id	sid	tid	token	lemma	pos
ap-1354	1	1	wykresx.eps	wykresx.eps	X
ap-1354	1	2	acta	acta	PROPN
ap-1354	1	3	polytechnica	polytechnica	PROPN
ap-1354	1	4	vol	vol	NOUN
ap-1354	1	5	.	.	PUNCT
ap-1354	2	1	51	51	NUM
ap-1354	2	2	no	no	NOUN
ap-1354	2	3	.	.	PUNCT
ap-1354	3	1	1/2011	1/2011	NUM
ap-1354	3	2	path	path	NOUN
ap-1354	3	3	integral	integral	ADJ
ap-1354	3	4	solution	solution	NOUN
ap-1354	3	5	of	of	ADP
ap-1354	3	6	pt-/non	pt-/non	PROPN
ap-1354	3	7	-	-	PUNCT
ap-1354	3	8	pt	pt	NOUN
ap-1354	3	9	-	-	PUNCT
ap-1354	3	10	symmetric	symmetric	ADJ
ap-1354	3	11	and	and	CCONJ
ap-1354	3	12	non	non	ADJ
ap-1354	3	13	-	-	ADJ
ap-1354	3	14	hermitian	hermitian	ADJ
ap-1354	3	15	hulthen	hulthen	ADJ
ap-1354	3	16	potential	potential	ADJ
ap-1354	3	17	n.	n.	PROPN
ap-1354	3	18	kandirmaz	kandirmaz	PROPN
ap-1354	3	19	,	,	PUNCT
ap-1354	3	20	r.	r.	PROPN
ap-1354	3	21	sever	sever	VERB
ap-1354	3	22	abstract	abstract	ADJ
ap-1354	3	23	the	the	DET
ap-1354	3	24	wave	wave	NOUN
ap-1354	3	25	functions	function	NOUN
ap-1354	3	26	and	and	CCONJ
ap-1354	3	27	the	the	DET
ap-1354	3	28	energy	energy	NOUN
ap-1354	3	29	spectrum	spectrum	NOUN
ap-1354	3	30	of	of	ADP
ap-1354	3	31	pt-/non	pt-/non	PROPN
ap-1354	3	32	-	-	PUNCT
ap-1354	3	33	pt	pt	NOUN
ap-1354	3	34	-	-	PUNCT
ap-1354	3	35	symmetric	symmetric	ADJ
ap-1354	3	36	and	and	CCONJ
ap-1354	3	37	non	non	ADJ
ap-1354	3	38	-	-	ADJ
ap-1354	3	39	hermitian	hermitian	ADJ
ap-1354	3	40	hulthen	hulthen	ADJ
ap-1354	3	41	potential	potential	NOUN
ap-1354	3	42	are	be	AUX
ap-1354	3	43	of	of	ADP
ap-1354	3	44	an	an	DET
ap-1354	3	45	exponential	exponential	ADJ
ap-1354	3	46	type	type	NOUN
ap-1354	3	47	and	and	CCONJ
ap-1354	3	48	are	be	AUX
ap-1354	3	49	obtained	obtain	VERB
ap-1354	3	50	via	via	ADP
ap-1354	3	51	the	the	DET
ap-1354	3	52	path	path	NOUN
ap-1354	3	53	integral	integral	ADJ
ap-1354	3	54	.	.	PUNCT
ap-1354	4	1	the	the	DET
ap-1354	4	2	path	path	NOUN
ap-1354	4	3	integral	integral	NOUN
ap-1354	4	4	is	be	AUX
ap-1354	4	5	constructed	construct	VERB
ap-1354	4	6	using	use	VERB
ap-1354	4	7	parametric	parametric	ADJ
ap-1354	4	8	time	time	NOUN
ap-1354	4	9	and	and	CCONJ
ap-1354	4	10	point	point	NOUN
ap-1354	4	11	transformation	transformation	NOUN
ap-1354	4	12	.	.	PUNCT
ap-1354	5	1	keywords	keyword	NOUN
ap-1354	5	2	:	:	PUNCT
ap-1354	5	3	pt	pt	NOUN
ap-1354	5	4	-	-	PUNCT
ap-1354	5	5	symmetry	symmetry	NOUN
ap-1354	5	6	,	,	PUNCT
ap-1354	5	7	coherent	coherent	ADJ
ap-1354	5	8	states	state	NOUN
ap-1354	5	9	,	,	PUNCT
ap-1354	5	10	path	path	NOUN
ap-1354	5	11	integral	integral	ADJ
ap-1354	5	12	,	,	PUNCT
ap-1354	5	13	hulthen	hulthen	ADJ
ap-1354	5	14	potential	potential	NOUN
ap-1354	5	15	.	.	PUNCT
ap-1354	6	1	1	1	NUM
ap-1354	6	2	introduction	introduction	NOUN
ap-1354	6	3	a	a	DET
ap-1354	6	4	suggestion	suggestion	NOUN
ap-1354	6	5	by	by	ADP
ap-1354	6	6	bender	bender	NOUN
ap-1354	6	7	and	and	CCONJ
ap-1354	6	8	boetcher	boetcher	ADV
ap-1354	6	9	on	on	ADP
ap-1354	6	10	ptsymmetric	ptsymmetric	ADJ
ap-1354	6	11	quantum	quantum	ADJ
ap-1354	6	12	mechanics	mechanic	NOUN
ap-1354	6	13	has	have	AUX
ap-1354	6	14	put	put	VERB
ap-1354	6	15	forward	forward	ADV
ap-1354	6	16	a	a	DET
ap-1354	6	17	different	different	ADJ
ap-1354	6	18	point	point	NOUN
ap-1354	6	19	of	of	ADP
ap-1354	6	20	view	view	NOUN
ap-1354	6	21	from	from	ADP
ap-1354	6	22	standard	standard	ADJ
ap-1354	6	23	quantum	quantum	ADJ
ap-1354	6	24	mechanics	mechanic	NOUN
ap-1354	6	25	.	.	PUNCT
ap-1354	7	1	for	for	ADP
ap-1354	7	2	a	a	DET
ap-1354	7	3	quantum	quantum	ADJ
ap-1354	7	4	mechanical	mechanical	ADJ
ap-1354	7	5	system	system	NOUN
ap-1354	7	6	have	have	VERB
ap-1354	7	7	to	to	ADP
ap-1354	7	8	a	a	DET
ap-1354	7	9	real	real	ADJ
ap-1354	7	10	energy	energy	NOUN
ap-1354	7	11	spectrum	spectrum	NOUN
ap-1354	7	12	,	,	PUNCT
ap-1354	7	13	the	the	DET
ap-1354	7	14	hamiltonian	hamiltonian	NOUN
ap-1354	7	15	must	must	AUX
ap-1354	7	16	be	be	AUX
ap-1354	7	17	hermitian	hermitian	ADJ
ap-1354	7	18	.	.	PUNCT
ap-1354	8	1	bender	bender	NOUN
ap-1354	8	2	and	and	CCONJ
ap-1354	8	3	his	his	PRON
ap-1354	8	4	co	co	NOUN
ap-1354	8	5	-	-	NOUN
ap-1354	8	6	workers	worker	NOUN
ap-1354	8	7	showed	show	VERB
ap-1354	8	8	that	that	SCONJ
ap-1354	8	9	even	even	ADV
ap-1354	8	10	if	if	SCONJ
ap-1354	8	11	a	a	DET
ap-1354	8	12	hamiltonian	hamiltonian	NOUN
ap-1354	8	13	is	be	AUX
ap-1354	8	14	not	not	PART
ap-1354	8	15	hermitian	hermitian	ADJ
ap-1354	8	16	,	,	PUNCT
ap-1354	8	17	it	it	PRON
ap-1354	8	18	has	have	VERB
ap-1354	8	19	a	a	DET
ap-1354	8	20	real	real	ADJ
ap-1354	8	21	energy	energy	NOUN
ap-1354	8	22	spectrum	spectrum	NOUN
ap-1354	8	23	[	[	X
ap-1354	8	24	1	1	NUM
ap-1354	8	25	]	]	PUNCT
ap-1354	8	26	.	.	PUNCT
ap-1354	9	1	pt	pt	NOUN
ap-1354	9	2	-	-	PUNCT
ap-1354	9	3	symmetric	symmetric	ADJ
ap-1354	9	4	and	and	CCONJ
ap-1354	9	5	non	non	PROPN
ap-1354	9	6	hermitian	hermitian	PROPN
ap-1354	9	7	potentials	potential	NOUN
ap-1354	9	8	have	have	AUX
ap-1354	9	9	been	be	AUX
ap-1354	9	10	studied	study	VERB
ap-1354	9	11	to	to	PART
ap-1354	9	12	prove	prove	VERB
ap-1354	9	13	they	they	PRON
ap-1354	9	14	have	have	VERB
ap-1354	9	15	a	a	DET
ap-1354	9	16	real	real	ADJ
ap-1354	9	17	energy	energy	NOUN
ap-1354	9	18	spectrum	spectrum	NOUN
ap-1354	9	19	,	,	PUNCT
ap-1354	9	20	using	use	VERB
ap-1354	9	21	numerical	numerical	ADJ
ap-1354	9	22	and	and	CCONJ
ap-1354	9	23	analytical	analytical	ADJ
ap-1354	9	24	techniques	technique	NOUN
ap-1354	9	25	.	.	PUNCT
ap-1354	10	1	the	the	DET
ap-1354	10	2	energy	energy	NOUN
ap-1354	10	3	spectrum	spectrum	NOUN
ap-1354	10	4	corresponding	correspond	VERB
ap-1354	10	5	to	to	ADP
ap-1354	10	6	the	the	DET
ap-1354	10	7	wave	wave	NOUN
ap-1354	10	8	functions	function	NOUN
ap-1354	10	9	is	be	AUX
ap-1354	10	10	also	also	ADV
ap-1354	10	11	calculated	calculate	VERB
ap-1354	10	12	[	[	PUNCT
ap-1354	10	13	2–9	2–9	NOUN
ap-1354	10	14	]	]	X
ap-1354	10	15	.	.	PUNCT
ap-1354	11	1	in	in	ADP
ap-1354	11	2	this	this	DET
ap-1354	11	3	work	work	NOUN
ap-1354	11	4	,	,	PUNCT
ap-1354	11	5	we	we	PRON
ap-1354	11	6	have	have	AUX
ap-1354	11	7	used	use	VERB
ap-1354	11	8	feynman	feynman	PROPN
ap-1354	11	9	’s	’s	PART
ap-1354	11	10	path	path	PROPN
ap-1354	11	11	integral	integral	ADJ
ap-1354	11	12	method	method	NOUN
ap-1354	11	13	to	to	PART
ap-1354	11	14	get	get	VERB
ap-1354	11	15	the	the	DET
ap-1354	11	16	energy	energy	NOUN
ap-1354	11	17	spectrum	spectrum	NOUN
ap-1354	11	18	and	and	CCONJ
ap-1354	11	19	the	the	DET
ap-1354	11	20	wave	wave	NOUN
ap-1354	11	21	functions	function	NOUN
ap-1354	11	22	of	of	ADP
ap-1354	11	23	the	the	DET
ap-1354	11	24	pt-/non	pt-/non	PROPN
ap-1354	11	25	-	-	PUNCT
ap-1354	11	26	pt	pt	NOUN
ap-1354	11	27	-	-	PUNCT
ap-1354	11	28	symmetric	symmetric	ADJ
ap-1354	11	29	and	and	CCONJ
ap-1354	11	30	nonhermitian	nonhermitian	ADJ
ap-1354	11	31	exponential	exponential	ADJ
ap-1354	11	32	potential	potential	NOUN
ap-1354	11	33	.	.	PUNCT
ap-1354	12	1	the	the	DET
ap-1354	12	2	feynman	feynman	PROPN
ap-1354	12	3	path	path	PROPN
ap-1354	12	4	integral	integral	ADJ
ap-1354	12	5	is	be	AUX
ap-1354	12	6	a	a	DET
ap-1354	12	7	given	give	VERB
ap-1354	12	8	kernel	kernel	NOUN
ap-1354	12	9	which	which	PRON
ap-1354	12	10	has	have	VERB
ap-1354	12	11	transition	transition	NOUN
ap-1354	12	12	amplitudes	amplitude	NOUN
ap-1354	12	13	between	between	ADP
ap-1354	12	14	the	the	DET
ap-1354	12	15	initial	initial	ADJ
ap-1354	12	16	and	and	CCONJ
ap-1354	12	17	final	final	ADJ
ap-1354	12	18	positions	position	NOUN
ap-1354	12	19	of	of	ADP
ap-1354	12	20	the	the	DET
ap-1354	12	21	energy	energy	NOUN
ap-1354	12	22	dependent	dependent	ADJ
ap-1354	12	23	green	green	ADJ
ap-1354	12	24	function	function	NOUN
ap-1354	12	25	.	.	PUNCT
ap-1354	13	1	a	a	DET
ap-1354	13	2	feynman	feynman	PROPN
ap-1354	13	3	path	path	NOUN
ap-1354	13	4	integral	integral	ADJ
ap-1354	13	5	formalism	formalism	NOUN
ap-1354	13	6	for	for	ADP
ap-1354	13	7	deriving	derive	VERB
ap-1354	13	8	the	the	DET
ap-1354	13	9	kernel	kernel	NOUN
ap-1354	13	10	of	of	ADP
ap-1354	13	11	various	various	ADJ
ap-1354	13	12	potentials	potential	NOUN
ap-1354	13	13	was	be	AUX
ap-1354	13	14	developed	develop	VERB
ap-1354	13	15	in	in	ADP
ap-1354	13	16	[	[	X
ap-1354	13	17	10–16	10–16	NUM
ap-1354	13	18	]	]	PUNCT
ap-1354	13	19	.	.	PUNCT
ap-1354	14	1	duru	duru	PROPN
ap-1354	14	2	derived	derive	VERB
ap-1354	14	3	the	the	DET
ap-1354	14	4	wave	wave	NOUN
ap-1354	14	5	functions	function	NOUN
ap-1354	14	6	and	and	CCONJ
ap-1354	14	7	the	the	DET
ap-1354	14	8	energy	energy	NOUN
ap-1354	14	9	spectrum	spectrum	NOUN
ap-1354	14	10	of	of	ADP
ap-1354	14	11	the	the	DET
ap-1354	14	12	wood	wood	NOUN
ap-1354	14	13	-	-	PUNCT
ap-1354	14	14	saxon	saxon	NOUN
ap-1354	14	15	potential	potential	NOUN
ap-1354	14	16	for	for	ADP
ap-1354	14	17	s	s	NOUN
ap-1354	14	18	-	-	NOUN
ap-1354	14	19	waves	wave	NOUN
ap-1354	14	20	via	via	ADP
ap-1354	14	21	the	the	DET
ap-1354	14	22	radial	radial	ADJ
ap-1354	14	23	path	path	NOUN
ap-1354	14	24	integral	integral	ADJ
ap-1354	14	25	.	.	PUNCT
ap-1354	15	1	inomata	inomata	PROPN
ap-1354	15	2	obtained	obtain	VERB
ap-1354	15	3	the	the	DET
ap-1354	15	4	energy	energy	NOUN
ap-1354	15	5	spectrum	spectrum	NOUN
ap-1354	15	6	and	and	CCONJ
ap-1354	15	7	the	the	DET
ap-1354	15	8	normalized	normalized	ADJ
ap-1354	15	9	s	s	NOUN
ap-1354	15	10	-	-	PUNCT
ap-1354	15	11	state	state	NOUN
ap-1354	15	12	eigenfunctions	eigenfunction	NOUN
ap-1354	15	13	for	for	ADP
ap-1354	15	14	the	the	DET
ap-1354	15	15	hulthen	hulthen	NOUN
ap-1354	15	16	potential	potential	NOUN
ap-1354	15	17	using	use	VERB
ap-1354	15	18	the	the	DET
ap-1354	15	19	green	green	ADJ
ap-1354	15	20	function	function	NOUN
ap-1354	15	21	[	[	X
ap-1354	15	22	11	11	NUM
ap-1354	15	23	]	]	PUNCT
ap-1354	15	24	.	.	PUNCT
ap-1354	16	1	the	the	DET
ap-1354	16	2	kernel	kernel	NOUN
ap-1354	16	3	of	of	ADP
ap-1354	16	4	the	the	DET
ap-1354	16	5	hulthen	hulthen	NOUN
ap-1354	16	6	potential	potential	NOUN
ap-1354	16	7	can	can	AUX
ap-1354	16	8	be	be	AUX
ap-1354	16	9	exactly	exactly	ADV
ap-1354	16	10	solved	solve	VERB
ap-1354	16	11	given	give	VERB
ap-1354	16	12	the	the	DET
ap-1354	16	13	path	path	NOUN
ap-1354	16	14	integral	integral	ADJ
ap-1354	16	15	for	for	ADP
ap-1354	16	16	the	the	DET
ap-1354	16	17	particle	particle	NOUN
ap-1354	16	18	motion	motion	NOUN
ap-1354	16	19	on	on	ADP
ap-1354	16	20	the	the	DET
ap-1354	16	21	su(2	su(2	NOUN
ap-1354	16	22	)	)	PUNCT
ap-1354	16	23	manifold	manifold	ADJ
ap-1354	16	24	s3	s3	PROPN
ap-1354	17	1	[	[	X
ap-1354	17	2	10–12	10–12	NUM
ap-1354	17	3	]	]	PUNCT
ap-1354	17	4	.	.	PUNCT
ap-1354	18	1	in	in	ADP
ap-1354	18	2	sec	sec	PROPN
ap-1354	18	3	.	.	PROPN
ap-1354	18	4	ii	ii	PROPN
ap-1354	18	5	and	and	CCONJ
ap-1354	18	6	iii	iii	NOUN
ap-1354	18	7	,	,	PUNCT
ap-1354	18	8	we	we	PRON
ap-1354	18	9	derive	derive	VERB
ap-1354	18	10	the	the	DET
ap-1354	18	11	energy	energy	NOUN
ap-1354	18	12	dependent	dependent	ADJ
ap-1354	18	13	green	green	PROPN
ap-1354	18	14	’s	’s	PART
ap-1354	18	15	function	function	NOUN
ap-1354	18	16	of	of	ADP
ap-1354	18	17	the	the	DET
ap-1354	18	18	pt	pt	PROPN
ap-1354	18	19	/	/	SYM
ap-1354	18	20	non	non	ADJ
ap-1354	18	21	-	-	ADJ
ap-1354	18	22	pt	pt	ADJ
ap-1354	18	23	-	-	PUNCT
ap-1354	18	24	symmetric	symmetric	ADJ
ap-1354	18	25	and	and	CCONJ
ap-1354	18	26	non	non	ADJ
ap-1354	18	27	-	-	ADJ
ap-1354	18	28	hermitian	hermitian	ADJ
ap-1354	18	29	q	q	ADJ
ap-1354	18	30	-	-	PUNCT
ap-1354	18	31	deformed	deform	VERB
ap-1354	18	32	hulthen	hulthen	NOUN
ap-1354	18	33	potential	potential	NOUN
ap-1354	18	34	.	.	PUNCT
ap-1354	19	1	we	we	PRON
ap-1354	19	2	obtained	obtain	VERB
ap-1354	19	3	the	the	DET
ap-1354	19	4	energy	energy	NOUN
ap-1354	19	5	eigenvalues	eigenvalue	NOUN
ap-1354	19	6	and	and	CCONJ
ap-1354	19	7	the	the	DET
ap-1354	19	8	corresponding	corresponding	ADJ
ap-1354	19	9	wave	wave	NOUN
ap-1354	19	10	functions	function	NOUN
ap-1354	19	11	.	.	PUNCT
ap-1354	20	1	2	2	NUM
ap-1354	20	2	pt	pt	NOUN
ap-1354	20	3	-	-	PUNCT
ap-1354	20	4	symmetric	symmetric	ADJ
ap-1354	20	5	and	and	CCONJ
ap-1354	20	6	non	non	ADJ
ap-1354	20	7	-	-	ADJ
ap-1354	20	8	hermitian	hermitian	ADJ
ap-1354	20	9	hulthen	hulthen	NOUN
ap-1354	20	10	potential	potential	NOUN
ap-1354	20	11	the	the	DET
ap-1354	20	12	kernel	kernel	NOUN
ap-1354	20	13	of	of	ADP
ap-1354	20	14	a	a	DET
ap-1354	20	15	point	point	NOUN
ap-1354	20	16	particle	particle	NOUN
ap-1354	20	17	moving	move	VERB
ap-1354	20	18	in	in	ADP
ap-1354	20	19	the	the	DET
ap-1354	20	20	v	v	NOUN
ap-1354	20	21	(	(	PUNCT
ap-1354	20	22	x	x	NOUN
ap-1354	20	23	)	)	PUNCT
ap-1354	20	24	potential	potential	NOUN
ap-1354	20	25	in	in	ADP
ap-1354	20	26	one	one	NUM
ap-1354	20	27	dimension	dimension	NOUN
ap-1354	20	28	is	be	AUX
ap-1354	20	29	represented	represent	VERB
ap-1354	20	30	by	by	ADP
ap-1354	20	31	the	the	DET
ap-1354	20	32	following	following	ADJ
ap-1354	20	33	path	path	NOUN
ap-1354	20	34	integral	integral	ADJ
ap-1354	20	35	k(xb	k(xb	PROPN
ap-1354	20	36	,	,	PUNCT
ap-1354	20	37	tb;xa	tb;xa	PROPN
ap-1354	20	38	,	,	PUNCT
ap-1354	20	39	ta	ta	PROPN
ap-1354	20	40	)	)	PUNCT
ap-1354	21	1	=	=	SYM
ap-1354	21	2	∫	∫	PROPN
ap-1354	21	3	dxdp	dxdp	NOUN
ap-1354	21	4	2π	2π	PROPN
ap-1354	21	5	·	·	PUNCT
ap-1354	21	6	(	(	PUNCT
ap-1354	21	7	1	1	X
ap-1354	21	8	)	)	PUNCT
ap-1354	21	9	exp{i	exp{i	PROPN
ap-1354	21	10	∫	∫	PROPN
ap-1354	21	11	dt[pẋ	dt[pẋ	PROPN
ap-1354	21	12	−	−	PROPN
ap-1354	21	13	p2	p2	PROPN
ap-1354	21	14	2	2	NUM
ap-1354	21	15	m	m	NOUN
ap-1354	21	16	−	−	NOUN
ap-1354	21	17	v	v	NOUN
ap-1354	21	18	(	(	PUNCT
ap-1354	21	19	x	x	NOUN
ap-1354	21	20	)	)	PUNCT
ap-1354	21	21	]	]	PUNCT
ap-1354	21	22	}	}	PUNCT
ap-1354	21	23	where	where	SCONJ
ap-1354	21	24	h̄	h̄	NOUN
ap-1354	21	25	=	=	NOUN
ap-1354	21	26	1	1	X
ap-1354	21	27	.	.	PUNCT
ap-1354	22	1	the	the	DET
ap-1354	22	2	kernel	kernel	PROPN
ap-1354	22	3	expresses	express	VERB
ap-1354	22	4	the	the	DET
ap-1354	22	5	probability	probability	NOUN
ap-1354	22	6	amplitude	amplitude	NOUN
ap-1354	22	7	of	of	ADP
ap-1354	22	8	a	a	DET
ap-1354	22	9	particle	particle	NOUN
ap-1354	22	10	moving	move	VERB
ap-1354	22	11	to	to	PART
ap-1354	22	12	position	position	VERB
ap-1354	22	13	xb	xb	NOUN
ap-1354	22	14	at	at	ADP
ap-1354	22	15	time	time	NOUN
ap-1354	22	16	tb	tb	ADP
ap-1354	22	17	from	from	ADP
ap-1354	22	18	position	position	NOUN
ap-1354	22	19	xa	xa	PROPN
ap-1354	22	20	at	at	ADP
ap-1354	22	21	time	time	NOUN
ap-1354	22	22	ta	ta	PROPN
ap-1354	22	23	.	.	PUNCT
ap-1354	23	1	the	the	DET
ap-1354	23	2	time	time	NOUN
ap-1354	23	3	interval	interval	NOUN
ap-1354	23	4	can	can	AUX
ap-1354	23	5	be	be	AUX
ap-1354	23	6	divided	divide	VERB
ap-1354	23	7	into	into	ADP
ap-1354	23	8	n	n	CCONJ
ap-1354	23	9	equal	equal	ADJ
ap-1354	23	10	parts	part	NOUN
ap-1354	23	11	tj	tj	NOUN
ap-1354	23	12	−	−	NOUN
ap-1354	23	13	tj−1	tj−1	NOUN
ap-1354	23	14	=	=	SYM
ap-1354	23	15	tb	tb	ADP
ap-1354	23	16	−	−	PROPN
ap-1354	23	17	ta	ta	PROPN
ap-1354	23	18	=	=	SYM
ap-1354	23	19	t	t	PROPN
ap-1354	23	20	j	j	PROPN
ap-1354	23	21	=	=	SYM
ap-1354	23	22	1	1	NUM
ap-1354	23	23	,	,	PUNCT
ap-1354	23	24	2	2	NUM
ap-1354	23	25	,	,	PUNCT
ap-1354	23	26	3	3	NUM
ap-1354	23	27	,	,	PUNCT
ap-1354	23	28	.	.	PUNCT
ap-1354	23	29	.	.	PUNCT
ap-1354	24	1	.	.	PUNCT
ap-1354	25	1	,	,	PUNCT
ap-1354	25	2	n	n	X
ap-1354	25	3	(	(	PUNCT
ap-1354	25	4	2	2	NUM
ap-1354	25	5	)	)	PUNCT
ap-1354	26	1	and	and	CCONJ
ap-1354	26	2	taking	take	VERB
ap-1354	26	3	initial	initial	ADJ
ap-1354	26	4	position	position	NOUN
ap-1354	26	5	is	be	AUX
ap-1354	26	6	xa	xa	PROPN
ap-1354	26	7	and	and	CCONJ
ap-1354	26	8	final	final	ADJ
ap-1354	26	9	position	position	NOUN
ap-1354	26	10	xb	xb	PROPN
ap-1354	26	11	,	,	PUNCT
ap-1354	26	12	the	the	DET
ap-1354	26	13	kernel	kernel	NOUN
ap-1354	27	1	[	[	X
ap-1354	27	2	11	11	NUM
ap-1354	27	3	]	]	PUNCT
ap-1354	27	4	can	can	AUX
ap-1354	27	5	be	be	AUX
ap-1354	27	6	performed	perform	VERB
ap-1354	27	7	as	as	ADP
ap-1354	27	8	k(xb	k(xb	PROPN
ap-1354	27	9	,	,	PUNCT
ap-1354	27	10	t	t	PROPN
ap-1354	27	11	;	;	PUNCT
ap-1354	27	12	xa	xa	PROPN
ap-1354	27	13	,	,	PUNCT
ap-1354	27	14	0	0	NUM
ap-1354	27	15	)	)	PUNCT
ap-1354	27	16	=	=	SYM
ap-1354	28	1	∫	∫	PROPN
ap-1354	28	2	∞	∞	PROPN
ap-1354	29	1	−∞	−∞	PROPN
ap-1354	29	2	n∏	n∏	PROPN
ap-1354	29	3	i=1	i=1	PROPN
ap-1354	29	4	dxi	dxi	PROPN
ap-1354	29	5	n+1∏	n+1∏	PROPN
ap-1354	29	6	i=1	i=1	PROPN
ap-1354	30	1	dpi	dpi	PROPN
ap-1354	30	2	2π	2π	PROPN
ap-1354	30	3	·	·	PUNCT
ap-1354	30	4	(	(	PUNCT
ap-1354	30	5	3	3	X
ap-1354	30	6	)	)	PUNCT
ap-1354	30	7	exp{i	exp{i	PROPN
ap-1354	30	8	n+1∑	n+1∑	PROPN
ap-1354	30	9	i=1	i=1	PROPN
ap-1354	31	1	[	[	X
ap-1354	31	2	pi(xi	pi(xi	PROPN
ap-1354	31	3	−	−	PROPN
ap-1354	31	4	xi−1)−	xi−1)−	PROPN
ap-1354	31	5	p2i	p2i	PROPN
ap-1354	31	6	2	2	NUM
ap-1354	31	7	m	m	NOUN
ap-1354	31	8	−	−	NOUN
ap-1354	31	9	v	v	NOUN
ap-1354	31	10	(	(	PUNCT
ap-1354	31	11	xi	xi	PROPN
ap-1354	31	12	)	)	PUNCT
ap-1354	31	13	]	]	PUNCT
ap-1354	31	14	}	}	PUNCT
ap-1354	31	15	.	.	PUNCT
ap-1354	32	1	the	the	DET
ap-1354	32	2	ptsymmetric	ptsymmetric	ADJ
ap-1354	32	3	and	and	CCONJ
ap-1354	32	4	non	non	ADJ
ap-1354	32	5	-	-	ADJ
ap-1354	32	6	hermitian	hermitian	ADJ
ap-1354	32	7	potential	potential	NOUN
ap-1354	32	8	is	be	AUX
ap-1354	32	9	v	v	NOUN
ap-1354	32	10	(	(	PUNCT
ap-1354	32	11	x	x	NOUN
ap-1354	32	12	)	)	PUNCT
ap-1354	32	13	=	=	SYM
ap-1354	33	1	−	−	PROPN
ap-1354	33	2	voe	voe	PROPN
ap-1354	33	3	−ix	−ix	PROPN
ap-1354	33	4	/	/	SYM
ap-1354	33	5	a	a	DET
ap-1354	33	6	1−	1−	NUM
ap-1354	33	7	qe−ix	qe−ix	NOUN
ap-1354	33	8	/	/	SYM
ap-1354	33	9	a	a	PRON
ap-1354	33	10	(	(	PUNCT
ap-1354	33	11	4	4	NUM
ap-1354	33	12	)	)	PUNCT
ap-1354	33	13	which	which	PRON
ap-1354	33	14	is	be	AUX
ap-1354	33	15	determined	determine	VERB
ap-1354	33	16	by	by	ADP
ap-1354	33	17	taking	take	VERB
ap-1354	33	18	1	1	NUM
ap-1354	33	19	a	a	DET
ap-1354	33	20	−→	−→	NOUN
ap-1354	33	21	i	i	PRON
ap-1354	33	22	a	a	PRON
ap-1354	33	23	in	in	ADP
ap-1354	33	24	the	the	DET
ap-1354	33	25	q	q	ADV
ap-1354	33	26	-	-	PUNCT
ap-1354	33	27	deformed	deform	VERB
ap-1354	33	28	hulthen	hulthen	NOUN
ap-1354	33	29	potential	potential	NOUN
ap-1354	33	30	[	[	X
ap-1354	33	31	5	5	NUM
ap-1354	33	32	]	]	PUNCT
ap-1354	33	33	.	.	PUNCT
ap-1354	34	1	we	we	PRON
ap-1354	34	2	will	will	AUX
ap-1354	34	3	start	start	VERB
ap-1354	34	4	by	by	ADP
ap-1354	34	5	applying	apply	VERB
ap-1354	34	6	point	point	NOUN
ap-1354	34	7	transformation	transformation	NOUN
ap-1354	34	8	to	to	PART
ap-1354	34	9	get	get	VERB
ap-1354	34	10	a	a	DET
ap-1354	34	11	solvable	solvable	ADJ
ap-1354	34	12	path	path	NOUN
ap-1354	34	13	integral	integral	ADJ
ap-1354	34	14	form	form	NOUN
ap-1354	34	15	for	for	ADP
ap-1354	34	16	the	the	DET
ap-1354	34	17	hulthen	hulthen	NOUN
ap-1354	34	18	potential	potential	ADJ
ap-1354	34	19	1	1	NUM
ap-1354	34	20	1−	1−	NUM
ap-1354	34	21	qe−ix	qe−ix	NOUN
ap-1354	34	22	/	/	SYM
ap-1354	34	23	a	a	PRON
ap-1354	34	24	=	=	X
ap-1354	34	25	sin2	sin2	NOUN
ap-1354	35	1	θ	θ	PROPN
ap-1354	36	1	p	p	X
ap-1354	36	2	=	=	PUNCT
ap-1354	36	3	i	i	PRON
ap-1354	36	4	2a	2a	NUM
ap-1354	36	5	sin	sin	VERB
ap-1354	36	6	θ	θ	PROPN
ap-1354	36	7	cos	cos	PROPN
ap-1354	36	8	θpθ	θpθ	VERB
ap-1354	36	9	(	(	PUNCT
ap-1354	36	10	5	5	NUM
ap-1354	36	11	)	)	PUNCT
ap-1354	36	12	38	38	NUM
ap-1354	36	13	acta	acta	PROPN
ap-1354	36	14	polytechnica	polytechnica	PROPN
ap-1354	36	15	vol	vol	NOUN
ap-1354	36	16	.	.	PUNCT
ap-1354	37	1	51	51	NUM
ap-1354	37	2	no	no	NOUN
ap-1354	37	3	.	.	PUNCT
ap-1354	37	4	1/2011	1/2011	NUM
ap-1354	37	5	because	because	SCONJ
ap-1354	37	6	of	of	ADP
ap-1354	37	7	this	this	DET
ap-1354	37	8	transformation	transformation	NOUN
ap-1354	37	9	,	,	PUNCT
ap-1354	37	10	there	there	PRON
ap-1354	37	11	is	be	VERB
ap-1354	37	12	a	a	DET
ap-1354	37	13	contribution	contribution	NOUN
ap-1354	37	14	to	to	ADP
ap-1354	37	15	the	the	DET
ap-1354	37	16	jacobi	jacobi	PROPN
ap-1354	37	17	performed	perform	VERB
ap-1354	37	18	kernel	kernel	PROPN
ap-1354	37	19	k(xb	k(xb	PROPN
ap-1354	37	20	,	,	PUNCT
ap-1354	37	21	t	t	PROPN
ap-1354	37	22	;	;	PUNCT
ap-1354	37	23	xa	xa	PROPN
ap-1354	37	24	,	,	PUNCT
ap-1354	37	25	0	0	NUM
ap-1354	37	26	)	)	PUNCT
ap-1354	37	27	=	=	SYM
ap-1354	38	1	q	q	PROPN
ap-1354	38	2	2a	2a	NUM
ap-1354	38	3	sin	sin	VERB
ap-1354	38	4	θb	θb	ADP
ap-1354	38	5	cos	cos	PROPN
ap-1354	38	6	θb	θb	PROPN
ap-1354	38	7	∫	∫	PROPN
ap-1354	38	8	dθdpθ	dθdpθ	PROPN
ap-1354	38	9	×	×	PROPN
ap-1354	38	10	exp[i	exp[i	NOUN
ap-1354	38	11	∫	∫	X
ap-1354	38	12	dt(pθ	dt(pθ	PROPN
ap-1354	38	13	θ̇	θ̇	ADJ
ap-1354	38	14	+	+	CCONJ
ap-1354	38	15	sin2	sin2	NOUN
ap-1354	38	16	θ	θ	PROPN
ap-1354	38	17	cos2	cos2	VERB
ap-1354	38	18	θ	θ	PROPN
ap-1354	38	19	4α2	4α2	NUM
ap-1354	38	20	p2θ	p2θ	NOUN
ap-1354	38	21	2μ	2μ	NOUN
ap-1354	38	22	−	−	PROPN
ap-1354	38	23	v0	v0	NOUN
ap-1354	38	24	cos2	cos2	NOUN
ap-1354	38	25	θ	θ	PROPN
ap-1354	38	26	)	)	PUNCT
ap-1354	38	27	]	]	PUNCT
ap-1354	38	28	.	.	PUNCT
ap-1354	39	1	(	(	PUNCT
ap-1354	39	2	6	6	NUM
ap-1354	39	3	)	)	PUNCT
ap-1354	39	4	here	here	ADV
ap-1354	39	5	,	,	PUNCT
ap-1354	39	6	the	the	DET
ap-1354	39	7	kinetic	kinetic	ADJ
ap-1354	39	8	energy	energy	NOUN
ap-1354	39	9	term	term	NOUN
ap-1354	39	10	becomes	become	VERB
ap-1354	39	11	positive	positive	ADJ
ap-1354	39	12	.	.	PUNCT
ap-1354	40	1	we	we	PRON
ap-1354	40	2	define	define	VERB
ap-1354	40	3	a	a	DET
ap-1354	40	4	new	new	ADJ
ap-1354	40	5	time	time	NOUN
ap-1354	40	6	parameter	parameter	NOUN
ap-1354	40	7	s	s	PART
ap-1354	41	1	[	[	X
ap-1354	41	2	12	12	NUM
ap-1354	41	3	]	]	PUNCT
ap-1354	41	4	to	to	PART
ap-1354	41	5	eliminate	eliminate	VERB
ap-1354	41	6	the	the	DET
ap-1354	41	7	sin2	sin2	NOUN
ap-1354	41	8	θ	θ	PROPN
ap-1354	41	9	cos2	cos2	VERB
ap-1354	41	10	θ	θ	PROPN
ap-1354	41	11	4α2	4α2	NUM
ap-1354	41	12	part	part	NOUN
ap-1354	41	13	in	in	ADP
ap-1354	41	14	the	the	DET
ap-1354	41	15	kinetic	kinetic	ADJ
ap-1354	41	16	energy	energy	NOUN
ap-1354	41	17	term	term	NOUN
ap-1354	41	18	dt	dt	X
ap-1354	41	19	ds	ds	PROPN
ap-1354	41	20	=	=	ADJ
ap-1354	41	21	−	−	PROPN
ap-1354	41	22	4a2	4a2	NUM
ap-1354	41	23	sin2	sin2	NOUN
ap-1354	41	24	θ	θ	PROPN
ap-1354	41	25	cos2	cos2	PROPN
ap-1354	41	26	θ	θ	PROPN
ap-1354	41	27	or	or	CCONJ
ap-1354	41	28	t	t	PROPN
ap-1354	41	29	=	=	SYM
ap-1354	42	1	−4a2	−4a2	PROPN
ap-1354	42	2	∫	∫	PROPN
ap-1354	42	3	ds′	ds′	PROPN
ap-1354	42	4	sin2	sin2	PROPN
ap-1354	42	5	θ	θ	PROPN
ap-1354	42	6	cos2	cos2	PROPN
ap-1354	42	7	θ	θ	PROPN
ap-1354	42	8	.	.	PUNCT
ap-1354	43	1	(	(	PUNCT
ap-1354	43	2	7	7	X
ap-1354	43	3	)	)	PUNCT
ap-1354	43	4	if	if	SCONJ
ap-1354	43	5	we	we	PRON
ap-1354	43	6	use	use	VERB
ap-1354	43	7	the	the	DET
ap-1354	43	8	fourier	fourier	ADJ
ap-1354	43	9	transform	transform	NOUN
ap-1354	43	10	of	of	ADP
ap-1354	43	11	the	the	DET
ap-1354	43	12	δ−	δ−	ADJ
ap-1354	43	13	function	function	NOUN
ap-1354	43	14	,	,	PUNCT
ap-1354	43	15	we	we	PRON
ap-1354	43	16	can	can	AUX
ap-1354	43	17	write	write	VERB
ap-1354	43	18	1	1	NUM
ap-1354	43	19	=	=	SYM
ap-1354	43	20	∫	∫	X
ap-1354	43	21	ds	ds	PROPN
ap-1354	43	22	∫	∫	PROPN
ap-1354	43	23	de	de	PROPN
ap-1354	43	24	2π	2π	PROPN
ap-1354	43	25	4a2	4a2	NUM
ap-1354	43	26	sin2	sin2	NOUN
ap-1354	43	27	θb	θb	ADP
ap-1354	43	28	cos2	cos2	VERB
ap-1354	43	29	θb	θb	ADP
ap-1354	43	30	·	·	PUNCT
ap-1354	43	31	exp	exp	NOUN
ap-1354	43	32	[	[	PUNCT
ap-1354	43	33	−i	−i	PROPN
ap-1354	43	34	(	(	PUNCT
ap-1354	43	35	et	et	PROPN
ap-1354	43	36	−	−	PROPN
ap-1354	43	37	∫	∫	NOUN
ap-1354	44	1	ds	ds	ADJ
ap-1354	44	2	4a2e	4a2e	ADJ
ap-1354	44	3	sin2	sin2	NOUN
ap-1354	44	4	θ	θ	PROPN
ap-1354	44	5	cos2	cos2	PROPN
ap-1354	44	6	θ	θ	PROPN
ap-1354	44	7	)	)	PUNCT
ap-1354	44	8	]	]	PUNCT
ap-1354	45	1	(	(	PUNCT
ap-1354	45	2	8)	8)	NUM
ap-1354	45	3	where	where	SCONJ
ap-1354	45	4	s	s	VERB
ap-1354	45	5	=	=	X
ap-1354	45	6	sb	sb	PROPN
ap-1354	45	7	−	−	PROPN
ap-1354	45	8	sa	sa	PROPN
ap-1354	45	9	.	.	PUNCT
ap-1354	46	1	the	the	DET
ap-1354	46	2	factor	factor	NOUN
ap-1354	46	3	in	in	ADP
ap-1354	46	4	front	front	NOUN
ap-1354	46	5	of	of	ADP
ap-1354	46	6	the	the	DET
ap-1354	46	7	path	path	NOUN
ap-1354	46	8	integral	integral	ADJ
ap-1354	46	9	reached	reach	VERB
ap-1354	46	10	from	from	ADP
ap-1354	46	11	the	the	DET
ap-1354	46	12	jacobian	jacobian	PROPN
ap-1354	46	13	can	can	AUX
ap-1354	46	14	be	be	AUX
ap-1354	46	15	a	a	DET
ap-1354	46	16	symmetrization	symmetrization	NOUN
ap-1354	46	17	according	accord	VERB
ap-1354	46	18	to	to	ADP
ap-1354	46	19	points	point	NOUN
ap-1354	46	20	a	a	PRON
ap-1354	46	21	and	and	CCONJ
ap-1354	46	22	b	b	NOUN
ap-1354	46	23	,	,	PUNCT
ap-1354	46	24	as	as	SCONJ
ap-1354	46	25	follows	follow	VERB
ap-1354	46	26	1	1	NUM
ap-1354	46	27	sin	sin	NOUN
ap-1354	46	28	θb	θb	ADP
ap-1354	46	29	cos	cos	PROPN
ap-1354	46	30	θb	θb	PROPN
ap-1354	46	31	=	=	SYM
ap-1354	46	32	2√	2√	PROPN
ap-1354	46	33	sin	sin	NOUN
ap-1354	46	34	2θa	2θa	NOUN
ap-1354	46	35	sin	sin	VERB
ap-1354	46	36	2θb	2θb	NOUN
ap-1354	46	37	·	·	PUNCT
ap-1354	46	38	exp	exp	NOUN
ap-1354	47	1	(	(	PUNCT
ap-1354	47	2	i	i	PRON
ap-1354	47	3	∫	∫	PROPN
ap-1354	47	4	s	s	PART
ap-1354	47	5	0	0	NUM
ap-1354	47	6	ds	ds	ADJ
ap-1354	47	7	(	(	PUNCT
ap-1354	47	8	−i	−i	NOUN
ap-1354	47	9	)	)	PUNCT
ap-1354	47	10	cos	cos	ADP
ap-1354	47	11	2θ	2θ	NUM
ap-1354	47	12	sin	sin	VERB
ap-1354	47	13	2θ	2θ	NUM
ap-1354	47	14	θ̇	θ̇	NOUN
ap-1354	47	15	)	)	PUNCT
ap-1354	47	16	(	(	PUNCT
ap-1354	47	17	9	9	NUM
ap-1354	47	18	)	)	PUNCT
ap-1354	47	19	thus	thus	ADV
ap-1354	47	20	eq	eq	ADP
ap-1354	47	21	.	.	PUNCT
ap-1354	48	1	(	(	PUNCT
ap-1354	48	2	6	6	NUM
ap-1354	48	3	)	)	PUNCT
ap-1354	48	4	happens	happen	VERB
ap-1354	48	5	k(xb	k(xb	PROPN
ap-1354	48	6	,	,	PUNCT
ap-1354	48	7	xa	xa	PROPN
ap-1354	48	8	,	,	PUNCT
ap-1354	48	9	t	t	PROPN
ap-1354	48	10	)	)	PUNCT
ap-1354	49	1	=	=	PUNCT
ap-1354	49	2	∫	∫	PROPN
ap-1354	50	1	∞	∞	NOUN
ap-1354	50	2	0	0	NUM
ap-1354	51	1	dseis/2μ	dseis/2μ	NOUN
ap-1354	51	2	∫	∫	PROPN
ap-1354	51	3	∞	∞	PROPN
ap-1354	51	4	−∞	−∞	X
ap-1354	51	5	de	de	X
ap-1354	51	6	2π	2π	PROPN
ap-1354	51	7	eiet	eiet	NOUN
ap-1354	51	8	·	·	PUNCT
ap-1354	51	9	4iaq√	4iaq√	NOUN
ap-1354	51	10	sin	sin	VERB
ap-1354	51	11	2θa	2θa	NOUN
ap-1354	51	12	cos	cos	PROPN
ap-1354	51	13	2θb	2θb	PROPN
ap-1354	51	14	k	k	PROPN
ap-1354	51	15	(	(	PUNCT
ap-1354	51	16	θb	θb	PROPN
ap-1354	51	17	,	,	PUNCT
ap-1354	51	18	θa;s	θa;s	NUM
ap-1354	51	19	)	)	PUNCT
ap-1354	51	20	(	(	PUNCT
ap-1354	51	21	10	10	NUM
ap-1354	51	22	)	)	PUNCT
ap-1354	52	1	where	where	SCONJ
ap-1354	52	2	k	k	PROPN
ap-1354	52	3	(	(	PUNCT
ap-1354	52	4	θb	θb	PROPN
ap-1354	52	5	,	,	PUNCT
ap-1354	52	6	θa;s	θa;s	NOUN
ap-1354	52	7	)	)	PUNCT
ap-1354	52	8	=	=	SYM
ap-1354	52	9	∫	∫	PROPN
ap-1354	52	10	dθdpθ	dθdpθ	PROPN
ap-1354	52	11	·	·	PUNCT
ap-1354	52	12	exp	exp	NOUN
ap-1354	52	13	{	{	PUNCT
ap-1354	52	14	i	i	PRON
ap-1354	52	15	∫	∫	PROPN
ap-1354	52	16	s	s	PART
ap-1354	52	17	0	0	NUM
ap-1354	52	18	ds	ds	PROPN
ap-1354	52	19	[	[	PUNCT
ap-1354	52	20	pθθ̇	pθθ̇	PROPN
ap-1354	52	21	−	−	PROPN
ap-1354	52	22	p2θ	p2θ	NOUN
ap-1354	52	23	2μ	2μ	NOUN
ap-1354	52	24	−	−	PROPN
ap-1354	52	25	(	(	PUNCT
ap-1354	52	26	11	11	NUM
ap-1354	52	27	)	)	SYM
ap-1354	52	28	1	1	NUM
ap-1354	52	29	2μ	2μ	NOUN
ap-1354	52	30	(	(	PUNCT
ap-1354	52	31	k	k	X
ap-1354	52	32	(	(	PUNCT
ap-1354	52	33	k	k	NOUN
ap-1354	52	34	−	−	PROPN
ap-1354	52	35	1	1	X
ap-1354	52	36	)	)	PUNCT
ap-1354	52	37	sin2	sin2	NOUN
ap-1354	52	38	θ	θ	PROPN
ap-1354	53	1	+	+	CCONJ
ap-1354	53	2	λ	λ	X
ap-1354	53	3	(	(	PUNCT
ap-1354	53	4	λ	λ	X
ap-1354	53	5	−	−	NOUN
ap-1354	53	6	1	1	NUM
ap-1354	53	7	)	)	PUNCT
ap-1354	53	8	cos2	cos2	NOUN
ap-1354	53	9	θ	θ	PROPN
ap-1354	53	10	)	)	PUNCT
ap-1354	53	11	−	−	ADP
ap-1354	53	12	ipθ	ipθ	PROPN
ap-1354	53	13	cos	cos	ADP
ap-1354	53	14	2θ	2θ	NUM
ap-1354	53	15	2μ	2μ	NUM
ap-1354	53	16	sin	sin	VERB
ap-1354	53	17	2θ	2θ	NUM
ap-1354	53	18	]	]	PUNCT
ap-1354	53	19	}	}	PUNCT
ap-1354	53	20	and	and	CCONJ
ap-1354	53	21	k	k	PROPN
ap-1354	53	22	and	and	CCONJ
ap-1354	53	23	λ	λ	PROPN
ap-1354	53	24	are	be	AUX
ap-1354	53	25	k	k	X
ap-1354	53	26	=	=	SYM
ap-1354	53	27	1	1	NUM
ap-1354	53	28	2	2	NUM
ap-1354	53	29	[	[	PUNCT
ap-1354	53	30	1	1	NUM
ap-1354	53	31	+	+	CCONJ
ap-1354	53	32	√	√	NUM
ap-1354	53	33	32μa2	32μa2	NUM
ap-1354	53	34	(	(	PUNCT
ap-1354	53	35	v0	v0	NOUN
ap-1354	53	36	+	+	CCONJ
ap-1354	53	37	e	e	NOUN
ap-1354	53	38	)	)	PUNCT
ap-1354	53	39	]	]	PUNCT
ap-1354	54	1	λ	λ	X
ap-1354	54	2	=	=	NOUN
ap-1354	54	3	1	1	NUM
ap-1354	54	4	2	2	NUM
ap-1354	54	5	[	[	PUNCT
ap-1354	54	6	1	1	NUM
ap-1354	54	7	+	+	CCONJ
ap-1354	54	8	√	√	NUM
ap-1354	54	9	32μa2e	32μa2e	NUM
ap-1354	54	10	]	]	PUNCT
ap-1354	54	11	(	(	PUNCT
ap-1354	54	12	12	12	NUM
ap-1354	54	13	)	)	PUNCT
ap-1354	54	14	if	if	SCONJ
ap-1354	54	15	the	the	DET
ap-1354	54	16	factor	factor	NOUN
ap-1354	54	17	contribution	contribution	NOUN
ap-1354	54	18	to	to	ADP
ap-1354	54	19	the	the	DET
ap-1354	54	20	jacobian	jacobian	PROPN
ap-1354	54	21	is	be	AUX
ap-1354	54	22	symmetrized	symmetrize	VERB
ap-1354	54	23	as	as	ADP
ap-1354	54	24	[	[	X
ap-1354	54	25	11	11	NUM
ap-1354	54	26	]	]	PUNCT
ap-1354	54	27	the	the	DET
ap-1354	54	28	contributions	contribution	NOUN
ap-1354	54	29	to	to	ADP
ap-1354	54	30	the	the	DET
ap-1354	54	31	kernel	kernel	NOUN
ap-1354	54	32	become	become	VERB
ap-1354	54	33	θ̇j	θ̇j	ADJ
ap-1354	54	34	−→	−→	ADJ
ap-1354	54	35	θ̇j	θ̇j	NOUN
ap-1354	54	36	±	±	NUM
ap-1354	54	37	i	i	PRON
ap-1354	54	38	cos	cos	PROPN
ap-1354	54	39	θj	θj	DET
ap-1354	54	40	2μ	2μ	PROPN
ap-1354	54	41	sin	sin	VERB
ap-1354	54	42	θj	θj	NOUN
ap-1354	54	43	(	(	PUNCT
ap-1354	54	44	13	13	NUM
ap-1354	54	45	)	)	PUNCT
ap-1354	54	46	so	so	SCONJ
ap-1354	54	47	the	the	DET
ap-1354	54	48	problem	problem	NOUN
ap-1354	54	49	is	be	AUX
ap-1354	54	50	transformed	transform	VERB
ap-1354	54	51	into	into	ADP
ap-1354	54	52	the	the	DET
ap-1354	54	53	path	path	NOUN
ap-1354	54	54	integral	integral	ADJ
ap-1354	54	55	for	for	ADP
ap-1354	54	56	pöschl	pöschl	ADJ
ap-1354	54	57	-	-	PUNCT
ap-1354	54	58	teller	teller	NOUN
ap-1354	54	59	potential	potential	NOUN
ap-1354	54	60	,	,	PUNCT
ap-1354	54	61	for	for	ADP
ap-1354	54	62	which	which	PRON
ap-1354	54	63	an	an	DET
ap-1354	54	64	exact	exact	ADJ
ap-1354	54	65	solution	solution	NOUN
ap-1354	54	66	is	be	AUX
ap-1354	54	67	known	know	VERB
ap-1354	54	68	[	[	PUNCT
ap-1354	54	69	11	11	NUM
ap-1354	54	70	]	]	PUNCT
ap-1354	54	71	.	.	PUNCT
ap-1354	55	1	k	k	X
ap-1354	55	2	(	(	PUNCT
ap-1354	55	3	θb	θb	PROPN
ap-1354	55	4	,	,	PUNCT
ap-1354	55	5	θa;s	θa;s	PROPN
ap-1354	55	6	)	)	PUNCT
ap-1354	55	7	can	can	AUX
ap-1354	55	8	be	be	AUX
ap-1354	55	9	obtained	obtain	VERB
ap-1354	55	10	as	as	ADP
ap-1354	55	11	k	k	PROPN
ap-1354	55	12	(	(	PUNCT
ap-1354	55	13	θb	θb	PROPN
ap-1354	55	14	,	,	PUNCT
ap-1354	55	15	θa;s	θa;s	NOUN
ap-1354	55	16	)	)	PUNCT
ap-1354	56	1	=	=	SYM
ap-1354	56	2	∫	∫	PROPN
ap-1354	56	3	dθdpθ	dθdpθ	PROPN
ap-1354	56	4	·	·	PUNCT
ap-1354	56	5	exp	exp	NOUN
ap-1354	56	6	{	{	PUNCT
ap-1354	57	1	i	i	PRON
ap-1354	57	2	∫	∫	PROPN
ap-1354	57	3	s	s	PART
ap-1354	57	4	0	0	NUM
ap-1354	57	5	ds	ds	PROPN
ap-1354	57	6	[	[	PUNCT
ap-1354	57	7	pθθ̇	pθθ̇	PROPN
ap-1354	57	8	−	−	PROPN
ap-1354	57	9	p2θ	p2θ	NOUN
ap-1354	57	10	2μ	2μ	NOUN
ap-1354	57	11	−	−	PROPN
ap-1354	57	12	(	(	PUNCT
ap-1354	57	13	14	14	NUM
ap-1354	57	14	)	)	SYM
ap-1354	57	15	1	1	NUM
ap-1354	57	16	2μ	2μ	NOUN
ap-1354	57	17	(	(	PUNCT
ap-1354	57	18	k	k	X
ap-1354	57	19	(	(	PUNCT
ap-1354	57	20	k	k	NOUN
ap-1354	57	21	−	−	PROPN
ap-1354	57	22	1	1	X
ap-1354	57	23	)	)	PUNCT
ap-1354	57	24	sin2	sin2	NOUN
ap-1354	57	25	θ	θ	PROPN
ap-1354	58	1	+	+	CCONJ
ap-1354	58	2	λ	λ	X
ap-1354	58	3	(	(	PUNCT
ap-1354	58	4	λ−	λ−	PROPN
ap-1354	58	5	1	1	NUM
ap-1354	58	6	)	)	PUNCT
ap-1354	58	7	cos2	cos2	NOUN
ap-1354	58	8	θ	θ	PROPN
ap-1354	58	9	)	)	PUNCT
ap-1354	58	10	]	]	PUNCT
ap-1354	58	11	}	}	PUNCT
ap-1354	58	12	the	the	DET
ap-1354	58	13	kernel	kernel	NOUN
ap-1354	58	14	can	can	AUX
ap-1354	58	15	be	be	AUX
ap-1354	58	16	obtained	obtain	VERB
ap-1354	58	17	in	in	ADP
ap-1354	58	18	the	the	DET
ap-1354	58	19	form	form	NOUN
ap-1354	58	20	k	k	PROPN
ap-1354	58	21	(	(	PUNCT
ap-1354	58	22	θb	θb	PROPN
ap-1354	58	23	,	,	PUNCT
ap-1354	58	24	θa;s	θa;s	NOUN
ap-1354	58	25	)	)	PUNCT
ap-1354	59	1	=	=	PUNCT
ap-1354	59	2	(	(	PUNCT
ap-1354	59	3	15	15	NUM
ap-1354	59	4	)	)	PUNCT
ap-1354	59	5	∞∑	∞∑	PRON
ap-1354	59	6	n=0	n=0	NUM
ap-1354	59	7	exp	exp	NOUN
ap-1354	59	8	[	[	PUNCT
ap-1354	59	9	−i	−i	PROPN
ap-1354	59	10	(	(	PUNCT
ap-1354	59	11	s/2μ	s/2μ	NOUN
ap-1354	59	12	)	)	PUNCT
ap-1354	59	13	(	(	PUNCT
ap-1354	59	14	k	k	X
ap-1354	59	15	+	+	PUNCT
ap-1354	59	16	λ+	λ+	PUNCT
ap-1354	59	17	2n)2	2n)2	NUM
ap-1354	59	18	]	]	PUNCT
ap-1354	59	19	ψn	ψn	X
ap-1354	59	20	(	(	PUNCT
ap-1354	59	21	θa)ψ∗	θa)ψ∗	PROPN
ap-1354	59	22	n	n	CCONJ
ap-1354	59	23	(	(	PUNCT
ap-1354	59	24	θb	θb	NOUN
ap-1354	59	25	)	)	PUNCT
ap-1354	59	26	where	where	SCONJ
ap-1354	59	27	ψn	ψn	INTJ
ap-1354	59	28	(	(	PUNCT
ap-1354	59	29	θ	θ	NOUN
ap-1354	59	30	)	)	PUNCT
ap-1354	59	31	=	=	SYM
ap-1354	59	32	√	√	NUM
ap-1354	59	33	2	2	NUM
ap-1354	59	34	(	(	PUNCT
ap-1354	59	35	k	k	X
ap-1354	59	36	+	+	CCONJ
ap-1354	59	37	λ+	λ+	PUNCT
ap-1354	59	38	2n	2n	NUM
ap-1354	59	39	)	)	PUNCT
ap-1354	59	40	·	·	PUNCT
ap-1354	59	41	√	√	ADP
ap-1354	59	42	γ	γ	X
ap-1354	59	43	(	(	PUNCT
ap-1354	59	44	n+	n+	PROPN
ap-1354	59	45	1)γ	1)γ	PROPN
ap-1354	59	46	(	(	PUNCT
ap-1354	59	47	k	k	X
ap-1354	59	48	+	+	PUNCT
ap-1354	59	49	λ+	λ+	NUM
ap-1354	59	50	n	n	CCONJ
ap-1354	59	51	)	)	PUNCT
ap-1354	59	52	γ	γ	X
ap-1354	59	53	(	(	PUNCT
ap-1354	59	54	λ+	λ+	X
ap-1354	59	55	n+	n+	X
ap-1354	59	56	12	12	NUM
ap-1354	59	57	)	)	PUNCT
ap-1354	59	58	γ	γ	PROPN
ap-1354	59	59	(	(	PUNCT
ap-1354	59	60	k	k	PROPN
ap-1354	59	61	+	+	PROPN
ap-1354	59	62	n+	n+	NUM
ap-1354	59	63	12	12	NUM
ap-1354	59	64	)	)	PUNCT
ap-1354	59	65	×	×	NOUN
ap-1354	59	66	(	(	PUNCT
ap-1354	59	67	16	16	NUM
ap-1354	59	68	)	)	PUNCT
ap-1354	59	69	(	(	PUNCT
ap-1354	59	70	cos	cos	X
ap-1354	59	71	θ)λ	θ)λ	PROPN
ap-1354	59	72	(	(	PUNCT
ap-1354	59	73	sin	sin	NOUN
ap-1354	59	74	θ)k	θ)k	ADP
ap-1354	59	75	p	p	X
ap-1354	59	76	(	(	PUNCT
ap-1354	59	77	k−1/2,λ−1/2	k−1/2,λ−1/2	NOUN
ap-1354	59	78	)	)	PUNCT
ap-1354	59	79	n	n	CCONJ
ap-1354	59	80	·	·	PUNCT
ap-1354	59	81	(	(	PUNCT
ap-1354	59	82	1−	1−	NUM
ap-1354	59	83	2	2	NUM
ap-1354	59	84	sin2	sin2	NOUN
ap-1354	59	85	θ	θ	PROPN
ap-1354	59	86	)	)	PUNCT
ap-1354	59	87	with	with	ADP
ap-1354	59	88	integrating	integrate	VERB
ap-1354	59	89	over	over	ADP
ap-1354	59	90	ds	ds	PROPN
ap-1354	59	91	,	,	PUNCT
ap-1354	59	92	the	the	DET
ap-1354	59	93	green	green	NOUN
ap-1354	59	94	’s	’s	PART
ap-1354	59	95	function	function	NOUN
ap-1354	59	96	for	for	ADP
ap-1354	59	97	the	the	DET
ap-1354	59	98	hulthen	hulthen	NOUN
ap-1354	59	99	potential	potential	NOUN
ap-1354	59	100	can	can	AUX
ap-1354	59	101	be	be	AUX
ap-1354	59	102	obtained	obtain	VERB
ap-1354	59	103	as	as	ADP
ap-1354	59	104	g	g	PROPN
ap-1354	59	105	(	(	PUNCT
ap-1354	59	106	xb	xb	PROPN
ap-1354	59	107	,	,	PUNCT
ap-1354	59	108	xa;e	xa;e	NUM
ap-1354	59	109	)	)	PUNCT
ap-1354	60	1	=	=	SYM
ap-1354	60	2	8μaq√	8μaq√	PROPN
ap-1354	60	3	sin	sin	NOUN
ap-1354	60	4	2θa	2θa	NOUN
ap-1354	60	5	cos	cos	PROPN
ap-1354	60	6	2θb	2θb	PROPN
ap-1354	60	7	·	·	PUNCT
ap-1354	60	8	(	(	PUNCT
ap-1354	60	9	17	17	NUM
ap-1354	60	10	)	)	PUNCT
ap-1354	60	11	∞∑	∞∑	PRON
ap-1354	60	12	n=0	n=0	PUNCT
ap-1354	60	13	∞∫	∞∫	PROPN
ap-1354	60	14	−∞	−∞	ADP
ap-1354	60	15	de	de	X
ap-1354	60	16	2π	2π	PROPN
ap-1354	60	17	eiet	eiet	NOUN
ap-1354	60	18	(	(	PUNCT
ap-1354	60	19	k	k	PROPN
ap-1354	60	20	+	+	CCONJ
ap-1354	60	21	λ+	λ+	PUNCT
ap-1354	60	22	2n)2	2n)2	NUM
ap-1354	60	23	−	−	PROPN
ap-1354	60	24	1	1	NUM
ap-1354	60	25	ψn	ψn	INTJ
ap-1354	60	26	(	(	PUNCT
ap-1354	60	27	θa)ψ∗	θa)ψ∗	PROPN
ap-1354	60	28	n	n	CCONJ
ap-1354	60	29	(	(	PUNCT
ap-1354	60	30	θb	θb	NOUN
ap-1354	60	31	)	)	PUNCT
ap-1354	60	32	therefore	therefore	ADV
ap-1354	60	33	,	,	PUNCT
ap-1354	60	34	the	the	DET
ap-1354	60	35	kernel	kernel	NOUN
ap-1354	60	36	of	of	ADP
ap-1354	60	37	the	the	DET
ap-1354	60	38	physical	physical	ADJ
ap-1354	60	39	system	system	NOUN
ap-1354	60	40	is	be	AUX
ap-1354	60	41	rewritten	rewrite	VERB
ap-1354	60	42	as	as	ADP
ap-1354	60	43	k(xb	k(xb	PROPN
ap-1354	60	44	,	,	PUNCT
ap-1354	60	45	xa;e	xa;e	PRON
ap-1354	60	46	)	)	PUNCT
ap-1354	61	1	=	=	PUNCT
ap-1354	62	1	∞∑	∞∑	NUM
ap-1354	62	2	n=0	n=0	NUM
ap-1354	62	3	e−ient	e−ient	PRON
ap-1354	62	4	ϕn(xa)ϕ∗	ϕn(xa)ϕ∗	NOUN
ap-1354	62	5	n(xb	n(xb	PROPN
ap-1354	62	6	)	)	PUNCT
ap-1354	62	7	=	=	PUNCT
ap-1354	63	1	∞∑	∞∑	PRON
ap-1354	63	2	n=0	n=0	NUM
ap-1354	63	3	exp	exp	NOUN
ap-1354	63	4	{	{	PUNCT
ap-1354	63	5	[	[	PUNCT
ap-1354	63	6	−	−	PROPN
ap-1354	63	7	1	1	NUM
ap-1354	63	8	8μaq	8μaq	PROPN
ap-1354	63	9	(	(	PUNCT
ap-1354	63	10	n+	n+	NUM
ap-1354	63	11	1)2	1)2	NUM
ap-1354	63	12	·	·	PUNCT
ap-1354	63	13	[	[	PUNCT
ap-1354	63	14	(	(	PUNCT
ap-1354	63	15	n+	n+	NUM
ap-1354	63	16	1)2	1)2	NUM
ap-1354	63	17	+	+	NUM
ap-1354	63	18	2μa2v0	2μa2v0	NUM
ap-1354	63	19	]	]	PUNCT
ap-1354	63	20	2	2	NUM
ap-1354	63	21	]	]	PUNCT
ap-1354	63	22	t	t	PROPN
ap-1354	63	23	}	}	PUNCT
ap-1354	63	24	·	·	PUNCT
ap-1354	63	25	φn(ub)φ∗	φn(ub)φ∗	PROPN
ap-1354	63	26	n(ua	n(ua	NUM
ap-1354	63	27	)	)	PUNCT
ap-1354	63	28	.	.	PUNCT
ap-1354	64	1	(	(	PUNCT
ap-1354	64	2	18	18	NUM
ap-1354	64	3	)	)	PUNCT
ap-1354	64	4	integrating	integrate	VERB
ap-1354	64	5	over	over	ADP
ap-1354	64	6	de	de	ADV
ap-1354	64	7	,	,	PUNCT
ap-1354	64	8	we	we	PRON
ap-1354	64	9	can	can	AUX
ap-1354	64	10	get	get	VERB
ap-1354	64	11	the	the	DET
ap-1354	64	12	energy	energy	NOUN
ap-1354	64	13	eigenvalues	eigenvalue	VERB
ap-1354	64	14	en	en	NOUN
ap-1354	64	15	=	=	SYM
ap-1354	64	16	1	1	NUM
ap-1354	64	17	8μa2	8μa2	NUM
ap-1354	64	18	(	(	PUNCT
ap-1354	64	19	n+	n+	NUM
ap-1354	64	20	1)2	1)2	NUM
ap-1354	64	21	[	[	PUNCT
ap-1354	64	22	2μa2	2μa2	NUM
ap-1354	64	23	v0	v0	NOUN
ap-1354	64	24	q	q	NOUN
ap-1354	65	1	−	−	PROPN
ap-1354	66	1	(	(	PUNCT
ap-1354	66	2	n+	n+	NUM
ap-1354	66	3	1)2	1)2	NUM
ap-1354	66	4	]	]	SYM
ap-1354	66	5	2	2	NUM
ap-1354	66	6	(	(	PUNCT
ap-1354	66	7	19	19	NUM
ap-1354	66	8	)	)	PUNCT
ap-1354	66	9	39	39	NUM
ap-1354	66	10	acta	acta	PROPN
ap-1354	66	11	polytechnica	polytechnica	PROPN
ap-1354	66	12	vol	vol	NOUN
ap-1354	66	13	.	.	PUNCT
ap-1354	67	1	51	51	NUM
ap-1354	67	2	no	no	NOUN
ap-1354	67	3	.	.	PUNCT
ap-1354	68	1	1/2011	1/2011	NUM
ap-1354	68	2	and	and	CCONJ
ap-1354	68	3	the	the	DET
ap-1354	68	4	normalized	normalize	VERB
ap-1354	68	5	wave	wave	NOUN
ap-1354	68	6	functions	function	NOUN
ap-1354	68	7	in	in	ADP
ap-1354	68	8	terms	term	NOUN
ap-1354	68	9	of	of	ADP
ap-1354	68	10	jacobi	jacobi	PROPN
ap-1354	68	11	polynomials	polynomial	NOUN
ap-1354	68	12	are	be	AUX
ap-1354	68	13	φ(x	φ(x	NOUN
ap-1354	68	14	)	)	PUNCT
ap-1354	68	15	=	=	SYM
ap-1354	68	16	1	1	NUM
ap-1354	68	17	2	2	NUM
ap-1354	68	18	√	√	NUM
ap-1354	68	19	2	2	NUM
ap-1354	68	20	√	√	NUM
ap-1354	68	21	n+	n+	ADP
ap-1354	68	22	1	1	NUM
ap-1354	68	23	√	√	NUM
ap-1354	68	24	4	4	NUM
ap-1354	68	25	(	(	PUNCT
ap-1354	68	26	n+	n+	X
ap-1354	68	27	1)2	1)2	NUM
ap-1354	68	28	−	−	NOUN
ap-1354	69	1	(	(	PUNCT
ap-1354	69	2	λn	λn	PROPN
ap-1354	69	3	−kn	−kn	PROPN
ap-1354	69	4	)	)	PUNCT
ap-1354	69	5	2	2	NUM
ap-1354	69	6	·	·	SYM
ap-1354	69	7	√	√	ADP
ap-1354	69	8	γ	γ	X
ap-1354	69	9	(	(	PUNCT
ap-1354	69	10	n+	n+	NUM
ap-1354	69	11	1)γ	1)γ	PROPN
ap-1354	69	12	(	(	PUNCT
ap-1354	69	13	kn	kn	NOUN
ap-1354	69	14	+	+	CCONJ
ap-1354	69	15	λn	λn	PROPN
ap-1354	69	16	+	+	CCONJ
ap-1354	69	17	n	n	CCONJ
ap-1354	69	18	)	)	PUNCT
ap-1354	69	19	γ	γ	NOUN
ap-1354	69	20	(	(	PUNCT
ap-1354	69	21	λn	λn	PROPN
ap-1354	69	22	+	+	CCONJ
ap-1354	69	23	n+	n+	NUM
ap-1354	69	24	12	12	NUM
ap-1354	69	25	)	)	PUNCT
ap-1354	69	26	γ	γ	PROPN
ap-1354	69	27	(	(	PUNCT
ap-1354	69	28	kn	kn	PROPN
ap-1354	69	29	+	+	CCONJ
ap-1354	69	30	n+	n+	NUM
ap-1354	69	31	12	12	NUM
ap-1354	69	32	)	)	PUNCT
ap-1354	69	33	×	×	NOUN
ap-1354	69	34	exp	exp	NOUN
ap-1354	69	35	[	[	X
ap-1354	69	36	(	(	PUNCT
ap-1354	69	37	kn	kn	PROPN
ap-1354	69	38	−	−	PROPN
ap-1354	69	39	1/2)x/2a	1/2)x/2a	PROPN
ap-1354	69	40	]	]	X
ap-1354	69	41	(	(	PUNCT
ap-1354	69	42	1	1	NUM
ap-1354	69	43	+	+	NUM
ap-1354	69	44	e−x	e−x	NOUN
ap-1354	69	45	/	/	SYM
ap-1354	69	46	a	a	NOUN
ap-1354	69	47	)	)	PUNCT
ap-1354	69	48	(	(	PUNCT
ap-1354	69	49	kn+λn−1/2)p	kn+λn−1/2)p	PROPN
ap-1354	69	50	(	(	PUNCT
ap-1354	69	51	kn−1/2,λ−1/2	kn−1/2,λ−1/2	PROPN
ap-1354	69	52	)	)	PUNCT
ap-1354	69	53	n	n	NOUN
ap-1354	69	54	·	·	PUNCT
ap-1354	69	55	(	(	PUNCT
ap-1354	69	56	−1	−1	NOUN
ap-1354	69	57	+	+	CCONJ
ap-1354	69	58	e−ix	e−ix	NOUN
ap-1354	69	59	/	/	SYM
ap-1354	69	60	a	a	DET
ap-1354	69	61	1−	1−	NUM
ap-1354	69	62	e−ix	e−ix	NOUN
ap-1354	69	63	/	/	SYM
ap-1354	69	64	a	a	NOUN
ap-1354	69	65	)	)	PUNCT
ap-1354	69	66	(	(	PUNCT
ap-1354	69	67	20	20	NUM
ap-1354	69	68	)	)	PUNCT
ap-1354	69	69	where	where	SCONJ
ap-1354	69	70	we	we	PRON
ap-1354	69	71	got	get	VERB
ap-1354	69	72	kn	kn	PROPN
ap-1354	69	73	=	=	NOUN
ap-1354	69	74	1	1	NUM
ap-1354	69	75	8μa2	8μa2	NUM
ap-1354	69	76	(	(	PUNCT
ap-1354	69	77	n+	n+	NUM
ap-1354	69	78	1)2	1)2	NUM
ap-1354	69	79	[	[	PUNCT
ap-1354	69	80	(	(	PUNCT
ap-1354	69	81	n+	n+	NUM
ap-1354	69	82	1)2	1)2	NUM
ap-1354	69	83	−	−	PROPN
ap-1354	69	84	2μa2	2μa2	NUM
ap-1354	69	85	v0	v0	NOUN
ap-1354	69	86	q	q	PROPN
ap-1354	69	87	]	]	PUNCT
ap-1354	69	88	;	;	PUNCT
ap-1354	69	89	λn	λn	PROPN
ap-1354	69	90	=	=	NOUN
ap-1354	69	91	1	1	NUM
ap-1354	69	92	2	2	NUM
ap-1354	69	93	+	+	NUM
ap-1354	69	94	1	1	NUM
ap-1354	69	95	n+	n+	SYM
ap-1354	69	96	1	1	NUM
ap-1354	69	97	[	[	PUNCT
ap-1354	69	98	(	(	PUNCT
ap-1354	69	99	n+	n+	NUM
ap-1354	69	100	1)2	1)2	NUM
ap-1354	69	101	+	+	CCONJ
ap-1354	69	102	2μa2	2μa2	NUM
ap-1354	69	103	v0	v0	NOUN
ap-1354	69	104	q	q	X
ap-1354	69	105	]	]	X
ap-1354	69	106	(	(	PUNCT
ap-1354	69	107	21	21	NUM
ap-1354	69	108	)	)	PUNCT
ap-1354	69	109	here	here	ADV
ap-1354	69	110	we	we	PRON
ap-1354	69	111	see	see	VERB
ap-1354	69	112	that	that	SCONJ
ap-1354	69	113	the	the	DET
ap-1354	69	114	pt	pt	PROPN
ap-1354	69	115	symmetric	symmetric	ADJ
ap-1354	69	116	and	and	CCONJ
ap-1354	69	117	nonhermitian	nonhermitian	ADJ
ap-1354	69	118	hulthen	hulthen	ADJ
ap-1354	69	119	potential	potential	NOUN
ap-1354	69	120	has	have	VERB
ap-1354	69	121	real	real	ADJ
ap-1354	69	122	energy	energy	NOUN
ap-1354	69	123	spectra	spectra	NOUN
ap-1354	69	124	.	.	PROPN
ap-1354	69	125	3	3	NUM
ap-1354	69	126	nonpt	nonpt	ADJ
ap-1354	69	127	-	-	PUNCT
ap-1354	69	128	symmetric	symmetric	ADJ
ap-1354	69	129	and	and	CCONJ
ap-1354	69	130	non	non	ADJ
ap-1354	69	131	-	-	ADJ
ap-1354	69	132	hermitian	hermitian	ADJ
ap-1354	69	133	hulthen	hulthen	NOUN
ap-1354	69	134	potential	potential	NOUN
ap-1354	69	135	the	the	DET
ap-1354	69	136	non	non	ADJ
ap-1354	69	137	pt	pt	NOUN
ap-1354	69	138	-	-	ADJ
ap-1354	69	139	symmetric	symmetric	ADJ
ap-1354	69	140	and	and	CCONJ
ap-1354	69	141	non	non	ADJ
ap-1354	69	142	hermitian	hermitian	ADJ
ap-1354	69	143	hulthen	hulthen	ADJ
ap-1354	69	144	potential	potential	NOUN
ap-1354	69	145	is	be	AUX
ap-1354	69	146	determined	determine	VERB
ap-1354	69	147	by	by	ADP
ap-1354	69	148	taking	take	VERB
ap-1354	69	149	1	1	NUM
ap-1354	69	150	a	a	PRON
ap-1354	69	151	→	→	X
ap-1354	69	152	i	i	PRON
ap-1354	69	153	a	a	DET
ap-1354	69	154	,	,	PUNCT
ap-1354	69	155	v0	v0	NOUN
ap-1354	69	156	→	→	SYM
ap-1354	69	157	a+	a+	PUNCT
ap-1354	69	158	ib	ib	NOUN
ap-1354	69	159	and	and	CCONJ
ap-1354	69	160	q	q	PROPN
ap-1354	69	161	→	→	SYM
ap-1354	69	162	iq	iq	NOUN
ap-1354	69	163	as	as	ADP
ap-1354	69	164	v	v	X
ap-1354	69	165	(	(	PUNCT
ap-1354	69	166	x	x	NOUN
ap-1354	69	167	)	)	PUNCT
ap-1354	69	168	=	=	SYM
ap-1354	69	169	−	−	PROPN
ap-1354	69	170	ivoe	ivoe	VERB
ap-1354	69	171	−ix	−ix	PROPN
ap-1354	69	172	/	/	SYM
ap-1354	69	173	a	a	DET
ap-1354	69	174	1−	1−	NUM
ap-1354	69	175	iqe−ix	iqe−ix	NOUN
ap-1354	69	176	/	/	SYM
ap-1354	69	177	a	a	DET
ap-1354	69	178	(	(	PUNCT
ap-1354	69	179	22	22	NUM
ap-1354	69	180	)	)	PUNCT
ap-1354	69	181	we	we	PRON
ap-1354	69	182	will	will	AUX
ap-1354	69	183	follow	follow	VERB
ap-1354	69	184	the	the	DET
ap-1354	69	185	same	same	ADJ
ap-1354	69	186	steps	step	NOUN
ap-1354	69	187	for	for	ADP
ap-1354	69	188	getting	get	VERB
ap-1354	69	189	the	the	DET
ap-1354	69	190	wave	wave	NOUN
ap-1354	69	191	function	function	NOUN
ap-1354	69	192	and	and	CCONJ
ap-1354	69	193	the	the	DET
ap-1354	69	194	energy	energy	NOUN
ap-1354	69	195	spectrum	spectrum	NOUN
ap-1354	69	196	.	.	PUNCT
ap-1354	70	1	a	a	DET
ap-1354	70	2	suitable	suitable	ADJ
ap-1354	70	3	coordinate	coordinate	NOUN
ap-1354	70	4	transformation	transformation	NOUN
ap-1354	70	5	kernel	kernel	NOUN
ap-1354	70	6	is	be	AUX
ap-1354	70	7	obtained	obtain	VERB
ap-1354	70	8	as	as	ADP
ap-1354	70	9	k(xb	k(xb	PROPN
ap-1354	70	10	,	,	PUNCT
ap-1354	70	11	t	t	PROPN
ap-1354	70	12	;	;	PUNCT
ap-1354	70	13	xa	xa	PROPN
ap-1354	70	14	,	,	PUNCT
ap-1354	70	15	0	0	NUM
ap-1354	70	16	)	)	PUNCT
ap-1354	70	17	=	=	SYM
ap-1354	70	18	q	q	PROPN
ap-1354	70	19	2a	2a	NUM
ap-1354	70	20	sin	sin	VERB
ap-1354	70	21	θb	θb	ADP
ap-1354	70	22	cos	cos	PROPN
ap-1354	70	23	θb	θb	PROPN
ap-1354	70	24	∫	∫	PROPN
ap-1354	70	25	dθdpθ	dθdpθ	PROPN
ap-1354	70	26	·	·	PUNCT
ap-1354	70	27	(	(	PUNCT
ap-1354	70	28	23	23	NUM
ap-1354	70	29	)	)	PUNCT
ap-1354	70	30	exp	exp	NOUN
ap-1354	70	31	[	[	PUNCT
ap-1354	70	32	i	i	PRON
ap-1354	70	33	∫	∫	PROPN
ap-1354	70	34	dt	dt	X
ap-1354	71	1	(	(	PUNCT
ap-1354	71	2	pθ	pθ	ADP
ap-1354	71	3	θ̇	θ̇	PRON
ap-1354	71	4	−	−	PROPN
ap-1354	72	1	sin2	sin2	NOUN
ap-1354	72	2	θ	θ	PROPN
ap-1354	72	3	cos2	cos2	VERB
ap-1354	72	4	θ	θ	PROPN
ap-1354	72	5	4α2	4α2	NUM
ap-1354	72	6	p2θ	p2θ	NOUN
ap-1354	72	7	2μ	2μ	NOUN
ap-1354	72	8	−	−	PROPN
ap-1354	72	9	v0	v0	NOUN
ap-1354	72	10	cos2	cos2	NOUN
ap-1354	72	11	θ	θ	PROPN
ap-1354	72	12	)	)	PUNCT
ap-1354	72	13	]	]	PUNCT
ap-1354	72	14	.	.	PUNCT
ap-1354	73	1	if	if	SCONJ
ap-1354	73	2	we	we	PRON
ap-1354	73	3	follow	follow	VERB
ap-1354	73	4	the	the	DET
ap-1354	73	5	steps	step	NOUN
ap-1354	73	6	in	in	ADP
ap-1354	73	7	sec	sec	PROPN
ap-1354	73	8	.	.	PUNCT
ap-1354	74	1	(	(	PUNCT
ap-1354	74	2	2	2	NUM
ap-1354	74	3	)	)	PUNCT
ap-1354	74	4	,	,	PUNCT
ap-1354	74	5	we	we	PRON
ap-1354	74	6	will	will	AUX
ap-1354	74	7	obtain	obtain	VERB
ap-1354	74	8	energy	energy	NOUN
ap-1354	74	9	eigenvalues	eigenvalue	NOUN
ap-1354	74	10	en	en	NOUN
ap-1354	74	11	=	=	SYM
ap-1354	74	12	1	1	NUM
ap-1354	74	13	8μa2	8μa2	NUM
ap-1354	74	14	(	(	PUNCT
ap-1354	74	15	n+	n+	NUM
ap-1354	74	16	1)2	1)2	NUM
ap-1354	74	17	·	·	PUNCT
ap-1354	74	18	[	[	PUNCT
ap-1354	74	19	(	(	PUNCT
ap-1354	74	20	n+	n+	NUM
ap-1354	74	21	1)2	1)2	NUM
ap-1354	74	22	+	+	CCONJ
ap-1354	74	23	2μa2	2μa2	NUM
ap-1354	74	24	(	(	PUNCT
ap-1354	74	25	ia	ia	PROPN
ap-1354	74	26	−b	−b	NOUN
ap-1354	74	27	)	)	PUNCT
ap-1354	74	28	q	q	X
ap-1354	75	1	]	]	X
ap-1354	75	2	2	2	NUM
ap-1354	75	3	(	(	PUNCT
ap-1354	75	4	24	24	NUM
ap-1354	75	5	)	)	PUNCT
ap-1354	75	6	and	and	CCONJ
ap-1354	75	7	the	the	DET
ap-1354	75	8	normalized	normalize	VERB
ap-1354	75	9	wave	wave	NOUN
ap-1354	75	10	functions	function	NOUN
ap-1354	75	11	in	in	ADP
ap-1354	75	12	terms	term	NOUN
ap-1354	75	13	of	of	ADP
ap-1354	75	14	jacobi	jacobi	PROPN
ap-1354	75	15	polynomials	polynomial	NOUN
ap-1354	75	16	are	be	AUX
ap-1354	75	17	φ(x	φ(x	NOUN
ap-1354	75	18	)	)	PUNCT
ap-1354	75	19	=	=	SYM
ap-1354	75	20	1	1	NUM
ap-1354	75	21	2	2	NUM
ap-1354	75	22	√	√	NUM
ap-1354	75	23	2	2	NUM
ap-1354	75	24	√	√	NUM
ap-1354	75	25	n+	n+	ADP
ap-1354	75	26	1	1	NUM
ap-1354	75	27	√	√	NUM
ap-1354	75	28	4	4	NUM
ap-1354	75	29	(	(	PUNCT
ap-1354	75	30	n+	n+	X
ap-1354	76	1	1)2	1)2	NUM
ap-1354	76	2	−	−	NOUN
ap-1354	76	3	(	(	PUNCT
ap-1354	76	4	λn	λn	PROPN
ap-1354	76	5	−kn	−kn	PROPN
ap-1354	76	6	)	)	PUNCT
ap-1354	76	7	2	2	NUM
ap-1354	76	8	·	·	PUNCT
ap-1354	76	9	√	√	ADP
ap-1354	76	10	γ	γ	PROPN
ap-1354	76	11	(	(	PUNCT
ap-1354	76	12	n+	n+	NUM
ap-1354	76	13	1)γ	1)γ	PROPN
ap-1354	76	14	(	(	PUNCT
ap-1354	76	15	kn	kn	NOUN
ap-1354	76	16	+	+	CCONJ
ap-1354	76	17	λn	λn	PROPN
ap-1354	76	18	+	+	CCONJ
ap-1354	76	19	n	n	CCONJ
ap-1354	76	20	)	)	PUNCT
ap-1354	76	21	γ	γ	NOUN
ap-1354	76	22	(	(	PUNCT
ap-1354	76	23	λn	λn	PROPN
ap-1354	76	24	+	+	CCONJ
ap-1354	76	25	n+	n+	NUM
ap-1354	76	26	12	12	NUM
ap-1354	76	27	)	)	PUNCT
ap-1354	76	28	γ	γ	PROPN
ap-1354	76	29	(	(	PUNCT
ap-1354	76	30	kn	kn	PROPN
ap-1354	76	31	+	+	CCONJ
ap-1354	76	32	n+	n+	NUM
ap-1354	76	33	12	12	NUM
ap-1354	76	34	)	)	PUNCT
ap-1354	76	35	×	×	NOUN
ap-1354	76	36	exp	exp	NOUN
ap-1354	76	37	[	[	X
ap-1354	76	38	(	(	PUNCT
ap-1354	76	39	kn	kn	PROPN
ap-1354	76	40	−	−	PROPN
ap-1354	76	41	1/2)x/2a	1/2)x/2a	PROPN
ap-1354	76	42	]	]	X
ap-1354	76	43	(	(	PUNCT
ap-1354	76	44	1	1	NUM
ap-1354	76	45	+	+	CCONJ
ap-1354	76	46	ex	ex	NOUN
ap-1354	76	47	/	/	SYM
ap-1354	76	48	a	a	NOUN
ap-1354	76	49	)	)	PUNCT
ap-1354	76	50	(	(	PUNCT
ap-1354	76	51	kn+λn−1/2	kn+λn−1/2	NOUN
ap-1354	76	52	)	)	PUNCT
ap-1354	76	53	·	·	PUNCT
ap-1354	77	1	p	p	X
ap-1354	77	2	(	(	PUNCT
ap-1354	77	3	kn−1/2,λ−1/2	kn−1/2,λ−1/2	PROPN
ap-1354	77	4	)	)	PUNCT
ap-1354	77	5	n	n	CCONJ
ap-1354	77	6	(	(	PUNCT
ap-1354	77	7	1−	1−	NUM
ap-1354	77	8	e−x	e−x	NOUN
ap-1354	77	9	/	/	SYM
ap-1354	77	10	a	a	DET
ap-1354	77	11	1	1	NUM
ap-1354	77	12	+	+	NUM
ap-1354	77	13	e−x	e−x	NOUN
ap-1354	77	14	/	/	SYM
ap-1354	77	15	a	a	NOUN
ap-1354	77	16	)	)	PUNCT
ap-1354	77	17	(	(	PUNCT
ap-1354	77	18	25	25	NUM
ap-1354	77	19	)	)	PUNCT
ap-1354	77	20	kn	kn	NOUN
ap-1354	77	21	and	and	CCONJ
ap-1354	77	22	λn	λn	PROPN
ap-1354	77	23	are	be	AUX
ap-1354	77	24	the	the	DET
ap-1354	77	25	same	same	ADJ
ap-1354	77	26	in	in	ADP
ap-1354	77	27	eq	eq	ADP
ap-1354	77	28	.	.	PUNCT
ap-1354	78	1	(	(	PUNCT
ap-1354	78	2	21	21	NUM
ap-1354	78	3	)	)	PUNCT
ap-1354	78	4	.	.	PUNCT
ap-1354	79	1	it	it	PRON
ap-1354	79	2	is	be	AUX
ap-1354	79	3	clear	clear	ADJ
ap-1354	79	4	that	that	SCONJ
ap-1354	79	5	the	the	DET
ap-1354	79	6	energy	energy	NOUN
ap-1354	79	7	spectra	spectra	NOUN
ap-1354	79	8	are	be	AUX
ap-1354	79	9	real	real	ADJ
ap-1354	79	10	only	only	ADV
ap-1354	79	11	if	if	SCONJ
ap-1354	79	12	re(v0	re(v0	ADJ
ap-1354	79	13	)	)	PUNCT
ap-1354	79	14	=	=	SYM
ap-1354	80	1	0	0	X
ap-1354	80	2	.	.	NOUN
ap-1354	80	3	4	4	NUM
ap-1354	80	4	conclusion	conclusion	NOUN
ap-1354	80	5	we	we	PRON
ap-1354	80	6	have	have	AUX
ap-1354	80	7	calculated	calculate	VERB
ap-1354	80	8	the	the	DET
ap-1354	80	9	energy	energy	NOUN
ap-1354	80	10	eigenvalues	eigenvalue	NOUN
ap-1354	80	11	and	and	CCONJ
ap-1354	80	12	the	the	DET
ap-1354	80	13	corresponding	corresponding	ADJ
ap-1354	80	14	wave	wave	NOUN
ap-1354	80	15	functions	function	NOUN
ap-1354	80	16	for	for	ADP
ap-1354	80	17	the	the	DET
ap-1354	80	18	pt-/non	pt-/non	PROPN
ap-1354	80	19	-	-	PUNCT
ap-1354	80	20	pt	pt	ADJ
ap-1354	80	21	symmetric	symmetric	ADJ
ap-1354	80	22	and	and	CCONJ
ap-1354	80	23	non	non	ADJ
ap-1354	80	24	-	-	ADJ
ap-1354	80	25	hermitian	hermitian	ADJ
ap-1354	80	26	deformed	deform	VERB
ap-1354	80	27	hulthen	hulthen	NOUN
ap-1354	80	28	potential	potential	NOUN
ap-1354	80	29	.	.	PUNCT
ap-1354	81	1	we	we	PRON
ap-1354	81	2	obtained	obtain	VERB
ap-1354	81	3	that	that	SCONJ
ap-1354	81	4	pt-/non	pt-/non	PROPN
ap-1354	81	5	-	-	PUNCT
ap-1354	81	6	pt	pt	ADJ
ap-1354	81	7	symmetric	symmetric	ADJ
ap-1354	81	8	and	and	CCONJ
ap-1354	81	9	non	non	ADJ
ap-1354	81	10	-	-	ADJ
ap-1354	81	11	hermitian	hermitian	ADJ
ap-1354	81	12	forms	form	NOUN
ap-1354	81	13	of	of	ADP
ap-1354	81	14	potentials	potential	NOUN
ap-1354	81	15	have	have	VERB
ap-1354	81	16	real	real	ADJ
ap-1354	81	17	energy	energy	NOUN
ap-1354	81	18	spectra	spectra	NOUN
ap-1354	81	19	by	by	ADP
ap-1354	81	20	restricting	restrict	VERB
ap-1354	81	21	the	the	DET
ap-1354	81	22	potential	potential	ADJ
ap-1354	81	23	parameters	parameter	NOUN
ap-1354	81	24	.	.	PUNCT
ap-1354	82	1	references	reference	NOUN
ap-1354	82	2	[	[	X
ap-1354	82	3	1	1	NUM
ap-1354	82	4	]	]	X
ap-1354	82	5	bender	bender	NOUN
ap-1354	82	6	,	,	PUNCT
ap-1354	82	7	c.	c.	PROPN
ap-1354	82	8	m.	m.	PROPN
ap-1354	82	9	:	:	PUNCT
ap-1354	82	10	reports	report	NOUN
ap-1354	82	11	on	on	ADP
ap-1354	82	12	progress	progress	NOUN
ap-1354	82	13	in	in	ADP
ap-1354	82	14	physics	physics	NOUN
ap-1354	82	15	70(6	70(6	PROPN
ap-1354	82	16	)	)	PUNCT
ap-1354	82	17	,	,	PUNCT
ap-1354	82	18	947–1018	947–1018	NUM
ap-1354	82	19	(	(	PUNCT
ap-1354	82	20	2007	2007	NUM
ap-1354	82	21	)	)	PUNCT
ap-1354	82	22	;	;	PUNCT
ap-1354	82	23	bender	bender	NOUN
ap-1354	82	24	,	,	PUNCT
ap-1354	82	25	c.	c.	PROPN
ap-1354	82	26	m.	m.	NOUN
ap-1354	82	27	,	,	PUNCT
ap-1354	82	28	darg	darg	NOUN
ap-1354	82	29	,	,	PUNCT
ap-1354	82	30	d.	d.	PROPN
ap-1354	82	31	w.	w.	PROPN
ap-1354	82	32	:	:	PUNCT
ap-1354	82	33	journal	journal	PROPN
ap-1354	82	34	of	of	ADP
ap-1354	82	35	mathematical	mathematical	ADJ
ap-1354	82	36	physics	physics	NOUN
ap-1354	82	37	48(4	48(4	PROPN
ap-1354	82	38	)	)	PUNCT
ap-1354	82	39	,	,	PUNCT
ap-1354	82	40	042703	042703	NUM
ap-1354	82	41	(	(	PUNCT
ap-1354	82	42	2007	2007	NUM
ap-1354	82	43	)	)	PUNCT
ap-1354	82	44	;	;	PUNCT
ap-1354	82	45	bender	bender	NOUN
ap-1354	82	46	,	,	PUNCT
ap-1354	82	47	c.	c.	PROPN
ap-1354	82	48	m.	m.	NOUN
ap-1354	82	49	,	,	PUNCT
ap-1354	82	50	boetcher	boetcher	ADV
ap-1354	82	51	,	,	PUNCT
ap-1354	82	52	s.	s.	PROPN
ap-1354	82	53	:	:	PUNCT
ap-1354	82	54	pys	pys	PROPN
ap-1354	82	55	.	.	PUNCT
ap-1354	83	1	lett	lett	PROPN
ap-1354	83	2	.	.	PROPN
ap-1354	84	1	80	80	NUM
ap-1354	84	2	,	,	PUNCT
ap-1354	84	3	5243	5243	NUM
ap-1354	84	4	(	(	PUNCT
ap-1354	84	5	1998	1998	NUM
ap-1354	84	6	)	)	PUNCT
ap-1354	84	7	;	;	PUNCT
ap-1354	85	1	bender	bender	NOUN
ap-1354	85	2	,	,	PUNCT
ap-1354	85	3	c.	c.	PROPN
ap-1354	85	4	m.	m.	NOUN
ap-1354	85	5	,	,	PUNCT
ap-1354	85	6	boetcher	boetcher	ADV
ap-1354	85	7	,	,	PUNCT
ap-1354	85	8	s.	s.	PROPN
ap-1354	85	9	,	,	PUNCT
ap-1354	85	10	meisenger	meisenger	PROPN
ap-1354	85	11	,	,	PUNCT
ap-1354	85	12	p.	p.	NOUN
ap-1354	85	13	n.	n.	NOUN
ap-1354	85	14	:	:	PUNCT
ap-1354	85	15	j.	j.	PROPN
ap-1354	85	16	math	math	PROPN
ap-1354	85	17	.	.	PUNCT
ap-1354	86	1	phys	phy	NOUN
ap-1354	86	2	.	.	PUNCT
ap-1354	87	1	40	40	NUM
ap-1354	87	2	,	,	PUNCT
ap-1354	87	3	2201	2201	NUM
ap-1354	87	4	(	(	PUNCT
ap-1354	87	5	1999	1999	NUM
ap-1354	87	6	)	)	PUNCT
ap-1354	87	7	;	;	PUNCT
ap-1354	88	1	bender	bender	NOUN
ap-1354	88	2	,	,	PUNCT
ap-1354	88	3	c.	c.	PROPN
ap-1354	88	4	m.	m.	PROPN
ap-1354	88	5	,	,	PUNCT
ap-1354	88	6	dunne	dunne	PROPN
ap-1354	88	7	,	,	PUNCT
ap-1354	88	8	g.	g.	PROPN
ap-1354	88	9	v.	v.	PROPN
ap-1354	88	10	,	,	PUNCT
ap-1354	88	11	meisenger	meisenger	PROPN
ap-1354	88	12	,	,	PUNCT
ap-1354	88	13	p.	p.	NOUN
ap-1354	88	14	n.	n.	NOUN
ap-1354	88	15	:	:	PUNCT
ap-1354	89	1	phys	phy	NOUN
ap-1354	89	2	.	.	PUNCT
ap-1354	90	1	lett	lett	PROPN
ap-1354	90	2	.	.	PUNCT
ap-1354	91	1	a	a	DET
ap-1354	91	2	,	,	PUNCT
ap-1354	91	3	252	252	NUM
ap-1354	91	4	,	,	PUNCT
ap-1354	91	5	272	272	NUM
ap-1354	91	6	(	(	PUNCT
ap-1354	91	7	1999	1999	NUM
ap-1354	91	8	)	)	PUNCT
ap-1354	91	9	.	.	PUNCT
ap-1354	92	1	[	[	X
ap-1354	92	2	2	2	NUM
ap-1354	92	3	]	]	X
ap-1354	92	4	yesiltas	yesilta	NOUN
ap-1354	92	5	,	,	PUNCT
ap-1354	92	6	o.	o.	PROPN
ap-1354	92	7	,	,	PUNCT
ap-1354	92	8	simsek	simsek	NOUN
ap-1354	92	9	,	,	PUNCT
ap-1354	92	10	m.	m.	NOUN
ap-1354	92	11	,	,	PUNCT
ap-1354	92	12	sever	sever	PROPN
ap-1354	92	13	,	,	PUNCT
ap-1354	92	14	r.	r.	PROPN
ap-1354	92	15	,	,	PUNCT
ap-1354	92	16	tezcan	tezcan	PROPN
ap-1354	92	17	,	,	PUNCT
ap-1354	92	18	c.	c.	NOUN
ap-1354	92	19	:	:	PUNCT
ap-1354	92	20	phys	phy	NOUN
ap-1354	92	21	.	.	PUNCT
ap-1354	92	22	scripta	scripta	PROPN
ap-1354	92	23	,	,	PUNCT
ap-1354	92	24	t67	t67	NOUN
ap-1354	92	25	,	,	PUNCT
ap-1354	92	26	472	472	NUM
ap-1354	92	27	(	(	PUNCT
ap-1354	92	28	2003	2003	NUM
ap-1354	92	29	)	)	PUNCT
ap-1354	92	30	.	.	PUNCT
ap-1354	93	1	[	[	X
ap-1354	93	2	3	3	NUM
ap-1354	93	3	]	]	PUNCT
ap-1354	93	4	berkdemir	berkdemir	PROPN
ap-1354	93	5	,	,	PUNCT
ap-1354	93	6	c.	c.	PROPN
ap-1354	93	7	,	,	PUNCT
ap-1354	93	8	berkdemir	berkdemir	PROPN
ap-1354	93	9	,	,	PUNCT
ap-1354	93	10	a.	a.	NOUN
ap-1354	93	11	,	,	PUNCT
ap-1354	93	12	sever	sever	VERB
ap-1354	93	13	,	,	PUNCT
ap-1354	93	14	r.	r.	PROPN
ap-1354	93	15	:	:	PUNCT
ap-1354	93	16	phys	phy	NOUN
ap-1354	93	17	.	.	PUNCT
ap-1354	93	18	rev	rev	PROPN
ap-1354	93	19	.	.	PROPN
ap-1354	93	20	c72	c72	PROPN
ap-1354	93	21	,	,	PUNCT
ap-1354	93	22	027001	027001	NUM
ap-1354	93	23	(	(	PUNCT
ap-1354	93	24	2005	2005	NUM
ap-1354	93	25	)	)	PUNCT
ap-1354	93	26	.	.	PUNCT
ap-1354	94	1	[	[	X
ap-1354	94	2	4	4	X
ap-1354	94	3	]	]	SYM
ap-1354	94	4	faridfathi	faridfathi	ADJ
ap-1354	94	5	,	,	PUNCT
ap-1354	94	6	g.	g.	PROPN
ap-1354	94	7	,	,	PUNCT
ap-1354	94	8	sever	sever	PROPN
ap-1354	94	9	,	,	PUNCT
ap-1354	94	10	r.	r.	PROPN
ap-1354	94	11	,	,	PUNCT
ap-1354	94	12	aktas	akta	NOUN
ap-1354	94	13	,	,	PUNCT
ap-1354	94	14	m.	m.	NOUN
ap-1354	94	15	:	:	PUNCT
ap-1354	94	16	j.	j.	PROPN
ap-1354	94	17	math	math	PROPN
ap-1354	94	18	.	.	PUNCT
ap-1354	95	1	chem	chem	PROPN
ap-1354	95	2	.	.	PUNCT
ap-1354	96	1	38	38	NUM
ap-1354	96	2	,	,	PUNCT
ap-1354	96	3	533	533	NUM
ap-1354	96	4	(	(	PUNCT
ap-1354	96	5	2005	2005	NUM
ap-1354	96	6	)	)	PUNCT
ap-1354	96	7	.	.	PUNCT
ap-1354	97	1	[	[	X
ap-1354	97	2	5	5	NUM
ap-1354	97	3	]	]	PUNCT
ap-1354	97	4	egrifes	egrife	NOUN
ap-1354	97	5	,	,	PUNCT
ap-1354	97	6	h.	h.	PROPN
ap-1354	97	7	,	,	PUNCT
ap-1354	97	8	sever	sever	PROPN
ap-1354	97	9	,	,	PUNCT
ap-1354	97	10	r.	r.	PROPN
ap-1354	97	11	:	:	PUNCT
ap-1354	97	12	int	int	PROPN
ap-1354	97	13	.	.	PUNCT
ap-1354	98	1	j.	j.	PROPN
ap-1354	98	2	theo	theo	PROPN
ap-1354	98	3	.	.	PUNCT
ap-1354	99	1	phys	phy	NOUN
ap-1354	99	2	.	.	PUNCT
ap-1354	100	1	46	46	NUM
ap-1354	100	2	,	,	PUNCT
ap-1354	100	3	935	935	NUM
ap-1354	100	4	(	(	PUNCT
ap-1354	100	5	2007	2007	NUM
ap-1354	100	6	)	)	PUNCT
ap-1354	100	7	.	.	PUNCT
ap-1354	101	1	[	[	X
ap-1354	101	2	6	6	NUM
ap-1354	101	3	]	]	PUNCT
ap-1354	101	4	ikhdair	ikhdair	NOUN
ap-1354	101	5	,	,	PUNCT
ap-1354	101	6	s.	s.	PROPN
ap-1354	101	7	m.	m.	PROPN
ap-1354	101	8	,	,	PUNCT
ap-1354	101	9	sever	sever	VERB
ap-1354	101	10	,	,	PUNCT
ap-1354	101	11	r.	r.	PROPN
ap-1354	101	12	:	:	PUNCT
ap-1354	101	13	j.	j.	PROPN
ap-1354	101	14	of	of	ADP
ap-1354	101	15	math	math	PROPN
ap-1354	101	16	.	.	PUNCT
ap-1354	102	1	chem	chem	NOUN
ap-1354	102	2	.	.	PUNCT
ap-1354	103	1	42	42	NUM
ap-1354	103	2	,	,	PUNCT
ap-1354	103	3	461	461	NUM
ap-1354	103	4	(	(	PUNCT
ap-1354	103	5	2007	2007	NUM
ap-1354	103	6	)	)	PUNCT
ap-1354	103	7	.	.	PUNCT
ap-1354	104	1	[	[	X
ap-1354	104	2	7	7	NUM
ap-1354	104	3	]	]	X
ap-1354	104	4	ikhdair	ikhdair	NOUN
ap-1354	104	5	,	,	PUNCT
ap-1354	104	6	s.	s.	PROPN
ap-1354	104	7	m.	m.	PROPN
ap-1354	104	8	,	,	PUNCT
ap-1354	104	9	sever	sever	VERB
ap-1354	104	10	,	,	PUNCT
ap-1354	104	11	r.	r.	PROPN
ap-1354	104	12	:	:	PUNCT
ap-1354	104	13	j.	j.	PROPN
ap-1354	104	14	mod	mod	PROPN
ap-1354	104	15	.	.	PUNCT
ap-1354	105	1	phys	phy	NOUN
ap-1354	105	2	.	.	PUNCT
ap-1354	106	1	e	e	PROPN
ap-1354	106	2	17	17	NUM
ap-1354	106	3	,	,	PUNCT
ap-1354	106	4	1107	1107	NUM
ap-1354	106	5	(	(	PUNCT
ap-1354	106	6	2008	2008	NUM
ap-1354	106	7	)	)	PUNCT
ap-1354	106	8	.	.	PUNCT
ap-1354	107	1	[	[	X
ap-1354	107	2	8	8	NUM
ap-1354	107	3	]	]	X
ap-1354	107	4	kandirmaz	kandirmaz	PROPN
ap-1354	107	5	,	,	PUNCT
ap-1354	107	6	n.	n.	PROPN
ap-1354	107	7	,	,	PUNCT
ap-1354	107	8	sever	sever	PROPN
ap-1354	107	9	,	,	PUNCT
ap-1354	107	10	r.	r.	PROPN
ap-1354	107	11	:	:	PUNCT
ap-1354	107	12	chinese	chinese	PROPN
ap-1354	107	13	j.	j.	PROPN
ap-1354	107	14	phys	phys	PROPN
ap-1354	107	15	.	.	PUNCT
ap-1354	108	1	47	47	NUM
ap-1354	108	2	,	,	PUNCT
ap-1354	108	3	47	47	NUM
ap-1354	108	4	(	(	PUNCT
ap-1354	108	5	2009	2009	NUM
ap-1354	108	6	)	)	PUNCT
ap-1354	108	7	.	.	PUNCT
ap-1354	109	1	[	[	X
ap-1354	109	2	9	9	NUM
ap-1354	109	3	]	]	X
ap-1354	109	4	kandirmaz	kandirmaz	NOUN
ap-1354	109	5	,	,	PUNCT
ap-1354	109	6	n.	n.	PROPN
ap-1354	109	7	,	,	PUNCT
ap-1354	109	8	sever	sever	PROPN
ap-1354	109	9	,	,	PUNCT
ap-1354	109	10	r.	r.	PROPN
ap-1354	109	11	:	:	PUNCT
ap-1354	109	12	physica	physica	PROPN
ap-1354	109	13	scripta	scripta	PROPN
ap-1354	109	14	,	,	PUNCT
ap-1354	109	15	87	87	NUM
ap-1354	109	16	,	,	PUNCT
ap-1354	109	17	3	3	NUM
ap-1354	109	18	,	,	PUNCT
ap-1354	109	19	(	(	PUNCT
ap-1354	109	20	2010	2010	NUM
ap-1354	109	21	)	)	PUNCT
ap-1354	109	22	.	.	PUNCT
ap-1354	110	1	[	[	X
ap-1354	110	2	10	10	NUM
ap-1354	110	3	]	]	X
ap-1354	110	4	feynmann	feynmann	PROPN
ap-1354	110	5	,	,	PUNCT
ap-1354	110	6	r.	r.	PROPN
ap-1354	110	7	,	,	PUNCT
ap-1354	110	8	hibbs	hibbs	PROPN
ap-1354	110	9	,	,	PUNCT
ap-1354	110	10	a.	a.	NOUN
ap-1354	110	11	:	:	PUNCT
ap-1354	110	12	quantum	quantum	ADJ
ap-1354	110	13	mechanics	mechanic	NOUN
ap-1354	110	14	and	and	CCONJ
ap-1354	110	15	path	path	NOUN
ap-1354	110	16	integrals	integral	NOUN
ap-1354	110	17	.	.	PUNCT
ap-1354	111	1	mcgraw	mcgraw	PROPN
ap-1354	111	2	hill	hill	PROPN
ap-1354	111	3	,	,	PUNCT
ap-1354	111	4	new	new	PROPN
ap-1354	111	5	york	york	PROPN
ap-1354	111	6	,	,	PUNCT
ap-1354	111	7	(	(	PUNCT
ap-1354	111	8	1965	1965	NUM
ap-1354	111	9	)	)	PUNCT
ap-1354	111	10	.	.	PUNCT
ap-1354	112	1	40	40	NUM
ap-1354	112	2	acta	acta	PROPN
ap-1354	112	3	polytechnica	polytechnica	PROPN
ap-1354	112	4	vol	vol	NOUN
ap-1354	112	5	.	.	PUNCT
ap-1354	113	1	51	51	NUM
ap-1354	113	2	no	no	INTJ
ap-1354	113	3	.	.	PUNCT
ap-1354	114	1	1/2011	1/2011	NUM
ap-1354	115	1	[	[	X
ap-1354	115	2	11	11	NUM
ap-1354	115	3	]	]	X
ap-1354	115	4	duru	duru	PROPN
ap-1354	115	5	,	,	PUNCT
ap-1354	115	6	i.	i.	PROPN
ap-1354	115	7	h.	h.	PROPN
ap-1354	115	8	:	:	PUNCT
ap-1354	115	9	phys	phy	NOUN
ap-1354	115	10	.	.	PUNCT
ap-1354	116	1	rev	rev	PROPN
ap-1354	116	2	.	.	PROPN
ap-1354	117	1	d	d	X
ap-1354	117	2	,	,	PUNCT
ap-1354	117	3	28	28	NUM
ap-1354	117	4	,	,	PUNCT
ap-1354	117	5	2689	2689	NUM
ap-1354	117	6	(	(	PUNCT
ap-1354	117	7	1983	1983	NUM
ap-1354	117	8	)	)	PUNCT
ap-1354	117	9	;	;	PUNCT
ap-1354	118	1	duru	duru	PROPN
ap-1354	118	2	,	,	PUNCT
ap-1354	118	3	i.	i.	PROPN
ap-1354	118	4	h.	h.	PROPN
ap-1354	118	5	,	,	PUNCT
ap-1354	118	6	kleinert	kleinert	PROPN
ap-1354	118	7	,	,	PUNCT
ap-1354	118	8	h.	h.	PROPN
ap-1354	118	9	:	:	PUNCT
ap-1354	118	10	phys	phy	NOUN
ap-1354	118	11	.	.	PUNCT
ap-1354	119	1	lett	lett	PROPN
ap-1354	119	2	.	.	PUNCT
ap-1354	120	1	b84	b84	PROPN
ap-1354	120	2	,	,	PUNCT
ap-1354	120	3	185	185	NUM
ap-1354	120	4	(	(	PUNCT
ap-1354	120	5	1979	1979	NUM
ap-1354	120	6	)	)	PUNCT
ap-1354	120	7	;	;	PUNCT
ap-1354	120	8	fortschr	fortschr	NOUN
ap-1354	120	9	.	.	PUNCT
ap-1354	121	1	phys	phy	NOUN
ap-1354	121	2	.	.	PUNCT
ap-1354	122	1	30	30	NUM
ap-1354	122	2	,	,	PUNCT
ap-1354	122	3	401	401	NUM
ap-1354	122	4	(	(	PUNCT
ap-1354	122	5	1982	1982	NUM
ap-1354	122	6	)	)	PUNCT
ap-1354	122	7	;	;	PUNCT
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ap-1354	123	2	,	,	PUNCT
ap-1354	123	3	i.	i.	PROPN
ap-1354	123	4	h.	h.	PROPN
ap-1354	123	5	:	:	PUNCT
ap-1354	123	6	phys.rev	phys.rev	X
ap-1354	123	7	.	.	PUNCT
ap-1354	124	1	d	d	NUM
ap-1354	124	2	,	,	PUNCT
ap-1354	124	3	30	30	NUM
ap-1354	124	4	,	,	PUNCT
ap-1354	124	5	2121	2121	NUM
ap-1354	124	6	(	(	PUNCT
ap-1354	124	7	1984	1984	NUM
ap-1354	124	8	)	)	PUNCT
ap-1354	124	9	;	;	PUNCT
ap-1354	125	1	duru	duru	PROPN
ap-1354	125	2	,	,	PUNCT
ap-1354	125	3	i.	i.	PROPN
ap-1354	125	4	h.	h.	PROPN
ap-1354	125	5	:	:	PUNCT
ap-1354	125	6	phys	phy	NOUN
ap-1354	125	7	.	.	PUNCT
ap-1354	126	1	lett	lett	PROPN
ap-1354	126	2	a	a	PRON
ap-1354	126	3	,	,	PUNCT
ap-1354	126	4	119	119	NUM
ap-1354	126	5	,	,	PUNCT
ap-1354	126	6	163	163	NUM
ap-1354	126	7	(	(	PUNCT
ap-1354	126	8	1986	1986	NUM
ap-1354	126	9	)	)	PUNCT
ap-1354	126	10	.	.	PUNCT
ap-1354	127	1	[	[	X
ap-1354	127	2	12	12	NUM
ap-1354	127	3	]	]	PUNCT
ap-1354	127	4	peak	peak	NOUN
ap-1354	127	5	,	,	PUNCT
ap-1354	127	6	d.	d.	PROPN
ap-1354	127	7	,	,	PUNCT
ap-1354	127	8	inomata	inomata	PROPN
ap-1354	127	9	,	,	PUNCT
ap-1354	127	10	a.	a.	NOUN
ap-1354	127	11	:	:	PUNCT
ap-1354	127	12	j.	j.	PROPN
ap-1354	127	13	math	math	PROPN
ap-1354	127	14	.	.	PUNCT
ap-1354	128	1	phys	phy	NOUN
ap-1354	128	2	.	.	PUNCT
ap-1354	129	1	10	10	NUM
ap-1354	129	2	,	,	PUNCT
ap-1354	129	3	1422	1422	NUM
ap-1354	129	4	(	(	PUNCT
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ap-1354	129	6	)	)	PUNCT
ap-1354	129	7	.	.	PUNCT
ap-1354	130	1	[	[	X
ap-1354	130	2	13	13	NUM
ap-1354	130	3	]	]	SYM
ap-1354	130	4	erkoc	erkoc	PROPN
ap-1354	130	5	,	,	PUNCT
ap-1354	130	6	s.	s.	PROPN
ap-1354	130	7	,	,	PUNCT
ap-1354	130	8	sever	sever	VERB
ap-1354	130	9	,	,	PUNCT
ap-1354	130	10	r.	r.	PROPN
ap-1354	130	11	:	:	PUNCT
ap-1354	130	12	phys	phy	NOUN
ap-1354	130	13	.	.	PUNCT
ap-1354	131	1	rev	rev	PROPN
ap-1354	131	2	d	d	PROPN
ap-1354	131	3	,	,	PUNCT
ap-1354	131	4	30	30	NUM
ap-1354	131	5	,	,	PUNCT
ap-1354	131	6	2117	2117	NUM
ap-1354	131	7	(	(	PUNCT
ap-1354	131	8	1984	1984	NUM
ap-1354	131	9	)	)	PUNCT
ap-1354	131	10	.	.	PUNCT
ap-1354	132	1	[	[	X
ap-1354	132	2	14	14	NUM
ap-1354	132	3	]	]	PUNCT
ap-1354	132	4	erkoc	erkoc	PROPN
ap-1354	132	5	,	,	PUNCT
ap-1354	132	6	s.	s.	PROPN
ap-1354	132	7	,	,	PUNCT
ap-1354	132	8	sever	sever	VERB
ap-1354	132	9	,	,	PUNCT
ap-1354	132	10	r.	r.	PROPN
ap-1354	132	11	:	:	PUNCT
ap-1354	132	12	phys	phy	NOUN
ap-1354	132	13	.	.	PUNCT
ap-1354	133	1	rev	rev	VERB
ap-1354	133	2	a	a	PRON
ap-1354	133	3	,	,	PUNCT
ap-1354	133	4	37	37	NUM
ap-1354	133	5	,	,	PUNCT
ap-1354	133	6	2687	2687	NUM
ap-1354	133	7	(	(	PUNCT
ap-1354	133	8	1988	1988	NUM
ap-1354	133	9	)	)	PUNCT
ap-1354	133	10	.	.	PUNCT
ap-1354	134	1	[	[	X
ap-1354	134	2	15	15	NUM
ap-1354	134	3	]	]	X
ap-1354	134	4	pak	pak	PROPN
ap-1354	134	5	,	,	PUNCT
ap-1354	134	6	n.	n.	PROPN
ap-1354	134	7	k.	k.	PROPN
ap-1354	134	8	,	,	PUNCT
ap-1354	134	9	sokmen	sokman	NOUN
ap-1354	134	10	,	,	PUNCT
ap-1354	134	11	i.	i.	NOUN
ap-1354	134	12	:	:	PUNCT
ap-1354	134	13	phys	phy	NOUN
ap-1354	134	14	.	.	PUNCT
ap-1354	135	1	lett	lett	PROPN
ap-1354	135	2	.	.	PUNCT
ap-1354	136	1	100a	100a	NOUN
ap-1354	136	2	,	,	PUNCT
ap-1354	136	3	327	327	NUM
ap-1354	136	4	(	(	PUNCT
ap-1354	136	5	1984	1984	NUM
ap-1354	136	6	)	)	PUNCT
ap-1354	136	7	.	.	PUNCT
ap-1354	137	1	[	[	X
ap-1354	137	2	16	16	NUM
ap-1354	137	3	]	]	X
ap-1354	137	4	gradshteyn	gradshteyn	PROPN
ap-1354	137	5	,	,	PUNCT
ap-1354	137	6	i.	i.	PROPN
ap-1354	137	7	s.	s.	PROPN
ap-1354	137	8	,	,	PUNCT
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ap-1354	137	10	,	,	PUNCT
ap-1354	137	11	i.	i.	NOUN
ap-1354	137	12	m.	m.	NOUN
ap-1354	137	13	:	:	PUNCT
ap-1354	137	14	table	table	NOUN
ap-1354	137	15	of	of	ADP
ap-1354	137	16	integrals	integral	NOUN
ap-1354	137	17	,	,	PUNCT
ap-1354	137	18	series	series	NOUN
ap-1354	137	19	,	,	PUNCT
ap-1354	137	20	and	and	CCONJ
ap-1354	137	21	products	product	NOUN
ap-1354	137	22	,	,	PUNCT
ap-1354	137	23	2nd	2nd	ADJ
ap-1354	137	24	ed	ed	NOUN
ap-1354	137	25	.	.	PROPN
ap-1354	137	26	,	,	PUNCT
ap-1354	137	27	academic	academic	ADJ
ap-1354	137	28	press	press	NOUN
ap-1354	137	29	,	,	PUNCT
ap-1354	137	30	new	new	PROPN
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ap-1354	137	32	,	,	PUNCT
ap-1354	137	33	(	(	PUNCT
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ap-1354	137	35	)	)	PUNCT
ap-1354	137	36	.	.	PUNCT
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ap-1354	138	2	kandirmaz	kandirmaz	PROPN
ap-1354	139	1	e	e	NOUN
ap-1354	139	2	-	-	NOUN
ap-1354	139	3	mail	mail	NOUN
ap-1354	139	4	:	:	PUNCT
ap-1354	139	5	nkandirmaz@mersin.edu.tr	nkandirmaz@mersin.edu.tr	PROPN
ap-1354	139	6	mersin	mersin	PROPN
ap-1354	139	7	university	university	PROPN
ap-1354	139	8	department	department	PROPN
ap-1354	139	9	of	of	ADP
ap-1354	139	10	physics	physics	PROPN
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ap-1354	139	12	,	,	PUNCT
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ap-1354	139	20	department	department	PROPN
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ap-1354	139	22	physics	physics	PROPN
ap-1354	139	23	ankara	ankara	PROPN
ap-1354	139	24	,	,	PUNCT
ap-1354	139	25	turkey	turkey	PROPN
ap-1354	139	26	41	41	NUM