id	sid	tid	token	lemma	pos
ap-1366	1	1	wykresx.eps	wykresx.eps	X
ap-1366	1	2	acta	acta	PROPN
ap-1366	1	3	polytechnica	polytechnica	PROPN
ap-1366	1	4	vol	vol	NOUN
ap-1366	1	5	.	.	PUNCT
ap-1366	2	1	51	51	NUM
ap-1366	2	2	no	no	NOUN
ap-1366	2	3	.	.	PUNCT
ap-1366	3	1	1/2011	1/2011	NUM
ap-1366	3	2	propagators	propagator	NOUN
ap-1366	3	3	of	of	ADP
ap-1366	3	4	generalized	generalize	VERB
ap-1366	3	5	schrödinger	schrödinger	NOUN
ap-1366	3	6	equations	equation	NOUN
ap-1366	3	7	related	relate	VERB
ap-1366	3	8	by	by	ADP
ap-1366	3	9	first	first	ADJ
ap-1366	3	10	-	-	PUNCT
ap-1366	3	11	order	order	NOUN
ap-1366	3	12	supersymmetry	supersymmetry	NOUN
ap-1366	3	13	a.	a.	NOUN
ap-1366	3	14	schulze	schulze	PROPN
ap-1366	3	15	-	-	PUNCT
ap-1366	3	16	halberg	halberg	NOUN
ap-1366	3	17	abstract	abstract	NOUN
ap-1366	3	18	we	we	PRON
ap-1366	3	19	construct	construct	VERB
ap-1366	3	20	an	an	DET
ap-1366	3	21	explicit	explicit	ADJ
ap-1366	3	22	relation	relation	NOUN
ap-1366	3	23	between	between	ADP
ap-1366	3	24	propagators	propagator	NOUN
ap-1366	3	25	of	of	ADP
ap-1366	3	26	generalized	generalize	VERB
ap-1366	3	27	schrödinger	schrödinger	NOUN
ap-1366	3	28	equations	equation	NOUN
ap-1366	3	29	that	that	PRON
ap-1366	3	30	are	be	AUX
ap-1366	3	31	linked	link	VERB
ap-1366	3	32	by	by	ADP
ap-1366	3	33	a	a	DET
ap-1366	3	34	first	first	ADJ
ap-1366	3	35	-	-	PUNCT
ap-1366	3	36	order	order	NOUN
ap-1366	3	37	supersymmetric	supersymmetric	ADJ
ap-1366	3	38	transformation	transformation	NOUN
ap-1366	3	39	.	.	PUNCT
ap-1366	4	1	our	our	PRON
ap-1366	4	2	findings	finding	NOUN
ap-1366	4	3	extend	extend	VERB
ap-1366	4	4	and	and	CCONJ
ap-1366	4	5	complement	complement	VERB
ap-1366	4	6	recent	recent	ADJ
ap-1366	4	7	results	result	NOUN
ap-1366	4	8	on	on	ADP
ap-1366	4	9	the	the	DET
ap-1366	4	10	conventional	conventional	ADJ
ap-1366	4	11	case	case	NOUN
ap-1366	4	12	[	[	X
ap-1366	4	13	1	1	NUM
ap-1366	4	14	]	]	PUNCT
ap-1366	4	15	.	.	PUNCT
ap-1366	5	1	keywords	keyword	NOUN
ap-1366	5	2	:	:	PUNCT
ap-1366	5	3	generalized	generalized	ADJ
ap-1366	5	4	schrödinger	schrödinger	NOUN
ap-1366	5	5	equation	equation	NOUN
ap-1366	5	6	,	,	PUNCT
ap-1366	5	7	propagator	propagator	NOUN
ap-1366	5	8	,	,	PUNCT
ap-1366	5	9	supersymmetry	supersymmetry	NOUN
ap-1366	5	10	.	.	PUNCT
ap-1366	6	1	1	1	NUM
ap-1366	6	2	introduction	introduction	NOUN
ap-1366	6	3	the	the	DET
ap-1366	6	4	formalism	formalism	NOUN
ap-1366	6	5	of	of	ADP
ap-1366	6	6	supersymmetry	supersymmetry	NOUN
ap-1366	6	7	(	(	PUNCT
ap-1366	6	8	susy	susy	NOUN
ap-1366	6	9	)	)	PUNCT
ap-1366	6	10	is	be	AUX
ap-1366	6	11	a	a	DET
ap-1366	6	12	wellknown	wellknown	ADJ
ap-1366	6	13	tool	tool	NOUN
ap-1366	6	14	for	for	ADP
ap-1366	6	15	identifying	identify	VERB
ap-1366	6	16	integrable	integrable	ADJ
ap-1366	6	17	cases	case	NOUN
ap-1366	6	18	of	of	ADP
ap-1366	6	19	the	the	DET
ap-1366	6	20	schrödinger	schrödinger	NOUN
ap-1366	6	21	equation	equation	NOUN
ap-1366	6	22	and	and	CCONJ
ap-1366	6	23	for	for	ADP
ap-1366	6	24	generating	generate	VERB
ap-1366	6	25	the	the	DET
ap-1366	6	26	corresponding	corresponding	ADJ
ap-1366	6	27	solutions	solution	NOUN
ap-1366	6	28	.	.	PUNCT
ap-1366	7	1	the	the	DET
ap-1366	7	2	principal	principal	ADJ
ap-1366	7	3	idea	idea	NOUN
ap-1366	7	4	is	be	AUX
ap-1366	7	5	to	to	PART
ap-1366	7	6	relate	relate	VERB
ap-1366	7	7	two	two	NUM
ap-1366	7	8	schrödinger	schrödinger	NOUN
ap-1366	7	9	equations	equation	NOUN
ap-1366	7	10	and	and	CCONJ
ap-1366	7	11	their	their	PRON
ap-1366	7	12	solutions	solution	NOUN
ap-1366	7	13	via	via	ADP
ap-1366	7	14	a	a	DET
ap-1366	7	15	supersymmetrical	supersymmetrical	ADJ
ap-1366	7	16	(	(	PUNCT
ap-1366	7	17	or	or	CCONJ
ap-1366	7	18	darboux	darboux	VERB
ap-1366	7	19	[	[	PUNCT
ap-1366	7	20	3	3	NUM
ap-1366	7	21	]	]	SYM
ap-1366	7	22	)	)	PUNCT
ap-1366	7	23	transformation	transformation	NOUN
ap-1366	7	24	,	,	PUNCT
ap-1366	7	25	such	such	ADJ
ap-1366	7	26	that	that	SCONJ
ap-1366	7	27	known	know	VERB
ap-1366	7	28	solutions	solution	NOUN
ap-1366	7	29	of	of	ADP
ap-1366	7	30	one	one	NUM
ap-1366	7	31	equation	equation	NOUN
ap-1366	7	32	can	can	AUX
ap-1366	7	33	be	be	AUX
ap-1366	7	34	mapped	map	VERB
ap-1366	7	35	onto	onto	ADP
ap-1366	7	36	solutions	solution	NOUN
ap-1366	7	37	of	of	ADP
ap-1366	7	38	the	the	DET
ap-1366	7	39	second	second	ADJ
ap-1366	7	40	equation	equation	NOUN
ap-1366	7	41	.	.	PUNCT
ap-1366	8	1	there	there	PRON
ap-1366	8	2	is	be	VERB
ap-1366	8	3	a	a	DET
ap-1366	8	4	vast	vast	ADJ
ap-1366	8	5	amount	amount	NOUN
ap-1366	8	6	of	of	ADP
ap-1366	8	7	literature	literature	NOUN
ap-1366	8	8	on	on	ADP
ap-1366	8	9	the	the	DET
ap-1366	8	10	susy	susy	NOUN
ap-1366	8	11	formalism	formalism	NOUN
ap-1366	8	12	and	and	CCONJ
ap-1366	8	13	its	its	PRON
ap-1366	8	14	applications	application	NOUN
ap-1366	8	15	,	,	PUNCT
ap-1366	8	16	for	for	ADP
ap-1366	8	17	details	detail	NOUN
ap-1366	8	18	we	we	PRON
ap-1366	8	19	refer	refer	VERB
ap-1366	8	20	the	the	DET
ap-1366	8	21	reader	reader	NOUN
ap-1366	8	22	to	to	ADP
ap-1366	8	23	[	[	X
ap-1366	8	24	5	5	NUM
ap-1366	8	25	,	,	PUNCT
ap-1366	8	26	2	2	NUM
ap-1366	8	27	]	]	PUNCT
ap-1366	8	28	and	and	CCONJ
ap-1366	8	29	references	reference	NOUN
ap-1366	8	30	therein	therein	ADV
ap-1366	8	31	.	.	PUNCT
ap-1366	9	1	while	while	SCONJ
ap-1366	9	2	the	the	DET
ap-1366	9	3	concept	concept	NOUN
ap-1366	9	4	of	of	ADP
ap-1366	9	5	the	the	DET
ap-1366	9	6	susy	susy	NOUN
ap-1366	9	7	formalism	formalism	NOUN
ap-1366	9	8	as	as	ADP
ap-1366	9	9	a	a	DET
ap-1366	9	10	method	method	NOUN
ap-1366	9	11	for	for	ADP
ap-1366	9	12	generating	generate	VERB
ap-1366	9	13	solutions	solution	NOUN
ap-1366	9	14	is	be	AUX
ap-1366	9	15	popular	popular	ADJ
ap-1366	9	16	,	,	PUNCT
ap-1366	9	17	it	it	PRON
ap-1366	9	18	is	be	AUX
ap-1366	9	19	less	less	ADV
ap-1366	9	20	known	known	ADJ
ap-1366	9	21	that	that	SCONJ
ap-1366	9	22	two	two	NUM
ap-1366	9	23	schrödinger	schrödinger	NOUN
ap-1366	9	24	equations	equation	NOUN
ap-1366	9	25	related	relate	VERB
ap-1366	9	26	by	by	ADP
ap-1366	9	27	a	a	DET
ap-1366	9	28	susy	susy	NOUN
ap-1366	9	29	transformation	transformation	NOUN
ap-1366	9	30	(	(	PUNCT
ap-1366	9	31	susy	susy	NOUN
ap-1366	9	32	partners	partner	NOUN
ap-1366	9	33	)	)	PUNCT
ap-1366	9	34	share	share	VERB
ap-1366	9	35	more	more	ADJ
ap-1366	9	36	properties	property	NOUN
ap-1366	9	37	than	than	ADP
ap-1366	9	38	the	the	DET
ap-1366	9	39	link	link	NOUN
ap-1366	9	40	between	between	ADP
ap-1366	9	41	their	their	PRON
ap-1366	9	42	solutions	solution	NOUN
ap-1366	9	43	.	.	PUNCT
ap-1366	10	1	in	in	ADP
ap-1366	10	2	particular	particular	ADJ
ap-1366	10	3	,	,	PUNCT
ap-1366	10	4	susy	susy	NOUN
ap-1366	10	5	establishes	establish	VERB
ap-1366	10	6	a	a	DET
ap-1366	10	7	connection	connection	NOUN
ap-1366	10	8	between	between	ADP
ap-1366	10	9	the	the	DET
ap-1366	10	10	propagators	propagator	NOUN
ap-1366	10	11	and	and	CCONJ
ap-1366	10	12	the	the	DET
ap-1366	10	13	green	green	PROPN
ap-1366	10	14	’s	’s	PART
ap-1366	10	15	functions	function	NOUN
ap-1366	10	16	of	of	ADP
ap-1366	10	17	the	the	DET
ap-1366	10	18	underlying	underlie	VERB
ap-1366	10	19	partner	partner	NOUN
ap-1366	10	20	equations	equation	NOUN
ap-1366	10	21	:	:	PUNCT
ap-1366	10	22	the	the	DET
ap-1366	10	23	propagators	propagator	NOUN
ap-1366	10	24	are	be	AUX
ap-1366	10	25	linked	link	VERB
ap-1366	10	26	by	by	ADP
ap-1366	10	27	means	mean	NOUN
ap-1366	10	28	of	of	ADP
ap-1366	10	29	an	an	DET
ap-1366	10	30	integral	integral	ADJ
ap-1366	10	31	expression	expression	NOUN
ap-1366	10	32	[	[	X
ap-1366	10	33	1	1	NUM
ap-1366	10	34	]	]	PUNCT
ap-1366	10	35	,	,	PUNCT
ap-1366	10	36	while	while	SCONJ
ap-1366	10	37	the	the	DET
ap-1366	10	38	green	green	PROPN
ap-1366	10	39	’s	’s	PART
ap-1366	10	40	functions	function	NOUN
ap-1366	10	41	satisfy	satisfy	VERB
ap-1366	10	42	a	a	DET
ap-1366	10	43	simple	simple	ADJ
ap-1366	10	44	trace	trace	NOUN
ap-1366	10	45	formula	formula	NOUN
ap-1366	11	1	[	[	X
ap-1366	11	2	9	9	NUM
ap-1366	11	3	,	,	PUNCT
ap-1366	11	4	6	6	NUM
ap-1366	11	5	]	]	PUNCT
ap-1366	11	6	.	.	PUNCT
ap-1366	12	1	it	it	PRON
ap-1366	12	2	is	be	AUX
ap-1366	12	3	interesting	interesting	ADJ
ap-1366	12	4	to	to	PART
ap-1366	12	5	note	note	VERB
ap-1366	12	6	that	that	SCONJ
ap-1366	12	7	this	this	DET
ap-1366	12	8	trace	trace	NOUN
ap-1366	12	9	formula	formula	NOUN
ap-1366	12	10	persists	persist	VERB
ap-1366	12	11	under	under	ADP
ap-1366	12	12	generalization	generalization	NOUN
ap-1366	12	13	of	of	ADP
ap-1366	12	14	the	the	DET
ap-1366	12	15	schrödinger	schrödinger	NOUN
ap-1366	12	16	equation	equation	NOUN
ap-1366	12	17	to	to	ADP
ap-1366	12	18	the	the	DET
ap-1366	12	19	effective	effective	ADJ
ap-1366	12	20	mass	mass	NOUN
ap-1366	12	21	case	case	NOUN
ap-1366	12	22	[	[	X
ap-1366	12	23	8	8	NUM
ap-1366	12	24	]	]	PUNCT
ap-1366	12	25	or	or	CCONJ
ap-1366	12	26	to	to	ADP
ap-1366	12	27	a	a	DET
ap-1366	12	28	generalized	generalize	VERB
ap-1366	12	29	sturm	sturm	NOUN
ap-1366	12	30	-	-	PUNCT
ap-1366	12	31	liouville	liouville	NOUN
ap-1366	12	32	problem	problem	NOUN
ap-1366	12	33	[	[	X
ap-1366	12	34	7	7	NUM
ap-1366	12	35	]	]	PUNCT
ap-1366	12	36	.	.	PUNCT
ap-1366	13	1	due	due	ADP
ap-1366	13	2	to	to	ADP
ap-1366	13	3	the	the	DET
ap-1366	13	4	close	close	ADJ
ap-1366	13	5	relation	relation	NOUN
ap-1366	13	6	between	between	ADP
ap-1366	13	7	green	green	PROPN
ap-1366	13	8	’s	’s	PART
ap-1366	13	9	function	function	NOUN
ap-1366	13	10	and	and	CCONJ
ap-1366	13	11	the	the	DET
ap-1366	13	12	propagator	propagator	NOUN
ap-1366	13	13	,	,	PUNCT
ap-1366	13	14	one	one	PRON
ap-1366	13	15	would	would	AUX
ap-1366	13	16	expect	expect	VERB
ap-1366	13	17	that	that	SCONJ
ap-1366	13	18	the	the	DET
ap-1366	13	19	propagator	propagator	NOUN
ap-1366	13	20	relation	relation	NOUN
ap-1366	13	21	found	find	VERB
ap-1366	13	22	in	in	ADP
ap-1366	13	23	[	[	X
ap-1366	13	24	1	1	X
ap-1366	13	25	]	]	PUNCT
ap-1366	13	26	also	also	ADV
ap-1366	13	27	extends	extend	VERB
ap-1366	13	28	to	to	ADP
ap-1366	13	29	generalized	generalized	ADJ
ap-1366	13	30	cases	case	NOUN
ap-1366	13	31	of	of	ADP
ap-1366	13	32	the	the	DET
ap-1366	13	33	schrödinger	schrödinger	NOUN
ap-1366	13	34	equation	equation	NOUN
ap-1366	13	35	.	.	PUNCT
ap-1366	14	1	this	this	PRON
ap-1366	14	2	is	be	AUX
ap-1366	14	3	in	in	ADP
ap-1366	14	4	fact	fact	NOUN
ap-1366	14	5	true	true	ADJ
ap-1366	14	6	,	,	PUNCT
ap-1366	14	7	as	as	SCONJ
ap-1366	14	8	will	will	AUX
ap-1366	14	9	be	be	AUX
ap-1366	14	10	shown	show	VERB
ap-1366	14	11	in	in	ADP
ap-1366	14	12	this	this	DET
ap-1366	14	13	note	note	NOUN
ap-1366	14	14	.	.	PUNCT
ap-1366	15	1	we	we	PRON
ap-1366	15	2	restrict	restrict	VERB
ap-1366	15	3	ourselves	ourselves	PRON
ap-1366	15	4	to	to	ADP
ap-1366	15	5	first	first	ADJ
ap-1366	15	6	-	-	PUNCT
ap-1366	15	7	order	order	NOUN
ap-1366	15	8	susy	susy	NOUN
ap-1366	15	9	transformations	transformation	NOUN
ap-1366	15	10	of	of	ADP
ap-1366	15	11	generalized	generalized	ADJ
ap-1366	15	12	schrödinger	schrödinger	NOUN
ap-1366	15	13	equations	equation	NOUN
ap-1366	15	14	,	,	PUNCT
ap-1366	15	15	a	a	DET
ap-1366	15	16	brief	brief	ADJ
ap-1366	15	17	review	review	NOUN
ap-1366	15	18	of	of	ADP
ap-1366	15	19	which	which	PRON
ap-1366	15	20	and	and	CCONJ
ap-1366	15	21	of	of	ADP
ap-1366	15	22	related	related	ADJ
ap-1366	15	23	theory	theory	NOUN
ap-1366	15	24	is	be	AUX
ap-1366	15	25	given	give	VERB
ap-1366	15	26	in	in	ADP
ap-1366	15	27	section	section	NOUN
ap-1366	15	28	2	2	NUM
ap-1366	15	29	.	.	PUNCT
ap-1366	15	30	subsequently	subsequently	ADV
ap-1366	15	31	,	,	PUNCT
ap-1366	15	32	the	the	DET
ap-1366	15	33	explicit	explicit	ADJ
ap-1366	15	34	integral	integral	ADJ
ap-1366	15	35	formula	formula	NOUN
ap-1366	15	36	that	that	PRON
ap-1366	15	37	links	link	VERB
ap-1366	15	38	the	the	DET
ap-1366	15	39	propagators	propagator	NOUN
ap-1366	15	40	of	of	ADP
ap-1366	15	41	our	our	PRON
ap-1366	15	42	susy	susy	NOUN
ap-1366	15	43	partner	partner	NOUN
ap-1366	15	44	equations	equation	NOUN
ap-1366	15	45	is	be	AUX
ap-1366	15	46	done	do	VERB
ap-1366	15	47	in	in	ADP
ap-1366	15	48	section	section	NOUN
ap-1366	15	49	3	3	NUM
ap-1366	15	50	.	.	SYM
ap-1366	15	51	2	2	NUM
ap-1366	15	52	preliminaries	preliminary	NOUN
ap-1366	15	53	in	in	ADP
ap-1366	15	54	the	the	DET
ap-1366	15	55	following	following	NOUN
ap-1366	15	56	we	we	PRON
ap-1366	15	57	briefly	briefly	ADV
ap-1366	15	58	summarize	summarize	VERB
ap-1366	15	59	basic	basic	ADJ
ap-1366	15	60	facts	fact	NOUN
ap-1366	15	61	about	about	ADP
ap-1366	15	62	generalized	generalized	ADJ
ap-1366	15	63	schrödinger	schrödinger	NOUN
ap-1366	15	64	equations	equation	NOUN
ap-1366	15	65	,	,	PUNCT
ap-1366	15	66	their	their	PRON
ap-1366	15	67	susy	susy	NOUN
ap-1366	15	68	formalism	formalism	NOUN
ap-1366	15	69	,	,	PUNCT
ap-1366	15	70	propagators	propagator	NOUN
ap-1366	15	71	and	and	CCONJ
ap-1366	15	72	green	green	PROPN
ap-1366	15	73	’s	’s	PART
ap-1366	15	74	functions	function	NOUN
ap-1366	15	75	.	.	PUNCT
ap-1366	16	1	generalized	generalize	VERB
ap-1366	16	2	schrödinger	schrödinger	NOUN
ap-1366	16	3	equation	equation	NOUN
ap-1366	16	4	.	.	PUNCT
ap-1366	17	1	we	we	PRON
ap-1366	17	2	consider	consider	VERB
ap-1366	17	3	the	the	DET
ap-1366	17	4	following	follow	VERB
ap-1366	17	5	generalized	generalize	VERB
ap-1366	17	6	sturm	sturm	PROPN
ap-1366	17	7	-	-	PUNCT
ap-1366	17	8	liouville	liouville	NOUN
ap-1366	17	9	problem	problem	NOUN
ap-1366	17	10	on	on	ADP
ap-1366	17	11	the	the	DET
ap-1366	17	12	real	real	ADJ
ap-1366	17	13	interval	interval	NOUN
ap-1366	17	14	(	(	PUNCT
ap-1366	17	15	a	a	DET
ap-1366	17	16	,	,	PUNCT
ap-1366	17	17	b	b	NOUN
ap-1366	17	18	)	)	PUNCT
ap-1366	17	19	,	,	PUNCT
ap-1366	17	20	equipped	equip	VERB
ap-1366	17	21	with	with	ADP
ap-1366	17	22	dirichlet	dirichlet	PROPN
ap-1366	17	23	boundary	boundary	ADJ
ap-1366	17	24	conditions	condition	NOUN
ap-1366	17	25	:	:	PUNCT
ap-1366	17	26	f(x)ψ′′(x	f(x)ψ′′(x	NOUN
ap-1366	17	27	)	)	PUNCT
ap-1366	18	1	+	+	NUM
ap-1366	18	2	f	f	PROPN
ap-1366	18	3	′(x)ψ′(x	′(x)ψ′(x	PROPN
ap-1366	18	4	)	)	PUNCT
ap-1366	19	1	+	+	CCONJ
ap-1366	20	1	[	[	X
ap-1366	20	2	eh(x)−	eh(x)−	PROPN
ap-1366	20	3	v	v	NOUN
ap-1366	20	4	(	(	PUNCT
ap-1366	20	5	x)]ψ(x	x)]ψ(x	PROPN
ap-1366	20	6	)	)	PUNCT
ap-1366	20	7	=	=	SYM
ap-1366	20	8	0	0	NUM
ap-1366	20	9	,	,	PUNCT
ap-1366	20	10	x	x	SYM
ap-1366	20	11	∈	∈	PROPN
ap-1366	20	12	(	(	PUNCT
ap-1366	20	13	a	a	DET
ap-1366	20	14	,	,	PUNCT
ap-1366	20	15	b	b	NOUN
ap-1366	20	16	)	)	PUNCT
ap-1366	20	17	(	(	PUNCT
ap-1366	20	18	1	1	X
ap-1366	20	19	)	)	PUNCT
ap-1366	20	20	ψ(a	ψ(a	PROPN
ap-1366	20	21	)	)	PUNCT
ap-1366	20	22	=	=	SYM
ap-1366	20	23	ψ(b	ψ(b	NOUN
ap-1366	20	24	)	)	PUNCT
ap-1366	20	25	=	=	SYM
ap-1366	20	26	0	0	X
ap-1366	20	27	.	.	PUNCT
ap-1366	20	28	(	(	PUNCT
ap-1366	20	29	2	2	X
ap-1366	20	30	)	)	PUNCT
ap-1366	20	31	here	here	ADV
ap-1366	20	32	f	f	X
ap-1366	20	33	,	,	PUNCT
ap-1366	20	34	h	h	NOUN
ap-1366	20	35	,	,	PUNCT
ap-1366	20	36	v	v	NOUN
ap-1366	20	37	are	be	AUX
ap-1366	20	38	smooth	smooth	ADJ
ap-1366	20	39	,	,	PUNCT
ap-1366	20	40	real	real	ADJ
ap-1366	20	41	functions	function	NOUN
ap-1366	20	42	,	,	PUNCT
ap-1366	20	43	with	with	ADP
ap-1366	20	44	f	f	PROPN
ap-1366	20	45	,	,	PUNCT
ap-1366	20	46	h	h	NOUN
ap-1366	20	47	positive	positive	ADJ
ap-1366	20	48	and	and	CCONJ
ap-1366	20	49	bounded	bound	VERB
ap-1366	20	50	in	in	ADP
ap-1366	20	51	a	a	PRON
ap-1366	20	52	and	and	CCONJ
ap-1366	20	53	b.	b.	X
ap-1366	21	1	the	the	DET
ap-1366	21	2	constant	constant	ADJ
ap-1366	21	3	e	e	NOUN
ap-1366	21	4	will	will	AUX
ap-1366	21	5	be	be	AUX
ap-1366	21	6	referred	refer	VERB
ap-1366	21	7	to	to	ADP
ap-1366	21	8	as	as	ADP
ap-1366	21	9	energy	energy	NOUN
ap-1366	21	10	,	,	PUNCT
ap-1366	21	11	and	and	CCONJ
ap-1366	21	12	in	in	ADP
ap-1366	21	13	solutions	solution	NOUN
ap-1366	21	14	of	of	ADP
ap-1366	21	15	(	(	PUNCT
ap-1366	21	16	1	1	NUM
ap-1366	21	17	)	)	PUNCT
ap-1366	21	18	,	,	PUNCT
ap-1366	21	19	(	(	PUNCT
ap-1366	21	20	2	2	X
ap-1366	21	21	)	)	PUNCT
ap-1366	21	22	that	that	PRON
ap-1366	21	23	belong	belong	VERB
ap-1366	21	24	to	to	ADP
ap-1366	21	25	the	the	DET
ap-1366	21	26	discrete	discrete	ADJ
ap-1366	21	27	spectrum	spectrum	NOUN
ap-1366	21	28	,	,	PUNCT
ap-1366	21	29	e	e	PROPN
ap-1366	21	30	stands	stand	VERB
ap-1366	21	31	for	for	ADP
ap-1366	21	32	the	the	DET
ap-1366	21	33	spectral	spectral	ADJ
ap-1366	21	34	value	value	NOUN
ap-1366	21	35	.	.	PUNCT
ap-1366	22	1	any	any	DET
ap-1366	22	2	solution	solution	NOUN
ap-1366	22	3	ψ	ψ	X
ap-1366	22	4	of	of	ADP
ap-1366	22	5	(	(	PUNCT
ap-1366	22	6	1	1	NUM
ap-1366	22	7	)	)	PUNCT
ap-1366	22	8	,	,	PUNCT
ap-1366	22	9	(	(	PUNCT
ap-1366	22	10	2	2	X
ap-1366	22	11	)	)	PUNCT
ap-1366	22	12	belonging	belong	VERB
ap-1366	22	13	to	to	ADP
ap-1366	22	14	a	a	DET
ap-1366	22	15	value	value	NOUN
ap-1366	22	16	e	e	NOUN
ap-1366	22	17	from	from	ADP
ap-1366	22	18	the	the	DET
ap-1366	22	19	discrete	discrete	ADJ
ap-1366	22	20	spectrum	spectrum	NOUN
ap-1366	22	21	,	,	PUNCT
ap-1366	22	22	is	be	AUX
ap-1366	22	23	located	locate	VERB
ap-1366	22	24	in	in	ADP
ap-1366	22	25	the	the	DET
ap-1366	22	26	weighted	weight	VERB
ap-1366	22	27	hilbert	hilbert	PROPN
ap-1366	22	28	space	space	PROPN
ap-1366	22	29	l2h(a	l2h(a	PROPN
ap-1366	22	30	,	,	PUNCT
ap-1366	22	31	b	b	NOUN
ap-1366	22	32	)	)	PUNCT
ap-1366	22	33	with	with	ADP
ap-1366	22	34	weight	weight	NOUN
ap-1366	22	35	function	function	NOUN
ap-1366	22	36	h	h	NOUN
ap-1366	23	1	[	[	X
ap-1366	23	2	4	4	NUM
ap-1366	23	3	]	]	PUNCT
ap-1366	23	4	.	.	PUNCT
ap-1366	24	1	the	the	DET
ap-1366	24	2	lowest	low	ADJ
ap-1366	24	3	value	value	NOUN
ap-1366	24	4	of	of	ADP
ap-1366	24	5	the	the	DET
ap-1366	24	6	discrete	discrete	ADJ
ap-1366	24	7	spectrum	spectrum	NOUN
ap-1366	24	8	will	will	AUX
ap-1366	24	9	be	be	AUX
ap-1366	24	10	called	call	VERB
ap-1366	24	11	the	the	DET
ap-1366	24	12	ground	ground	NOUN
ap-1366	24	13	state	state	NOUN
ap-1366	24	14	and	and	CCONJ
ap-1366	24	15	denoted	denote	VERB
ap-1366	24	16	by	by	ADP
ap-1366	24	17	e0	e0	PROPN
ap-1366	24	18	with	with	ADP
ap-1366	24	19	corresponding	corresponding	ADJ
ap-1366	24	20	solution	solution	NOUN
ap-1366	24	21	ψ0	ψ0	PROPN
ap-1366	24	22	.	.	PUNCT
ap-1366	25	1	the	the	DET
ap-1366	25	2	interval	interval	NOUN
ap-1366	25	3	(	(	PUNCT
ap-1366	25	4	a	a	DET
ap-1366	25	5	,	,	PUNCT
ap-1366	25	6	b	b	NOUN
ap-1366	25	7	)	)	PUNCT
ap-1366	25	8	can	can	AUX
ap-1366	25	9	be	be	AUX
ap-1366	25	10	unbounded	unbounde	VERB
ap-1366	25	11	,	,	PUNCT
ap-1366	25	12	that	that	ADV
ap-1366	25	13	is	is	ADV
ap-1366	25	14	,	,	PUNCT
ap-1366	25	15	a	a	PRON
ap-1366	25	16	or	or	CCONJ
ap-1366	25	17	b	b	NOUN
ap-1366	25	18	can	can	AUX
ap-1366	25	19	represent	represent	VERB
ap-1366	25	20	minus	minus	ADP
ap-1366	25	21	infinity	infinity	NOUN
ap-1366	25	22	or	or	CCONJ
ap-1366	25	23	infinity	infinity	NOUN
ap-1366	25	24	,	,	PUNCT
ap-1366	25	25	respectively	respectively	ADV
ap-1366	25	26	(	(	PUNCT
ap-1366	25	27	however	however	ADV
ap-1366	25	28	,	,	PUNCT
ap-1366	25	29	if	if	SCONJ
ap-1366	25	30	a	a	DET
ap-1366	25	31	and/or	and/or	CCONJ
ap-1366	25	32	b	b	NOUN
ap-1366	25	33	are	be	AUX
ap-1366	25	34	finite	finite	ADJ
ap-1366	25	35	,	,	PUNCT
ap-1366	25	36	then	then	ADV
ap-1366	25	37	we	we	PRON
ap-1366	25	38	require	require	VERB
ap-1366	25	39	f	f	PROPN
ap-1366	25	40	,	,	PUNCT
ap-1366	25	41	h	h	NOUN
ap-1366	25	42	,	,	PUNCT
ap-1366	25	43	v	v	NOUN
ap-1366	25	44	to	to	PART
ap-1366	25	45	be	be	AUX
ap-1366	25	46	continuous	continuous	ADJ
ap-1366	25	47	there	there	ADV
ap-1366	25	48	)	)	PUNCT
ap-1366	25	49	.	.	PUNCT
ap-1366	26	1	we	we	PRON
ap-1366	26	2	see	see	VERB
ap-1366	26	3	that	that	SCONJ
ap-1366	26	4	the	the	DET
ap-1366	26	5	problem	problem	NOUN
ap-1366	26	6	(	(	PUNCT
ap-1366	26	7	1	1	NUM
ap-1366	26	8	)	)	PUNCT
ap-1366	26	9	,	,	PUNCT
ap-1366	26	10	(	(	PUNCT
ap-1366	26	11	2	2	X
ap-1366	26	12	)	)	PUNCT
ap-1366	26	13	can	can	AUX
ap-1366	26	14	be	be	AUX
ap-1366	26	15	singular	singular	ADJ
ap-1366	26	16	,	,	PUNCT
ap-1366	26	17	which	which	PRON
ap-1366	26	18	means	mean	VERB
ap-1366	26	19	that	that	SCONJ
ap-1366	26	20	its	its	PRON
ap-1366	26	21	spectrum	spectrum	NOUN
ap-1366	26	22	can	can	AUX
ap-1366	26	23	admit	admit	VERB
ap-1366	26	24	a	a	DET
ap-1366	26	25	continuous	continuous	ADJ
ap-1366	26	26	part	part	NOUN
ap-1366	26	27	.	.	PUNCT
ap-1366	27	1	equation	equation	NOUN
ap-1366	27	2	(	(	PUNCT
ap-1366	27	3	1	1	X
ap-1366	27	4	)	)	PUNCT
ap-1366	27	5	will	will	AUX
ap-1366	27	6	be	be	AUX
ap-1366	27	7	referred	refer	VERB
ap-1366	27	8	to	to	ADP
ap-1366	27	9	as	as	ADP
ap-1366	27	10	the	the	DET
ap-1366	27	11	generalized	generalized	ADJ
ap-1366	27	12	schrödinger	schrödinger	NOUN
ap-1366	27	13	equation	equation	NOUN
ap-1366	27	14	,	,	PUNCT
ap-1366	27	15	since	since	SCONJ
ap-1366	27	16	its	its	PRON
ap-1366	27	17	special	special	ADJ
ap-1366	27	18	cases	case	NOUN
ap-1366	27	19	are	be	AUX
ap-1366	27	20	frequently	frequently	ADV
ap-1366	27	21	encountered	encounter	VERB
ap-1366	27	22	in	in	ADP
ap-1366	27	23	quantum	quantum	ADJ
ap-1366	27	24	mechanics	mechanic	NOUN
ap-1366	27	25	,	,	PUNCT
ap-1366	27	26	such	such	ADJ
ap-1366	27	27	as	as	ADP
ap-1366	27	28	the	the	DET
ap-1366	27	29	schrödinger	schrödinger	NOUN
ap-1366	27	30	equation	equation	NOUN
ap-1366	27	31	for	for	ADP
ap-1366	27	32	effective	effective	ADJ
ap-1366	27	33	mass	mass	NOUN
ap-1366	27	34	or	or	CCONJ
ap-1366	27	35	with	with	ADP
ap-1366	27	36	a	a	DET
ap-1366	27	37	linearly	linearly	ADV
ap-1366	27	38	energy	energy	NOUN
ap-1366	27	39	-	-	PUNCT
ap-1366	27	40	dependent	dependent	ADJ
ap-1366	27	41	potential	potential	NOUN
ap-1366	27	42	.	.	PUNCT
ap-1366	28	1	in	in	ADP
ap-1366	28	2	the	the	DET
ap-1366	28	3	quantum	quantum	NOUN
ap-1366	28	4	-	-	ADJ
ap-1366	28	5	mechanical	mechanical	ADJ
ap-1366	28	6	context	context	NOUN
ap-1366	28	7	,	,	PUNCT
ap-1366	28	8	e	e	PROPN
ap-1366	28	9	denotes	denote	VERB
ap-1366	28	10	the	the	DET
ap-1366	28	11	energy	energy	NOUN
ap-1366	28	12	associated	associate	VERB
ap-1366	28	13	with	with	ADP
ap-1366	28	14	a	a	DET
ap-1366	28	15	solution	solution	NOUN
ap-1366	28	16	ψ	ψ	NOUN
ap-1366	28	17	,	,	PUNCT
ap-1366	28	18	and	and	CCONJ
ap-1366	28	19	v	v	X
ap-1366	28	20	stands	stand	VERB
ap-1366	28	21	for	for	ADP
ap-1366	28	22	the	the	DET
ap-1366	28	23	potential	potential	NOUN
ap-1366	28	24	.	.	PUNCT
ap-1366	29	1	generalized	generalized	ADJ
ap-1366	29	2	susy	susy	NOUN
ap-1366	29	3	formalism	formalism	NOUN
ap-1366	29	4	.	.	PUNCT
ap-1366	30	1	we	we	PRON
ap-1366	30	2	summarize	summarize	VERB
ap-1366	30	3	results	result	NOUN
ap-1366	30	4	from	from	ADP
ap-1366	30	5	[	[	X
ap-1366	30	6	10	10	NUM
ap-1366	30	7	]	]	PUNCT
ap-1366	30	8	.	.	PUNCT
ap-1366	31	1	the	the	DET
ap-1366	31	2	boundary	boundary	ADJ
ap-1366	31	3	-	-	PUNCT
ap-1366	31	4	value	value	NOUN
ap-1366	31	5	problem	problem	NOUN
ap-1366	31	6	(	(	PUNCT
ap-1366	31	7	1	1	NUM
ap-1366	31	8	)	)	PUNCT
ap-1366	31	9	,	,	PUNCT
ap-1366	31	10	(	(	PUNCT
ap-1366	31	11	2	2	X
ap-1366	31	12	)	)	PUNCT
ap-1366	31	13	can	can	AUX
ap-1366	31	14	be	be	AUX
ap-1366	31	15	linked	link	VERB
ap-1366	31	16	to	to	ADP
ap-1366	31	17	another	another	DET
ap-1366	31	18	problem	problem	NOUN
ap-1366	31	19	of	of	ADP
ap-1366	31	20	the	the	DET
ap-1366	31	21	same	same	ADJ
ap-1366	31	22	kind	kind	NOUN
ap-1366	31	23	by	by	ADP
ap-1366	31	24	means	mean	NOUN
ap-1366	31	25	of	of	ADP
ap-1366	31	26	the	the	DET
ap-1366	31	27	susy	susy	NOUN
ap-1366	31	28	transformation	transformation	NOUN
ap-1366	31	29	method	method	NOUN
ap-1366	31	30	.	.	PUNCT
ap-1366	32	1	consider	consider	VERB
ap-1366	32	2	f(x)φ′′(x	f(x)φ′′(x	NOUN
ap-1366	32	3	)	)	PUNCT
ap-1366	33	1	+	+	NUM
ap-1366	33	2	f	f	PROPN
ap-1366	33	3	′(x)φ′(x	′(x)φ′(x	NOUN
ap-1366	33	4	)	)	PUNCT
ap-1366	33	5	+	+	CCONJ
ap-1366	33	6	63	63	NUM
ap-1366	33	7	acta	acta	PROPN
ap-1366	33	8	polytechnica	polytechnica	PROPN
ap-1366	33	9	vol	vol	NOUN
ap-1366	33	10	.	.	PUNCT
ap-1366	34	1	51	51	NUM
ap-1366	35	1	no	no	INTJ
ap-1366	35	2	.	.	PUNCT
ap-1366	36	1	1/2011	1/2011	NUM
ap-1366	37	1	[	[	X
ap-1366	37	2	eh(x	eh(x	NUM
ap-1366	37	3	)	)	PUNCT
ap-1366	37	4	−	−	PROPN
ap-1366	37	5	u(x)]φ(x	u(x)]φ(x	PROPN
ap-1366	37	6	)	)	PUNCT
ap-1366	37	7	=	=	SYM
ap-1366	38	1	0	0	NUM
ap-1366	38	2	,	,	PUNCT
ap-1366	38	3	x	x	SYM
ap-1366	38	4	∈	∈	PROPN
ap-1366	38	5	(	(	PUNCT
ap-1366	38	6	a	a	DET
ap-1366	38	7	,	,	PUNCT
ap-1366	38	8	b	b	NOUN
ap-1366	38	9	)	)	PUNCT
ap-1366	38	10	(	(	PUNCT
ap-1366	38	11	3	3	X
ap-1366	38	12	)	)	PUNCT
ap-1366	38	13	φ(a	φ(a	ADJ
ap-1366	38	14	)	)	PUNCT
ap-1366	38	15	=	=	PUNCT
ap-1366	39	1	φ(b	φ(b	X
ap-1366	39	2	)	)	PUNCT
ap-1366	39	3	=	=	SYM
ap-1366	39	4	0	0	NUM
ap-1366	39	5	,	,	PUNCT
ap-1366	39	6	(	(	PUNCT
ap-1366	39	7	4	4	X
ap-1366	39	8	)	)	PUNCT
ap-1366	39	9	where	where	SCONJ
ap-1366	39	10	the	the	DET
ap-1366	39	11	same	same	ADJ
ap-1366	39	12	settings	setting	NOUN
ap-1366	39	13	imposed	impose	VERB
ap-1366	39	14	for	for	ADP
ap-1366	39	15	(	(	PUNCT
ap-1366	39	16	1	1	NUM
ap-1366	39	17	)	)	PUNCT
ap-1366	39	18	,	,	PUNCT
ap-1366	39	19	(	(	PUNCT
ap-1366	39	20	2	2	X
ap-1366	39	21	)	)	PUNCT
ap-1366	39	22	apply	apply	VERB
ap-1366	39	23	.	.	PUNCT
ap-1366	40	1	clearly	clearly	ADV
ap-1366	40	2	,	,	PUNCT
ap-1366	40	3	a	a	DET
ap-1366	40	4	solution	solution	NOUN
ap-1366	40	5	φ	φ	NOUN
ap-1366	40	6	=	=	SYM
ap-1366	40	7	φ(x	φ(x	PROPN
ap-1366	40	8	)	)	PUNCT
ap-1366	40	9	and	and	CCONJ
ap-1366	40	10	the	the	DET
ap-1366	40	11	potential	potential	ADJ
ap-1366	40	12	u	u	NOUN
ap-1366	40	13	=	=	SYM
ap-1366	40	14	u(x	u(x	PROPN
ap-1366	40	15	)	)	PUNCT
ap-1366	40	16	are	be	AUX
ap-1366	40	17	in	in	ADP
ap-1366	40	18	general	general	ADJ
ap-1366	40	19	different	different	ADJ
ap-1366	40	20	from	from	ADP
ap-1366	40	21	their	their	PRON
ap-1366	40	22	respective	respective	ADJ
ap-1366	40	23	counterparts	counterpart	NOUN
ap-1366	40	24	ψ	ψ	PROPN
ap-1366	40	25	and	and	CCONJ
ap-1366	40	26	v	v	NOUN
ap-1366	40	27	.	.	PUNCT
ap-1366	41	1	now	now	ADV
ap-1366	41	2	,	,	PUNCT
ap-1366	41	3	suppose	suppose	VERB
ap-1366	41	4	that	that	SCONJ
ap-1366	41	5	ψ	ψ	PROPN
ap-1366	41	6	and	and	CCONJ
ap-1366	41	7	u	u	NOUN
ap-1366	41	8	are	be	AUX
ap-1366	41	9	solutions	solution	NOUN
ap-1366	41	10	of	of	ADP
ap-1366	41	11	the	the	DET
ap-1366	41	12	boundary	boundary	ADJ
ap-1366	41	13	-	-	PUNCT
ap-1366	41	14	value	value	NOUN
ap-1366	41	15	problem	problem	NOUN
ap-1366	41	16	(	(	PUNCT
ap-1366	41	17	1	1	NUM
ap-1366	41	18	)	)	PUNCT
ap-1366	41	19	,	,	PUNCT
ap-1366	41	20	(	(	PUNCT
ap-1366	41	21	2	2	NUM
ap-1366	41	22	)	)	PUNCT
ap-1366	41	23	and	and	CCONJ
ap-1366	41	24	of	of	ADP
ap-1366	41	25	equation	equation	NOUN
ap-1366	41	26	(	(	PUNCT
ap-1366	41	27	1	1	NUM
ap-1366	41	28	)	)	PUNCT
ap-1366	41	29	at	at	ADP
ap-1366	41	30	real	real	ADJ
ap-1366	41	31	energies	energy	NOUN
ap-1366	41	32	e	e	NOUN
ap-1366	41	33	and	and	CCONJ
ap-1366	41	34	λ	λ	X
ap-1366	41	35	≤	≤	NOUN
ap-1366	41	36	e	e	NOUN
ap-1366	41	37	,	,	PUNCT
ap-1366	41	38	respectively	respectively	ADV
ap-1366	41	39	.	.	PUNCT
ap-1366	42	1	define	define	VERB
ap-1366	42	2	the	the	DET
ap-1366	42	3	susy	susy	NOUN
ap-1366	42	4	transformation	transformation	NOUN
ap-1366	42	5	of	of	ADP
ap-1366	42	6	ψ	ψ	NOUN
ap-1366	42	7	as	as	ADP
ap-1366	42	8	du	du	PROPN
ap-1366	42	9	,	,	PUNCT
ap-1366	42	10	xψ(x	xψ(x	NUM
ap-1366	42	11	)	)	PUNCT
ap-1366	42	12	=	=	SYM
ap-1366	42	13	√	√	NUM
ap-1366	42	14	f(x	f(x	PROPN
ap-1366	42	15	)	)	PUNCT
ap-1366	42	16	h(x	h(x	PROPN
ap-1366	42	17	)	)	PUNCT
ap-1366	43	1	w	w	PROPN
ap-1366	43	2	(	(	PUNCT
ap-1366	43	3	u	u	NOUN
ap-1366	43	4	,	,	PUNCT
ap-1366	43	5	ψ)(x	ψ)(x	NOUN
ap-1366	43	6	)	)	PUNCT
ap-1366	43	7	u(x	u(x	PROPN
ap-1366	43	8	)	)	PUNCT
ap-1366	44	1	=	=	VERB
ap-1366	44	2	√	√	NUM
ap-1366	44	3	f(x	f(x	PROPN
ap-1366	44	4	)	)	PUNCT
ap-1366	44	5	h(x	h(x	PROPN
ap-1366	44	6	)	)	PUNCT
ap-1366	44	7	[	[	PUNCT
ap-1366	44	8	−u′(x	−u′(x	PROPN
ap-1366	44	9	)	)	PUNCT
ap-1366	44	10	u(x	u(x	PROPN
ap-1366	44	11	)	)	PUNCT
ap-1366	44	12	ψ(x	ψ(x	NOUN
ap-1366	44	13	)	)	PUNCT
ap-1366	45	1	+	+	PUNCT
ap-1366	45	2	ψ′(x	ψ′(x	X
ap-1366	45	3	)	)	PUNCT
ap-1366	45	4	]	]	PUNCT
ap-1366	45	5	,	,	PUNCT
ap-1366	45	6	(	(	PUNCT
ap-1366	45	7	5	5	X
ap-1366	45	8	)	)	PUNCT
ap-1366	45	9	where	where	SCONJ
ap-1366	45	10	w	w	PROPN
ap-1366	45	11	(	(	PUNCT
ap-1366	45	12	u	u	NOUN
ap-1366	45	13	,	,	PUNCT
ap-1366	45	14	ψ	ψ	NOUN
ap-1366	45	15	)	)	PUNCT
ap-1366	45	16	stands	stand	VERB
ap-1366	45	17	for	for	ADP
ap-1366	45	18	the	the	DET
ap-1366	45	19	wronskian	wronskian	NOUN
ap-1366	45	20	of	of	ADP
ap-1366	45	21	the	the	DET
ap-1366	45	22	functions	function	NOUN
ap-1366	45	23	u	u	NOUN
ap-1366	45	24	,	,	PUNCT
ap-1366	45	25	ψ	ψ	X
ap-1366	45	26	and	and	CCONJ
ap-1366	45	27	the	the	DET
ap-1366	45	28	second	second	ADJ
ap-1366	45	29	index	index	NOUN
ap-1366	45	30	ofd	ofd	NOUN
ap-1366	45	31	denotes	denote	VERB
ap-1366	45	32	the	the	DET
ap-1366	45	33	variable	variable	NOUN
ap-1366	45	34	which	which	PRON
ap-1366	45	35	the	the	DET
ap-1366	45	36	derivatives	derivative	NOUN
ap-1366	45	37	in	in	ADP
ap-1366	45	38	the	the	DET
ap-1366	45	39	wronskian	wronskian	NOUN
ap-1366	45	40	apply	apply	VERB
ap-1366	45	41	to	to	ADP
ap-1366	45	42	.	.	PUNCT
ap-1366	46	1	the	the	DET
ap-1366	46	2	function	function	NOUN
ap-1366	46	3	φ	φ	NOUN
ap-1366	46	4	=	=	SYM
ap-1366	46	5	du	du	PROPN
ap-1366	46	6	,	,	PUNCT
ap-1366	46	7	xψ	xψ	ADP
ap-1366	46	8	as	as	SCONJ
ap-1366	46	9	defined	define	VERB
ap-1366	46	10	in	in	ADP
ap-1366	46	11	(	(	PUNCT
ap-1366	46	12	5	5	X
ap-1366	46	13	)	)	PUNCT
ap-1366	46	14	solves	solve	VERB
ap-1366	46	15	the	the	DET
ap-1366	46	16	boundary	boundary	ADJ
ap-1366	46	17	-	-	PUNCT
ap-1366	46	18	value	value	NOUN
ap-1366	46	19	problem	problem	NOUN
ap-1366	46	20	(	(	PUNCT
ap-1366	46	21	3	3	NUM
ap-1366	46	22	)	)	PUNCT
ap-1366	46	23	,	,	PUNCT
ap-1366	46	24	(	(	PUNCT
ap-1366	46	25	4	4	NUM
ap-1366	46	26	)	)	PUNCT
ap-1366	46	27	,	,	PUNCT
ap-1366	46	28	if	if	SCONJ
ap-1366	46	29	the	the	DET
ap-1366	46	30	potential	potential	ADJ
ap-1366	46	31	u	u	NOUN
ap-1366	46	32	is	be	AUX
ap-1366	46	33	given	give	VERB
ap-1366	46	34	in	in	ADP
ap-1366	46	35	terms	term	NOUN
ap-1366	46	36	of	of	ADP
ap-1366	46	37	its	its	PRON
ap-1366	46	38	counterpart	counterpart	NOUN
ap-1366	46	39	v	v	NOUN
ap-1366	46	40	,	,	PUNCT
ap-1366	46	41	as	as	SCONJ
ap-1366	46	42	follows	follow	VERB
ap-1366	46	43	:	:	PUNCT
ap-1366	46	44	u(x	u(x	NOUN
ap-1366	46	45	)	)	PUNCT
ap-1366	47	1	=	=	SYM
ap-1366	47	2	v	v	X
ap-1366	47	3	(	(	PUNCT
ap-1366	47	4	x	x	NOUN
ap-1366	47	5	)	)	PUNCT
ap-1366	47	6	−	−	PROPN
ap-1366	47	7	2f(x	2f(x	NUM
ap-1366	47	8	)	)	PUNCT
ap-1366	47	9	d	d	ADP
ap-1366	47	10	2	2	NUM
ap-1366	47	11	dx2	dx2	NOUN
ap-1366	47	12	{	{	PUNCT
ap-1366	47	13	log	log	NOUN
ap-1366	47	14	[	[	X
ap-1366	47	15	u(x	u(x	NOUN
ap-1366	47	16	)	)	PUNCT
ap-1366	47	17	]	]	PUNCT
ap-1366	47	18	}	}	PUNCT
ap-1366	48	1	+	+	PROPN
ap-1366	48	2	[	[	PUNCT
ap-1366	48	3	f(x)h′(x	f(x)h′(x	PROPN
ap-1366	48	4	)	)	PUNCT
ap-1366	48	5	h(x	h(x	PROPN
ap-1366	48	6	)	)	PUNCT
ap-1366	49	1	−	−	PROPN
ap-1366	49	2	f	f	PROPN
ap-1366	49	3	′(x	′(x	PROPN
ap-1366	49	4	)	)	PUNCT
ap-1366	49	5	]	]	PUNCT
ap-1366	49	6	u′(x	u′(x	X
ap-1366	49	7	)	)	PUNCT
ap-1366	49	8	u(x	u(x	PROPN
ap-1366	49	9	)	)	PUNCT
ap-1366	49	10	−	−	PROPN
ap-1366	49	11	f	f	PROPN
ap-1366	49	12	′′(x	′′(x	NOUN
ap-1366	49	13	)	)	PUNCT
ap-1366	49	14	2	2	NUM
ap-1366	50	1	+	+	CCONJ
ap-1366	50	2	[	[	X
ap-1366	50	3	f	f	X
ap-1366	50	4	′(x)]2	′(x)]2	PUNCT
ap-1366	50	5	4f(x	4f(x	NUM
ap-1366	50	6	)	)	PUNCT
ap-1366	51	1	+	+	CCONJ
ap-1366	51	2	3f(x)[h′(x)]2	3f(x)[h′(x)]2	NUM
ap-1366	51	3	4h2(x	4h2(x	NUM
ap-1366	51	4	)	)	PUNCT
ap-1366	51	5	−	−	PRON
ap-1366	51	6	f(x)h′′(x	f(x)h′′(x	PROPN
ap-1366	51	7	)	)	PUNCT
ap-1366	51	8	h(x	h(x	PROPN
ap-1366	51	9	)	)	PUNCT
ap-1366	51	10	.	.	PUNCT
ap-1366	52	1	(	(	PUNCT
ap-1366	52	2	6	6	X
ap-1366	52	3	)	)	PUNCT
ap-1366	52	4	note	note	NOUN
ap-1366	52	5	that	that	SCONJ
ap-1366	52	6	(	(	PUNCT
ap-1366	52	7	5	5	X
ap-1366	52	8	)	)	PUNCT
ap-1366	52	9	remains	remain	VERB
ap-1366	52	10	valid	valid	ADJ
ap-1366	52	11	when	when	SCONJ
ap-1366	52	12	multiplied	multiply	VERB
ap-1366	52	13	by	by	ADP
ap-1366	52	14	a	a	DET
ap-1366	52	15	constant	constant	ADJ
ap-1366	52	16	,	,	PUNCT
ap-1366	52	17	which	which	PRON
ap-1366	52	18	can	can	AUX
ap-1366	52	19	be	be	AUX
ap-1366	52	20	used	use	VERB
ap-1366	52	21	for	for	ADP
ap-1366	52	22	normalization	normalization	NOUN
ap-1366	52	23	.	.	PUNCT
ap-1366	53	1	now	now	ADV
ap-1366	53	2	,	,	PUNCT
ap-1366	53	3	depending	depend	VERB
ap-1366	53	4	on	on	ADP
ap-1366	53	5	the	the	DET
ap-1366	53	6	choice	choice	NOUN
ap-1366	53	7	of	of	ADP
ap-1366	53	8	the	the	DET
ap-1366	53	9	auxiliary	auxiliary	ADJ
ap-1366	53	10	solution	solution	NOUN
ap-1366	53	11	u	u	NOUN
ap-1366	53	12	in	in	ADP
ap-1366	53	13	(	(	PUNCT
ap-1366	53	14	5	5	NUM
ap-1366	53	15	)	)	PUNCT
ap-1366	53	16	,	,	PUNCT
ap-1366	53	17	the	the	DET
ap-1366	53	18	discrete	discrete	ADJ
ap-1366	53	19	spectrum	spectrum	NOUN
ap-1366	53	20	of	of	ADP
ap-1366	53	21	problem	problem	NOUN
ap-1366	53	22	(	(	PUNCT
ap-1366	53	23	3	3	NUM
ap-1366	53	24	)	)	PUNCT
ap-1366	53	25	,	,	PUNCT
ap-1366	53	26	(	(	PUNCT
ap-1366	53	27	4	4	X
ap-1366	53	28	)	)	PUNCT
ap-1366	53	29	can	can	AUX
ap-1366	53	30	be	be	AUX
ap-1366	53	31	affected	affect	VERB
ap-1366	53	32	in	in	ADP
ap-1366	53	33	three	three	NUM
ap-1366	53	34	possible	possible	ADJ
ap-1366	53	35	ways	way	NOUN
ap-1366	53	36	:	:	PUNCT
ap-1366	53	37	if	if	SCONJ
ap-1366	53	38	λ	λ	PROPN
ap-1366	53	39	=	=	SYM
ap-1366	53	40	e0	e0	PROPN
ap-1366	53	41	and	and	CCONJ
ap-1366	53	42	u	u	NOUN
ap-1366	53	43	=	=	PROPN
ap-1366	53	44	ψ0	ψ0	PROPN
ap-1366	53	45	,	,	PUNCT
ap-1366	53	46	then	then	ADV
ap-1366	53	47	e0	e0	PROPN
ap-1366	53	48	is	be	AUX
ap-1366	53	49	removed	remove	VERB
ap-1366	53	50	from	from	ADP
ap-1366	53	51	the	the	DET
ap-1366	53	52	spectrum	spectrum	NOUN
ap-1366	53	53	of	of	ADP
ap-1366	53	54	(	(	PUNCT
ap-1366	53	55	3	3	NUM
ap-1366	53	56	)	)	PUNCT
ap-1366	53	57	,	,	PUNCT
ap-1366	53	58	(	(	PUNCT
ap-1366	53	59	4	4	NUM
ap-1366	53	60	)	)	PUNCT
ap-1366	53	61	.	.	PUNCT
ap-1366	54	1	the	the	DET
ap-1366	54	2	opposite	opposite	ADJ
ap-1366	54	3	case	case	NOUN
ap-1366	54	4	,	,	PUNCT
ap-1366	54	5	creation	creation	NOUN
ap-1366	54	6	of	of	ADP
ap-1366	54	7	a	a	DET
ap-1366	54	8	new	new	ADJ
ap-1366	54	9	spectral	spectral	ADJ
ap-1366	54	10	value	value	NOUN
ap-1366	54	11	λ	λ	PROPN
ap-1366	54	12	<	<	X
ap-1366	54	13	e0	e0	PROPN
ap-1366	54	14	,	,	PUNCT
ap-1366	54	15	happens	happen	VERB
ap-1366	54	16	if	if	SCONJ
ap-1366	54	17	the	the	DET
ap-1366	54	18	auxiliary	auxiliary	ADJ
ap-1366	54	19	solution	solution	NOUN
ap-1366	54	20	u	u	NOUN
ap-1366	54	21	does	do	AUX
ap-1366	54	22	not	not	PART
ap-1366	54	23	fulfill	fulfill	VERB
ap-1366	54	24	the	the	DET
ap-1366	54	25	boundary	boundary	ADJ
ap-1366	54	26	conditions	condition	NOUN
ap-1366	54	27	(	(	PUNCT
ap-1366	54	28	4	4	NUM
ap-1366	54	29	)	)	PUNCT
ap-1366	54	30	.	.	PUNCT
ap-1366	55	1	finally	finally	ADV
ap-1366	55	2	,	,	PUNCT
ap-1366	55	3	the	the	DET
ap-1366	55	4	spectra	spectra	NOUN
ap-1366	55	5	of	of	ADP
ap-1366	55	6	both	both	DET
ap-1366	55	7	problems	problem	NOUN
ap-1366	55	8	(	(	PUNCT
ap-1366	55	9	1	1	NUM
ap-1366	55	10	)	)	PUNCT
ap-1366	55	11	,	,	PUNCT
ap-1366	55	12	(	(	PUNCT
ap-1366	55	13	2	2	X
ap-1366	55	14	)	)	PUNCT
ap-1366	55	15	and	and	CCONJ
ap-1366	55	16	(	(	PUNCT
ap-1366	55	17	3	3	NUM
ap-1366	55	18	)	)	PUNCT
ap-1366	55	19	,	,	PUNCT
ap-1366	55	20	(	(	PUNCT
ap-1366	55	21	4	4	X
ap-1366	55	22	)	)	PUNCT
ap-1366	55	23	are	be	AUX
ap-1366	55	24	the	the	DET
ap-1366	55	25	same	same	ADJ
ap-1366	55	26	,	,	PUNCT
ap-1366	55	27	if	if	SCONJ
ap-1366	55	28	we	we	PRON
ap-1366	55	29	pick	pick	VERB
ap-1366	55	30	λ	λ	PROPN
ap-1366	55	31	<	<	X
ap-1366	55	32	e0	e0	PROPN
ap-1366	55	33	and	and	CCONJ
ap-1366	55	34	u	u	NOUN
ap-1366	55	35	that	that	PRON
ap-1366	55	36	fulfills	fulfill	VERB
ap-1366	55	37	only	only	ADV
ap-1366	55	38	one	one	NUM
ap-1366	55	39	of	of	ADP
ap-1366	55	40	the	the	DET
ap-1366	55	41	boundary	boundary	ADJ
ap-1366	55	42	conditions	condition	NOUN
ap-1366	55	43	(	(	PUNCT
ap-1366	55	44	2	2	NUM
ap-1366	55	45	)	)	PUNCT
ap-1366	55	46	.	.	PUNCT
ap-1366	56	1	propagator	propagator	NOUN
ap-1366	56	2	and	and	CCONJ
ap-1366	56	3	green	green	PROPN
ap-1366	56	4	’s	’s	PART
ap-1366	56	5	function	function	NOUN
ap-1366	56	6	.	.	PUNCT
ap-1366	57	1	the	the	DET
ap-1366	57	2	propagator	propagator	NOUN
ap-1366	57	3	governs	govern	VERB
ap-1366	57	4	a	a	DET
ap-1366	57	5	quantum	quantum	ADJ
ap-1366	57	6	system	system	NOUN
ap-1366	57	7	’s	’s	PART
ap-1366	57	8	time	time	NOUN
ap-1366	57	9	evolution	evolution	NOUN
ap-1366	57	10	.	.	PUNCT
ap-1366	58	1	for	for	ADP
ap-1366	58	2	a	a	DET
ap-1366	58	3	stationary	stationary	ADJ
ap-1366	58	4	schrödinger	schrödinger	NOUN
ap-1366	58	5	equation	equation	NOUN
ap-1366	58	6	,	,	PUNCT
ap-1366	58	7	the	the	DET
ap-1366	58	8	propagatork	propagatork	NOUN
ap-1366	58	9	has	have	VERB
ap-1366	58	10	the	the	DET
ap-1366	58	11	defining	define	VERB
ap-1366	58	12	property	property	NOUN
ap-1366	58	13	ψ(x	ψ(x	PROPN
ap-1366	58	14	,	,	PUNCT
ap-1366	58	15	t	t	PROPN
ap-1366	58	16	)	)	PUNCT
ap-1366	58	17	=	=	SYM
ap-1366	58	18	exp(−iet)ψ(x	exp(−iet)ψ(x	ADJ
ap-1366	58	19	)	)	PUNCT
ap-1366	59	1	=	=	NOUN
ap-1366	59	2	∫	∫	X
ap-1366	59	3	(	(	PUNCT
ap-1366	59	4	a	a	PRON
ap-1366	59	5	,	,	PUNCT
ap-1366	59	6	b	b	NOUN
ap-1366	59	7	)	)	PUNCT
ap-1366	59	8	k(x	k(x	PROPN
ap-1366	59	9	,	,	PUNCT
ap-1366	59	10	y	y	PROPN
ap-1366	59	11	,	,	PUNCT
ap-1366	59	12	t)ψ(y	t)ψ(y	NUM
ap-1366	59	13	)	)	PUNCT
ap-1366	59	14	dy	dy	NOUN
ap-1366	59	15	,	,	PUNCT
ap-1366	59	16	(	(	PUNCT
ap-1366	59	17	7	7	X
ap-1366	59	18	)	)	PUNCT
ap-1366	59	19	as	as	ADP
ap-1366	59	20	the	the	DET
ap-1366	59	21	solution	solution	NOUN
ap-1366	59	22	ψ	ψ	X
ap-1366	59	23	of	of	ADP
ap-1366	59	24	the	the	DET
ap-1366	59	25	time	time	NOUN
ap-1366	59	26	-	-	PUNCT
ap-1366	59	27	dependent	dependent	ADJ
ap-1366	59	28	schrödinger	schrödinger	NOUN
ap-1366	59	29	equation	equation	NOUN
ap-1366	59	30	is	be	AUX
ap-1366	59	31	related	relate	VERB
ap-1366	59	32	to	to	ADP
ap-1366	59	33	its	its	PRON
ap-1366	59	34	stationary	stationary	ADJ
ap-1366	59	35	counterpart	counterpart	NOUN
ap-1366	59	36	ψ	ψ	NOUN
ap-1366	59	37	by	by	ADP
ap-1366	59	38	the	the	DET
ap-1366	59	39	exponential	exponential	ADJ
ap-1366	59	40	factor	factor	NOUN
ap-1366	59	41	used	use	VERB
ap-1366	59	42	for	for	ADP
ap-1366	59	43	separating	separate	VERB
ap-1366	59	44	time	time	NOUN
ap-1366	59	45	and	and	CCONJ
ap-1366	59	46	spatial	spatial	ADJ
ap-1366	59	47	variable	variable	NOUN
ap-1366	59	48	.	.	PUNCT
ap-1366	60	1	suppose	suppose	VERB
ap-1366	60	2	problem	problem	NOUN
ap-1366	60	3	(	(	PUNCT
ap-1366	60	4	1	1	NUM
ap-1366	60	5	)	)	PUNCT
ap-1366	60	6	,	,	PUNCT
ap-1366	60	7	(	(	PUNCT
ap-1366	60	8	2	2	X
ap-1366	60	9	)	)	PUNCT
ap-1366	60	10	admits	admit	VERB
ap-1366	60	11	a	a	DET
ap-1366	60	12	complete	complete	ADJ
ap-1366	60	13	set	set	NOUN
ap-1366	60	14	of	of	ADP
ap-1366	60	15	eigenfunctions	eigenfunction	NOUN
ap-1366	60	16	(	(	PUNCT
ap-1366	60	17	ψn	ψn	NUM
ap-1366	60	18	)	)	PUNCT
ap-1366	60	19	,	,	PUNCT
ap-1366	60	20	n	n	NOUN
ap-1366	60	21	=	=	SYM
ap-1366	60	22	0	0	NUM
ap-1366	60	23	,	,	PUNCT
ap-1366	60	24	1	1	NUM
ap-1366	60	25	,	,	PUNCT
ap-1366	60	26	2	2	NUM
ap-1366	60	27	,	,	PUNCT
ap-1366	60	28	.	.	PUNCT
ap-1366	60	29	.	.	PUNCT
ap-1366	61	1	.	.	PUNCT
ap-1366	62	1	,	,	PUNCT
ap-1366	62	2	m	m	PROPN
ap-1366	62	3	∈	∈	PROPN
ap-1366	62	4	n0	n0	NOUN
ap-1366	62	5	,	,	PUNCT
ap-1366	62	6	where	where	SCONJ
ap-1366	62	7	m	m	PROPN
ap-1366	62	8	can	can	AUX
ap-1366	62	9	stand	stand	VERB
ap-1366	62	10	for	for	ADP
ap-1366	62	11	infinity	infinity	NOUN
ap-1366	62	12	,	,	PUNCT
ap-1366	62	13	and	and	CCONJ
ap-1366	62	14	(	(	PUNCT
ap-1366	62	15	ψk	ψk	NOUN
ap-1366	62	16	)	)	PUNCT
ap-1366	62	17	,	,	PUNCT
ap-1366	62	18	k	k	PROPN
ap-1366	62	19	∈	∈	PROPN
ap-1366	62	20	r	r	NOUN
ap-1366	62	21	,	,	PUNCT
ap-1366	62	22	belonging	belong	VERB
ap-1366	62	23	to	to	ADP
ap-1366	62	24	the	the	DET
ap-1366	62	25	discrete	discrete	NOUN
ap-1366	62	26	and	and	CCONJ
ap-1366	62	27	the	the	DET
ap-1366	62	28	continuous	continuous	ADJ
ap-1366	62	29	part	part	NOUN
ap-1366	62	30	of	of	ADP
ap-1366	62	31	the	the	DET
ap-1366	62	32	spectrum	spectrum	NOUN
ap-1366	62	33	,	,	PUNCT
ap-1366	62	34	respectively	respectively	ADV
ap-1366	62	35	.	.	PUNCT
ap-1366	63	1	then	then	ADV
ap-1366	63	2	the	the	DET
ap-1366	63	3	propagator	propagator	NOUN
ap-1366	63	4	k	k	PROPN
ap-1366	63	5	has	have	VERB
ap-1366	63	6	the	the	DET
ap-1366	63	7	representation	representation	NOUN
ap-1366	63	8	k(x	k(x	PROPN
ap-1366	63	9	,	,	PUNCT
ap-1366	63	10	y	y	PROPN
ap-1366	63	11	,	,	PUNCT
ap-1366	63	12	t	t	PROPN
ap-1366	63	13	)	)	PUNCT
ap-1366	63	14	=	=	SYM
ap-1366	63	15	h(y	h(y	ADV
ap-1366	63	16	)	)	PUNCT
ap-1366	63	17	[	[	PUNCT
ap-1366	63	18	m∑	m∑	CCONJ
ap-1366	63	19	n=0	n=0	NUM
ap-1366	63	20	ψn(x	ψn(x	ADP
ap-1366	63	21	)	)	PUNCT
ap-1366	63	22	exp(−ient)ψn(y	exp(−ient)ψn(y	X
ap-1366	63	23	)	)	PUNCT
ap-1366	64	1	+	+	NOUN
ap-1366	64	2	∫	∫	X
ap-1366	64	3	r	r	NOUN
ap-1366	64	4	ψk(x	ψk(x	NOUN
ap-1366	64	5	)	)	PUNCT
ap-1366	64	6	exp(−ik2t)ψk(y	exp(−ik2t)ψk(y	NUM
ap-1366	64	7	)	)	PUNCT
ap-1366	65	1	dk	dk	X
ap-1366	65	2	]	]	PUNCT
ap-1366	65	3	,	,	PUNCT
ap-1366	65	4	(	(	PUNCT
ap-1366	65	5	8)	8)	NUM
ap-1366	65	6	where	where	SCONJ
ap-1366	65	7	en	en	X
ap-1366	65	8	and	and	CCONJ
ap-1366	65	9	k2	k2	ADJ
ap-1366	65	10	stand	stand	NOUN
ap-1366	65	11	for	for	ADP
ap-1366	65	12	the	the	DET
ap-1366	65	13	spectral	spectral	ADJ
ap-1366	65	14	values	value	NOUN
ap-1366	65	15	belonging	belong	VERB
ap-1366	65	16	to	to	ADP
ap-1366	65	17	the	the	DET
ap-1366	65	18	discrete	discrete	ADJ
ap-1366	65	19	and	and	CCONJ
ap-1366	65	20	continuous	continuous	ADJ
ap-1366	65	21	spectrum	spectrum	NOUN
ap-1366	65	22	,	,	PUNCT
ap-1366	65	23	respectively	respectively	ADV
ap-1366	65	24	.	.	PUNCT
ap-1366	66	1	the	the	DET
ap-1366	66	2	green	green	PROPN
ap-1366	66	3	’s	’s	PART
ap-1366	66	4	function	function	NOUN
ap-1366	66	5	g	g	PROPN
ap-1366	66	6	of	of	ADP
ap-1366	66	7	problem	problem	NOUN
ap-1366	66	8	(	(	PUNCT
ap-1366	66	9	1	1	NUM
ap-1366	66	10	)	)	PUNCT
ap-1366	66	11	,	,	PUNCT
ap-1366	66	12	(	(	PUNCT
ap-1366	66	13	2	2	X
ap-1366	66	14	)	)	PUNCT
ap-1366	66	15	has	have	VERB
ap-1366	66	16	two	two	NUM
ap-1366	66	17	equivalent	equivalent	ADJ
ap-1366	66	18	representations	representation	NOUN
ap-1366	66	19	[	[	X
ap-1366	66	20	4	4	NUM
ap-1366	66	21	]	]	PUNCT
ap-1366	66	22	,	,	PUNCT
ap-1366	66	23	both	both	PRON
ap-1366	66	24	of	of	ADP
ap-1366	66	25	which	which	PRON
ap-1366	66	26	we	we	PRON
ap-1366	66	27	will	will	AUX
ap-1366	66	28	use	use	VERB
ap-1366	66	29	here	here	ADV
ap-1366	66	30	.	.	PUNCT
ap-1366	67	1	in	in	ADP
ap-1366	67	2	order	order	NOUN
ap-1366	67	3	to	to	PART
ap-1366	67	4	state	state	VERB
ap-1366	67	5	the	the	DET
ap-1366	67	6	first	first	ADJ
ap-1366	67	7	representation	representation	NOUN
ap-1366	67	8	,	,	PUNCT
ap-1366	67	9	let	let	VERB
ap-1366	67	10	ψ0,l	ψ0,l	PROPN
ap-1366	67	11	and	and	CCONJ
ap-1366	67	12	ψ0,r	ψ0,r	ADP
ap-1366	67	13	be	be	AUX
ap-1366	67	14	solutions	solution	NOUN
ap-1366	67	15	of	of	ADP
ap-1366	67	16	equation	equation	NOUN
ap-1366	67	17	(	(	PUNCT
ap-1366	67	18	1	1	NUM
ap-1366	67	19	)	)	PUNCT
ap-1366	67	20	that	that	PRON
ap-1366	67	21	fulfill	fulfill	VERB
ap-1366	67	22	the	the	DET
ap-1366	67	23	unilateral	unilateral	ADJ
ap-1366	67	24	boundary	boundary	ADJ
ap-1366	67	25	conditions	condition	NOUN
ap-1366	67	26	ψ0,l(a	ψ0,l(a	ADJ
ap-1366	67	27	)	)	PUNCT
ap-1366	67	28	=	=	SYM
ap-1366	67	29	ψ0,r(b	ψ0,r(b	NOUN
ap-1366	67	30	)	)	PUNCT
ap-1366	67	31	=	=	NOUN
ap-1366	68	1	0	0	X
ap-1366	68	2	.	.	PUNCT
ap-1366	69	1	the	the	DET
ap-1366	69	2	wronskian	wronskian	PROPN
ap-1366	69	3	w	w	PROPN
ap-1366	69	4	(	(	PUNCT
ap-1366	69	5	ψ0,l	ψ0,l	PROPN
ap-1366	69	6	,	,	PUNCT
ap-1366	69	7	ψ0,r	ψ0,r	PROPN
ap-1366	69	8	)	)	PUNCT
ap-1366	69	9	of	of	ADP
ap-1366	69	10	these	these	DET
ap-1366	69	11	funtions	funtion	NOUN
ap-1366	69	12	is	be	AUX
ap-1366	69	13	given	give	VERB
ap-1366	69	14	by	by	ADP
ap-1366	69	15	w	w	PROPN
ap-1366	69	16	(	(	PUNCT
ap-1366	69	17	ψ0,l	ψ0,l	PROPN
ap-1366	69	18	,	,	PUNCT
ap-1366	69	19	ψ0,r)(x	ψ0,r)(x	NOUN
ap-1366	69	20	)	)	PUNCT
ap-1366	69	21	=	=	SYM
ap-1366	69	22	c0	c0	PROPN
ap-1366	69	23	f(x	f(x	PROPN
ap-1366	69	24	)	)	PUNCT
ap-1366	69	25	,	,	PUNCT
ap-1366	69	26	(	(	PUNCT
ap-1366	69	27	9	9	X
ap-1366	69	28	)	)	PUNCT
ap-1366	69	29	where	where	SCONJ
ap-1366	69	30	c0	c0	PROPN
ap-1366	69	31	is	be	AUX
ap-1366	69	32	a	a	DET
ap-1366	69	33	constant	constant	ADJ
ap-1366	69	34	that	that	PRON
ap-1366	69	35	depends	depend	VERB
ap-1366	69	36	on	on	ADP
ap-1366	69	37	the	the	DET
ap-1366	69	38	explicit	explicit	ADJ
ap-1366	69	39	form	form	NOUN
ap-1366	69	40	of	of	ADP
ap-1366	69	41	ψ0,l	ψ0,l	PROPN
ap-1366	69	42	and	and	CCONJ
ap-1366	69	43	ψ0,r	ψ0,r	PROPN
ap-1366	69	44	.	.	PUNCT
ap-1366	70	1	now	now	ADV
ap-1366	70	2	we	we	PRON
ap-1366	70	3	can	can	AUX
ap-1366	70	4	give	give	VERB
ap-1366	70	5	the	the	DET
ap-1366	70	6	first	first	ADJ
ap-1366	70	7	representation	representation	NOUN
ap-1366	70	8	of	of	ADP
ap-1366	70	9	the	the	DET
ap-1366	70	10	green	green	PROPN
ap-1366	70	11	’s	’s	PART
ap-1366	70	12	function	function	PROPN
ap-1366	70	13	g0	g0	NOUN
ap-1366	70	14	for	for	ADP
ap-1366	70	15	our	our	PRON
ap-1366	70	16	boundary	boundary	ADJ
ap-1366	70	17	value	value	NOUN
ap-1366	70	18	problem	problem	NOUN
ap-1366	70	19	(	(	PUNCT
ap-1366	70	20	1	1	NUM
ap-1366	70	21	)	)	PUNCT
ap-1366	70	22	,	,	PUNCT
ap-1366	70	23	(	(	PUNCT
ap-1366	70	24	2	2	NUM
ap-1366	70	25	):	):	PUNCT
ap-1366	70	26	g(x	g(x	PROPN
ap-1366	70	27	,	,	PUNCT
ap-1366	70	28	y	y	NOUN
ap-1366	70	29	)	)	PUNCT
ap-1366	70	30	=	=	SYM
ap-1366	71	1	−	−	PROPN
ap-1366	71	2	1	1	NUM
ap-1366	71	3	c0	c0	NOUN
ap-1366	71	4	[	[	PUNCT
ap-1366	71	5	ψ0,l(y)ψ0,r(x)θ(x	ψ0,l(y)ψ0,r(x)θ(x	PROPN
ap-1366	71	6	−	−	PROPN
ap-1366	71	7	y	y	PROPN
ap-1366	71	8	)	)	PUNCT
ap-1366	72	1	+	+	CCONJ
ap-1366	72	2	ψ0,l(x)ψ0,r(y)θ(y	ψ0,l(x)ψ0,r(y)θ(y	X
ap-1366	72	3	−	−	NOUN
ap-1366	72	4	x	x	NOUN
ap-1366	72	5	)	)	PUNCT
ap-1366	72	6	]	]	PUNCT
ap-1366	72	7	,	,	PUNCT
ap-1366	72	8	(	(	PUNCT
ap-1366	72	9	10	10	NUM
ap-1366	72	10	)	)	PUNCT
ap-1366	72	11	where	where	SCONJ
ap-1366	72	12	c0	c0	PROPN
ap-1366	72	13	is	be	AUX
ap-1366	72	14	the	the	DET
ap-1366	72	15	constant	constant	ADJ
ap-1366	72	16	from	from	ADP
ap-1366	72	17	(	(	PUNCT
ap-1366	72	18	9	9	NUM
ap-1366	72	19	)	)	PUNCT
ap-1366	72	20	and	and	CCONJ
ap-1366	72	21	θ	θ	PROPN
ap-1366	72	22	stands	stand	VERB
ap-1366	72	23	for	for	ADP
ap-1366	72	24	the	the	DET
ap-1366	72	25	heaviside	heaviside	ADJ
ap-1366	72	26	distribution	distribution	NOUN
ap-1366	72	27	.	.	PUNCT
ap-1366	73	1	the	the	DET
ap-1366	73	2	second	second	ADJ
ap-1366	73	3	representation	representation	NOUN
ap-1366	73	4	of	of	ADP
ap-1366	73	5	the	the	DET
ap-1366	73	6	green	green	PROPN
ap-1366	73	7	’s	’s	PART
ap-1366	73	8	function	function	NOUN
ap-1366	73	9	g	g	PROPN
ap-1366	73	10	can	can	AUX
ap-1366	73	11	be	be	AUX
ap-1366	73	12	obtained	obtain	VERB
ap-1366	73	13	as	as	ADP
ap-1366	73	14	follows	follow	NOUN
ap-1366	73	15	,	,	PUNCT
ap-1366	73	16	provided	provide	VERB
ap-1366	73	17	problem	problem	NOUN
ap-1366	73	18	(	(	PUNCT
ap-1366	73	19	1	1	NUM
ap-1366	73	20	)	)	PUNCT
ap-1366	73	21	,	,	PUNCT
ap-1366	73	22	(	(	PUNCT
ap-1366	73	23	2	2	X
ap-1366	73	24	)	)	PUNCT
ap-1366	73	25	admits	admit	VERB
ap-1366	73	26	a	a	DET
ap-1366	73	27	complete	complete	ADJ
ap-1366	73	28	set	set	NOUN
ap-1366	73	29	of	of	ADP
ap-1366	73	30	solutions	solution	NOUN
ap-1366	73	31	:	:	PUNCT
ap-1366	73	32	g(x	g(x	NUM
ap-1366	73	33	,	,	PUNCT
ap-1366	73	34	y	y	NOUN
ap-1366	73	35	)	)	PUNCT
ap-1366	73	36	=	=	PUNCT
ap-1366	74	1	m∑	m∑	CCONJ
ap-1366	74	2	n=0	n=0	PROPN
ap-1366	74	3	ψn(x)ψn(y	ψn(x)ψn(y	NOUN
ap-1366	74	4	)	)	PUNCT
ap-1366	75	1	en	en	ADP
ap-1366	75	2	−	−	PROPN
ap-1366	75	3	e	e	X
ap-1366	75	4	+	+	NOUN
ap-1366	75	5	∫	∫	PROPN
ap-1366	75	6	r	r	NOUN
ap-1366	75	7	ψk(x)ψk(y	ψk(x)ψk(y	NOUN
ap-1366	75	8	)	)	PUNCT
ap-1366	75	9	k2	k2	NOUN
ap-1366	75	10	−	−	PROPN
ap-1366	75	11	e	e	PROPN
ap-1366	75	12	dk	dk	PROPN
ap-1366	75	13	,	,	PUNCT
ap-1366	75	14	(	(	PUNCT
ap-1366	75	15	11	11	NUM
ap-1366	75	16	)	)	PUNCT
ap-1366	75	17	where	where	SCONJ
ap-1366	75	18	the	the	DET
ap-1366	75	19	notation	notation	NOUN
ap-1366	75	20	is	be	AUX
ap-1366	75	21	the	the	DET
ap-1366	75	22	same	same	ADJ
ap-1366	75	23	as	as	ADP
ap-1366	75	24	in	in	ADP
ap-1366	75	25	(	(	PUNCT
ap-1366	75	26	8)	8)	NUM
ap-1366	75	27	.	.	NOUN
ap-1366	75	28	3	3	NUM
ap-1366	75	29	propagators	propagator	NOUN
ap-1366	75	30	related	relate	VERB
ap-1366	75	31	by	by	ADP
ap-1366	75	32	generalized	generalized	ADJ
ap-1366	75	33	susy	susy	NOUN
ap-1366	75	34	in	in	ADP
ap-1366	75	35	order	order	NOUN
ap-1366	75	36	to	to	PART
ap-1366	75	37	obtain	obtain	VERB
ap-1366	75	38	a	a	DET
ap-1366	75	39	relation	relation	NOUN
ap-1366	75	40	between	between	ADP
ap-1366	75	41	the	the	DET
ap-1366	75	42	propagators	propagator	NOUN
ap-1366	75	43	of	of	ADP
ap-1366	75	44	the	the	DET
ap-1366	75	45	two	two	NUM
ap-1366	75	46	boundary	boundary	ADJ
ap-1366	75	47	-	-	PUNCT
ap-1366	75	48	value	value	NOUN
ap-1366	75	49	problems	problem	NOUN
ap-1366	75	50	(	(	PUNCT
ap-1366	75	51	1	1	NUM
ap-1366	75	52	)	)	PUNCT
ap-1366	75	53	,	,	PUNCT
ap-1366	75	54	(	(	PUNCT
ap-1366	75	55	2	2	X
ap-1366	75	56	)	)	PUNCT
ap-1366	75	57	and	and	CCONJ
ap-1366	75	58	(	(	PUNCT
ap-1366	75	59	3	3	NUM
ap-1366	75	60	)	)	PUNCT
ap-1366	75	61	,	,	PUNCT
ap-1366	75	62	(	(	PUNCT
ap-1366	75	63	4	4	NUM
ap-1366	75	64	)	)	PUNCT
ap-1366	75	65	,	,	PUNCT
ap-1366	75	66	we	we	PRON
ap-1366	75	67	take	take	VERB
ap-1366	75	68	the	the	DET
ap-1366	75	69	propagatork1	propagatork1	NOUN
ap-1366	75	70	of	of	ADP
ap-1366	75	71	the	the	DET
ap-1366	75	72	second	second	ADJ
ap-1366	75	73	problem	problem	NOUN
ap-1366	75	74	and	and	CCONJ
ap-1366	75	75	express	express	VERB
ap-1366	75	76	it	it	PRON
ap-1366	75	77	through	through	ADP
ap-1366	75	78	quantities	quantity	NOUN
ap-1366	75	79	related	relate	VERB
ap-1366	75	80	to	to	ADP
ap-1366	75	81	the	the	DET
ap-1366	75	82	first	first	ADJ
ap-1366	75	83	problem	problem	NOUN
ap-1366	75	84	.	.	PUNCT
ap-1366	76	1	for	for	ADP
ap-1366	76	2	the	the	DET
ap-1366	76	3	sake	sake	NOUN
ap-1366	76	4	of	of	ADP
ap-1366	76	5	simplicity	simplicity	NOUN
ap-1366	76	6	we	we	PRON
ap-1366	76	7	assume	assume	VERB
ap-1366	76	8	for	for	ADP
ap-1366	76	9	now	now	ADV
ap-1366	76	10	that	that	SCONJ
ap-1366	76	11	the	the	DET
ap-1366	76	12	two	two	NUM
ap-1366	76	13	boundary	boundary	ADJ
ap-1366	76	14	-	-	PUNCT
ap-1366	76	15	value	value	NOUN
ap-1366	76	16	problems	problem	NOUN
ap-1366	76	17	have	have	VERB
ap-1366	76	18	the	the	DET
ap-1366	76	19	64	64	NUM
ap-1366	76	20	acta	acta	PROPN
ap-1366	76	21	polytechnica	polytechnica	PROPN
ap-1366	76	22	vol	vol	NOUN
ap-1366	76	23	.	.	PUNCT
ap-1366	77	1	51	51	NUM
ap-1366	77	2	no	no	NOUN
ap-1366	77	3	.	.	PUNCT
ap-1366	78	1	1/2011	1/2011	NUM
ap-1366	78	2	same	same	ADJ
ap-1366	78	3	discrete	discrete	NOUN
ap-1366	78	4	spectrum	spectrum	NOUN
ap-1366	78	5	and	and	CCONJ
ap-1366	78	6	that	that	SCONJ
ap-1366	78	7	both	both	PRON
ap-1366	78	8	of	of	ADP
ap-1366	78	9	them	they	PRON
ap-1366	78	10	admit	admit	VERB
ap-1366	78	11	a	a	DET
ap-1366	78	12	complete	complete	ADJ
ap-1366	78	13	set	set	NOUN
ap-1366	78	14	of	of	ADP
ap-1366	78	15	solutions	solution	NOUN
ap-1366	78	16	belonging	belong	VERB
ap-1366	78	17	to	to	ADP
ap-1366	78	18	a	a	DET
ap-1366	78	19	discrete	discrete	NOUN
ap-1366	78	20	and	and	CCONJ
ap-1366	78	21	a	a	DET
ap-1366	78	22	continuous	continuous	ADJ
ap-1366	78	23	part	part	NOUN
ap-1366	78	24	of	of	ADP
ap-1366	78	25	the	the	DET
ap-1366	78	26	spectrum	spectrum	NOUN
ap-1366	78	27	.	.	PUNCT
ap-1366	79	1	furthermore	furthermore	ADV
ap-1366	79	2	,	,	PUNCT
ap-1366	79	3	we	we	PRON
ap-1366	79	4	assume	assume	VERB
ap-1366	79	5	that	that	SCONJ
ap-1366	79	6	the	the	DET
ap-1366	79	7	solutions	solution	NOUN
ap-1366	79	8	of	of	ADP
ap-1366	79	9	problem	problem	NOUN
ap-1366	79	10	(	(	PUNCT
ap-1366	79	11	1	1	NUM
ap-1366	79	12	)	)	PUNCT
ap-1366	79	13	,	,	PUNCT
ap-1366	79	14	(	(	PUNCT
ap-1366	79	15	2	2	X
ap-1366	79	16	)	)	PUNCT
ap-1366	79	17	are	be	AUX
ap-1366	79	18	realvalued	realvalue	VERB
ap-1366	79	19	functions	function	NOUN
ap-1366	79	20	.	.	PUNCT
ap-1366	80	1	this	this	PRON
ap-1366	80	2	is	be	AUX
ap-1366	80	3	no	no	DET
ap-1366	80	4	restriction	restriction	NOUN
ap-1366	80	5	,	,	PUNCT
ap-1366	80	6	as	as	SCONJ
ap-1366	80	7	equation	equation	NOUN
ap-1366	80	8	(	(	PUNCT
ap-1366	80	9	1	1	X
ap-1366	80	10	)	)	PUNCT
ap-1366	80	11	involves	involve	VERB
ap-1366	80	12	only	only	ADV
ap-1366	80	13	real	real	ADJ
ap-1366	80	14	functions	function	NOUN
ap-1366	80	15	.	.	PUNCT
ap-1366	81	1	3.1	3.1	NUM
ap-1366	81	2	general	general	ADJ
ap-1366	81	3	case	case	NOUN
ap-1366	81	4	the	the	DET
ap-1366	81	5	construction	construction	NOUN
ap-1366	81	6	of	of	ADP
ap-1366	81	7	our	our	PRON
ap-1366	81	8	propagator	propagator	NOUN
ap-1366	81	9	k1	k1	NOUN
ap-1366	81	10	is	be	AUX
ap-1366	81	11	similar	similar	ADJ
ap-1366	81	12	to	to	ADP
ap-1366	81	13	the	the	DET
ap-1366	81	14	way	way	NOUN
ap-1366	81	15	it	it	PRON
ap-1366	81	16	was	be	AUX
ap-1366	81	17	done	do	VERB
ap-1366	81	18	in	in	ADP
ap-1366	81	19	[	[	X
ap-1366	81	20	1	1	NUM
ap-1366	81	21	]	]	PUNCT
ap-1366	81	22	.	.	PUNCT
ap-1366	82	1	according	accord	VERB
ap-1366	82	2	to	to	ADP
ap-1366	82	3	representation	representation	NOUN
ap-1366	82	4	(	(	PUNCT
ap-1366	82	5	8)	8)	NUM
ap-1366	82	6	we	we	PRON
ap-1366	82	7	have	have	VERB
ap-1366	82	8	k1(x	k1(x	PROPN
ap-1366	82	9	,	,	PUNCT
ap-1366	82	10	y	y	PROPN
ap-1366	82	11	,	,	PUNCT
ap-1366	82	12	t	t	PROPN
ap-1366	82	13	)	)	PUNCT
ap-1366	82	14	=	=	SYM
ap-1366	82	15	h(y	h(y	ADV
ap-1366	82	16	)	)	PUNCT
ap-1366	82	17	[	[	PUNCT
ap-1366	82	18	m∑	m∑	CCONJ
ap-1366	82	19	n=0	n=0	NUM
ap-1366	82	20	φn(x	φn(x	NUM
ap-1366	82	21	)	)	PUNCT
ap-1366	82	22	exp(−ient)φn(y	exp(−ient)φn(y	NOUN
ap-1366	82	23	)	)	PUNCT
ap-1366	83	1	+	+	NOUN
ap-1366	83	2	∫	∫	X
ap-1366	83	3	r	r	NOUN
ap-1366	83	4	φk(x	φk(x	NOUN
ap-1366	83	5	)	)	PUNCT
ap-1366	83	6	exp(−ik2t)φk(y	exp(−ik2t)φk(y	NOUN
ap-1366	83	7	)	)	PUNCT
ap-1366	83	8	dk	dk	X
ap-1366	83	9	]	]	PUNCT
ap-1366	83	10	.	.	PUNCT
ap-1366	84	1	(	(	PUNCT
ap-1366	84	2	12	12	NUM
ap-1366	84	3	)	)	PUNCT
ap-1366	84	4	the	the	DET
ap-1366	84	5	notation	notation	NOUN
ap-1366	84	6	is	be	AUX
ap-1366	84	7	the	the	DET
ap-1366	84	8	same	same	ADJ
ap-1366	84	9	as	as	ADP
ap-1366	84	10	in	in	ADP
ap-1366	84	11	(	(	PUNCT
ap-1366	84	12	8)	8)	NUM
ap-1366	84	13	,	,	PUNCT
ap-1366	84	14	only	only	ADV
ap-1366	84	15	φn	φn	ADP
ap-1366	84	16	and	and	CCONJ
ap-1366	84	17	φk	φk	AUX
ap-1366	84	18	must	must	AUX
ap-1366	84	19	be	be	AUX
ap-1366	84	20	replaced	replace	VERB
ap-1366	84	21	by	by	ADP
ap-1366	84	22	ψn	ψn	INTJ
ap-1366	84	23	and	and	CCONJ
ap-1366	84	24	ψk	ψk	VERB
ap-1366	84	25	,	,	PUNCT
ap-1366	84	26	respectively	respectively	ADV
ap-1366	84	27	.	.	PUNCT
ap-1366	85	1	now	now	ADV
ap-1366	85	2	,	,	PUNCT
ap-1366	85	3	since	since	SCONJ
ap-1366	85	4	the	the	DET
ap-1366	85	5	solutions	solution	NOUN
ap-1366	85	6	φn	φn	VERB
ap-1366	85	7	,	,	PUNCT
ap-1366	85	8	φk	φk	AUX
ap-1366	85	9	are	be	AUX
ap-1366	85	10	obtained	obtain	VERB
ap-1366	85	11	by	by	ADP
ap-1366	85	12	means	mean	NOUN
ap-1366	85	13	of	of	ADP
ap-1366	85	14	a	a	DET
ap-1366	85	15	susy	susy	NOUN
ap-1366	85	16	transformation	transformation	NOUN
ap-1366	85	17	(	(	PUNCT
ap-1366	85	18	5	5	NUM
ap-1366	85	19	)	)	PUNCT
ap-1366	85	20	from	from	ADP
ap-1366	85	21	ψn	ψn	PROPN
ap-1366	85	22	,	,	PUNCT
ap-1366	85	23	ψk	ψk	VERB
ap-1366	85	24	,	,	PUNCT
ap-1366	85	25	we	we	PRON
ap-1366	85	26	can	can	AUX
ap-1366	85	27	rewrite	rewrite	VERB
ap-1366	85	28	(	(	PUNCT
ap-1366	85	29	12	12	NUM
ap-1366	85	30	)	)	PUNCT
ap-1366	85	31	as	as	SCONJ
ap-1366	85	32	follows	follow	VERB
ap-1366	85	33	,	,	PUNCT
ap-1366	85	34	taking	take	VERB
ap-1366	85	35	into	into	ADP
ap-1366	85	36	account	account	NOUN
ap-1366	85	37	normalization	normalization	NOUN
ap-1366	85	38	constants	constant	NOUN
ap-1366	85	39	ln	ln	ADJ
ap-1366	85	40	and	and	CCONJ
ap-1366	85	41	lk	lk	NOUN
ap-1366	85	42	,	,	PUNCT
ap-1366	85	43	respectively	respectively	ADV
ap-1366	85	44	:	:	PUNCT
ap-1366	85	45	k1(x	k1(x	NOUN
ap-1366	85	46	,	,	PUNCT
ap-1366	85	47	y	y	PROPN
ap-1366	85	48	,	,	PUNCT
ap-1366	85	49	t	t	PROPN
ap-1366	85	50	)	)	PUNCT
ap-1366	85	51	=	=	SYM
ap-1366	85	52	h(y)du	h(y)du	PROPN
ap-1366	85	53	,	,	PUNCT
ap-1366	85	54	xdu	xdu	PROPN
ap-1366	85	55	,	,	PUNCT
ap-1366	85	56	y	y	PROPN
ap-1366	85	57	·	·	PUNCT
ap-1366	85	58	[	[	PUNCT
ap-1366	85	59	m∑	m∑	ADP
ap-1366	85	60	n=0	n=0	NUM
ap-1366	85	61	l2nψn(x	l2nψn(x	NUM
ap-1366	85	62	)	)	PUNCT
ap-1366	85	63	exp(−ient)ψn(y	exp(−ient)ψn(y	PUNCT
ap-1366	85	64	)	)	PUNCT
ap-1366	86	1	+	+	CCONJ
ap-1366	87	1	+	+	NUM
ap-1366	87	2	∫	∫	PROPN
ap-1366	87	3	r	r	NOUN
ap-1366	87	4	l2kψk(x	l2kψk(x	PROPN
ap-1366	87	5	)	)	PUNCT
ap-1366	88	1	exp(−ik2t)ψk(y	exp(−ik2t)ψk(y	NUM
ap-1366	88	2	)	)	PUNCT
ap-1366	89	1	dk	dk	NOUN
ap-1366	89	2	]	]	PUNCT
ap-1366	89	3	.	.	PUNCT
ap-1366	90	1	in	in	ADP
ap-1366	90	2	the	the	DET
ap-1366	90	3	next	next	ADJ
ap-1366	90	4	step	step	NOUN
ap-1366	90	5	we	we	PRON
ap-1366	90	6	apply	apply	VERB
ap-1366	90	7	the	the	DET
ap-1366	90	8	defining	define	VERB
ap-1366	90	9	property	property	NOUN
ap-1366	90	10	(	(	PUNCT
ap-1366	90	11	7	7	NUM
ap-1366	90	12	)	)	PUNCT
ap-1366	90	13	to	to	ADP
ap-1366	90	14	the	the	DET
ap-1366	90	15	previously	previously	ADV
ap-1366	90	16	obtained	obtain	VERB
ap-1366	90	17	expression	expression	NOUN
ap-1366	90	18	:	:	PUNCT
ap-1366	90	19	k1(x	k1(x	NOUN
ap-1366	90	20	,	,	PUNCT
ap-1366	90	21	y	y	PROPN
ap-1366	90	22	,	,	PUNCT
ap-1366	90	23	t	t	PROPN
ap-1366	90	24	)	)	PUNCT
ap-1366	90	25	=	=	SYM
ap-1366	90	26	h(y)du	h(y)du	PROPN
ap-1366	90	27	,	,	PUNCT
ap-1366	90	28	xdu	xdu	PROPN
ap-1366	90	29	,	,	PUNCT
ap-1366	90	30	y	y	PROPN
ap-1366	90	31	·	·	PUNCT
ap-1366	90	32	[	[	PUNCT
ap-1366	90	33	m∑	m∑	CCONJ
ap-1366	90	34	n=0	n=0	NUM
ap-1366	90	35	l2n	l2n	PROPN
ap-1366	90	36	∫	∫	PROPN
ap-1366	90	37	(	(	PUNCT
ap-1366	90	38	a	a	PRON
ap-1366	90	39	,	,	PUNCT
ap-1366	90	40	b	b	NOUN
ap-1366	90	41	)	)	PUNCT
ap-1366	90	42	k0(x	k0(x	NOUN
ap-1366	90	43	,	,	PUNCT
ap-1366	90	44	z	z	PROPN
ap-1366	90	45	,	,	PUNCT
ap-1366	90	46	t)ψn(z	t)ψn(z	PROPN
ap-1366	90	47	)	)	PUNCT
ap-1366	90	48	dzψn(y	dzψn(y	NOUN
ap-1366	90	49	)	)	PUNCT
ap-1366	91	1	+	+	CCONJ
ap-1366	91	2	∫	∫	PROPN
ap-1366	91	3	r	r	PROPN
ap-1366	91	4	l2k	l2k	PROPN
ap-1366	91	5	∫	∫	PROPN
ap-1366	91	6	(	(	PUNCT
ap-1366	91	7	a	a	PRON
ap-1366	91	8	,	,	PUNCT
ap-1366	91	9	b	b	NOUN
ap-1366	91	10	)	)	PUNCT
ap-1366	91	11	k0(x	k0(x	NOUN
ap-1366	91	12	,	,	PUNCT
ap-1366	91	13	z	z	PROPN
ap-1366	91	14	,	,	PUNCT
ap-1366	91	15	t)ψk(z	t)ψk(z	PROPN
ap-1366	91	16	)	)	PUNCT
ap-1366	91	17	dzψk(y	dzψk(y	NOUN
ap-1366	91	18	)	)	PUNCT
ap-1366	91	19	dk	dk	X
ap-1366	91	20	]	]	PUNCT
ap-1366	91	21	.	.	PUNCT
ap-1366	92	1	(	(	PUNCT
ap-1366	92	2	13	13	NUM
ap-1366	92	3	)	)	PUNCT
ap-1366	92	4	we	we	PRON
ap-1366	92	5	choose	choose	VERB
ap-1366	92	6	the	the	DET
ap-1366	92	7	free	free	ADJ
ap-1366	92	8	constants	constant	NOUN
ap-1366	92	9	as	as	ADP
ap-1366	92	10	ln	ln	NOUN
ap-1366	92	11	=	=	SYM
ap-1366	92	12	1/(en	1/(en	NUM
ap-1366	92	13	−	−	PROPN
ap-1366	92	14	λ	λ	NOUN
ap-1366	92	15	)	)	PUNCT
ap-1366	92	16	1	1	NUM
ap-1366	92	17	2	2	NUM
ap-1366	92	18	,	,	PUNCT
ap-1366	92	19	n	n	NOUN
ap-1366	92	20	=	=	SYM
ap-1366	92	21	1	1	NUM
ap-1366	92	22	,	,	PUNCT
ap-1366	92	23	.	.	PUNCT
ap-1366	92	24	.	.	PUNCT
ap-1366	93	1	.	.	PUNCT
ap-1366	94	1	,	,	PUNCT
ap-1366	94	2	m	m	VERB
ap-1366	94	3	,	,	PUNCT
ap-1366	94	4	and	and	CCONJ
ap-1366	94	5	lk	lk	PROPN
ap-1366	94	6	=	=	PROPN
ap-1366	94	7	1/(k2	1/(k2	NUM
ap-1366	94	8	−	−	PROPN
ap-1366	94	9	λ	λ	NOUN
ap-1366	94	10	)	)	PUNCT
ap-1366	94	11	1	1	NUM
ap-1366	94	12	2	2	NUM
ap-1366	94	13	,	,	PUNCT
ap-1366	94	14	k	k	PROPN
ap-1366	94	15	∈	∈	PROPN
ap-1366	94	16	r	r	NOUN
ap-1366	94	17	,	,	PUNCT
ap-1366	94	18	where	where	SCONJ
ap-1366	94	19	λ	λ	PROPN
ap-1366	94	20	is	be	AUX
ap-1366	94	21	the	the	DET
ap-1366	94	22	discrete	discrete	ADJ
ap-1366	94	23	spectral	spectral	ADJ
ap-1366	94	24	value	value	NOUN
ap-1366	94	25	associated	associate	VERB
ap-1366	94	26	with	with	ADP
ap-1366	94	27	the	the	DET
ap-1366	94	28	auxiliary	auxiliary	ADJ
ap-1366	94	29	function	function	NOUN
ap-1366	94	30	u.	u.	ADV
ap-1366	94	31	after	after	ADP
ap-1366	94	32	regrouping	regroup	VERB
ap-1366	94	33	terms	term	NOUN
ap-1366	94	34	,	,	PUNCT
ap-1366	94	35	these	these	DET
ap-1366	94	36	settings	setting	NOUN
ap-1366	94	37	render	render	VERB
ap-1366	94	38	(	(	PUNCT
ap-1366	94	39	13	13	NUM
ap-1366	94	40	)	)	PUNCT
ap-1366	94	41	in	in	ADP
ap-1366	94	42	the	the	DET
ap-1366	94	43	form	form	NOUN
ap-1366	94	44	k1(x	k1(x	PROPN
ap-1366	94	45	,	,	PUNCT
ap-1366	94	46	y	y	PROPN
ap-1366	94	47	,	,	PUNCT
ap-1366	94	48	t	t	PROPN
ap-1366	94	49	)	)	PUNCT
ap-1366	94	50	=	=	SYM
ap-1366	94	51	h(y)du	h(y)du	PROPN
ap-1366	94	52	,	,	PUNCT
ap-1366	94	53	xdu	xdu	PROPN
ap-1366	94	54	,	,	PUNCT
ap-1366	94	55	y	y	PROPN
ap-1366	94	56	{	{	PUNCT
ap-1366	94	57	∫	∫	PROPN
ap-1366	94	58	(	(	PUNCT
ap-1366	94	59	a	a	PRON
ap-1366	94	60	,	,	PUNCT
ap-1366	94	61	b	b	NOUN
ap-1366	94	62	)	)	PUNCT
ap-1366	94	63	k0(x	k0(x	NOUN
ap-1366	94	64	,	,	PUNCT
ap-1366	94	65	z	z	PROPN
ap-1366	94	66	,	,	PUNCT
ap-1366	94	67	t	t	PROPN
ap-1366	94	68	)	)	PUNCT
ap-1366	94	69	·	·	PUNCT
ap-1366	94	70	[	[	PUNCT
ap-1366	94	71	m∑	m∑	CCONJ
ap-1366	94	72	n=0	n=0	NUM
ap-1366	94	73	ψn(z)ψn(y	ψn(z)ψn(y	NOUN
ap-1366	94	74	)	)	PUNCT
ap-1366	94	75	en	en	ADP
ap-1366	94	76	−	−	PROPN
ap-1366	94	77	λ	λ	PROPN
ap-1366	95	1	+	+	CCONJ
ap-1366	95	2	∫	∫	PROPN
ap-1366	95	3	r	r	NOUN
ap-1366	95	4	ψk(z)ψk(y	ψk(z)ψk(y	PROPN
ap-1366	95	5	)	)	PUNCT
ap-1366	95	6	k2	k2	NOUN
ap-1366	95	7	−	−	PROPN
ap-1366	96	1	λ	λ	X
ap-1366	96	2	dk	dk	X
ap-1366	96	3	]	]	X
ap-1366	96	4	dz	dz	PROPN
ap-1366	96	5	}	}	PUNCT
ap-1366	96	6	=	=	SYM
ap-1366	96	7	(	(	PUNCT
ap-1366	96	8	14	14	NUM
ap-1366	96	9	)	)	PUNCT
ap-1366	96	10	h(y)du	h(y)du	PROPN
ap-1366	96	11	,	,	PUNCT
ap-1366	96	12	xdu	xdu	PROPN
ap-1366	96	13	,	,	PUNCT
ap-1366	96	14	y	y	PROPN
ap-1366	96	15	∫	∫	PROPN
ap-1366	96	16	(	(	PUNCT
ap-1366	96	17	a	a	PRON
ap-1366	96	18	,	,	PUNCT
ap-1366	96	19	b	b	NOUN
ap-1366	96	20	)	)	PUNCT
ap-1366	96	21	k0(x	k0(x	NOUN
ap-1366	96	22	,	,	PUNCT
ap-1366	96	23	z	z	PROPN
ap-1366	96	24	,	,	PUNCT
ap-1366	96	25	t)g0(z	t)g0(z	NUM
ap-1366	96	26	,	,	PUNCT
ap-1366	96	27	y	y	NOUN
ap-1366	96	28	)	)	PUNCT
ap-1366	96	29	dz	dz	PROPN
ap-1366	96	30	,	,	PUNCT
ap-1366	96	31	(	(	PUNCT
ap-1366	96	32	15	15	NUM
ap-1366	96	33	)	)	PUNCT
ap-1366	96	34	where	where	SCONJ
ap-1366	96	35	g0	g0	PROPN
ap-1366	96	36	is	be	AUX
ap-1366	96	37	the	the	DET
ap-1366	96	38	green	green	PROPN
ap-1366	96	39	’s	’s	PART
ap-1366	96	40	function	function	NOUN
ap-1366	96	41	of	of	ADP
ap-1366	96	42	our	our	PRON
ap-1366	96	43	boundaryvalue	boundaryvalue	NOUN
ap-1366	96	44	problem	problem	NOUN
ap-1366	96	45	(	(	PUNCT
ap-1366	96	46	1	1	NUM
ap-1366	96	47	)	)	PUNCT
ap-1366	96	48	,	,	PUNCT
ap-1366	96	49	(	(	PUNCT
ap-1366	96	50	2	2	X
ap-1366	96	51	)	)	PUNCT
ap-1366	96	52	in	in	ADP
ap-1366	96	53	its	its	PRON
ap-1366	96	54	form	form	NOUN
ap-1366	96	55	(	(	PUNCT
ap-1366	96	56	11	11	NUM
ap-1366	96	57	)	)	PUNCT
ap-1366	96	58	,	,	PUNCT
ap-1366	96	59	taken	take	VERB
ap-1366	96	60	at	at	ADP
ap-1366	96	61	energy	energy	NOUN
ap-1366	96	62	λ	λ	PROPN
ap-1366	96	63	.	.	PUNCT
ap-1366	96	64	relation	relation	NOUN
ap-1366	96	65	(	(	PUNCT
ap-1366	96	66	15	15	NUM
ap-1366	96	67	)	)	PUNCT
ap-1366	96	68	gives	give	VERB
ap-1366	96	69	the	the	DET
ap-1366	96	70	final	final	ADJ
ap-1366	96	71	connection	connection	NOUN
ap-1366	96	72	between	between	ADP
ap-1366	96	73	the	the	DET
ap-1366	96	74	propagators	propagator	NOUN
ap-1366	96	75	of	of	ADP
ap-1366	96	76	our	our	PRON
ap-1366	96	77	two	two	NUM
ap-1366	96	78	boundary	boundary	ADJ
ap-1366	96	79	-	-	PUNCT
ap-1366	96	80	value	value	NOUN
ap-1366	96	81	problems	problem	NOUN
ap-1366	96	82	,	,	PUNCT
ap-1366	96	83	provided	provide	VERB
ap-1366	96	84	they	they	PRON
ap-1366	96	85	admit	admit	VERB
ap-1366	96	86	the	the	DET
ap-1366	96	87	same	same	ADJ
ap-1366	96	88	discrete	discrete	ADJ
ap-1366	96	89	spectrum	spectrum	NOUN
ap-1366	96	90	.	.	PUNCT
ap-1366	97	1	in	in	ADP
ap-1366	97	2	the	the	DET
ap-1366	97	3	case	case	NOUN
ap-1366	97	4	that	that	DET
ap-1366	97	5	problem	problem	NOUN
ap-1366	97	6	(	(	PUNCT
ap-1366	97	7	3	3	NUM
ap-1366	97	8	)	)	PUNCT
ap-1366	97	9	,	,	PUNCT
ap-1366	97	10	(	(	PUNCT
ap-1366	97	11	4	4	X
ap-1366	97	12	)	)	PUNCT
ap-1366	97	13	admits	admit	VERB
ap-1366	97	14	an	an	DET
ap-1366	97	15	additional	additional	ADJ
ap-1366	97	16	discrete	discrete	ADJ
ap-1366	97	17	spectral	spectral	ADJ
ap-1366	97	18	value	value	NOUN
ap-1366	97	19	λ	λ	PROPN
ap-1366	97	20	with	with	ADP
ap-1366	97	21	the	the	DET
ap-1366	97	22	corresponding	corresponding	ADJ
ap-1366	97	23	solution	solution	NOUN
ap-1366	97	24	φ−1	φ−1	PROPN
ap-1366	97	25	,	,	PUNCT
ap-1366	97	26	formula	formula	NOUN
ap-1366	97	27	(	(	PUNCT
ap-1366	97	28	12	12	NUM
ap-1366	97	29	)	)	PUNCT
ap-1366	97	30	must	must	AUX
ap-1366	97	31	be	be	AUX
ap-1366	97	32	modified	modify	VERB
ap-1366	97	33	as	as	SCONJ
ap-1366	97	34	follows	follow	VERB
ap-1366	97	35	:	:	PUNCT
ap-1366	97	36	k1(x	k1(x	NOUN
ap-1366	97	37	,	,	PUNCT
ap-1366	97	38	y	y	PROPN
ap-1366	97	39	,	,	PUNCT
ap-1366	97	40	t	t	PROPN
ap-1366	97	41	)	)	PUNCT
ap-1366	97	42	=	=	SYM
ap-1366	97	43	h(y	h(y	ADV
ap-1366	97	44	)	)	PUNCT
ap-1366	98	1	[	[	PUNCT
ap-1366	98	2	m∑	m∑	CCONJ
ap-1366	98	3	n=0	n=0	NUM
ap-1366	98	4	φn(x	φn(x	NUM
ap-1366	98	5	)	)	PUNCT
ap-1366	98	6	exp(−ient)φn(y	exp(−ient)φn(y	NOUN
ap-1366	98	7	)	)	PUNCT
ap-1366	98	8	+	+	CCONJ
ap-1366	98	9	φ−1(x	φ−1(x	NOUN
ap-1366	98	10	)	)	PUNCT
ap-1366	98	11	exp(−iλt)φ−1(y	exp(−iλt)φ−1(y	PROPN
ap-1366	98	12	)	)	PUNCT
ap-1366	99	1	+	+	NOUN
ap-1366	99	2	∫	∫	X
ap-1366	99	3	r	r	NOUN
ap-1366	99	4	φk(x	φk(x	NOUN
ap-1366	99	5	)	)	PUNCT
ap-1366	99	6	exp(−ik2t)φk(y	exp(−ik2t)φk(y	NOUN
ap-1366	99	7	)	)	PUNCT
ap-1366	99	8	dk	dk	X
ap-1366	99	9	]	]	PUNCT
ap-1366	99	10	.	.	PUNCT
ap-1366	100	1	(	(	PUNCT
ap-1366	100	2	16	16	NUM
ap-1366	100	3	)	)	PUNCT
ap-1366	100	4	from	from	ADP
ap-1366	100	5	this	this	DET
ap-1366	100	6	point	point	NOUN
ap-1366	100	7	,	,	PUNCT
ap-1366	100	8	the	the	DET
ap-1366	100	9	additional	additional	ADJ
ap-1366	100	10	term	term	NOUN
ap-1366	100	11	is	be	AUX
ap-1366	100	12	maintained	maintain	VERB
ap-1366	100	13	until	until	ADP
ap-1366	100	14	the	the	DET
ap-1366	100	15	final	final	ADJ
ap-1366	100	16	relation	relation	NOUN
ap-1366	100	17	between	between	ADP
ap-1366	100	18	the	the	DET
ap-1366	100	19	propagators	propagator	NOUN
ap-1366	100	20	k0	k0	PROPN
ap-1366	100	21	and	and	CCONJ
ap-1366	100	22	k1	k1	PROPN
ap-1366	100	23	results	result	NOUN
ap-1366	100	24	as	as	ADP
ap-1366	100	25	k1(x	k1(x	PROPN
ap-1366	100	26	,	,	PUNCT
ap-1366	100	27	y	y	PROPN
ap-1366	100	28	,	,	PUNCT
ap-1366	100	29	t	t	PROPN
ap-1366	100	30	)	)	PUNCT
ap-1366	100	31	=	=	SYM
ap-1366	101	1	h(y	h(y	ADV
ap-1366	101	2	)	)	PUNCT
ap-1366	101	3	{	{	PUNCT
ap-1366	101	4	du	du	PROPN
ap-1366	101	5	,	,	PUNCT
ap-1366	101	6	xdu	xdu	PROPN
ap-1366	101	7	,	,	PUNCT
ap-1366	101	8	y	y	PROPN
ap-1366	102	1	[	[	X
ap-1366	102	2	∫	∫	X
ap-1366	102	3	(	(	PUNCT
ap-1366	102	4	a	a	PRON
ap-1366	102	5	,	,	PUNCT
ap-1366	102	6	b	b	NOUN
ap-1366	102	7	)	)	PUNCT
ap-1366	102	8	k0(x	k0(x	NOUN
ap-1366	102	9	,	,	PUNCT
ap-1366	102	10	z	z	PROPN
ap-1366	102	11	,	,	PUNCT
ap-1366	102	12	t)g0(z	t)g0(z	NUM
ap-1366	102	13	,	,	PUNCT
ap-1366	102	14	y	y	NOUN
ap-1366	102	15	)	)	PUNCT
ap-1366	102	16	dz	dz	X
ap-1366	102	17	]	]	PUNCT
ap-1366	103	1	+	+	CCONJ
ap-1366	103	2	φ−1(x	φ−1(x	NOUN
ap-1366	103	3	)	)	PUNCT
ap-1366	103	4	exp(−iλt)φ−1(y	exp(−iλt)φ−1(y	PROPN
ap-1366	103	5	)	)	PUNCT
ap-1366	103	6	}	}	PUNCT
ap-1366	103	7	,	,	PUNCT
ap-1366	103	8	where	where	SCONJ
ap-1366	103	9	the	the	DET
ap-1366	103	10	green	green	PROPN
ap-1366	103	11	’s	’s	PART
ap-1366	103	12	function	function	PROPN
ap-1366	103	13	g0	g0	PROPN
ap-1366	103	14	is	be	AUX
ap-1366	103	15	to	to	PART
ap-1366	103	16	be	be	AUX
ap-1366	103	17	taken	take	VERB
ap-1366	103	18	at	at	ADP
ap-1366	103	19	energy	energy	NOUN
ap-1366	103	20	λ	λ	PROPN
ap-1366	103	21	.	.	PUNCT
ap-1366	104	1	finally	finally	ADV
ap-1366	104	2	,	,	PUNCT
ap-1366	104	3	if	if	SCONJ
ap-1366	104	4	problem	problem	NOUN
ap-1366	104	5	(	(	PUNCT
ap-1366	104	6	3	3	NUM
ap-1366	104	7	)	)	PUNCT
ap-1366	104	8	,	,	PUNCT
ap-1366	104	9	(	(	PUNCT
ap-1366	104	10	4	4	X
ap-1366	104	11	)	)	PUNCT
ap-1366	104	12	admits	admit	VERB
ap-1366	104	13	one	one	NUM
ap-1366	104	14	discrete	discrete	ADJ
ap-1366	104	15	spectral	spectral	ADJ
ap-1366	104	16	value	value	NOUN
ap-1366	104	17	less	less	ADJ
ap-1366	104	18	than	than	ADP
ap-1366	104	19	its	its	PRON
ap-1366	104	20	initial	initial	ADJ
ap-1366	104	21	counterpart	counterpart	NOUN
ap-1366	104	22	,	,	PUNCT
ap-1366	104	23	formula	formula	NOUN
ap-1366	104	24	(	(	PUNCT
ap-1366	104	25	12	12	NUM
ap-1366	104	26	)	)	PUNCT
ap-1366	104	27	remains	remain	VERB
ap-1366	104	28	the	the	DET
ap-1366	104	29	same	same	ADJ
ap-1366	104	30	except	except	SCONJ
ap-1366	104	31	that	that	SCONJ
ap-1366	104	32	the	the	DET
ap-1366	104	33	sum	sum	NOUN
ap-1366	104	34	starts	start	VERB
ap-1366	104	35	at	at	ADP
ap-1366	104	36	one	one	NUM
ap-1366	104	37	instead	instead	ADV
ap-1366	104	38	of	of	ADP
ap-1366	104	39	at	at	ADP
ap-1366	104	40	zero	zero	NUM
ap-1366	104	41	.	.	PUNCT
ap-1366	105	1	this	this	PRON
ap-1366	105	2	is	be	AUX
ap-1366	105	3	maintained	maintain	VERB
ap-1366	105	4	until	until	ADP
ap-1366	105	5	formula	formula	NOUN
ap-1366	105	6	(	(	PUNCT
ap-1366	105	7	14	14	NUM
ap-1366	105	8	)	)	PUNCT
ap-1366	105	9	,	,	PUNCT
ap-1366	105	10	where	where	SCONJ
ap-1366	105	11	summation	summation	NOUN
ap-1366	105	12	now	now	ADV
ap-1366	105	13	starts	start	VERB
ap-1366	105	14	at	at	ADP
ap-1366	105	15	one	one	NUM
ap-1366	105	16	.	.	PUNCT
ap-1366	106	1	expression	expression	NOUN
ap-1366	106	2	(	(	PUNCT
ap-1366	106	3	15	15	NUM
ap-1366	106	4	)	)	PUNCT
ap-1366	106	5	then	then	ADV
ap-1366	106	6	turns	turn	VERB
ap-1366	106	7	into	into	ADP
ap-1366	106	8	k1(x	k1(x	PROPN
ap-1366	106	9	,	,	PUNCT
ap-1366	106	10	y	y	PROPN
ap-1366	106	11	,	,	PUNCT
ap-1366	106	12	t	t	PROPN
ap-1366	106	13	)	)	PUNCT
ap-1366	106	14	=	=	SYM
ap-1366	107	1	h(y)du	h(y)du	PROPN
ap-1366	107	2	,	,	PUNCT
ap-1366	107	3	xdu	xdu	PROPN
ap-1366	107	4	,	,	PUNCT
ap-1366	107	5	y	y	PROPN
ap-1366	107	6	∫	∫	PROPN
ap-1366	107	7	(	(	PUNCT
ap-1366	107	8	a	a	PRON
ap-1366	107	9	,	,	PUNCT
ap-1366	107	10	b	b	NOUN
ap-1366	107	11	)	)	PUNCT
ap-1366	107	12	k0(x	k0(x	NOUN
ap-1366	107	13	,	,	PUNCT
ap-1366	107	14	z	z	PROPN
ap-1366	107	15	,	,	PUNCT
ap-1366	107	16	t	t	PROPN
ap-1366	107	17	)	)	PUNCT
ap-1366	107	18	·	·	PUNCT
ap-1366	108	1	lim	lim	PROPN
ap-1366	108	2	e→e0	e→e0	PROPN
ap-1366	108	3	[	[	PUNCT
ap-1366	108	4	g0(z	g0(z	NOUN
ap-1366	108	5	,	,	PUNCT
ap-1366	108	6	y)−	y)−	PROPN
ap-1366	108	7	ψ0(z)ψ0(y	ψ0(z)ψ0(y	X
ap-1366	108	8	)	)	PUNCT
ap-1366	108	9	e0	e0	PROPN
ap-1366	108	10	−	−	PROPN
ap-1366	108	11	e	e	X
ap-1366	108	12	]	]	PUNCT
ap-1366	108	13	dz,(17	dz,(17	PROPN
ap-1366	108	14	)	)	PUNCT
ap-1366	108	15	where	where	SCONJ
ap-1366	108	16	the	the	DET
ap-1366	108	17	green	green	PROPN
ap-1366	108	18	’s	’s	PART
ap-1366	108	19	function	function	PROPN
ap-1366	108	20	g0	g0	PROPN
ap-1366	108	21	is	be	AUX
ap-1366	108	22	to	to	PART
ap-1366	108	23	be	be	AUX
ap-1366	108	24	taken	take	VERB
ap-1366	108	25	at	at	ADP
ap-1366	108	26	energy	energy	NOUN
ap-1366	108	27	e.	e.	PROPN
ap-1366	108	28	in	in	ADP
ap-1366	108	29	summary	summary	NOUN
ap-1366	108	30	,	,	PUNCT
ap-1366	108	31	the	the	DET
ap-1366	108	32	last	last	ADJ
ap-1366	108	33	three	three	NUM
ap-1366	108	34	expressions	expression	NOUN
ap-1366	108	35	stand	stand	VERB
ap-1366	108	36	for	for	ADP
ap-1366	108	37	the	the	DET
ap-1366	108	38	final	final	ADJ
ap-1366	108	39	relations	relation	NOUN
ap-1366	108	40	between	between	ADP
ap-1366	108	41	the	the	DET
ap-1366	108	42	propagators	propagator	NOUN
ap-1366	108	43	of	of	ADP
ap-1366	108	44	our	our	PRON
ap-1366	108	45	two	two	NUM
ap-1366	108	46	boundary	boundary	ADJ
ap-1366	108	47	-	-	PUNCT
ap-1366	108	48	value	value	NOUN
ap-1366	108	49	problems	problem	NOUN
ap-1366	108	50	.	.	PUNCT
ap-1366	109	1	clearly	clearly	ADV
ap-1366	109	2	,	,	PUNCT
ap-1366	109	3	in	in	ADP
ap-1366	109	4	the	the	DET
ap-1366	109	5	conventional	conventional	ADJ
ap-1366	109	6	case	case	NOUN
ap-1366	109	7	h	h	NOUN
ap-1366	109	8	=	=	SYM
ap-1366	109	9	1	1	NUM
ap-1366	109	10	,	,	PUNCT
ap-1366	109	11	the	the	DET
ap-1366	109	12	above	above	ADJ
ap-1366	109	13	expressions	expression	NOUN
ap-1366	109	14	reduce	reduce	VERB
ap-1366	109	15	correctly	correctly	ADV
ap-1366	109	16	to	to	ADP
ap-1366	109	17	the	the	DET
ap-1366	109	18	known	know	VERB
ap-1366	109	19	relations	relation	NOUN
ap-1366	109	20	[	[	X
ap-1366	109	21	1	1	NUM
ap-1366	109	22	]	]	PUNCT
ap-1366	109	23	.	.	PUNCT
ap-1366	110	1	in	in	ADP
ap-1366	110	2	general	general	ADJ
ap-1366	110	3	,	,	PUNCT
ap-1366	110	4	our	our	PRON
ap-1366	110	5	expressions	expression	NOUN
ap-1366	110	6	can	can	AUX
ap-1366	110	7	not	not	PART
ap-1366	110	8	be	be	AUX
ap-1366	110	9	simplified	simplify	VERB
ap-1366	110	10	anymore	anymore	ADV
ap-1366	110	11	,	,	PUNCT
ap-1366	110	12	unless	unless	SCONJ
ap-1366	110	13	more	more	ADJ
ap-1366	110	14	information	information	NOUN
ap-1366	110	15	on	on	ADP
ap-1366	110	16	the	the	DET
ap-1366	110	17	auxiliary	auxiliary	ADJ
ap-1366	110	18	solution	solution	NOUN
ap-1366	110	19	u	u	NOUN
ap-1366	110	20	is	be	AUX
ap-1366	110	21	known	know	VERB
ap-1366	110	22	.	.	PUNCT
ap-1366	111	1	we	we	PRON
ap-1366	111	2	will	will	AUX
ap-1366	111	3	now	now	ADV
ap-1366	111	4	study	study	VERB
ap-1366	111	5	such	such	DET
ap-1366	111	6	a	a	DET
ap-1366	111	7	case	case	NOUN
ap-1366	111	8	.	.	PUNCT
ap-1366	112	1	3.2	3.2	NUM
ap-1366	112	2	special	special	ADJ
ap-1366	112	3	case	case	NOUN
ap-1366	112	4	:	:	PUNCT
ap-1366	112	5	ground	ground	NOUN
ap-1366	112	6	state	state	NOUN
ap-1366	112	7	as	as	ADP
ap-1366	112	8	auxiliary	auxiliary	ADJ
ap-1366	112	9	solution	solution	NOUN
ap-1366	112	10	let	let	VERB
ap-1366	112	11	us	we	PRON
ap-1366	112	12	assume	assume	VERB
ap-1366	112	13	that	that	SCONJ
ap-1366	112	14	the	the	DET
ap-1366	112	15	auxiliary	auxiliary	ADJ
ap-1366	112	16	solution	solution	NOUN
ap-1366	112	17	u	u	NOUN
ap-1366	112	18	is	be	AUX
ap-1366	112	19	chosen	choose	VERB
ap-1366	112	20	to	to	PART
ap-1366	112	21	be	be	AUX
ap-1366	112	22	the	the	DET
ap-1366	112	23	ground	ground	NOUN
ap-1366	112	24	state	state	NOUN
ap-1366	112	25	ψ0	ψ0	PROPN
ap-1366	112	26	,	,	PUNCT
ap-1366	112	27	associated	associate	VERB
ap-1366	112	28	with	with	ADP
ap-1366	112	29	the	the	DET
ap-1366	112	30	spectral	spectral	ADJ
ap-1366	112	31	value	value	NOUN
ap-1366	112	32	e0	e0	PROPN
ap-1366	112	33	,	,	PUNCT
ap-1366	112	34	of	of	ADP
ap-1366	112	35	problem	problem	NOUN
ap-1366	112	36	(	(	PUNCT
ap-1366	112	37	1	1	NUM
ap-1366	112	38	)	)	PUNCT
ap-1366	112	39	,	,	PUNCT
ap-1366	112	40	(	(	PUNCT
ap-1366	112	41	2	2	NUM
ap-1366	112	42	)	)	PUNCT
ap-1366	112	43	.	.	PUNCT
ap-1366	113	1	according	accord	VERB
ap-1366	113	2	to	to	ADP
ap-1366	113	3	our	our	PRON
ap-1366	113	4	65	65	NUM
ap-1366	113	5	acta	acta	PROPN
ap-1366	113	6	polytechnica	polytechnica	PROPN
ap-1366	113	7	vol	vol	NOUN
ap-1366	113	8	.	.	PUNCT
ap-1366	114	1	51	51	NUM
ap-1366	114	2	no	no	NOUN
ap-1366	114	3	.	.	PUNCT
ap-1366	115	1	1/2011	1/2011	NUM
ap-1366	115	2	brief	brief	ADJ
ap-1366	115	3	susy	susy	PROPN
ap-1366	115	4	review	review	PROPN
ap-1366	115	5	in	in	ADP
ap-1366	115	6	section	section	NOUN
ap-1366	115	7	2	2	NUM
ap-1366	115	8	,	,	PUNCT
ap-1366	115	9	this	this	DET
ap-1366	115	10	choice	choice	NOUN
ap-1366	115	11	implies	imply	VERB
ap-1366	115	12	that	that	SCONJ
ap-1366	115	13	the	the	DET
ap-1366	115	14	discrete	discrete	ADJ
ap-1366	115	15	spectrum	spectrum	NOUN
ap-1366	115	16	of	of	ADP
ap-1366	115	17	problem	problem	NOUN
ap-1366	115	18	(	(	PUNCT
ap-1366	115	19	3	3	NUM
ap-1366	115	20	)	)	PUNCT
ap-1366	115	21	,	,	PUNCT
ap-1366	115	22	(	(	PUNCT
ap-1366	115	23	4	4	X
ap-1366	115	24	)	)	PUNCT
ap-1366	115	25	will	will	AUX
ap-1366	115	26	not	not	PART
ap-1366	115	27	contain	contain	VERB
ap-1366	115	28	the	the	DET
ap-1366	115	29	value	value	NOUN
ap-1366	115	30	e0	e0	PROPN
ap-1366	115	31	anymore	anymore	ADV
ap-1366	115	32	.	.	PUNCT
ap-1366	116	1	we	we	PRON
ap-1366	116	2	will	will	AUX
ap-1366	116	3	now	now	ADV
ap-1366	116	4	show	show	VERB
ap-1366	116	5	that	that	SCONJ
ap-1366	116	6	the	the	DET
ap-1366	116	7	corresponding	correspond	VERB
ap-1366	116	8	relation	relation	NOUN
ap-1366	116	9	between	between	ADP
ap-1366	116	10	the	the	DET
ap-1366	116	11	propagators	propagator	NOUN
ap-1366	116	12	(	(	PUNCT
ap-1366	116	13	17	17	NUM
ap-1366	116	14	)	)	PUNCT
ap-1366	116	15	,	,	PUNCT
ap-1366	116	16	where	where	SCONJ
ap-1366	116	17	u	u	NOUN
ap-1366	116	18	is	be	AUX
ap-1366	116	19	replaced	replace	VERB
ap-1366	116	20	by	by	ADP
ap-1366	116	21	ψ0	ψ0	PROPN
ap-1366	116	22	,	,	PUNCT
ap-1366	116	23	can	can	AUX
ap-1366	116	24	be	be	AUX
ap-1366	116	25	simplified	simplify	VERB
ap-1366	116	26	considerably	considerably	ADV
ap-1366	116	27	.	.	PUNCT
ap-1366	117	1	while	while	SCONJ
ap-1366	117	2	the	the	DET
ap-1366	117	3	general	general	ADJ
ap-1366	117	4	procedure	procedure	NOUN
ap-1366	117	5	of	of	ADP
ap-1366	117	6	simplification	simplification	NOUN
ap-1366	117	7	follows	follow	VERB
ap-1366	117	8	a	a	DET
ap-1366	117	9	similar	similar	ADJ
ap-1366	117	10	way	way	NOUN
ap-1366	117	11	as	as	ADP
ap-1366	117	12	in	in	ADP
ap-1366	117	13	the	the	DET
ap-1366	117	14	conventional	conventional	ADJ
ap-1366	117	15	case	case	NOUN
ap-1366	117	16	[	[	X
ap-1366	117	17	1	1	NUM
ap-1366	117	18	]	]	PUNCT
ap-1366	117	19	,	,	PUNCT
ap-1366	117	20	one	one	PRON
ap-1366	117	21	must	must	AUX
ap-1366	117	22	keep	keep	VERB
ap-1366	117	23	track	track	NOUN
ap-1366	117	24	of	of	ADP
ap-1366	117	25	the	the	DET
ap-1366	117	26	nonconstant	nonconstant	ADJ
ap-1366	117	27	factor	factor	NOUN
ap-1366	117	28	in	in	ADP
ap-1366	117	29	front	front	NOUN
ap-1366	117	30	of	of	ADP
ap-1366	117	31	(	(	PUNCT
ap-1366	117	32	5	5	NUM
ap-1366	117	33	)	)	PUNCT
ap-1366	117	34	.	.	PUNCT
ap-1366	118	1	before	before	SCONJ
ap-1366	118	2	we	we	PRON
ap-1366	118	3	start	start	VERB
ap-1366	118	4	simplifying	simplify	VERB
ap-1366	118	5	(	(	PUNCT
ap-1366	118	6	17	17	NUM
ap-1366	118	7	)	)	PUNCT
ap-1366	118	8	,	,	PUNCT
ap-1366	118	9	we	we	PRON
ap-1366	118	10	observe	observe	VERB
ap-1366	118	11	that	that	SCONJ
ap-1366	118	12	the	the	DET
ap-1366	118	13	limit	limit	NOUN
ap-1366	118	14	and	and	CCONJ
ap-1366	118	15	the	the	DET
ap-1366	118	16	operator	operator	NOUN
ap-1366	118	17	dψ0,y	dψ0,y	NOUN
ap-1366	118	18	in	in	ADP
ap-1366	118	19	(	(	PUNCT
ap-1366	118	20	17	17	NUM
ap-1366	118	21	)	)	PUNCT
ap-1366	118	22	commute	commute	NOUN
ap-1366	118	23	,	,	PUNCT
ap-1366	118	24	because	because	SCONJ
ap-1366	118	25	dψ0,y	dψ0,y	PROPN
ap-1366	118	26	lim	lim	PROPN
ap-1366	118	27	e→e0	e→e0	PROPN
ap-1366	118	28	[	[	PUNCT
ap-1366	118	29	g0(z	g0(z	NOUN
ap-1366	118	30	,	,	PUNCT
ap-1366	118	31	y)−	y)−	PROPN
ap-1366	118	32	ψ0(z)ψ0(y	ψ0(z)ψ0(y	X
ap-1366	118	33	)	)	PUNCT
ap-1366	118	34	e0	e0	PROPN
ap-1366	119	1	−	−	PROPN
ap-1366	119	2	e	e	NOUN
ap-1366	119	3	]	]	X
ap-1366	119	4	=	=	SYM
ap-1366	119	5	lim	lim	PROPN
ap-1366	119	6	e→e0	e→e0	PROPN
ap-1366	119	7	[	[	PUNCT
ap-1366	119	8	m∑	m∑	CCONJ
ap-1366	119	9	n=1	n=1	PROPN
ap-1366	119	10	ψn(z)dψ0,yψn(y	ψn(z)dψ0,yψn(y	NOUN
ap-1366	119	11	)	)	PUNCT
ap-1366	119	12	en	en	ADP
ap-1366	119	13	−	−	PROPN
ap-1366	119	14	e	e	X
ap-1366	120	1	+	+	NOUN
ap-1366	120	2	∫	∫	X
ap-1366	120	3	r	r	NOUN
ap-1366	120	4	ψk(z)dψ0,yψk(y	ψk(z)dψ0,yψk(y	NOUN
ap-1366	120	5	)	)	PUNCT
ap-1366	120	6	k2	k2	NOUN
ap-1366	120	7	−	−	PROPN
ap-1366	120	8	e	e	NOUN
ap-1366	120	9	dk	dk	PROPN
ap-1366	120	10	]	]	PUNCT
ap-1366	120	11	.	.	PUNCT
ap-1366	121	1	the	the	DET
ap-1366	121	2	first	first	ADJ
ap-1366	121	3	term	term	NOUN
ap-1366	121	4	in	in	ADP
ap-1366	121	5	the	the	DET
ap-1366	121	6	sum	sum	NOUN
ap-1366	121	7	vanishes	vanish	VERB
ap-1366	121	8	,	,	PUNCT
ap-1366	121	9	as	as	ADP
ap-1366	121	10	dψ0,yψ0(y	dψ0,yψ0(y	X
ap-1366	121	11	)	)	PUNCT
ap-1366	121	12	=	=	SYM
ap-1366	121	13	0	0	NUM
ap-1366	121	14	,	,	PUNCT
ap-1366	121	15	so	so	SCONJ
ap-1366	121	16	we	we	PRON
ap-1366	121	17	obtain	obtain	VERB
ap-1366	121	18	dψ0,y	dψ0,y	ADJ
ap-1366	121	19	lim	lim	NOUN
ap-1366	121	20	e→e0	e→e0	PROPN
ap-1366	121	21	[	[	PUNCT
ap-1366	121	22	g0(z	g0(z	NOUN
ap-1366	121	23	,	,	PUNCT
ap-1366	121	24	y)−	y)−	PROPN
ap-1366	121	25	ψ0(z)ψ0(y	ψ0(z)ψ0(y	X
ap-1366	121	26	)	)	PUNCT
ap-1366	121	27	e0	e0	PROPN
ap-1366	122	1	−	−	PROPN
ap-1366	122	2	e	e	NOUN
ap-1366	122	3	]	]	X
ap-1366	122	4	=	=	PUNCT
ap-1366	123	1	lim	lim	PROPN
ap-1366	123	2	e→e0	e→e0	VERB
ap-1366	124	1	[	[	X
ap-1366	124	2	dψ0,yg0(z	dψ0,yg0(z	PROPN
ap-1366	124	3	,	,	PUNCT
ap-1366	124	4	y	y	PROPN
ap-1366	124	5	)	)	PUNCT
ap-1366	124	6	]	]	PUNCT
ap-1366	124	7	.	.	PUNCT
ap-1366	125	1	this	this	DET
ap-1366	125	2	property	property	NOUN
ap-1366	125	3	will	will	AUX
ap-1366	125	4	be	be	AUX
ap-1366	125	5	useful	useful	ADJ
ap-1366	125	6	for	for	ADP
ap-1366	125	7	rewriting	rewrite	VERB
ap-1366	125	8	(	(	PUNCT
ap-1366	125	9	17	17	NUM
ap-1366	125	10	)	)	PUNCT
ap-1366	125	11	.	.	PUNCT
ap-1366	126	1	note	note	VERB
ap-1366	126	2	that	that	SCONJ
ap-1366	126	3	for	for	ADP
ap-1366	126	4	the	the	DET
ap-1366	126	5	sake	sake	NOUN
ap-1366	126	6	of	of	ADP
ap-1366	126	7	simplicity	simplicity	NOUN
ap-1366	126	8	we	we	PRON
ap-1366	126	9	divide	divide	VERB
ap-1366	126	10	by	by	ADP
ap-1366	126	11	the	the	DET
ap-1366	126	12	factor	factor	NOUN
ap-1366	126	13	h	h	NOUN
ap-1366	126	14	:	:	PUNCT
ap-1366	126	15	1	1	NUM
ap-1366	126	16	h(y	h(y	ADV
ap-1366	126	17	)	)	PUNCT
ap-1366	127	1	k1(x	k1(x	NOUN
ap-1366	127	2	,	,	PUNCT
ap-1366	127	3	y	y	PROPN
ap-1366	127	4	,	,	PUNCT
ap-1366	127	5	t	t	PROPN
ap-1366	127	6	)	)	PUNCT
ap-1366	127	7	=	=	SYM
ap-1366	128	1	dψ0,x	dψ0,x	PROPN
ap-1366	128	2	∫	∫	PROPN
ap-1366	128	3	(	(	PUNCT
ap-1366	128	4	a	a	PRON
ap-1366	128	5	,	,	PUNCT
ap-1366	128	6	b	b	NOUN
ap-1366	128	7	)	)	PUNCT
ap-1366	128	8	k0(x	k0(x	NOUN
ap-1366	128	9	,	,	PUNCT
ap-1366	128	10	z	z	PROPN
ap-1366	128	11	,	,	PUNCT
ap-1366	128	12	t	t	PROPN
ap-1366	128	13	)	)	PUNCT
ap-1366	128	14	lim	lim	NOUN
ap-1366	128	15	e→e0	e→e0	VERB
ap-1366	129	1	[	[	X
ap-1366	129	2	dψ0,yg0(z	dψ0,yg0(z	PROPN
ap-1366	129	3	,	,	PUNCT
ap-1366	129	4	y	y	NOUN
ap-1366	129	5	)	)	PUNCT
ap-1366	129	6	]	]	PUNCT
ap-1366	129	7	dz	dz	PROPN
ap-1366	129	8	=	=	SYM
ap-1366	129	9	dψ0,x	dψ0,x	PROPN
ap-1366	129	10	∫	∫	PROPN
ap-1366	129	11	(	(	PUNCT
ap-1366	129	12	a	a	PRON
ap-1366	129	13	,	,	PUNCT
ap-1366	129	14	y	y	NOUN
ap-1366	129	15	)	)	PUNCT
ap-1366	129	16	k0(x	k0(x	NOUN
ap-1366	129	17	,	,	PUNCT
ap-1366	129	18	z	z	PROPN
ap-1366	129	19	,	,	PUNCT
ap-1366	129	20	t	t	PROPN
ap-1366	129	21	)	)	PUNCT
ap-1366	129	22	·	·	PUNCT
ap-1366	130	1	lim	lim	PROPN
ap-1366	130	2	e→e0	e→e0	PROPN
ap-1366	130	3	[	[	PUNCT
ap-1366	130	4	−	−	PROPN
ap-1366	130	5	1	1	NUM
ap-1366	130	6	c0	c0	PROPN
ap-1366	130	7	dψ0,yψ0,l(y)ψ0,r(z	dψ0,yψ0,l(y)ψ0,r(z	PROPN
ap-1366	130	8	)	)	PUNCT
ap-1366	130	9	]	]	PUNCT
ap-1366	131	1	dz	dz	PROPN
ap-1366	131	2	+	+	CCONJ
ap-1366	131	3	dψ0,x	dψ0,x	PROPN
ap-1366	131	4	∫	∫	PROPN
ap-1366	131	5	(	(	PUNCT
ap-1366	131	6	y	y	PROPN
ap-1366	131	7	,	,	PUNCT
ap-1366	131	8	b	b	NOUN
ap-1366	131	9	)	)	PUNCT
ap-1366	131	10	k0(x	k0(x	NOUN
ap-1366	131	11	,	,	PUNCT
ap-1366	131	12	z	z	PROPN
ap-1366	131	13	,	,	PUNCT
ap-1366	131	14	t	t	PROPN
ap-1366	131	15	)	)	PUNCT
ap-1366	131	16	·	·	PUNCT
ap-1366	132	1	lim	lim	PROPN
ap-1366	132	2	e→e0	e→e0	PROPN
ap-1366	132	3	[	[	PUNCT
ap-1366	132	4	−	−	PROPN
ap-1366	132	5	1	1	NUM
ap-1366	132	6	c0	c0	NOUN
ap-1366	132	7	ψ0,l(z)dψ0,yψ0,r(y	ψ0,l(z)dψ0,yψ0,r(y	X
ap-1366	132	8	)	)	PUNCT
ap-1366	132	9	]	]	PUNCT
ap-1366	133	1	dz	dz	PROPN
ap-1366	133	2	.	.	PUNCT
ap-1366	133	3	(	(	PUNCT
ap-1366	133	4	18	18	NUM
ap-1366	133	5	)	)	PUNCT
ap-1366	133	6	we	we	PRON
ap-1366	133	7	will	will	AUX
ap-1366	133	8	now	now	ADV
ap-1366	133	9	determine	determine	VERB
ap-1366	133	10	the	the	DET
ap-1366	133	11	limits	limit	NOUN
ap-1366	133	12	that	that	SCONJ
ap-1366	133	13	the	the	DET
ap-1366	133	14	integrals	integral	NOUN
ap-1366	133	15	contain	contain	VERB
ap-1366	133	16	.	.	PUNCT
ap-1366	134	1	to	to	ADP
ap-1366	134	2	this	this	DET
ap-1366	134	3	end	end	NOUN
ap-1366	134	4	,	,	PUNCT
ap-1366	134	5	first	first	ADV
ap-1366	134	6	note	note	VERB
ap-1366	134	7	that	that	SCONJ
ap-1366	134	8	according	accord	VERB
ap-1366	134	9	to	to	ADP
ap-1366	134	10	(	(	PUNCT
ap-1366	134	11	5	5	NUM
ap-1366	134	12	)	)	PUNCT
ap-1366	134	13	the	the	DET
ap-1366	134	14	wronskian	wronskian	PROPN
ap-1366	134	15	w	w	PROPN
ap-1366	134	16	(	(	PUNCT
ap-1366	134	17	ψ0	ψ0	PROPN
ap-1366	134	18	,	,	PUNCT
ap-1366	134	19	ψ0,r	ψ0,r	PRON
ap-1366	134	20	)	)	PUNCT
ap-1366	134	21	is	be	AUX
ap-1366	134	22	involved	involve	VERB
ap-1366	134	23	in	in	ADP
ap-1366	134	24	the	the	DET
ap-1366	134	25	limits	limit	NOUN
ap-1366	134	26	,	,	PUNCT
ap-1366	134	27	which	which	PRON
ap-1366	134	28	we	we	PRON
ap-1366	134	29	will	will	AUX
ap-1366	134	30	now	now	ADV
ap-1366	134	31	find	find	VERB
ap-1366	134	32	by	by	ADP
ap-1366	134	33	means	mean	NOUN
ap-1366	134	34	of	of	ADP
ap-1366	134	35	the	the	DET
ap-1366	134	36	differential	differential	ADJ
ap-1366	134	37	equation	equation	NOUN
ap-1366	134	38	that	that	SCONJ
ap-1366	134	39	it	it	PRON
ap-1366	134	40	obeys	obey	VERB
ap-1366	134	41	.	.	PUNCT
ap-1366	135	1	we	we	PRON
ap-1366	135	2	have	have	VERB
ap-1366	135	3	w	w	PROPN
ap-1366	135	4	(	(	PUNCT
ap-1366	135	5	ψ0	ψ0	ADJ
ap-1366	135	6	,	,	PUNCT
ap-1366	135	7	ψ0,r)′(y	ψ0,r)′(y	PROPN
ap-1366	135	8	)	)	PUNCT
ap-1366	135	9	=	=	PUNCT
ap-1366	136	1	d	d	X
ap-1366	136	2	dy	dy	NOUN
ap-1366	136	3	[	[	PUNCT
ap-1366	136	4	ψ0(y)ψ′	ψ0(y)ψ′	NUM
ap-1366	136	5	0,r(y)−	0,r(y)−	NUM
ap-1366	136	6	ψ0,r(y)ψ′	ψ0,r(y)ψ′	NUM
ap-1366	136	7	0(y	0(y	NUM
ap-1366	136	8	)	)	PUNCT
ap-1366	136	9	]	]	PUNCT
ap-1366	137	1	=	=	PUNCT
ap-1366	137	2	ψ0(y)ψ′′	ψ0(y)ψ′′	NOUN
ap-1366	137	3	0,r(y)−	0,r(y)−	NUM
ap-1366	137	4	ψ′′	ψ′′	NOUN
ap-1366	137	5	0	0	PUNCT
ap-1366	138	1	(	(	PUNCT
ap-1366	138	2	y)ψ0,r(y	y)ψ0,r(y	PROPN
ap-1366	138	3	)	)	PUNCT
ap-1366	138	4	=	=	PUNCT
ap-1366	138	5	(	(	PUNCT
ap-1366	138	6	19	19	NUM
ap-1366	138	7	)	)	PUNCT
ap-1366	138	8	h(y	h(y	ADJ
ap-1366	138	9	)	)	PUNCT
ap-1366	138	10	f(y	f(y	NOUN
ap-1366	138	11	)	)	PUNCT
ap-1366	138	12	ψ0(y)ψ0,r(y)(e0	ψ0(y)ψ0,r(y)(e0	NOUN
ap-1366	138	13	−	−	PROPN
ap-1366	138	14	e)−	e)−	PROPN
ap-1366	138	15	f	f	PROPN
ap-1366	138	16	′(y	′(y	NOUN
ap-1366	138	17	)	)	PUNCT
ap-1366	138	18	f(y	f(y	NOUN
ap-1366	138	19	)	)	PUNCT
ap-1366	139	1	w	w	PROPN
ap-1366	140	1	(	(	PUNCT
ap-1366	140	2	ψ0	ψ0	ADJ
ap-1366	140	3	,	,	PUNCT
ap-1366	140	4	ψ0,r)(y	ψ0,r)(y	NUM
ap-1366	140	5	)	)	PUNCT
ap-1366	140	6	.	.	PUNCT
ap-1366	141	1	note	note	VERB
ap-1366	141	2	that	that	SCONJ
ap-1366	141	3	in	in	ADP
ap-1366	141	4	the	the	DET
ap-1366	141	5	third	third	ADJ
ap-1366	141	6	line	line	NOUN
ap-1366	141	7	we	we	PRON
ap-1366	141	8	replaced	replace	VERB
ap-1366	141	9	the	the	DET
ap-1366	141	10	second	second	ADJ
ap-1366	141	11	derivatives	derivative	NOUN
ap-1366	141	12	by	by	ADP
ap-1366	141	13	means	mean	NOUN
ap-1366	141	14	of	of	ADP
ap-1366	141	15	the	the	DET
ap-1366	141	16	generalized	generalize	VERB
ap-1366	141	17	schrödinger	schrödinger	NOUN
ap-1366	141	18	equation	equation	NOUN
ap-1366	141	19	(	(	PUNCT
ap-1366	141	20	1	1	NUM
ap-1366	141	21	)	)	PUNCT
ap-1366	141	22	.	.	PUNCT
ap-1366	142	1	equation	equation	NOUN
ap-1366	142	2	(	(	PUNCT
ap-1366	142	3	19	19	NUM
ap-1366	142	4	)	)	PUNCT
ap-1366	142	5	can	can	AUX
ap-1366	142	6	be	be	AUX
ap-1366	142	7	solved	solve	VERB
ap-1366	142	8	with	with	ADP
ap-1366	142	9	respect	respect	NOUN
ap-1366	142	10	to	to	ADP
ap-1366	142	11	the	the	DET
ap-1366	142	12	wronskian	wronskian	NOUN
ap-1366	142	13	,	,	PUNCT
ap-1366	142	14	giving	give	VERB
ap-1366	142	15	w	w	ADP
ap-1366	142	16	(	(	PUNCT
ap-1366	142	17	ψ0	ψ0	ADJ
ap-1366	142	18	,	,	PUNCT
ap-1366	142	19	ψ0,r)(y	ψ0,r)(y	PUNCT
ap-1366	142	20	)	)	PUNCT
ap-1366	143	1	=	=	SYM
ap-1366	143	2	e0	e0	PROPN
ap-1366	143	3	−	−	PROPN
ap-1366	143	4	e	e	PROPN
ap-1366	143	5	f(y	f(y	PROPN
ap-1366	143	6	)	)	PUNCT
ap-1366	143	7	∫	∫	PROPN
ap-1366	143	8	(	(	PUNCT
ap-1366	143	9	y	y	PROPN
ap-1366	143	10	,	,	PUNCT
ap-1366	143	11	b	b	NOUN
ap-1366	143	12	)	)	PUNCT
ap-1366	143	13	h(z)ψ0(z)ψ0,r(z	h(z)ψ0(z)ψ0,r(z	NOUN
ap-1366	143	14	)	)	PUNCT
ap-1366	143	15	dz	dz	PROPN
ap-1366	143	16	,	,	PUNCT
ap-1366	143	17	where	where	SCONJ
ap-1366	143	18	a	a	DET
ap-1366	143	19	constant	constant	NOUN
ap-1366	143	20	of	of	ADP
ap-1366	143	21	integration	integration	NOUN
ap-1366	143	22	has	have	AUX
ap-1366	143	23	been	be	AUX
ap-1366	143	24	set	set	VERB
ap-1366	143	25	to	to	ADP
ap-1366	143	26	zero	zero	NUM
ap-1366	143	27	.	.	PUNCT
ap-1366	144	1	thus	thus	ADV
ap-1366	144	2	,	,	PUNCT
ap-1366	144	3	we	we	PRON
ap-1366	144	4	have	have	AUX
ap-1366	144	5	dψ0,yψ0,r(y	dψ0,yψ0,r(y	VERB
ap-1366	144	6	)	)	PUNCT
ap-1366	144	7	=	=	PUNCT
ap-1366	144	8	√	√	ADP
ap-1366	144	9	1	1	NUM
ap-1366	144	10	f(y)h(y	f(y)h(y	ADV
ap-1366	144	11	)	)	PUNCT
ap-1366	144	12	e0	e0	PROPN
ap-1366	144	13	−	−	PROPN
ap-1366	144	14	e	e	X
ap-1366	144	15	ψ0(y	ψ0(y	PROPN
ap-1366	144	16	)	)	PUNCT
ap-1366	144	17	·	·	SYM
ap-1366	144	18	∫	∫	PROPN
ap-1366	144	19	(	(	PUNCT
ap-1366	144	20	y	y	PROPN
ap-1366	144	21	,	,	PUNCT
ap-1366	144	22	b	b	NOUN
ap-1366	144	23	)	)	PUNCT
ap-1366	144	24	h(z)ψ0(z)ψ0,r(z	h(z)ψ0(z)ψ0,r(z	NOUN
ap-1366	144	25	)	)	PUNCT
ap-1366	144	26	dz	dz	PROPN
ap-1366	144	27	.	.	PUNCT
ap-1366	145	1	thus	thus	ADV
ap-1366	145	2	,	,	PUNCT
ap-1366	145	3	the	the	DET
ap-1366	145	4	term	term	NOUN
ap-1366	145	5	inside	inside	ADP
ap-1366	145	6	the	the	DET
ap-1366	145	7	limit	limit	NOUN
ap-1366	145	8	in	in	ADP
ap-1366	145	9	(	(	PUNCT
ap-1366	145	10	18	18	NUM
ap-1366	145	11	)	)	PUNCT
ap-1366	145	12	reads	read	VERB
ap-1366	145	13	−	−	PROPN
ap-1366	145	14	1	1	NUM
ap-1366	145	15	c0	c0	NOUN
ap-1366	145	16	ψ0,l(z)dψ0,yψ0,r(y	ψ0,l(z)dψ0,yψ0,r(y	X
ap-1366	145	17	)	)	PUNCT
ap-1366	146	1	=	=	PUNCT
ap-1366	146	2	−e0	−e0	NOUN
ap-1366	146	3	−	−	PROPN
ap-1366	147	1	e	e	NOUN
ap-1366	147	2	c0	c0	NOUN
ap-1366	147	3	√	√	VERB
ap-1366	147	4	1	1	NUM
ap-1366	147	5	f(y)h(y	f(y)h(y	ADP
ap-1366	147	6	)	)	PUNCT
ap-1366	147	7	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	147	8	)	)	PUNCT
ap-1366	147	9	ψ0(y	ψ0(y	NUM
ap-1366	147	10	)	)	PUNCT
ap-1366	147	11	·	·	SYM
ap-1366	147	12	∫	∫	PROPN
ap-1366	147	13	(	(	PUNCT
ap-1366	147	14	y	y	PROPN
ap-1366	147	15	,	,	PUNCT
ap-1366	147	16	b	b	NOUN
ap-1366	147	17	)	)	PUNCT
ap-1366	147	18	h(z)ψ0(z)ψ0,r(z	h(z)ψ0(z)ψ0,r(z	NOUN
ap-1366	147	19	)	)	PUNCT
ap-1366	147	20	dz	dz	PROPN
ap-1366	147	21	.	.	PUNCT
ap-1366	148	1	(	(	PUNCT
ap-1366	148	2	20	20	NUM
ap-1366	148	3	)	)	PUNCT
ap-1366	148	4	according	accord	VERB
ap-1366	148	5	to	to	ADP
ap-1366	148	6	(	(	PUNCT
ap-1366	148	7	9	9	NUM
ap-1366	148	8	)	)	PUNCT
ap-1366	148	9	,	,	PUNCT
ap-1366	148	10	we	we	PRON
ap-1366	148	11	have	have	VERB
ap-1366	148	12	c0	c0	NOUN
ap-1366	148	13	=	=	SYM
ap-1366	148	14	f(b)wψ0,l	f(b)wψ0,l	PROPN
ap-1366	148	15	,	,	PUNCT
ap-1366	148	16	ψ0,r	ψ0,r	PROPN
ap-1366	148	17	(	(	PUNCT
ap-1366	148	18	b	b	NOUN
ap-1366	148	19	)	)	PUNCT
ap-1366	148	20	,	,	PUNCT
ap-1366	148	21	where	where	SCONJ
ap-1366	148	22	the	the	DET
ap-1366	148	23	right	right	ADJ
ap-1366	148	24	hand	hand	NOUN
ap-1366	148	25	side	side	NOUN
ap-1366	148	26	could	could	AUX
ap-1366	148	27	have	have	AUX
ap-1366	148	28	been	be	AUX
ap-1366	148	29	evaluated	evaluate	VERB
ap-1366	148	30	at	at	ADP
ap-1366	148	31	any	any	DET
ap-1366	148	32	point	point	NOUN
ap-1366	148	33	of	of	ADP
ap-1366	148	34	[	[	X
ap-1366	148	35	a	a	X
ap-1366	148	36	,	,	PUNCT
ap-1366	148	37	b	b	NOUN
ap-1366	148	38	]	]	X
ap-1366	148	39	;	;	PUNCT
ap-1366	148	40	the	the	DET
ap-1366	148	41	choice	choice	NOUN
ap-1366	148	42	b	b	NOUN
ap-1366	148	43	will	will	AUX
ap-1366	148	44	prove	prove	VERB
ap-1366	148	45	convenient	convenient	ADJ
ap-1366	148	46	in	in	ADP
ap-1366	148	47	subsequent	subsequent	ADJ
ap-1366	148	48	calculations	calculation	NOUN
ap-1366	148	49	.	.	PUNCT
ap-1366	149	1	thus	thus	ADV
ap-1366	149	2	,	,	PUNCT
ap-1366	149	3	taking	take	VERB
ap-1366	149	4	into	into	ADP
ap-1366	149	5	account	account	NOUN
ap-1366	149	6	the	the	DET
ap-1366	149	7	fact	fact	NOUN
ap-1366	149	8	that	that	SCONJ
ap-1366	149	9	ψ0,r(b	ψ0,r(b	ADP
ap-1366	149	10	)	)	PUNCT
ap-1366	149	11	=	=	SYM
ap-1366	149	12	0	0	NUM
ap-1366	149	13	,	,	PUNCT
ap-1366	149	14	we	we	PRON
ap-1366	149	15	have	have	AUX
ap-1366	149	16	c0	c0	NOUN
ap-1366	149	17	=	=	PUNCT
ap-1366	149	18	−f(b)ψ0,l(b)ψ′	−f(b)ψ0,l(b)ψ′	NOUN
ap-1366	149	19	0,r(b	0,r(b	NUM
ap-1366	149	20	)	)	PUNCT
ap-1366	149	21	,	,	PUNCT
ap-1366	149	22	which	which	PRON
ap-1366	149	23	we	we	PRON
ap-1366	149	24	will	will	AUX
ap-1366	149	25	now	now	ADV
ap-1366	149	26	express	express	VERB
ap-1366	149	27	by	by	ADP
ap-1366	149	28	means	mean	NOUN
ap-1366	149	29	of	of	ADP
ap-1366	149	30	an	an	DET
ap-1366	149	31	integral	integral	ADJ
ap-1366	149	32	.	.	PUNCT
ap-1366	150	1	to	to	ADP
ap-1366	150	2	this	this	DET
ap-1366	150	3	end	end	NOUN
ap-1366	150	4	,	,	PUNCT
ap-1366	150	5	consider	consider	VERB
ap-1366	150	6	our	our	PRON
ap-1366	150	7	generalized	generalized	ADJ
ap-1366	150	8	schrödinger	schrödinger	NOUN
ap-1366	150	9	equation	equation	NOUN
ap-1366	150	10	(	(	PUNCT
ap-1366	150	11	1	1	NUM
ap-1366	150	12	)	)	PUNCT
ap-1366	150	13	and	and	CCONJ
ap-1366	150	14	its	its	PRON
ap-1366	150	15	derivative	derivative	NOUN
ap-1366	150	16	with	with	ADP
ap-1366	150	17	respect	respect	NOUN
ap-1366	150	18	to	to	ADP
ap-1366	150	19	e	e	NOUN
ap-1366	150	20	,	,	PUNCT
ap-1366	150	21	each	each	PRON
ap-1366	150	22	multiplied	multiply	VERB
ap-1366	150	23	by	by	ADP
ap-1366	150	24	a	a	DET
ap-1366	150	25	ψ0,l	ψ0,l	PROPN
ap-1366	150	26	and	and	CCONJ
ap-1366	150	27	its	its	PRON
ap-1366	150	28	derivative	derivative	NOUN
ap-1366	150	29	with	with	ADP
ap-1366	150	30	respect	respect	NOUN
ap-1366	150	31	to	to	ADP
ap-1366	150	32	e	e	NOUN
ap-1366	150	33	,	,	PUNCT
ap-1366	150	34	respectively	respectively	ADV
ap-1366	150	35	:	:	PUNCT
ap-1366	150	36	{	{	PUNCT
ap-1366	150	37	f(z)ψ′′	f(z)ψ′′	NUM
ap-1366	150	38	0,l(z	0,l(z	NOUN
ap-1366	150	39	)	)	PUNCT
ap-1366	151	1	+	+	NUM
ap-1366	151	2	f	f	X
ap-1366	151	3	′(z)ψ′	′(z)ψ′	NOUN
ap-1366	151	4	0,l(z	0,l(z	NOUN
ap-1366	151	5	)	)	PUNCT
ap-1366	151	6	+	+	CCONJ
ap-1366	152	1	[	[	X
ap-1366	152	2	eh(z)−	eh(z)−	ADJ
ap-1366	152	3	v	v	X
ap-1366	152	4	(	(	PUNCT
ap-1366	152	5	z)]ψ0,l(z	z)]ψ0,l(z	NOUN
ap-1366	152	6	)	)	PUNCT
ap-1366	152	7	}	}	PUNCT
ap-1366	152	8	∂	∂	NUM
ap-1366	152	9	∂e	∂e	NOUN
ap-1366	152	10	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	152	11	)	)	PUNCT
ap-1366	152	12	=	=	SYM
ap-1366	152	13	0	0	NUM
ap-1366	152	14	[	[	PUNCT
ap-1366	152	15	f(z	f(z	PROPN
ap-1366	152	16	)	)	PUNCT
ap-1366	152	17	∂	∂	NUM
ap-1366	152	18	∂e	∂e	PROPN
ap-1366	152	19	ψ′′	ψ′′	NOUN
ap-1366	152	20	0,l(z	0,l(z	NOUN
ap-1366	152	21	)	)	PUNCT
ap-1366	153	1	+	+	CCONJ
ap-1366	153	2	f	f	PROPN
ap-1366	153	3	′(z	′(z	NOUN
ap-1366	153	4	)	)	PUNCT
ap-1366	153	5	∂	∂	NUM
ap-1366	153	6	∂e	∂e	PROPN
ap-1366	153	7	ψ′	ψ′	NUM
ap-1366	153	8	0,l(z	0,l(z	NOUN
ap-1366	153	9	)	)	PUNCT
ap-1366	154	1	+	+	NUM
ap-1366	154	2	h(z)ψ0,l(z	h(z)ψ0,l(z	NOUN
ap-1366	154	3	)	)	PUNCT
ap-1366	155	1	+	+	SYM
ap-1366	155	2	eh(z	eh(z	X
ap-1366	155	3	)	)	PUNCT
ap-1366	155	4	∂	∂	NOUN
ap-1366	156	1	∂e	∂e	PROPN
ap-1366	156	2	ψ0,l	ψ0,l	PROPN
ap-1366	156	3	−	−	PROPN
ap-1366	156	4	v	v	NOUN
ap-1366	156	5	(	(	PUNCT
ap-1366	156	6	z	z	NOUN
ap-1366	156	7	)	)	PUNCT
ap-1366	156	8	∂	∂	NOUN
ap-1366	156	9	∂e	∂e	PROPN
ap-1366	156	10	ψ0,l	ψ0,l	PROPN
ap-1366	156	11	]	]	PUNCT
ap-1366	156	12	×	×	NOUN
ap-1366	156	13	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	156	14	)	)	PUNCT
ap-1366	156	15	=	=	SYM
ap-1366	156	16	0	0	PUNCT
ap-1366	157	1	taking	take	VERB
ap-1366	157	2	the	the	DET
ap-1366	157	3	difference	difference	NOUN
ap-1366	157	4	of	of	ADP
ap-1366	157	5	these	these	DET
ap-1366	157	6	two	two	NUM
ap-1366	157	7	equations	equation	NOUN
ap-1366	157	8	yields	yield	VERB
ap-1366	157	9	the	the	DET
ap-1366	157	10	following	follow	VERB
ap-1366	157	11	result	result	NOUN
ap-1366	157	12	:	:	PUNCT
ap-1366	157	13	f	f	X
ap-1366	157	14	′(z)ψ′	′(z)ψ′	NOUN
ap-1366	157	15	0,l(z	0,l(z	NOUN
ap-1366	157	16	)	)	PUNCT
ap-1366	157	17	∂	∂	NUM
ap-1366	157	18	∂e	∂e	PROPN
ap-1366	157	19	ψ0,l(z)−	ψ0,l(z)−	PROPN
ap-1366	157	20	f	f	PROPN
ap-1366	157	21	′(z)ψ0,l(z	′(z)ψ0,l(z	PROPN
ap-1366	157	22	)	)	PUNCT
ap-1366	157	23	∂	∂	NUM
ap-1366	157	24	∂e	∂e	PROPN
ap-1366	157	25	ψ′	ψ′	NUM
ap-1366	157	26	0,l(z)−	0,l(z)−	NUM
ap-1366	157	27	h(z)ψ20,l(z	h(z)ψ20,l(z	PROPN
ap-1366	157	28	)	)	PUNCT
ap-1366	158	1	+	+	CCONJ
ap-1366	158	2	f(z)ψ′′	f(z)ψ′′	NUM
ap-1366	158	3	0,l(z	0,l(z	NOUN
ap-1366	158	4	)	)	PUNCT
ap-1366	158	5	∂	∂	NUM
ap-1366	158	6	∂e	∂e	NOUN
ap-1366	158	7	ψ0,l(z)−	ψ0,l(z)−	PROPN
ap-1366	158	8	f(z)ψ0,l(z	f(z)ψ0,l(z	PROPN
ap-1366	158	9	)	)	PUNCT
ap-1366	158	10	∂	∂	NUM
ap-1366	158	11	∂e	∂e	PROPN
ap-1366	158	12	ψ′′	ψ′′	NOUN
ap-1366	158	13	0,l(z	0,l(z	NOUN
ap-1366	158	14	)	)	PUNCT
ap-1366	158	15	=	=	SYM
ap-1366	158	16	0	0	X
ap-1366	158	17	.	.	X
ap-1366	158	18	66	66	NUM
ap-1366	158	19	acta	acta	PROPN
ap-1366	158	20	polytechnica	polytechnica	PROPN
ap-1366	158	21	vol	vol	NOUN
ap-1366	158	22	.	.	PUNCT
ap-1366	159	1	51	51	NUM
ap-1366	159	2	no	no	NOUN
ap-1366	159	3	.	.	PUNCT
ap-1366	160	1	1/2011	1/2011	NUM
ap-1366	160	2	rewriting	rewrite	VERB
ap-1366	160	3	and	and	CCONJ
ap-1366	160	4	integrating	integrate	VERB
ap-1366	160	5	this	this	DET
ap-1366	160	6	equation	equation	NOUN
ap-1366	160	7	gives∫	gives∫	NOUN
ap-1366	160	8	(	(	PUNCT
ap-1366	160	9	a	a	PRON
ap-1366	160	10	,	,	PUNCT
ap-1366	160	11	b	b	NOUN
ap-1366	160	12	)	)	PUNCT
ap-1366	160	13	h(z)ψ20,l(z	h(z)ψ20,l(z	PROPN
ap-1366	160	14	)	)	PUNCT
ap-1366	160	15	dz	dz	PROPN
ap-1366	161	1	=	=	SYM
ap-1366	161	2	∫	∫	PROPN
ap-1366	161	3	(	(	PUNCT
ap-1366	161	4	a	a	DET
ap-1366	161	5	,	,	PUNCT
ap-1366	161	6	b	b	NOUN
ap-1366	161	7	)	)	PUNCT
ap-1366	161	8	d	d	NOUN
ap-1366	161	9	dz	dz	X
ap-1366	161	10	[	[	PUNCT
ap-1366	161	11	f(z)ψ′	f(z)ψ′	NOUN
ap-1366	161	12	0,l(z	0,l(z	NOUN
ap-1366	161	13	)	)	PUNCT
ap-1366	161	14	]	]	PUNCT
ap-1366	161	15	∂	∂	NUM
ap-1366	161	16	∂e	∂e	PROPN
ap-1366	161	17	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	161	18	)	)	PUNCT
ap-1366	161	19	dz	dz	X
ap-1366	161	20	−∫	−∫	NOUN
ap-1366	161	21	(	(	PUNCT
ap-1366	161	22	a	a	DET
ap-1366	161	23	,	,	PUNCT
ap-1366	161	24	b	b	NOUN
ap-1366	161	25	)	)	PUNCT
ap-1366	161	26	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	161	27	)	)	PUNCT
ap-1366	161	28	d	d	X
ap-1366	161	29	dz	dz	X
ap-1366	161	30	[	[	PUNCT
ap-1366	161	31	f(z	f(z	PROPN
ap-1366	161	32	)	)	PUNCT
ap-1366	161	33	∂	∂	NUM
ap-1366	161	34	∂e	∂e	NOUN
ap-1366	161	35	ψ′	ψ′	NUM
ap-1366	161	36	0,l(z	0,l(z	NOUN
ap-1366	161	37	)	)	PUNCT
ap-1366	161	38	]	]	PUNCT
ap-1366	161	39	dz	dz	PROPN
ap-1366	161	40	.	.	PUNCT
ap-1366	162	1	the	the	DET
ap-1366	162	2	two	two	NUM
ap-1366	162	3	integrals	integral	NOUN
ap-1366	162	4	on	on	ADP
ap-1366	162	5	the	the	DET
ap-1366	162	6	right	right	ADJ
ap-1366	162	7	hand	hand	NOUN
ap-1366	162	8	side	side	NOUN
ap-1366	162	9	can	can	AUX
ap-1366	162	10	each	each	PRON
ap-1366	162	11	be	be	AUX
ap-1366	162	12	reformulated	reformulate	VERB
ap-1366	162	13	using	use	VERB
ap-1366	162	14	integration	integration	NOUN
ap-1366	162	15	by	by	ADP
ap-1366	162	16	parts.∫	parts.∫	PROPN
ap-1366	162	17	(	(	PUNCT
ap-1366	162	18	a	a	DET
ap-1366	162	19	,	,	PUNCT
ap-1366	162	20	b	b	NOUN
ap-1366	162	21	)	)	PUNCT
ap-1366	163	1	d	d	NOUN
ap-1366	163	2	dz	dz	X
ap-1366	163	3	[	[	PUNCT
ap-1366	163	4	f(z)ψ′	f(z)ψ′	NOUN
ap-1366	163	5	0,l(z	0,l(z	NOUN
ap-1366	163	6	)	)	PUNCT
ap-1366	163	7	]	]	PUNCT
ap-1366	163	8	∂	∂	NUM
ap-1366	163	9	∂e	∂e	PROPN
ap-1366	163	10	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	163	11	)	)	PUNCT
ap-1366	163	12	dz	dz	PROPN
ap-1366	163	13	=	=	SYM
ap-1366	163	14	∂	∂	NUM
ap-1366	163	15	∂e	∂e	PROPN
ap-1366	163	16	ψ0,l(z)f(z)ψ0,l(z	ψ0,l(z)f(z)ψ0,l(z	NOUN
ap-1366	163	17	)	)	PUNCT
ap-1366	164	1	∣∣∣∣∣	∣∣∣∣∣	NOUN
ap-1366	164	2	b	b	ADP
ap-1366	164	3	a	a	DET
ap-1366	164	4	−∫	−∫	NOUN
ap-1366	164	5	(	(	PUNCT
ap-1366	164	6	a	a	PRON
ap-1366	164	7	,	,	PUNCT
ap-1366	164	8	b	b	NOUN
ap-1366	164	9	)	)	PUNCT
ap-1366	164	10	f(z)ψ0,l(z	f(z)ψ0,l(z	NOUN
ap-1366	164	11	)	)	PUNCT
ap-1366	164	12	∂	∂	NUM
ap-1366	164	13	∂e	∂e	NOUN
ap-1366	164	14	ψ′	ψ′	NUM
ap-1366	164	15	0,l(z	0,l(z	NOUN
ap-1366	164	16	)	)	PUNCT
ap-1366	164	17	dz∫	dz∫	NOUN
ap-1366	164	18	(	(	PUNCT
ap-1366	164	19	a	a	PRON
ap-1366	164	20	,	,	PUNCT
ap-1366	164	21	b	b	NOUN
ap-1366	164	22	)	)	PUNCT
ap-1366	164	23	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	164	24	)	)	PUNCT
ap-1366	165	1	d	d	X
ap-1366	165	2	dz	dz	X
ap-1366	165	3	[	[	PUNCT
ap-1366	165	4	f(z	f(z	PROPN
ap-1366	165	5	)	)	PUNCT
ap-1366	165	6	∂	∂	NUM
ap-1366	165	7	∂e	∂e	NOUN
ap-1366	165	8	ψ′	ψ′	NUM
ap-1366	165	9	0,l(z	0,l(z	NOUN
ap-1366	165	10	)	)	PUNCT
ap-1366	165	11	]	]	PUNCT
ap-1366	165	12	dz	dz	PROPN
ap-1366	165	13	=	=	PUNCT
ap-1366	165	14	f(z)ψ0,l(z	f(z)ψ0,l(z	PROPN
ap-1366	165	15	)	)	PUNCT
ap-1366	165	16	∂	∂	NUM
ap-1366	165	17	∂e	∂e	NOUN
ap-1366	165	18	ψ′	ψ′	NUM
ap-1366	165	19	0,l(z	0,l(z	NOUN
ap-1366	165	20	)	)	PUNCT
ap-1366	165	21	∣∣∣∣∣	∣∣∣∣∣	ADP
ap-1366	165	22	b	b	X
ap-1366	165	23	a	a	DET
ap-1366	165	24	−∫	−∫	NOUN
ap-1366	165	25	(	(	PUNCT
ap-1366	165	26	a	a	PRON
ap-1366	165	27	,	,	PUNCT
ap-1366	165	28	b	b	NOUN
ap-1366	165	29	)	)	PUNCT
ap-1366	165	30	f(z)ψ0,l(z	f(z)ψ0,l(z	NOUN
ap-1366	165	31	)	)	PUNCT
ap-1366	165	32	∂	∂	NUM
ap-1366	165	33	∂e	∂e	NOUN
ap-1366	165	34	ψ′	ψ′	NUM
ap-1366	165	35	0,l(z	0,l(z	NOUN
ap-1366	165	36	)	)	PUNCT
ap-1366	166	1	dz	dz	PROPN
ap-1366	166	2	.	.	PROPN
ap-1366	166	3	observe	observe	VERB
ap-1366	166	4	that	that	SCONJ
ap-1366	166	5	both	both	DET
ap-1366	166	6	expressions	expression	NOUN
ap-1366	166	7	involve	involve	VERB
ap-1366	166	8	the	the	DET
ap-1366	166	9	same	same	ADJ
ap-1366	166	10	integral	integral	ADJ
ap-1366	166	11	term	term	NOUN
ap-1366	166	12	on	on	ADP
ap-1366	166	13	their	their	PRON
ap-1366	166	14	right	right	ADJ
ap-1366	166	15	hand	hand	NOUN
ap-1366	166	16	sides	side	NOUN
ap-1366	166	17	.	.	PUNCT
ap-1366	167	1	therefore	therefore	ADV
ap-1366	167	2	,	,	PUNCT
ap-1366	167	3	if	if	SCONJ
ap-1366	167	4	we	we	PRON
ap-1366	167	5	substitute	substitute	VERB
ap-1366	167	6	into	into	ADP
ap-1366	167	7	their	their	PRON
ap-1366	167	8	difference	difference	NOUN
ap-1366	167	9	above	above	ADV
ap-1366	167	10	,	,	PUNCT
ap-1366	167	11	we	we	PRON
ap-1366	167	12	obtain∫	obtain∫	VERB
ap-1366	167	13	(	(	PUNCT
ap-1366	167	14	a	a	PRON
ap-1366	167	15	,	,	PUNCT
ap-1366	167	16	b	b	NOUN
ap-1366	167	17	)	)	PUNCT
ap-1366	167	18	h(z)ψ20,l(z	h(z)ψ20,l(z	PROPN
ap-1366	167	19	)	)	PUNCT
ap-1366	167	20	dz	dz	NOUN
ap-1366	168	1	=	=	PUNCT
ap-1366	169	1	f(b)ψ′	f(b)ψ′	PROPN
ap-1366	169	2	0,l(b	0,l(b	NUM
ap-1366	169	3	)	)	PUNCT
ap-1366	169	4	∂	∂	NOUN
ap-1366	169	5	∂e	∂e	PROPN
ap-1366	169	6	ψ0,l(b)−	ψ0,l(b)−	VERB
ap-1366	169	7	f(b)ψ0,l(b	f(b)ψ0,l(b	PROPN
ap-1366	169	8	)	)	PUNCT
ap-1366	169	9	∂	∂	NUM
ap-1366	169	10	∂e	∂e	PROPN
ap-1366	169	11	ψ′	ψ′	NUM
ap-1366	169	12	0,l(b	0,l(b	NUM
ap-1366	169	13	)	)	PUNCT
ap-1366	169	14	.	.	PUNCT
ap-1366	170	1	(	(	PUNCT
ap-1366	170	2	21	21	NUM
ap-1366	170	3	)	)	PUNCT
ap-1366	170	4	note	note	VERB
ap-1366	170	5	that	that	SCONJ
ap-1366	170	6	in	in	ADP
ap-1366	170	7	the	the	DET
ap-1366	170	8	last	last	ADJ
ap-1366	170	9	step	step	NOUN
ap-1366	170	10	we	we	PRON
ap-1366	170	11	substituted	substitute	VERB
ap-1366	170	12	the	the	DET
ap-1366	170	13	limits	limit	NOUN
ap-1366	170	14	of	of	ADP
ap-1366	170	15	integration	integration	NOUN
ap-1366	170	16	and	and	CCONJ
ap-1366	170	17	made	make	VERB
ap-1366	170	18	use	use	NOUN
ap-1366	170	19	of	of	ADP
ap-1366	170	20	the	the	DET
ap-1366	170	21	fact	fact	NOUN
ap-1366	171	1	that	that	SCONJ
ap-1366	171	2	ψ0,l(a	ψ0,l(a	NOUN
ap-1366	171	3	)	)	PUNCT
ap-1366	171	4	=	=	SYM
ap-1366	171	5	0	0	X
ap-1366	171	6	.	.	PUNCT
ap-1366	171	7	now	now	ADV
ap-1366	171	8	we	we	PRON
ap-1366	171	9	are	be	AUX
ap-1366	171	10	ready	ready	ADJ
ap-1366	171	11	to	to	PART
ap-1366	171	12	compute	compute	VERB
ap-1366	171	13	the	the	DET
ap-1366	171	14	limits	limit	NOUN
ap-1366	171	15	in	in	ADP
ap-1366	171	16	(	(	PUNCT
ap-1366	171	17	18	18	NUM
ap-1366	171	18	)	)	PUNCT
ap-1366	171	19	.	.	PUNCT
ap-1366	172	1	according	accord	VERB
ap-1366	172	2	to	to	ADP
ap-1366	172	3	(	(	PUNCT
ap-1366	172	4	20	20	NUM
ap-1366	172	5	)	)	PUNCT
ap-1366	172	6	,	,	PUNCT
ap-1366	172	7	the	the	DET
ap-1366	172	8	first	first	ADJ
ap-1366	172	9	limit	limit	NOUN
ap-1366	172	10	reads	read	VERB
ap-1366	172	11	lim	lim	PROPN
ap-1366	172	12	e→e0	e→e0	PROPN
ap-1366	172	13	[	[	PUNCT
ap-1366	172	14	−	−	PROPN
ap-1366	172	15	1	1	NUM
ap-1366	172	16	c0	c0	PROPN
ap-1366	172	17	dψ0,yψ0,l(y)ψ0,r(z	dψ0,yψ0,l(y)ψ0,r(z	PROPN
ap-1366	172	18	)	)	PUNCT
ap-1366	172	19	]	]	PUNCT
ap-1366	173	1	=	=	PUNCT
ap-1366	173	2	lim	lim	PROPN
ap-1366	173	3	e→e0	e→e0	PROPN
ap-1366	173	4	[	[	PUNCT
ap-1366	173	5	e0	e0	PROPN
ap-1366	173	6	−	−	PROPN
ap-1366	173	7	e	e	NOUN
ap-1366	173	8	f(b)ψ0,l(b)ψ′	f(b)ψ0,l(b)ψ′	NOUN
ap-1366	173	9	0,r(b	0,r(b	NUM
ap-1366	173	10	)	)	PUNCT
ap-1366	173	11	√	√	ADV
ap-1366	173	12	1	1	NUM
ap-1366	173	13	f(y)h(y	f(y)h(y	NUM
ap-1366	173	14	)	)	PUNCT
ap-1366	173	15	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	173	16	)	)	PUNCT
ap-1366	173	17	ψ0(y	ψ0(y	NUM
ap-1366	173	18	)	)	PUNCT
ap-1366	173	19	·	·	PUNCT
ap-1366	173	20	∫	∫	PROPN
ap-1366	173	21	(	(	PUNCT
ap-1366	173	22	y	y	PROPN
ap-1366	173	23	,	,	PUNCT
ap-1366	173	24	b	b	NOUN
ap-1366	173	25	)	)	PUNCT
ap-1366	173	26	h(z)ψ0(z)ψ0,r(z	h(z)ψ0(z)ψ0,r(z	NOUN
ap-1366	173	27	)	)	PUNCT
ap-1366	173	28	dz	dz	X
ap-1366	173	29	]	]	PUNCT
ap-1366	174	1	=	=	SYM
ap-1366	174	2	lim	lim	PROPN
ap-1366	174	3	e→e0	e→e0	PROPN
ap-1366	174	4	[	[	PUNCT
ap-1366	174	5	e0	e0	PROPN
ap-1366	174	6	−	−	PROPN
ap-1366	174	7	e	e	NOUN
ap-1366	174	8	ψ0,l(b	ψ0,l(b	NOUN
ap-1366	174	9	)	)	PUNCT
ap-1366	174	10	]	]	PUNCT
ap-1366	174	11	·	·	PUNCT
ap-1366	175	1	lim	lim	PROPN
ap-1366	175	2	e→e0	e→e0	PROPN
ap-1366	175	3	[	[	PUNCT
ap-1366	175	4	1	1	NUM
ap-1366	175	5	f(b)ψ′	f(b)ψ′	ADJ
ap-1366	175	6	0,r(b	0,r(b	NUM
ap-1366	175	7	)	)	PUNCT
ap-1366	175	8	√	√	ADV
ap-1366	175	9	1	1	NUM
ap-1366	175	10	f(y)h(y	f(y)h(y	NUM
ap-1366	175	11	)	)	PUNCT
ap-1366	175	12	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	175	13	)	)	PUNCT
ap-1366	175	14	ψ0(y	ψ0(y	NUM
ap-1366	175	15	)	)	PUNCT
ap-1366	175	16	·	·	PUNCT
ap-1366	176	1	∫	∫	PROPN
ap-1366	176	2	(	(	PUNCT
ap-1366	176	3	y	y	PROPN
ap-1366	176	4	,	,	PUNCT
ap-1366	176	5	b	b	NOUN
ap-1366	176	6	)	)	PUNCT
ap-1366	176	7	h(z)ψ0(z)ψ0,r(z	h(z)ψ0(z)ψ0,r(z	NOUN
ap-1366	176	8	)	)	PUNCT
ap-1366	176	9	dz	dz	X
ap-1366	176	10	]	]	PUNCT
ap-1366	177	1	=	=	PUNCT
ap-1366	177	2	−	−	PROPN
ap-1366	177	3	1	1	NUM
ap-1366	177	4	∂	∂	NUM
ap-1366	177	5	∂e	∂e	NOUN
ap-1366	177	6	ψ0,l(b	ψ0,l(b	NOUN
ap-1366	177	7	)	)	PUNCT
ap-1366	178	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ap-1366	178	2	e	e	X
ap-1366	178	3	=	=	PROPN
ap-1366	178	4	e0	e0	X
ap-1366	178	5	·	·	PUNCT
ap-1366	178	6	lim	lim	PROPN
ap-1366	178	7	e→e0	e→e0	PROPN
ap-1366	178	8	[	[	PUNCT
ap-1366	178	9	1	1	NUM
ap-1366	178	10	f(b)ψ′	f(b)ψ′	ADJ
ap-1366	178	11	0,r(b	0,r(b	NUM
ap-1366	178	12	)	)	PUNCT
ap-1366	178	13	√	√	ADV
ap-1366	178	14	1	1	NUM
ap-1366	178	15	f(y)h(y	f(y)h(y	NUM
ap-1366	178	16	)	)	PUNCT
ap-1366	178	17	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	178	18	)	)	PUNCT
ap-1366	178	19	ψ0(y	ψ0(y	NUM
ap-1366	178	20	)	)	PUNCT
ap-1366	178	21	·	·	PUNCT
ap-1366	179	1	∫	∫	PROPN
ap-1366	179	2	(	(	PUNCT
ap-1366	179	3	y	y	PROPN
ap-1366	179	4	,	,	PUNCT
ap-1366	179	5	b	b	NOUN
ap-1366	179	6	)	)	PUNCT
ap-1366	179	7	h(z)ψ0(z)ψ0,r(z	h(z)ψ0(z)ψ0,r(z	NOUN
ap-1366	179	8	)	)	PUNCT
ap-1366	179	9	dz	dz	PROPN
ap-1366	179	10	]	]	PUNCT
ap-1366	179	11	.	.	PUNCT
ap-1366	180	1	(	(	PUNCT
ap-1366	180	2	22	22	NUM
ap-1366	180	3	)	)	PUNCT
ap-1366	180	4	in	in	ADP
ap-1366	180	5	the	the	DET
ap-1366	180	6	next	next	ADJ
ap-1366	180	7	step	step	NOUN
ap-1366	180	8	we	we	PRON
ap-1366	180	9	substitute	substitute	VERB
ap-1366	180	10	the	the	DET
ap-1366	180	11	first	first	ADJ
ap-1366	180	12	factor	factor	NOUN
ap-1366	180	13	using	use	VERB
ap-1366	180	14	our	our	PRON
ap-1366	180	15	relation	relation	NOUN
ap-1366	180	16	(	(	PUNCT
ap-1366	180	17	21	21	NUM
ap-1366	180	18	)	)	PUNCT
ap-1366	180	19	,	,	PUNCT
ap-1366	180	20	which	which	PRON
ap-1366	180	21	we	we	PRON
ap-1366	180	22	need	need	VERB
ap-1366	180	23	to	to	PART
ap-1366	180	24	evaluate	evaluate	VERB
ap-1366	180	25	at	at	ADP
ap-1366	180	26	e	e	X
ap-1366	180	27	=	=	PROPN
ap-1366	180	28	e0	e0	PROPN
ap-1366	180	29	.	.	PUNCT
ap-1366	181	1	since	since	SCONJ
ap-1366	181	2	our	our	PRON
ap-1366	181	3	generalized	generalized	ADJ
ap-1366	181	4	schrödinger	schrödinger	NOUN
ap-1366	181	5	equation	equation	NOUN
ap-1366	181	6	(	(	PUNCT
ap-1366	181	7	1	1	X
ap-1366	181	8	)	)	PUNCT
ap-1366	181	9	can	can	AUX
ap-1366	181	10	only	only	ADV
ap-1366	181	11	have	have	VERB
ap-1366	181	12	two	two	NUM
ap-1366	181	13	linearly	linearly	ADV
ap-1366	181	14	independent	independent	ADJ
ap-1366	181	15	solutions	solution	NOUN
ap-1366	181	16	at	at	ADP
ap-1366	181	17	e	e	PROPN
ap-1366	181	18	=	=	SYM
ap-1366	181	19	e0	e0	PROPN
ap-1366	181	20	,	,	PUNCT
ap-1366	181	21	the	the	DET
ap-1366	181	22	three	three	NUM
ap-1366	181	23	solutions	solution	NOUN
ap-1366	181	24	ψ0,l	ψ0,l	PROPN
ap-1366	181	25	,	,	PUNCT
ap-1366	181	26	ψ0,r	ψ0,r	PROPN
ap-1366	181	27	and	and	CCONJ
ap-1366	181	28	ψ0	ψ0	ADV
ap-1366	181	29	become	become	VERB
ap-1366	181	30	linearly	linearly	ADV
ap-1366	181	31	dependent	dependent	ADJ
ap-1366	181	32	there	there	ADV
ap-1366	181	33	.	.	PUNCT
ap-1366	182	1	in	in	ADP
ap-1366	182	2	particular	particular	ADJ
ap-1366	182	3	,	,	PUNCT
ap-1366	182	4	they	they	PRON
ap-1366	182	5	must	must	AUX
ap-1366	182	6	all	all	ADV
ap-1366	182	7	fulfill	fulfill	VERB
ap-1366	182	8	the	the	DET
ap-1366	182	9	same	same	ADJ
ap-1366	182	10	boundary	boundary	ADJ
ap-1366	182	11	conditions	condition	NOUN
ap-1366	182	12	(	(	PUNCT
ap-1366	182	13	2	2	NUM
ap-1366	182	14	)	)	PUNCT
ap-1366	182	15	,	,	PUNCT
ap-1366	182	16	which	which	PRON
ap-1366	182	17	implies	imply	VERB
ap-1366	182	18	for	for	ADP
ap-1366	182	19	the	the	DET
ap-1366	182	20	right	right	ADJ
ap-1366	182	21	hand	hand	NOUN
ap-1366	182	22	side	side	NOUN
ap-1366	182	23	of	of	ADP
ap-1366	182	24	(	(	PUNCT
ap-1366	182	25	21	21	NUM
ap-1366	182	26	)	)	PUNCT
ap-1366	182	27	that	that	SCONJ
ap-1366	182	28	[	[	PUNCT
ap-1366	182	29	f(b)ψ′	f(b)ψ′	PROPN
ap-1366	182	30	0,l(b	0,l(b	NUM
ap-1366	182	31	)	)	PUNCT
ap-1366	182	32	∂	∂	NOUN
ap-1366	182	33	∂e	∂e	PROPN
ap-1366	182	34	ψ0,l(b)−	ψ0,l(b)−	VERB
ap-1366	182	35	f(b)ψ0,l(b	f(b)ψ0,l(b	PROPN
ap-1366	182	36	)	)	PUNCT
ap-1366	182	37	∂	∂	NUM
ap-1366	182	38	∂e	∂e	PROPN
ap-1366	182	39	ψ′	ψ′	NUM
ap-1366	182	40	0,l(b	0,l(b	NUM
ap-1366	182	41	)	)	PUNCT
ap-1366	182	42	]	]	PUNCT
ap-1366	183	1	∣∣∣∣∣	∣∣∣∣∣	X
ap-1366	183	2	e	e	X
ap-1366	183	3	=	=	NOUN
ap-1366	183	4	e0	e0	NOUN
ap-1366	183	5	=	=	PUNCT
ap-1366	183	6	f(b)ψ′	f(b)ψ′	PROPN
ap-1366	183	7	0,l(b	0,l(b	NUM
ap-1366	183	8	)	)	PUNCT
ap-1366	183	9	∂	∂	NOUN
ap-1366	183	10	∂e	∂e	NOUN
ap-1366	183	11	ψ0,l(b	ψ0,l(b	NOUN
ap-1366	183	12	)	)	PUNCT
ap-1366	183	13	∣∣∣∣∣	∣∣∣∣∣	ADP
ap-1366	184	1	e	e	X
ap-1366	184	2	=	=	PROPN
ap-1366	184	3	e0	e0	PROPN
ap-1366	184	4	.	.	PUNCT
ap-1366	185	1	now	now	ADV
ap-1366	185	2	,	,	PUNCT
ap-1366	185	3	(	(	PUNCT
ap-1366	185	4	21	21	NUM
ap-1366	185	5	)	)	PUNCT
ap-1366	185	6	can	can	AUX
ap-1366	185	7	be	be	AUX
ap-1366	185	8	solved	solve	VERB
ap-1366	185	9	for	for	ADP
ap-1366	185	10	∂	∂	NOUN
ap-1366	185	11	∂e	∂e	PROPN
ap-1366	185	12	ψ0,l(b	ψ0,l(b	NOUN
ap-1366	185	13	):	):	PUNCT
ap-1366	185	14	∂	∂	NUM
ap-1366	185	15	∂e	∂e	NOUN
ap-1366	185	16	ψ0,l(b	ψ0,l(b	NOUN
ap-1366	185	17	)	)	PUNCT
ap-1366	185	18	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ap-1366	186	1	e	e	X
ap-1366	186	2	=	=	NOUN
ap-1366	186	3	e0	e0	NOUN
ap-1366	186	4	=[	=[	NOUN
ap-1366	186	5	1	1	NUM
ap-1366	186	6	f(b)ψ′	f(b)ψ′	ADJ
ap-1366	186	7	0,l(b	0,l(b	NUM
ap-1366	186	8	)	)	PUNCT
ap-1366	186	9	∫	∫	PROPN
ap-1366	187	1	(	(	PUNCT
ap-1366	187	2	a	a	PRON
ap-1366	187	3	,	,	PUNCT
ap-1366	187	4	b	b	NOUN
ap-1366	187	5	)	)	PUNCT
ap-1366	187	6	h(z)ψ20,l(z	h(z)ψ20,l(z	PROPN
ap-1366	187	7	)	)	PUNCT
ap-1366	187	8	dz	dz	X
ap-1366	187	9	]	]	PUNCT
ap-1366	187	10	∣∣∣∣∣	∣∣∣∣∣	ADJ
ap-1366	187	11	e	e	X
ap-1366	187	12	=	=	PROPN
ap-1366	187	13	e0	e0	PROPN
ap-1366	187	14	.	.	PUNCT
ap-1366	188	1	we	we	PRON
ap-1366	188	2	use	use	VERB
ap-1366	188	3	this	this	PRON
ap-1366	188	4	to	to	PART
ap-1366	188	5	replace	replace	VERB
ap-1366	188	6	the	the	DET
ap-1366	188	7	first	first	ADJ
ap-1366	188	8	factor	factor	NOUN
ap-1366	188	9	of	of	ADP
ap-1366	188	10	(	(	PUNCT
ap-1366	188	11	22	22	NUM
ap-1366	188	12	)	)	PUNCT
ap-1366	188	13	and	and	CCONJ
ap-1366	188	14	get	get	VERB
ap-1366	188	15	lim	lim	PROPN
ap-1366	188	16	e→e0	e→e0	NOUN
ap-1366	188	17	[	[	PUNCT
ap-1366	188	18	−	−	PROPN
ap-1366	188	19	1	1	NUM
ap-1366	188	20	c0	c0	PROPN
ap-1366	188	21	dψ0,yψ0,l(y)ψ0,r(z	dψ0,yψ0,l(y)ψ0,r(z	PROPN
ap-1366	188	22	)	)	PUNCT
ap-1366	188	23	]	]	PUNCT
ap-1366	189	1	=	=	PUNCT
ap-1366	189	2	−	−	PROPN
ap-1366	189	3	lim	lim	PROPN
ap-1366	189	4	e→e0	e→e0	PROPN
ap-1366	189	5	[	[	PUNCT
ap-1366	189	6	ψ′	ψ′	NUM
ap-1366	189	7	0,l(b	0,l(b	NUM
ap-1366	189	8	)	)	PUNCT
ap-1366	189	9	ψ′	ψ′	NUM
ap-1366	189	10	0,r(b	0,r(b	NOUN
ap-1366	189	11	)	)	PUNCT
ap-1366	189	12	√	√	ADV
ap-1366	189	13	1	1	NUM
ap-1366	189	14	f(y)h(y	f(y)h(y	NUM
ap-1366	189	15	)	)	PUNCT
ap-1366	189	16	ψ0,l(z	ψ0,l(z	NOUN
ap-1366	189	17	)	)	PUNCT
ap-1366	189	18	ψ0(y	ψ0(y	NUM
ap-1366	189	19	)	)	PUNCT
ap-1366	189	20	·	·	SYM
ap-1366	189	21	∫	∫	PROPN
ap-1366	189	22	(	(	PUNCT
ap-1366	189	23	y	y	PROPN
ap-1366	189	24	,	,	PUNCT
ap-1366	189	25	b	b	NOUN
ap-1366	189	26	)	)	PUNCT
ap-1366	189	27	h(z)ψ0(z)ψ0,r(z	h(z)ψ0(z)ψ0,r(z	NOUN
ap-1366	189	28	)	)	PUNCT
ap-1366	189	29	dz∫	dz∫	NOUN
ap-1366	189	30	(	(	PUNCT
ap-1366	189	31	a	a	PRON
ap-1366	189	32	,	,	PUNCT
ap-1366	189	33	b	b	NOUN
ap-1366	189	34	)	)	PUNCT
ap-1366	189	35	h(z)ψ	h(z)ψ	PROPN
ap-1366	189	36	2	2	NUM
ap-1366	189	37	0,l(z	0,l(z	NOUN
ap-1366	189	38	)	)	PUNCT
ap-1366	189	39	dz	dz	NOUN
ap-1366	189	40	]	]	PUNCT
ap-1366	189	41	.	.	PUNCT
ap-1366	190	1	for	for	ADP
ap-1366	190	2	taking	take	VERB
ap-1366	190	3	the	the	DET
ap-1366	190	4	limit	limit	NOUN
ap-1366	190	5	we	we	PRON
ap-1366	190	6	recall	recall	VERB
ap-1366	190	7	that	that	PRON
ap-1366	190	8	at	at	ADP
ap-1366	190	9	e	e	PROPN
ap-1366	190	10	=	=	SYM
ap-1366	190	11	e0	e0	PROPN
ap-1366	190	12	the	the	DET
ap-1366	190	13	functions	function	NOUN
ap-1366	190	14	ψ0,l	ψ0,l	PROPN
ap-1366	190	15	,	,	PUNCT
ap-1366	190	16	ψ0,r	ψ0,r	PROPN
ap-1366	190	17	and	and	CCONJ
ap-1366	190	18	ψ0	ψ0	ADV
ap-1366	190	19	become	become	VERB
ap-1366	190	20	linearly	linearly	ADV
ap-1366	190	21	dependent	dependent	ADJ
ap-1366	190	22	.	.	PUNCT
ap-1366	191	1	the	the	DET
ap-1366	191	2	respective	respective	ADJ
ap-1366	191	3	proportionality	proportionality	NOUN
ap-1366	191	4	constants	constant	NOUN
ap-1366	191	5	cancel	cancel	VERB
ap-1366	191	6	out	out	ADP
ap-1366	191	7	and	and	CCONJ
ap-1366	191	8	we	we	PRON
ap-1366	191	9	obtain	obtain	VERB
ap-1366	191	10	lim	lim	NOUN
ap-1366	191	11	e→e0	e→e0	PROPN
ap-1366	191	12	[	[	PUNCT
ap-1366	191	13	−	−	PROPN
ap-1366	191	14	1	1	NUM
ap-1366	191	15	c0	c0	PROPN
ap-1366	191	16	dψ0,yψ0,l(y)ψ0,r(z	dψ0,yψ0,l(y)ψ0,r(z	PROPN
ap-1366	191	17	)	)	PUNCT
ap-1366	191	18	]	]	PUNCT
ap-1366	192	1	=	=	PUNCT
ap-1366	193	1	−	−	PROPN
ap-1366	193	2	√	√	NUM
ap-1366	193	3	1	1	NUM
ap-1366	193	4	f(y)h(y	f(y)h(y	ADP
ap-1366	193	5	)	)	PUNCT
ap-1366	193	6	ψ0(z	ψ0(z	PROPN
ap-1366	193	7	)	)	PUNCT
ap-1366	193	8	ψ0(y	ψ0(y	X
ap-1366	193	9	)	)	PUNCT
ap-1366	193	10	∫	∫	PROPN
ap-1366	194	1	(	(	PUNCT
ap-1366	194	2	y	y	PROPN
ap-1366	194	3	,	,	PUNCT
ap-1366	194	4	b	b	NOUN
ap-1366	194	5	)	)	PUNCT
ap-1366	194	6	h(z)ψ	h(z)ψ	PROPN
ap-1366	194	7	2	2	NUM
ap-1366	194	8	0(z	0(z	NOUN
ap-1366	194	9	)	)	PUNCT
ap-1366	194	10	dz∫	dz∫	NOUN
ap-1366	194	11	(	(	PUNCT
ap-1366	194	12	a	a	PRON
ap-1366	194	13	,	,	PUNCT
ap-1366	194	14	b	b	NOUN
ap-1366	194	15	)	)	PUNCT
ap-1366	194	16	h(z)ψ	h(z)ψ	PROPN
ap-1366	194	17	2	2	NUM
ap-1366	194	18	0(z	0(z	NUM
ap-1366	194	19	)	)	PUNCT
ap-1366	194	20	dz	dz	PROPN
ap-1366	194	21	.	.	PUNCT
ap-1366	195	1	67	67	NUM
ap-1366	195	2	acta	acta	PROPN
ap-1366	195	3	polytechnica	polytechnica	PROPN
ap-1366	195	4	vol	vol	NOUN
ap-1366	195	5	.	.	PUNCT
ap-1366	196	1	51	51	NUM
ap-1366	196	2	no	no	INTJ
ap-1366	196	3	.	.	PUNCT
ap-1366	197	1	1/2011	1/2011	NUM
ap-1366	197	2	the	the	DET
ap-1366	197	3	second	second	ADJ
ap-1366	197	4	limit	limit	NOUN
ap-1366	197	5	in	in	ADP
ap-1366	197	6	(	(	PUNCT
ap-1366	197	7	18	18	NUM
ap-1366	197	8	)	)	PUNCT
ap-1366	197	9	is	be	AUX
ap-1366	197	10	found	find	VERB
ap-1366	197	11	in	in	ADP
ap-1366	197	12	a	a	DET
ap-1366	197	13	similar	similar	ADJ
ap-1366	197	14	fashion	fashion	NOUN
ap-1366	197	15	,	,	PUNCT
ap-1366	197	16	yielding	yield	VERB
ap-1366	197	17	lim	lim	PROPN
ap-1366	197	18	e→e0	e→e0	PROPN
ap-1366	197	19	[	[	PUNCT
ap-1366	197	20	−	−	PROPN
ap-1366	197	21	1	1	NUM
ap-1366	197	22	c0	c0	NOUN
ap-1366	197	23	ψ0,l(z)dψ0,yψ0,r(y	ψ0,l(z)dψ0,yψ0,r(y	X
ap-1366	197	24	)	)	PUNCT
ap-1366	197	25	]	]	PUNCT
ap-1366	198	1	=	=	PUNCT
ap-1366	198	2	√	√	ADJ
ap-1366	198	3	1	1	NUM
ap-1366	198	4	f(y)h(y	f(y)h(y	ADP
ap-1366	198	5	)	)	PUNCT
ap-1366	198	6	ψ0(z	ψ0(z	PROPN
ap-1366	198	7	)	)	PUNCT
ap-1366	198	8	ψ0(y	ψ0(y	X
ap-1366	198	9	)	)	PUNCT
ap-1366	198	10	∫	∫	PROPN
ap-1366	198	11	(	(	PUNCT
ap-1366	198	12	a	a	PRON
ap-1366	198	13	,	,	PUNCT
ap-1366	198	14	y	y	NOUN
ap-1366	198	15	)	)	PUNCT
ap-1366	198	16	h(z)ψ	h(z)ψ	PROPN
ap-1366	198	17	2	2	NUM
ap-1366	198	18	0(z	0(z	NOUN
ap-1366	198	19	)	)	PUNCT
ap-1366	199	1	dz∫	dz∫	NOUN
ap-1366	199	2	(	(	PUNCT
ap-1366	199	3	a	a	PRON
ap-1366	199	4	,	,	PUNCT
ap-1366	199	5	b	b	NOUN
ap-1366	199	6	)	)	PUNCT
ap-1366	199	7	h(z)ψ	h(z)ψ	PROPN
ap-1366	199	8	2	2	NUM
ap-1366	199	9	0(z	0(z	NUM
ap-1366	199	10	)	)	PUNCT
ap-1366	199	11	dz	dz	NOUN
ap-1366	199	12	,	,	PUNCT
ap-1366	199	13	note	note	VERB
ap-1366	199	14	that	that	SCONJ
ap-1366	199	15	there	there	PRON
ap-1366	199	16	is	be	VERB
ap-1366	199	17	no	no	DET
ap-1366	199	18	negative	negative	ADJ
ap-1366	199	19	sign	sign	NOUN
ap-1366	199	20	in	in	ADP
ap-1366	199	21	front	front	NOUN
ap-1366	199	22	.	.	PUNCT
ap-1366	200	1	now	now	ADV
ap-1366	200	2	our	our	PRON
ap-1366	200	3	two	two	NUM
ap-1366	200	4	limits	limit	NOUN
ap-1366	200	5	can	can	AUX
ap-1366	200	6	be	be	AUX
ap-1366	200	7	plugged	plug	VERB
ap-1366	200	8	into	into	ADP
ap-1366	200	9	the	the	DET
ap-1366	200	10	propagator	propagator	NOUN
ap-1366	200	11	(	(	PUNCT
ap-1366	200	12	18	18	NUM
ap-1366	200	13	):	):	SYM
ap-1366	200	14	1	1	NUM
ap-1366	200	15	h(y	h(y	ADV
ap-1366	200	16	)	)	PUNCT
ap-1366	201	1	k1(x	k1(x	NOUN
ap-1366	201	2	,	,	PUNCT
ap-1366	201	3	y	y	PROPN
ap-1366	201	4	,	,	PUNCT
ap-1366	201	5	t	t	PROPN
ap-1366	201	6	)	)	PUNCT
ap-1366	201	7	=	=	SYM
ap-1366	202	1	dψ0,x	dψ0,x	PROPN
ap-1366	202	2	∫	∫	PROPN
ap-1366	202	3	(	(	PUNCT
ap-1366	202	4	a	a	PRON
ap-1366	202	5	,	,	PUNCT
ap-1366	202	6	y	y	NOUN
ap-1366	202	7	)	)	PUNCT
ap-1366	202	8	k0(x	k0(x	NOUN
ap-1366	202	9	,	,	PUNCT
ap-1366	202	10	z	z	PROPN
ap-1366	202	11	,	,	PUNCT
ap-1366	202	12	t	t	PROPN
ap-1366	202	13	)	)	PUNCT
ap-1366	202	14	·	·	PUNCT
ap-1366	202	15	[	[	PUNCT
ap-1366	202	16	−	−	PROPN
ap-1366	202	17	√	√	NUM
ap-1366	202	18	1	1	NUM
ap-1366	202	19	f(y)h(y	f(y)h(y	ADP
ap-1366	202	20	)	)	PUNCT
ap-1366	202	21	ψ0(z	ψ0(z	PROPN
ap-1366	202	22	)	)	PUNCT
ap-1366	202	23	ψ0(y	ψ0(y	X
ap-1366	202	24	)	)	PUNCT
ap-1366	202	25	∫	∫	PROPN
ap-1366	202	26	(	(	PUNCT
ap-1366	202	27	y	y	PROPN
ap-1366	202	28	,	,	PUNCT
ap-1366	202	29	b	b	NOUN
ap-1366	202	30	)	)	PUNCT
ap-1366	202	31	h(w)ψ	h(w)ψ	PROPN
ap-1366	202	32	2	2	NUM
ap-1366	202	33	0(w	0(w	NUM
ap-1366	202	34	)	)	PUNCT
ap-1366	202	35	dw∫	dw∫	PROPN
ap-1366	202	36	(	(	PUNCT
ap-1366	202	37	a	a	DET
ap-1366	202	38	,	,	PUNCT
ap-1366	202	39	b	b	NOUN
ap-1366	202	40	)	)	PUNCT
ap-1366	203	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	203	2	2	2	NUM
ap-1366	203	3	0(w	0(w	NUM
ap-1366	203	4	)	)	PUNCT
ap-1366	203	5	dw	dw	NOUN
ap-1366	203	6	]	]	PUNCT
ap-1366	203	7	dz	dz	PROPN
ap-1366	204	1	+	+	CCONJ
ap-1366	204	2	dψ0,x	dψ0,x	NUM
ap-1366	204	3	∫	∫	PROPN
ap-1366	204	4	(	(	PUNCT
ap-1366	204	5	y	y	PROPN
ap-1366	204	6	,	,	PUNCT
ap-1366	204	7	b	b	NOUN
ap-1366	204	8	)	)	PUNCT
ap-1366	204	9	k0(x	k0(x	NOUN
ap-1366	204	10	,	,	PUNCT
ap-1366	204	11	z	z	PROPN
ap-1366	204	12	,	,	PUNCT
ap-1366	204	13	t	t	PROPN
ap-1366	204	14	)	)	PUNCT
ap-1366	204	15	·	·	PUNCT
ap-1366	204	16	[	[	X
ap-1366	204	17	√	√	ADP
ap-1366	204	18	1	1	NUM
ap-1366	204	19	f(y)h(y	f(y)h(y	ADP
ap-1366	204	20	)	)	PUNCT
ap-1366	204	21	ψ0(z	ψ0(z	PROPN
ap-1366	204	22	)	)	PUNCT
ap-1366	204	23	ψ0(y	ψ0(y	X
ap-1366	204	24	)	)	PUNCT
ap-1366	204	25	∫	∫	PROPN
ap-1366	204	26	(	(	PUNCT
ap-1366	204	27	a	a	PRON
ap-1366	204	28	,	,	PUNCT
ap-1366	204	29	y	y	NOUN
ap-1366	204	30	)	)	PUNCT
ap-1366	205	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	205	2	2	2	NUM
ap-1366	205	3	0(w	0(w	NUM
ap-1366	205	4	)	)	PUNCT
ap-1366	205	5	dw∫	dw∫	PROPN
ap-1366	205	6	(	(	PUNCT
ap-1366	205	7	a	a	DET
ap-1366	205	8	,	,	PUNCT
ap-1366	205	9	b	b	NOUN
ap-1366	205	10	)	)	PUNCT
ap-1366	206	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	206	2	2	2	NUM
ap-1366	206	3	0(w	0(w	NUM
ap-1366	206	4	)	)	PUNCT
ap-1366	206	5	dw	dw	NOUN
ap-1366	206	6	]	]	PUNCT
ap-1366	206	7	dz	dz	PROPN
ap-1366	206	8	.	.	PUNCT
ap-1366	207	1	(	(	PUNCT
ap-1366	207	2	23	23	NUM
ap-1366	207	3	)	)	PUNCT
ap-1366	207	4	in	in	ADP
ap-1366	207	5	order	order	NOUN
ap-1366	207	6	to	to	PART
ap-1366	207	7	join	join	VERB
ap-1366	207	8	the	the	DET
ap-1366	207	9	two	two	NUM
ap-1366	207	10	terms	term	NOUN
ap-1366	207	11	,	,	PUNCT
ap-1366	207	12	we	we	PRON
ap-1366	207	13	rewrite	rewrite	VERB
ap-1366	207	14	the	the	DET
ap-1366	207	15	inner	inner	ADJ
ap-1366	207	16	integral	integral	ADJ
ap-1366	207	17	over	over	ADP
ap-1366	207	18	(	(	PUNCT
ap-1366	207	19	y	y	PROPN
ap-1366	207	20	,	,	PUNCT
ap-1366	207	21	b	b	NOUN
ap-1366	207	22	)	)	PUNCT
ap-1366	207	23	as	as	ADP
ap-1366	207	24	a	a	DET
ap-1366	207	25	difference	difference	NOUN
ap-1366	207	26	of	of	ADP
ap-1366	207	27	integrals	integral	NOUN
ap-1366	207	28	over	over	ADP
ap-1366	207	29	(	(	PUNCT
ap-1366	207	30	a	a	DET
ap-1366	207	31	,	,	PUNCT
ap-1366	207	32	b	b	NOUN
ap-1366	207	33	)	)	PUNCT
ap-1366	207	34	and	and	CCONJ
ap-1366	207	35	(	(	PUNCT
ap-1366	207	36	a	a	DET
ap-1366	207	37	,	,	PUNCT
ap-1366	207	38	y	y	PROPN
ap-1366	207	39	)	)	PUNCT
ap-1366	207	40	,	,	PUNCT
ap-1366	207	41	respectively	respectively	ADV
ap-1366	207	42	:	:	PUNCT
ap-1366	207	43	1	1	NUM
ap-1366	207	44	h(y	h(y	ADV
ap-1366	207	45	)	)	PUNCT
ap-1366	208	1	k1(x	k1(x	NOUN
ap-1366	208	2	,	,	PUNCT
ap-1366	208	3	y	y	PROPN
ap-1366	208	4	,	,	PUNCT
ap-1366	208	5	t	t	PROPN
ap-1366	208	6	)	)	PUNCT
ap-1366	208	7	=	=	SYM
ap-1366	209	1	dψ0,x	dψ0,x	PROPN
ap-1366	209	2	∫	∫	PROPN
ap-1366	209	3	(	(	PUNCT
ap-1366	209	4	a	a	PRON
ap-1366	209	5	,	,	PUNCT
ap-1366	209	6	y	y	NOUN
ap-1366	209	7	)	)	PUNCT
ap-1366	209	8	k0(x	k0(x	NOUN
ap-1366	209	9	,	,	PUNCT
ap-1366	209	10	z	z	PROPN
ap-1366	209	11	,	,	PUNCT
ap-1366	209	12	t	t	PROPN
ap-1366	209	13	)	)	PUNCT
ap-1366	209	14	·	·	PUNCT
ap-1366	209	15	[	[	PUNCT
ap-1366	209	16	−	−	PROPN
ap-1366	209	17	√	√	NUM
ap-1366	209	18	1	1	NUM
ap-1366	209	19	f(y)h(y	f(y)h(y	ADP
ap-1366	209	20	)	)	PUNCT
ap-1366	209	21	ψ0(z	ψ0(z	PROPN
ap-1366	209	22	)	)	PUNCT
ap-1366	209	23	ψ0(y	ψ0(y	X
ap-1366	209	24	)	)	PUNCT
ap-1366	209	25	]	]	PUNCT
ap-1366	210	1	dz	dz	PROPN
ap-1366	210	2	+	+	CCONJ
ap-1366	210	3	dψ0,x	dψ0,x	PROPN
ap-1366	210	4	∫	∫	PROPN
ap-1366	210	5	(	(	PUNCT
ap-1366	210	6	a	a	PRON
ap-1366	210	7	,	,	PUNCT
ap-1366	210	8	y	y	NOUN
ap-1366	210	9	)	)	PUNCT
ap-1366	210	10	k0(x	k0(x	NOUN
ap-1366	210	11	,	,	PUNCT
ap-1366	210	12	z	z	PROPN
ap-1366	210	13	,	,	PUNCT
ap-1366	210	14	t	t	PROPN
ap-1366	210	15	)	)	PUNCT
ap-1366	210	16	·	·	PUNCT
ap-1366	211	1	[	[	X
ap-1366	211	2	√	√	ADP
ap-1366	211	3	1	1	NUM
ap-1366	211	4	f(y)h(y	f(y)h(y	ADP
ap-1366	211	5	)	)	PUNCT
ap-1366	211	6	ψ0(z	ψ0(z	PROPN
ap-1366	211	7	)	)	PUNCT
ap-1366	211	8	ψ0(y	ψ0(y	X
ap-1366	211	9	)	)	PUNCT
ap-1366	211	10	∫	∫	PROPN
ap-1366	211	11	(	(	PUNCT
ap-1366	211	12	a	a	PRON
ap-1366	211	13	,	,	PUNCT
ap-1366	211	14	y	y	NOUN
ap-1366	211	15	)	)	PUNCT
ap-1366	212	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	212	2	2	2	NUM
ap-1366	212	3	0(w	0(w	NUM
ap-1366	212	4	)	)	PUNCT
ap-1366	212	5	dw∫	dw∫	PROPN
ap-1366	212	6	(	(	PUNCT
ap-1366	212	7	a	a	DET
ap-1366	212	8	,	,	PUNCT
ap-1366	212	9	b	b	NOUN
ap-1366	212	10	)	)	PUNCT
ap-1366	213	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	213	2	2	2	NUM
ap-1366	213	3	0(w	0(w	NUM
ap-1366	213	4	)	)	PUNCT
ap-1366	213	5	dw	dw	NOUN
ap-1366	213	6	]	]	PUNCT
ap-1366	213	7	dz	dz	PROPN
ap-1366	214	1	+	+	CCONJ
ap-1366	214	2	dψ0,x	dψ0,x	NUM
ap-1366	214	3	∫	∫	PROPN
ap-1366	214	4	(	(	PUNCT
ap-1366	214	5	y	y	PROPN
ap-1366	214	6	,	,	PUNCT
ap-1366	214	7	b	b	NOUN
ap-1366	214	8	)	)	PUNCT
ap-1366	214	9	k0(x	k0(x	NOUN
ap-1366	214	10	,	,	PUNCT
ap-1366	214	11	z	z	PROPN
ap-1366	214	12	,	,	PUNCT
ap-1366	214	13	t	t	PROPN
ap-1366	214	14	)	)	PUNCT
ap-1366	214	15	·	·	PUNCT
ap-1366	214	16	[	[	X
ap-1366	214	17	√	√	ADP
ap-1366	214	18	1	1	NUM
ap-1366	214	19	f(y)h(y	f(y)h(y	ADP
ap-1366	214	20	)	)	PUNCT
ap-1366	214	21	ψ0(z	ψ0(z	PROPN
ap-1366	214	22	)	)	PUNCT
ap-1366	214	23	ψ0(y	ψ0(y	X
ap-1366	214	24	)	)	PUNCT
ap-1366	214	25	∫	∫	PROPN
ap-1366	214	26	(	(	PUNCT
ap-1366	214	27	a	a	PRON
ap-1366	214	28	,	,	PUNCT
ap-1366	214	29	y	y	NOUN
ap-1366	214	30	)	)	PUNCT
ap-1366	215	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	215	2	2	2	NUM
ap-1366	215	3	0(w	0(w	NUM
ap-1366	215	4	)	)	PUNCT
ap-1366	215	5	dw∫	dw∫	PROPN
ap-1366	215	6	(	(	PUNCT
ap-1366	215	7	a	a	DET
ap-1366	215	8	,	,	PUNCT
ap-1366	215	9	b	b	NOUN
ap-1366	215	10	)	)	PUNCT
ap-1366	216	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	216	2	2	2	NUM
ap-1366	216	3	0(w	0(w	NUM
ap-1366	216	4	)	)	PUNCT
ap-1366	216	5	dw	dw	NOUN
ap-1366	216	6	]	]	PUNCT
ap-1366	216	7	dz	dz	PROPN
ap-1366	217	1	=	=	PUNCT
ap-1366	217	2	−	−	PROPN
ap-1366	217	3	√	√	NUM
ap-1366	217	4	1	1	NUM
ap-1366	217	5	f(y)h(y	f(y)h(y	NUM
ap-1366	217	6	)	)	PUNCT
ap-1366	217	7	1	1	NUM
ap-1366	217	8	ψ0(y	ψ0(y	SYM
ap-1366	217	9	)	)	PUNCT
ap-1366	217	10	dψ0,x	dψ0,x	PROPN
ap-1366	217	11	·	·	SYM
ap-1366	217	12	∫	∫	PROPN
ap-1366	217	13	(	(	PUNCT
ap-1366	217	14	a	a	PROPN
ap-1366	217	15	,	,	PUNCT
ap-1366	217	16	y	y	NOUN
ap-1366	217	17	)	)	PUNCT
ap-1366	217	18	k0(x	k0(x	PROPN
ap-1366	217	19	,	,	PUNCT
ap-1366	217	20	z	z	NOUN
ap-1366	217	21	,	,	PUNCT
ap-1366	217	22	t)ψ0(z	t)ψ0(z	NUM
ap-1366	217	23	)	)	PUNCT
ap-1366	217	24	dz	dz	NOUN
ap-1366	218	1	+	+	ADV
ap-1366	218	2	√	√	ADJ
ap-1366	218	3	1	1	NUM
ap-1366	218	4	f(y)h(y	f(y)h(y	NUM
ap-1366	218	5	)	)	PUNCT
ap-1366	218	6	∫	∫	PROPN
ap-1366	218	7	(	(	PUNCT
ap-1366	218	8	a	a	PRON
ap-1366	218	9	,	,	PUNCT
ap-1366	218	10	y	y	NOUN
ap-1366	218	11	)	)	PUNCT
ap-1366	219	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	219	2	2	2	NUM
ap-1366	219	3	0(w	0(w	NUM
ap-1366	219	4	)	)	PUNCT
ap-1366	219	5	dw	dw	NOUN
ap-1366	219	6	ψ0(y	ψ0(y	PROPN
ap-1366	219	7	)	)	PUNCT
ap-1366	219	8	∫	∫	PROPN
ap-1366	219	9	(	(	PUNCT
ap-1366	219	10	a	a	DET
ap-1366	219	11	,	,	PUNCT
ap-1366	219	12	b	b	NOUN
ap-1366	219	13	)	)	PUNCT
ap-1366	220	1	h(w)ψ	h(w)ψ	PROPN
ap-1366	220	2	2	2	NUM
ap-1366	220	3	0(w	0(w	NUM
ap-1366	220	4	)	)	PUNCT
ap-1366	220	5	dw	dw	NOUN
ap-1366	220	6	dψ0,x	dψ0,x	PROPN
ap-1366	220	7	·	·	SYM
ap-1366	220	8	∫	∫	PROPN
ap-1366	220	9	(	(	PUNCT
ap-1366	220	10	a	a	PRON
ap-1366	220	11	,	,	PUNCT
ap-1366	220	12	b	b	NOUN
ap-1366	220	13	)	)	PUNCT
ap-1366	220	14	k0(x	k0(x	NOUN
ap-1366	220	15	,	,	PUNCT
ap-1366	220	16	z	z	NOUN
ap-1366	220	17	,	,	PUNCT
ap-1366	220	18	t)ψ0(z	t)ψ0(z	NUM
ap-1366	220	19	)	)	PUNCT
ap-1366	220	20	dz	dz	PROPN
ap-1366	220	21	.	.	PUNCT
ap-1366	221	1	(	(	PUNCT
ap-1366	221	2	24	24	NUM
ap-1366	221	3	)	)	PUNCT
ap-1366	221	4	since	since	SCONJ
ap-1366	221	5	according	accord	VERB
ap-1366	221	6	to	to	ADP
ap-1366	221	7	(	(	PUNCT
ap-1366	221	8	5	5	X
ap-1366	221	9	)	)	PUNCT
ap-1366	221	10	we	we	PRON
ap-1366	221	11	have	have	VERB
ap-1366	221	12	dψ0,x	dψ0,x	PROPN
ap-1366	221	13	∫	∫	PROPN
ap-1366	221	14	(	(	PUNCT
ap-1366	221	15	a	a	PRON
ap-1366	221	16	,	,	PUNCT
ap-1366	221	17	b	b	NOUN
ap-1366	221	18	)	)	PUNCT
ap-1366	221	19	k0(x	k0(x	NOUN
ap-1366	221	20	,	,	PUNCT
ap-1366	221	21	z	z	NOUN
ap-1366	221	22	,	,	PUNCT
ap-1366	221	23	t)ψ0(z	t)ψ0(z	NUM
ap-1366	221	24	)	)	PUNCT
ap-1366	221	25	dz	dz	NOUN
ap-1366	221	26	=	=	SYM
ap-1366	221	27	exp(−ie0t)dψ0,xψ0(x	exp(−ie0t)dψ0,xψ0(x	PROPN
ap-1366	221	28	)	)	PUNCT
ap-1366	221	29	=	=	SYM
ap-1366	221	30	0	0	NUM
ap-1366	221	31	,	,	PUNCT
ap-1366	221	32	relation	relation	NOUN
ap-1366	221	33	(	(	PUNCT
ap-1366	221	34	24	24	NUM
ap-1366	221	35	)	)	PUNCT
ap-1366	221	36	turns	turn	VERB
ap-1366	221	37	after	after	ADP
ap-1366	221	38	multiplication	multiplication	NOUN
ap-1366	221	39	by	by	ADP
ap-1366	221	40	h	h	NOUN
ap-1366	221	41	into	into	ADP
ap-1366	221	42	its	its	PRON
ap-1366	221	43	final	final	ADJ
ap-1366	221	44	form	form	NOUN
ap-1366	221	45	k1(x	k1(x	PROPN
ap-1366	221	46	,	,	PUNCT
ap-1366	221	47	y	y	PROPN
ap-1366	221	48	,	,	PUNCT
ap-1366	221	49	t	t	PROPN
ap-1366	221	50	)	)	PUNCT
ap-1366	221	51	=	=	SYM
ap-1366	222	1	−	−	PROPN
ap-1366	222	2	√	√	NUM
ap-1366	222	3	h(y	h(y	ADV
ap-1366	222	4	)	)	PUNCT
ap-1366	222	5	f(y	f(y	NOUN
ap-1366	222	6	)	)	PUNCT
ap-1366	222	7	1	1	NUM
ap-1366	222	8	ψ0(y	ψ0(y	SYM
ap-1366	222	9	)	)	PUNCT
ap-1366	222	10	dψ0,x	dψ0,x	PROPN
ap-1366	222	11	·	·	SYM
ap-1366	222	12	∫	∫	PROPN
ap-1366	222	13	(	(	PUNCT
ap-1366	222	14	a	a	PROPN
ap-1366	222	15	,	,	PUNCT
ap-1366	222	16	y	y	NOUN
ap-1366	222	17	)	)	PUNCT
ap-1366	222	18	k0(x	k0(x	PROPN
ap-1366	222	19	,	,	PUNCT
ap-1366	222	20	z	z	NOUN
ap-1366	222	21	,	,	PUNCT
ap-1366	222	22	t)ψ0(z	t)ψ0(z	NUM
ap-1366	222	23	)	)	PUNCT
ap-1366	222	24	dz	dz	PROPN
ap-1366	222	25	.	.	PUNCT
ap-1366	223	1	(	(	PUNCT
ap-1366	223	2	25	25	NUM
ap-1366	223	3	)	)	PUNCT
ap-1366	223	4	alternatively	alternatively	ADV
ap-1366	223	5	,	,	PUNCT
ap-1366	223	6	in	in	ADP
ap-1366	223	7	(	(	PUNCT
ap-1366	223	8	23	23	NUM
ap-1366	223	9	)	)	PUNCT
ap-1366	223	10	one	one	PRON
ap-1366	223	11	can	can	AUX
ap-1366	223	12	write	write	VERB
ap-1366	223	13	the	the	DET
ap-1366	223	14	inner	inner	ADJ
ap-1366	223	15	integral	integral	ADJ
ap-1366	223	16	over	over	ADP
ap-1366	223	17	(	(	PUNCT
ap-1366	223	18	a	a	DET
ap-1366	223	19	,	,	PUNCT
ap-1366	223	20	y	y	NOUN
ap-1366	223	21	)	)	PUNCT
ap-1366	223	22	as	as	ADP
ap-1366	223	23	a	a	DET
ap-1366	223	24	difference	difference	NOUN
ap-1366	223	25	of	of	ADP
ap-1366	223	26	integrals	integral	NOUN
ap-1366	223	27	over	over	ADP
ap-1366	223	28	(	(	PUNCT
ap-1366	223	29	a	a	DET
ap-1366	223	30	,	,	PUNCT
ap-1366	223	31	b	b	NOUN
ap-1366	223	32	)	)	PUNCT
ap-1366	223	33	and	and	CCONJ
ap-1366	223	34	(	(	PUNCT
ap-1366	223	35	y	y	PROPN
ap-1366	223	36	,	,	PUNCT
ap-1366	223	37	b	b	NOUN
ap-1366	223	38	)	)	PUNCT
ap-1366	223	39	,	,	PUNCT
ap-1366	223	40	respectively	respectively	ADV
ap-1366	223	41	.	.	PUNCT
ap-1366	224	1	this	this	PRON
ap-1366	224	2	gives	give	VERB
ap-1366	224	3	a	a	DET
ap-1366	224	4	result	result	NOUN
ap-1366	224	5	slightly	slightly	ADV
ap-1366	224	6	different	different	ADJ
ap-1366	224	7	from	from	ADP
ap-1366	224	8	(	(	PUNCT
ap-1366	224	9	25	25	NUM
ap-1366	224	10	):	):	PUNCT
ap-1366	224	11	k1(x	k1(x	PROPN
ap-1366	224	12	,	,	PUNCT
ap-1366	224	13	y	y	PROPN
ap-1366	224	14	,	,	PUNCT
ap-1366	224	15	t	t	PROPN
ap-1366	224	16	)	)	PUNCT
ap-1366	224	17	=	=	SYM
ap-1366	224	18	√	√	NUM
ap-1366	224	19	h(y	h(y	ADV
ap-1366	224	20	)	)	PUNCT
ap-1366	224	21	f(y	f(y	NOUN
ap-1366	224	22	)	)	PUNCT
ap-1366	224	23	1	1	NUM
ap-1366	224	24	ψ0(y	ψ0(y	SYM
ap-1366	224	25	)	)	PUNCT
ap-1366	224	26	dψ0,x	dψ0,x	PROPN
ap-1366	224	27	·	·	SYM
ap-1366	224	28	∫	∫	PROPN
ap-1366	224	29	(	(	PUNCT
ap-1366	224	30	y	y	PROPN
ap-1366	224	31	,	,	PUNCT
ap-1366	224	32	b	b	NOUN
ap-1366	224	33	)	)	PUNCT
ap-1366	224	34	k0(x	k0(x	NOUN
ap-1366	224	35	,	,	PUNCT
ap-1366	224	36	z	z	NOUN
ap-1366	224	37	,	,	PUNCT
ap-1366	224	38	t)ψ0(z	t)ψ0(z	NUM
ap-1366	224	39	)	)	PUNCT
ap-1366	224	40	dz	dz	PROPN
ap-1366	224	41	.	.	PUNCT
ap-1366	225	1	it	it	PRON
ap-1366	225	2	can	can	AUX
ap-1366	225	3	be	be	AUX
ap-1366	225	4	seen	see	VERB
ap-1366	225	5	immediately	immediately	ADV
ap-1366	225	6	that	that	SCONJ
ap-1366	225	7	for	for	ADP
ap-1366	225	8	a	a	DET
ap-1366	225	9	conventional	conventional	ADJ
ap-1366	225	10	schrödinger	schrödinger	NOUN
ap-1366	225	11	equation	equation	NOUN
ap-1366	225	12	(	(	PUNCT
ap-1366	225	13	1	1	NUM
ap-1366	225	14	)	)	PUNCT
ap-1366	225	15	with	with	ADP
ap-1366	225	16	f	f	PROPN
ap-1366	225	17	=	=	SYM
ap-1366	225	18	1	1	NUM
ap-1366	225	19	and	and	CCONJ
ap-1366	225	20	h	h	NOUN
ap-1366	225	21	=	=	NOUN
ap-1366	225	22	1	1	NUM
ap-1366	225	23	,	,	PUNCT
ap-1366	225	24	our	our	PRON
ap-1366	225	25	results	result	NOUN
ap-1366	225	26	reduce	reduce	VERB
ap-1366	225	27	correctly	correctly	ADV
ap-1366	225	28	to	to	ADP
ap-1366	225	29	the	the	DET
ap-1366	225	30	known	know	VERB
ap-1366	225	31	findings	finding	NOUN
ap-1366	225	32	[	[	X
ap-1366	225	33	1	1	NUM
ap-1366	225	34	]	]	PUNCT
ap-1366	225	35	.	.	PUNCT
ap-1366	226	1	4	4	NUM
ap-1366	226	2	concluding	conclude	VERB
ap-1366	226	3	remarks	remark	NOUN
ap-1366	226	4	we	we	PRON
ap-1366	226	5	have	have	AUX
ap-1366	226	6	obtained	obtain	VERB
ap-1366	226	7	a	a	DET
ap-1366	226	8	relation	relation	NOUN
ap-1366	226	9	between	between	ADP
ap-1366	226	10	propagators	propagator	NOUN
ap-1366	226	11	of	of	ADP
ap-1366	226	12	generalized	generalize	VERB
ap-1366	226	13	sturm	sturm	PROPN
ap-1366	226	14	-	-	PUNCT
ap-1366	226	15	liouville	liouville	NOUN
ap-1366	226	16	problems	problem	NOUN
ap-1366	226	17	that	that	PRON
ap-1366	226	18	are	be	AUX
ap-1366	226	19	connected	connect	VERB
ap-1366	226	20	by	by	ADP
ap-1366	226	21	means	mean	NOUN
ap-1366	226	22	of	of	ADP
ap-1366	226	23	susy	susy	NOUN
ap-1366	226	24	transformations	transformation	NOUN
ap-1366	226	25	.	.	PUNCT
ap-1366	227	1	our	our	PRON
ap-1366	227	2	results	result	NOUN
ap-1366	227	3	complement	complement	VERB
ap-1366	227	4	and	and	CCONJ
ap-1366	227	5	generalize	generalize	VERB
ap-1366	227	6	former	former	ADJ
ap-1366	227	7	findings	finding	NOUN
ap-1366	227	8	for	for	ADP
ap-1366	227	9	the	the	DET
ap-1366	227	10	conventional	conventional	ADJ
ap-1366	227	11	schrödinger	schrödinger	NOUN
ap-1366	227	12	equation	equation	NOUN
ap-1366	227	13	[	[	X
ap-1366	227	14	1	1	NUM
ap-1366	227	15	]	]	PUNCT
ap-1366	227	16	.	.	PUNCT
ap-1366	228	1	while	while	SCONJ
ap-1366	228	2	in	in	ADP
ap-1366	228	3	the	the	DET
ap-1366	228	4	latter	latter	ADJ
ap-1366	228	5	reference	reference	NOUN
ap-1366	228	6	propagators	propagator	NOUN
ap-1366	228	7	related	relate	VERB
ap-1366	228	8	by	by	ADP
ap-1366	228	9	higherorder	higherorder	NOUN
ap-1366	228	10	susy	susy	NOUN
ap-1366	228	11	transformations	transformation	NOUN
ap-1366	228	12	are	be	AUX
ap-1366	228	13	also	also	ADV
ap-1366	228	14	found	find	VERB
ap-1366	228	15	to	to	PART
ap-1366	228	16	satisfy	satisfy	VERB
ap-1366	228	17	simple	simple	ADJ
ap-1366	228	18	interrelations	interrelation	NOUN
ap-1366	228	19	,	,	PUNCT
ap-1366	228	20	the	the	DET
ap-1366	228	21	corresponding	correspond	VERB
ap-1366	228	22	situation	situation	NOUN
ap-1366	228	23	in	in	ADP
ap-1366	228	24	the	the	DET
ap-1366	228	25	generalized	generalized	ADJ
ap-1366	228	26	case	case	NOUN
ap-1366	228	27	is	be	AUX
ap-1366	228	28	subject	subject	ADJ
ap-1366	228	29	to	to	ADP
ap-1366	228	30	ongoing	ongoing	ADJ
ap-1366	228	31	research	research	NOUN
ap-1366	228	32	.	.	PUNCT
ap-1366	229	1	references	reference	NOUN
ap-1366	229	2	[	[	X
ap-1366	229	3	1	1	NUM
ap-1366	229	4	]	]	PUNCT
ap-1366	229	5	pupasov	pupasov	NOUN
ap-1366	229	6	,	,	PUNCT
ap-1366	229	7	a.	a.	NOUN
ap-1366	229	8	m.	m.	NOUN
ap-1366	229	9	,	,	PUNCT
ap-1366	229	10	samsonov	samsonov	PROPN
ap-1366	229	11	,	,	PUNCT
ap-1366	229	12	b.	b.	PROPN
ap-1366	229	13	f.	f.	PROPN
ap-1366	229	14	,	,	PUNCT
ap-1366	229	15	günther	günther	PROPN
ap-1366	229	16	,	,	PUNCT
ap-1366	229	17	u.	u.	NOUN
ap-1366	229	18	:	:	PUNCT
ap-1366	229	19	exact	exact	ADJ
ap-1366	229	20	propagators	propagator	NOUN
ap-1366	229	21	for	for	ADP
ap-1366	229	22	susy	susy	NOUN
ap-1366	229	23	partners	partner	NOUN
ap-1366	229	24	,	,	PUNCT
ap-1366	229	25	j.	j.	PROPN
ap-1366	229	26	phys	phys	PROPN
ap-1366	229	27	.	.	PUNCT
ap-1366	230	1	a	a	DET
ap-1366	230	2	40	40	NUM
ap-1366	230	3	(	(	PUNCT
ap-1366	230	4	2007	2007	NUM
ap-1366	230	5	)	)	PUNCT
ap-1366	230	6	,	,	PUNCT
ap-1366	230	7	10	10	NUM
ap-1366	230	8	557–10589	557–10589	NUM
ap-1366	230	9	.	.	PUNCT
ap-1366	231	1	[	[	X
ap-1366	231	2	2	2	NUM
ap-1366	231	3	]	]	PUNCT
ap-1366	231	4	cooper	cooper	NOUN
ap-1366	231	5	,	,	PUNCT
ap-1366	231	6	f.	f.	PROPN
ap-1366	231	7	,	,	PUNCT
ap-1366	231	8	khare	khare	PROPN
ap-1366	231	9	,	,	PUNCT
ap-1366	231	10	a.	a.	PROPN
ap-1366	231	11	,	,	PUNCT
ap-1366	231	12	sukhatme	sukhatme	NOUN
ap-1366	231	13	,	,	PUNCT
ap-1366	231	14	u.	u.	NOUN
ap-1366	231	15	:	:	PUNCT
ap-1366	231	16	supersymmetry	supersymmetry	NOUN
ap-1366	231	17	and	and	CCONJ
ap-1366	231	18	quantum	quantum	NOUN
ap-1366	231	19	mechanics	mechanic	NOUN
ap-1366	231	20	,	,	PUNCT
ap-1366	231	21	phys	phy	NOUN
ap-1366	231	22	.	.	PUNCT
ap-1366	231	23	rep	rep	PROPN
ap-1366	231	24	.	.	PROPN
ap-1366	231	25	251	251	NUM
ap-1366	231	26	(	(	PUNCT
ap-1366	231	27	1995	1995	NUM
ap-1366	231	28	)	)	PUNCT
ap-1366	231	29	,	,	PUNCT
ap-1366	231	30	267–388	267–388	NUM
ap-1366	231	31	.	.	PUNCT
ap-1366	232	1	[	[	X
ap-1366	232	2	3	3	NUM
ap-1366	232	3	]	]	PUNCT
ap-1366	232	4	darboux	darboux	NOUN
ap-1366	232	5	,	,	PUNCT
ap-1366	232	6	m.	m.	NOUN
ap-1366	232	7	g.	g.	PROPN
ap-1366	232	8	:	:	PUNCT
ap-1366	232	9	sur	sur	PROPN
ap-1366	232	10	une	une	PROPN
ap-1366	232	11	proposition	proposition	PROPN
ap-1366	232	12	relative	relative	ADJ
ap-1366	232	13	aux	aux	PROPN
ap-1366	232	14	équations	équations	PROPN
ap-1366	232	15	linéaires	linéaire	NOUN
ap-1366	232	16	,	,	PUNCT
ap-1366	232	17	comptes	compte	VERB
ap-1366	232	18	rendus	rendus	PROPN
ap-1366	232	19	acad	acad	PROPN
ap-1366	232	20	.	.	PUNCT
ap-1366	233	1	sci	sci	PROPN
ap-1366	233	2	.	.	PROPN
ap-1366	234	1	paris	paris	PROPN
ap-1366	234	2	94	94	NUM
ap-1366	234	3	(	(	PUNCT
ap-1366	234	4	1882	1882	NUM
ap-1366	234	5	)	)	PUNCT
ap-1366	234	6	,	,	PUNCT
ap-1366	234	7	1	1	NUM
ap-1366	234	8	456–1	456–1	NUM
ap-1366	234	9	459	459	NUM
ap-1366	234	10	.	.	PUNCT
ap-1366	235	1	[	[	X
ap-1366	235	2	4	4	NUM
ap-1366	235	3	]	]	X
ap-1366	235	4	duffy	duffy	PROPN
ap-1366	235	5	,	,	PUNCT
ap-1366	235	6	d.	d.	PROPN
ap-1366	235	7	g.	g.	PROPN
ap-1366	235	8	:	:	PUNCT
ap-1366	235	9	green	green	PROPN
ap-1366	235	10	’s	’s	PART
ap-1366	235	11	functions	function	NOUN
ap-1366	235	12	with	with	ADP
ap-1366	235	13	applications	application	NOUN
ap-1366	235	14	,	,	PUNCT
ap-1366	235	15	chapman	chapman	NOUN
ap-1366	235	16	and	and	CCONJ
ap-1366	235	17	hall	hall	PROPN
ap-1366	235	18	,	,	PUNCT
ap-1366	235	19	new	new	PROPN
ap-1366	235	20	york	york	PROPN
ap-1366	235	21	,	,	PUNCT
ap-1366	235	22	2001	2001	NUM
ap-1366	235	23	.	.	PUNCT
ap-1366	236	1	[	[	X
ap-1366	236	2	5	5	NUM
ap-1366	236	3	]	]	X
ap-1366	236	4	fernandez	fernandez	PROPN
ap-1366	236	5	,	,	PUNCT
ap-1366	236	6	d.	d.	PROPN
ap-1366	236	7	j.	j.	PROPN
ap-1366	236	8	c.	c.	PROPN
ap-1366	236	9	:	:	PUNCT
ap-1366	236	10	supersymmetric	supersymmetric	ADJ
ap-1366	236	11	quantum	quantum	NOUN
ap-1366	236	12	mechanics	mechanic	NOUN
ap-1366	236	13	,	,	PUNCT
ap-1366	236	14	quant	quant	NOUN
ap-1366	236	15	-	-	PUNCT
ap-1366	236	16	ph/0910.0192	ph/0910.0192	NOUN
ap-1366	236	17	.	.	PUNCT
ap-1366	236	18	68	68	NUM
ap-1366	236	19	acta	acta	PROPN
ap-1366	236	20	polytechnica	polytechnica	PROPN
ap-1366	236	21	vol	vol	NOUN
ap-1366	236	22	.	.	PUNCT
ap-1366	237	1	51	51	NUM
ap-1366	237	2	no	no	INTJ
ap-1366	237	3	.	.	PUNCT
ap-1366	238	1	1/2011	1/2011	NUM
ap-1366	239	1	[	[	SYM
ap-1366	239	2	6	6	NUM
ap-1366	239	3	]	]	X
ap-1366	239	4	samsonov	samsonov	NOUN
ap-1366	239	5	,	,	PUNCT
ap-1366	239	6	b.	b.	PROPN
ap-1366	239	7	f.	f.	PROPN
ap-1366	239	8	,	,	PUNCT
ap-1366	239	9	sukumar	sukumar	PROPN
ap-1366	239	10	,	,	PUNCT
ap-1366	239	11	c.	c.	PROPN
ap-1366	239	12	v.	v.	PROPN
ap-1366	239	13	,	,	PUNCT
ap-1366	239	14	pupasov	pupasov	PROPN
ap-1366	239	15	,	,	PUNCT
ap-1366	239	16	a.	a.	NOUN
ap-1366	239	17	m.	m.	NOUN
ap-1366	239	18	:	:	PUNCT
ap-1366	239	19	susy	susy	NOUN
ap-1366	239	20	transformation	transformation	NOUN
ap-1366	239	21	of	of	ADP
ap-1366	239	22	the	the	DET
ap-1366	239	23	green	green	ADJ
ap-1366	239	24	function	function	NOUN
ap-1366	239	25	and	and	CCONJ
ap-1366	239	26	a	a	DET
ap-1366	239	27	trace	trace	NOUN
ap-1366	239	28	formula	formula	NOUN
ap-1366	239	29	,	,	PUNCT
ap-1366	239	30	j.	j.	PROPN
ap-1366	239	31	phys	phys	PROPN
ap-1366	239	32	.	.	PUNCT
ap-1366	240	1	a	a	DET
ap-1366	240	2	38	38	NUM
ap-1366	240	3	(	(	PUNCT
ap-1366	240	4	2005	2005	NUM
ap-1366	240	5	)	)	PUNCT
ap-1366	240	6	,	,	PUNCT
ap-1366	240	7	7	7	NUM
ap-1366	240	8	557–7565	557–7565	NUM
ap-1366	240	9	.	.	PUNCT
ap-1366	241	1	[	[	X
ap-1366	241	2	7	7	X
ap-1366	241	3	]	]	X
ap-1366	241	4	schulze	schulze	NOUN
ap-1366	241	5	-	-	PUNCT
ap-1366	241	6	halberg	halberg	PROPN
ap-1366	241	7	,	,	PUNCT
ap-1366	241	8	a.	a.	NOUN
ap-1366	241	9	:	:	PUNCT
ap-1366	241	10	green	green	PROPN
ap-1366	241	11	’s	’s	PART
ap-1366	241	12	functions	function	NOUN
ap-1366	241	13	and	and	CCONJ
ap-1366	241	14	trace	trace	NOUN
ap-1366	241	15	formulas	formula	NOUN
ap-1366	241	16	for	for	ADP
ap-1366	241	17	generalized	generalized	ADJ
ap-1366	241	18	sturm	sturm	PROPN
ap-1366	241	19	-	-	PUNCT
ap-1366	241	20	liouville	liouville	NOUN
ap-1366	241	21	problems	problem	NOUN
ap-1366	241	22	related	relate	VERB
ap-1366	241	23	by	by	ADP
ap-1366	241	24	darboux	darboux	ADJ
ap-1366	241	25	transformations	transformation	NOUN
ap-1366	241	26	,	,	PUNCT
ap-1366	241	27	j.	j.	PROPN
ap-1366	241	28	math	math	PROPN
ap-1366	241	29	.	.	PUNCT
ap-1366	242	1	phys	phy	NOUN
ap-1366	242	2	.	.	PUNCT
ap-1366	243	1	51	51	NUM
ap-1366	243	2	(	(	PUNCT
ap-1366	243	3	2010	2010	NUM
ap-1366	243	4	)	)	PUNCT
ap-1366	243	5	,	,	PUNCT
ap-1366	243	6	053501	053501	NUM
ap-1366	243	7	(	(	PUNCT
ap-1366	243	8	13pp	13pp	NOUN
ap-1366	243	9	)	)	PUNCT
ap-1366	243	10	.	.	PUNCT
ap-1366	244	1	[	[	X
ap-1366	244	2	8	8	NUM
ap-1366	244	3	]	]	X
ap-1366	244	4	pozdeeva	pozdeeva	X
ap-1366	244	5	,	,	PUNCT
ap-1366	244	6	e.	e.	PROPN
ap-1366	244	7	,	,	PUNCT
ap-1366	244	8	schulze	schulze	NOUN
ap-1366	244	9	-	-	PUNCT
ap-1366	244	10	halberg	halberg	PROPN
ap-1366	244	11	,	,	PUNCT
ap-1366	244	12	a.	a.	NOUN
ap-1366	244	13	:	:	PUNCT
ap-1366	244	14	trace	trace	NOUN
ap-1366	244	15	formula	formula	NOUN
ap-1366	244	16	for	for	ADP
ap-1366	244	17	green	green	PROPN
ap-1366	244	18	’s	’s	PART
ap-1366	244	19	functions	function	NOUN
ap-1366	244	20	of	of	ADP
ap-1366	244	21	effective	effective	ADJ
ap-1366	244	22	mass	mass	NOUN
ap-1366	244	23	schrödinger	schrödinger	NOUN
ap-1366	244	24	equations	equation	NOUN
ap-1366	244	25	and	and	CCONJ
ap-1366	244	26	n	n	CCONJ
ap-1366	244	27	-	-	PUNCT
ap-1366	244	28	th	th	VERB
ap-1366	244	29	order	order	NOUN
ap-1366	244	30	darboux	darboux	VERB
ap-1366	244	31	transformations	transformation	NOUN
ap-1366	244	32	,	,	PUNCT
ap-1366	244	33	internat	internat	NOUN
ap-1366	244	34	.	.	PUNCT
ap-1366	245	1	j.	j.	PROPN
ap-1366	245	2	modern	modern	PROPN
ap-1366	245	3	phys	phys	PROPN
ap-1366	245	4	.	.	PUNCT
ap-1366	246	1	a	a	DET
ap-1366	246	2	23	23	NUM
ap-1366	246	3	(	(	PUNCT
ap-1366	246	4	2008	2008	NUM
ap-1366	246	5	)	)	PUNCT
ap-1366	246	6	,	,	PUNCT
ap-1366	246	7	2	2	NUM
ap-1366	246	8	635–2647	635–2647	NUM
ap-1366	246	9	.	.	PUNCT
ap-1366	247	1	[	[	X
ap-1366	247	2	9	9	NUM
ap-1366	247	3	]	]	X
ap-1366	247	4	sukumar	sukumar	PROPN
ap-1366	247	5	,	,	PUNCT
ap-1366	247	6	c.	c.	PROPN
ap-1366	247	7	v.	v.	PROPN
ap-1366	247	8	:	:	PUNCT
ap-1366	247	9	green	green	PROPN
ap-1366	247	10	’s	’s	PART
ap-1366	247	11	functions	function	NOUN
ap-1366	247	12	,	,	PUNCT
ap-1366	247	13	sum	sum	NOUN
ap-1366	247	14	rules	rule	NOUN
ap-1366	247	15	and	and	CCONJ
ap-1366	247	16	matrix	matrix	NOUN
ap-1366	247	17	elements	element	NOUN
ap-1366	247	18	for	for	ADP
ap-1366	247	19	susy	susy	NOUN
ap-1366	247	20	partners	partner	NOUN
ap-1366	247	21	,	,	PUNCT
ap-1366	247	22	j.	j.	PROPN
ap-1366	247	23	phys	phys	PROPN
ap-1366	247	24	.	.	PUNCT
ap-1366	248	1	a	a	DET
ap-1366	248	2	37	37	NUM
ap-1366	248	3	(	(	PUNCT
ap-1366	248	4	2004	2004	NUM
ap-1366	248	5	)	)	PUNCT
ap-1366	248	6	,	,	PUNCT
ap-1366	248	7	10	10	NUM
ap-1366	248	8	287–10295	287–10295	NUM
ap-1366	248	9	.	.	PUNCT
ap-1366	249	1	[	[	X
ap-1366	249	2	10	10	NUM
ap-1366	249	3	]	]	X
ap-1366	249	4	suzko	suzko	PROPN
ap-1366	249	5	,	,	PUNCT
ap-1366	249	6	a.	a.	NOUN
ap-1366	249	7	a.	a.	PROPN
ap-1366	249	8	,	,	PUNCT
ap-1366	249	9	schulze	schulze	NOUN
ap-1366	249	10	-	-	PUNCT
ap-1366	249	11	halberg	halberg	NOUN
ap-1366	249	12	,	,	PUNCT
ap-1366	249	13	a.	a.	NOUN
ap-1366	249	14	:	:	PUNCT
ap-1366	249	15	darboux	darboux	VERB
ap-1366	249	16	transformations	transformation	NOUN
ap-1366	249	17	and	and	CCONJ
ap-1366	249	18	supersymmetry	supersymmetry	NOUN
ap-1366	249	19	for	for	ADP
ap-1366	249	20	the	the	DET
ap-1366	249	21	generalized	generalize	VERB
ap-1366	249	22	schrödinger	schrödinger	NOUN
ap-1366	249	23	equations	equation	NOUN
ap-1366	249	24	in	in	ADP
ap-1366	249	25	(	(	PUNCT
ap-1366	249	26	1	1	NUM
ap-1366	249	27	+	+	NOUN
ap-1366	249	28	1	1	NUM
ap-1366	249	29	)	)	PUNCT
ap-1366	249	30	dimensions	dimension	NOUN
ap-1366	249	31	,	,	PUNCT
ap-1366	249	32	j.	j.	PROPN
ap-1366	249	33	phys	phys	PROPN
ap-1366	249	34	.	.	PUNCT
ap-1366	250	1	a	a	DET
ap-1366	250	2	42	42	NUM
ap-1366	250	3	(	(	PUNCT
ap-1366	250	4	2009	2009	NUM
ap-1366	250	5	)	)	PUNCT
ap-1366	250	6	,	,	PUNCT
ap-1366	250	7	295	295	NUM
ap-1366	250	8	203–295217	203–295217	NUM
ap-1366	250	9	.	.	PUNCT
ap-1366	251	1	axel	axel	PROPN
ap-1366	251	2	schulze	schulze	PROPN
ap-1366	251	3	-	-	PUNCT
ap-1366	251	4	halberg	halberg	NOUN
ap-1366	251	5	e	e	NOUN
ap-1366	251	6	-	-	NOUN
ap-1366	251	7	mail	mail	NOUN
ap-1366	251	8	:	:	PUNCT
ap-1366	252	1	xbataxel@gmail.com	xbataxel@gmail.com	X
ap-1366	253	1	department	department	PROPN
ap-1366	253	2	of	of	ADP
ap-1366	253	3	mathematics	mathematic	NOUN
ap-1366	253	4	and	and	CCONJ
ap-1366	253	5	actuarial	actuarial	ADJ
ap-1366	253	6	science	science	PROPN
ap-1366	253	7	indiana	indiana	PROPN
ap-1366	253	8	university	university	PROPN
ap-1366	253	9	northwest	northwest	PROPN
ap-1366	253	10	3400	3400	NUM
ap-1366	253	11	broadway	broadway	PROPN
ap-1366	253	12	,	,	PUNCT
ap-1366	253	13	gary	gary	PROPN
ap-1366	253	14	,	,	PUNCT
ap-1366	253	15	in	in	ADP
ap-1366	253	16	46408	46408	NUM
ap-1366	253	17	,	,	PUNCT
ap-1366	253	18	usa	usa	PROPN
ap-1366	253	19	69	69	NUM