	ADV
ap-9818	417	2	though	though	SCONJ
ap-9818	417	3	the	the	DET
ap-9818	417	4	latter	latter	ADJ
ap-9818	417	5	class	class	NOUN
ap-9818	417	6	contains	contain	VERB
ap-9818	417	7	many	many	ADJ
ap-9818	417	8	commonly	commonly	ADV
ap-9818	417	9	used	use	VERB
ap-9818	417	10	mass	mass	NOUN
ap-9818	417	11	profiles	profile	NOUN
ap-9818	417	12	as	as	ADP
ap-9818	417	13	special	special	ADJ
ap-9818	417	14	cases	case	NOUN
ap-9818	417	15	(	(	PUNCT
ap-9818	417	16	see	see	VERB
ap-9818	417	17	section	section	NOUN
ap-9818	417	18	3	3	NUM
ap-9818	417	19	)	)	PUNCT
ap-9818	417	20	,	,	PUNCT
ap-9818	417	21	there	there	PRON
ap-9818	417	22	is	be	VERB
ap-9818	417	23	a	a	DET
ap-9818	417	24	vast	vast	ADJ
ap-9818	417	25	amount	amount	NOUN
ap-9818	417	26	of	of	ADP
ap-9818	417	27	profiles	profile	NOUN
ap-9818	417	28	that	that	PRON
ap-9818	417	29	can	can	AUX
ap-9818	417	30	not	not	PART
ap-9818	417	31	be	be	AUX
ap-9818	417	32	written	write	VERB
ap-9818	417	33	in	in	ADP
ap-9818	417	34	the	the	DET
ap-9818	417	35	form	form	NOUN
ap-9818	417	36	(	(	PUNCT
ap-9818	417	37	17	17	NUM
ap-9818	417	38	)	)	PUNCT
ap-9818	417	39	.	.	PUNCT
ap-9818	418	1	an	an	DET
ap-9818	418	2	example	example	NOUN
ap-9818	418	3	is	be	AUX
ap-9818	418	4	given	give	VERB
ap-9818	418	5	by	by	ADP
ap-9818	418	6	hyperbolic	hyperbolic	ADJ
ap-9818	418	7	functions	function	NOUN
ap-9818	418	8	that	that	PRON
ap-9818	418	9	are	be	AUX
ap-9818	418	10	often	often	ADV
ap-9818	418	11	used	use	VERB
ap-9818	418	12	as	as	ADP
ap-9818	418	13	smooth	smooth	ADJ
ap-9818	418	14	steps	step	NOUN
ap-9818	418	15	(	(	PUNCT
ap-9818	418	16	hyperbolic	hyperbolic	ADJ
ap-9818	418	17	tangent	tangent	NOUN
ap-9818	418	18	)	)	PUNCT
ap-9818	418	19	or	or	CCONJ
ap-9818	418	20	finite	finite	ADJ
ap-9818	418	21	wells	well	NOUN
ap-9818	418	22	(	(	PUNCT
ap-9818	418	23	hyperbolic	hyperbolic	ADJ
ap-9818	418	24	secant	secant	NOUN
ap-9818	418	25	)	)	PUNCT
ap-9818	418	26	.	.	PUNCT
ap-9818	419	1	•	•	NUM
ap-9818	419	2	a	a	DET
ap-9818	419	3	further	further	ADJ
ap-9818	419	4	restriction	restriction	NOUN
ap-9818	419	5	of	of	ADP
ap-9818	419	6	our	our	PRON
ap-9818	419	7	method	method	NOUN
ap-9818	419	8	concerns	concern	VERB
ap-9818	419	9	the	the	DET
ap-9818	419	10	potential	potential	NOUN
ap-9818	419	11	in	in	ADP
ap-9818	419	12	the	the	DET
ap-9818	419	13	schrödinger	schrödinger	ADJ
ap-9818	419	14	equation	equation	NOUN
ap-9818	419	15	that	that	PRON
ap-9818	419	16	must	must	AUX
ap-9818	419	17	contain	contain	VERB
ap-9818	419	18	an	an	DET
ap-9818	419	19	inverse	inverse	ADJ
ap-9818	419	20	quadratic	quadratic	ADJ
ap-9818	419	21	term	term	NOUN
ap-9818	419	22	,	,	PUNCT
ap-9818	419	23	see	see	VERB
ap-9818	419	24	(	(	PUNCT
ap-9818	419	25	19	19	NUM
ap-9818	419	26	)	)	PUNCT
ap-9818	419	27	.	.	PUNCT
ap-9818	420	1	while	while	SCONJ
ap-9818	420	2	this	this	PRON
ap-9818	420	3	is	be	AUX
ap-9818	420	4	compatible	compatible	ADJ
ap-9818	420	5	with	with	ADP
ap-9818	420	6	certain	certain	ADJ
ap-9818	420	7	classes	class	NOUN
ap-9818	420	8	of	of	ADP
ap-9818	420	9	systems	system	NOUN
ap-9818	420	10	,	,	PUNCT
ap-9818	420	11	such	such	ADJ
ap-9818	420	12	as	as	ADP
ap-9818	420	13	those	those	PRON
ap-9818	420	14	governed	govern	VERB
ap-9818	420	15	by	by	ADP
ap-9818	420	16	radial	radial	ADJ
ap-9818	420	17	equations	equation	NOUN
ap-9818	420	18	after	after	ADP
ap-9818	420	19	a	a	DET
ap-9818	420	20	separation	separation	NOUN
ap-9818	420	21	in	in	ADP
ap-9818	420	22	spherical	spherical	ADJ
ap-9818	420	23	coordinates	coordinate	NOUN
ap-9818	420	24	,	,	PUNCT
ap-9818	420	25	in	in	ADP
ap-9818	420	26	general	general	ADJ
ap-9818	420	27	condition	condition	NOUN
ap-9818	420	28	(	(	PUNCT
ap-9818	420	29	19	19	NUM
ap-9818	420	30	)	)	PUNCT
ap-9818	420	31	is	be	AUX
ap-9818	420	32	not	not	PART
ap-9818	420	33	satisfied	satisfied	ADJ
ap-9818	420	34	.	.	PUNCT
ap-9818	421	1	as	as	ADP
ap-9818	421	2	examples	example	NOUN
ap-9818	421	3	we	we	PRON
ap-9818	421	4	can	can	AUX
ap-9818	421	5	mention	mention	VERB
ap-9818	421	6	exponential	exponential	ADJ
ap-9818	421	7	potentials	potential	NOUN
ap-9818	421	8	that	that	PRON
ap-9818	421	9	include	include	VERB
ap-9818	421	10	the	the	DET
ap-9818	421	11	hyperbolic	hyperbolic	ADJ
ap-9818	421	12	and	and	CCONJ
ap-9818	421	13	trigonometric	trigonometric	ADJ
ap-9818	421	14	cases	case	NOUN
ap-9818	421	15	.	.	PUNCT
ap-9818	422	1	•	•	NUM
ap-9818	422	2	besides	besides	SCONJ
ap-9818	422	3	the	the	DET
ap-9818	422	4	two	two	NUM
ap-9818	422	5	restrictions	restriction	NOUN
ap-9818	422	6	,	,	PUNCT
ap-9818	422	7	there	there	PRON
ap-9818	422	8	are	be	VERB
ap-9818	422	9	also	also	ADV
ap-9818	422	10	ways	way	NOUN
ap-9818	422	11	to	to	PART
ap-9818	422	12	extend	extend	VERB
ap-9818	422	13	the	the	DET
ap-9818	422	14	method	method	NOUN
ap-9818	422	15	proposed	propose	VERB
ap-9818	422	16	in	in	ADP
ap-9818	422	17	this	this	DET
ap-9818	422	18	work	work	NOUN
ap-9818	422	19	,	,	PUNCT
ap-9818	422	20	such	such	ADJ
ap-9818	422	21	as	as	ADP
ap-9818	422	22	its	its	PRON
ap-9818	422	23	generalisation	generalisation	NOUN
ap-9818	422	24	to	to	ADP
ap-9818	422	25	equations	equation	NOUN
ap-9818	422	26	different	different	ADJ
ap-9818	422	27	from	from	ADP
ap-9818	422	28	the	the	DET
ap-9818	422	29	schrödinger	schrödinger	ADJ
ap-9818	422	30	case	case	NOUN
ap-9818	422	31	,	,	PUNCT
ap-9818	422	32	for	for	ADP
ap-9818	422	33	example	example	NOUN
ap-9818	422	34	,	,	PUNCT
ap-9818	422	35	the	the	DET
ap-9818	422	36	klein	klein	PROPN
ap-9818	422	37	-	-	PUNCT
ap-9818	422	38	gordon	gordon	PROPN
ap-9818	422	39	and	and	CCONJ
ap-9818	422	40	the	the	DET
ap-9818	422	41	dirac	dirac	NOUN
ap-9818	422	42	equation	equation	NOUN
ap-9818	422	43	.	.	PUNCT
ap-9818	423	1	here	here	ADV
ap-9818	423	2	,	,	PUNCT
ap-9818	423	3	the	the	DET
ap-9818	423	4	simplest	simple	ADJ
ap-9818	423	5	case	case	NOUN
ap-9818	423	6	is	be	AUX
ap-9818	423	7	the	the	DET
ap-9818	423	8	one	one	NUM
ap-9818	423	9	-	-	PUNCT
ap-9818	423	10	dimensional	dimensional	ADJ
ap-9818	423	11	klein	klein	PROPN
ap-9818	423	12	-	-	PUNCT
ap-9818	423	13	gordon	gordon	PROPN
ap-9818	423	14	equation	equation	NOUN
ap-9818	423	15	.	.	PUNCT
ap-9818	424	1	since	since	SCONJ
ap-9818	424	2	it	it	PRON
ap-9818	424	3	is	be	AUX
ap-9818	424	4	not	not	PART
ap-9818	424	5	built	build	VERB
ap-9818	424	6	from	from	ADP
ap-9818	424	7	a	a	DET
ap-9818	424	8	hamiltonian	hamiltonian	NOUN
ap-9818	424	9	,	,	PUNCT
ap-9818	424	10	the	the	DET
ap-9818	424	11	equation	equation	NOUN
ap-9818	424	12	does	do	AUX
ap-9818	424	13	not	not	PART
ap-9818	424	14	contain	contain	VERB
ap-9818	424	15	derivatives	derivative	NOUN
ap-9818	424	16	of	of	ADP
ap-9818	424	17	the	the	DET
ap-9818	424	18	position	position	NOUN
ap-9818	424	19	-	-	PUNCT
ap-9818	424	20	dependent	dependent	ADJ
ap-9818	424	21	mass	mass	NOUN
ap-9818	424	22	.	.	PUNCT
ap-9818	425	1	therefore	therefore	ADV
ap-9818	425	2	,	,	PUNCT
ap-9818	425	3	the	the	DET
ap-9818	425	4	solvability	solvability	NOUN
ap-9818	425	5	conditions	condition	NOUN
ap-9818	425	6	will	will	AUX
ap-9818	425	7	simply	simply	ADV
ap-9818	425	8	require	require	VERB
ap-9818	425	9	that	that	SCONJ
ap-9818	425	10	an	an	DET
ap-9818	425	11	inverse	inverse	ADJ
ap-9818	425	12	quadratic	quadratic	ADJ
ap-9818	425	13	term	term	NOUN
ap-9818	425	14	is	be	AUX
ap-9818	425	15	present	present	ADJ
ap-9818	425	16	in	in	ADP
ap-9818	425	17	the	the	DET
ap-9818	425	18	effective	effective	ADJ
ap-9818	425	19	potential	potential	NOUN
ap-9818	425	20	.	.	PUNCT
ap-9818	426	1	this	this	DET
ap-9818	426	2	term	term	NOUN
ap-9818	426	3	can	can	AUX
ap-9818	426	4	be	be	AUX
ap-9818	426	5	contributed	contribute	VERB
ap-9818	426	6	either	either	CCONJ
ap-9818	426	7	by	by	ADP
ap-9818	426	8	the	the	DET
ap-9818	426	9	position	position	NOUN
ap-9818	426	10	-	-	PUNCT
ap-9818	426	11	dependent	dependent	ADJ
ap-9818	426	12	mass	mass	NOUN
ap-9818	426	13	or	or	CCONJ
ap-9818	426	14	the	the	DET
ap-9818	426	15	potential	potential	NOUN
ap-9818	426	16	.	.	PUNCT
ap-9818	427	1	a	a	DET
ap-9818	427	2	similar	similar	ADJ
ap-9818	427	3	situation	situation	NOUN
ap-9818	427	4	occurs	occur	VERB
ap-9818	427	5	in	in	ADP
ap-9818	427	6	the	the	DET
ap-9818	427	7	higher	higher	ADV
ap-9818	427	8	-	-	PUNCT
ap-9818	427	9	dimensional	dimensional	ADJ
ap-9818	427	10	case	case	NOUN
ap-9818	427	11	,	,	PUNCT
ap-9818	427	12	if	if	SCONJ
ap-9818	427	13	spherical	spherical	ADJ
ap-9818	427	14	symmetry	symmetry	NOUN
ap-9818	427	15	can	can	AUX
ap-9818	427	16	be	be	AUX
ap-9818	427	17	used	use	VERB
ap-9818	427	18	.	.	PUNCT
ap-9818	428	1	for	for	ADP
ap-9818	428	2	other	other	ADJ
ap-9818	428	3	systems	system	NOUN
ap-9818	428	4	,	,	PUNCT
ap-9818	428	5	involving	involve	VERB
ap-9818	428	6	for	for	ADP
ap-9818	428	7	example	example	NOUN
ap-9818	428	8	angular	angular	ADJ
ap-9818	428	9	-	-	PUNCT
ap-9818	428	10	dependent	dependent	ADJ
ap-9818	428	11	potentials	potential	NOUN
ap-9818	428	12	,	,	PUNCT
ap-9818	428	13	the	the	DET
ap-9818	428	14	solvability	solvability	NOUN
ap-9818	428	15	conditions	condition	NOUN
ap-9818	428	16	can	can	AUX
ap-9818	428	17	become	become	VERB
ap-9818	428	18	much	much	ADV
ap-9818	428	19	more	more	ADV
ap-9818	428	20	complicated	complicated	ADJ
ap-9818	428	21	.	.	PUNCT
ap-9818	429	1	the	the	DET
ap-9818	429	2	same	same	ADJ
ap-9818	429	3	is	be	AUX
ap-9818	429	4	true	true	ADJ
ap-9818	429	5	for	for	ADP
ap-9818	429	6	the	the	DET
ap-9818	429	7	dirac	dirac	NOUN
ap-9818	429	8	equation	equation	NOUN
ap-9818	429	9	,	,	PUNCT
ap-9818	429	10	where	where	SCONJ
ap-9818	429	11	the	the	DET
ap-9818	429	12	latter	latter	ADJ
ap-9818	429	13	conditions	condition	NOUN
ap-9818	429	14	depend	depend	VERB
ap-9818	429	15	on	on	ADP
ap-9818	429	16	the	the	DET
ap-9818	429	17	symmetries	symmetry	NOUN
ap-9818	429	18	of	of	ADP
ap-9818	429	19	the	the	DET
ap-9818	429	20	potential	potential	NOUN
ap-9818	429	21	and	and	CCONJ
ap-9818	429	22	the	the	DET
ap-9818	429	23	vector	vector	NOUN
ap-9818	429	24	potential	potential	NOUN
ap-9818	429	25	coupled	couple	VERB
ap-9818	429	26	to	to	ADP
ap-9818	429	27	the	the	DET
ap-9818	429	28	system	system	NOUN
ap-9818	429	29	.	.	PUNCT
ap-9818	430	1	specific	specific	ADJ
ap-9818	430	2	systems	system	NOUN
ap-9818	430	3	involving	involve	VERB
ap-9818	430	4	the	the	DET
ap-9818	430	5	latter	latter	ADJ
ap-9818	430	6	two	two	NUM
ap-9818	430	7	equations	equation	NOUN
ap-9818	430	8	have	have	AUX
ap-9818	430	9	already	already	ADV
ap-9818	430	10	been	be	AUX
ap-9818	430	11	considered	consider	VERB
ap-9818	430	12	in	in	ADP
ap-9818	430	13	recent	recent	ADJ
ap-9818	430	14	literature	literature	NOUN
ap-9818	430	15	,	,	PUNCT
ap-9818	430	16	as	as	SCONJ
ap-9818	430	17	mentioned	mention	VERB
ap-9818	430	18	in	in	ADP
ap-9818	430	19	the	the	DET
ap-9818	430	20	introduction	introduction	NOUN
ap-9818	430	21	.	.	PUNCT
ap-9818	431	1	these	these	DET
ap-9818	431	2	topics	topic	NOUN
ap-9818	431	3	will	will	AUX
ap-9818	431	4	be	be	AUX
ap-9818	431	5	investigated	investigate	VERB
ap-9818	431	6	in	in	ADP
ap-9818	431	7	future	future	ADJ
ap-9818	431	8	research	research	NOUN
ap-9818	431	9	.	.	PUNCT
ap-9818	432	1	list	list	NOUN
ap-9818	432	2	of	of	ADP
ap-9818	432	3	symbols	symbol	NOUN
ap-9818	432	4	hν	hν	VERB
ap-9818	432	5	hamiltonian	hamiltonian	ADJ
ap-9818	432	6	for	for	ADP
ap-9818	432	7	parameter	parameter	NOUN
ap-9818	432	8	ν	ν	X
ap-9818	432	9	>	>	X
ap-9818	432	10	−	−	PROPN
ap-9818	432	11	1	1	NUM
ap-9818	432	12	2	2	NUM
ap-9818	432	13	α	α	NOUN
ap-9818	432	14	,	,	PUNCT
ap-9818	432	15	γ	γ	PROPN
ap-9818	432	16	constants	constant	NOUN
ap-9818	432	17	in	in	ADP
ap-9818	432	18	the	the	DET
ap-9818	432	19	hamiltonian	hamiltonian	NOUN
ap-9818	432	20	v	v	ADP
ap-9818	432	21	potential	potential	NOUN
ap-9818	432	22	of	of	ADP
ap-9818	432	23	the	the	DET
ap-9818	432	24	system	system	NOUN
ap-9818	432	25	e	e	NOUN
ap-9818	432	26	stationary	stationary	ADJ
ap-9818	432	27	energy	energy	NOUN
ap-9818	432	28	dν	dν	VERB
ap-9818	432	29	dunkl	dunkl	NOUN
ap-9818	432	30	operator	operator	NOUN
ap-9818	432	31	for	for	ADP
ap-9818	432	32	parameter	parameter	NOUN
ap-9818	432	33	ν	ν	X
ap-9818	432	34	>	>	X
ap-9818	433	1	−	−	PROPN
ap-9818	434	1	1	1	NUM
ap-9818	434	2	2	2	NUM
ap-9818	434	3	δ	δ	NOUN
ap-9818	434	4	constant	constant	ADJ
ap-9818	434	5	determining	determine	VERB
ap-9818	434	6	parity	parity	NOUN
ap-9818	434	7	of	of	ADP
ap-9818	434	8	the	the	DET
ap-9818	434	9	solution	solution	NOUN
ap-9818	434	10	m	m	NOUN
ap-9818	434	11	position	position	NOUN
ap-9818	434	12	-	-	PUNCT
ap-9818	434	13	dependent	dependent	ADJ
ap-9818	434	14	mass	mass	NOUN
ap-9818	434	15	uν	uν	ADP
ap-9818	434	16	potential	potential	NOUN
ap-9818	434	17	of	of	ADP
ap-9818	434	18	reduced	reduce	VERB
ap-9818	434	19	schrödinger	schrödinger	ADJ
ap-9818	434	20	equation	equation	NOUN
ap-9818	434	21	for	for	ADP
ap-9818	434	22	parameter	parameter	NOUN
ap-9818	434	23	ν	ν	X
ap-9818	434	24	>	>	X
ap-9818	434	25	−	−	NUM
ap-9818	434	26	1	1	NUM
ap-9818	434	27	2	2	NUM
ap-9818	434	28	c1	c1	NOUN
ap-9818	434	29	,	,	PUNCT
ap-9818	434	30	c2	c2	PROPN
ap-9818	434	31	,	,	PUNCT
ap-9818	434	32	c3	c3	PROPN
ap-9818	434	33	,	,	PUNCT
ap-9818	434	34	a	a	DET
ap-9818	434	35	,	,	PUNCT
ap-9818	434	36	b	b	NOUN
ap-9818	434	37	,	,	PUNCT
ap-9818	434	38	λ	λ	PROPN
ap-9818	434	39	constants	constant	NOUN
ap-9818	434	40	in	in	ADP
ap-9818	434	41	the	the	DET
ap-9818	434	42	constrained	constrain	VERB
ap-9818	434	43	position	position	NOUN
ap-9818	434	44	-	-	PUNCT
ap-9818	434	45	dependent	dependent	ADJ
ap-9818	434	46	mass	mass	NOUN
ap-9818	434	47	c	c	PROPN
ap-9818	434	48	constant	constant	ADJ
ap-9818	434	49	in	in	ADP
ap-9818	434	50	the	the	DET
ap-9818	434	51	constrained	constrain	VERB
ap-9818	434	52	potential	potential	NOUN
ap-9818	434	53	v	v	X
ap-9818	434	54	w	w	NOUN
ap-9818	434	55	term	term	NOUN
ap-9818	434	56	in	in	ADP
ap-9818	434	57	the	the	DET
ap-9818	434	58	constrained	constrain	VERB
ap-9818	434	59	potential	potential	NOUN
ap-9818	434	60	v	v	PRON
ap-9818	434	61	f1	f1	NOUN
ap-9818	434	62	,	,	PUNCT
ap-9818	434	63	f2	f2	PROPN
ap-9818	434	64	,	,	PUNCT
ap-9818	434	65	g1	g1	PROPN
ap-9818	434	66	,	,	PUNCT
ap-9818	434	67	g2	g2	PROPN
ap-9818	434	68	,	,	PUNCT
ap-9818	434	69	v1	v1	NOUN
ap-9818	434	70	abbreviations	abbreviation	NOUN
ap-9818	434	71	used	use	VERB
ap-9818	434	72	in	in	ADP
ap-9818	434	73	the	the	DET
ap-9818	434	74	examples	example	NOUN
ap-9818	434	75	references	reference	NOUN
ap-9818	434	76	[	[	X
ap-9818	434	77	1	1	NUM
ap-9818	434	78	]	]	PUNCT
ap-9818	434	79	e.	e.	PROPN
ap-9818	434	80	p.	p.	PROPN
ap-9818	434	81	wigner	wigner	NOUN
ap-9818	434	82	.	.	PUNCT
ap-9818	435	1	do	do	AUX
ap-9818	435	2	the	the	DET
ap-9818	435	3	equations	equation	NOUN
ap-9818	435	4	of	of	ADP
ap-9818	435	5	motion	motion	NOUN
ap-9818	435	6	determine	determine	VERB
ap-9818	435	7	the	the	DET
ap-9818	435	8	quantum	quantum	ADJ
ap-9818	435	9	mechanical	mechanical	ADJ
ap-9818	435	10	commutation	commutation	NOUN
ap-9818	435	11	relations	relation	NOUN
ap-9818	435	12	?	?	PUNCT
ap-9818	436	1	physical	physical	ADJ
ap-9818	436	2	review	review	PROPN
ap-9818	436	3	77:711–712	77:711–712	PROPN
ap-9818	436	4	,	,	PUNCT
ap-9818	436	5	1950	1950	NUM
ap-9818	436	6	.	.	PUNCT
ap-9818	437	1	https://doi.org/10.1103/physrev.77.711	https://doi.org/10.1103/physrev.77.711	VERB
ap-9818	437	2	[	[	X
ap-9818	437	3	2	2	NUM
ap-9818	437	4	]	]	PUNCT
ap-9818	437	5	l.	l.	PROPN
ap-9818	437	6	m.	m.	PROPN
ap-9818	437	7	yang	yang	PROPN
ap-9818	437	8	.	.	PUNCT
ap-9818	438	1	a	a	DET
ap-9818	438	2	note	note	NOUN
ap-9818	438	3	on	on	ADP
ap-9818	438	4	the	the	DET
ap-9818	438	5	quantum	quantum	ADJ
ap-9818	438	6	rule	rule	NOUN
ap-9818	438	7	of	of	ADP
ap-9818	438	8	the	the	DET
ap-9818	438	9	harmonic	harmonic	ADJ
ap-9818	438	10	oscillator	oscillator	NOUN
ap-9818	438	11	.	.	PUNCT
ap-9818	439	1	physical	physical	ADJ
ap-9818	439	2	review	review	NOUN
ap-9818	439	3	84:788–790	84:788–790	NUM
ap-9818	439	4	,	,	PUNCT
ap-9818	439	5	1951	1951	NUM
ap-9818	439	6	.	.	PUNCT
ap-9818	440	1	https://doi.org/10.1103/physrev.84.788	https://doi.org/10.1103/physrev.84.788	NOUN
ap-9818	441	1	[	[	X
ap-9818	441	2	3	3	NUM
ap-9818	441	3	]	]	PUNCT
ap-9818	441	4	h.	h.	PROPN
ap-9818	441	5	s.	s.	PROPN
ap-9818	441	6	green	green	PROPN
ap-9818	441	7	.	.	PUNCT
ap-9818	442	1	a	a	DET
ap-9818	442	2	generalized	generalized	ADJ
ap-9818	442	3	method	method	NOUN
ap-9818	442	4	of	of	ADP
ap-9818	442	5	field	field	NOUN
ap-9818	442	6	quantization	quantization	NOUN
ap-9818	442	7	.	.	PUNCT
ap-9818	443	1	physical	physical	ADJ
ap-9818	443	2	review	review	NOUN
ap-9818	443	3	90:270–273	90:270–273	NUM
ap-9818	443	4	,	,	PUNCT
ap-9818	443	5	1953	1953	NUM
ap-9818	443	6	.	.	PUNCT
ap-9818	444	1	https://doi.org/10.1103/physrev.90.270	https://doi.org/10.1103/physrev.90.270	NOUN
ap-9818	445	1	[	[	X
ap-9818	445	2	4	4	X
ap-9818	445	3	]	]	X
ap-9818	445	4	o.	o.	PROPN
ap-9818	445	5	w.	w.	PROPN
ap-9818	445	6	greenberg	greenberg	PROPN
ap-9818	445	7	,	,	PUNCT
ap-9818	445	8	a.	a.	PROPN
ap-9818	445	9	m.	m.	PROPN
ap-9818	445	10	l.	l.	PROPN
ap-9818	445	11	messiah	messiah	PROPN
ap-9818	445	12	.	.	PROPN
ap-9818	445	13	selection	selection	NOUN
ap-9818	445	14	rules	rule	NOUN
ap-9818	445	15	for	for	ADP
ap-9818	445	16	parafields	parafield	NOUN
ap-9818	445	17	and	and	CCONJ
ap-9818	445	18	the	the	DET
ap-9818	445	19	absence	absence	NOUN
ap-9818	445	20	of	of	ADP
ap-9818	445	21	para	para	NOUN
ap-9818	445	22	particles	particle	NOUN
ap-9818	445	23	in	in	ADP
ap-9818	445	24	nature	nature	NOUN
ap-9818	445	25	.	.	PUNCT
ap-9818	446	1	physical	physical	ADJ
ap-9818	446	2	review	review	NOUN
ap-9818	446	3	138	138	NUM
ap-9818	446	4	:	:	PUNCT
ap-9818	446	5	b1155	b1155	PROPN
ap-9818	446	6	–	–	PUNCT
ap-9818	446	7	b1167	b1167	PROPN
ap-9818	446	8	,	,	PUNCT
ap-9818	446	9	1965	1965	NUM
ap-9818	446	10	.	.	PUNCT
ap-9818	447	1	https://doi.org/10.1103/physrev.138.b1155	https://doi.org/10.1103/physrev.138.b1155	X
ap-9818	448	1	[	[	X
ap-9818	448	2	5	5	NUM
ap-9818	448	3	]	]	PUNCT
ap-9818	448	4	m.	m.	NOUN
ap-9818	448	5	s.	s.	PROPN
ap-9818	448	6	plyushchay	plyushchay	PROPN
ap-9818	448	7	.	.	PUNCT
ap-9818	449	1	deformed	deform	VERB
ap-9818	449	2	heisenberg	heisenberg	PROPN
ap-9818	449	3	algebra	algebra	PROPN
ap-9818	449	4	and	and	CCONJ
ap-9818	449	5	fractional	fractional	ADJ
ap-9818	449	6	spin	spin	NOUN
ap-9818	449	7	field	field	NOUN
ap-9818	449	8	in	in	ADP
ap-9818	449	9	2	2	NUM
ap-9818	449	10	+	+	SYM
ap-9818	449	11	1	1	NUM
ap-9818	449	12	dimensions	dimension	NOUN
ap-9818	449	13	.	.	PUNCT
ap-9818	450	1	physics	physics	NOUN
ap-9818	450	2	letters	letters	PROPN
ap-9818	450	3	b	b	PROPN
ap-9818	450	4	320(1–2):91–95	320(1–2):91–95	NUM
ap-9818	450	5	,	,	PUNCT
ap-9818	450	6	1994	1994	NUM
ap-9818	450	7	.	.	PUNCT
ap-9818	451	1	https://doi.org/10.1016/0370-2693(94)90828-1	https://doi.org/10.1016/0370-2693(94)90828-1	NOUN
ap-9818	451	2	234	234	NUM
ap-9818	451	3	https://doi.org/10.1103/physrev.77.711	https://doi.org/10.1103/physrev.77.711	NOUN
ap-9818	451	4	https://doi.org/10.1103/physrev.84.788	https://doi.org/10.1103/physrev.84.788	NOUN
ap-9818	451	5	https://doi.org/10.1103/physrev.90.270	https://doi.org/10.1103/physrev.90.270	PROPN
ap-9818	451	6	https://doi.org/10.1103/physrev.138.b1155	https://doi.org/10.1103/physrev.138.b1155	NOUN
ap-9818	451	7	https://doi.org/10.1016/0370-2693(94)90828-1	https://doi.org/10.1016/0370-2693(94)90828-1	PROPN
ap-9818	451	8	vol	vol	NOUN
ap-9818	451	9	.	.	PUNCT
ap-9818	452	1	65	65	NUM
ap-9818	452	2	no	no	NOUN
ap-9818	452	3	.	.	PUNCT
ap-9818	453	1	2/2025	2/2025	NUM
ap-9818	453	2	persistence	persistence	NOUN
ap-9818	453	3	of	of	ADP
ap-9818	453	4	solvability	solvability	NOUN
ap-9818	453	5	in	in	ADP
ap-9818	453	6	quantum	quantum	NOUN
ap-9818	453	7	systems	system	NOUN
ap-9818	453	8	deformed	deform	VERB
ap-9818	453	9	by	by	ADP
ap-9818	453	10	dunkl	dunkl	PROPN
ap-9818	453	11	.	.	PUNCT
ap-9818	453	12	.	.	PUNCT
ap-9818	453	13	.	.	PUNCT
ap-9818	454	1	[	[	X
ap-9818	454	2	6	6	NUM
ap-9818	454	3	]	]	PUNCT
ap-9818	454	4	m.	m.	NOUN
ap-9818	454	5	s.	s.	PROPN
ap-9818	454	6	plyushchay	plyushchay	PROPN
ap-9818	454	7	.	.	PUNCT
ap-9818	455	1	deformed	deform	VERB
ap-9818	455	2	heisenberg	heisenberg	PROPN
ap-9818	455	3	algebra	algebra	PROPN
ap-9818	455	4	with	with	ADP
ap-9818	455	5	reflection	reflection	NOUN
ap-9818	455	6	.	.	PUNCT
ap-9818	456	1	nuclear	nuclear	ADJ
ap-9818	456	2	physics	physics	PROPN
ap-9818	456	3	b	b	PROPN
ap-9818	456	4	491(3):619–634	491(3):619–634	PROPN
ap-9818	456	5	,	,	PUNCT
ap-9818	456	6	1997	1997	NUM
ap-9818	456	7	.	.	PUNCT
ap-9818	457	1	https://doi.org/10.1016/s0550-3213(97)00065-5	https://doi.org/10.1016/s0550-3213(97)00065-5	VERB
ap-9818	458	1	[	[	X
ap-9818	458	2	7	7	X
ap-9818	458	3	]	]	PUNCT
ap-9818	458	4	m.	m.	NOUN
ap-9818	458	5	plyushchay	plyushchay	PROPN
ap-9818	458	6	.	.	PUNCT
ap-9818	459	1	hidden	hide	VERB
ap-9818	459	2	nonlinear	nonlinear	ADJ
ap-9818	459	3	supersymmetries	supersymmetry	NOUN
ap-9818	459	4	in	in	ADP
ap-9818	459	5	pure	pure	ADJ
ap-9818	459	6	parabosonic	parabosonic	ADJ
ap-9818	459	7	systems	system	NOUN
ap-9818	459	8	.	.	PUNCT
ap-9818	460	1	international	international	ADJ
ap-9818	460	2	journal	journal	NOUN
ap-9818	460	3	of	of	ADP
ap-9818	460	4	modern	modern	ADJ
ap-9818	460	5	physics	physic	NOUN
ap-9818	460	6	a	a	DET
ap-9818	460	7	15(23):3679–3698	15(23):3679–3698	NUM
ap-9818	460	8	,	,	PUNCT
ap-9818	460	9	2000	2000	NUM
ap-9818	460	10	.	.	PUNCT
ap-9818	461	1	https://doi.org/10.1142/s0217751x00001981	https://doi.org/10.1142/s0217751x00001981	NOUN
ap-9818	461	2	[	[	X
ap-9818	461	3	8	8	NUM
ap-9818	461	4	]	]	X
ap-9818	461	5	c.	c.	PROPN
ap-9818	461	6	f.	f.	PROPN
ap-9818	461	7	dunkl	dunkl	PROPN
ap-9818	461	8	.	.	PUNCT
ap-9818	462	1	differential	differential	ADJ
ap-9818	462	2	-	-	PUNCT
ap-9818	462	3	difference	difference	NOUN
ap-9818	462	4	operators	operator	NOUN
ap-9818	462	5	associated	associate	VERB
ap-9818	462	6	to	to	ADP
ap-9818	462	7	reflection	reflection	NOUN
ap-9818	462	8	groups	group	NOUN
ap-9818	462	9	.	.	PUNCT
ap-9818	463	1	transactions	transaction	NOUN
ap-9818	463	2	of	of	ADP
ap-9818	463	3	the	the	DET
ap-9818	463	4	american	american	PROPN
ap-9818	463	5	mathematical	mathematical	PROPN
ap-9818	463	6	society	society	NOUN
ap-9818	463	7	311:167–183	311:167–183	NUM
ap-9818	463	8	,	,	PUNCT
ap-9818	463	9	1989	1989	NUM
ap-9818	463	10	.	.	PUNCT
ap-9818	464	1	https://doi.org/10.1090/s0002-9947-1989-0951883-8	https://doi.org/10.1090/s0002-9947-1989-0951883-8	NOUN
ap-9818	464	2	[	[	X
ap-9818	464	3	9	9	NUM
ap-9818	464	4	]	]	PUNCT
ap-9818	464	5	j.	j.	PROPN
ap-9818	464	6	f.	f.	PROPN
ap-9818	464	7	van	van	PROPN
ap-9818	464	8	diejen	diejen	PROPN
ap-9818	464	9	,	,	PUNCT
ap-9818	464	10	l.	l.	PROPN
ap-9818	464	11	vinet	vinet	PROPN
ap-9818	464	12	.	.	PUNCT
ap-9818	465	1	calogero	calogero	PROPN
ap-9818	465	2	-	-	PUNCT
ap-9818	465	3	moser	moser	PROPN
ap-9818	465	4	-	-	PUNCT
ap-9818	465	5	sutherland	sutherland	PROPN
ap-9818	465	6	models	model	NOUN
ap-9818	465	7	.	.	PUNCT
ap-9818	466	1	crm	crm	PROPN
ap-9818	466	2	series	series	PROPN
ap-9818	466	3	in	in	ADP
ap-9818	466	4	mathematical	mathematical	ADJ
ap-9818	466	5	physics	physics	PROPN
ap-9818	466	6	.	.	PUNCT
ap-9818	467	1	springer	springer	NOUN
ap-9818	467	2	-	-	PUNCT
ap-9818	467	3	verlag	verlag	PROPN
ap-9818	467	4	,	,	PUNCT
ap-9818	467	5	new	new	PROPN
ap-9818	467	6	york	york	PROPN
ap-9818	467	7	,	,	PUNCT
ap-9818	467	8	2000	2000	NUM
ap-9818	467	9	.	.	PUNCT
ap-9818	468	1	https://doi.org/10.1007/978-1-4612-1206-5	https://doi.org/10.1007/978-1-4612-1206-5	PROPN
ap-9818	469	1	[	[	X
ap-9818	469	2	10	10	NUM
ap-9818	469	3	]	]	X
ap-9818	469	4	b.	b.	PROPN
ap-9818	469	5	hamil	hamil	PROPN
ap-9818	469	6	,	,	PUNCT
ap-9818	469	7	b.	b.	PROPN
ap-9818	469	8	c.	c.	PROPN
ap-9818	469	9	lütfüoğlu	lütfüoğlu	PROPN
ap-9818	469	10	,	,	PUNCT
ap-9818	469	11	m.	m.	NOUN
ap-9818	469	12	merad	merad	PROPN
ap-9818	469	13	.	.	PUNCT
ap-9818	470	1	dunkl	dunkl	PROPN
ap-9818	470	2	-	-	PUNCT
ap-9818	470	3	schrödinger	schrödinger	NOUN
ap-9818	470	4	equation	equation	NOUN
ap-9818	470	5	in	in	ADP
ap-9818	470	6	higher	high	ADJ
ap-9818	470	7	dimensions	dimension	NOUN
ap-9818	470	8	.	.	PUNCT
ap-9818	471	1	physica	physica	PROPN
ap-9818	471	2	scripta	scripta	PROPN
ap-9818	471	3	100(3):035301	100(3):035301	NUM
ap-9818	471	4	,	,	PUNCT
ap-9818	471	5	2025	2025	NUM
ap-9818	471	6	.	.	PUNCT
ap-9818	472	1	https://doi.org/10.1088/1402-4896/ada9b2	https://doi.org/10.1088/1402-4896/ada9b2	PROPN
ap-9818	473	1	[	[	X
ap-9818	473	2	11	11	NUM
ap-9818	473	3	]	]	PUNCT
ap-9818	473	4	a.	a.	NOUN
ap-9818	473	5	benchikha	benchikha	PROPN
ap-9818	473	6	,	,	PUNCT
ap-9818	473	7	b.	b.	PROPN
ap-9818	473	8	hamil	hamil	PROPN
ap-9818	473	9	,	,	PUNCT
ap-9818	473	10	b.	b.	PROPN
ap-9818	473	11	c.	c.	PROPN
ap-9818	473	12	lütfüoğlu	lütfüoğlu	PROPN
ap-9818	473	13	,	,	PUNCT
ap-9818	473	14	b.	b.	PROPN
ap-9818	473	15	khantoul	khantoul	PROPN
ap-9818	473	16	.	.	PUNCT
ap-9818	474	1	dunkl	dunkl	PROPN
ap-9818	474	2	-	-	PUNCT
ap-9818	474	3	schrödinger	schrödinger	NOUN
ap-9818	474	4	equation	equation	NOUN
ap-9818	474	5	with	with	ADP
ap-9818	474	6	time	time	NOUN
ap-9818	474	7	-	-	PUNCT
ap-9818	474	8	dependent	dependent	ADJ
ap-9818	474	9	harmonic	harmonic	ADJ
ap-9818	474	10	oscillator	oscillator	NOUN
ap-9818	474	11	potential	potential	NOUN
ap-9818	474	12	.	.	PUNCT
ap-9818	475	1	international	international	ADJ
ap-9818	475	2	journal	journal	PROPN
ap-9818	475	3	of	of	ADP
ap-9818	475	4	theoretical	theoretical	ADJ
ap-9818	475	5	physics	physics	NOUN
ap-9818	475	6	63(10):248	63(10):248	NUM
ap-9818	475	7	,	,	PUNCT
ap-9818	475	8	2024	2024	NUM
ap-9818	475	9	.	.	PUNCT
ap-9818	476	1	https://doi.org/10.1007/s10773-024-05786-6	https://doi.org/10.1007/s10773-024-05786-6	NUM
ap-9818	477	1	[	[	X
ap-9818	477	2	12	12	NUM
ap-9818	477	3	]	]	PUNCT
ap-9818	477	4	a.	a.	NOUN
ap-9818	477	5	benchikha	benchikha	PROPN
ap-9818	477	6	,	,	PUNCT
ap-9818	477	7	b.	b.	PROPN
ap-9818	477	8	hamil	hamil	PROPN
ap-9818	477	9	,	,	PUNCT
ap-9818	477	10	b.	b.	PROPN
ap-9818	477	11	c.	c.	PROPN
ap-9818	477	12	lütfüoğlu	lütfüoğlu	PROPN
ap-9818	477	13	.	.	PUNCT
ap-9818	478	1	a	a	DET
ap-9818	478	2	path	path	NOUN
ap-9818	478	3	integral	integral	ADJ
ap-9818	478	4	treatment	treatment	NOUN
ap-9818	478	5	of	of	ADP
ap-9818	478	6	time	time	NOUN
ap-9818	478	7	-	-	PUNCT
ap-9818	478	8	dependent	dependent	ADJ
ap-9818	478	9	dunkl	dunkl	NOUN
ap-9818	478	10	quantum	quantum	NOUN
ap-9818	478	11	mechanics	mechanic	NOUN
ap-9818	478	12	.	.	PUNCT
ap-9818	479	1	international	international	ADJ
ap-9818	479	2	journal	journal	PROPN
ap-9818	479	3	of	of	ADP
ap-9818	479	4	geometric	geometric	ADJ
ap-9818	479	5	methods	method	NOUN
ap-9818	479	6	in	in	ADP
ap-9818	479	7	modern	modern	ADJ
ap-9818	479	8	physics	physics	NOUN
ap-9818	479	9	p.	p.	NOUN
ap-9818	479	10	2550113	2550113	NUM
ap-9818	479	11	.	.	PUNCT
ap-9818	480	1	preprint	preprint	NOUN
ap-9818	480	2	.	.	PUNCT
ap-9818	481	1	https://doi.org/10.1142/s0219887825501130	https://doi.org/10.1142/s0219887825501130	NUM
ap-9818	482	1	[	[	X
ap-9818	482	2	13	13	NUM
ap-9818	482	3	]	]	X
ap-9818	482	4	h.	h.	NOUN
ap-9818	482	5	bouguerne	bouguerne	PROPN
ap-9818	482	6	,	,	PUNCT
ap-9818	482	7	b.	b.	PROPN
ap-9818	482	8	hamil	hamil	PROPN
ap-9818	482	9	,	,	PUNCT
ap-9818	482	10	b.	b.	PROPN
ap-9818	482	11	c.	c.	PROPN
ap-9818	482	12	lütfüoğlu	lütfüoğlu	PROPN
ap-9818	482	13	,	,	PUNCT
ap-9818	482	14	m.	m.	NOUN
ap-9818	482	15	merad	merad	PROPN
ap-9818	482	16	.	.	PUNCT
ap-9818	483	1	dunkl	dunkl	PROPN
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ap-9818	483	3	and	and	CCONJ
ap-9818	483	4	vacuum	vacuum	NOUN
ap-9818	483	5	pair	pair	NOUN
ap-9818	483	6	creation	creation	NOUN
ap-9818	483	7	:	:	PUNCT
ap-9818	483	8	exact	exact	ADJ
ap-9818	483	9	analytical	analytical	ADJ
ap-9818	483	10	results	result	NOUN
ap-9818	483	11	via	via	ADP
ap-9818	483	12	bogoliubov	bogoliubov	PROPN
ap-9818	483	13	method	method	NOUN
ap-9818	483	14	.	.	PUNCT
ap-9818	484	1	nuclear	nuclear	ADJ
ap-9818	484	2	physics	physics	PROPN
ap-9818	484	3	b	b	PROPN
ap-9818	484	4	1007:116684	1007:116684	NUM
ap-9818	484	5	,	,	PUNCT
ap-9818	484	6	2024	2024	NUM
ap-9818	484	7	.	.	PUNCT
ap-9818	485	1	https://doi.org/10.1016/j.nuclphysb.2024.116684	https://doi.org/10.1016/j.nuclphysb.2024.116684	PROPN
ap-9818	485	2	[	[	X
ap-9818	485	3	14	14	NUM
ap-9818	485	4	]	]	PUNCT
ap-9818	485	5	a.	a.	NOUN
ap-9818	485	6	hocine	hocine	PROPN
ap-9818	485	7	,	,	PUNCT
ap-9818	485	8	b.	b.	PROPN
ap-9818	485	9	hamil	hamil	PROPN
ap-9818	485	10	,	,	PUNCT
ap-9818	485	11	f.	f.	PROPN
ap-9818	485	12	merabtine	merabtine	PROPN
ap-9818	485	13	,	,	PUNCT
ap-9818	485	14	et	et	PROPN
ap-9818	485	15	al	al	PROPN
ap-9818	485	16	.	.	PROPN
ap-9818	486	1	on	on	ADP
ap-9818	486	2	dunkl	dunkl	PROPN
ap-9818	486	3	-	-	PUNCT
ap-9818	486	4	bose	bose	NOUN
ap-9818	486	5	-	-	PUNCT
ap-9818	486	6	einstein	einstein	NOUN
ap-9818	486	7	condensation	condensation	NOUN
ap-9818	486	8	in	in	ADP
ap-9818	486	9	harmonic	harmonic	ADJ
ap-9818	486	10	traps	trap	NOUN
ap-9818	486	11	.	.	PUNCT
ap-9818	487	1	revista	revista	PROPN
ap-9818	487	2	mexicana	mexicana	PROPN
ap-9818	487	3	de	de	PROPN
ap-9818	487	4	física	física	PROPN
ap-9818	487	5	70(5):051701	70(5):051701	PROPN
ap-9818	487	6	,	,	PUNCT
ap-9818	487	7	2024	2024	NUM
ap-9818	487	8	.	.	PUNCT
ap-9818	488	1	https://doi.org/10.31349/revmexfis.70.051701	https://doi.org/10.31349/revmexfis.70.051701	NOUN
ap-9818	489	1	[	[	X
ap-9818	489	2	15	15	NUM
ap-9818	489	3	]	]	X
ap-9818	489	4	m.	m.	NOUN
ap-9818	489	5	rosenblum	rosenblum	PROPN
ap-9818	489	6	.	.	PUNCT
ap-9818	490	1	generalized	generalize	VERB
ap-9818	490	2	hermite	hermite	ADJ
ap-9818	490	3	polynomials	polynomial	NOUN
ap-9818	490	4	and	and	CCONJ
ap-9818	490	5	the	the	DET
ap-9818	490	6	bose	bose	NOUN
ap-9818	490	7	-	-	PUNCT
ap-9818	490	8	like	like	ADJ
ap-9818	490	9	oscillator	oscillator	NOUN
ap-9818	490	10	calculus	calculus	NOUN
ap-9818	490	11	.	.	PUNCT
ap-9818	491	1	in	in	ADP
ap-9818	491	2	a.	a.	PROPN
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ap-9818	491	4	,	,	PUNCT
ap-9818	491	5	i.	i.	PROPN
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ap-9818	491	7	(	(	PUNCT
ap-9818	491	8	eds	ed	NOUN
ap-9818	491	9	.	.	PUNCT
ap-9818	491	10	)	)	PUNCT
ap-9818	491	11	,	,	PUNCT
ap-9818	491	12	nonselfadjoint	nonselfadjoint	NOUN
ap-9818	491	13	operators	operator	NOUN
ap-9818	491	14	and	and	CCONJ
ap-9818	491	15	related	related	ADJ
ap-9818	491	16	topics	topic	NOUN
ap-9818	491	17	,	,	PUNCT
ap-9818	491	18	vol	vol	NOUN
ap-9818	491	19	.	.	PROPN
ap-9818	491	20	73	73	NUM
ap-9818	491	21	,	,	PUNCT
ap-9818	491	22	pp	pp	ADJ
ap-9818	491	23	.	.	PUNCT
ap-9818	492	1	369–396	369–396	NUM
ap-9818	492	2	.	.	PUNCT
ap-9818	493	1	birkhäuser	birkhäuser	PROPN
ap-9818	493	2	,	,	PUNCT
ap-9818	493	3	basel	basel	PROPN
ap-9818	493	4	,	,	PUNCT
ap-9818	493	5	1994	1994	NUM
ap-9818	493	6	.	.	PUNCT
ap-9818	494	1	https://doi.org/10.1007/978-3-0348-8522-5_15	https://doi.org/10.1007/978-3-0348-8522-5_15	PROPN
ap-9818	495	1	[	[	X
ap-9818	495	2	16	16	NUM
ap-9818	495	3	]	]	PUNCT
ap-9818	495	4	b.	b.	PROPN
ap-9818	495	5	hamil	hamil	PROPN
ap-9818	495	6	,	,	PUNCT
ap-9818	495	7	b.	b.	PROPN
ap-9818	495	8	c.	c.	PROPN
ap-9818	495	9	lütfüoğlu	lütfüoğlu	PROPN
ap-9818	495	10	.	.	PUNCT
ap-9818	496	1	dunkl	dunkl	NOUN
ap-9818	496	2	graphene	graphene	NOUN
ap-9818	496	3	in	in	ADP
ap-9818	496	4	constant	constant	ADJ
ap-9818	496	5	magnetic	magnetic	ADJ
ap-9818	496	6	field	field	NOUN
ap-9818	496	7	.	.	PUNCT
ap-9818	497	1	the	the	DET
ap-9818	497	2	european	european	PROPN
ap-9818	497	3	physical	physical	PROPN
ap-9818	497	4	journal	journal	PROPN
ap-9818	497	5	plus	plus	CCONJ
ap-9818	497	6	137(11):1241	137(11):1241	PROPN
ap-9818	497	7	,	,	PUNCT
ap-9818	497	8	2022	2022	NUM
ap-9818	497	9	.	.	PUNCT
ap-9818	498	1	https://doi.org/10.1140/epjp/s13360-022-03463-3	https://doi.org/10.1140/epjp/s13360-022-03463-3	PROPN
ap-9818	498	2	[	[	X
ap-9818	498	3	17	17	NUM
ap-9818	498	4	]	]	PUNCT
ap-9818	498	5	c.	c.	NOUN
ap-9818	498	6	quesne	quesne	NOUN
ap-9818	498	7	.	.	PUNCT
ap-9818	499	1	rational	rational	ADJ
ap-9818	499	2	extensions	extension	NOUN
ap-9818	499	3	of	of	ADP
ap-9818	499	4	the	the	DET
ap-9818	499	5	dunkl	dunkl	NOUN
ap-9818	499	6	oscillator	oscillator	NOUN
ap-9818	499	7	in	in	ADP
ap-9818	499	8	the	the	DET
ap-9818	499	9	plane	plane	NOUN
ap-9818	499	10	and	and	CCONJ
ap-9818	499	11	exceptional	exceptional	ADJ
ap-9818	499	12	orthogonal	orthogonal	ADJ
ap-9818	499	13	polynomials	polynomial	NOUN
ap-9818	499	14	.	.	PUNCT
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ap-9818	500	2	physics	physics	NOUN
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ap-9818	500	4	a	a	DET
ap-9818	500	5	38(22–23):2350108	38(22–23):2350108	NUM
ap-9818	500	6	,	,	PUNCT
ap-9818	500	7	2023	2023	NUM
ap-9818	500	8	.	.	PUNCT
ap-9818	501	1	https://doi.org/10.1142/s0217732323501080	https://doi.org/10.1142/s0217732323501080	NUM
ap-9818	501	2	[	[	X
ap-9818	501	3	18	18	NUM
ap-9818	501	4	]	]	X
ap-9818	501	5	b.	b.	PROPN
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ap-9818	501	7	,	,	PUNCT
ap-9818	501	8	b.	b.	PROPN
ap-9818	501	9	c.	c.	PROPN
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ap-9818	501	11	.	.	PUNCT
ap-9818	502	1	dunkl	dunkl	PROPN
ap-9818	502	2	-	-	PUNCT
ap-9818	502	3	klein	klein	PROPN
ap-9818	502	4	-	-	PUNCT
ap-9818	502	5	gordon	gordon	PROPN
ap-9818	502	6	equation	equation	NOUN
ap-9818	502	7	in	in	ADP
ap-9818	502	8	three	three	NUM
ap-9818	502	9	-	-	PUNCT
ap-9818	502	10	dimensions	dimension	NOUN
ap-9818	502	11	:	:	PUNCT
ap-9818	502	12	the	the	DET
ap-9818	502	13	klein	klein	PROPN
ap-9818	502	14	-	-	PUNCT
ap-9818	502	15	gordon	gordon	PROPN
ap-9818	502	16	oscillator	oscillator	NOUN
ap-9818	502	17	and	and	CCONJ
ap-9818	502	18	coulomb	coulomb	NOUN
ap-9818	502	19	potential	potential	NOUN
ap-9818	502	20	.	.	PUNCT
ap-9818	503	1	few	few	ADJ
ap-9818	503	2	-	-	PUNCT
ap-9818	503	3	body	body	NOUN
ap-9818	503	4	systems	system	NOUN
ap-9818	503	5	63(4):74	63(4):74	PROPN
ap-9818	503	6	,	,	PUNCT
ap-9818	503	7	2022	2022	NUM
ap-9818	503	8	.	.	PUNCT
ap-9818	503	9	https://doi.org/10.1007/s00601-022-01776-8	https://doi.org/10.1007/s00601-022-01776-8	X
ap-9818	504	1	[	[	X
ap-9818	504	2	19	19	NUM
ap-9818	504	3	]	]	PUNCT
ap-9818	504	4	g.	g.	PROPN
ap-9818	504	5	junker	junker	PROPN
ap-9818	504	6	.	.	PUNCT
ap-9818	505	1	on	on	ADP
ap-9818	505	2	the	the	DET
ap-9818	505	3	path	path	NOUN
ap-9818	505	4	integral	integral	ADJ
ap-9818	505	5	formulation	formulation	NOUN
ap-9818	505	6	of	of	ADP
ap-9818	505	7	wigner	wigner	NOUN
ap-9818	505	8	-	-	PUNCT
ap-9818	505	9	dunkl	dunkl	NOUN
ap-9818	505	10	quantum	quantum	NOUN
ap-9818	505	11	mechanics	mechanic	NOUN
ap-9818	505	12	.	.	PUNCT
ap-9818	506	1	journal	journal	PROPN
ap-9818	506	2	of	of	ADP
ap-9818	506	3	physics	physics	PROPN
ap-9818	506	4	a	a	PRON
ap-9818	506	5	:	:	PUNCT
ap-9818	506	6	mathematical	mathematical	ADJ
ap-9818	506	7	and	and	CCONJ
ap-9818	506	8	theoretical	theoretical	ADJ
ap-9818	506	9	57(7):075201	57(7):075201	NUM
ap-9818	506	10	,	,	PUNCT
ap-9818	506	11	2024	2024	NUM
ap-9818	506	12	.	.	PUNCT
ap-9818	506	13	https://doi.org/10.1088/1751-8121/ad213d	https://doi.org/10.1088/1751-8121/ad213d	PUNCT
ap-9818	507	1	[	[	X
ap-9818	507	2	20	20	NUM
ap-9818	507	3	]	]	PUNCT
ap-9818	507	4	r.	r.	PROPN
ap-9818	507	5	d.	d.	PROPN
ap-9818	507	6	mota	mota	PROPN
ap-9818	507	7	,	,	PUNCT
ap-9818	507	8	d.	d.	PROPN
ap-9818	507	9	ojeda	ojeda	PROPN
ap-9818	507	10	-	-	PUNCT
ap-9818	507	11	guillén	guillén	PROPN
ap-9818	507	12	,	,	PUNCT
ap-9818	507	13	m.	m.	NOUN
ap-9818	507	14	a.	a.	PROPN
ap-9818	507	15	xicoténcatl	xicoténcatl	PROPN
ap-9818	507	16	.	.	PUNCT
ap-9818	508	1	the	the	DET
ap-9818	508	2	generalized	generalize	VERB
ap-9818	508	3	fokker	fokker	NOUN
ap-9818	508	4	-	-	PUNCT
ap-9818	508	5	planck	planck	NOUN
ap-9818	508	6	equation	equation	NOUN
ap-9818	508	7	in	in	ADP
ap-9818	508	8	terms	term	NOUN
ap-9818	508	9	of	of	ADP
ap-9818	508	10	dunkl	dunkl	NOUN
ap-9818	508	11	-	-	PUNCT
ap-9818	508	12	type	type	NOUN
ap-9818	508	13	derivatives	derivative	NOUN
ap-9818	508	14	.	.	PUNCT
ap-9818	509	1	physica	physica	VERB
ap-9818	509	2	a	a	DET
ap-9818	509	3	:	:	PUNCT
ap-9818	509	4	statistical	statistical	ADJ
ap-9818	509	5	mechanics	mechanic	NOUN
ap-9818	509	6	and	and	CCONJ
ap-9818	509	7	its	its	PRON
ap-9818	509	8	applications	application	NOUN
ap-9818	509	9	635:129525	635:129525	NOUN
ap-9818	509	10	,	,	PUNCT
ap-9818	509	11	2024	2024	NUM
ap-9818	509	12	.	.	PUNCT
ap-9818	510	1	https://doi.org/10.1016/j.physa.2024.129525	https://doi.org/10.1016/j.physa.2024.129525	PROPN
ap-9818	510	2	[	[	X
ap-9818	510	3	21	21	NUM
ap-9818	510	4	]	]	X
ap-9818	510	5	h.	h.	NOUN
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ap-9818	510	8	b.	b.	PROPN
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ap-9818	510	10	,	,	PUNCT
ap-9818	510	11	b.	b.	PROPN
ap-9818	510	12	c.	c.	PROPN
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ap-9818	510	14	,	,	PUNCT
ap-9818	510	15	m.	m.	NOUN
ap-9818	510	16	merad	merad	PROPN
ap-9818	510	17	.	.	PUNCT
ap-9818	511	1	dunkl	dunkl	PROPN
ap-9818	511	2	-	-	PUNCT
ap-9818	511	3	pauli	pauli	PROPN
ap-9818	511	4	equation	equation	NOUN
ap-9818	511	5	in	in	ADP
ap-9818	511	6	the	the	DET
ap-9818	511	7	presence	presence	NOUN
ap-9818	511	8	of	of	ADP
ap-9818	511	9	a	a	DET
ap-9818	511	10	magnetic	magnetic	ADJ
ap-9818	511	11	field	field	NOUN
ap-9818	511	12	.	.	PUNCT
ap-9818	512	1	indian	indian	PROPN
ap-9818	512	2	journal	journal	PROPN
ap-9818	512	3	of	of	ADP
ap-9818	512	4	physics	physics	PROPN
ap-9818	512	5	98(12):4093–4105	98(12):4093–4105	NUM
ap-9818	512	6	,	,	PUNCT
ap-9818	512	7	2024	2024	NUM
ap-9818	512	8	.	.	PUNCT
ap-9818	513	1	https://doi.org/10.1007/s12648-024-03170-y	https://doi.org/10.1007/s12648-024-03170-y	PROPN
ap-9818	513	2	[	[	X
ap-9818	513	3	22	22	NUM
ap-9818	513	4	]	]	PUNCT
ap-9818	513	5	r.	r.	PROPN
ap-9818	513	6	d.	d.	PROPN
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ap-9818	513	8	,	,	PUNCT
ap-9818	513	9	d.	d.	PROPN
ap-9818	513	10	ojeda	ojeda	PROPN
ap-9818	513	11	-	-	PUNCT
ap-9818	513	12	guillén	guillén	NOUN
ap-9818	513	13	.	.	PUNCT
ap-9818	514	1	effect	effect	NOUN
ap-9818	514	2	of	of	ADP
ap-9818	514	3	the	the	DET
ap-9818	514	4	two	two	NUM
ap-9818	514	5	-	-	PUNCT
ap-9818	514	6	parameter	parameter	NOUN
ap-9818	514	7	generalized	generalize	VERB
ap-9818	514	8	dunkl	dunkl	NOUN
ap-9818	514	9	derivative	derivative	NOUN
ap-9818	514	10	on	on	ADP
ap-9818	514	11	the	the	DET
ap-9818	514	12	two	two	NUM
ap-9818	514	13	-	-	PUNCT
ap-9818	514	14	dimensional	dimensional	ADJ
ap-9818	514	15	schrödinger	schrödinger	ADJ
ap-9818	514	16	equation	equation	NOUN
ap-9818	514	17	.	.	PUNCT
ap-9818	515	1	modern	modern	ADJ
ap-9818	515	2	physics	physics	NOUN
ap-9818	515	3	letters	letter	NOUN
ap-9818	515	4	a	a	DET
ap-9818	515	5	37(33–34):2250224	37(33–34):2250224	NUM
ap-9818	515	6	,	,	PUNCT
ap-9818	515	7	2022	2022	NUM
ap-9818	515	8	.	.	PUNCT
ap-9818	516	1	https://doi.org/10.1142/s0217732322502248	https://doi.org/10.1142/s0217732322502248	NUM
ap-9818	517	1	[	[	X
ap-9818	517	2	23	23	NUM
ap-9818	517	3	]	]	PUNCT
ap-9818	517	4	r.	r.	PROPN
ap-9818	517	5	d.	d.	PROPN
ap-9818	517	6	mota	mota	PROPN
ap-9818	517	7	,	,	PUNCT
ap-9818	517	8	d.	d.	PROPN
ap-9818	517	9	ojeda	ojeda	PROPN
ap-9818	517	10	-	-	PUNCT
ap-9818	517	11	guillén	guillén	PROPN
ap-9818	517	12	.	.	PUNCT
ap-9818	518	1	exact	exact	ADJ
ap-9818	518	2	solutions	solution	NOUN
ap-9818	518	3	of	of	ADP
ap-9818	518	4	the	the	DET
ap-9818	518	5	schrödinger	schrödinger	ADJ
ap-9818	518	6	equation	equation	NOUN
ap-9818	518	7	with	with	ADP
ap-9818	518	8	dunkl	dunkl	PROPN
ap-9818	518	9	derivative	derivative	NOUN
ap-9818	518	10	for	for	ADP
ap-9818	518	11	the	the	DET
ap-9818	518	12	free	free	ADJ
ap-9818	518	13	-	-	PUNCT
ap-9818	518	14	particle	particle	NOUN
ap-9818	518	15	spherical	spherical	ADJ
ap-9818	518	16	waves	wave	NOUN
ap-9818	518	17	,	,	PUNCT
ap-9818	518	18	the	the	DET
ap-9818	518	19	pseudo	pseudo	NOUN
ap-9818	518	20	-	-	ADJ
ap-9818	518	21	harmonic	harmonic	ADJ
ap-9818	518	22	oscillator	oscillator	NOUN
ap-9818	518	23	and	and	CCONJ
ap-9818	518	24	the	the	DET
ap-9818	518	25	mie	mie	NOUN
ap-9818	518	26	-	-	PUNCT
ap-9818	518	27	type	type	NOUN
ap-9818	518	28	potential	potential	NOUN
ap-9818	518	29	.	.	PUNCT
ap-9818	519	1	modern	modern	ADJ
ap-9818	519	2	physics	physics	NOUN
ap-9818	519	3	letters	letter	NOUN
ap-9818	519	4	a	a	DET
ap-9818	519	5	37(1):2250006	37(1):2250006	NUM
ap-9818	519	6	,	,	PUNCT
ap-9818	519	7	2022	2022	NUM
ap-9818	519	8	.	.	PUNCT
ap-9818	520	1	https://doi.org/10.1142/s0217732322500067	https://doi.org/10.1142/s0217732322500067	NUM
ap-9818	520	2	[	[	X
ap-9818	520	3	24	24	NUM
ap-9818	520	4	]	]	PUNCT
ap-9818	520	5	a.	a.	NOUN
ap-9818	520	6	schulze	schulze	PROPN
ap-9818	520	7	-	-	PUNCT
ap-9818	520	8	halberg	halberg	PROPN
ap-9818	520	9	.	.	PUNCT
ap-9818	521	1	closed	close	VERB
ap-9818	521	2	-	-	PUNCT
ap-9818	521	3	form	form	NOUN
ap-9818	521	4	bound	bind	VERB
ap-9818	521	5	states	state	NOUN
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ap-9818	521	7	two	two	NUM
ap-9818	521	8	dunkl	dunkl	PROPN
ap-9818	521	9	-	-	PUNCT
ap-9818	521	10	liénard	liénard	PROPN
ap-9818	521	11	oscillator	oscillator	NOUN
ap-9818	521	12	systems	system	NOUN
ap-9818	521	13	.	.	PUNCT
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ap-9818	522	2	journal	journal	NOUN
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ap-9818	522	6	a	a	DET
ap-9818	522	7	39(2–3):2450013	39(2–3):2450013	NUM
ap-9818	522	8	,	,	PUNCT
ap-9818	522	9	2024	2024	NUM
ap-9818	522	10	.	.	PUNCT
ap-9818	522	11	https://doi.org/10.1142/s0217751x24500131	https://doi.org/10.1142/s0217751x24500131	X
ap-9818	523	1	[	[	X
ap-9818	523	2	25	25	NUM
ap-9818	523	3	]	]	PUNCT
ap-9818	523	4	t.	t.	PROPN
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ap-9818	523	9	.	.	PUNCT
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ap-9818	524	4	homogeneous	homogeneous	ADJ
ap-9818	524	5	and	and	CCONJ
ap-9818	524	6	inhomogeneous	inhomogeneous	ADJ
ap-9818	524	7	mixed	mixed	ADJ
ap-9818	524	8	semiconductors	semiconductor	NOUN
ap-9818	524	9	.	.	PUNCT
ap-9818	525	1	in	in	ADP
ap-9818	525	2	d.	d.	PROPN
ap-9818	525	3	g.	g.	PROPN
ap-9818	525	4	thomas	thomas	PROPN
ap-9818	526	1	(	(	PUNCT
ap-9818	526	2	ed	ed	NOUN
ap-9818	526	3	.	.	PUNCT
ap-9818	526	4	)	)	PUNCT
ap-9818	526	5	,	,	PUNCT
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ap-9818	526	7	–	–	PUNCT
ap-9818	526	8	vi	vi	NOUN
ap-9818	526	9	semiconducting	semiconducting	NOUN
ap-9818	526	10	compounds	compound	NOUN
ap-9818	526	11	.	.	PUNCT
ap-9818	527	1	benjamin	benjamin	PROPN
ap-9818	527	2	,	,	PUNCT
ap-9818	527	3	new	new	PROPN
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ap-9818	527	5	,	,	PUNCT
ap-9818	527	6	1967	1967	NUM
ap-9818	527	7	.	.	PUNCT
ap-9818	528	1	[	[	X
ap-9818	528	2	26	26	NUM
ap-9818	528	3	]	]	PUNCT
ap-9818	528	4	t.	t.	PROPN
ap-9818	528	5	gora	gora	PROPN
ap-9818	528	6	,	,	PUNCT
ap-9818	528	7	f.	f.	PROPN
ap-9818	528	8	williams	williams	PROPN
ap-9818	528	9	.	.	PUNCT
ap-9818	529	1	theory	theory	NOUN
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ap-9818	529	4	states	state	NOUN
ap-9818	529	5	and	and	CCONJ
ap-9818	529	6	transport	transport	NOUN
ap-9818	529	7	in	in	ADP
ap-9818	529	8	graded	grade	VERB
ap-9818	529	9	mixed	mixed	ADJ
ap-9818	529	10	semiconductors	semiconductor	NOUN
ap-9818	529	11	.	.	PUNCT
ap-9818	530	1	physical	physical	PROPN
ap-9818	530	2	review	review	PROPN
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ap-9818	530	4	,	,	PUNCT
ap-9818	530	5	1969	1969	NUM
ap-9818	530	6	.	.	PUNCT
ap-9818	531	1	https://doi.org/10.1103/physrev.177.1179	https://doi.org/10.1103/physrev.177.1179	VERB
ap-9818	531	2	[	[	X
ap-9818	532	1	27	27	NUM
ap-9818	532	2	]	]	PUNCT
ap-9818	532	3	p.	p.	NOUN
ap-9818	532	4	t.	t.	PROPN
ap-9818	532	5	landsberg	landsberg	PROPN
ap-9818	532	6	.	.	PUNCT
ap-9818	533	1	solid	solid	ADJ
ap-9818	533	2	state	state	NOUN
ap-9818	533	3	theory	theory	NOUN
ap-9818	533	4	:	:	PUNCT
ap-9818	533	5	methods	method	NOUN
ap-9818	533	6	and	and	CCONJ
ap-9818	533	7	applications	application	NOUN
ap-9818	533	8	.	.	PUNCT
ap-9818	534	1	wiley	wiley	PROPN
ap-9818	534	2	-	-	PUNCT
ap-9818	534	3	interscience	interscience	PROPN
ap-9818	534	4	,	,	PUNCT
ap-9818	534	5	london	london	PROPN
ap-9818	534	6	,	,	PUNCT
ap-9818	534	7	1969	1969	NUM
ap-9818	534	8	.	.	PUNCT
ap-9818	535	1	[	[	X
ap-9818	535	2	28	28	NUM
ap-9818	535	3	]	]	X
ap-9818	535	4	o.	o.	PROPN
ap-9818	535	5	von	von	PROPN
ap-9818	535	6	roos	roos	PROPN
ap-9818	535	7	,	,	PUNCT
ap-9818	535	8	h.	h.	PROPN
ap-9818	535	9	mavromatis	mavromatis	PROPN
ap-9818	535	10	.	.	PUNCT
ap-9818	536	1	position	position	NOUN
ap-9818	536	2	-	-	PUNCT
ap-9818	536	3	dependent	dependent	ADJ
ap-9818	536	4	effective	effective	ADJ
ap-9818	536	5	masses	masse	NOUN
ap-9818	536	6	in	in	ADP
ap-9818	536	7	semiconductor	semiconductor	NOUN
ap-9818	536	8	theory	theory	NOUN
ap-9818	536	9	.	.	PUNCT
ap-9818	537	1	ii	ii	PROPN
ap-9818	537	2	.	.	PUNCT
ap-9818	538	1	physical	physical	PROPN
ap-9818	538	2	review	review	PROPN
ap-9818	538	3	b	b	PROPN
ap-9818	538	4	31:2294–2298	31:2294–2298	NUM
ap-9818	538	5	,	,	PUNCT
ap-9818	538	6	1985	1985	NUM
ap-9818	538	7	.	.	PUNCT
ap-9818	539	1	https://doi.org/10.1103/physrevb.31.2294	https://doi.org/10.1103/physrevb.31.2294	NOUN
ap-9818	540	1	[	[	X
ap-9818	540	2	29	29	NUM
ap-9818	540	3	]	]	X
ap-9818	540	4	o.	o.	PROPN
ap-9818	540	5	von	von	PROPN
ap-9818	540	6	roos	roos	PROPN
ap-9818	540	7	.	.	PUNCT
ap-9818	541	1	position	position	NOUN
ap-9818	541	2	-	-	PUNCT
ap-9818	541	3	dependent	dependent	ADJ
ap-9818	541	4	effective	effective	ADJ
ap-9818	541	5	masses	masse	NOUN
ap-9818	541	6	in	in	ADP
ap-9818	541	7	semiconductor	semiconductor	NOUN
ap-9818	541	8	theory	theory	NOUN
ap-9818	541	9	.	.	PUNCT
ap-9818	542	1	physical	physical	PROPN
ap-9818	542	2	review	review	PROPN
ap-9818	542	3	b	b	PROPN
ap-9818	542	4	27:7547–7552	27:7547–7552	NUM
ap-9818	542	5	,	,	PUNCT
ap-9818	542	6	1983	1983	NUM
ap-9818	542	7	.	.	PUNCT
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ap-9818	544	2	30	30	NUM
ap-9818	544	3	]	]	X
ap-9818	544	4	r.	r.	PROPN
ap-9818	544	5	m.	m.	PROPN
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ap-9818	544	7	,	,	PUNCT
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ap-9818	544	9	r.	r.	PROPN
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ap-9818	545	4	with	with	ADP
ap-9818	545	5	position	position	NOUN
ap-9818	545	6	-	-	PUNCT
ap-9818	545	7	dependent	dependent	ADJ
ap-9818	545	8	mass	mass	NOUN
ap-9818	545	9	.	.	PUNCT
ap-9818	546	1	physica	physica	PROPN
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ap-9818	546	5	-	-	PUNCT
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ap-9818	546	11	,	,	PUNCT
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ap-9818	546	13	.	.	PUNCT
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ap-9818	547	21	https://doi.org/10.1142/s0217751x24500131	https://doi.org/10.1142/s0217751x24500131	NUM
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ap-9818	547	30	acta	acta	PROPN
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ap-9818	548	1	[	[	X
ap-9818	548	2	31	31	NUM
ap-9818	548	3	]	]	X
ap-9818	548	4	o.	o.	PROPN
ap-9818	548	5	rosas	rosas	PROPN
ap-9818	548	6	-	-	PUNCT
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ap-9818	548	8	.	.	PUNCT
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ap-9818	549	2	-	-	PUNCT
ap-9818	549	3	dependent	dependent	ADJ
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ap-9818	549	5	systems	system	NOUN
ap-9818	549	6	:	:	PUNCT
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ap-9818	550	13	)	)	PUNCT
ap-9818	550	14	,	,	PUNCT
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ap-9818	550	18	physics	physics	PROPN
ap-9818	550	19	xxxviii	xxxviii	PROPN
ap-9818	550	20	,	,	PUNCT
ap-9818	550	21	pp	pp	ADP
ap-9818	550	22	.	.	PUNCT
ap-9818	551	1	351–361	351–361	NUM
ap-9818	551	2	.	.	PUNCT
ap-9818	552	1	springer	springer	NOUN
ap-9818	552	2	international	international	ADJ
ap-9818	552	3	publishing	publishing	NOUN
ap-9818	552	4	,	,	PUNCT
ap-9818	552	5	cham	cham	PROPN
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ap-9818	552	8	.	.	PUNCT
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ap-9818	554	1	[	[	X
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ap-9818	554	3	]	]	PUNCT
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ap-9818	554	7	.	.	PUNCT
ap-9818	555	1	a	a	DET
ap-9818	555	2	quantum	quantum	ADJ
ap-9818	555	3	quasi	quasi	ADJ
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ap-9818	555	9	an	an	DET
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ap-9818	555	12	.	.	PUNCT
ap-9818	556	1	journal	journal	PROPN
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ap-9818	556	5	55(8):082108	55(8):082108	NUM
ap-9818	556	6	,	,	PUNCT
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ap-9818	556	8	.	.	PUNCT
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ap-9818	558	1	[	[	X
ap-9818	558	2	33	33	NUM
ap-9818	558	3	]	]	PUNCT
ap-9818	558	4	p.	p.	NOUN
ap-9818	558	5	m.	m.	NOUN
ap-9818	558	6	mathews	mathews	PROPN
ap-9818	558	7	,	,	PUNCT
ap-9818	558	8	m.	m.	NOUN
ap-9818	558	9	lakshmanan	lakshmanan	PROPN
ap-9818	558	10	.	.	PUNCT
ap-9818	559	1	on	on	ADP
ap-9818	559	2	a	a	DET
ap-9818	559	3	unique	unique	ADJ
ap-9818	559	4	nonlinear	nonlinear	ADJ
ap-9818	559	5	oscillator	oscillator	NOUN
ap-9818	559	6	.	.	PUNCT
ap-9818	560	1	quarterly	quarterly	ADJ
ap-9818	560	2	of	of	ADP
ap-9818	560	3	applied	apply	VERB
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ap-9818	560	5	32(2):215–218	32(2):215–218	NUM
ap-9818	560	6	,	,	PUNCT
ap-9818	560	7	1974	1974	NUM
ap-9818	560	8	.	.	PUNCT
ap-9818	561	1	[	[	X
ap-9818	561	2	34	34	NUM
ap-9818	561	3	]	]	X
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ap-9818	561	5	m.	m.	NOUN
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ap-9818	561	7	,	,	PUNCT
ap-9818	561	8	m.	m.	NOUN
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ap-9818	561	10	.	.	PUNCT
ap-9818	562	1	a	a	DET
ap-9818	562	2	quantum	quantum	NOUN
ap-9818	562	3	-	-	PUNCT
ap-9818	562	4	mechanically	mechanically	ADV
ap-9818	562	5	solvable	solvable	ADJ
ap-9818	562	6	nonpolynomial	nonpolynomial	ADJ
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ap-9818	562	8	with	with	ADP
ap-9818	562	9	velocity	velocity	NOUN
ap-9818	562	10	-	-	PUNCT
ap-9818	562	11	dependent	dependent	ADJ
ap-9818	562	12	interaction	interaction	NOUN
ap-9818	562	13	.	.	PUNCT
ap-9818	563	1	il	il	PROPN
ap-9818	563	2	nuovo	nuovo	PROPN
ap-9818	563	3	cimento	cimento	PROPN
ap-9818	563	4	a	a	DET
ap-9818	563	5	(	(	PUNCT
ap-9818	563	6	1965–1970	1965–1970	NUM
ap-9818	563	7	)	)	PUNCT
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ap-9818	563	9	,	,	PUNCT
ap-9818	563	10	1975	1975	NUM
ap-9818	563	11	.	.	PUNCT
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ap-9818	564	1	[	[	X
ap-9818	564	2	35	35	NUM
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ap-9818	564	4	s.	s.	PROPN
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ap-9818	565	9	mass	mass	NOUN
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ap-9818	565	16	.	.	PUNCT
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ap-9818	566	8	.	.	PUNCT
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ap-9818	568	9	.	.	PUNCT
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ap-9818	570	8	.	.	PUNCT
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ap-9818	571	6	.	.	PUNCT
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ap-9818	577	6	,	,	PUNCT
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ap-9818	577	8	.	.	PUNCT
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ap-9818	580	6	1	1	NUM
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