id	sid	tid	token	lemma	pos
ap-8348	1	1	acta	acta	PROPN
ap-8348	1	2	polytechnica	polytechnica	PROPN
ap-8348	1	3	https://doi.org/10.14311/ap.2023.63.0132	https://doi.org/10.14311/ap.2023.63.0132	PROPN
ap-8348	1	4	acta	acta	PROPN
ap-8348	1	5	polytechnica	polytechnica	PROPN
ap-8348	1	6	63(2):132–139	63(2):132–139	PROPN
ap-8348	1	7	,	,	PUNCT
ap-8348	1	8	2023	2023	NUM
ap-8348	1	9	©	©	ADP
ap-8348	1	10	2023	2023	NUM
ap-8348	1	11	the	the	DET
ap-8348	1	12	author(s	author(s	NOUN
ap-8348	1	13	)	)	PUNCT
ap-8348	1	14	.	.	PUNCT
ap-8348	2	1	licensed	license	VERB
ap-8348	2	2	under	under	ADP
ap-8348	2	3	a	a	DET
ap-8348	2	4	cc	cc	NOUN
ap-8348	2	5	-	-	PUNCT
ap-8348	2	6	by	by	ADP
ap-8348	2	7	4.0	4.0	NUM
ap-8348	2	8	licence	licence	NOUN
ap-8348	2	9	published	publish	VERB
ap-8348	2	10	by	by	ADP
ap-8348	2	11	the	the	DET
ap-8348	2	12	czech	czech	PROPN
ap-8348	2	13	technical	technical	PROPN
ap-8348	2	14	university	university	PROPN
ap-8348	2	15	in	in	ADP
ap-8348	2	16	prague	prague	PROPN
ap-8348	2	17	exact	exact	ADJ
ap-8348	2	18	solutions	solution	NOUN
ap-8348	2	19	for	for	ADP
ap-8348	2	20	time	time	NOUN
ap-8348	2	21	-	-	PUNCT
ap-8348	2	22	dependent	dependent	ADJ
ap-8348	2	23	complex	complex	ADJ
ap-8348	2	24	symmetric	symmetric	ADJ
ap-8348	2	25	potential	potential	NOUN
ap-8348	2	26	well	well	INTJ
ap-8348	2	27	boubakeur	boubakeur	NOUN
ap-8348	2	28	khantoula	khantoula	NOUN
ap-8348	2	29	,	,	PUNCT
ap-8348	2	30	b	b	NOUN
ap-8348	2	31	,	,	PUNCT
ap-8348	2	32	abdelhafid	abdelhafid	ADV
ap-8348	2	33	bounamesa,∗	bounamesa,∗	NOUN
ap-8348	2	34	a	a	DET
ap-8348	2	35	university	university	NOUN
ap-8348	2	36	of	of	ADP
ap-8348	2	37	jijel	jijel	NOUN
ap-8348	2	38	,	,	PUNCT
ap-8348	2	39	department	department	NOUN
ap-8348	2	40	of	of	ADP
ap-8348	2	41	physics	physics	PROPN
ap-8348	2	42	,	,	PUNCT
ap-8348	2	43	laboratory	laboratory	NOUN
ap-8348	2	44	of	of	ADP
ap-8348	2	45	theoretical	theoretical	ADJ
ap-8348	2	46	physics	physics	NOUN
ap-8348	2	47	,	,	PUNCT
ap-8348	2	48	bp	bp	PROPN
ap-8348	2	49	98	98	NUM
ap-8348	2	50	ouled	oule	VERB
ap-8348	2	51	aissa	aissa	NOUN
ap-8348	2	52	,	,	PUNCT
ap-8348	2	53	18000	18000	NUM
ap-8348	2	54	jijel	jijel	NOUN
ap-8348	2	55	,	,	PUNCT
ap-8348	2	56	algeria	algeria	PROPN
ap-8348	2	57	b	b	PROPN
ap-8348	2	58	university	university	PROPN
ap-8348	2	59	of	of	ADP
ap-8348	2	60	constantine	constantine	PROPN
ap-8348	2	61	3	3	NUM
ap-8348	2	62	–	–	PUNCT
ap-8348	2	63	salah	salah	PROPN
ap-8348	2	64	boubnider	boubnider	PROPN
ap-8348	2	65	university	university	PROPN
ap-8348	2	66	,	,	PUNCT
ap-8348	2	67	department	department	NOUN
ap-8348	2	68	of	of	ADP
ap-8348	2	69	process	process	NOUN
ap-8348	2	70	engineering	engineering	NOUN
ap-8348	2	71	,	,	PUNCT
ap-8348	2	72	bp	bp	PROPN
ap-8348	2	73	b72	b72	PROPN
ap-8348	2	74	ali	ali	PROPN
ap-8348	2	75	mendjeli	mendjeli	PROPN
ap-8348	2	76	,	,	PUNCT
ap-8348	2	77	25000	25000	NUM
ap-8348	2	78	constantine	constantine	PROPN
ap-8348	2	79	,	,	PUNCT
ap-8348	2	80	algeria	algeria	PROPN
ap-8348	2	81	∗	∗	NOUN
ap-8348	2	82	corresponding	correspond	VERB
ap-8348	2	83	author	author	NOUN
ap-8348	2	84	:	:	PUNCT
ap-8348	2	85	bounames@univ-jijel.dz	bounames@univ-jijel.dz	ADJ
ap-8348	2	86	abstract	abstract	NOUN
ap-8348	2	87	.	.	PUNCT
ap-8348	3	1	using	use	VERB
ap-8348	3	2	the	the	DET
ap-8348	3	3	pseudo	pseudo	NOUN
ap-8348	3	4	-	-	ADJ
ap-8348	3	5	invariant	invariant	ADJ
ap-8348	3	6	operator	operator	NOUN
ap-8348	3	7	method	method	NOUN
ap-8348	3	8	,	,	PUNCT
ap-8348	3	9	we	we	PRON
ap-8348	3	10	investigate	investigate	VERB
ap-8348	3	11	the	the	DET
ap-8348	3	12	model	model	NOUN
ap-8348	3	13	of	of	ADP
ap-8348	3	14	a	a	DET
ap-8348	3	15	particle	particle	NOUN
ap-8348	3	16	with	with	ADP
ap-8348	3	17	a	a	DET
ap-8348	3	18	time	time	NOUN
ap-8348	3	19	-	-	PUNCT
ap-8348	3	20	dependent	dependent	ADJ
ap-8348	3	21	mass	mass	NOUN
ap-8348	3	22	in	in	ADP
ap-8348	3	23	a	a	DET
ap-8348	3	24	complex	complex	ADJ
ap-8348	3	25	time	time	NOUN
ap-8348	3	26	-	-	PUNCT
ap-8348	3	27	dependent	dependent	ADJ
ap-8348	3	28	symmetric	symmetric	ADJ
ap-8348	3	29	potential	potential	ADJ
ap-8348	3	30	well	well	NOUN
ap-8348	3	31	v	v	NOUN
ap-8348	3	32	(	(	PUNCT
ap-8348	3	33	x	x	NOUN
ap-8348	3	34	,	,	PUNCT
ap-8348	3	35	t	t	PROPN
ap-8348	3	36	)	)	PUNCT
ap-8348	3	37	=	=	PUNCT
ap-8348	4	1	if	if	SCONJ
ap-8348	4	2	(	(	PUNCT
ap-8348	4	3	t	t	NOUN
ap-8348	4	4	)	)	PUNCT
ap-8348	4	5	|x|	|x|	PROPN
ap-8348	4	6	.	.	PUNCT
ap-8348	5	1	the	the	DET
ap-8348	5	2	problem	problem	NOUN
ap-8348	5	3	is	be	AUX
ap-8348	5	4	exactly	exactly	ADV
ap-8348	5	5	solvable	solvable	ADJ
ap-8348	5	6	and	and	CCONJ
ap-8348	5	7	the	the	DET
ap-8348	5	8	analytic	analytic	ADJ
ap-8348	5	9	expressions	expression	NOUN
ap-8348	5	10	of	of	ADP
ap-8348	5	11	the	the	DET
ap-8348	5	12	schrödinger	schrödinger	ADJ
ap-8348	5	13	wavefunctions	wavefunction	NOUN
ap-8348	5	14	are	be	AUX
ap-8348	5	15	given	give	VERB
ap-8348	5	16	in	in	ADP
ap-8348	5	17	terms	term	NOUN
ap-8348	5	18	of	of	ADP
ap-8348	5	19	the	the	DET
ap-8348	5	20	airy	airy	ADJ
ap-8348	5	21	function	function	NOUN
ap-8348	5	22	.	.	PUNCT
ap-8348	6	1	indeed	indeed	ADV
ap-8348	6	2	,	,	PUNCT
ap-8348	6	3	with	with	ADP
ap-8348	6	4	an	an	DET
ap-8348	6	5	appropriate	appropriate	ADJ
ap-8348	6	6	choice	choice	NOUN
ap-8348	6	7	of	of	ADP
ap-8348	6	8	the	the	DET
ap-8348	6	9	time	time	NOUN
ap-8348	6	10	-	-	PUNCT
ap-8348	6	11	dependent	dependent	ADJ
ap-8348	6	12	metric	metric	ADJ
ap-8348	6	13	operators	operator	NOUN
ap-8348	6	14	and	and	CCONJ
ap-8348	6	15	the	the	DET
ap-8348	6	16	unitary	unitary	ADJ
ap-8348	6	17	transformations	transformation	NOUN
ap-8348	6	18	,	,	PUNCT
ap-8348	6	19	for	for	ADP
ap-8348	6	20	each	each	DET
ap-8348	6	21	region	region	NOUN
ap-8348	6	22	,	,	PUNCT
ap-8348	6	23	the	the	DET
ap-8348	6	24	two	two	NUM
ap-8348	6	25	corresponding	corresponding	ADJ
ap-8348	6	26	pseudo	pseudo	NOUN
ap-8348	6	27	-	-	ADJ
ap-8348	6	28	hermitian	hermitian	ADJ
ap-8348	6	29	invariants	invariant	NOUN
ap-8348	6	30	transform	transform	VERB
ap-8348	6	31	into	into	ADP
ap-8348	6	32	a	a	DET
ap-8348	6	33	well	well	ADV
ap-8348	6	34	-	-	PUNCT
ap-8348	6	35	known	know	VERB
ap-8348	6	36	time	time	NOUN
ap-8348	6	37	-	-	PUNCT
ap-8348	6	38	independent	independent	ADJ
ap-8348	6	39	hermitian	hermitian	ADJ
ap-8348	6	40	invariant	invariant	PROPN
ap-8348	6	41	which	which	PRON
ap-8348	6	42	is	be	AUX
ap-8348	6	43	the	the	DET
ap-8348	6	44	hamiltonian	hamiltonian	NOUN
ap-8348	6	45	of	of	ADP
ap-8348	6	46	a	a	DET
ap-8348	6	47	particle	particle	NOUN
ap-8348	6	48	confined	confine	VERB
ap-8348	6	49	in	in	ADP
ap-8348	6	50	a	a	DET
ap-8348	6	51	symmetric	symmetric	ADJ
ap-8348	6	52	linear	linear	ADJ
ap-8348	6	53	potential	potential	NOUN
ap-8348	6	54	well	well	ADV
ap-8348	6	55	.	.	PUNCT
ap-8348	7	1	the	the	DET
ap-8348	7	2	eigenfunctions	eigenfunction	NOUN
ap-8348	7	3	of	of	ADP
ap-8348	7	4	the	the	DET
ap-8348	7	5	last	last	ADJ
ap-8348	7	6	invariant	invariant	NOUN
ap-8348	7	7	are	be	AUX
ap-8348	7	8	the	the	DET
ap-8348	7	9	airy	airy	ADJ
ap-8348	7	10	functions	function	NOUN
ap-8348	7	11	.	.	PUNCT
ap-8348	8	1	then	then	ADV
ap-8348	8	2	,	,	PUNCT
ap-8348	8	3	the	the	DET
ap-8348	8	4	phases	phase	NOUN
ap-8348	8	5	obtained	obtain	VERB
ap-8348	8	6	are	be	AUX
ap-8348	8	7	real	real	ADJ
ap-8348	8	8	for	for	SCONJ
ap-8348	8	9	both	both	DET
ap-8348	8	10	regions	region	NOUN
ap-8348	8	11	and	and	CCONJ
ap-8348	8	12	the	the	DET
ap-8348	8	13	general	general	ADJ
ap-8348	8	14	solution	solution	NOUN
ap-8348	8	15	to	to	ADP
ap-8348	8	16	the	the	DET
ap-8348	8	17	problem	problem	NOUN
ap-8348	8	18	is	be	AUX
ap-8348	8	19	deduced	deduce	VERB
ap-8348	8	20	.	.	PUNCT
ap-8348	9	1	keywords	keyword	NOUN
ap-8348	9	2	:	:	PUNCT
ap-8348	9	3	non	non	ADJ
ap-8348	9	4	-	-	ADJ
ap-8348	9	5	hermitian	hermitian	ADJ
ap-8348	9	6	hamiltonian	hamiltonian	NOUN
ap-8348	9	7	,	,	PUNCT
ap-8348	9	8	time	time	NOUN
ap-8348	9	9	-	-	PUNCT
ap-8348	9	10	dependent	dependent	ADJ
ap-8348	9	11	hamiltonian	hamiltonian	NOUN
ap-8348	9	12	,	,	PUNCT
ap-8348	9	13	pseudo	pseudo	NOUN
ap-8348	9	14	-	-	ADJ
ap-8348	9	15	invariant	invariant	ADJ
ap-8348	9	16	method	method	NOUN
ap-8348	9	17	,	,	PUNCT
ap-8348	9	18	pt	pt	NOUN
ap-8348	9	19	-	-	PUNCT
ap-8348	9	20	symmetry	symmetry	NOUN
ap-8348	9	21	,	,	PUNCT
ap-8348	9	22	pseudo	pseudo	NOUN
ap-8348	9	23	-	-	NOUN
ap-8348	9	24	hermiticity	hermiticity	NOUN
ap-8348	9	25	.	.	PUNCT
ap-8348	10	1	1	1	X
ap-8348	10	2	.	.	X
ap-8348	10	3	introduction	introduction	NOUN
ap-8348	10	4	the	the	DET
ap-8348	10	5	discovery	discovery	NOUN
ap-8348	10	6	of	of	ADP
ap-8348	10	7	a	a	DET
ap-8348	10	8	class	class	NOUN
ap-8348	10	9	of	of	ADP
ap-8348	10	10	non	non	ADJ
ap-8348	10	11	-	-	ADJ
ap-8348	10	12	hermitian	hermitian	ADJ
ap-8348	10	13	hamiltonian	hamiltonian	NOUN
ap-8348	10	14	that	that	PRON
ap-8348	10	15	may	may	AUX
ap-8348	10	16	have	have	VERB
ap-8348	10	17	a	a	DET
ap-8348	10	18	real	real	ADJ
ap-8348	10	19	spectrum	spectrum	NOUN
ap-8348	10	20	has	have	AUX
ap-8348	10	21	prompted	prompt	VERB
ap-8348	10	22	a	a	DET
ap-8348	10	23	revival	revival	NOUN
ap-8348	10	24	of	of	ADP
ap-8348	10	25	theoretical	theoretical	ADJ
ap-8348	10	26	and	and	CCONJ
ap-8348	10	27	applied	apply	VERB
ap-8348	10	28	research	research	NOUN
ap-8348	10	29	in	in	ADP
ap-8348	10	30	quantum	quantum	ADJ
ap-8348	10	31	physics	physics	NOUN
ap-8348	10	32	.	.	PUNCT
ap-8348	11	1	in	in	ADP
ap-8348	11	2	fact	fact	NOUN
ap-8348	11	3	,	,	PUNCT
ap-8348	11	4	in	in	ADP
ap-8348	11	5	1998	1998	NUM
ap-8348	11	6	,	,	PUNCT
ap-8348	11	7	c.m	c.m	PROPN
ap-8348	11	8	.	.	PROPN
ap-8348	11	9	bender	bender	PROPN
ap-8348	11	10	and	and	CCONJ
ap-8348	11	11	s.	s.	PROPN
ap-8348	11	12	boettcher	boettcher	PROPN
ap-8348	11	13	showed	show	VERB
ap-8348	11	14	that	that	SCONJ
ap-8348	11	15	any	any	DET
ap-8348	11	16	non	non	ADJ
ap-8348	11	17	-	-	ADJ
ap-8348	11	18	hermitian	hermitian	ADJ
ap-8348	11	19	hamiltonian	hamiltonian	NOUN
ap-8348	11	20	invariant	invariant	PROPN
ap-8348	11	21	under	under	ADP
ap-8348	11	22	the	the	DET
ap-8348	11	23	unbroken	unbroken	ADJ
ap-8348	11	24	space	space	NOUN
ap-8348	11	25	-	-	PUNCT
ap-8348	11	26	time	time	NOUN
ap-8348	11	27	reflection	reflection	NOUN
ap-8348	11	28	,	,	PUNCT
ap-8348	11	29	or	or	CCONJ
ap-8348	11	30	pt	pt	PROPN
ap-8348	11	31	-symmetry	-symmetry	NOUN
ap-8348	11	32	,	,	PUNCT
ap-8348	11	33	has	have	VERB
ap-8348	11	34	real	real	ADJ
ap-8348	11	35	eigenvalues	eigenvalue	NOUN
ap-8348	11	36	and	and	CCONJ
ap-8348	11	37	satisfies	satisfy	VERB
ap-8348	11	38	all	all	DET
ap-8348	11	39	the	the	DET
ap-8348	11	40	physical	physical	ADJ
ap-8348	11	41	axioms	axiom	NOUN
ap-8348	11	42	of	of	ADP
ap-8348	11	43	quantum	quantum	ADJ
ap-8348	11	44	mechanics	mechanic	NOUN
ap-8348	11	45	[	[	X
ap-8348	11	46	1–3	1–3	NOUN
ap-8348	11	47	]	]	X
ap-8348	11	48	.	.	PUNCT
ap-8348	12	1	in	in	ADP
ap-8348	12	2	2002	2002	NUM
ap-8348	12	3	,	,	PUNCT
ap-8348	12	4	a.	a.	NOUN
ap-8348	12	5	mostafazadeh	mostafazadeh	PROPN
ap-8348	12	6	presented	present	VERB
ap-8348	12	7	a	a	DET
ap-8348	12	8	more	more	ADV
ap-8348	12	9	extended	extended	ADJ
ap-8348	12	10	version	version	NOUN
ap-8348	12	11	of	of	ADP
ap-8348	12	12	non	non	ADJ
ap-8348	12	13	-	-	ADJ
ap-8348	12	14	hermitian	hermitian	ADJ
ap-8348	12	15	hamiltonians	hamiltonian	NOUN
ap-8348	12	16	having	have	VERB
ap-8348	12	17	a	a	DET
ap-8348	12	18	real	real	ADJ
ap-8348	12	19	spectrum	spectrum	NOUN
ap-8348	12	20	,	,	PUNCT
ap-8348	12	21	proving	prove	VERB
ap-8348	12	22	that	that	SCONJ
ap-8348	12	23	the	the	DET
ap-8348	12	24	hermiticity	hermiticity	NOUN
ap-8348	12	25	of	of	ADP
ap-8348	12	26	the	the	DET
ap-8348	12	27	hamiltonian	hamiltonian	NOUN
ap-8348	12	28	with	with	ADP
ap-8348	12	29	respect	respect	NOUN
ap-8348	12	30	to	to	ADP
ap-8348	12	31	a	a	DET
ap-8348	12	32	positive	positive	ADJ
ap-8348	12	33	definite	definite	ADJ
ap-8348	12	34	inner	inner	ADJ
ap-8348	12	35	product	product	NOUN
ap-8348	12	36	,	,	PUNCT
ap-8348	12	37	⟨.	⟨.	PROPN
ap-8348	12	38	,	,	PUNCT
ap-8348	12	39	.⟩η	.⟩η	PUNCT
ap-8348	13	1	=	=	PUNCT
ap-8348	13	2	⟨.|	⟨.|	ADV
ap-8348	13	3	η	η	PROPN
ap-8348	13	4	|.⟩	|.⟩	PROPN
ap-8348	13	5	,	,	PUNCT
ap-8348	13	6	is	be	AUX
ap-8348	13	7	a	a	DET
ap-8348	13	8	necessary	necessary	ADJ
ap-8348	13	9	and	and	CCONJ
ap-8348	13	10	sufficient	sufficient	ADJ
ap-8348	13	11	condition	condition	NOUN
ap-8348	13	12	for	for	ADP
ap-8348	13	13	the	the	DET
ap-8348	13	14	reality	reality	NOUN
ap-8348	13	15	of	of	ADP
ap-8348	13	16	the	the	DET
ap-8348	13	17	spectrum	spectrum	NOUN
ap-8348	13	18	,	,	PUNCT
ap-8348	13	19	where	where	SCONJ
ap-8348	13	20	η	η	PROPN
ap-8348	13	21	is	be	AUX
ap-8348	13	22	the	the	DET
ap-8348	13	23	metric	metric	ADJ
ap-8348	13	24	operator	operator	NOUN
ap-8348	13	25	which	which	PRON
ap-8348	13	26	is	be	AUX
ap-8348	13	27	linear	linear	ADJ
ap-8348	13	28	,	,	PUNCT
ap-8348	13	29	hermitian	hermitian	ADJ
ap-8348	13	30	,	,	PUNCT
ap-8348	13	31	invertible	invertible	ADJ
ap-8348	13	32	and	and	CCONJ
ap-8348	13	33	positive	positive	ADJ
ap-8348	13	34	.	.	PUNCT
ap-8348	14	1	this	this	DET
ap-8348	14	2	condition	condition	NOUN
ap-8348	14	3	requires	require	VERB
ap-8348	14	4	that	that	SCONJ
ap-8348	14	5	the	the	DET
ap-8348	14	6	hamiltonian	hamiltonian	ADJ
ap-8348	14	7	h	h	PROPN
ap-8348	14	8	satisfies	satisfy	VERB
ap-8348	14	9	the	the	DET
ap-8348	14	10	pseudo	pseudo	NOUN
ap-8348	14	11	-	-	ADJ
ap-8348	14	12	hermitian	hermitian	ADJ
ap-8348	14	13	relation	relation	NOUN
ap-8348	15	1	[	[	X
ap-8348	15	2	4–6	4–6	X
ap-8348	15	3	]	]	X
ap-8348	15	4	:	:	PUNCT
ap-8348	15	5	h†	h†	ADJ
ap-8348	15	6	=	=	SYM
ap-8348	15	7	ηhη†	ηhη†	PROPN
ap-8348	15	8	.	.	PUNCT
ap-8348	16	1	(	(	PUNCT
ap-8348	16	2	1	1	X
ap-8348	16	3	)	)	PUNCT
ap-8348	16	4	moreover	moreover	ADV
ap-8348	16	5	in	in	ADP
ap-8348	16	6	recent	recent	ADJ
ap-8348	16	7	years	year	NOUN
ap-8348	16	8	,	,	PUNCT
ap-8348	16	9	a	a	DET
ap-8348	16	10	significant	significant	ADJ
ap-8348	16	11	progress	progress	NOUN
ap-8348	16	12	has	have	AUX
ap-8348	16	13	been	be	AUX
ap-8348	16	14	achieved	achieve	VERB
ap-8348	16	15	in	in	ADP
ap-8348	16	16	the	the	DET
ap-8348	16	17	study	study	NOUN
ap-8348	16	18	of	of	ADP
ap-8348	16	19	time	time	NOUN
ap-8348	16	20	-	-	PUNCT
ap-8348	16	21	dependent	dependent	ADJ
ap-8348	16	22	(	(	PUNCT
ap-8348	16	23	td	td	NOUN
ap-8348	16	24	)	)	PUNCT
ap-8348	16	25	non	non	ADJ
ap-8348	16	26	-	-	ADJ
ap-8348	16	27	hermitian	hermitian	ADJ
ap-8348	16	28	quantum	quantum	NOUN
ap-8348	16	29	systems	system	NOUN
ap-8348	16	30	in	in	ADP
ap-8348	16	31	several	several	ADJ
ap-8348	16	32	branches	branch	NOUN
ap-8348	16	33	of	of	ADP
ap-8348	16	34	physics	physics	PROPN
ap-8348	16	35	.	.	PUNCT
ap-8348	17	1	finding	find	VERB
ap-8348	17	2	exact	exact	ADJ
ap-8348	17	3	solutions	solution	NOUN
ap-8348	17	4	to	to	ADP
ap-8348	17	5	the	the	DET
ap-8348	17	6	td	td	NOUN
ap-8348	17	7	schrödinger	schrödinger	ADJ
ap-8348	17	8	equation	equation	NOUN
ap-8348	17	9	,	,	PUNCT
ap-8348	17	10	which	which	PRON
ap-8348	17	11	can	can	AUX
ap-8348	17	12	not	not	PART
ap-8348	17	13	be	be	AUX
ap-8348	17	14	reduced	reduce	VERB
ap-8348	17	15	to	to	PART
ap-8348	17	16	eigenvalues	eigenvalue	VERB
ap-8348	17	17	equation	equation	NOUN
ap-8348	17	18	in	in	ADP
ap-8348	17	19	general	general	ADJ
ap-8348	17	20	,	,	PUNCT
ap-8348	17	21	is	be	AUX
ap-8348	17	22	a	a	DET
ap-8348	17	23	problem	problem	NOUN
ap-8348	17	24	of	of	ADP
ap-8348	17	25	intriguing	intriguing	ADJ
ap-8348	17	26	difficulty	difficulty	NOUN
ap-8348	17	27	.	.	PUNCT
ap-8348	18	1	different	different	ADJ
ap-8348	18	2	methods	method	NOUN
ap-8348	18	3	are	be	AUX
ap-8348	18	4	used	use	VERB
ap-8348	18	5	to	to	PART
ap-8348	18	6	obtain	obtain	VERB
ap-8348	18	7	solutions	solution	NOUN
ap-8348	18	8	of	of	ADP
ap-8348	18	9	schrödinger	schrödinger	NOUN
ap-8348	18	10	’s	’s	PART
ap-8348	18	11	equation	equation	NOUN
ap-8348	18	12	for	for	ADP
ap-8348	18	13	explicitly	explicitly	ADV
ap-8348	18	14	td	td	NOUN
ap-8348	18	15	systems	system	NOUN
ap-8348	18	16	,	,	PUNCT
ap-8348	18	17	such	such	ADJ
ap-8348	18	18	as	as	ADP
ap-8348	18	19	unitary	unitary	ADJ
ap-8348	18	20	and	and	CCONJ
ap-8348	18	21	non	non	ADJ
ap-8348	18	22	-	-	ADJ
ap-8348	18	23	unitary	unitary	ADJ
ap-8348	18	24	transformations	transformation	NOUN
ap-8348	18	25	,	,	PUNCT
ap-8348	18	26	the	the	DET
ap-8348	18	27	pseudo	pseudo	NOUN
ap-8348	18	28	-	-	ADJ
ap-8348	18	29	invariant	invariant	ADJ
ap-8348	18	30	method	method	NOUN
ap-8348	18	31	,	,	PUNCT
ap-8348	18	32	dyson	dyson	PROPN
ap-8348	18	33	’s	’s	PART
ap-8348	18	34	maps	map	NOUN
ap-8348	18	35	,	,	PUNCT
ap-8348	18	36	point	point	NOUN
ap-8348	18	37	transformations	transformation	NOUN
ap-8348	18	38	,	,	PUNCT
ap-8348	18	39	darboux	darboux	VERB
ap-8348	18	40	transformations	transformation	NOUN
ap-8348	18	41	,	,	PUNCT
ap-8348	18	42	perturbation	perturbation	NOUN
ap-8348	18	43	theory	theory	NOUN
ap-8348	18	44	and	and	CCONJ
ap-8348	18	45	adiabatic	adiabatic	ADJ
ap-8348	18	46	approximation	approximation	NOUN
ap-8348	18	47	[	[	X
ap-8348	18	48	7–31	7–31	PROPN
ap-8348	18	49	]	]	PUNCT
ap-8348	18	50	.	.	PUNCT
ap-8348	19	1	however	however	ADV
ap-8348	19	2	,	,	PUNCT
ap-8348	19	3	the	the	DET
ap-8348	19	4	emergence	emergence	NOUN
ap-8348	19	5	of	of	ADP
ap-8348	19	6	a	a	DET
ap-8348	19	7	non	non	ADJ
ap-8348	19	8	-	-	ADJ
ap-8348	19	9	linear	linear	ADJ
ap-8348	19	10	ermakov	ermakov	NOUN
ap-8348	19	11	-	-	PUNCT
ap-8348	19	12	type	type	NOUN
ap-8348	19	13	auxiliary	auxiliary	ADJ
ap-8348	19	14	equation	equation	NOUN
ap-8348	19	15	for	for	ADP
ap-8348	19	16	several	several	ADJ
ap-8348	19	17	td	td	NOUN
ap-8348	19	18	systems	system	NOUN
ap-8348	19	19	,	,	PUNCT
ap-8348	19	20	which	which	PRON
ap-8348	19	21	is	be	AUX
ap-8348	19	22	difficult	difficult	ADJ
ap-8348	19	23	to	to	PART
ap-8348	19	24	solve	solve	VERB
ap-8348	19	25	,	,	PUNCT
ap-8348	19	26	constitutes	constitute	VERB
ap-8348	19	27	an	an	DET
ap-8348	19	28	additional	additional	ADJ
ap-8348	19	29	constraint	constraint	NOUN
ap-8348	19	30	to	to	PART
ap-8348	19	31	obtain	obtain	VERB
ap-8348	19	32	exact	exact	ADJ
ap-8348	19	33	analytical	analytical	ADJ
ap-8348	19	34	solutions	solution	NOUN
ap-8348	19	35	[	[	X
ap-8348	19	36	32	32	NUM
ap-8348	19	37	,	,	PUNCT
ap-8348	19	38	33	33	NUM
ap-8348	19	39	]	]	PUNCT
ap-8348	19	40	.	.	PUNCT
ap-8348	20	1	this	this	PRON
ap-8348	20	2	greatly	greatly	ADV
ap-8348	20	3	reduces	reduce	VERB
ap-8348	20	4	the	the	DET
ap-8348	20	5	number	number	NOUN
ap-8348	20	6	of	of	ADP
ap-8348	20	7	exactly	exactly	ADV
ap-8348	20	8	solvable	solvable	ADJ
ap-8348	20	9	time	time	NOUN
ap-8348	20	10	-	-	PUNCT
ap-8348	20	11	dependent	dependent	ADJ
ap-8348	20	12	non	non	ADJ
ap-8348	20	13	-	-	ADJ
ap-8348	20	14	hermitian	hermitian	ADJ
ap-8348	20	15	systems	system	NOUN
ap-8348	20	16	[	[	X
ap-8348	20	17	34–38	34–38	NUM
ap-8348	20	18	]	]	PUNCT
ap-8348	20	19	.	.	PUNCT
ap-8348	21	1	in	in	ADP
ap-8348	21	2	particular	particular	ADJ
ap-8348	21	3	,	,	PUNCT
ap-8348	21	4	other	other	ADJ
ap-8348	21	5	works	work	NOUN
ap-8348	21	6	have	have	AUX
ap-8348	21	7	been	be	AUX
ap-8348	21	8	concerned	concern	VERB
ap-8348	21	9	with	with	ADP
ap-8348	21	10	studying	study	VERB
ap-8348	21	11	exact	exact	ADJ
ap-8348	21	12	solutions	solution	NOUN
ap-8348	21	13	of	of	ADP
ap-8348	21	14	td	td	NOUN
ap-8348	21	15	hamiltonians	hamiltonian	NOUN
ap-8348	21	16	with	with	ADP
ap-8348	21	17	a	a	DET
ap-8348	21	18	specific	specific	ADJ
ap-8348	21	19	td	td	NOUN
ap-8348	21	20	mass	mass	NOUN
ap-8348	21	21	in	in	ADP
ap-8348	21	22	the	the	DET
ap-8348	21	23	non	non	ADJ
ap-8348	21	24	-	-	ADJ
ap-8348	21	25	hermitian	hermitian	ADJ
ap-8348	21	26	case	case	NOUN
ap-8348	21	27	[	[	X
ap-8348	21	28	39	39	NUM
ap-8348	21	29	,	,	PUNCT
ap-8348	21	30	40	40	NUM
ap-8348	21	31	]	]	PUNCT
ap-8348	21	32	and	and	CCONJ
ap-8348	21	33	also	also	ADV
ap-8348	21	34	in	in	ADP
ap-8348	21	35	the	the	DET
ap-8348	21	36	hermitian	hermitian	ADJ
ap-8348	21	37	case	case	NOUN
ap-8348	22	1	[	[	X
ap-8348	22	2	41–45	41–45	NUM
ap-8348	22	3	]	]	PUNCT
ap-8348	22	4	.	.	PUNCT
ap-8348	23	1	in	in	ADP
ap-8348	23	2	the	the	DET
ap-8348	23	3	present	present	ADJ
ap-8348	23	4	work	work	NOUN
ap-8348	23	5	,	,	PUNCT
ap-8348	23	6	we	we	PRON
ap-8348	23	7	used	use	VERB
ap-8348	23	8	the	the	DET
ap-8348	23	9	pseudo	pseudo	NOUN
ap-8348	23	10	-	-	ADJ
ap-8348	23	11	invariant	invariant	ADJ
ap-8348	23	12	method	method	NOUN
ap-8348	23	13	[	[	X
ap-8348	23	14	17	17	NUM
ap-8348	23	15	]	]	PUNCT
ap-8348	23	16	to	to	PART
ap-8348	23	17	obtain	obtain	VERB
ap-8348	23	18	the	the	DET
ap-8348	23	19	exact	exact	ADJ
ap-8348	23	20	solutions	solution	NOUN
ap-8348	23	21	of	of	ADP
ap-8348	23	22	the	the	DET
ap-8348	23	23	schrödinger	schrödinger	ADJ
ap-8348	23	24	equation	equation	NOUN
ap-8348	23	25	for	for	ADP
ap-8348	23	26	a	a	DET
ap-8348	23	27	particle	particle	NOUN
ap-8348	23	28	with	with	ADP
ap-8348	23	29	td	td	NOUN
ap-8348	23	30	mass	mass	NOUN
ap-8348	23	31	moving	move	VERB
ap-8348	23	32	in	in	ADP
ap-8348	23	33	a	a	DET
ap-8348	23	34	td	td	NOUN
ap-8348	23	35	complex	complex	ADJ
ap-8348	23	36	symmetric	symmetric	ADJ
ap-8348	23	37	potential	potential	NOUN
ap-8348	24	1	well	well	ADV
ap-8348	24	2	:	:	PUNCT
ap-8348	24	3	v	v	X
ap-8348	24	4	(	(	PUNCT
ap-8348	24	5	x	x	NOUN
ap-8348	24	6	,	,	PUNCT
ap-8348	24	7	t	t	PROPN
ap-8348	24	8	)	)	PUNCT
ap-8348	24	9	=	=	SYM
ap-8348	24	10	if(t	if(t	NOUN
ap-8348	24	11	)	)	PUNCT
ap-8348	24	12	|x|	|x|	PROPN
ap-8348	24	13	,	,	PUNCT
ap-8348	24	14	(	(	PUNCT
ap-8348	24	15	2	2	X
ap-8348	24	16	)	)	PUNCT
ap-8348	24	17	where	where	SCONJ
ap-8348	24	18	f(t	f(t	NOUN
ap-8348	24	19	)	)	PUNCT
ap-8348	24	20	is	be	AUX
ap-8348	24	21	an	an	DET
ap-8348	24	22	arbitrary	arbitrary	ADJ
ap-8348	24	23	real	real	ADJ
ap-8348	24	24	td	td	NOUN
ap-8348	24	25	function	function	NOUN
ap-8348	24	26	.	.	PUNCT
ap-8348	25	1	the	the	DET
ap-8348	25	2	manuscript	manuscript	NOUN
ap-8348	25	3	is	be	AUX
ap-8348	25	4	organised	organise	VERB
ap-8348	25	5	as	as	SCONJ
ap-8348	25	6	follows	follow	VERB
ap-8348	25	7	:	:	PUNCT
ap-8348	25	8	in	in	ADP
ap-8348	25	9	section	section	NOUN
ap-8348	25	10	2	2	NUM
ap-8348	25	11	,	,	PUNCT
ap-8348	25	12	we	we	PRON
ap-8348	25	13	introduce	introduce	VERB
ap-8348	25	14	some	some	PRON
ap-8348	25	15	of	of	ADP
ap-8348	25	16	the	the	DET
ap-8348	25	17	basic	basic	ADJ
ap-8348	25	18	equations	equation	NOUN
ap-8348	25	19	of	of	ADP
ap-8348	25	20	the	the	DET
ap-8348	25	21	td	td	NOUN
ap-8348	25	22	non	non	ADJ
ap-8348	25	23	-	-	ADJ
ap-8348	25	24	hermitian	hermitian	ADJ
ap-8348	25	25	hamiltonians	hamiltonian	NOUN
ap-8348	25	26	and	and	CCONJ
ap-8348	25	27	their	their	PRON
ap-8348	25	28	time	time	NOUN
ap-8348	25	29	-	-	PUNCT
ap-8348	25	30	dependent	dependent	ADJ
ap-8348	25	31	schrödinger	schrödinger	ADJ
ap-8348	25	32	equation	equation	NOUN
ap-8348	25	33	(	(	PUNCT
ap-8348	25	34	tdse	tdse	NOUN
ap-8348	25	35	)	)	PUNCT
ap-8348	25	36	with	with	ADP
ap-8348	25	37	a	a	DET
ap-8348	25	38	td	td	NOUN
ap-8348	25	39	metric	metric	NOUN
ap-8348	25	40	.	.	PUNCT
ap-8348	26	1	in	in	ADP
ap-8348	26	2	section	section	NOUN
ap-8348	26	3	3	3	NUM
ap-8348	26	4	,	,	PUNCT
ap-8348	26	5	we	we	PRON
ap-8348	26	6	discuss	discuss	VERB
ap-8348	26	7	the	the	DET
ap-8348	26	8	use	use	NOUN
ap-8348	26	9	of	of	ADP
ap-8348	26	10	the	the	DET
ap-8348	26	11	lewis	lewis	NOUN
ap-8348	26	12	-	-	PUNCT
ap-8348	26	13	riesenfeld	riesenfeld	NOUN
ap-8348	26	14	invariant	invariant	ADJ
ap-8348	26	15	method	method	NOUN
ap-8348	26	16	to	to	PART
ap-8348	26	17	address	address	VERB
ap-8348	26	18	the	the	DET
ap-8348	26	19	schrödinger	schrödinger	ADJ
ap-8348	26	20	equation	equation	NOUN
ap-8348	26	21	for	for	ADP
ap-8348	26	22	an	an	DET
ap-8348	26	23	explicitly	explicitly	ADV
ap-8348	26	24	td	td	NOUN
ap-8348	26	25	nonhermitian	nonhermitian	ADJ
ap-8348	26	26	hamiltonian	hamiltonian	NOUN
ap-8348	26	27	.	.	PUNCT
ap-8348	27	1	in	in	ADP
ap-8348	27	2	section	section	NOUN
ap-8348	27	3	4	4	NUM
ap-8348	27	4	,	,	PUNCT
ap-8348	27	5	we	we	PRON
ap-8348	27	6	use	use	VERB
ap-8348	27	7	the	the	DET
ap-8348	27	8	lewis	lewis	PROPN
ap-8348	27	9	-	-	PUNCT
ap-8348	27	10	riesenfeld	riesenfeld	NOUN
ap-8348	27	11	method	method	NOUN
ap-8348	27	12	to	to	PART
ap-8348	27	13	solve	solve	VERB
ap-8348	27	14	the	the	DET
ap-8348	27	15	td	td	NOUN
ap-8348	27	16	schrödinger	schrödinger	ADJ
ap-8348	27	17	equation	equation	NOUN
ap-8348	27	18	for	for	ADP
ap-8348	27	19	a	a	DET
ap-8348	27	20	particle	particle	NOUN
ap-8348	27	21	with	with	ADP
ap-8348	27	22	td	td	NOUN
ap-8348	27	23	mass	mass	NOUN
ap-8348	27	24	in	in	ADP
ap-8348	27	25	a	a	DET
ap-8348	27	26	td	td	NOUN
ap-8348	27	27	complex	complex	ADJ
ap-8348	27	28	symmetric	symmetric	ADJ
ap-8348	27	29	potential	potential	NOUN
ap-8348	27	30	well	well	ADV
ap-8348	27	31	.	.	PUNCT
ap-8348	28	1	finally	finally	ADV
ap-8348	28	2	,	,	PUNCT
ap-8348	28	3	in	in	ADP
ap-8348	28	4	section	section	NOUN
ap-8348	28	5	5	5	NUM
ap-8348	28	6	,	,	PUNCT
ap-8348	28	7	we	we	PRON
ap-8348	28	8	conclude	conclude	VERB
ap-8348	28	9	with	with	ADP
ap-8348	28	10	a	a	DET
ap-8348	28	11	brief	brief	ADJ
ap-8348	28	12	review	review	NOUN
ap-8348	28	13	of	of	ADP
ap-8348	28	14	the	the	DET
ap-8348	28	15	obtained	obtain	VERB
ap-8348	28	16	results	result	NOUN
ap-8348	28	17	.	.	PUNCT
ap-8348	29	1	132	132	NUM
ap-8348	29	2	https://doi.org/10.14311/ap.2023.63.0132	https://doi.org/10.14311/ap.2023.63.0132	NOUN
ap-8348	29	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-8348	29	4	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-8348	29	5	vol	vol	NOUN
ap-8348	29	6	.	.	PROPN
ap-8348	30	1	63	63	NUM
ap-8348	30	2	no	no	NOUN
ap-8348	30	3	.	.	PUNCT
ap-8348	31	1	2/2023	2/2023	NUM
ap-8348	31	2	exact	exact	ADJ
ap-8348	31	3	solutions	solution	NOUN
ap-8348	31	4	for	for	ADP
ap-8348	31	5	time	time	NOUN
ap-8348	31	6	-	-	PUNCT
ap-8348	31	7	dependent	dependent	ADJ
ap-8348	31	8	complex	complex	ADJ
ap-8348	31	9	symmetric	symmetric	ADJ
ap-8348	31	10	potential	potential	NOUN
ap-8348	31	11	well	well	NOUN
ap-8348	31	12	2	2	NUM
ap-8348	31	13	.	.	X
ap-8348	32	1	td	td	VERB
ap-8348	32	2	non	non	ADJ
ap-8348	32	3	-	-	ADJ
ap-8348	32	4	hermitian	hermitian	ADJ
ap-8348	32	5	hamiltonian	hamiltonian	NOUN
ap-8348	32	6	with	with	ADP
ap-8348	32	7	td	td	PROPN
ap-8348	32	8	metric	metric	NOUN
ap-8348	32	9	let	let	VERB
ap-8348	32	10	h(t	h(t	PRON
ap-8348	32	11	)	)	PUNCT
ap-8348	32	12	be	be	AUX
ap-8348	32	13	a	a	DET
ap-8348	32	14	non	non	ADJ
ap-8348	32	15	-	-	ADJ
ap-8348	32	16	hermitian	hermitian	ADJ
ap-8348	32	17	td	td	NOUN
ap-8348	32	18	hamiltonian	hamiltonian	NOUN
ap-8348	32	19	and	and	CCONJ
ap-8348	32	20	h(t	h(t	PROPN
ap-8348	32	21	)	)	PUNCT
ap-8348	32	22	its	its	PRON
ap-8348	32	23	associated	associated	ADJ
ap-8348	32	24	td	td	PROPN
ap-8348	32	25	hermitian	hermitian	ADJ
ap-8348	32	26	hamiltonian	hamiltonian	NOUN
ap-8348	32	27	.	.	PUNCT
ap-8348	33	1	the	the	DET
ap-8348	33	2	two	two	NUM
ap-8348	33	3	corresponding	correspond	VERB
ap-8348	33	4	td	td	NOUN
ap-8348	33	5	schrödinger	schrödinger	ADJ
ap-8348	33	6	equations	equation	NOUN
ap-8348	33	7	describing	describe	VERB
ap-8348	33	8	the	the	DET
ap-8348	33	9	quantum	quantum	ADJ
ap-8348	33	10	evolution	evolution	NOUN
ap-8348	33	11	are	be	AUX
ap-8348	33	12	:	:	PUNCT
ap-8348	33	13	h(t	h(t	X
ap-8348	33	14	)	)	PUNCT
ap-8348	33	15	∣∣φh(t	∣∣φh(t	NOUN
ap-8348	33	16	)	)	PUNCT
ap-8348	33	17	〉	〉	NOUN
ap-8348	33	18	=	=	VERB
ap-8348	33	19	iℏ∂t	iℏ∂t	ADJ
ap-8348	33	20	∣∣φh(t	∣∣φh(t	NOUN
ap-8348	33	21	)	)	PUNCT
ap-8348	33	22	〉	〉	NOUN
ap-8348	33	23	,	,	PUNCT
ap-8348	33	24	(	(	PUNCT
ap-8348	33	25	3	3	X
ap-8348	33	26	)	)	PUNCT
ap-8348	33	27	h(t	h(t	PROPN
ap-8348	33	28	)	)	PUNCT
ap-8348	33	29	∣∣ψh(t	∣∣ψh(t	NOUN
ap-8348	33	30	)	)	PUNCT
ap-8348	33	31	〉	〉	NOUN
ap-8348	33	32	=	=	VERB
ap-8348	33	33	iℏ∂t	iℏ∂t	ADJ
ap-8348	33	34	∣∣ψh(t	∣∣ψh(t	NOUN
ap-8348	33	35	)	)	PUNCT
ap-8348	33	36	〉	〉	NOUN
ap-8348	33	37	,	,	PUNCT
ap-8348	33	38	(	(	PUNCT
ap-8348	33	39	4	4	NUM
ap-8348	33	40	)	)	PUNCT
ap-8348	33	41	where	where	SCONJ
ap-8348	33	42	the	the	DET
ap-8348	33	43	two	two	NUM
ap-8348	33	44	hamiltonians	hamiltonian	NOUN
ap-8348	33	45	are	be	AUX
ap-8348	33	46	related	relate	VERB
ap-8348	33	47	by	by	ADP
ap-8348	33	48	the	the	DET
ap-8348	33	49	dyson	dyson	PROPN
ap-8348	33	50	maps	map	NOUN
ap-8348	33	51	ρ(t	ρ(t	PROPN
ap-8348	33	52	)	)	PUNCT
ap-8348	33	53	as	as	ADP
ap-8348	33	54	h(t	h(t	NUM
ap-8348	33	55	)	)	PUNCT
ap-8348	33	56	=	=	SYM
ap-8348	33	57	ρ−1(t)h(t	ρ−1(t)h(t	X
ap-8348	33	58	)	)	PUNCT
ap-8348	33	59	ρ(t	ρ(t	NUM
ap-8348	33	60	)	)	PUNCT
ap-8348	33	61	−	−	NOUN
ap-8348	33	62	iℏρ−1(t	iℏρ−1(t	PUNCT
ap-8348	33	63	)	)	PUNCT
ap-8348	34	1	ρ̇(t	ρ̇(t	ADP
ap-8348	34	2	)	)	PUNCT
ap-8348	34	3	,	,	PUNCT
ap-8348	34	4	(	(	PUNCT
ap-8348	34	5	5	5	NUM
ap-8348	34	6	)	)	PUNCT
ap-8348	34	7	and	and	CCONJ
ap-8348	34	8	their	their	PRON
ap-8348	34	9	wavefunctions	wavefunction	NOUN
ap-8348	34	10	∣∣φh(t	∣∣φh(t	NOUN
ap-8348	34	11	)	)	PUNCT
ap-8348	34	12	〉	〉	NOUN
ap-8348	34	13	and	and	CCONJ
ap-8348	34	14	∣∣ψh(t	∣∣ψh(t	NOUN
ap-8348	34	15	)	)	PUNCT
ap-8348	34	16	〉	〉	NOUN
ap-8348	34	17	as∣∣ψh(t	as∣∣ψh(t	NOUN
ap-8348	34	18	)	)	PUNCT
ap-8348	34	19	〉	〉	NOUN
ap-8348	34	20	=	=	SYM
ap-8348	34	21	ρ(t	ρ(t	NUM
ap-8348	34	22	)	)	PUNCT
ap-8348	34	23	∣∣φh(t	∣∣φh(t	NOUN
ap-8348	34	24	)	)	PUNCT
ap-8348	34	25	〉	〉	NOUN
ap-8348	34	26	.	.	PUNCT
ap-8348	35	1	(	(	PUNCT
ap-8348	35	2	6	6	X
ap-8348	35	3	)	)	PUNCT
ap-8348	35	4	the	the	DET
ap-8348	35	5	hermiticity	hermiticity	NOUN
ap-8348	35	6	of	of	ADP
ap-8348	35	7	h(t	h(t	PROPN
ap-8348	35	8	)	)	PUNCT
ap-8348	35	9	allowed	allow	VERB
ap-8348	35	10	us	we	PRON
ap-8348	35	11	to	to	PART
ap-8348	35	12	establish	establish	VERB
ap-8348	35	13	the	the	DET
ap-8348	35	14	connection	connection	NOUN
ap-8348	35	15	between	between	ADP
ap-8348	35	16	the	the	DET
ap-8348	35	17	hamiltonian	hamiltonian	ADJ
ap-8348	35	18	h(t	h(t	PROPN
ap-8348	35	19	)	)	PUNCT
ap-8348	35	20	and	and	CCONJ
ap-8348	35	21	its	its	PRON
ap-8348	35	22	hermitian	hermitian	ADJ
ap-8348	35	23	conjugate	conjugate	NOUN
ap-8348	35	24	h†(t	h†(t	NOUN
ap-8348	35	25	)	)	PUNCT
ap-8348	35	26	as	as	ADP
ap-8348	35	27	h†(t	h†(t	X
ap-8348	35	28	)	)	PUNCT
ap-8348	35	29	=	=	SYM
ap-8348	35	30	η(t)h(t	η(t)h(t	NOUN
ap-8348	35	31	)	)	PUNCT
ap-8348	35	32	η−1(t	η−1(t	PROPN
ap-8348	35	33	)	)	PUNCT
ap-8348	35	34	+	+	CCONJ
ap-8348	35	35	iℏη̇(t	iℏη̇(t	PROPN
ap-8348	35	36	)	)	PUNCT
ap-8348	35	37	η−1(t	η−1(t	PROPN
ap-8348	35	38	)	)	PUNCT
ap-8348	35	39	,	,	PUNCT
ap-8348	35	40	(	(	PUNCT
ap-8348	35	41	7	7	X
ap-8348	35	42	)	)	PUNCT
ap-8348	35	43	which	which	PRON
ap-8348	35	44	is	be	AUX
ap-8348	35	45	a	a	DET
ap-8348	35	46	generalisation	generalisation	NOUN
ap-8348	35	47	of	of	ADP
ap-8348	35	48	the	the	DET
ap-8348	35	49	well	well	ADV
ap-8348	35	50	-	-	PUNCT
ap-8348	35	51	known	know	VERB
ap-8348	35	52	conventional	conventional	ADJ
ap-8348	35	53	quasi	quasi	ADJ
ap-8348	35	54	-	-	ADJ
ap-8348	35	55	hermiticity	hermiticity	ADJ
ap-8348	35	56	equation	equation	NOUN
ap-8348	35	57	(	(	PUNCT
ap-8348	35	58	1	1	NUM
ap-8348	35	59	)	)	PUNCT
ap-8348	35	60	,	,	PUNCT
ap-8348	35	61	and	and	CCONJ
ap-8348	35	62	the	the	DET
ap-8348	35	63	td	td	NOUN
ap-8348	35	64	metric	metric	ADJ
ap-8348	35	65	operator	operator	NOUN
ap-8348	35	66	is	be	AUX
ap-8348	35	67	hermitian	hermitian	ADJ
ap-8348	35	68	and	and	CCONJ
ap-8348	35	69	defined	define	VERB
ap-8348	35	70	as	as	ADP
ap-8348	35	71	η(t	η(t	NOUN
ap-8348	35	72	)	)	PUNCT
ap-8348	35	73	=	=	SYM
ap-8348	35	74	ρ†(t	ρ†(t	NOUN
ap-8348	35	75	)	)	PUNCT
ap-8348	35	76	ρ(t	ρ(t	NUM
ap-8348	35	77	)	)	PUNCT
ap-8348	35	78	.	.	PUNCT
ap-8348	36	1	3	3	X
ap-8348	36	2	.	.	X
ap-8348	36	3	pseudo	pseudo	NOUN
ap-8348	36	4	-	-	ADJ
ap-8348	36	5	invariant	invariant	ADJ
ap-8348	36	6	operator	operator	NOUN
ap-8348	36	7	method	method	NOUN
ap-8348	36	8	let	let	VERB
ap-8348	36	9	us	we	PRON
ap-8348	36	10	start	start	VERB
ap-8348	36	11	with	with	ADP
ap-8348	36	12	the	the	DET
ap-8348	36	13	description	description	NOUN
ap-8348	36	14	of	of	ADP
ap-8348	36	15	the	the	DET
ap-8348	36	16	lewisriesenfeld	lewisriesenfeld	NOUN
ap-8348	36	17	theory	theory	NOUN
ap-8348	36	18	[	[	X
ap-8348	36	19	46	46	NUM
ap-8348	36	20	]	]	PUNCT
ap-8348	36	21	for	for	ADP
ap-8348	36	22	a	a	DET
ap-8348	36	23	td	td	NOUN
ap-8348	36	24	hermitian	hermitian	ADJ
ap-8348	36	25	hamiltonian	hamiltonian	NOUN
ap-8348	36	26	h(t	h(t	PROPN
ap-8348	36	27	)	)	PUNCT
ap-8348	36	28	with	with	ADP
ap-8348	36	29	a	a	DET
ap-8348	36	30	hermitian	hermitian	ADJ
ap-8348	36	31	td	td	NOUN
ap-8348	36	32	invariant	invariant	ADJ
ap-8348	36	33	ih(t	ih(t	PRON
ap-8348	36	34	)	)	PUNCT
ap-8348	36	35	.	.	PUNCT
ap-8348	37	1	the	the	DET
ap-8348	37	2	dynamic	dynamic	ADJ
ap-8348	37	3	invariant	invariant	NOUN
ap-8348	37	4	ih(t	ih(t	PRON
ap-8348	37	5	)	)	PUNCT
ap-8348	37	6	satisfies	satisfie	NOUN
ap-8348	37	7	:	:	PUNCT
ap-8348	37	8	dih(t	dih(t	NUM
ap-8348	37	9	)	)	PUNCT
ap-8348	37	10	dt	dt	PART
ap-8348	38	1	=	=	SYM
ap-8348	38	2	∂ih(t	∂ih(t	PROPN
ap-8348	38	3	)	)	PUNCT
ap-8348	39	1	∂t	∂t	PROPN
ap-8348	39	2	−	−	PROPN
ap-8348	40	1	i	i	PRON
ap-8348	40	2	ℏ	ℏ	X
ap-8348	40	3	[	[	PUNCT
ap-8348	40	4	ih(t	ih(t	X
ap-8348	40	5	)	)	PUNCT
ap-8348	40	6	,	,	PUNCT
ap-8348	40	7	h(t	h(t	PROPN
ap-8348	40	8	)	)	PUNCT
ap-8348	40	9	]	]	PUNCT
ap-8348	41	1	=	=	PUNCT
ap-8348	41	2	0	0	X
ap-8348	41	3	.	.	PUNCT
ap-8348	42	1	(	(	PUNCT
ap-8348	42	2	8)	8)	NUM
ap-8348	42	3	the	the	DET
ap-8348	42	4	eigenvalue	eigenvalue	NOUN
ap-8348	42	5	equation	equation	NOUN
ap-8348	42	6	for	for	ADP
ap-8348	42	7	ih(t	ih(t	PRON
ap-8348	42	8	)	)	PUNCT
ap-8348	42	9	is	be	AUX
ap-8348	42	10	:	:	PUNCT
ap-8348	42	11	ih(t	ih(t	X
ap-8348	42	12	)	)	PUNCT
ap-8348	42	13	∣∣ψh	∣∣ψh	VERB
ap-8348	42	14	n(t	n(t	NOUN
ap-8348	42	15	)	)	PUNCT
ap-8348	42	16	〉	〉	NOUN
ap-8348	42	17	=	=	PRON
ap-8348	42	18	λn	λn	AUX
ap-8348	42	19	∣∣ψh	∣∣ψh	VERB
ap-8348	42	20	n(t	n(t	PROPN
ap-8348	42	21	)	)	PUNCT
ap-8348	42	22	〉	〉	NOUN
ap-8348	42	23	,	,	PUNCT
ap-8348	42	24	(	(	PUNCT
ap-8348	42	25	9	9	NUM
ap-8348	42	26	)	)	PUNCT
ap-8348	42	27	where	where	SCONJ
ap-8348	42	28	the	the	DET
ap-8348	42	29	eigenvalues	eigenvalue	NOUN
ap-8348	42	30	λn	λn	PROPN
ap-8348	42	31	of	of	ADP
ap-8348	42	32	ih(t	ih(t	PUNCT
ap-8348	42	33	)	)	PUNCT
ap-8348	42	34	are	be	AUX
ap-8348	42	35	reals	real	NOUN
ap-8348	42	36	and	and	CCONJ
ap-8348	42	37	timeindependent	timeindependent	NOUN
ap-8348	42	38	,	,	PUNCT
ap-8348	42	39	and	and	CCONJ
ap-8348	42	40	the	the	DET
ap-8348	42	41	lewis	lewis	PROPN
ap-8348	42	42	-	-	PUNCT
ap-8348	42	43	riesenfeld	riesenfeld	NOUN
ap-8348	42	44	phase	phase	NOUN
ap-8348	42	45	is	be	AUX
ap-8348	42	46	defined	define	VERB
ap-8348	42	47	as	as	ADP
ap-8348	42	48	:	:	PUNCT
ap-8348	42	49	ℏ	ℏ	PROPN
ap-8348	42	50	d	d	NOUN
ap-8348	42	51	dt	dt	NOUN
ap-8348	42	52	εn(t	εn(t	NUM
ap-8348	42	53	)	)	PUNCT
ap-8348	43	1	=	=	PUNCT
ap-8348	43	2	〈	〈	PROPN
ap-8348	43	3	ψh	ψh	ADP
ap-8348	43	4	n(t	n(t	PROPN
ap-8348	43	5	)	)	PUNCT
ap-8348	43	6	∣∣	∣∣	X
ap-8348	43	7	iℏ	iℏ	ADP
ap-8348	43	8	∂	∂	NOUN
ap-8348	43	9	∂t	∂t	PROPN
ap-8348	43	10	−	−	PROPN
ap-8348	43	11	h(t	h(t	PROPN
ap-8348	43	12	)	)	PUNCT
ap-8348	43	13	∣∣ψh	∣∣ψh	VERB
ap-8348	43	14	n(t	n(t	NOUN
ap-8348	43	15	)	)	PUNCT
ap-8348	43	16	〉	〉	NOUN
ap-8348	43	17	,	,	PUNCT
ap-8348	43	18	(	(	PUNCT
ap-8348	43	19	10	10	NUM
ap-8348	43	20	)	)	PUNCT
ap-8348	43	21	and	and	CCONJ
ap-8348	43	22	the	the	DET
ap-8348	43	23	solution	solution	NOUN
ap-8348	43	24	of	of	ADP
ap-8348	43	25	the	the	DET
ap-8348	43	26	tdse	tdse	NOUN
ap-8348	43	27	of	of	ADP
ap-8348	43	28	h(t	h(t	PROPN
ap-8348	43	29	)	)	PUNCT
ap-8348	43	30	is	be	AUX
ap-8348	43	31	given	give	VERB
ap-8348	43	32	as∣∣ψh(t	as∣∣ψh(t	NOUN
ap-8348	43	33	)	)	PUNCT
ap-8348	43	34	〉	〉	NOUN
ap-8348	43	35	=	=	SYM
ap-8348	43	36	exp	exp	NOUN
ap-8348	43	37	[	[	X
ap-8348	43	38	iεn(t	iεn(t	PROPN
ap-8348	43	39	)	)	PUNCT
ap-8348	43	40	]	]	PUNCT
ap-8348	43	41	∣∣ψh	∣∣ψh	PROPN
ap-8348	43	42	n(t	n(t	NOUN
ap-8348	43	43	)	)	PUNCT
ap-8348	43	44	〉	〉	NOUN
ap-8348	43	45	.	.	PUNCT
ap-8348	44	1	(	(	PUNCT
ap-8348	44	2	11	11	NUM
ap-8348	44	3	)	)	PUNCT
ap-8348	44	4	in	in	ADP
ap-8348	44	5	the	the	DET
ap-8348	44	6	paper	paper	NOUN
ap-8348	44	7	[	[	X
ap-8348	44	8	17	17	NUM
ap-8348	44	9	]	]	PUNCT
ap-8348	44	10	,	,	PUNCT
ap-8348	44	11	we	we	PRON
ap-8348	44	12	showed	show	VERB
ap-8348	44	13	that	that	SCONJ
ap-8348	44	14	any	any	DET
ap-8348	44	15	td	td	NOUN
ap-8348	44	16	hamiltonian	hamiltonian	NOUN
ap-8348	44	17	h(t	h(t	PROPN
ap-8348	44	18	)	)	PUNCT
ap-8348	44	19	satisfying	satisfy	VERB
ap-8348	44	20	the	the	DET
ap-8348	44	21	td	td	NOUN
ap-8348	44	22	quasi	quasi	ADJ
ap-8348	44	23	-	-	ADJ
ap-8348	44	24	hermiticity	hermiticity	ADJ
ap-8348	44	25	equation	equation	NOUN
ap-8348	44	26	(	(	PUNCT
ap-8348	44	27	7	7	X
ap-8348	44	28	)	)	PUNCT
ap-8348	44	29	admits	admit	VERB
ap-8348	44	30	a	a	DET
ap-8348	44	31	pseudo	pseudo	NOUN
ap-8348	44	32	-	-	ADJ
ap-8348	44	33	hermitician	hermitician	ADJ
ap-8348	44	34	invariant	invariant	PROPN
ap-8348	44	35	iph(t	iph(t	PROPN
ap-8348	44	36	)	)	PUNCT
ap-8348	44	37	such	such	ADJ
ap-8348	44	38	that	that	SCONJ
ap-8348	44	39	:	:	PUNCT
ap-8348	44	40	iph†(t	iph†(t	NOUN
ap-8348	44	41	)	)	PUNCT
ap-8348	44	42	=	=	SYM
ap-8348	44	43	η(t)iph(t)η−1(t	η(t)iph(t)η−1(t	X
ap-8348	44	44	)	)	PUNCT
ap-8348	44	45	⇔	⇔	NOUN
ap-8348	44	46	ih(t	ih(t	X
ap-8348	44	47	)	)	PUNCT
ap-8348	44	48	=	=	PUNCT
ap-8348	44	49	ρ(t)iph(t)ρ−1(t	ρ(t)iph(t)ρ−1(t	X
ap-8348	44	50	)	)	PUNCT
ap-8348	44	51	=	=	SYM
ap-8348	44	52	ih†(t	ih†(t	NOUN
ap-8348	44	53	)	)	PUNCT
ap-8348	44	54	.	.	PUNCT
ap-8348	45	1	(	(	PUNCT
ap-8348	45	2	12	12	NUM
ap-8348	45	3	)	)	PUNCT
ap-8348	45	4	since	since	SCONJ
ap-8348	45	5	the	the	DET
ap-8348	45	6	hermitian	hermitian	ADJ
ap-8348	45	7	invariant	invariant	NOUN
ap-8348	45	8	ih(t	ih(t	PUNCT
ap-8348	45	9	)	)	PUNCT
ap-8348	45	10	satisfies	satisfy	VERB
ap-8348	45	11	the	the	DET
ap-8348	45	12	eigenvalues	eigenvalue	NOUN
ap-8348	45	13	equation	equation	NOUN
ap-8348	45	14	(	(	PUNCT
ap-8348	45	15	9	9	NUM
ap-8348	45	16	)	)	PUNCT
ap-8348	45	17	,	,	PUNCT
ap-8348	45	18	equation	equation	NOUN
ap-8348	45	19	(	(	PUNCT
ap-8348	45	20	12	12	NUM
ap-8348	45	21	)	)	PUNCT
ap-8348	45	22	ensures	ensure	VERB
ap-8348	45	23	that	that	SCONJ
ap-8348	45	24	the	the	DET
ap-8348	45	25	pseudo	pseudo	NOUN
ap-8348	45	26	-	-	ADJ
ap-8348	45	27	hermitian	hermitian	ADJ
ap-8348	45	28	invariant	invariant	PROPN
ap-8348	45	29	’s	’s	PART
ap-8348	45	30	spectrum	spectrum	NOUN
ap-8348	45	31	is	be	AUX
ap-8348	45	32	real	real	ADJ
ap-8348	45	33	with	with	ADP
ap-8348	45	34	the	the	DET
ap-8348	45	35	same	same	ADJ
ap-8348	45	36	eigenvalues	eigenvalue	NOUN
ap-8348	45	37	λn	λn	NOUN
ap-8348	45	38	of	of	ADP
ap-8348	45	39	ih(t	ih(t	PRON
ap-8348	45	40	):	):	PUNCT
ap-8348	45	41	ih(t	ih(t	X
ap-8348	45	42	)	)	PUNCT
ap-8348	45	43	∣∣ψh	∣∣ψh	VERB
ap-8348	45	44	n(t	n(t	NOUN
ap-8348	45	45	)	)	PUNCT
ap-8348	45	46	〉	〉	NOUN
ap-8348	45	47	=	=	PRON
ap-8348	45	48	λn	λn	AUX
ap-8348	45	49	∣∣ψh	∣∣ψh	VERB
ap-8348	45	50	n(t	n(t	PROPN
ap-8348	45	51	)	)	PUNCT
ap-8348	45	52	〉	〉	NOUN
ap-8348	45	53	,	,	PUNCT
ap-8348	45	54	(	(	PUNCT
ap-8348	45	55	13	13	NUM
ap-8348	45	56	)	)	PUNCT
ap-8348	45	57	iph(t	iph(t	PROPN
ap-8348	45	58	)	)	PUNCT
ap-8348	45	59	∣∣ϕph	∣∣ϕph	NOUN
ap-8348	45	60	n	n	CCONJ
ap-8348	45	61	(	(	PUNCT
ap-8348	45	62	t)n(t	t)n(t	NOUN
ap-8348	45	63	)	)	PUNCT
ap-8348	45	64	〉	〉	NOUN
ap-8348	45	65	=	=	PUNCT
ap-8348	45	66	λn	λn	PROPN
ap-8348	45	67	∣∣ϕph	∣∣ϕph	PROPN
ap-8348	45	68	n	n	CCONJ
ap-8348	45	69	(	(	PUNCT
ap-8348	45	70	t	t	NOUN
ap-8348	45	71	)	)	PUNCT
ap-8348	45	72	〉	〉	NOUN
ap-8348	45	73	,	,	PUNCT
ap-8348	45	74	(	(	PUNCT
ap-8348	45	75	14	14	NUM
ap-8348	45	76	)	)	PUNCT
ap-8348	45	77	where	where	SCONJ
ap-8348	45	78	the	the	DET
ap-8348	45	79	eigenfunctions	eigenfunction	NOUN
ap-8348	45	80	∣∣ψh	∣∣ψh	VERB
ap-8348	45	81	n(t	n(t	NOUN
ap-8348	45	82	)	)	PUNCT
ap-8348	45	83	〉	〉	NOUN
ap-8348	45	84	and	and	CCONJ
ap-8348	45	85	∣∣ϕph	∣∣ϕph	NOUN
ap-8348	45	86	n	n	CCONJ
ap-8348	45	87	(	(	PUNCT
ap-8348	45	88	t	t	NOUN
ap-8348	45	89	)	)	PUNCT
ap-8348	45	90	〉	〉	NOUN
ap-8348	45	91	,	,	PUNCT
ap-8348	45	92	of	of	ADP
ap-8348	45	93	ih(t	ih(t	PRON
ap-8348	45	94	)	)	PUNCT
ap-8348	45	95	and	and	CCONJ
ap-8348	45	96	iph(t	iph(t	PROPN
ap-8348	45	97	)	)	PUNCT
ap-8348	45	98	,	,	PUNCT
ap-8348	45	99	respectively	respectively	ADV
ap-8348	45	100	,	,	PUNCT
ap-8348	45	101	are	be	AUX
ap-8348	45	102	related	relate	VERB
ap-8348	45	103	as∣∣ψh	as∣∣ψh	NOUN
ap-8348	45	104	n(t	n(t	NOUN
ap-8348	45	105	)	)	PUNCT
ap-8348	45	106	〉	〉	NOUN
ap-8348	45	107	=	=	SYM
ap-8348	45	108	ρ(t	ρ(t	NUM
ap-8348	45	109	)	)	PUNCT
ap-8348	46	1	∣∣ϕph	∣∣ϕph	PROPN
ap-8348	46	2	n	n	CCONJ
ap-8348	46	3	(	(	PUNCT
ap-8348	46	4	t	t	NOUN
ap-8348	46	5	)	)	PUNCT
ap-8348	46	6	〉	〉	NOUN
ap-8348	46	7	.	.	PUNCT
ap-8348	47	1	(	(	PUNCT
ap-8348	47	2	15	15	NUM
ap-8348	47	3	)	)	PUNCT
ap-8348	47	4	the	the	DET
ap-8348	47	5	inner	inner	ADJ
ap-8348	47	6	products	product	NOUN
ap-8348	47	7	of	of	ADP
ap-8348	47	8	the	the	DET
ap-8348	47	9	eigenfunctions	eigenfunction	NOUN
ap-8348	47	10	associated	associate	VERB
ap-8348	47	11	with	with	ADP
ap-8348	47	12	the	the	DET
ap-8348	47	13	non	non	ADJ
ap-8348	47	14	-	-	ADJ
ap-8348	47	15	hermitian	hermitian	ADJ
ap-8348	47	16	invariant	invariant	PROPN
ap-8348	47	17	iph(t	iph(t	PROPN
ap-8348	47	18	)	)	PUNCT
ap-8348	47	19	can	can	AUX
ap-8348	47	20	now	now	ADV
ap-8348	47	21	be	be	AUX
ap-8348	47	22	written	write	VERB
ap-8348	47	23	as	as	ADP
ap-8348	47	24	⟨ϕph	⟨ϕph	PROPN
ap-8348	47	25	m	m	PROPN
ap-8348	47	26	(	(	PUNCT
ap-8348	47	27	t	t	PROPN
ap-8348	47	28	)	)	PUNCT
ap-8348	47	29	∣∣ϕph	∣∣ϕph	PROPN
ap-8348	47	30	n	n	CCONJ
ap-8348	47	31	(	(	PUNCT
ap-8348	47	32	t	t	NOUN
ap-8348	47	33	)	)	PUNCT
ap-8348	47	34	〉	〉	NOUN
ap-8348	48	1	η	η	PROPN
ap-8348	48	2	=	=	PROPN
ap-8348	48	3	⟨ϕph	⟨ϕph	PROPN
ap-8348	48	4	m	m	PROPN
ap-8348	48	5	(	(	PUNCT
ap-8348	48	6	t)|η	t)|η	ADV
ap-8348	48	7	∣∣ϕph	∣∣ϕph	NOUN
ap-8348	48	8	n	n	CCONJ
ap-8348	48	9	(	(	PUNCT
ap-8348	48	10	t	t	NOUN
ap-8348	48	11	)	)	PUNCT
ap-8348	48	12	〉	〉	NOUN
ap-8348	48	13	=	=	PUNCT
ap-8348	48	14	δmn	δmn	NOUN
ap-8348	48	15	,	,	PUNCT
ap-8348	48	16	(	(	PUNCT
ap-8348	48	17	16	16	NUM
ap-8348	48	18	)	)	PUNCT
ap-8348	48	19	and	and	CCONJ
ap-8348	48	20	it	it	PRON
ap-8348	48	21	corresponds	correspond	VERB
ap-8348	48	22	to	to	ADP
ap-8348	48	23	the	the	DET
ap-8348	48	24	conventional	conventional	ADJ
ap-8348	48	25	inner	inner	ADJ
ap-8348	48	26	product	product	NOUN
ap-8348	48	27	associated	associate	VERB
ap-8348	48	28	to	to	ADP
ap-8348	48	29	the	the	DET
ap-8348	48	30	hermitian	hermitian	ADJ
ap-8348	48	31	invariant	invariant	NOUN
ap-8348	48	32	ih(t	ih(t	PUNCT
ap-8348	48	33	)	)	PUNCT
ap-8348	48	34	.	.	PUNCT
ap-8348	49	1	it	it	PRON
ap-8348	49	2	is	be	AUX
ap-8348	49	3	easy	easy	ADJ
ap-8348	49	4	to	to	PART
ap-8348	49	5	verify	verify	VERB
ap-8348	49	6	,	,	PUNCT
ap-8348	49	7	by	by	ADP
ap-8348	49	8	a	a	DET
ap-8348	49	9	direct	direct	ADJ
ap-8348	49	10	substitution	substitution	NOUN
ap-8348	49	11	of	of	ADP
ap-8348	49	12	the	the	DET
ap-8348	49	13	hermitian	hermitian	ADJ
ap-8348	49	14	hamiltonian	hamiltonian	NOUN
ap-8348	49	15	h(t	h(t	PROPN
ap-8348	49	16	)	)	PUNCT
ap-8348	49	17	and	and	CCONJ
ap-8348	49	18	the	the	DET
ap-8348	49	19	hermitian	hermitian	ADJ
ap-8348	49	20	invariant	invariant	NOUN
ap-8348	49	21	ih(t	ih(t	PRON
ap-8348	49	22	)	)	PUNCT
ap-8348	49	23	by	by	ADP
ap-8348	49	24	their	their	PRON
ap-8348	49	25	equivalents	equivalent	NOUN
ap-8348	49	26	in	in	ADP
ap-8348	49	27	the	the	DET
ap-8348	49	28	expressions	expression	NOUN
ap-8348	49	29	(	(	PUNCT
ap-8348	49	30	5	5	NUM
ap-8348	49	31	)	)	PUNCT
ap-8348	49	32	and	and	CCONJ
ap-8348	49	33	(	(	PUNCT
ap-8348	49	34	12	12	NUM
ap-8348	49	35	)	)	PUNCT
ap-8348	49	36	,	,	PUNCT
ap-8348	49	37	respectively	respectively	ADV
ap-8348	49	38	,	,	PUNCT
ap-8348	49	39	that	that	SCONJ
ap-8348	49	40	the	the	DET
ap-8348	49	41	pseudo	pseudo	NOUN
ap-8348	49	42	hermitian	hermitian	NOUN
ap-8348	49	43	invariant	invariant	PROPN
ap-8348	49	44	iph(t	iph(t	PROPN
ap-8348	49	45	)	)	PUNCT
ap-8348	49	46	satisfies	satisfie	NOUN
ap-8348	49	47	:	:	PUNCT
ap-8348	49	48	∂iph(t	∂iph(t	ADJ
ap-8348	49	49	)	)	PUNCT
ap-8348	50	1	∂t	∂t	PROPN
ap-8348	51	1	=	=	PUNCT
ap-8348	51	2	i	i	PRON
ap-8348	51	3	ℏ	ℏ	PROPN
ap-8348	51	4	[	[	PUNCT
ap-8348	51	5	iph(t	iph(t	PROPN
ap-8348	51	6	)	)	PUNCT
ap-8348	51	7	,	,	PUNCT
ap-8348	51	8	h(t	h(t	PROPN
ap-8348	51	9	)	)	PUNCT
ap-8348	51	10	]	]	PUNCT
ap-8348	51	11	.	.	PUNCT
ap-8348	52	1	(	(	PUNCT
ap-8348	52	2	17	17	NUM
ap-8348	52	3	)	)	PUNCT
ap-8348	52	4	we	we	PRON
ap-8348	52	5	should	should	AUX
ap-8348	52	6	remark	remark	VERB
ap-8348	52	7	that	that	SCONJ
ap-8348	52	8	the	the	DET
ap-8348	52	9	invariant	invariant	ADJ
ap-8348	52	10	operator	operator	NOUN
ap-8348	52	11	’s	’s	PART
ap-8348	52	12	eigenstates	eigenstate	NOUN
ap-8348	52	13	and	and	CCONJ
ap-8348	52	14	eigenvalues	eigenvalue	NOUN
ap-8348	52	15	can	can	AUX
ap-8348	52	16	be	be	AUX
ap-8348	52	17	computed	compute	VERB
ap-8348	52	18	using	use	VERB
ap-8348	52	19	the	the	DET
ap-8348	52	20	same	same	ADJ
ap-8348	52	21	procedure	procedure	NOUN
ap-8348	52	22	as	as	ADP
ap-8348	52	23	the	the	DET
ap-8348	52	24	hermitian	hermitian	ADJ
ap-8348	52	25	case	case	NOUN
ap-8348	52	26	.	.	PUNCT
ap-8348	53	1	the	the	DET
ap-8348	53	2	solution	solution	NOUN
ap-8348	53	3	∣∣φh(t	∣∣φh(t	NOUN
ap-8348	53	4	)	)	PUNCT
ap-8348	53	5	〉	〉	NOUN
ap-8348	53	6	of	of	ADP
ap-8348	53	7	the	the	DET
ap-8348	53	8	schrödinger	schrödinger	ADJ
ap-8348	53	9	equation	equation	NOUN
ap-8348	53	10	(	(	PUNCT
ap-8348	53	11	3	3	X
ap-8348	53	12	)	)	PUNCT
ap-8348	53	13	is	be	AUX
ap-8348	53	14	different	different	ADJ
ap-8348	53	15	from	from	ADP
ap-8348	53	16	∣∣ϕph	∣∣ϕph	PROPN
ap-8348	53	17	n	n	CCONJ
ap-8348	53	18	(	(	PUNCT
ap-8348	53	19	t	t	NOUN
ap-8348	53	20	)	)	PUNCT
ap-8348	53	21	〉	〉	NOUN
ap-8348	53	22	in	in	ADP
ap-8348	53	23	equation	equation	NOUN
ap-8348	53	24	(	(	PUNCT
ap-8348	53	25	14	14	NUM
ap-8348	53	26	)	)	PUNCT
ap-8348	53	27	only	only	ADV
ap-8348	53	28	by	by	ADP
ap-8348	53	29	the	the	DET
ap-8348	53	30	factor	factor	NOUN
ap-8348	53	31	eiεph	eiεph	NOUN
ap-8348	53	32	n	n	PROPN
ap-8348	53	33	(	(	PUNCT
ap-8348	53	34	t	t	PROPN
ap-8348	53	35	)	)	PUNCT
ap-8348	53	36	where	where	SCONJ
ap-8348	53	37	εph	εph	VERB
ap-8348	53	38	n	n	PROPN
ap-8348	53	39	(	(	PUNCT
ap-8348	53	40	t	t	PROPN
ap-8348	53	41	)	)	PUNCT
ap-8348	53	42	is	be	AUX
ap-8348	53	43	a	a	DET
ap-8348	53	44	real	real	ADJ
ap-8348	53	45	phase	phase	NOUN
ap-8348	53	46	given	give	VERB
ap-8348	53	47	by	by	ADP
ap-8348	53	48	:	:	PUNCT
ap-8348	53	49	ℏ	ℏ	PROPN
ap-8348	53	50	d	d	X
ap-8348	53	51	dt	dt	X
ap-8348	53	52	εph	εph	PROPN
ap-8348	53	53	n	n	PROPN
ap-8348	53	54	(	(	PUNCT
ap-8348	53	55	t	t	PROPN
ap-8348	53	56	)	)	PUNCT
ap-8348	54	1	=	=	PUNCT
ap-8348	55	1	〈	〈	PROPN
ap-8348	55	2	ϕph	ϕph	NOUN
ap-8348	55	3	n	n	CCONJ
ap-8348	55	4	(	(	PUNCT
ap-8348	55	5	t	t	PROPN
ap-8348	55	6	)	)	PUNCT
ap-8348	55	7	∣∣	∣∣	NUM
ap-8348	55	8	η(t	η(t	NOUN
ap-8348	55	9	)	)	PUNCT
ap-8348	55	10	[	[	PUNCT
ap-8348	55	11	iℏ	iℏ	NOUN
ap-8348	55	12	∂	∂	NOUN
ap-8348	55	13	∂t	∂t	PROPN
ap-8348	55	14	−	−	PROPN
ap-8348	55	15	h(t	h(t	PROPN
ap-8348	55	16	)	)	PUNCT
ap-8348	55	17	]	]	PUNCT
ap-8348	56	1	∣∣ϕph	∣∣ϕph	INTJ
ap-8348	56	2	n	n	CCONJ
ap-8348	56	3	(	(	PUNCT
ap-8348	56	4	t	t	NOUN
ap-8348	56	5	)	)	PUNCT
ap-8348	56	6	〉	〉	NOUN
ap-8348	56	7	.	.	PUNCT
ap-8348	57	1	(	(	PUNCT
ap-8348	57	2	18	18	NUM
ap-8348	57	3	)	)	SYM
ap-8348	57	4	4	4	NUM
ap-8348	57	5	.	.	X
ap-8348	57	6	particle	particle	NOUN
ap-8348	57	7	in	in	ADP
ap-8348	57	8	td	td	NOUN
ap-8348	57	9	complex	complex	ADJ
ap-8348	57	10	symmetric	symmetric	ADJ
ap-8348	57	11	potential	potential	NOUN
ap-8348	57	12	well	well	INTJ
ap-8348	57	13	let	let	VERB
ap-8348	57	14	us	we	PRON
ap-8348	57	15	consider	consider	VERB
ap-8348	57	16	a	a	DET
ap-8348	57	17	particle	particle	NOUN
ap-8348	57	18	with	with	ADP
ap-8348	57	19	a	a	DET
ap-8348	57	20	td	td	NOUN
ap-8348	57	21	mass	mass	NOUN
ap-8348	57	22	m(t	m(t	NOUN
ap-8348	57	23	)	)	PUNCT
ap-8348	57	24	in	in	ADP
ap-8348	57	25	the	the	DET
ap-8348	57	26	presence	presence	NOUN
ap-8348	57	27	of	of	ADP
ap-8348	57	28	a	a	DET
ap-8348	57	29	pure	pure	ADJ
ap-8348	57	30	imaginary	imaginary	ADJ
ap-8348	57	31	td	td	NOUN
ap-8348	57	32	symmetric	symmetric	ADJ
ap-8348	57	33	potential	potential	ADJ
ap-8348	57	34	well	well	NOUN
ap-8348	57	35	equation	equation	NOUN
ap-8348	57	36	(	(	PUNCT
ap-8348	57	37	2	2	NUM
ap-8348	57	38	)	)	PUNCT
ap-8348	57	39	,	,	PUNCT
ap-8348	57	40	where	where	SCONJ
ap-8348	57	41	its	its	PRON
ap-8348	57	42	hamiltonian	hamiltonian	NOUN
ap-8348	57	43	can	can	AUX
ap-8348	57	44	be	be	AUX
ap-8348	57	45	written	write	VERB
ap-8348	57	46	as	as	ADP
ap-8348	57	47	:	:	PUNCT
ap-8348	57	48	h(t	h(t	X
ap-8348	57	49	)	)	PUNCT
ap-8348	58	1	=	=	PRON
ap-8348	58	2	{	{	PUNCT
ap-8348	58	3	p2	p2	PROPN
ap-8348	58	4	2m(t	2m(t	NUM
ap-8348	58	5	)	)	PUNCT
ap-8348	59	1	+	+	CCONJ
ap-8348	59	2	if(t)x	if(t)x	NUM
ap-8348	59	3	if	if	SCONJ
ap-8348	59	4	x	x	PRON
ap-8348	59	5	≥	≥	X
ap-8348	59	6	0	0	NUM
ap-8348	59	7	p2	p2	PROPN
ap-8348	59	8	2m(t	2m(t	NUM
ap-8348	59	9	)	)	PUNCT
ap-8348	59	10	−	−	PROPN
ap-8348	60	1	if(t)x	if(t)x	PROPN
ap-8348	60	2	if	if	SCONJ
ap-8348	60	3	x	x	SYM
ap-8348	60	4	≤	≤	NUM
ap-8348	60	5	0	0	NUM
ap-8348	60	6	,	,	PUNCT
ap-8348	60	7	(	(	PUNCT
ap-8348	60	8	19	19	NUM
ap-8348	60	9	)	)	PUNCT
ap-8348	60	10	the	the	DET
ap-8348	60	11	associated	associated	ADJ
ap-8348	60	12	tdse	tdse	NOUN
ap-8348	60	13	of	of	ADP
ap-8348	60	14	the	the	DET
ap-8348	60	15	system	system	NOUN
ap-8348	60	16	is	be	AUX
ap-8348	60	17	:	:	PUNCT
ap-8348	60	18	133	133	NUM
ap-8348	60	19	boubakeur	boubakeur	NOUN
ap-8348	60	20	khantoul	khantoul	PROPN
ap-8348	60	21	,	,	PUNCT
ap-8348	60	22	abdelhafid	abdelhafid	ADV
ap-8348	60	23	bounames	bouname	NOUN
ap-8348	60	24	acta	acta	PROPN
ap-8348	60	25	polytechnica	polytechnica	PROPN
ap-8348	60	26	[	[	PUNCT
ap-8348	60	27	p2	p2	PROPN
ap-8348	60	28	2m(t	2m(t	NUM
ap-8348	60	29	)	)	PUNCT
ap-8348	61	1	+	+	CCONJ
ap-8348	61	2	if(t	if(t	NOUN
ap-8348	61	3	)	)	PUNCT
ap-8348	61	4	|x|	|x|	PROPN
ap-8348	61	5	]	]	PUNCT
ap-8348	61	6	ψ(x	ψ(x	PROPN
ap-8348	61	7	,	,	PUNCT
ap-8348	61	8	t	t	PROPN
ap-8348	61	9	)	)	PUNCT
ap-8348	61	10	=	=	PUNCT
ap-8348	62	1	i	i	PRON
ap-8348	62	2	∂	∂	NOUN
ap-8348	62	3	∂t	∂t	PROPN
ap-8348	62	4	ψ(x	ψ(x	PROPN
ap-8348	62	5	,	,	PUNCT
ap-8348	62	6	t	t	PROPN
ap-8348	62	7	)	)	PUNCT
ap-8348	62	8	,	,	PUNCT
ap-8348	62	9	(	(	PUNCT
ap-8348	62	10	20	20	NUM
ap-8348	62	11	)	)	PUNCT
ap-8348	62	12	where	where	SCONJ
ap-8348	62	13	m(t	m(t	NOUN
ap-8348	62	14	)	)	PUNCT
ap-8348	62	15	is	be	AUX
ap-8348	62	16	the	the	DET
ap-8348	62	17	particle	particle	NOUN
ap-8348	62	18	td	td	NOUN
ap-8348	62	19	mass	mass	NOUN
ap-8348	62	20	and	and	CCONJ
ap-8348	62	21	f(t	f(t	NOUN
ap-8348	62	22	)	)	PUNCT
ap-8348	62	23	an	an	DET
ap-8348	62	24	arbitrary	arbitrary	ADJ
ap-8348	62	25	real	real	ADJ
ap-8348	62	26	td	td	NOUN
ap-8348	62	27	function	function	NOUN
ap-8348	62	28	,	,	PUNCT
ap-8348	62	29	and	and	CCONJ
ap-8348	62	30	the	the	DET
ap-8348	62	31	unit	unit	NOUN
ap-8348	62	32	of	of	ADP
ap-8348	62	33	ℏ	ℏ	PROPN
ap-8348	62	34	=	=	PUNCT
ap-8348	62	35	1	1	X
ap-8348	62	36	.	.	PUNCT
ap-8348	63	1	this	this	DET
ap-8348	63	2	model	model	NOUN
ap-8348	63	3	can	can	AUX
ap-8348	63	4	be	be	AUX
ap-8348	63	5	considered	consider	VERB
ap-8348	63	6	as	as	ADP
ap-8348	63	7	the	the	DET
ap-8348	63	8	complex	complex	ADJ
ap-8348	63	9	version	version	NOUN
ap-8348	63	10	of	of	ADP
ap-8348	63	11	the	the	DET
ap-8348	63	12	hermitian	hermitian	ADJ
ap-8348	63	13	case	case	NOUN
ap-8348	63	14	of	of	ADP
ap-8348	63	15	a	a	DET
ap-8348	63	16	particle	particle	NOUN
ap-8348	63	17	,	,	PUNCT
ap-8348	63	18	with	with	ADP
ap-8348	63	19	td	td	NOUN
ap-8348	63	20	mass	mass	NOUN
ap-8348	63	21	and	and	CCONJ
ap-8348	63	22	charge	charge	NOUN
ap-8348	63	23	q	q	NOUN
ap-8348	63	24	,	,	PUNCT
ap-8348	63	25	moving	move	VERB
ap-8348	63	26	under	under	ADP
ap-8348	63	27	the	the	DET
ap-8348	63	28	action	action	NOUN
ap-8348	63	29	of	of	ADP
ap-8348	63	30	td	td	PROPN
ap-8348	63	31	electric	electric	ADJ
ap-8348	63	32	field	field	NOUN
ap-8348	63	33	e(t	e(t	NOUN
ap-8348	63	34	)	)	PUNCT
ap-8348	63	35	and	and	CCONJ
ap-8348	63	36	confined	confine	VERB
ap-8348	63	37	in	in	ADP
ap-8348	63	38	a	a	DET
ap-8348	63	39	pure	pure	ADJ
ap-8348	63	40	imaginary	imaginary	ADJ
ap-8348	63	41	symmetric	symmetric	ADJ
ap-8348	63	42	linear	linear	ADJ
ap-8348	63	43	potential	potential	NOUN
ap-8348	63	44	well	well	ADV
ap-8348	63	45	:	:	PUNCT
ap-8348	63	46	if(t)x	if(t)x	PROPN
ap-8348	63	47	for	for	ADP
ap-8348	63	48	x	x	X
ap-8348	63	49	≥	≥	NOUN
ap-8348	63	50	0	0	NUM
ap-8348	63	51	and	and	CCONJ
ap-8348	63	52	−if(t)x	−if(t)x	X
ap-8348	63	53	for	for	ADP
ap-8348	63	54	x	x	SYM
ap-8348	63	55	≤	≤	NOUN
ap-8348	63	56	0	0	NUM
ap-8348	63	57	,	,	PUNCT
ap-8348	63	58	where	where	SCONJ
ap-8348	63	59	f(t	f(t	NOUN
ap-8348	63	60	)	)	PUNCT
ap-8348	63	61	=	=	PUNCT
ap-8348	63	62	−qe(t	−qe(t	NOUN
ap-8348	63	63	)	)	PUNCT
ap-8348	63	64	.	.	PUNCT
ap-8348	64	1	according	accord	VERB
ap-8348	64	2	to	to	ADP
ap-8348	64	3	the	the	DET
ap-8348	64	4	results	result	NOUN
ap-8348	64	5	in	in	ADP
ap-8348	64	6	[	[	X
ap-8348	64	7	17	17	NUM
ap-8348	64	8	]	]	PUNCT
ap-8348	64	9	,	,	PUNCT
ap-8348	64	10	the	the	DET
ap-8348	64	11	solution	solution	NOUN
ap-8348	64	12	to	to	ADP
ap-8348	64	13	the	the	DET
ap-8348	64	14	td	td	NOUN
ap-8348	64	15	schrödinger	schrödinger	ADJ
ap-8348	64	16	equation	equation	NOUN
ap-8348	64	17	with	with	ADP
ap-8348	64	18	a	a	DET
ap-8348	64	19	td	td	NOUN
ap-8348	64	20	non	non	ADJ
ap-8348	64	21	-	-	ADJ
ap-8348	64	22	hermitian	hermitian	ADJ
ap-8348	64	23	hamiltonian	hamiltonian	NOUN
ap-8348	64	24	is	be	AUX
ap-8348	64	25	easily	easily	ADV
ap-8348	64	26	found	find	VERB
ap-8348	64	27	if	if	SCONJ
ap-8348	64	28	a	a	DET
ap-8348	64	29	nontrivial	nontrivial	NOUN
ap-8348	64	30	td	td	NOUN
ap-8348	64	31	pseudohermitian	pseudohermitian	ADJ
ap-8348	64	32	invariant	invariant	PROPN
ap-8348	64	33	iph(t	iph(t	PROPN
ap-8348	64	34	)	)	PUNCT
ap-8348	64	35	exists	exist	VERB
ap-8348	64	36	and	and	CCONJ
ap-8348	64	37	satisfies	satisfy	VERB
ap-8348	64	38	the	the	DET
ap-8348	64	39	vonneumann	vonneumann	NOUN
ap-8348	64	40	equation	equation	NOUN
ap-8348	64	41	(	(	PUNCT
ap-8348	64	42	17	17	NUM
ap-8348	64	43	)	)	PUNCT
ap-8348	64	44	.	.	PUNCT
ap-8348	65	1	in	in	ADP
ap-8348	65	2	the	the	DET
ap-8348	65	3	current	current	ADJ
ap-8348	65	4	problem	problem	NOUN
ap-8348	65	5	,	,	PUNCT
ap-8348	65	6	in	in	ADP
ap-8348	65	7	order	order	NOUN
ap-8348	65	8	to	to	PART
ap-8348	65	9	solve	solve	VERB
ap-8348	65	10	the	the	DET
ap-8348	65	11	td	td	NOUN
ap-8348	65	12	shrödinger	shrödinger	NOUN
ap-8348	65	13	equation	equation	NOUN
ap-8348	65	14	(	(	PUNCT
ap-8348	65	15	20	20	NUM
ap-8348	65	16	)	)	PUNCT
ap-8348	65	17	we	we	PRON
ap-8348	65	18	assume	assume	VERB
ap-8348	65	19	that	that	SCONJ
ap-8348	65	20	the	the	DET
ap-8348	65	21	hamiltonian	hamiltonian	ADJ
ap-8348	65	22	h(t	h(t	PROPN
ap-8348	65	23	)	)	PUNCT
ap-8348	65	24	admits	admit	VERB
ap-8348	65	25	an	an	DET
ap-8348	65	26	invariant	invariant	NOUN
ap-8348	65	27	in	in	ADP
ap-8348	65	28	each	each	DET
ap-8348	65	29	region	region	NOUN
ap-8348	65	30	:	:	PUNCT
ap-8348	65	31	let	let	VERB
ap-8348	65	32	iph	iph	NOUN
ap-8348	65	33	1	1	NUM
ap-8348	65	34	(	(	PUNCT
ap-8348	65	35	t	t	NOUN
ap-8348	65	36	)	)	PUNCT
ap-8348	65	37	for	for	ADP
ap-8348	65	38	x	x	X
ap-8348	65	39	≥	≥	NOUN
ap-8348	65	40	0	0	NUM
ap-8348	65	41	and	and	CCONJ
ap-8348	65	42	iph	iph	PRON
ap-8348	65	43	2	2	NUM
ap-8348	65	44	(	(	PUNCT
ap-8348	65	45	t	t	PROPN
ap-8348	65	46	)	)	PUNCT
ap-8348	65	47	for	for	ADP
ap-8348	65	48	x	x	SYM
ap-8348	65	49	≤	≤	NOUN
ap-8348	65	50	0	0	NUM
ap-8348	65	51	.	.	PUNCT
ap-8348	66	1	for	for	ADP
ap-8348	66	2	the	the	DET
ap-8348	66	3	region	region	NOUN
ap-8348	66	4	x	x	PUNCT
ap-8348	66	5	≥	≥	NOUN
ap-8348	66	6	0	0	NUM
ap-8348	66	7	,	,	PUNCT
ap-8348	66	8	let	let	VERB
ap-8348	66	9	us	we	PRON
ap-8348	66	10	look	look	VERB
ap-8348	66	11	for	for	ADP
ap-8348	66	12	a	a	DET
ap-8348	66	13	non	non	ADJ
ap-8348	66	14	-	-	ADJ
ap-8348	66	15	hermitian	hermitian	ADJ
ap-8348	66	16	td	td	NOUN
ap-8348	66	17	invariant	invariant	ADJ
ap-8348	66	18	in	in	ADP
ap-8348	66	19	the	the	DET
ap-8348	66	20	following	follow	VERB
ap-8348	66	21	quadratic	quadratic	ADJ
ap-8348	66	22	form	form	NOUN
ap-8348	66	23	:	:	PUNCT
ap-8348	66	24	iph	iph	NOUN
ap-8348	66	25	1	1	NUM
ap-8348	66	26	(	(	PUNCT
ap-8348	66	27	t	t	NOUN
ap-8348	66	28	)	)	PUNCT
ap-8348	66	29	=	=	NOUN
ap-8348	66	30	β1(t)p2	β1(t)p2	X
ap-8348	67	1	+	+	CCONJ
ap-8348	67	2	β2(t)x+	β2(t)x+	X
ap-8348	67	3	β3(t)p+	β3(t)p+	NOUN
ap-8348	67	4	β4(t	β4(t	NUM
ap-8348	67	5	)	)	PUNCT
ap-8348	67	6	,	,	PUNCT
ap-8348	67	7	(	(	PUNCT
ap-8348	67	8	21	21	NUM
ap-8348	67	9	)	)	PUNCT
ap-8348	67	10	where	where	SCONJ
ap-8348	67	11	βi(t	βi(t	PUNCT
ap-8348	67	12	)	)	PUNCT
ap-8348	67	13	are	be	AUX
ap-8348	67	14	arbitrary	arbitrary	ADJ
ap-8348	67	15	complex	complex	ADJ
ap-8348	67	16	functions	function	NOUN
ap-8348	67	17	to	to	PART
ap-8348	67	18	be	be	AUX
ap-8348	67	19	determined	determine	VERB
ap-8348	67	20	.	.	PUNCT
ap-8348	68	1	by	by	ADP
ap-8348	68	2	inserting	insert	VERB
ap-8348	68	3	the	the	DET
ap-8348	68	4	expressions	expression	NOUN
ap-8348	68	5	(	(	PUNCT
ap-8348	68	6	19	19	NUM
ap-8348	68	7	)	)	PUNCT
ap-8348	68	8	and	and	CCONJ
ap-8348	68	9	(	(	PUNCT
ap-8348	68	10	21	21	NUM
ap-8348	68	11	)	)	PUNCT
ap-8348	68	12	in	in	ADP
ap-8348	68	13	equation	equation	NOUN
ap-8348	68	14	17	17	NUM
ap-8348	68	15	,	,	PUNCT
ap-8348	68	16	the	the	DET
ap-8348	68	17	following	follow	VERB
ap-8348	68	18	system	system	NOUN
ap-8348	68	19	of	of	ADP
ap-8348	68	20	equations	equation	NOUN
ap-8348	68	21	can	can	AUX
ap-8348	68	22	be	be	AUX
ap-8348	68	23	found	find	VERB
ap-8348	68	24	:	:	PUNCT
ap-8348	68	25			NUM
ap-8348	68	26	β̇1(t	β̇1(t	PROPN
ap-8348	68	27	)	)	PUNCT
ap-8348	68	28	=	=	SYM
ap-8348	68	29	0	0	NUM
ap-8348	68	30	,	,	PUNCT
ap-8348	68	31	β̇2(t	β̇2(t	PROPN
ap-8348	68	32	)	)	PUNCT
ap-8348	68	33	=	=	SYM
ap-8348	68	34	0	0	NUM
ap-8348	68	35	,	,	PUNCT
ap-8348	68	36	β̇3(t	β̇3(t	PROPN
ap-8348	68	37	)	)	PUNCT
ap-8348	68	38	=	=	PUNCT
ap-8348	69	1	−	−	ADP
ap-8348	69	2	β2(t	β2(t	NUM
ap-8348	69	3	)	)	PUNCT
ap-8348	69	4	m(t	m(t	NOUN
ap-8348	69	5	)	)	PUNCT
ap-8348	70	1	+	+	CCONJ
ap-8348	70	2	2	2	NUM
ap-8348	70	3	if(t)β1(t	if(t)β1(t	NOUN
ap-8348	70	4	)	)	PUNCT
ap-8348	70	5	,	,	PUNCT
ap-8348	70	6	β̇4(t	β̇4(t	PROPN
ap-8348	70	7	)	)	PUNCT
ap-8348	70	8	=	=	SYM
ap-8348	70	9	if(t)β3(t	if(t)β3(t	VERB
ap-8348	70	10	)	)	PUNCT
ap-8348	70	11	,	,	PUNCT
ap-8348	70	12	(	(	PUNCT
ap-8348	70	13	22	22	NUM
ap-8348	70	14	)	)	PUNCT
ap-8348	70	15	to	to	PART
ap-8348	70	16	simplify	simplify	VERB
ap-8348	70	17	the	the	DET
ap-8348	70	18	calculations	calculation	NOUN
ap-8348	70	19	,	,	PUNCT
ap-8348	70	20	we	we	PRON
ap-8348	70	21	take	take	VERB
ap-8348	70	22	β1(t	β1(t	PRON
ap-8348	70	23	)	)	PUNCT
ap-8348	70	24	=	=	SYM
ap-8348	70	25	1	1	NUM
ap-8348	70	26	and	and	CCONJ
ap-8348	70	27	β2(t	β2(t	NUM
ap-8348	70	28	)	)	PUNCT
ap-8348	70	29	=	=	SYM
ap-8348	70	30	1	1	NUM
ap-8348	70	31	,	,	PUNCT
ap-8348	70	32	so	so	ADV
ap-8348	70	33	β3(t	β3(t	NOUN
ap-8348	70	34	)	)	PUNCT
ap-8348	70	35	and	and	CCONJ
ap-8348	70	36	β4(t	β4(t	X
ap-8348	70	37	)	)	PUNCT
ap-8348	70	38	are	be	AUX
ap-8348	70	39	given	give	VERB
ap-8348	70	40	by	by	ADP
ap-8348	70	41	:	:	PUNCT
ap-8348	70	42	β3(t	β3(t	NUM
ap-8348	70	43	)	)	PUNCT
ap-8348	70	44	=	=	SYM
ap-8348	70	45	g(t	g(t	PROPN
ap-8348	70	46	)	)	PUNCT
ap-8348	70	47	+	+	CCONJ
ap-8348	70	48	ik(t	ik(t	NOUN
ap-8348	70	49	)	)	PUNCT
ap-8348	70	50	,	,	PUNCT
ap-8348	70	51	(	(	PUNCT
ap-8348	70	52	23	23	NUM
ap-8348	70	53	)	)	PUNCT
ap-8348	70	54	β4(t	β4(t	PROPN
ap-8348	70	55	)	)	PUNCT
ap-8348	70	56	=	=	SYM
ap-8348	70	57	s(t	s(t	PROPN
ap-8348	70	58	)	)	PUNCT
ap-8348	70	59	+	+	NUM
ap-8348	70	60	iw(t	iw(t	X
ap-8348	70	61	)	)	PUNCT
ap-8348	70	62	,	,	PUNCT
ap-8348	70	63	(	(	PUNCT
ap-8348	70	64	24	24	NUM
ap-8348	70	65	)	)	PUNCT
ap-8348	70	66	where	where	SCONJ
ap-8348	70	67	g(t	g(t	NOUN
ap-8348	70	68	)	)	PUNCT
ap-8348	71	1	=	=	PUNCT
ap-8348	71	2	−	−	PROPN
ap-8348	71	3	∫	∫	PROPN
ap-8348	71	4	dt	dt	X
ap-8348	71	5	m(t	m(t	PROPN
ap-8348	71	6	)	)	PUNCT
ap-8348	71	7	,	,	PUNCT
ap-8348	71	8	k(t	k(t	NOUN
ap-8348	71	9	)	)	PUNCT
ap-8348	71	10	=	=	SYM
ap-8348	71	11	2	2	NUM
ap-8348	71	12	∫	∫	NOUN
ap-8348	71	13	f(t)dt	f(t)dt	PROPN
ap-8348	71	14	,	,	PUNCT
ap-8348	71	15	s(t	s(t	PROPN
ap-8348	71	16	)	)	PUNCT
ap-8348	71	17	=	=	PUNCT
ap-8348	72	1	−	−	PROPN
ap-8348	72	2	∫	∫	PROPN
ap-8348	72	3	f(t)k(t)dt	f(t)k(t)dt	PROPN
ap-8348	72	4	and	and	CCONJ
ap-8348	72	5	w(t	w(t	PROPN
ap-8348	72	6	)	)	PUNCT
ap-8348	73	1	=	=	SYM
ap-8348	73	2	∫	∫	PROPN
ap-8348	73	3	f(t)g(t)dt	f(t)g(t)dt	NOUN
ap-8348	73	4	.	.	PUNCT
ap-8348	74	1	substituting	substitute	VERB
ap-8348	74	2	expressions	expression	NOUN
ap-8348	74	3	(	(	PUNCT
ap-8348	74	4	23	23	NUM
ap-8348	74	5	)	)	PUNCT
ap-8348	74	6	and	and	CCONJ
ap-8348	74	7	(	(	PUNCT
ap-8348	74	8	24	24	NUM
ap-8348	74	9	)	)	PUNCT
ap-8348	74	10	in	in	ADP
ap-8348	74	11	equation	equation	NOUN
ap-8348	74	12	(	(	PUNCT
ap-8348	74	13	21	21	NUM
ap-8348	74	14	)	)	PUNCT
ap-8348	74	15	we	we	PRON
ap-8348	74	16	found	find	VERB
ap-8348	74	17	:	:	PUNCT
ap-8348	74	18	iph	iph	NOUN
ap-8348	74	19	1	1	NUM
ap-8348	74	20	(	(	PUNCT
ap-8348	74	21	t	t	NOUN
ap-8348	74	22	)	)	PUNCT
ap-8348	74	23	=	=	PUNCT
ap-8348	75	1	p2	p2	PROPN
ap-8348	76	1	+	+	ADJ
ap-8348	77	1	x+	x+	ADJ
ap-8348	77	2	[	[	X
ap-8348	77	3	g(t	g(t	NOUN
ap-8348	77	4	)	)	PUNCT
ap-8348	78	1	+	+	CCONJ
ap-8348	79	1	ik(t	ik(t	NOUN
ap-8348	79	2	)	)	PUNCT
ap-8348	79	3	]	]	PUNCT
ap-8348	79	4	p+	p+	VERB
ap-8348	79	5	s(t	s(t	PROPN
ap-8348	79	6	)	)	PUNCT
ap-8348	80	1	+	+	CCONJ
ap-8348	81	1	iw(t	iw(t	X
ap-8348	81	2	)	)	PUNCT
ap-8348	81	3	.	.	PUNCT
ap-8348	82	1	(	(	PUNCT
ap-8348	82	2	25	25	NUM
ap-8348	82	3	)	)	PUNCT
ap-8348	82	4	its	its	PRON
ap-8348	82	5	eigenvalue	eigenvalue	ADJ
ap-8348	82	6	equation	equation	NOUN
ap-8348	82	7	is	be	AUX
ap-8348	82	8	as	as	SCONJ
ap-8348	82	9	follows	follow	VERB
ap-8348	82	10	:	:	PUNCT
ap-8348	82	11	iph	iph	NOUN
ap-8348	82	12	1	1	NUM
ap-8348	82	13	(	(	PUNCT
ap-8348	82	14	t	t	PROPN
ap-8348	82	15	)	)	PUNCT
ap-8348	82	16	|ψ(t)⟩	|ψ(t)⟩	PROPN
ap-8348	82	17	=	=	SYM
ap-8348	82	18	λ1	λ1	PROPN
ap-8348	82	19	|ψ(t)⟩	|ψ(t)⟩	PROPN
ap-8348	82	20	,	,	PUNCT
ap-8348	82	21	(	(	PUNCT
ap-8348	82	22	26	26	NUM
ap-8348	82	23	)	)	PUNCT
ap-8348	82	24	in	in	ADP
ap-8348	82	25	order	order	NOUN
ap-8348	82	26	to	to	PART
ap-8348	82	27	show	show	VERB
ap-8348	82	28	that	that	SCONJ
ap-8348	82	29	the	the	DET
ap-8348	82	30	spectrum	spectrum	NOUN
ap-8348	82	31	of	of	ADP
ap-8348	82	32	iph	iph	NOUN
ap-8348	82	33	1	1	NUM
ap-8348	82	34	(	(	PUNCT
ap-8348	82	35	t	t	NOUN
ap-8348	82	36	)	)	PUNCT
ap-8348	82	37	is	be	AUX
ap-8348	82	38	real	real	ADJ
ap-8348	82	39	,	,	PUNCT
ap-8348	82	40	we	we	PRON
ap-8348	82	41	search	search	VERB
ap-8348	82	42	for	for	ADP
ap-8348	82	43	a	a	DET
ap-8348	82	44	metric	metric	ADJ
ap-8348	82	45	operator	operator	NOUN
ap-8348	82	46	that	that	PRON
ap-8348	82	47	fulfills	fulfill	VERB
ap-8348	82	48	the	the	DET
ap-8348	82	49	pseudo	pseudo	NOUN
ap-8348	82	50	hermiticity	hermiticity	NOUN
ap-8348	82	51	relation	relation	NOUN
ap-8348	82	52	:	:	PUNCT
ap-8348	82	53	iph†	iph†	PROPN
ap-8348	82	54	1	1	NUM
ap-8348	82	55	(	(	PUNCT
ap-8348	82	56	t	t	NOUN
ap-8348	82	57	)	)	PUNCT
ap-8348	82	58	=	=	NOUN
ap-8348	83	1	η1(t)iph	η1(t)iph	X
ap-8348	83	2	1	1	NUM
ap-8348	83	3	(	(	PUNCT
ap-8348	83	4	t)η−1	t)η−1	NOUN
ap-8348	83	5	1	1	NUM
ap-8348	83	6	(	(	PUNCT
ap-8348	83	7	t	t	PROPN
ap-8348	83	8	)	)	PUNCT
ap-8348	83	9	,	,	PUNCT
ap-8348	83	10	(	(	PUNCT
ap-8348	83	11	27	27	NUM
ap-8348	83	12	)	)	PUNCT
ap-8348	83	13	and	and	CCONJ
ap-8348	83	14	we	we	PRON
ap-8348	83	15	make	make	VERB
ap-8348	83	16	the	the	DET
ap-8348	83	17	following	follow	VERB
ap-8348	83	18	choice	choice	NOUN
ap-8348	83	19	for	for	ADP
ap-8348	83	20	metric	metric	ADJ
ap-8348	83	21	:	:	PUNCT
ap-8348	83	22	η1(t	η1(t	X
ap-8348	83	23	)	)	PUNCT
ap-8348	83	24	=	=	SYM
ap-8348	83	25	exp[−α(t)x−	exp[−α(t)x−	PROPN
ap-8348	83	26	β(t)p	β(t)p	PROPN
ap-8348	83	27	]	]	PUNCT
ap-8348	83	28	,	,	PUNCT
ap-8348	83	29	(	(	PUNCT
ap-8348	83	30	28	28	NUM
ap-8348	83	31	)	)	PUNCT
ap-8348	83	32	where	where	SCONJ
ap-8348	83	33	α(t	α(t	VERB
ap-8348	83	34	)	)	PUNCT
ap-8348	83	35	and	and	CCONJ
ap-8348	83	36	β(t	β(t	PROPN
ap-8348	83	37	)	)	PUNCT
ap-8348	83	38	are	be	AUX
ap-8348	83	39	chosen	choose	VERB
ap-8348	83	40	as	as	ADP
ap-8348	83	41	real	real	ADJ
ap-8348	83	42	functions	function	NOUN
ap-8348	83	43	in	in	ADP
ap-8348	83	44	order	order	NOUN
ap-8348	83	45	that	that	SCONJ
ap-8348	83	46	the	the	DET
ap-8348	83	47	metric	metric	ADJ
ap-8348	83	48	operator	operator	NOUN
ap-8348	83	49	η1(t	η1(t	PRON
ap-8348	83	50	)	)	PUNCT
ap-8348	83	51	is	be	AUX
ap-8348	83	52	hermitian	hermitian	ADJ
ap-8348	83	53	.	.	PUNCT
ap-8348	84	1	the	the	DET
ap-8348	84	2	position	position	NOUN
ap-8348	84	3	and	and	CCONJ
ap-8348	84	4	momentum	momentum	NOUN
ap-8348	84	5	operators	operator	NOUN
ap-8348	84	6	transform	transform	VERB
ap-8348	84	7	according	accord	VERB
ap-8348	84	8	to	to	ADP
ap-8348	84	9	the	the	DET
ap-8348	84	10	transformation	transformation	NOUN
ap-8348	84	11	η1(t	η1(t	PROPN
ap-8348	84	12	)	)	PUNCT
ap-8348	84	13	as	as	ADP
ap-8348	84	14	:	:	PUNCT
ap-8348	84	15	η1(t)xη−1	η1(t)xη−1	PROPN
ap-8348	84	16	1	1	NUM
ap-8348	84	17	(	(	PUNCT
ap-8348	84	18	t	t	NOUN
ap-8348	84	19	)	)	PUNCT
ap-8348	84	20	=	=	SYM
ap-8348	84	21	x+	x+	X
ap-8348	84	22	iβ(t	iβ(t	X
ap-8348	84	23	)	)	PUNCT
ap-8348	84	24	,	,	PUNCT
ap-8348	84	25	(	(	PUNCT
ap-8348	84	26	29	29	NUM
ap-8348	84	27	)	)	PUNCT
ap-8348	84	28	η1(t)pη−1	η1(t)pη−1	PROPN
ap-8348	84	29	1	1	NUM
ap-8348	84	30	(	(	PUNCT
ap-8348	84	31	t	t	NOUN
ap-8348	84	32	)	)	PUNCT
ap-8348	84	33	=	=	NOUN
ap-8348	84	34	p−	p−	NOUN
ap-8348	84	35	iα(t	iα(t	NOUN
ap-8348	84	36	)	)	PUNCT
ap-8348	84	37	,	,	PUNCT
ap-8348	84	38	(	(	PUNCT
ap-8348	84	39	30	30	X
ap-8348	84	40	)	)	PUNCT
ap-8348	84	41	incorporating	incorporate	VERB
ap-8348	84	42	these	these	DET
ap-8348	84	43	relationships	relationship	NOUN
ap-8348	84	44	into	into	ADP
ap-8348	84	45	equation	equation	NOUN
ap-8348	84	46	(	(	PUNCT
ap-8348	84	47	27	27	NUM
ap-8348	84	48	)	)	PUNCT
ap-8348	84	49	,	,	PUNCT
ap-8348	84	50	we	we	PRON
ap-8348	84	51	found	find	VERB
ap-8348	84	52	:	:	PUNCT
ap-8348	84	53	α(t	α(t	NUM
ap-8348	84	54	)	)	PUNCT
ap-8348	84	55	=	=	PUNCT
ap-8348	84	56	k(t	k(t	NOUN
ap-8348	84	57	)	)	PUNCT
ap-8348	84	58	,	,	PUNCT
ap-8348	84	59	(	(	PUNCT
ap-8348	84	60	31	31	NUM
ap-8348	84	61	)	)	PUNCT
ap-8348	84	62	β(t	β(t	NOUN
ap-8348	84	63	)	)	PUNCT
ap-8348	84	64	=	=	SYM
ap-8348	84	65	g(t)k(t	g(t)k(t	NOUN
ap-8348	84	66	)	)	PUNCT
ap-8348	84	67	−	−	PROPN
ap-8348	84	68	2w(t	2w(t	NUM
ap-8348	84	69	)	)	PUNCT
ap-8348	84	70	,	,	PUNCT
ap-8348	84	71	(	(	PUNCT
ap-8348	84	72	32	32	NUM
ap-8348	84	73	)	)	PUNCT
ap-8348	84	74	then	then	ADV
ap-8348	84	75	the	the	DET
ap-8348	84	76	td	td	NOUN
ap-8348	84	77	metric	metric	ADJ
ap-8348	84	78	operator	operator	NOUN
ap-8348	84	79	η1(t	η1(t	PRON
ap-8348	84	80	)	)	PUNCT
ap-8348	84	81	is	be	AUX
ap-8348	84	82	given	give	VERB
ap-8348	84	83	by	by	ADP
ap-8348	84	84	:	:	PUNCT
ap-8348	84	85	η1(t	η1(t	X
ap-8348	84	86	)	)	PUNCT
ap-8348	84	87	=	=	SYM
ap-8348	84	88	exp[−k(t)x−	exp[−k(t)x−	NOUN
ap-8348	84	89	(	(	PUNCT
ap-8348	84	90	g(t)k(t	g(t)k(t	NOUN
ap-8348	84	91	)	)	PUNCT
ap-8348	84	92	−	−	PROPN
ap-8348	84	93	2w(t))p	2w(t))p	PROPN
ap-8348	84	94	]	]	PUNCT
ap-8348	84	95	,	,	PUNCT
ap-8348	84	96	(	(	PUNCT
ap-8348	84	97	33	33	NUM
ap-8348	84	98	)	)	PUNCT
ap-8348	84	99	according	accord	VERB
ap-8348	84	100	to	to	ADP
ap-8348	84	101	the	the	DET
ap-8348	84	102	relation	relation	NOUN
ap-8348	84	103	η1(t	η1(t	PROPN
ap-8348	84	104	)	)	PUNCT
ap-8348	84	105	=	=	SYM
ap-8348	84	106	ρ†	ρ†	NUM
ap-8348	84	107	1(t)ρ1(t	1(t)ρ1(t	NUM
ap-8348	84	108	)	)	PUNCT
ap-8348	84	109	,	,	PUNCT
ap-8348	84	110	and	and	CCONJ
ap-8348	84	111	since	since	SCONJ
ap-8348	84	112	ρ1(t	ρ1(t	PROPN
ap-8348	84	113	)	)	PUNCT
ap-8348	84	114	is	be	AUX
ap-8348	84	115	not	not	PART
ap-8348	84	116	unique	unique	ADJ
ap-8348	84	117	,	,	PUNCT
ap-8348	84	118	we	we	PRON
ap-8348	84	119	can	can	AUX
ap-8348	84	120	take	take	VERB
ap-8348	84	121	it	it	PRON
ap-8348	84	122	as	as	ADP
ap-8348	84	123	a	a	DET
ap-8348	84	124	hermitian	hermitian	ADJ
ap-8348	84	125	operator	operator	NOUN
ap-8348	84	126	in	in	ADP
ap-8348	84	127	order	order	NOUN
ap-8348	84	128	to	to	PART
ap-8348	84	129	simplify	simplify	VERB
ap-8348	84	130	the	the	DET
ap-8348	84	131	calculations	calculation	NOUN
ap-8348	84	132	:	:	PUNCT
ap-8348	84	133	ρ1(t	ρ1(t	X
ap-8348	84	134	)	)	PUNCT
ap-8348	84	135	=	=	SYM
ap-8348	84	136	exp	exp	NOUN
ap-8348	84	137	[	[	PUNCT
ap-8348	84	138	−k(t	−k(t	NOUN
ap-8348	84	139	)	)	PUNCT
ap-8348	84	140	2	2	NUM
ap-8348	84	141	x−	x−	PROPN
ap-8348	84	142	[	[	PUNCT
ap-8348	84	143	g(t)k(t	g(t)k(t	NOUN
ap-8348	84	144	)	)	PUNCT
ap-8348	84	145	2	2	NUM
ap-8348	84	146	−	−	NOUN
ap-8348	84	147	w(t	w(t	PROPN
ap-8348	84	148	)	)	PUNCT
ap-8348	84	149	]	]	PUNCT
ap-8348	85	1	p	p	X
ap-8348	85	2	]	]	PUNCT
ap-8348	85	3	,	,	PUNCT
ap-8348	85	4	(	(	PUNCT
ap-8348	85	5	34	34	NUM
ap-8348	85	6	)	)	PUNCT
ap-8348	85	7	the	the	DET
ap-8348	85	8	hermitian	hermitian	ADJ
ap-8348	85	9	invariant	invariant	VERB
ap-8348	85	10	ih	ih	X
ap-8348	85	11	1	1	NUM
ap-8348	85	12	(	(	PUNCT
ap-8348	85	13	t	t	NOUN
ap-8348	85	14	)	)	PUNCT
ap-8348	85	15	associated	associate	VERB
ap-8348	85	16	with	with	ADP
ap-8348	85	17	the	the	DET
ap-8348	85	18	pseudo	pseudo	NOUN
ap-8348	85	19	-	-	ADJ
ap-8348	85	20	hermitian	hermitian	ADJ
ap-8348	85	21	invariant	invariant	ADJ
ap-8348	85	22	iph	iph	NOUN
ap-8348	85	23	1	1	NUM
ap-8348	85	24	(	(	PUNCT
ap-8348	85	25	t	t	NOUN
ap-8348	85	26	)	)	PUNCT
ap-8348	85	27	is	be	AUX
ap-8348	85	28	given	give	VERB
ap-8348	85	29	by	by	ADP
ap-8348	85	30	:	:	PUNCT
ap-8348	85	31	ih	ih	PROPN
ap-8348	85	32	1	1	NUM
ap-8348	85	33	(	(	PUNCT
ap-8348	85	34	t	t	NOUN
ap-8348	85	35	)	)	PUNCT
ap-8348	85	36	=	=	PUNCT
ap-8348	86	1	ρ(t)iph	ρ(t)iph	NOUN
ap-8348	86	2	1	1	NUM
ap-8348	86	3	ρ−1(t	ρ−1(t	NOUN
ap-8348	86	4	)	)	PUNCT
ap-8348	87	1	=	=	SYM
ap-8348	87	2	p2+x+g(t)p+	p2+x+g(t)p+	PROPN
ap-8348	87	3	k2(t	k2(t	PROPN
ap-8348	87	4	)	)	PUNCT
ap-8348	87	5	4	4	NUM
ap-8348	87	6	+	+	NOUN
ap-8348	87	7	s(t	s(t	ADJ
ap-8348	87	8	)	)	PUNCT
ap-8348	87	9	.	.	PUNCT
ap-8348	88	1	(	(	PUNCT
ap-8348	88	2	35	35	NUM
ap-8348	88	3	)	)	PUNCT
ap-8348	88	4	for	for	ADP
ap-8348	88	5	the	the	DET
ap-8348	88	6	region	region	NOUN
ap-8348	88	7	x	x	PUNCT
ap-8348	88	8	≤	≤	ADV
ap-8348	88	9	0	0	NUM
ap-8348	88	10	,	,	PUNCT
ap-8348	88	11	we	we	PRON
ap-8348	88	12	take	take	VERB
ap-8348	88	13	the	the	DET
ap-8348	88	14	non	non	ADJ
ap-8348	88	15	-	-	ADJ
ap-8348	88	16	hermitian	hermitian	ADJ
ap-8348	88	17	invariant	invariant	ADJ
ap-8348	88	18	iph	iph	NOUN
ap-8348	88	19	2	2	NUM
ap-8348	88	20	as	as	ADP
ap-8348	88	21	iph	iph	NOUN
ap-8348	88	22	2	2	NUM
ap-8348	88	23	(	(	PUNCT
ap-8348	88	24	t	t	NOUN
ap-8348	88	25	)	)	PUNCT
ap-8348	88	26	=	=	SYM
ap-8348	88	27	α1(t)p2	α1(t)p2	NOUN
ap-8348	89	1	+	+	CCONJ
ap-8348	89	2	α2(t)x+	α2(t)x+	NUM
ap-8348	89	3	α3(t)p+	α3(t)p+	NUM
ap-8348	89	4	α4(t	α4(t	NUM
ap-8348	89	5	)	)	PUNCT
ap-8348	89	6	,	,	PUNCT
ap-8348	89	7	(	(	PUNCT
ap-8348	89	8	36	36	NUM
ap-8348	89	9	)	)	PUNCT
ap-8348	90	1	where	where	SCONJ
ap-8348	90	2	αi(t	αi(t	NOUN
ap-8348	90	3	)	)	PUNCT
ap-8348	90	4	are	be	AUX
ap-8348	90	5	arbitrary	arbitrary	ADJ
ap-8348	90	6	complex	complex	ADJ
ap-8348	90	7	functions	function	NOUN
ap-8348	90	8	to	to	PART
ap-8348	90	9	be	be	AUX
ap-8348	90	10	determined	determine	VERB
ap-8348	90	11	.	.	PUNCT
ap-8348	91	1	in	in	ADP
ap-8348	91	2	the	the	DET
ap-8348	91	3	same	same	ADJ
ap-8348	91	4	way	way	NOUN
ap-8348	91	5	as	as	ADP
ap-8348	91	6	the	the	DET
ap-8348	91	7	precedent	precedent	NOUN
ap-8348	91	8	case	case	NOUN
ap-8348	91	9	,	,	PUNCT
ap-8348	91	10	inserting	insert	VERB
ap-8348	91	11	the	the	DET
ap-8348	91	12	expressions	expression	NOUN
ap-8348	91	13	(	(	PUNCT
ap-8348	91	14	19	19	NUM
ap-8348	91	15	)	)	PUNCT
ap-8348	91	16	and	and	CCONJ
ap-8348	91	17	(	(	PUNCT
ap-8348	91	18	36	36	NUM
ap-8348	91	19	)	)	PUNCT
ap-8348	91	20	in	in	ADP
ap-8348	91	21	equation	equation	NOUN
ap-8348	91	22	(	(	PUNCT
ap-8348	91	23	17	17	NUM
ap-8348	91	24	)	)	PUNCT
ap-8348	91	25	,	,	PUNCT
ap-8348	91	26	where	where	SCONJ
ap-8348	91	27	we	we	PRON
ap-8348	91	28	take	take	VERB
ap-8348	91	29	α1(t	α1(t	PRON
ap-8348	91	30	)	)	PUNCT
ap-8348	91	31	=	=	SYM
ap-8348	91	32	1	1	NUM
ap-8348	91	33	and	and	CCONJ
ap-8348	91	34	α2(t	α2(t	NUM
ap-8348	91	35	)	)	PUNCT
ap-8348	91	36	=	=	SYM
ap-8348	91	37	−1	−1	NOUN
ap-8348	91	38	,	,	PUNCT
ap-8348	91	39	so	so	ADV
ap-8348	91	40	α3(t	α3(t	NUM
ap-8348	91	41	)	)	PUNCT
ap-8348	91	42	and	and	CCONJ
ap-8348	91	43	α4(t	α4(t	NUM
ap-8348	91	44	)	)	PUNCT
ap-8348	91	45	are	be	AUX
ap-8348	91	46	given	give	VERB
ap-8348	91	47	by	by	ADP
ap-8348	91	48	:	:	PUNCT
ap-8348	91	49	α3(t	α3(t	NUM
ap-8348	91	50	)	)	PUNCT
ap-8348	91	51	=	=	SYM
ap-8348	91	52	−g(t	−g(t	ADJ
ap-8348	91	53	)	)	PUNCT
ap-8348	91	54	−	−	NOUN
ap-8348	91	55	ik(t	ik(t	NOUN
ap-8348	91	56	)	)	PUNCT
ap-8348	91	57	,	,	PUNCT
ap-8348	91	58	(	(	PUNCT
ap-8348	91	59	37	37	NUM
ap-8348	91	60	)	)	PUNCT
ap-8348	91	61	α4(t	α4(t	PROPN
ap-8348	91	62	)	)	PUNCT
ap-8348	91	63	=	=	PUNCT
ap-8348	91	64	s(t	s(t	PROPN
ap-8348	91	65	)	)	PUNCT
ap-8348	91	66	+	+	NUM
ap-8348	91	67	iw(t	iw(t	X
ap-8348	91	68	)	)	PUNCT
ap-8348	91	69	.	.	PUNCT
ap-8348	92	1	(	(	PUNCT
ap-8348	92	2	38	38	NUM
ap-8348	92	3	)	)	PUNCT
ap-8348	92	4	134	134	NUM
ap-8348	92	5	vol	vol	NOUN
ap-8348	92	6	.	.	PUNCT
ap-8348	92	7	63	63	NUM
ap-8348	93	1	no	no	NOUN
ap-8348	93	2	.	.	PUNCT
ap-8348	94	1	2/2023	2/2023	NUM
ap-8348	94	2	exact	exact	ADJ
ap-8348	94	3	solutions	solution	NOUN
ap-8348	94	4	for	for	ADP
ap-8348	94	5	time	time	NOUN
ap-8348	94	6	-	-	PUNCT
ap-8348	94	7	dependent	dependent	ADJ
ap-8348	94	8	complex	complex	ADJ
ap-8348	94	9	symmetric	symmetric	ADJ
ap-8348	94	10	potential	potential	NOUN
ap-8348	94	11	well	well	ADV
ap-8348	94	12	then	then	ADV
ap-8348	94	13	,	,	PUNCT
ap-8348	94	14	the	the	DET
ap-8348	94	15	final	final	ADJ
ap-8348	94	16	results	result	NOUN
ap-8348	94	17	of	of	ADP
ap-8348	94	18	iph	iph	NOUN
ap-8348	94	19	2	2	NUM
ap-8348	94	20	(	(	PUNCT
ap-8348	94	21	t	t	PROPN
ap-8348	94	22	)	)	PUNCT
ap-8348	94	23	and	and	CCONJ
ap-8348	94	24	η2(t	η2(t	PROPN
ap-8348	94	25	)	)	PUNCT
ap-8348	94	26	are	be	AUX
ap-8348	94	27	:	:	PUNCT
ap-8348	94	28	iph	iph	NOUN
ap-8348	94	29	2	2	NUM
ap-8348	94	30	(	(	PUNCT
ap-8348	94	31	t	t	NOUN
ap-8348	94	32	)	)	PUNCT
ap-8348	94	33	=	=	PUNCT
ap-8348	95	1	p2	p2	X
ap-8348	95	2	−x−	−x−	X
ap-8348	96	1	[	[	X
ap-8348	96	2	g(t	g(t	NOUN
ap-8348	96	3	)	)	PUNCT
ap-8348	96	4	+	+	CCONJ
ap-8348	96	5	ik(t	ik(t	NOUN
ap-8348	96	6	)	)	PUNCT
ap-8348	96	7	]	]	PUNCT
ap-8348	96	8	p+	p+	VERB
ap-8348	96	9	s(t	s(t	PROPN
ap-8348	96	10	)	)	PUNCT
ap-8348	96	11	+	+	CCONJ
ap-8348	96	12	iw(t	iw(t	X
ap-8348	96	13	)	)	PUNCT
ap-8348	96	14	,	,	PUNCT
ap-8348	96	15	(	(	PUNCT
ap-8348	96	16	39	39	NUM
ap-8348	96	17	)	)	PUNCT
ap-8348	96	18	η2(t	η2(t	PROPN
ap-8348	96	19	)	)	PUNCT
ap-8348	96	20	=	=	SYM
ap-8348	97	1	exp[k(t)x−	exp[k(t)x−	PROPN
ap-8348	98	1	[	[	X
ap-8348	98	2	2w(t	2w(t	NUM
ap-8348	98	3	)	)	PUNCT
ap-8348	98	4	−	−	PROPN
ap-8348	98	5	g(t)k(t	g(t)k(t	NOUN
ap-8348	98	6	)	)	PUNCT
ap-8348	98	7	]	]	PUNCT
ap-8348	99	1	p	p	X
ap-8348	99	2	]	]	PUNCT
ap-8348	99	3	.	.	PUNCT
ap-8348	100	1	(	(	PUNCT
ap-8348	100	2	40	40	NUM
ap-8348	100	3	)	)	PUNCT
ap-8348	100	4	we	we	PRON
ap-8348	100	5	take	take	VERB
ap-8348	100	6	ρ2(t	ρ2(t	NUM
ap-8348	100	7	)	)	PUNCT
ap-8348	100	8	as	as	ADP
ap-8348	100	9	a	a	DET
ap-8348	100	10	hermitian	hermitian	ADJ
ap-8348	100	11	operator	operator	NOUN
ap-8348	100	12	,	,	PUNCT
ap-8348	100	13	then	then	ADV
ap-8348	100	14	η2(t	η2(t	PROPN
ap-8348	100	15	)	)	PUNCT
ap-8348	100	16	=	=	SYM
ap-8348	101	1	ρ2	ρ2	NOUN
ap-8348	101	2	2	2	NUM
ap-8348	101	3	,	,	PUNCT
ap-8348	101	4	ρ2(t	ρ2(t	NUM
ap-8348	101	5	)	)	PUNCT
ap-8348	101	6	=	=	SYM
ap-8348	101	7	exp	exp	NOUN
ap-8348	101	8	[	[	PUNCT
ap-8348	101	9	k(t	k(t	NOUN
ap-8348	101	10	)	)	PUNCT
ap-8348	101	11	2	2	NUM
ap-8348	101	12	x+	x+	X
ap-8348	101	13	[	[	PUNCT
ap-8348	101	14	k(t)g(t	k(t)g(t	NOUN
ap-8348	101	15	)	)	PUNCT
ap-8348	101	16	2	2	NUM
ap-8348	101	17	−	−	NOUN
ap-8348	101	18	w(t	w(t	PROPN
ap-8348	101	19	)	)	PUNCT
ap-8348	101	20	]	]	PUNCT
ap-8348	102	1	p	p	X
ap-8348	102	2	]	]	PUNCT
ap-8348	102	3	,	,	PUNCT
ap-8348	102	4	(	(	PUNCT
ap-8348	102	5	41	41	NUM
ap-8348	102	6	)	)	PUNCT
ap-8348	102	7	and	and	CCONJ
ap-8348	102	8	the	the	DET
ap-8348	102	9	related	relate	VERB
ap-8348	102	10	hermitian	hermitian	NOUN
ap-8348	102	11	invariant	invariant	ADJ
ap-8348	102	12	ih	ih	PROPN
ap-8348	102	13	2	2	NUM
ap-8348	102	14	(	(	PUNCT
ap-8348	102	15	t	t	PROPN
ap-8348	102	16	)	)	PUNCT
ap-8348	102	17	is	be	AUX
ap-8348	102	18	:	:	PUNCT
ap-8348	102	19	ih	ih	PROPN
ap-8348	102	20	2	2	NUM
ap-8348	102	21	(	(	PUNCT
ap-8348	102	22	t	t	NOUN
ap-8348	102	23	)	)	PUNCT
ap-8348	102	24	=	=	PUNCT
ap-8348	102	25	p2	p2	PROPN
ap-8348	102	26	−	−	PROPN
ap-8348	103	1	x−	x−	PROPN
ap-8348	103	2	g(t)p+	g(t)p+	X
ap-8348	103	3	k2(t	k2(t	PROPN
ap-8348	103	4	)	)	PUNCT
ap-8348	103	5	4	4	NUM
ap-8348	103	6	+	+	NUM
ap-8348	103	7	s(t	s(t	NUM
ap-8348	103	8	)	)	PUNCT
ap-8348	103	9	.	.	PUNCT
ap-8348	104	1	(	(	PUNCT
ap-8348	104	2	42	42	NUM
ap-8348	104	3	)	)	PUNCT
ap-8348	104	4	to	to	PART
ap-8348	104	5	derive	derive	VERB
ap-8348	104	6	the	the	DET
ap-8348	104	7	eigenvalues	eigenvalue	NOUN
ap-8348	104	8	equations	equation	NOUN
ap-8348	104	9	of	of	ADP
ap-8348	104	10	the	the	DET
ap-8348	104	11	invariants	invariant	NOUN
ap-8348	104	12	ih	ih	PROPN
ap-8348	104	13	j	j	PROPN
ap-8348	104	14	(	(	PUNCT
ap-8348	104	15	t	t	PROPN
ap-8348	104	16	)	)	PUNCT
ap-8348	104	17	for	for	ADP
ap-8348	104	18	the	the	DET
ap-8348	104	19	two	two	NUM
ap-8348	104	20	regions	region	NOUN
ap-8348	104	21	(	(	PUNCT
ap-8348	104	22	j	j	NOUN
ap-8348	104	23	=	=	SYM
ap-8348	104	24	1	1	NUM
ap-8348	104	25	,	,	PUNCT
ap-8348	104	26	2	2	NUM
ap-8348	104	27	)	)	PUNCT
ap-8348	104	28	,	,	PUNCT
ap-8348	104	29	we	we	PRON
ap-8348	104	30	introduce	introduce	VERB
ap-8348	104	31	the	the	DET
ap-8348	104	32	unitary	unitary	ADJ
ap-8348	104	33	transformations	transformation	NOUN
ap-8348	104	34	uj(t	uj(t	PUNCT
ap-8348	104	35	):	):	PUNCT
ap-8348	104	36	|ϕn	|ϕn	PROPN
ap-8348	104	37	,	,	PUNCT
ap-8348	104	38	j(t)⟩	j(t)⟩	NOUN
ap-8348	104	39	=	=	SYM
ap-8348	104	40	uj(t	uj(t	ADJ
ap-8348	104	41	)	)	PUNCT
ap-8348	104	42	|φn⟩	|φn⟩	NOUN
ap-8348	104	43	,	,	PUNCT
ap-8348	104	44	j	j	PROPN
ap-8348	104	45	=	=	SYM
ap-8348	104	46	1	1	NUM
ap-8348	104	47	,	,	PUNCT
ap-8348	104	48	2	2	NUM
ap-8348	104	49	,	,	PUNCT
ap-8348	104	50	(	(	PUNCT
ap-8348	104	51	43	43	NUM
ap-8348	104	52	)	)	PUNCT
ap-8348	104	53	where	where	SCONJ
ap-8348	104	54	φn	φn	NOUN
ap-8348	104	55	will	will	AUX
ap-8348	104	56	be	be	AUX
ap-8348	104	57	determined	determine	VERB
ap-8348	104	58	later	later	ADV
ap-8348	104	59	and	and	CCONJ
ap-8348	104	60	u1(t	u1(t	ADP
ap-8348	104	61	)	)	PUNCT
ap-8348	104	62	=	=	SYM
ap-8348	104	63	exp	exp	NOUN
ap-8348	104	64	[	[	PUNCT
ap-8348	104	65	−ig(t	−ig(t	NOUN
ap-8348	104	66	)	)	PUNCT
ap-8348	104	67	2	2	NUM
ap-8348	104	68	x+	x+	SYM
ap-8348	104	69	i	i	PRON
ap-8348	104	70	4	4	X
ap-8348	104	71	[	[	PUNCT
ap-8348	104	72	k2(t	k2(t	PROPN
ap-8348	104	73	)	)	PUNCT
ap-8348	104	74	−	−	PROPN
ap-8348	104	75	g2(t	g2(t	PROPN
ap-8348	104	76	)	)	PUNCT
ap-8348	104	77	+	+	NUM
ap-8348	104	78	4s(t	4s(t	NUM
ap-8348	104	79	)	)	PUNCT
ap-8348	104	80	]	]	PUNCT
ap-8348	105	1	p	p	X
ap-8348	105	2	]	]	PUNCT
ap-8348	105	3	,	,	PUNCT
ap-8348	105	4	(	(	PUNCT
ap-8348	105	5	44	44	NUM
ap-8348	105	6	)	)	PUNCT
ap-8348	105	7	u2(t	u2(t	NOUN
ap-8348	105	8	)	)	PUNCT
ap-8348	105	9	=	=	SYM
ap-8348	105	10	exp	exp	NOUN
ap-8348	105	11	[	[	PUNCT
ap-8348	105	12	i	i	PROPN
ap-8348	105	13	g(t	g(t	PROPN
ap-8348	105	14	)	)	PUNCT
ap-8348	105	15	2	2	NUM
ap-8348	105	16	x−	x−	NOUN
ap-8348	105	17	i	i	PRON
ap-8348	105	18	4	4	X
ap-8348	105	19	[	[	PUNCT
ap-8348	105	20	k2(t	k2(t	PROPN
ap-8348	105	21	)	)	PUNCT
ap-8348	105	22	−	−	PROPN
ap-8348	105	23	g2(t	g2(t	PROPN
ap-8348	105	24	)	)	PUNCT
ap-8348	105	25	+	+	NUM
ap-8348	105	26	4s(t	4s(t	NUM
ap-8348	105	27	)	)	PUNCT
ap-8348	105	28	]	]	PUNCT
ap-8348	106	1	p	p	X
ap-8348	106	2	]	]	PUNCT
ap-8348	106	3	.	.	PUNCT
ap-8348	107	1	(	(	PUNCT
ap-8348	107	2	45	45	NUM
ap-8348	107	3	)	)	PUNCT
ap-8348	107	4	according	accord	VERB
ap-8348	107	5	to	to	ADP
ap-8348	107	6	these	these	DET
ap-8348	107	7	transformations	transformation	NOUN
ap-8348	107	8	,	,	PUNCT
ap-8348	107	9	the	the	DET
ap-8348	107	10	invariants	invariant	NOUN
ap-8348	107	11	ih	ih	PRON
ap-8348	107	12	1	1	NUM
ap-8348	107	13	(	(	PUNCT
ap-8348	107	14	t	t	PROPN
ap-8348	107	15	)	)	PUNCT
ap-8348	107	16	and	and	CCONJ
ap-8348	107	17	ih	ih	PROPN
ap-8348	107	18	2	2	NUM
ap-8348	107	19	(	(	PUNCT
ap-8348	107	20	t	t	NOUN
ap-8348	107	21	)	)	PUNCT
ap-8348	107	22	turn	turn	VERB
ap-8348	107	23	into	into	ADP
ap-8348	107	24	:	:	PUNCT
ap-8348	107	25	i1	i1	PROPN
ap-8348	107	26	=	=	PUNCT
ap-8348	108	1	u†	u†	ADJ
ap-8348	108	2	1	1	NUM
ap-8348	108	3	(	(	PUNCT
ap-8348	108	4	t)ih	t)ih	PROPN
ap-8348	108	5	1	1	NUM
ap-8348	108	6	(	(	PUNCT
ap-8348	108	7	t)u1(t	t)u1(t	PROPN
ap-8348	108	8	)	)	PUNCT
ap-8348	109	1	=	=	SYM
ap-8348	109	2	p2	p2	PROPN
ap-8348	109	3	+	+	CCONJ
ap-8348	109	4	x	x	SYM
ap-8348	109	5	,	,	PUNCT
ap-8348	109	6	(	(	PUNCT
ap-8348	109	7	46	46	NUM
ap-8348	109	8	)	)	PUNCT
ap-8348	109	9	i2	i2	NOUN
ap-8348	109	10	=	=	PUNCT
ap-8348	109	11	u†	u†	ADJ
ap-8348	109	12	2	2	NUM
ap-8348	109	13	(	(	PUNCT
ap-8348	109	14	t)ih	t)ih	PROPN
ap-8348	109	15	2	2	NUM
ap-8348	109	16	(	(	PUNCT
ap-8348	109	17	t)u2(t	t)u2(t	PROPN
ap-8348	109	18	)	)	PUNCT
ap-8348	109	19	=	=	PUNCT
ap-8348	109	20	p2	p2	PROPN
ap-8348	110	1	−	−	NOUN
ap-8348	110	2	x	x	SYM
ap-8348	110	3	,	,	PUNCT
ap-8348	110	4	(	(	PUNCT
ap-8348	110	5	47	47	NUM
ap-8348	110	6	)	)	PUNCT
ap-8348	111	1	and	and	CCONJ
ap-8348	111	2	they	they	PRON
ap-8348	111	3	can	can	AUX
ap-8348	111	4	be	be	AUX
ap-8348	111	5	written	write	VERB
ap-8348	111	6	in	in	ADP
ap-8348	111	7	the	the	DET
ap-8348	111	8	following	follow	VERB
ap-8348	111	9	combined	combined	ADJ
ap-8348	111	10	form	form	NOUN
ap-8348	111	11	:	:	PUNCT
ap-8348	111	12	i	i	NOUN
ap-8348	111	13	=	=	PUNCT
ap-8348	111	14	p2	p2	PROPN
ap-8348	112	1	+	+	X
ap-8348	112	2	|x|	|x|	PROPN
ap-8348	112	3	.	.	PUNCT
ap-8348	113	1	(	(	PUNCT
ap-8348	113	2	48	48	NUM
ap-8348	113	3	)	)	PUNCT
ap-8348	113	4	we	we	PRON
ap-8348	113	5	note	note	VERB
ap-8348	113	6	here	here	ADV
ap-8348	113	7	that	that	SCONJ
ap-8348	113	8	i	i	PRON
ap-8348	113	9	can	can	AUX
ap-8348	113	10	be	be	AUX
ap-8348	113	11	considered	consider	VERB
ap-8348	113	12	as	as	ADP
ap-8348	113	13	the	the	DET
ap-8348	113	14	hamiltonian	hamiltonian	NOUN
ap-8348	113	15	of	of	ADP
ap-8348	113	16	a	a	DET
ap-8348	113	17	particle	particle	NOUN
ap-8348	113	18	of	of	ADP
ap-8348	113	19	mass	mass	ADJ
ap-8348	113	20	m0	m0	NOUN
ap-8348	113	21	=	=	SYM
ap-8348	113	22	1/2	1/2	NUM
ap-8348	113	23	confined	confine	VERB
ap-8348	113	24	in	in	ADP
ap-8348	113	25	the	the	DET
ap-8348	113	26	linear	linear	ADJ
ap-8348	113	27	symmetric	symmetric	ADJ
ap-8348	113	28	potential	potential	NOUN
ap-8348	114	1	well	well	INTJ
ap-8348	114	2	|x|	|x|	PROPN
ap-8348	114	3	.	.	PUNCT
ap-8348	115	1	therefore	therefore	ADV
ap-8348	115	2	,	,	PUNCT
ap-8348	115	3	the	the	DET
ap-8348	115	4	eigenvalue	eigenvalue	ADJ
ap-8348	115	5	equation	equation	NOUN
ap-8348	115	6	of	of	ADP
ap-8348	115	7	the	the	DET
ap-8348	115	8	invariant	invariant	PROPN
ap-8348	115	9	i	i	PRON
ap-8348	115	10	:	:	PUNCT
ap-8348	115	11	[	[	PUNCT
ap-8348	115	12	d2	d2	PROPN
ap-8348	115	13	dx2	dx2	PROPN
ap-8348	115	14	+	+	CCONJ
ap-8348	115	15	(	(	PUNCT
ap-8348	115	16	λn	λn	PROPN
ap-8348	115	17	−	−	PROPN
ap-8348	115	18	|x|	|x|	PROPN
ap-8348	115	19	)	)	PUNCT
ap-8348	115	20	]	]	PUNCT
ap-8348	115	21	φn(x	φn(x	PUNCT
ap-8348	115	22	)	)	PUNCT
ap-8348	115	23	=	=	SYM
ap-8348	115	24	0	0	NUM
ap-8348	115	25	,	,	PUNCT
ap-8348	115	26	(	(	PUNCT
ap-8348	115	27	49	49	NUM
ap-8348	115	28	)	)	PUNCT
ap-8348	115	29	is	be	AUX
ap-8348	115	30	a	a	DET
ap-8348	115	31	well	well	ADV
ap-8348	115	32	-	-	PUNCT
ap-8348	115	33	known	know	VERB
ap-8348	115	34	problem	problem	NOUN
ap-8348	115	35	in	in	ADP
ap-8348	115	36	quantum	quantum	ADJ
ap-8348	115	37	mechanics	mechanic	NOUN
ap-8348	115	38	.	.	PUNCT
ap-8348	116	1	the	the	DET
ap-8348	116	2	bound	bind	VERB
ap-8348	116	3	states	state	NOUN
ap-8348	116	4	φn(x	φn(x	PUNCT
ap-8348	116	5	)	)	PUNCT
ap-8348	116	6	are	be	AUX
ap-8348	116	7	given	give	VERB
ap-8348	116	8	in	in	ADP
ap-8348	116	9	terms	term	NOUN
ap-8348	116	10	of	of	ADP
ap-8348	116	11	the	the	DET
ap-8348	116	12	airy	airy	ADJ
ap-8348	116	13	functions	function	NOUN
ap-8348	116	14	ai	ai	VERB
ap-8348	116	15	and	and	CCONJ
ap-8348	116	16	bi	bi	NOUN
ap-8348	117	1	[	[	X
ap-8348	117	2	47	47	NUM
ap-8348	117	3	,	,	PUNCT
ap-8348	117	4	48	48	NUM
ap-8348	117	5	]	]	SYM
ap-8348	117	6	:	:	PUNCT
ap-8348	117	7	φn(x	φn(x	NUM
ap-8348	117	8	)	)	PUNCT
ap-8348	117	9	=	=	SYM
ap-8348	117	10	nn	nn	X
ap-8348	117	11	ai(|x|	ai(|x|	PROPN
ap-8348	117	12	−	−	PROPN
ap-8348	117	13	λn	λn	NOUN
ap-8348	117	14	)	)	PUNCT
ap-8348	118	1	+	+	NOUN
ap-8348	118	2	n	n	PROPN
ap-8348	118	3	′	′	NUM
ap-8348	118	4	n	n	CCONJ
ap-8348	118	5	bi(|x|	bi(|x|	PROPN
ap-8348	118	6	−	−	PROPN
ap-8348	118	7	λn	λn	NOUN
ap-8348	118	8	)	)	PUNCT
ap-8348	118	9	.	.	PUNCT
ap-8348	119	1	(	(	PUNCT
ap-8348	119	2	50	50	NUM
ap-8348	119	3	)	)	PUNCT
ap-8348	119	4	this	this	DET
ap-8348	119	5	solution	solution	NOUN
ap-8348	119	6	is	be	AUX
ap-8348	119	7	not	not	PART
ap-8348	119	8	relevant	relevant	ADJ
ap-8348	119	9	because	because	SCONJ
ap-8348	119	10	bi(|x|−λn	bi(|x|−λn	NOUN
ap-8348	119	11	)	)	PUNCT
ap-8348	119	12	tends	tend	VERB
ap-8348	119	13	to	to	PART
ap-8348	119	14	infinity	infinity	VERB
ap-8348	119	15	for	for	ADP
ap-8348	119	16	(	(	PUNCT
ap-8348	119	17	|x|	|x|	PROPN
ap-8348	119	18	−	−	PROPN
ap-8348	119	19	λn	λn	NOUN
ap-8348	119	20	)	)	PUNCT
ap-8348	119	21	>	>	X
ap-8348	120	1	0	0	X
ap-8348	120	2	.	.	PUNCT
ap-8348	121	1	thus	thus	ADV
ap-8348	121	2	,	,	PUNCT
ap-8348	121	3	we	we	PRON
ap-8348	121	4	take	take	VERB
ap-8348	121	5	n	n	PRON
ap-8348	121	6	′	′	NUM
ap-8348	122	1	n	n	CCONJ
ap-8348	122	2	=	=	SYM
ap-8348	122	3	0	0	NUM
ap-8348	122	4	and	and	CCONJ
ap-8348	122	5	the	the	DET
ap-8348	122	6	above	above	ADJ
ap-8348	122	7	solution	solution	NOUN
ap-8348	122	8	reduces	reduce	VERB
ap-8348	122	9	to	to	ADP
ap-8348	122	10	:	:	PUNCT
ap-8348	122	11	φn(x	φn(x	PUNCT
ap-8348	122	12	)	)	PUNCT
ap-8348	122	13	=	=	SYM
ap-8348	122	14	nn	nn	X
ap-8348	122	15	ai(|x|	ai(|x|	PROPN
ap-8348	122	16	−	−	PROPN
ap-8348	122	17	λn	λn	NOUN
ap-8348	122	18	)	)	PUNCT
ap-8348	122	19	.	.	PUNCT
ap-8348	123	1	(	(	PUNCT
ap-8348	123	2	51	51	NUM
ap-8348	123	3	)	)	PUNCT
ap-8348	123	4	the	the	DET
ap-8348	123	5	eingenvalues	eingenvalue	NOUN
ap-8348	123	6	λn	λn	NOUN
ap-8348	123	7	are	be	AUX
ap-8348	123	8	determined	determine	VERB
ap-8348	123	9	by	by	ADP
ap-8348	123	10	matching	match	VERB
ap-8348	123	11	the	the	DET
ap-8348	123	12	functions	function	NOUN
ap-8348	123	13	φn(x	φn(x	PUNCT
ap-8348	123	14	)	)	PUNCT
ap-8348	123	15	and	and	CCONJ
ap-8348	123	16	their	their	PRON
ap-8348	123	17	derivatives	derivative	NOUN
ap-8348	123	18	in	in	ADP
ap-8348	123	19	the	the	DET
ap-8348	123	20	two	two	NUM
ap-8348	123	21	regions	region	NOUN
ap-8348	123	22	at	at	ADP
ap-8348	123	23	the	the	DET
ap-8348	123	24	point	point	NOUN
ap-8348	123	25	x	x	PUNCT
ap-8348	123	26	=	=	NOUN
ap-8348	123	27	0	0	NUM
ap-8348	123	28	:	:	PUNCT
ap-8348	123	29	φ(1	φ(1	PROPN
ap-8348	123	30	)	)	PUNCT
ap-8348	123	31	n	n	CCONJ
ap-8348	123	32	(	(	PUNCT
ap-8348	123	33	0	0	NUM
ap-8348	123	34	)	)	PUNCT
ap-8348	123	35	=	=	SYM
ap-8348	123	36	φ(2	φ(2	PROPN
ap-8348	123	37	)	)	PUNCT
ap-8348	123	38	n	n	CCONJ
ap-8348	123	39	(	(	PUNCT
ap-8348	123	40	0	0	NUM
ap-8348	123	41	)	)	PUNCT
ap-8348	123	42	,	,	PUNCT
ap-8348	123	43	(	(	PUNCT
ap-8348	123	44	52	52	NUM
ap-8348	123	45	)	)	PUNCT
ap-8348	123	46	φ	φ	PROPN
ap-8348	123	47	′(1	′(1	PROPN
ap-8348	123	48	)	)	PUNCT
ap-8348	123	49	n	n	CCONJ
ap-8348	123	50	(	(	PUNCT
ap-8348	123	51	0	0	NUM
ap-8348	123	52	)	)	PUNCT
ap-8348	123	53	=	=	PUNCT
ap-8348	123	54	±φ	±φ	NUM
ap-8348	123	55	′(2	′(2	PROPN
ap-8348	123	56	)	)	PUNCT
ap-8348	123	57	n	n	CCONJ
ap-8348	123	58	(	(	PUNCT
ap-8348	123	59	0	0	NUM
ap-8348	123	60	)	)	PUNCT
ap-8348	123	61	,	,	PUNCT
ap-8348	123	62	(	(	PUNCT
ap-8348	123	63	53	53	NUM
ap-8348	123	64	)	)	PUNCT
ap-8348	123	65	from	from	ADP
ap-8348	123	66	which	which	PRON
ap-8348	123	67	there	there	PRON
ap-8348	123	68	are	be	VERB
ap-8348	123	69	two	two	NUM
ap-8348	123	70	possibilities	possibility	NOUN
ap-8348	123	71	for	for	ADP
ap-8348	123	72	λn	λn	NOUN
ap-8348	123	73	and	and	CCONJ
ap-8348	123	74	the	the	DET
ap-8348	123	75	normalisation	normalisation	NOUN
ap-8348	123	76	constant	constant	ADJ
ap-8348	123	77	nn	nn	INTJ
ap-8348	123	78	depending	depend	VERB
ap-8348	123	79	on	on	ADP
ap-8348	123	80	whether	whether	SCONJ
ap-8348	123	81	n	n	PRON
ap-8348	123	82	is	be	AUX
ap-8348	123	83	even	even	ADV
ap-8348	123	84	or	or	CCONJ
ap-8348	123	85	odd	odd	ADJ
ap-8348	123	86	:	:	PUNCT
ap-8348	123	87	•	•	ADP
ap-8348	123	88	if	if	SCONJ
ap-8348	123	89	n	n	PRON
ap-8348	123	90	is	be	AUX
ap-8348	123	91	even	even	ADV
ap-8348	123	92	:	:	PUNCT
ap-8348	123	93	λn	λn	X
ap-8348	123	94	=	=	PUNCT
ap-8348	124	1	−a′	−a′	PROPN
ap-8348	124	2	n	n	PRON
ap-8348	124	3	2	2	NUM
ap-8348	124	4	+1	+1	NOUN
ap-8348	124	5	,	,	PUNCT
ap-8348	124	6	(	(	PUNCT
ap-8348	124	7	54	54	NUM
ap-8348	124	8	)	)	PUNCT
ap-8348	124	9	where	where	SCONJ
ap-8348	124	10	a′	a′	PROPN
ap-8348	124	11	k	k	PROPN
ap-8348	124	12	is	be	AUX
ap-8348	124	13	the	the	DET
ap-8348	124	14	kth	kth	PROPN
ap-8348	124	15	zero	zero	NUM
ap-8348	124	16	of	of	ADP
ap-8348	124	17	the	the	DET
ap-8348	124	18	derivative	derivative	ADJ
ap-8348	124	19	ai′	ai′	NOUN
ap-8348	124	20	of	of	ADP
ap-8348	124	21	the	the	DET
ap-8348	124	22	airy	airy	ADJ
ap-8348	124	23	function	function	NOUN
ap-8348	124	24	,	,	PUNCT
ap-8348	124	25	and	and	CCONJ
ap-8348	124	26	all	all	DET
ap-8348	124	27	values	value	NOUN
ap-8348	124	28	of	of	ADP
ap-8348	124	29	a′	a′	PROPN
ap-8348	124	30	k	k	PROPN
ap-8348	124	31	are	be	AUX
ap-8348	124	32	negative	negative	ADJ
ap-8348	124	33	numbers	number	NOUN
ap-8348	124	34	[	[	X
ap-8348	124	35	49	49	NUM
ap-8348	124	36	]	]	PUNCT
ap-8348	124	37	.	.	PUNCT
ap-8348	125	1	the	the	DET
ap-8348	125	2	normalisation	normalisation	NOUN
ap-8348	125	3	constant	constant	ADJ
ap-8348	125	4	is	be	AUX
ap-8348	125	5	:	:	PUNCT
ap-8348	125	6	nn	nn	PROPN
ap-8348	125	7	=	=	SYM
ap-8348	125	8	1√	1√	PROPN
ap-8348	125	9	−2a′	−2a′	PROPN
ap-8348	125	10	n	n	CCONJ
ap-8348	125	11	2	2	NUM
ap-8348	125	12	+1ai(a′	+1ai(a′	NOUN
ap-8348	125	13	n	n	CCONJ
ap-8348	125	14	2	2	NUM
ap-8348	125	15	+1	+1	NOUN
ap-8348	125	16	)	)	PUNCT
ap-8348	125	17	,	,	PUNCT
ap-8348	125	18	(	(	PUNCT
ap-8348	125	19	55	55	NUM
ap-8348	125	20	)	)	PUNCT
ap-8348	125	21	and	and	CCONJ
ap-8348	125	22	the	the	DET
ap-8348	125	23	corresponding	correspond	VERB
ap-8348	125	24	eigenfunction	eigenfunction	NOUN
ap-8348	125	25	of	of	ADP
ap-8348	125	26	i	i	PRON
ap-8348	125	27	is	be	AUX
ap-8348	125	28	:	:	PUNCT
ap-8348	125	29	φn(x	φn(x	PUNCT
ap-8348	125	30	)	)	PUNCT
ap-8348	125	31	=	=	SYM
ap-8348	125	32	1√	1√	PROPN
ap-8348	125	33	−2a′	−2a′	PROPN
ap-8348	125	34	n	n	CCONJ
ap-8348	125	35	2	2	NUM
ap-8348	125	36	+1ai(a′	+1ai(a′	NOUN
ap-8348	125	37	n	n	CCONJ
ap-8348	125	38	2	2	NUM
ap-8348	125	39	+1	+1	NOUN
ap-8348	125	40	)	)	PUNCT
ap-8348	125	41	ai(|x|	ai(|x|	X
ap-8348	126	1	+	+	CCONJ
ap-8348	126	2	a′	a′	PROPN
ap-8348	126	3	n	n	CCONJ
ap-8348	126	4	2	2	NUM
ap-8348	126	5	+1	+1	NOUN
ap-8348	126	6	)	)	PUNCT
ap-8348	126	7	,	,	PUNCT
ap-8348	126	8	(	(	PUNCT
ap-8348	126	9	56	56	NUM
ap-8348	126	10	)	)	PUNCT
ap-8348	126	11	•	•	NOUN
ap-8348	126	12	if	if	SCONJ
ap-8348	126	13	n	n	NOUN
ap-8348	126	14	is	be	AUX
ap-8348	126	15	odd	odd	ADJ
ap-8348	126	16	:	:	PUNCT
ap-8348	126	17	λn	λn	PROPN
ap-8348	126	18	=	=	SYM
ap-8348	126	19	−an+1	−an+1	PROPN
ap-8348	126	20	2	2	NUM
ap-8348	126	21	,	,	PUNCT
ap-8348	126	22	(	(	PUNCT
ap-8348	126	23	57	57	NUM
ap-8348	126	24	)	)	PUNCT
ap-8348	126	25	where	where	SCONJ
ap-8348	126	26	ak	ak	PROPN
ap-8348	126	27	is	be	AUX
ap-8348	126	28	the	the	DET
ap-8348	126	29	kth	kth	PROPN
ap-8348	126	30	zero	zero	NUM
ap-8348	126	31	of	of	ADP
ap-8348	126	32	the	the	DET
ap-8348	126	33	airy	airy	ADJ
ap-8348	126	34	function	function	NOUN
ap-8348	126	35	ai	ai	VERB
ap-8348	126	36	,	,	PUNCT
ap-8348	126	37	and	and	CCONJ
ap-8348	126	38	all	all	DET
ap-8348	126	39	values	value	NOUN
ap-8348	126	40	of	of	ADP
ap-8348	126	41	ak	ak	PROPN
ap-8348	126	42	are	be	AUX
ap-8348	126	43	negative	negative	ADJ
ap-8348	126	44	numbers	number	NOUN
ap-8348	126	45	[	[	X
ap-8348	126	46	49	49	NUM
ap-8348	126	47	]	]	PUNCT
ap-8348	126	48	.	.	PUNCT
ap-8348	127	1	the	the	DET
ap-8348	127	2	normalisation	normalisation	NOUN
ap-8348	127	3	constant	constant	ADJ
ap-8348	127	4	is	be	AUX
ap-8348	127	5	:	:	PUNCT
ap-8348	127	6	nn	nn	PROPN
ap-8348	127	7	=	=	PROPN
ap-8348	127	8	1√	1√	PROPN
ap-8348	127	9	2ai′(an+1	2ai′(an+1	NUM
ap-8348	127	10	2	2	NUM
ap-8348	127	11	)	)	PUNCT
ap-8348	127	12	,	,	PUNCT
ap-8348	127	13	(	(	PUNCT
ap-8348	127	14	58	58	NUM
ap-8348	127	15	)	)	PUNCT
ap-8348	127	16	and	and	CCONJ
ap-8348	127	17	the	the	DET
ap-8348	127	18	corresponding	correspond	VERB
ap-8348	127	19	eigenfunction	eigenfunction	NOUN
ap-8348	127	20	of	of	ADP
ap-8348	127	21	i	i	PRON
ap-8348	127	22	is	be	AUX
ap-8348	127	23	:	:	PUNCT
ap-8348	127	24	φn(x	φn(x	PUNCT
ap-8348	127	25	)	)	PUNCT
ap-8348	127	26	=	=	SYM
ap-8348	127	27	sgn(x	sgn(x	X
ap-8348	127	28	)	)	PUNCT
ap-8348	127	29	1√	1√	PROPN
ap-8348	127	30	2ai′(an+1	2ai′(an+1	NUM
ap-8348	127	31	2	2	NUM
ap-8348	127	32	)	)	PUNCT
ap-8348	127	33	ai(|x|+an+1	ai(|x|+an+1	NOUN
ap-8348	127	34	2	2	NUM
ap-8348	127	35	)	)	PUNCT
ap-8348	127	36	.	.	PUNCT
ap-8348	128	1	(	(	PUNCT
ap-8348	128	2	59	59	NUM
ap-8348	128	3	)	)	PUNCT
ap-8348	128	4	the	the	DET
ap-8348	128	5	eigenfunctions	eigenfunction	NOUN
ap-8348	128	6	of	of	ADP
ap-8348	128	7	the	the	DET
ap-8348	128	8	hermitian	hermitian	ADJ
ap-8348	128	9	invariants	invariant	NOUN
ap-8348	128	10	ih	ih	PRON
ap-8348	128	11	j	j	PROPN
ap-8348	128	12	(	(	PUNCT
ap-8348	128	13	t	t	PROPN
ap-8348	128	14	)	)	PUNCT
ap-8348	128	15	are	be	AUX
ap-8348	128	16	written	write	VERB
ap-8348	128	17	for	for	ADP
ap-8348	128	18	each	each	DET
ap-8348	128	19	region	region	NOUN
ap-8348	128	20	as	as	ADP
ap-8348	128	21	:	:	PUNCT
ap-8348	128	22	|ϕn	|ϕn	NUM
ap-8348	128	23	,	,	PUNCT
ap-8348	128	24	j(t)⟩	j(t)⟩	NOUN
ap-8348	128	25	=	=	SYM
ap-8348	128	26	uj(t	uj(t	ADJ
ap-8348	128	27	)	)	PUNCT
ap-8348	128	28	|φn⟩	|φn⟩	NOUN
ap-8348	128	29	,	,	PUNCT
ap-8348	128	30	(	(	PUNCT
ap-8348	128	31	60	60	NUM
ap-8348	128	32	)	)	PUNCT
ap-8348	128	33	then	then	ADV
ap-8348	128	34	,	,	PUNCT
ap-8348	128	35	the	the	DET
ap-8348	128	36	eigenfunctions	eigenfunction	NOUN
ap-8348	128	37	of	of	ADP
ap-8348	128	38	the	the	DET
ap-8348	128	39	pseudo	pseudo	NOUN
ap-8348	128	40	-	-	ADJ
ap-8348	128	41	hermitian	hermitian	ADJ
ap-8348	128	42	invariants	invariant	NOUN
ap-8348	128	43	iph	iph	VERB
ap-8348	128	44	j	j	PROPN
ap-8348	128	45	(	(	PUNCT
ap-8348	128	46	t	t	PROPN
ap-8348	128	47	)	)	PUNCT
ap-8348	128	48	are	be	AUX
ap-8348	128	49	given	give	VERB
ap-8348	128	50	by	by	ADP
ap-8348	128	51	:	:	PUNCT
ap-8348	128	52	|ψn	|ψn	NOUN
ap-8348	128	53	,	,	PUNCT
ap-8348	128	54	j(t)⟩	j(t)⟩	NOUN
ap-8348	128	55	=	=	SYM
ap-8348	128	56	ρ−1	ρ−1	PROPN
ap-8348	128	57	j	j	PROPN
ap-8348	128	58	(	(	PUNCT
ap-8348	128	59	t)uj(t	t)uj(t	PROPN
ap-8348	128	60	)	)	PUNCT
ap-8348	128	61	|φn⟩	|φn⟩	NOUN
ap-8348	128	62	,	,	PUNCT
ap-8348	128	63	(	(	PUNCT
ap-8348	128	64	61	61	NUM
ap-8348	128	65	)	)	SYM
ap-8348	128	66	135	135	NUM
ap-8348	128	67	boubakeur	boubakeur	NOUN
ap-8348	128	68	khantoul	khantoul	NOUN
ap-8348	128	69	,	,	PUNCT
ap-8348	128	70	abdelhafid	abdelhafid	ADV
ap-8348	128	71	bounames	bouname	NOUN
ap-8348	128	72	acta	acta	PROPN
ap-8348	128	73	polytechnica	polytechnica	PROPN
ap-8348	128	74	thus	thus	ADV
ap-8348	128	75	,	,	PUNCT
ap-8348	128	76	the	the	DET
ap-8348	128	77	solutions	solution	NOUN
ap-8348	128	78	of	of	ADP
ap-8348	128	79	the	the	DET
ap-8348	128	80	time	time	NOUN
ap-8348	128	81	-	-	PUNCT
ap-8348	128	82	dependent	dependent	ADJ
ap-8348	128	83	schrödinger	schrödinger	ADJ
ap-8348	128	84	equation	equation	NOUN
ap-8348	128	85	(	(	PUNCT
ap-8348	128	86	20	20	NUM
ap-8348	128	87	)	)	PUNCT
ap-8348	128	88	take	take	VERB
ap-8348	128	89	the	the	DET
ap-8348	128	90	form	form	NOUN
ap-8348	128	91	:	:	PUNCT
ap-8348	128	92	|ψn	|ψn	NUM
ap-8348	128	93	,	,	PUNCT
ap-8348	128	94	j(t)⟩	j(t)⟩	NOUN
ap-8348	128	95	=	=	SYM
ap-8348	128	96	eiϵj	eiϵj	ADJ
ap-8348	128	97	n(t	n(t	PROPN
ap-8348	128	98	)	)	PUNCT
ap-8348	128	99	|ψn	|ψn	ADP
ap-8348	128	100	,	,	PUNCT
ap-8348	128	101	j(t)⟩	j(t)⟩	NOUN
ap-8348	128	102	,	,	PUNCT
ap-8348	128	103	(	(	PUNCT
ap-8348	128	104	62	62	NUM
ap-8348	128	105	)	)	PUNCT
ap-8348	128	106	where	where	SCONJ
ap-8348	128	107	ϵjn(t	ϵjn(t	NOUN
ap-8348	128	108	)	)	PUNCT
ap-8348	128	109	is	be	AUX
ap-8348	128	110	the	the	DET
ap-8348	128	111	phase	phase	NOUN
ap-8348	128	112	(	(	PUNCT
ap-8348	128	113	ϵ1n(t	ϵ1n(t	PROPN
ap-8348	128	114	)	)	PUNCT
ap-8348	128	115	for	for	ADP
ap-8348	128	116	x	x	X
ap-8348	128	117	≥	≥	NOUN
ap-8348	128	118	0	0	NUM
ap-8348	128	119	and	and	CCONJ
ap-8348	128	120	ϵ2n(t	ϵ2n(t	NUM
ap-8348	128	121	)	)	PUNCT
ap-8348	128	122	for	for	ADP
ap-8348	128	123	x	x	SYM
ap-8348	128	124	≤	≤	NUM
ap-8348	128	125	0	0	NUM
ap-8348	128	126	)	)	PUNCT
ap-8348	128	127	,	,	PUNCT
ap-8348	128	128	which	which	PRON
ap-8348	128	129	is	be	AUX
ap-8348	128	130	obtained	obtain	VERB
ap-8348	128	131	from	from	ADP
ap-8348	128	132	the	the	DET
ap-8348	128	133	following	follow	VERB
ap-8348	128	134	relation	relation	NOUN
ap-8348	128	135	:	:	PUNCT
ap-8348	128	136	ϵ̇jn(t	ϵ̇jn(t	PROPN
ap-8348	128	137	)	)	PUNCT
ap-8348	129	1	=	=	PUNCT
ap-8348	129	2	⟨ψn	⟨ψn	PROPN
ap-8348	129	3	,	,	PUNCT
ap-8348	129	4	j(t)|	j(t)|	ADJ
ap-8348	129	5	ηj(t	ηj(t	PUNCT
ap-8348	129	6	)	)	PUNCT
ap-8348	130	1	[	[	PUNCT
ap-8348	130	2	i	i	PRON
ap-8348	130	3	∂	∂	NOUN
ap-8348	130	4	∂t	∂t	PROPN
ap-8348	130	5	−h(t	−h(t	PROPN
ap-8348	130	6	)	)	PUNCT
ap-8348	130	7	]	]	PUNCT
ap-8348	130	8	|ψn	|ψn	X
ap-8348	130	9	,	,	PUNCT
ap-8348	130	10	j(t)⟩	j(t)⟩	NOUN
ap-8348	130	11	=	=	SYM
ap-8348	130	12	⟨ϕn	⟨ϕn	PROPN
ap-8348	130	13	,	,	PUNCT
ap-8348	130	14	j(t)|	j(t)|	ADJ
ap-8348	130	15	iρj(t)ρ̇−1	iρj(t)ρ̇−1	ADJ
ap-8348	130	16	j	j	PROPN
ap-8348	130	17	(	(	PUNCT
ap-8348	130	18	t	t	PROPN
ap-8348	130	19	)	)	PUNCT
ap-8348	130	20	|ϕn	|ϕn	PROPN
ap-8348	130	21	,	,	PUNCT
ap-8348	130	22	j(t)⟩	j(t)⟩	NOUN
ap-8348	130	23	−	−	PROPN
ap-8348	130	24	⟨ϕn	⟨ϕn	PROPN
ap-8348	130	25	,	,	PUNCT
ap-8348	130	26	j(t)|	j(t)|	ADJ
ap-8348	130	27	ρj(t)h(t)ρ−1	ρj(t)h(t)ρ−1	PROPN
ap-8348	130	28	j	j	PROPN
ap-8348	130	29	(	(	PUNCT
ap-8348	130	30	t	t	PROPN
ap-8348	130	31	)	)	PUNCT
ap-8348	130	32	|ϕn	|ϕn	PROPN
ap-8348	130	33	,	,	PUNCT
ap-8348	130	34	j(t)⟩	j(t)⟩	NOUN
ap-8348	130	35	+	+	X
ap-8348	130	36	⟨ϕn	⟨ϕn	VERB
ap-8348	130	37	,	,	PUNCT
ap-8348	130	38	j(t)|	j(t)|	VERB
ap-8348	130	39	i	i	PRON
ap-8348	130	40	∂	∂	ADV
ap-8348	130	41	∂t	∂t	PROPN
ap-8348	130	42	|ϕn	|ϕn	PROPN
ap-8348	130	43	,	,	PUNCT
ap-8348	130	44	j(t)⟩	j(t)⟩	NOUN
ap-8348	130	45	=	=	SYM
ap-8348	130	46	θ(t	θ(t	PROPN
ap-8348	130	47	)	)	PUNCT
ap-8348	130	48	−	−	PROPN
ap-8348	131	1	⟨ϕn	⟨ϕn	PROPN
ap-8348	131	2	,	,	PUNCT
ap-8348	131	3	j(t)|	j(t)|	ADJ
ap-8348	131	4	p2	p2	PROPN
ap-8348	131	5	2m(t	2m(t	NUM
ap-8348	131	6	)	)	PUNCT
ap-8348	131	7	|ϕn	|ϕn	PROPN
ap-8348	131	8	,	,	PUNCT
ap-8348	131	9	j(t)⟩	j(t)⟩	NOUN
ap-8348	131	10	+	+	X
ap-8348	131	11	⟨ϕn	⟨ϕn	VERB
ap-8348	131	12	,	,	PUNCT
ap-8348	131	13	j(t)|	j(t)|	VERB
ap-8348	131	14	i	i	PRON
ap-8348	131	15	∂	∂	ADV
ap-8348	131	16	∂t	∂t	PROPN
ap-8348	131	17	|ϕn	|ϕn	PROPN
ap-8348	131	18	,	,	PUNCT
ap-8348	131	19	j(t)⟩	j(t)⟩	NOUN
ap-8348	131	20	,	,	PUNCT
ap-8348	131	21	(	(	PUNCT
ap-8348	131	22	63	63	NUM
ap-8348	131	23	)	)	PUNCT
ap-8348	131	24	where	where	SCONJ
ap-8348	131	25	θ(t	θ(t	VERB
ap-8348	131	26	)	)	PUNCT
ap-8348	131	27	=	=	NOUN
ap-8348	131	28	1	1	NUM
ap-8348	131	29	2f(t	2f(t	NUM
ap-8348	131	30	)	)	PUNCT
ap-8348	131	31	[	[	PUNCT
ap-8348	131	32	k(t	k(t	NOUN
ap-8348	131	33	)	)	PUNCT
ap-8348	131	34	2	2	NUM
ap-8348	131	35	g(t	g(t	PROPN
ap-8348	131	36	)	)	PUNCT
ap-8348	131	37	−	−	PROPN
ap-8348	131	38	w(t	w(t	PROPN
ap-8348	131	39	)	)	PUNCT
ap-8348	131	40	]	]	PUNCT
ap-8348	131	41	.	.	PUNCT
ap-8348	132	1	(	(	PUNCT
ap-8348	132	2	64	64	NUM
ap-8348	132	3	)	)	PUNCT
ap-8348	132	4	using	use	VERB
ap-8348	132	5	the	the	DET
ap-8348	132	6	unitary	unitary	ADJ
ap-8348	132	7	transformations	transformation	NOUN
ap-8348	132	8	uj(t	uj(t	PUNCT
ap-8348	132	9	)	)	PUNCT
ap-8348	132	10	,	,	PUNCT
ap-8348	132	11	we	we	PRON
ap-8348	132	12	found	find	VERB
ap-8348	132	13	:	:	PUNCT
ap-8348	132	14	ϵ̇jn(t	ϵ̇jn(t	PROPN
ap-8348	132	15	)	)	PUNCT
ap-8348	132	16	=	=	SYM
ap-8348	132	17	χj(t	χj(t	X
ap-8348	132	18	)	)	PUNCT
ap-8348	132	19	−	−	PROPN
ap-8348	132	20	1	1	NUM
ap-8348	132	21	2m(t	2m(t	NUM
ap-8348	132	22	)	)	PUNCT
ap-8348	132	23	⟨φn(t)|	⟨φn(t)|	NOUN
ap-8348	132	24	(	(	PUNCT
ap-8348	132	25	p2	p2	PROPN
ap-8348	132	26	±	±	NUM
ap-8348	132	27	x	x	NOUN
ap-8348	132	28	)	)	PUNCT
ap-8348	132	29	|φn(t)⟩	|φn(t)⟩	NUM
ap-8348	132	30	,	,	PUNCT
ap-8348	132	31	(	(	PUNCT
ap-8348	132	32	65	65	NUM
ap-8348	132	33	)	)	PUNCT
ap-8348	132	34	where	where	SCONJ
ap-8348	132	35	χ1(t	χ1(t	VERB
ap-8348	132	36	)	)	PUNCT
ap-8348	132	37	=	=	SYM
ap-8348	132	38	θ(t)−	θ(t)−	PROPN
ap-8348	132	39	1	1	NUM
ap-8348	132	40	16m(t	16m(t	NUM
ap-8348	132	41	)	)	PUNCT
ap-8348	132	42	[	[	PUNCT
ap-8348	132	43	k2(t	k2(t	X
ap-8348	132	44	)	)	PUNCT
ap-8348	132	45	+	+	NOUN
ap-8348	132	46	3g2(t	3g2(t	NUM
ap-8348	132	47	)	)	PUNCT
ap-8348	133	1	+	+	NUM
ap-8348	133	2	4s(t	4s(t	NUM
ap-8348	133	3	)	)	PUNCT
ap-8348	134	1	]	]	PUNCT
ap-8348	134	2	,	,	PUNCT
ap-8348	134	3	(	(	PUNCT
ap-8348	134	4	66	66	NUM
ap-8348	134	5	)	)	PUNCT
ap-8348	134	6	χ2(t	χ2(t	PRON
ap-8348	134	7	)	)	PUNCT
ap-8348	134	8	=	=	PUNCT
ap-8348	134	9	θ(t	θ(t	PROPN
ap-8348	134	10	)	)	PUNCT
ap-8348	134	11	+	+	CCONJ
ap-8348	134	12	1	1	NUM
ap-8348	134	13	16m(t	16m(t	NUM
ap-8348	134	14	)	)	PUNCT
ap-8348	134	15	[	[	PUNCT
ap-8348	134	16	k2(t	k2(t	PROPN
ap-8348	134	17	)	)	PUNCT
ap-8348	134	18	−	−	PROPN
ap-8348	134	19	g2(t	g2(t	PROPN
ap-8348	134	20	)	)	PUNCT
ap-8348	134	21	+	+	NUM
ap-8348	134	22	4s(t	4s(t	NUM
ap-8348	134	23	)	)	PUNCT
ap-8348	134	24	]	]	PUNCT
ap-8348	134	25	.	.	PUNCT
ap-8348	135	1	(	(	PUNCT
ap-8348	135	2	67	67	NUM
ap-8348	135	3	)	)	PUNCT
ap-8348	135	4	from	from	ADP
ap-8348	135	5	the	the	DET
ap-8348	135	6	eigenvalue	eigenvalue	ADJ
ap-8348	135	7	equation	equation	NOUN
ap-8348	135	8	of	of	ADP
ap-8348	135	9	the	the	DET
ap-8348	135	10	invariant	invariant	PROPN
ap-8348	135	11	i	i	PRON
ap-8348	135	12	,	,	PUNCT
ap-8348	135	13	we	we	PRON
ap-8348	135	14	have	have	VERB
ap-8348	135	15	:	:	PUNCT
ap-8348	135	16	(	(	PUNCT
ap-8348	135	17	p2	p2	PROPN
ap-8348	135	18	±	±	NUM
ap-8348	135	19	x	x	NOUN
ap-8348	135	20	)	)	PUNCT
ap-8348	136	1	|φn(t)⟩	|φn(t)⟩	PRON
ap-8348	136	2	=	=	NOUN
ap-8348	136	3	λn	λn	NOUN
ap-8348	136	4	|φn(t)⟩	|φn(t)⟩	NUM
ap-8348	136	5	,	,	PUNCT
ap-8348	136	6	(	(	PUNCT
ap-8348	136	7	68	68	NUM
ap-8348	136	8	)	)	PUNCT
ap-8348	136	9	then	then	ADV
ap-8348	136	10	,	,	PUNCT
ap-8348	136	11	the	the	DET
ap-8348	136	12	phases	phase	NOUN
ap-8348	136	13	ϵjn(t	ϵjn(t	PRON
ap-8348	136	14	)	)	PUNCT
ap-8348	136	15	take	take	VERB
ap-8348	136	16	the	the	DET
ap-8348	136	17	form	form	NOUN
ap-8348	136	18	:	:	PUNCT
ap-8348	136	19	ϵjn(t	ϵjn(t	NOUN
ap-8348	136	20	)	)	PUNCT
ap-8348	137	1	=	=	SYM
ap-8348	137	2	∫	∫	PROPN
ap-8348	137	3	(	(	PUNCT
ap-8348	137	4	χj(t	χj(t	PROPN
ap-8348	137	5	)	)	PUNCT
ap-8348	137	6	−	−	PROPN
ap-8348	137	7	λn	λn	PROPN
ap-8348	137	8	2m(t	2m(t	NUM
ap-8348	137	9	)	)	PUNCT
ap-8348	137	10	)	)	PUNCT
ap-8348	138	1	dt	dt	NOUN
ap-8348	138	2	,	,	PUNCT
ap-8348	138	3	(	(	PUNCT
ap-8348	138	4	69	69	NUM
ap-8348	138	5	)	)	PUNCT
ap-8348	138	6	and	and	CCONJ
ap-8348	138	7	the	the	DET
ap-8348	138	8	solution	solution	NOUN
ap-8348	138	9	of	of	ADP
ap-8348	138	10	the	the	DET
ap-8348	138	11	td	td	NOUN
ap-8348	138	12	schrödinger	schrödinger	ADJ
ap-8348	138	13	equation	equation	NOUN
ap-8348	138	14	(	(	PUNCT
ap-8348	138	15	20	20	NUM
ap-8348	138	16	)	)	PUNCT
ap-8348	138	17	is	be	AUX
ap-8348	138	18	given	give	VERB
ap-8348	138	19	by	by	ADP
ap-8348	138	20	:	:	PUNCT
ap-8348	138	21	|ψn	|ψn	NOUN
ap-8348	138	22	,	,	PUNCT
ap-8348	138	23	j(t)⟩	j(t)⟩	NOUN
ap-8348	138	24	=	=	SYM
ap-8348	138	25	exp	exp	NOUN
ap-8348	138	26	[	[	PUNCT
ap-8348	138	27	iϵjn(t	iϵjn(t	PROPN
ap-8348	138	28	)	)	PUNCT
ap-8348	138	29	]	]	PUNCT
ap-8348	138	30	ρj(t)−1	ρj(t)−1	PUNCT
ap-8348	138	31	|ϕn	|ϕn	X
ap-8348	138	32	,	,	PUNCT
ap-8348	138	33	j(t)⟩	j(t)⟩	NOUN
ap-8348	138	34	.	.	PUNCT
ap-8348	139	1	(	(	PUNCT
ap-8348	139	2	70	70	NUM
ap-8348	139	3	)	)	PUNCT
ap-8348	139	4	in	in	ADP
ap-8348	139	5	position	position	NOUN
ap-8348	139	6	representation	representation	NOUN
ap-8348	139	7	we	we	PRON
ap-8348	139	8	have	have	VERB
ap-8348	139	9	:	:	PUNCT
ap-8348	139	10	〈	〈	PROPN
ap-8348	139	11	x	x	PUNCT
ap-8348	139	12	∣∣ρ−1	∣∣ρ−1	PROPN
ap-8348	139	13	j	j	PROPN
ap-8348	139	14	(	(	PUNCT
ap-8348	139	15	t	t	PROPN
ap-8348	139	16	)	)	PUNCT
ap-8348	139	17	∣∣ϕj(t	∣∣ϕj(t	PROPN
ap-8348	139	18	)	)	PUNCT
ap-8348	139	19	〉	〉	NOUN
ap-8348	139	20	=	=	SYM
ap-8348	139	21	exp	exp	NOUN
ap-8348	139	22	[	[	NOUN
ap-8348	139	23	iζ(t	iζ(t	NOUN
ap-8348	139	24	)	)	PUNCT
ap-8348	139	25	]	]	PUNCT
ap-8348	139	26	exp	exp	NOUN
ap-8348	139	27	[	[	PUNCT
ap-8348	139	28	±k(t	±k(t	NOUN
ap-8348	139	29	)	)	PUNCT
ap-8348	139	30	2	2	NUM
ap-8348	139	31	x	x	SYM
ap-8348	139	32	]	]	X
ap-8348	139	33	×	×	NOUN
ap-8348	139	34	ϕj(x±	ϕj(x±	SYM
ap-8348	139	35	i(g(t)k(t	i(g(t)k(t	NOUN
ap-8348	139	36	)	)	PUNCT
ap-8348	139	37	2	2	NUM
ap-8348	139	38	−	−	PROPN
ap-8348	139	39	w(t	w(t	PROPN
ap-8348	139	40	)	)	PUNCT
ap-8348	139	41	)	)	PUNCT
ap-8348	139	42	,	,	PUNCT
ap-8348	139	43	t	t	PROPN
ap-8348	139	44	)	)	PUNCT
ap-8348	139	45	,	,	PUNCT
ap-8348	139	46	(	(	PUNCT
ap-8348	139	47	71	71	NUM
ap-8348	139	48	)	)	PUNCT
ap-8348	139	49	where	where	SCONJ
ap-8348	139	50	(	(	PUNCT
ap-8348	139	51	+	+	NOUN
ap-8348	139	52	)	)	PUNCT
ap-8348	139	53	is	be	AUX
ap-8348	139	54	for	for	ADP
ap-8348	139	55	the	the	DET
ap-8348	139	56	positive	positive	ADJ
ap-8348	139	57	region	region	NOUN
ap-8348	139	58	while	while	SCONJ
ap-8348	139	59	(	(	PUNCT
ap-8348	139	60	−	−	NOUN
ap-8348	139	61	)	)	PUNCT
ap-8348	139	62	is	be	AUX
ap-8348	139	63	for	for	ADP
ap-8348	139	64	the	the	DET
ap-8348	139	65	negative	negative	ADJ
ap-8348	139	66	region	region	NOUN
ap-8348	139	67	,	,	PUNCT
ap-8348	139	68	and	and	CCONJ
ap-8348	139	69	ζ(t	ζ(t	PROPN
ap-8348	139	70	)	)	PUNCT
ap-8348	139	71	=	=	PRON
ap-8348	140	1	−k	−k	ADJ
ap-8348	140	2	4	4	NUM
ap-8348	140	3	(	(	PUNCT
ap-8348	140	4	g(t)k(t	g(t)k(t	NOUN
ap-8348	140	5	)	)	PUNCT
ap-8348	140	6	2	2	NUM
ap-8348	140	7	−	−	NOUN
ap-8348	140	8	w(t	w(t	PROPN
ap-8348	140	9	)	)	PUNCT
ap-8348	140	10	)	)	PUNCT
ap-8348	140	11	.	.	PUNCT
ap-8348	141	1	(	(	PUNCT
ap-8348	141	2	72	72	NUM
ap-8348	141	3	)	)	PUNCT
ap-8348	141	4	then	then	ADV
ap-8348	141	5	,	,	PUNCT
ap-8348	141	6	the	the	DET
ap-8348	141	7	solution	solution	NOUN
ap-8348	141	8	of	of	ADP
ap-8348	141	9	the	the	DET
ap-8348	141	10	schrödinger	schrödinger	ADJ
ap-8348	141	11	equation	equation	NOUN
ap-8348	141	12	for	for	ADP
ap-8348	141	13	each	each	DET
ap-8348	141	14	region	region	NOUN
ap-8348	141	15	(	(	PUNCT
ap-8348	141	16	70	70	NUM
ap-8348	141	17	)	)	PUNCT
ap-8348	141	18	can	can	AUX
ap-8348	141	19	be	be	AUX
ap-8348	141	20	written	write	VERB
ap-8348	141	21	as	as	ADP
ap-8348	141	22	:	:	PUNCT
ap-8348	141	23	ψn	ψn	NUM
ap-8348	141	24	,	,	PUNCT
ap-8348	141	25	j(x	j(x	PROPN
ap-8348	141	26	,	,	PUNCT
ap-8348	141	27	t	t	PROPN
ap-8348	141	28	)	)	PUNCT
ap-8348	141	29	=	=	SYM
ap-8348	141	30	exp	exp	NOUN
ap-8348	141	31	[	[	PUNCT
ap-8348	141	32	i(ϵjn(t	i(ϵjn(t	NOUN
ap-8348	141	33	)	)	PUNCT
ap-8348	141	34	+	+	CCONJ
ap-8348	141	35	ζ(t	ζ(t	NOUN
ap-8348	141	36	)	)	PUNCT
ap-8348	141	37	)	)	PUNCT
ap-8348	141	38	]	]	PUNCT
ap-8348	142	1	exp	exp	NOUN
ap-8348	142	2	[	[	PUNCT
ap-8348	142	3	±k(t	±k(t	NOUN
ap-8348	142	4	)	)	PUNCT
ap-8348	142	5	2	2	NUM
ap-8348	142	6	x	x	SYM
ap-8348	142	7	]	]	X
ap-8348	142	8	×	×	X
ap-8348	142	9	ϕn	ϕn	INTJ
ap-8348	142	10	,	,	PUNCT
ap-8348	142	11	j(x±	j(x±	PROPN
ap-8348	142	12	i(g(t)k(t	i(g(t)k(t	NOUN
ap-8348	142	13	)	)	PUNCT
ap-8348	142	14	2	2	NUM
ap-8348	142	15	−	−	PROPN
ap-8348	142	16	w(t	w(t	PROPN
ap-8348	142	17	)	)	PUNCT
ap-8348	142	18	)	)	PUNCT
ap-8348	142	19	,	,	PUNCT
ap-8348	142	20	t	t	PROPN
ap-8348	142	21	)	)	PUNCT
ap-8348	142	22	,	,	PUNCT
ap-8348	142	23	(	(	PUNCT
ap-8348	142	24	73	73	NUM
ap-8348	142	25	)	)	PUNCT
ap-8348	142	26	and	and	CCONJ
ap-8348	142	27	the	the	DET
ap-8348	142	28	general	general	ADJ
ap-8348	142	29	solution	solution	NOUN
ap-8348	142	30	of	of	ADP
ap-8348	142	31	the	the	DET
ap-8348	142	32	schrödinger	schrödinger	ADJ
ap-8348	142	33	equation	equation	NOUN
ap-8348	142	34	(	(	PUNCT
ap-8348	142	35	20	20	NUM
ap-8348	142	36	)	)	PUNCT
ap-8348	142	37	is	be	AUX
ap-8348	142	38	given	give	VERB
ap-8348	142	39	by	by	ADP
ap-8348	142	40	:	:	PUNCT
ap-8348	142	41	ψ(x	ψ(x	PROPN
ap-8348	142	42	,	,	PUNCT
ap-8348	142	43	t	t	PROPN
ap-8348	142	44	)	)	PUNCT
ap-8348	142	45	=	=	PRON
ap-8348	142	46	{	{	PUNCT
ap-8348	142	47	ψn,1(x	ψn,1(x	NOUN
ap-8348	142	48	,	,	PUNCT
ap-8348	142	49	t	t	PROPN
ap-8348	142	50	)	)	PUNCT
ap-8348	142	51	for	for	ADP
ap-8348	142	52	x	x	X
ap-8348	142	53	≥	≥	NOUN
ap-8348	142	54	0	0	NUM
ap-8348	142	55	,	,	PUNCT
ap-8348	142	56	ψn,2(x	ψn,2(x	PROPN
ap-8348	142	57	,	,	PUNCT
ap-8348	142	58	t	t	PROPN
ap-8348	142	59	)	)	PUNCT
ap-8348	142	60	for	for	ADP
ap-8348	142	61	x	x	SYM
ap-8348	142	62	≤	≤	NOUN
ap-8348	142	63	0	0	NUM
ap-8348	142	64	.	.	PUNCT
ap-8348	143	1	(	(	PUNCT
ap-8348	143	2	74	74	NUM
ap-8348	143	3	)	)	PUNCT
ap-8348	143	4	according	accord	VERB
ap-8348	143	5	to	to	ADP
ap-8348	143	6	the	the	DET
ap-8348	143	7	equations	equation	NOUN
ap-8348	143	8	(	(	PUNCT
ap-8348	143	9	51	51	NUM
ap-8348	143	10	)	)	PUNCT
ap-8348	143	11	,	,	PUNCT
ap-8348	143	12	(	(	PUNCT
ap-8348	143	13	60	60	NUM
ap-8348	143	14	)	)	PUNCT
ap-8348	143	15	,	,	PUNCT
ap-8348	143	16	(	(	PUNCT
ap-8348	143	17	61	61	NUM
ap-8348	143	18	)	)	PUNCT
ap-8348	143	19	and	and	CCONJ
ap-8348	143	20	(	(	PUNCT
ap-8348	143	21	62	62	NUM
ap-8348	143	22	)	)	PUNCT
ap-8348	143	23	,	,	PUNCT
ap-8348	143	24	the	the	DET
ap-8348	143	25	probability	probability	NOUN
ap-8348	143	26	density	density	NOUN
ap-8348	143	27	function	function	NOUN
ap-8348	143	28	is	be	AUX
ap-8348	143	29	given	give	VERB
ap-8348	143	30	by	by	ADP
ap-8348	143	31	:	:	PUNCT
ap-8348	143	32	|ρ1(t)ψn,1|2	|ρ1(t)ψn,1|2	X
ap-8348	143	33	+	+	X
ap-8348	143	34	|ρ2(t)ψn,2|2	|ρ2(t)ψn,2|2	NOUN
ap-8348	143	35	=	=	NOUN
ap-8348	143	36	=	=	PUNCT
ap-8348	144	1	|ϕn,1|2	|ϕn,1|2	X
ap-8348	144	2	+	+	NUM
ap-8348	144	3	|ϕn,2|2	|ϕn,2|2	ADJ
ap-8348	144	4	=	=	SYM
ap-8348	144	5	|φn|2	|φn|2	PROPN
ap-8348	144	6	,	,	PUNCT
ap-8348	144	7	(	(	PUNCT
ap-8348	144	8	75	75	NUM
ap-8348	144	9	)	)	PUNCT
ap-8348	144	10	and	and	CCONJ
ap-8348	144	11	because	because	SCONJ
ap-8348	144	12	φn(x	φn(x	NUM
ap-8348	144	13	)	)	PUNCT
ap-8348	144	14	is	be	AUX
ap-8348	144	15	determined	determine	VERB
ap-8348	144	16	in	in	ADP
ap-8348	144	17	terms	term	NOUN
ap-8348	144	18	of	of	ADP
ap-8348	144	19	airy	airy	ADJ
ap-8348	144	20	function	function	NOUN
ap-8348	144	21	ai(x	ai(x	NUM
ap-8348	144	22	)	)	PUNCT
ap-8348	144	23	,	,	PUNCT
ap-8348	144	24	which	which	PRON
ap-8348	144	25	is	be	AUX
ap-8348	144	26	a	a	DET
ap-8348	144	27	real	real	ADJ
ap-8348	144	28	function	function	NOUN
ap-8348	144	29	,	,	PUNCT
ap-8348	144	30	and	and	CCONJ
ap-8348	144	31	according	accord	VERB
ap-8348	144	32	to	to	ADP
ap-8348	144	33	equations	equation	NOUN
ap-8348	144	34	(	(	PUNCT
ap-8348	144	35	56	56	NUM
ap-8348	144	36	)	)	PUNCT
ap-8348	144	37	and	and	CCONJ
ap-8348	144	38	(	(	PUNCT
ap-8348	144	39	59	59	NUM
ap-8348	144	40	)	)	PUNCT
ap-8348	144	41	,	,	PUNCT
ap-8348	144	42	the	the	DET
ap-8348	144	43	probability	probability	NOUN
ap-8348	144	44	density	density	NOUN
ap-8348	144	45	expression	expression	NOUN
ap-8348	144	46	can	can	AUX
ap-8348	144	47	be	be	AUX
ap-8348	144	48	written	write	VERB
ap-8348	144	49	as	as	ADP
ap-8348	144	50	:	:	PUNCT
ap-8348	144	51	•	•	NOUN
ap-8348	144	52	for	for	ADP
ap-8348	144	53	n	n	X
ap-8348	144	54	is	be	AUX
ap-8348	144	55	even	even	ADV
ap-8348	144	56	|φn(x)|2	|φn(x)|2	NOUN
ap-8348	144	57	=	=	SYM
ap-8348	144	58	1	1	NUM
ap-8348	144	59	(	(	PUNCT
ap-8348	144	60	−2a′	−2a′	PROPN
ap-8348	144	61	n	n	CCONJ
ap-8348	144	62	2	2	NUM
ap-8348	144	63	+1	+1	NOUN
ap-8348	144	64	)	)	PUNCT
ap-8348	145	1	[	[	PUNCT
ap-8348	145	2	ai(an	ai(an	NOUN
ap-8348	145	3	2	2	NUM
ap-8348	145	4	+1	+1	PROPN
ap-8348	145	5	)	)	PUNCT
ap-8348	145	6	]	]	PUNCT
ap-8348	145	7	2	2	NUM
ap-8348	145	8	[	[	PUNCT
ap-8348	145	9	ai(|x|	ai(|x|	X
ap-8348	146	1	+	+	CCONJ
ap-8348	146	2	a′	a′	PROPN
ap-8348	146	3	n	n	CCONJ
ap-8348	146	4	2	2	NUM
ap-8348	146	5	+1	+1	PROPN
ap-8348	146	6	)	)	PUNCT
ap-8348	146	7	]	]	PUNCT
ap-8348	146	8	2	2	NUM
ap-8348	146	9	,	,	PUNCT
ap-8348	146	10	(	(	PUNCT
ap-8348	146	11	76	76	NUM
ap-8348	146	12	)	)	PUNCT
ap-8348	146	13	and	and	CCONJ
ap-8348	146	14	which	which	PRON
ap-8348	146	15	is	be	AUX
ap-8348	146	16	represented	represent	VERB
ap-8348	146	17	in	in	ADP
ap-8348	146	18	figure	figure	NOUN
ap-8348	146	19	1	1	NUM
ap-8348	146	20	for	for	ADP
ap-8348	146	21	the	the	DET
ap-8348	146	22	first	first	ADJ
ap-8348	146	23	three	three	NUM
ap-8348	146	24	even	even	ADV
ap-8348	146	25	states	state	NOUN
ap-8348	146	26	(	(	PUNCT
ap-8348	146	27	n	n	NOUN
ap-8348	146	28	=	=	SYM
ap-8348	146	29	0	0	NUM
ap-8348	146	30	,	,	PUNCT
ap-8348	146	31	2	2	NUM
ap-8348	146	32	,	,	PUNCT
ap-8348	146	33	4	4	NUM
ap-8348	146	34	)	)	PUNCT
ap-8348	146	35	.	.	PUNCT
ap-8348	147	1	•	•	NOUN
ap-8348	147	2	for	for	ADP
ap-8348	147	3	n	n	NOUN
ap-8348	147	4	is	be	AUX
ap-8348	147	5	odd	odd	ADJ
ap-8348	147	6	|φn(x)|2	|φn(x)|2	NOUN
ap-8348	147	7	=	=	SYM
ap-8348	147	8	1	1	NUM
ap-8348	147	9	2	2	NUM
ap-8348	147	10	[	[	PUNCT
ap-8348	147	11	ai′(an+1	ai′(an+1	X
ap-8348	147	12	2	2	NUM
ap-8348	147	13	)	)	PUNCT
ap-8348	147	14	]	]	PUNCT
ap-8348	147	15	2	2	NUM
ap-8348	147	16	[	[	PUNCT
ap-8348	147	17	ai(|x|	ai(|x|	X
ap-8348	148	1	+	+	CCONJ
ap-8348	148	2	an+1	an+1	NOUN
ap-8348	148	3	2	2	NUM
ap-8348	148	4	)	)	PUNCT
ap-8348	148	5	]	]	SYM
ap-8348	148	6	2	2	NUM
ap-8348	148	7	,	,	PUNCT
ap-8348	148	8	(	(	PUNCT
ap-8348	148	9	77	77	NUM
ap-8348	148	10	)	)	PUNCT
ap-8348	148	11	and	and	CCONJ
ap-8348	148	12	which	which	PRON
ap-8348	148	13	is	be	AUX
ap-8348	148	14	represented	represent	VERB
ap-8348	148	15	in	in	ADP
ap-8348	148	16	figure	figure	NOUN
ap-8348	148	17	2	2	NUM
ap-8348	148	18	for	for	ADP
ap-8348	148	19	the	the	DET
ap-8348	148	20	first	first	ADJ
ap-8348	148	21	three	three	NUM
ap-8348	148	22	odd	odd	ADJ
ap-8348	148	23	states	state	NOUN
ap-8348	148	24	(	(	PUNCT
ap-8348	148	25	n	n	NOUN
ap-8348	148	26	=	=	SYM
ap-8348	148	27	1	1	NUM
ap-8348	148	28	,	,	PUNCT
ap-8348	148	29	3	3	NUM
ap-8348	148	30	,	,	PUNCT
ap-8348	148	31	5	5	NUM
ap-8348	148	32	)	)	PUNCT
ap-8348	148	33	.	.	PUNCT
ap-8348	149	1	we	we	PRON
ap-8348	149	2	note	note	VERB
ap-8348	149	3	here	here	ADV
ap-8348	149	4	that	that	SCONJ
ap-8348	149	5	the	the	DET
ap-8348	149	6	probability	probability	NOUN
ap-8348	149	7	in	in	ADP
ap-8348	149	8	the	the	DET
ap-8348	149	9	region	region	NOUN
ap-8348	149	10	x	x	PUNCT
ap-8348	149	11	≤	≤	NOUN
ap-8348	149	12	0	0	NUM
ap-8348	149	13	is	be	AUX
ap-8348	149	14	⟨ψn,2(t)|	⟨ψn,2(t)|	ADJ
ap-8348	149	15	η2(t	η2(t	NOUN
ap-8348	149	16	)	)	PUNCT
ap-8348	149	17	|ψn,2(t)⟩	|ψn,2(t)⟩	PROPN
ap-8348	149	18	=	=	SYM
ap-8348	149	19	⟨φn|	⟨φn|	PROPN
ap-8348	149	20	φn⟩x≤0	φn⟩x≤0	NUM
ap-8348	149	21	=	=	SYM
ap-8348	149	22	0∫	0∫	PROPN
ap-8348	150	1	−∞	−∞	ADP
ap-8348	150	2	φ∗	φ∗	NOUN
ap-8348	150	3	n(x)φn(x)dx	n(x)φn(x)dx	NOUN
ap-8348	150	4	=	=	NOUN
ap-8348	150	5	1	1	NUM
ap-8348	150	6	2	2	NUM
ap-8348	150	7	,	,	PUNCT
ap-8348	150	8	(	(	PUNCT
ap-8348	150	9	78	78	NUM
ap-8348	150	10	)	)	PUNCT
ap-8348	150	11	and	and	CCONJ
ap-8348	150	12	the	the	DET
ap-8348	150	13	probability	probability	NOUN
ap-8348	150	14	in	in	ADP
ap-8348	150	15	the	the	DET
ap-8348	150	16	region	region	NOUN
ap-8348	150	17	x	x	X
ap-8348	150	18	≥	≥	X
ap-8348	150	19	0	0	NUM
ap-8348	150	20	is	be	AUX
ap-8348	150	21	136	136	NUM
ap-8348	150	22	vol	vol	NOUN
ap-8348	150	23	.	.	PUNCT
ap-8348	151	1	63	63	NUM
ap-8348	152	1	no	no	NOUN
ap-8348	152	2	.	.	PUNCT
ap-8348	153	1	2/2023	2/2023	NUM
ap-8348	153	2	exact	exact	ADJ
ap-8348	153	3	solutions	solution	NOUN
ap-8348	153	4	for	for	ADP
ap-8348	153	5	time	time	NOUN
ap-8348	153	6	-	-	PUNCT
ap-8348	153	7	dependent	dependent	ADJ
ap-8348	153	8	complex	complex	ADJ
ap-8348	153	9	symmetric	symmetric	ADJ
ap-8348	153	10	potential	potential	NOUN
ap-8348	153	11	well	well	INTJ
ap-8348	154	1	-6	-6	INTJ
ap-8348	154	2	-4	-4	INTJ
ap-8348	154	3	-2	-2	INTJ
ap-8348	154	4	2	2	NUM
ap-8348	154	5	4	4	NUM
ap-8348	154	6	6	6	NUM
ap-8348	154	7	x	x	SYM
ap-8348	154	8	0.1	0.1	NUM
ap-8348	154	9	0.2	0.2	NUM
ap-8348	154	10	0.3	0.3	NUM
ap-8348	154	11	0.4	0.4	NUM
ap-8348	154	12	0.5	0.5	NUM
ap-8348	154	13	φn	φn	PROPN
ap-8348	154	14	2	2	NUM
ap-8348	154	15	n=4	n=4	X
ap-8348	154	16	n=2	n=2	X
ap-8348	154	17	n=0	n=0	NUM
ap-8348	154	18	figure	figure	NOUN
ap-8348	154	19	1	1	NUM
ap-8348	154	20	.	.	NOUN
ap-8348	154	21	probability	probability	NOUN
ap-8348	154	22	density	density	NOUN
ap-8348	154	23	of	of	ADP
ap-8348	154	24	equation	equation	NOUN
ap-8348	154	25	76	76	NUM
ap-8348	154	26	for	for	ADP
ap-8348	154	27	even	even	ADV
ap-8348	154	28	values	value	NOUN
ap-8348	154	29	of	of	ADP
ap-8348	154	30	n	n	NOUN
ap-8348	154	31	=	=	SYM
ap-8348	154	32	0	0	NUM
ap-8348	154	33	,	,	PUNCT
ap-8348	154	34	2	2	NUM
ap-8348	154	35	,	,	PUNCT
ap-8348	154	36	4	4	NUM
ap-8348	154	37	.	.	PUNCT
ap-8348	154	38	⟨ψn,1(t)|	⟨ψn,1(t)|	NUM
ap-8348	154	39	η1(t	η1(t	X
ap-8348	154	40	)	)	PUNCT
ap-8348	154	41	|ψn,1(t)⟩	|ψn,1(t)⟩	PROPN
ap-8348	154	42	=	=	PUNCT
ap-8348	154	43	⟨φn|	⟨φn|	PROPN
ap-8348	154	44	φn⟩x≥0	φn⟩x≥0	PROPN
ap-8348	154	45	=	=	SYM
ap-8348	154	46	∞∫	∞∫	PROPN
ap-8348	154	47	0	0	NUM
ap-8348	154	48	φ∗	φ∗	NOUN
ap-8348	154	49	n(x)φn(x)dx	n(x)φn(x)dx	NOUN
ap-8348	154	50	=	=	NOUN
ap-8348	154	51	1	1	NUM
ap-8348	154	52	2	2	NUM
ap-8348	154	53	.	.	PUNCT
ap-8348	155	1	(	(	PUNCT
ap-8348	155	2	79	79	NUM
ap-8348	155	3	)	)	PUNCT
ap-8348	155	4	so	so	SCONJ
ap-8348	155	5	the	the	DET
ap-8348	155	6	two	two	NUM
ap-8348	155	7	regions	region	NOUN
ap-8348	155	8	are	be	AUX
ap-8348	155	9	equiprobable	equiprobable	ADJ
ap-8348	155	10	and	and	CCONJ
ap-8348	155	11	the	the	DET
ap-8348	155	12	probability	probability	NOUN
ap-8348	155	13	in	in	ADP
ap-8348	155	14	all	all	DET
ap-8348	155	15	space	space	NOUN
ap-8348	155	16	is	be	AUX
ap-8348	155	17	equal	equal	ADJ
ap-8348	155	18	to	to	ADP
ap-8348	155	19	one	one	NUM
ap-8348	155	20	⟨ψ(t	⟨ψ(t	NOUN
ap-8348	155	21	)	)	PUNCT
ap-8348	155	22	,	,	PUNCT
ap-8348	155	23	ψ(t)⟩η	ψ(t)⟩η	NUM
ap-8348	156	1	=	=	PUNCT
ap-8348	156	2	⟨ψn,1|	⟨ψn,1|	PROPN
ap-8348	156	3	η1(t	η1(t	X
ap-8348	156	4	)	)	PUNCT
ap-8348	156	5	|ψn,1⟩	|ψn,1⟩	NOUN
ap-8348	156	6	+	+	CCONJ
ap-8348	156	7	⟨ψn,2|	⟨ψn,2|	ADP
ap-8348	156	8	ηn,2(t	ηn,2(t	ADJ
ap-8348	156	9	)	)	PUNCT
ap-8348	156	10	|ψ2⟩	|ψ2⟩	NOUN
ap-8348	157	1	=	=	SYM
ap-8348	157	2	∞∫	∞∫	PROPN
ap-8348	157	3	−∞	−∞	ADP
ap-8348	157	4	φ∗	φ∗	NOUN
ap-8348	157	5	n(x)φn(x)dx	n(x)φn(x)dx	VERB
ap-8348	157	6	=	=	NOUN
ap-8348	157	7	1	1	X
ap-8348	157	8	.	.	PUNCT
ap-8348	158	1	(	(	PUNCT
ap-8348	158	2	80	80	NUM
ap-8348	158	3	)	)	PUNCT
ap-8348	158	4	5	5	NUM
ap-8348	158	5	.	.	X
ap-8348	158	6	conclusion	conclusion	VERB
ap-8348	158	7	the	the	DET
ap-8348	158	8	pseudo	pseudo	NOUN
ap-8348	158	9	-	-	ADJ
ap-8348	158	10	invariant	invariant	ADJ
ap-8348	158	11	method	method	NOUN
ap-8348	158	12	has	have	AUX
ap-8348	158	13	been	be	AUX
ap-8348	158	14	used	use	VERB
ap-8348	158	15	to	to	PART
ap-8348	158	16	obtain	obtain	VERB
ap-8348	158	17	the	the	DET
ap-8348	158	18	exact	exact	ADJ
ap-8348	158	19	analytical	analytical	ADJ
ap-8348	158	20	solutions	solution	NOUN
ap-8348	158	21	of	of	ADP
ap-8348	158	22	the	the	DET
ap-8348	158	23	timedependent	timedependent	NOUN
ap-8348	158	24	schrödinger	schrödinger	ADJ
ap-8348	158	25	equation	equation	NOUN
ap-8348	158	26	for	for	ADP
ap-8348	158	27	a	a	DET
ap-8348	158	28	particle	particle	NOUN
ap-8348	158	29	with	with	ADP
ap-8348	158	30	time	time	NOUN
ap-8348	158	31	-	-	PUNCT
ap-8348	158	32	dependent	dependent	ADJ
ap-8348	158	33	mass	mass	NOUN
ap-8348	158	34	moving	move	VERB
ap-8348	158	35	in	in	ADP
ap-8348	158	36	a	a	DET
ap-8348	158	37	complex	complex	ADJ
ap-8348	158	38	timedependent	timedependent	NOUN
ap-8348	158	39	symmetric	symmetric	ADJ
ap-8348	158	40	potential	potential	NOUN
ap-8348	158	41	well	well	ADV
ap-8348	158	42	.	.	PUNCT
ap-8348	159	1	we	we	PRON
ap-8348	159	2	have	have	AUX
ap-8348	159	3	shown	show	VERB
ap-8348	159	4	that	that	SCONJ
ap-8348	159	5	the	the	DET
ap-8348	159	6	problem	problem	NOUN
ap-8348	159	7	can	can	AUX
ap-8348	159	8	be	be	AUX
ap-8348	159	9	reduced	reduce	VERB
ap-8348	159	10	to	to	PART
ap-8348	159	11	solve	solve	VERB
ap-8348	159	12	a	a	DET
ap-8348	159	13	well	well	ADV
ap-8348	159	14	-	-	PUNCT
ap-8348	159	15	known	know	VERB
ap-8348	159	16	eigenvalue	eigenvalue	NOUN
ap-8348	159	17	equation	equation	NOUN
ap-8348	159	18	for	for	ADP
ap-8348	159	19	a	a	DET
ap-8348	159	20	time	time	NOUN
ap-8348	159	21	-	-	PUNCT
ap-8348	159	22	independent	independent	ADJ
ap-8348	159	23	hermitian	hermitian	ADJ
ap-8348	159	24	invariant	invariant	NOUN
ap-8348	159	25	.	.	PUNCT
ap-8348	160	1	in	in	ADP
ap-8348	160	2	fact	fact	NOUN
ap-8348	160	3	,	,	PUNCT
ap-8348	160	4	with	with	ADP
ap-8348	160	5	a	a	DET
ap-8348	160	6	specific	specific	ADJ
ap-8348	160	7	choice	choice	NOUN
ap-8348	160	8	of	of	ADP
ap-8348	160	9	the	the	DET
ap-8348	160	10	td	td	NOUN
ap-8348	160	11	metric	metric	ADJ
ap-8348	160	12	operators	operator	NOUN
ap-8348	160	13	,	,	PUNCT
ap-8348	160	14	η1(t	η1(t	PROPN
ap-8348	160	15	)	)	PUNCT
ap-8348	160	16	and	and	CCONJ
ap-8348	160	17	η2(t	η2(t	PROPN
ap-8348	160	18	)	)	PUNCT
ap-8348	160	19	,	,	PUNCT
ap-8348	160	20	and	and	CCONJ
ap-8348	160	21	the	the	DET
ap-8348	160	22	dyson	dyson	NOUN
ap-8348	160	23	maps	map	NOUN
ap-8348	160	24	,	,	PUNCT
ap-8348	160	25	ρ1(t	ρ1(t	PROPN
ap-8348	160	26	)	)	PUNCT
ap-8348	160	27	and	and	CCONJ
ap-8348	160	28	ρ2(t	ρ2(t	NUM
ap-8348	160	29	)	)	PUNCT
ap-8348	160	30	,	,	PUNCT
ap-8348	160	31	and	and	CCONJ
ap-8348	160	32	using	use	VERB
ap-8348	160	33	unitary	unitary	ADJ
ap-8348	160	34	transformations	transformation	NOUN
ap-8348	160	35	,	,	PUNCT
ap-8348	160	36	the	the	DET
ap-8348	160	37	pseudo	pseudo	NOUN
ap-8348	160	38	-	-	PUNCT
ap-8348	160	39	invariants	invariant	NOUN
ap-8348	160	40	operators	operator	NOUN
ap-8348	160	41	(	(	PUNCT
ap-8348	160	42	iph	iph	PROPN
ap-8348	160	43	1	1	NUM
ap-8348	160	44	(	(	PUNCT
ap-8348	160	45	t	t	NOUN
ap-8348	160	46	)	)	PUNCT
ap-8348	160	47	for	for	ADP
ap-8348	160	48	x	x	SYM
ap-8348	160	49	⩾	⩾	PROPN
ap-8348	160	50	0	0	NUM
ap-8348	160	51	and	and	CCONJ
ap-8348	160	52	iph	iph	PRON
ap-8348	160	53	2	2	NUM
ap-8348	160	54	(	(	PUNCT
ap-8348	160	55	t	t	PROPN
ap-8348	160	56	)	)	PUNCT
ap-8348	160	57	for	for	ADP
ap-8348	160	58	x	x	SYM
ap-8348	160	59	⩽	⩽	NOUN
ap-8348	160	60	0	0	NUM
ap-8348	160	61	)	)	PUNCT
ap-8348	160	62	are	be	AUX
ap-8348	160	63	mapped	map	VERB
ap-8348	160	64	to	to	ADP
ap-8348	160	65	two	two	NUM
ap-8348	160	66	time	time	NOUN
ap-8348	160	67	-	-	PUNCT
ap-8348	160	68	independent	independent	ADJ
ap-8348	160	69	hermitian	hermitian	ADJ
ap-8348	160	70	invariants	invariant	NOUN
ap-8348	160	71	ih	ih	PRON
ap-8348	160	72	1	1	NUM
ap-8348	160	73	(	(	PUNCT
ap-8348	160	74	t	t	PROPN
ap-8348	160	75	)	)	PUNCT
ap-8348	160	76	and	and	CCONJ
ap-8348	160	77	ih	ih	PROPN
ap-8348	160	78	2	2	NUM
ap-8348	160	79	(	(	PUNCT
ap-8348	160	80	t	t	PROPN
ap-8348	160	81	)	)	PUNCT
ap-8348	160	82	,	,	PUNCT
ap-8348	160	83	which	which	PRON
ap-8348	160	84	can	can	AUX
ap-8348	160	85	be	be	AUX
ap-8348	160	86	combined	combine	VERB
ap-8348	160	87	in	in	ADP
ap-8348	160	88	a	a	DET
ap-8348	160	89	unique	unique	ADJ
ap-8348	160	90	form	form	NOUN
ap-8348	160	91	i	i	NOUN
ap-8348	160	92	=	=	PUNCT
ap-8348	160	93	p2	p2	PROPN
ap-8348	160	94	+	+	X
ap-8348	160	95	|x|	|x|	PROPN
ap-8348	160	96	.	.	PUNCT
ap-8348	161	1	the	the	DET
ap-8348	161	2	latter	latter	ADJ
ap-8348	161	3	can	can	AUX
ap-8348	161	4	be	be	AUX
ap-8348	161	5	considered	consider	VERB
ap-8348	161	6	as	as	ADP
ap-8348	161	7	the	the	DET
ap-8348	161	8	hamiltonian	hamiltonian	NOUN
ap-8348	161	9	of	of	ADP
ap-8348	161	10	a	a	DET
ap-8348	161	11	particle	particle	NOUN
ap-8348	161	12	confined	confine	VERB
ap-8348	161	13	in	in	ADP
ap-8348	161	14	a	a	DET
ap-8348	161	15	linear	linear	ADJ
ap-8348	161	16	time	time	NOUN
ap-8348	161	17	-	-	PUNCT
ap-8348	161	18	independent	independent	ADJ
ap-8348	161	19	symmetric	symmetric	ADJ
ap-8348	161	20	potential	potential	NOUN
ap-8348	161	21	well	well	INTJ
ap-8348	161	22	,	,	PUNCT
ap-8348	161	23	where	where	SCONJ
ap-8348	161	24	its	its	PRON
ap-8348	161	25	eigenfunctions	eigenfunction	NOUN
ap-8348	161	26	are	be	AUX
ap-8348	161	27	given	give	VERB
ap-8348	161	28	in	in	ADP
ap-8348	161	29	terms	term	NOUN
ap-8348	161	30	of	of	ADP
ap-8348	161	31	the	the	DET
ap-8348	161	32	airy	airy	ADJ
ap-8348	161	33	function	function	NOUN
ap-8348	161	34	ai	ai	VERB
ap-8348	161	35	.	.	PUNCT
ap-8348	162	1	the	the	DET
ap-8348	162	2	phases	phase	NOUN
ap-8348	162	3	have	have	AUX
ap-8348	162	4	been	be	AUX
ap-8348	162	5	calculated	calculate	VERB
ap-8348	162	6	for	for	ADP
ap-8348	162	7	the	the	DET
ap-8348	162	8	two	two	NUM
ap-8348	162	9	regions	region	NOUN
ap-8348	162	10	and	and	CCONJ
ap-8348	162	11	are	be	AUX
ap-8348	162	12	real	real	ADJ
ap-8348	162	13	.	.	PUNCT
ap-8348	163	1	thus	thus	ADV
ap-8348	163	2	,	,	PUNCT
ap-8348	163	3	the	the	DET
ap-8348	163	4	exact	exact	ADJ
ap-8348	163	5	analytical	analytical	ADJ
ap-8348	163	6	solution	solution	NOUN
ap-8348	163	7	of	of	ADP
ap-8348	163	8	the	the	DET
ap-8348	163	9	problem	problem	NOUN
ap-8348	163	10	has	have	AUX
ap-8348	163	11	been	be	AUX
ap-8348	163	12	deduced	deduce	VERB
ap-8348	163	13	.	.	PUNCT
ap-8348	164	1	finally	finally	ADV
ap-8348	164	2	,	,	PUNCT
ap-8348	164	3	let	let	VERB
ap-8348	164	4	us	we	PRON
ap-8348	164	5	highlight	highlight	VERB
ap-8348	164	6	the	the	DET
ap-8348	164	7	fact	fact	NOUN
ap-8348	164	8	that	that	SCONJ
ap-8348	164	9	the	the	DET
ap-8348	164	10	probability	probability	NOUN
ap-8348	164	11	density	density	NOUN
ap-8348	164	12	associated	associate	VERB
ap-8348	164	13	with	with	ADP
ap-8348	164	14	the	the	DET
ap-8348	164	15	model	model	NOUN
ap-8348	164	16	in	in	ADP
ap-8348	164	17	question	question	NOUN
ap-8348	164	18	is	be	AUX
ap-8348	164	19	time	time	NOUN
ap-8348	164	20	-	-	PUNCT
ap-8348	164	21	independent	independent	ADJ
ap-8348	164	22	.	.	PUNCT
ap-8348	165	1	-6	-6	INTJ
ap-8348	165	2	-4	-4	INTJ
ap-8348	166	1	-2	-2	INTJ
ap-8348	167	1	2	2	NUM
ap-8348	167	2	4	4	NUM
ap-8348	167	3	6	6	NUM
ap-8348	167	4	x	x	SYM
ap-8348	167	5	0.05	0.05	NUM
ap-8348	167	6	0.10	0.10	NUM
ap-8348	167	7	0.15	0.15	NUM
ap-8348	167	8	0.20	0.20	NUM
ap-8348	167	9	0.25	0.25	NUM
ap-8348	167	10	0.30	0.30	NUM
ap-8348	167	11	φn	φn	PROPN
ap-8348	167	12	2	2	NUM
ap-8348	167	13	n=5	n=5	ADJ
ap-8348	167	14	n=3	n=3	PUNCT
ap-8348	167	15	n=1	n=1	NOUN
ap-8348	167	16	figure	figure	NOUN
ap-8348	167	17	2	2	NUM
ap-8348	167	18	.	.	NOUN
ap-8348	167	19	probability	probability	NOUN
ap-8348	167	20	density	density	NOUN
ap-8348	167	21	of	of	ADP
ap-8348	167	22	equation	equation	NOUN
ap-8348	167	23	77	77	NUM
ap-8348	167	24	.	.	PUNCT
ap-8348	168	1	for	for	ADP
ap-8348	168	2	odd	odd	ADJ
ap-8348	168	3	values	value	NOUN
ap-8348	168	4	of	of	ADP
ap-8348	168	5	n	n	NOUN
ap-8348	168	6	=	=	SYM
ap-8348	168	7	1	1	NUM
ap-8348	168	8	,	,	PUNCT
ap-8348	168	9	3	3	NUM
ap-8348	168	10	,	,	PUNCT
ap-8348	168	11	5	5	NUM
ap-8348	168	12	.	.	NUM
ap-8348	168	13	references	reference	NOUN
ap-8348	168	14	[	[	X
ap-8348	168	15	1	1	NUM
ap-8348	168	16	]	]	PUNCT
ap-8348	168	17	c.	c.	PROPN
ap-8348	168	18	bender	bender	PROPN
ap-8348	168	19	,	,	PUNCT
ap-8348	168	20	s.	s.	PROPN
ap-8348	168	21	boettcher	boettcher	PROPN
ap-8348	168	22	.	.	PUNCT
ap-8348	169	1	real	real	ADJ
ap-8348	169	2	spectra	spectra	NOUN
ap-8348	169	3	in	in	ADP
ap-8348	169	4	non	non	ADJ
ap-8348	169	5	-	-	ADJ
ap-8348	169	6	hermitian	hermitian	ADJ
ap-8348	169	7	hamiltonians	hamiltonian	NOUN
ap-8348	169	8	having	have	VERB
ap-8348	169	9	pt	pt	PRON
ap-8348	169	10	symmetry	symmetry	NOUN
ap-8348	169	11	.	.	PUNCT
ap-8348	170	1	physical	physical	PROPN
ap-8348	170	2	review	review	PROPN
ap-8348	170	3	letters	letter	NOUN
ap-8348	170	4	80(24):5243–5246	80(24):5243–5246	NUM
ap-8348	170	5	,	,	PUNCT
ap-8348	170	6	1998	1998	NUM
ap-8348	170	7	.	.	PUNCT
ap-8348	171	1	https://doi.org/10.1103/physrevlett.80.5243	https://doi.org/10.1103/physrevlett.80.5243	PROPN
ap-8348	172	1	[	[	X
ap-8348	172	2	2	2	NUM
ap-8348	172	3	]	]	PUNCT
ap-8348	172	4	f.	f.	PROPN
ap-8348	172	5	bagarello	bagarello	PROPN
ap-8348	172	6	,	,	PUNCT
ap-8348	172	7	j.	j.	PROPN
ap-8348	172	8	gazeau	gazeau	PROPN
ap-8348	172	9	,	,	PUNCT
ap-8348	172	10	f.	f.	PROPN
ap-8348	172	11	szaraniec	szaraniec	PROPN
ap-8348	172	12	,	,	PUNCT
ap-8348	172	13	m.	m.	NOUN
ap-8348	172	14	znojil	znojil	NOUN
ap-8348	172	15	.	.	PUNCT
ap-8348	173	1	non	non	ADJ
ap-8348	173	2	-	-	ADJ
ap-8348	173	3	self	self	ADJ
ap-8348	173	4	adjoint	adjoint	NOUN
ap-8348	173	5	operators	operator	NOUN
ap-8348	173	6	in	in	ADP
ap-8348	173	7	quantum	quantum	ADJ
ap-8348	173	8	physics	physics	NOUN
ap-8348	173	9	:	:	PUNCT
ap-8348	173	10	mathematical	mathematical	ADJ
ap-8348	173	11	aspects	aspect	NOUN
ap-8348	173	12	.	.	PUNCT
ap-8348	174	1	john	john	PROPN
ap-8348	174	2	wiley	wiley	PROPN
ap-8348	174	3	,	,	PUNCT
ap-8348	174	4	2015	2015	NUM
ap-8348	174	5	.	.	PUNCT
ap-8348	175	1	[	[	X
ap-8348	175	2	3	3	X
ap-8348	175	3	]	]	X
ap-8348	175	4	c.	c.	PROPN
ap-8348	175	5	bender	bender	PROPN
ap-8348	175	6	.	.	PUNCT
ap-8348	176	1	pt	pt	PROPN
ap-8348	176	2	symmetry	symmetry	NOUN
ap-8348	176	3	:	:	PUNCT
ap-8348	176	4	in	in	ADP
ap-8348	176	5	quantum	quantum	NOUN
ap-8348	176	6	and	and	CCONJ
ap-8348	176	7	classical	classical	ADJ
ap-8348	176	8	physics	physics	NOUN
ap-8348	176	9	.	.	PUNCT
ap-8348	177	1	world	world	PROPN
ap-8348	177	2	scientific	scientific	ADJ
ap-8348	177	3	,	,	PUNCT
ap-8348	177	4	2019	2019	NUM
ap-8348	177	5	.	.	PUNCT
ap-8348	178	1	[	[	X
ap-8348	178	2	4	4	NUM
ap-8348	178	3	]	]	PUNCT
ap-8348	178	4	a.	a.	NOUN
ap-8348	178	5	mostafazadeh	mostafazadeh	NOUN
ap-8348	178	6	.	.	PUNCT
ap-8348	179	1	pseudo	pseudo	NOUN
ap-8348	179	2	-	-	NOUN
ap-8348	179	3	hermiticity	hermiticity	NOUN
ap-8348	179	4	versus	versus	ADP
ap-8348	179	5	pt	pt	PROPN
ap-8348	179	6	symmetry	symmetry	NOUN
ap-8348	179	7	:	:	PUNCT
ap-8348	179	8	the	the	DET
ap-8348	179	9	necessary	necessary	ADJ
ap-8348	179	10	condition	condition	NOUN
ap-8348	179	11	for	for	ADP
ap-8348	179	12	the	the	DET
ap-8348	179	13	reality	reality	NOUN
ap-8348	179	14	of	of	ADP
ap-8348	179	15	the	the	DET
ap-8348	179	16	spectrum	spectrum	NOUN
ap-8348	179	17	of	of	ADP
ap-8348	179	18	a	a	DET
ap-8348	179	19	non	non	ADJ
ap-8348	179	20	-	-	ADJ
ap-8348	179	21	hermitian	hermitian	ADJ
ap-8348	179	22	hamiltonian	hamiltonian	NOUN
ap-8348	179	23	.	.	PUNCT
ap-8348	180	1	journal	journal	PROPN
ap-8348	180	2	of	of	ADP
ap-8348	180	3	mathematical	mathematical	ADJ
ap-8348	180	4	physics	physics	NOUN
ap-8348	180	5	43(1):205–214	43(1):205–214	PROPN
ap-8348	180	6	,	,	PUNCT
ap-8348	180	7	2002	2002	NUM
ap-8348	180	8	.	.	PUNCT
ap-8348	180	9	https://doi.org/10.1063/1.1418246	https://doi.org/10.1063/1.1418246	X
ap-8348	181	1	[	[	X
ap-8348	181	2	5	5	NUM
ap-8348	181	3	]	]	PUNCT
ap-8348	181	4	a.	a.	NOUN
ap-8348	181	5	mostafazadeh	mostafazadeh	NOUN
ap-8348	181	6	.	.	PUNCT
ap-8348	182	1	pseudo	pseudo	NOUN
ap-8348	182	2	-	-	NOUN
ap-8348	182	3	hermiticity	hermiticity	NOUN
ap-8348	182	4	versus	versus	ADP
ap-8348	182	5	pt	pt	PROPN
ap-8348	182	6	-	-	PUNCT
ap-8348	182	7	symmetry	symmetry	NOUN
ap-8348	182	8	ii	ii	PROPN
ap-8348	182	9	:	:	PUNCT
ap-8348	182	10	a	a	DET
ap-8348	182	11	complete	complete	ADJ
ap-8348	182	12	characterization	characterization	NOUN
ap-8348	182	13	of	of	ADP
ap-8348	182	14	non	non	ADJ
ap-8348	182	15	-	-	ADJ
ap-8348	182	16	hermitian	hermitian	ADJ
ap-8348	182	17	hamiltonians	hamiltonian	NOUN
ap-8348	182	18	with	with	ADP
ap-8348	182	19	a	a	DET
ap-8348	182	20	real	real	ADJ
ap-8348	182	21	spectrum	spectrum	NOUN
ap-8348	182	22	.	.	PUNCT
ap-8348	183	1	journal	journal	PROPN
ap-8348	183	2	of	of	ADP
ap-8348	183	3	mathematical	mathematical	ADJ
ap-8348	183	4	physics	physics	NOUN
ap-8348	183	5	43(5):2814	43(5):2814	NUM
ap-8348	183	6	,	,	PUNCT
ap-8348	183	7	2002	2002	NUM
ap-8348	183	8	.	.	PUNCT
ap-8348	184	1	https://doi.org/10.1063/1.1461427	https://doi.org/10.1063/1.1461427	VERB
ap-8348	185	1	[	[	X
ap-8348	185	2	6	6	NUM
ap-8348	185	3	]	]	PUNCT
ap-8348	185	4	a.	a.	NOUN
ap-8348	185	5	mostafazadeh	mostafazadeh	NOUN
ap-8348	185	6	.	.	PUNCT
ap-8348	186	1	pseudo	pseudo	NOUN
ap-8348	186	2	-	-	NOUN
ap-8348	186	3	hermiticity	hermiticity	NOUN
ap-8348	186	4	versus	versus	ADP
ap-8348	186	5	pt	pt	NOUN
ap-8348	186	6	-	-	PUNCT
ap-8348	186	7	symmetry	symmetry	NOUN
ap-8348	186	8	iii	iii	NOUN
ap-8348	186	9	:	:	PUNCT
ap-8348	186	10	equivalence	equivalence	NOUN
ap-8348	186	11	of	of	ADP
ap-8348	186	12	pseudo	pseudo	NOUN
ap-8348	186	13	-	-	NOUN
ap-8348	186	14	hermiticity	hermiticity	NOUN
ap-8348	186	15	and	and	CCONJ
ap-8348	186	16	the	the	DET
ap-8348	186	17	presence	presence	NOUN
ap-8348	186	18	of	of	ADP
ap-8348	186	19	antilinear	antilinear	ADJ
ap-8348	186	20	symmetries	symmetry	NOUN
ap-8348	186	21	.	.	PUNCT
ap-8348	187	1	journal	journal	PROPN
ap-8348	187	2	of	of	ADP
ap-8348	187	3	mathematical	mathematical	ADJ
ap-8348	187	4	physics	physics	PROPN
ap-8348	187	5	43(8):3944–3951	43(8):3944–3951	PROPN
ap-8348	187	6	,	,	PUNCT
ap-8348	187	7	2002	2002	NUM
ap-8348	187	8	.	.	PUNCT
ap-8348	188	1	https://doi.org/10.1063/1.1489072	https://doi.org/10.1063/1.1489072	NOUN
ap-8348	189	1	[	[	X
ap-8348	189	2	7	7	X
ap-8348	189	3	]	]	X
ap-8348	189	4	h.	h.	PROPN
ap-8348	189	5	choutri	choutri	PROPN
ap-8348	189	6	,	,	PUNCT
ap-8348	189	7	m.	m.	NOUN
ap-8348	189	8	maamache	maamache	PROPN
ap-8348	189	9	,	,	PUNCT
ap-8348	189	10	s.	s.	PROPN
ap-8348	189	11	menouar	menouar	PROPN
ap-8348	189	12	.	.	PUNCT
ap-8348	190	1	geometric	geometric	ADJ
ap-8348	190	2	phase	phase	NOUN
ap-8348	190	3	for	for	ADP
ap-8348	190	4	a	a	DET
ap-8348	190	5	periodic	periodic	ADJ
ap-8348	190	6	non	non	ADJ
ap-8348	190	7	-	-	ADJ
ap-8348	190	8	hermitian	hermitian	ADJ
ap-8348	190	9	hamiltonian	hamiltonian	NOUN
ap-8348	190	10	.	.	PUNCT
ap-8348	191	1	journal	journal	NOUN
ap-8348	191	2	-	-	PUNCT
ap-8348	191	3	korean	korean	ADJ
ap-8348	191	4	physical	physical	ADJ
ap-8348	191	5	society	society	NOUN
ap-8348	191	6	40(2):358–360	40(2):358–360	PROPN
ap-8348	191	7	,	,	PUNCT
ap-8348	191	8	2002	2002	NUM
ap-8348	191	9	.	.	PUNCT
ap-8348	192	1	[	[	X
ap-8348	192	2	8	8	NUM
ap-8348	192	3	]	]	X
ap-8348	192	4	c.	c.	NOUN
ap-8348	192	5	yuce	yuce	PROPN
ap-8348	192	6	.	.	PUNCT
ap-8348	193	1	time	time	NOUN
ap-8348	193	2	-	-	PUNCT
ap-8348	193	3	dependent	dependent	ADJ
ap-8348	193	4	pt	pt	NOUN
ap-8348	193	5	symmetric	symmetric	ADJ
ap-8348	193	6	problems	problem	NOUN
ap-8348	193	7	.	.	PUNCT
ap-8348	194	1	physics	physics	NOUN
ap-8348	194	2	letters	letter	NOUN
ap-8348	194	3	a	a	DET
ap-8348	194	4	336(4	336(4	NUM
ap-8348	194	5	-	-	SYM
ap-8348	194	6	5):290–294	5):290–294	NUM
ap-8348	194	7	,	,	PUNCT
ap-8348	194	8	2005	2005	NUM
ap-8348	194	9	.	.	PUNCT
ap-8348	195	1	https://doi.org/10.1016/j.physleta.2004.12.043	https://doi.org/10.1016/j.physleta.2004.12.043	NOUN
ap-8348	195	2	[	[	X
ap-8348	195	3	9	9	NUM
ap-8348	195	4	]	]	PUNCT
ap-8348	195	5	a.	a.	NOUN
ap-8348	195	6	dutra	dutra	PROPN
ap-8348	195	7	,	,	PUNCT
ap-8348	195	8	m.	m.	NOUN
ap-8348	195	9	hott	hott	PROPN
ap-8348	195	10	,	,	PUNCT
ap-8348	195	11	v.	v.	ADP
ap-8348	195	12	dos	dos	PROPN
ap-8348	195	13	santos	santos	PROPN
ap-8348	195	14	.	.	PUNCT
ap-8348	196	1	time	time	NOUN
ap-8348	196	2	-	-	PUNCT
ap-8348	196	3	dependent	dependent	ADJ
ap-8348	196	4	non	non	ADJ
ap-8348	196	5	-	-	ADJ
ap-8348	196	6	hermitian	hermitian	ADJ
ap-8348	196	7	hamiltonians	hamiltonian	NOUN
ap-8348	196	8	with	with	ADP
ap-8348	196	9	real	real	ADJ
ap-8348	196	10	energies	energy	NOUN
ap-8348	196	11	.	.	PUNCT
ap-8348	197	1	europhysics	europhysics	PROPN
ap-8348	197	2	letters	letter	NOUN
ap-8348	197	3	(	(	PUNCT
ap-8348	197	4	epl	epl	PROPN
ap-8348	197	5	)	)	PUNCT
ap-8348	197	6	71(2):166–171	71(2):166–171	PROPN
ap-8348	197	7	,	,	PUNCT
ap-8348	197	8	2005	2005	NUM
ap-8348	197	9	.	.	PUNCT
ap-8348	198	1	https://doi.org/10.1209/epl/i2005-10073-7	https://doi.org/10.1209/epl/i2005-10073-7	NUM
ap-8348	199	1	[	[	X
ap-8348	199	2	10	10	NUM
ap-8348	199	3	]	]	X
ap-8348	199	4	c.	c.	PROPN
ap-8348	199	5	faria	faria	PROPN
ap-8348	199	6	,	,	PUNCT
ap-8348	199	7	a.	a.	PROPN
ap-8348	199	8	fring	fring	PROPN
ap-8348	199	9	.	.	PUNCT
ap-8348	199	10	time	time	NOUN
ap-8348	199	11	evolution	evolution	NOUN
ap-8348	199	12	of	of	ADP
ap-8348	199	13	non	non	ADJ
ap-8348	199	14	-	-	ADJ
ap-8348	199	15	hermitian	hermitian	ADJ
ap-8348	199	16	hamiltonian	hamiltonian	ADJ
ap-8348	199	17	systems	system	NOUN
ap-8348	199	18	.	.	PUNCT
ap-8348	200	1	journal	journal	PROPN
ap-8348	200	2	of	of	ADP
ap-8348	200	3	physics	physics	PROPN
ap-8348	200	4	a	a	PRON
ap-8348	200	5	:	:	PUNCT
ap-8348	200	6	mathematical	mathematical	ADJ
ap-8348	200	7	and	and	CCONJ
ap-8348	200	8	general	general	ADJ
ap-8348	200	9	39(29):9269–9289	39(29):9269–9289	NUM
ap-8348	200	10	,	,	PUNCT
ap-8348	200	11	2006	2006	NUM
ap-8348	200	12	.	.	PUNCT
ap-8348	201	1	https://doi.org/10.1088/0305-4470/39/29/018	https://doi.org/10.1088/0305-4470/39/29/018	VERB
ap-8348	201	2	[	[	X
ap-8348	201	3	11	11	NUM
ap-8348	201	4	]	]	PUNCT
ap-8348	201	5	a.	a.	NOUN
ap-8348	201	6	mostafazadeh	mostafazadeh	PROPN
ap-8348	201	7	.	.	PUNCT
ap-8348	202	1	time	time	NOUN
ap-8348	202	2	-	-	PUNCT
ap-8348	202	3	dependent	dependent	ADJ
ap-8348	202	4	pseudo	pseudo	NOUN
ap-8348	202	5	-	-	ADJ
ap-8348	202	6	hermitian	hermitian	ADJ
ap-8348	202	7	hamiltonians	hamiltonian	NOUN
ap-8348	202	8	defining	define	VERB
ap-8348	202	9	a	a	DET
ap-8348	202	10	unitary	unitary	ADJ
ap-8348	202	11	quantum	quantum	ADJ
ap-8348	202	12	system	system	NOUN
ap-8348	202	13	and	and	CCONJ
ap-8348	202	14	uniqueness	uniqueness	NOUN
ap-8348	202	15	of	of	ADP
ap-8348	202	16	the	the	DET
ap-8348	202	17	metric	metric	ADJ
ap-8348	202	18	operator	operator	NOUN
ap-8348	202	19	.	.	PUNCT
ap-8348	203	1	physics	physics	NOUN
ap-8348	203	2	letters	letter	NOUN
ap-8348	203	3	b	b	PROPN
ap-8348	203	4	137	137	NUM
ap-8348	203	5	https://doi.org/10.1103/physrevlett.80.5243	https://doi.org/10.1103/physrevlett.80.5243	NOUN
ap-8348	203	6	https://doi.org/10.1063/1.1418246	https://doi.org/10.1063/1.1418246	PROPN
ap-8348	203	7	https://doi.org/10.1063/1.1461427	https://doi.org/10.1063/1.1461427	PROPN
ap-8348	203	8	https://doi.org/10.1063/1.1489072	https://doi.org/10.1063/1.1489072	NOUN
ap-8348	203	9	https://doi.org/10.1016/j.physleta.2004.12.043	https://doi.org/10.1016/j.physleta.2004.12.043	PROPN
ap-8348	203	10	https://doi.org/10.1209/epl/i2005-10073-7	https://doi.org/10.1209/epl/i2005-10073-7	VERB
ap-8348	203	11	https://doi.org/10.1088/0305-4470/39/29/018	https://doi.org/10.1088/0305-4470/39/29/018	NOUN
ap-8348	203	12	boubakeur	boubakeur	ADP
ap-8348	203	13	khantoul	khantoul	NOUN
ap-8348	203	14	,	,	PUNCT
ap-8348	203	15	abdelhafid	abdelhafid	ADV
ap-8348	203	16	bounames	bouname	NOUN
ap-8348	203	17	acta	acta	PROPN
ap-8348	203	18	polytechnica	polytechnica	PROPN
ap-8348	203	19	650(2	650(2	PROPN
ap-8348	203	20	-	-	SYM
ap-8348	203	21	3):208–212	3):208–212	NUM
ap-8348	203	22	,	,	PUNCT
ap-8348	203	23	2007	2007	NUM
ap-8348	203	24	.	.	PUNCT
ap-8348	204	1	https://doi.org/10.1016/j.physletb.2007.04.064	https://doi.org/10.1016/j.physletb.2007.04.064	NOUN
ap-8348	204	2	[	[	X
ap-8348	204	3	12	12	NUM
ap-8348	204	4	]	]	PUNCT
ap-8348	204	5	m.	m.	NOUN
ap-8348	204	6	znojil	znojil	PROPN
ap-8348	204	7	.	.	PUNCT
ap-8348	205	1	time	time	NOUN
ap-8348	205	2	-	-	PUNCT
ap-8348	205	3	dependent	dependent	ADJ
ap-8348	205	4	quasi	quasi	ADJ
ap-8348	205	5	-	-	ADJ
ap-8348	205	6	hermitian	hermitian	ADJ
ap-8348	205	7	hamiltonians	hamiltonian	NOUN
ap-8348	205	8	and	and	CCONJ
ap-8348	205	9	the	the	DET
ap-8348	205	10	unitarity	unitarity	NOUN
ap-8348	205	11	of	of	ADP
ap-8348	205	12	quantum	quantum	ADJ
ap-8348	205	13	evolution	evolution	NOUN
ap-8348	205	14	,	,	PUNCT
ap-8348	205	15	2007	2007	NUM
ap-8348	205	16	.	.	PUNCT
ap-8348	206	1	arxiv:0710.5653	arxiv:0710.5653	PROPN
ap-8348	207	1	[	[	X
ap-8348	207	2	13	13	NUM
ap-8348	207	3	]	]	PUNCT
ap-8348	207	4	m.	m.	NOUN
ap-8348	207	5	znojil	znojil	PROPN
ap-8348	207	6	.	.	PUNCT
ap-8348	207	7	time	time	NOUN
ap-8348	207	8	-	-	PUNCT
ap-8348	207	9	dependent	dependent	ADJ
ap-8348	207	10	version	version	NOUN
ap-8348	207	11	of	of	ADP
ap-8348	207	12	crypto	crypto	ADJ
ap-8348	207	13	-	-	ADJ
ap-8348	207	14	hermitian	hermitian	ADJ
ap-8348	207	15	quantum	quantum	NOUN
ap-8348	207	16	theory	theory	NOUN
ap-8348	207	17	.	.	PUNCT
ap-8348	208	1	physical	physical	ADJ
ap-8348	208	2	review	review	PROPN
ap-8348	208	3	d	d	PROPN
ap-8348	208	4	78(8):085003	78(8):085003	NUM
ap-8348	208	5	,	,	PUNCT
ap-8348	208	6	2008	2008	NUM
ap-8348	208	7	.	.	PUNCT
ap-8348	209	1	https://doi.org/10.1103/physrevd.78.085003	https://doi.org/10.1103/physrevd.78.085003	NOUN
ap-8348	210	1	[	[	X
ap-8348	210	2	14	14	NUM
ap-8348	210	3	]	]	PUNCT
ap-8348	210	4	j.	j.	PROPN
ap-8348	210	5	gong	gong	PROPN
ap-8348	210	6	,	,	PUNCT
ap-8348	210	7	q.	q.	PROPN
ap-8348	210	8	wang	wang	PROPN
ap-8348	210	9	.	.	PUNCT
ap-8348	211	1	time	time	NOUN
ap-8348	211	2	-	-	PUNCT
ap-8348	211	3	dependent	dependent	ADJ
ap-8348	211	4	pt	pt	ADJ
ap-8348	211	5	-	-	ADJ
ap-8348	211	6	symmetric	symmetric	ADJ
ap-8348	211	7	quantum	quantum	NOUN
ap-8348	211	8	mechanics	mechanic	NOUN
ap-8348	211	9	.	.	PUNCT
ap-8348	212	1	journal	journal	PROPN
ap-8348	212	2	of	of	ADP
ap-8348	212	3	physics	physics	PROPN
ap-8348	212	4	a	a	PRON
ap-8348	212	5	:	:	PUNCT
ap-8348	212	6	mathematical	mathematical	ADJ
ap-8348	212	7	and	and	CCONJ
ap-8348	212	8	theoretical	theoretical	ADJ
ap-8348	212	9	46(48):485302	46(48):485302	NUM
ap-8348	212	10	,	,	PUNCT
ap-8348	212	11	2013	2013	NUM
ap-8348	212	12	.	.	PUNCT
ap-8348	213	1	https://doi.org/10.1088/1751-8113/46/48/485302	https://doi.org/10.1088/1751-8113/46/48/485302	NOUN
ap-8348	214	1	[	[	X
ap-8348	214	2	15	15	NUM
ap-8348	214	3	]	]	X
ap-8348	214	4	a.	a.	NOUN
ap-8348	214	5	fring	fring	NOUN
ap-8348	214	6	,	,	PUNCT
ap-8348	214	7	m.	m.	NOUN
ap-8348	214	8	moussa	moussa	PROPN
ap-8348	214	9	.	.	PUNCT
ap-8348	215	1	unitary	unitary	ADJ
ap-8348	215	2	quantum	quantum	ADJ
ap-8348	215	3	evolution	evolution	NOUN
ap-8348	215	4	for	for	ADP
ap-8348	215	5	time	time	NOUN
ap-8348	215	6	-	-	PUNCT
ap-8348	215	7	dependent	dependent	ADJ
ap-8348	215	8	quasi	quasi	ADJ
ap-8348	215	9	-	-	ADJ
ap-8348	215	10	hermitian	hermitian	ADJ
ap-8348	215	11	systems	system	NOUN
ap-8348	215	12	with	with	ADP
ap-8348	215	13	nonobservable	nonobservable	ADJ
ap-8348	215	14	hamiltonians	hamiltonian	NOUN
ap-8348	215	15	.	.	PUNCT
ap-8348	216	1	physical	physical	ADJ
ap-8348	216	2	review	review	NOUN
ap-8348	216	3	a	a	DET
ap-8348	216	4	93(4):042114	93(4):042114	NUM
ap-8348	216	5	,	,	PUNCT
ap-8348	216	6	2016	2016	NUM
ap-8348	216	7	.	.	PUNCT
ap-8348	217	1	https://doi.org/10.1103/physreva.93.042114	https://doi.org/10.1103/physreva.93.042114	PROPN
ap-8348	218	1	[	[	X
ap-8348	218	2	16	16	NUM
ap-8348	218	3	]	]	X
ap-8348	218	4	a.	a.	NOUN
ap-8348	218	5	fring	fring	PROPN
ap-8348	218	6	,	,	PUNCT
ap-8348	218	7	m.	m.	NOUN
ap-8348	218	8	moussa	moussa	PROPN
ap-8348	218	9	.	.	PUNCT
ap-8348	219	1	non	non	ADJ
ap-8348	219	2	-	-	ADJ
ap-8348	219	3	hermitian	hermitian	ADJ
ap-8348	219	4	swanson	swanson	PROPN
ap-8348	219	5	model	model	NOUN
ap-8348	219	6	with	with	ADP
ap-8348	219	7	a	a	DET
ap-8348	219	8	time	time	NOUN
ap-8348	219	9	-	-	PUNCT
ap-8348	219	10	dependent	dependent	ADJ
ap-8348	219	11	metric	metric	NOUN
ap-8348	219	12	.	.	PUNCT
ap-8348	220	1	physical	physical	ADJ
ap-8348	220	2	review	review	NOUN
ap-8348	220	3	a	a	DET
ap-8348	220	4	94(4):042128	94(4):042128	NOUN
ap-8348	220	5	,	,	PUNCT
ap-8348	220	6	2016	2016	NUM
ap-8348	220	7	.	.	PUNCT
ap-8348	221	1	https://doi.org/10.1103/physreva.94.042128	https://doi.org/10.1103/physreva.94.042128	PROPN
ap-8348	222	1	[	[	X
ap-8348	222	2	17	17	NUM
ap-8348	222	3	]	]	X
ap-8348	222	4	b.	b.	PROPN
ap-8348	222	5	khantoul	khantoul	PROPN
ap-8348	222	6	,	,	PUNCT
ap-8348	222	7	a.	a.	NOUN
ap-8348	222	8	bounames	bouname	NOUN
ap-8348	222	9	,	,	PUNCT
ap-8348	222	10	m.	m.	NOUN
ap-8348	222	11	maamache	maamache	PROPN
ap-8348	222	12	.	.	PUNCT
ap-8348	223	1	on	on	ADP
ap-8348	223	2	the	the	DET
ap-8348	223	3	invariant	invariant	ADJ
ap-8348	223	4	method	method	NOUN
ap-8348	223	5	for	for	ADP
ap-8348	223	6	the	the	DET
ap-8348	223	7	time	time	NOUN
ap-8348	223	8	-	-	PUNCT
ap-8348	223	9	dependent	dependent	ADJ
ap-8348	223	10	non	non	ADJ
ap-8348	223	11	-	-	ADJ
ap-8348	223	12	hermitian	hermitian	ADJ
ap-8348	223	13	hamiltonians	hamiltonian	NOUN
ap-8348	223	14	.	.	PUNCT
ap-8348	224	1	the	the	DET
ap-8348	224	2	european	european	PROPN
ap-8348	224	3	physical	physical	PROPN
ap-8348	224	4	journal	journal	PROPN
ap-8348	224	5	plus	plus	CCONJ
ap-8348	224	6	132(6):258	132(6):258	NUM
ap-8348	224	7	,	,	PUNCT
ap-8348	224	8	2017	2017	NUM
ap-8348	224	9	.	.	PUNCT
ap-8348	225	1	https://doi.org/10.1140/epjp/i2017-11524-7	https://doi.org/10.1140/epjp/i2017-11524-7	X
ap-8348	226	1	[	[	X
ap-8348	226	2	18	18	NUM
ap-8348	226	3	]	]	PUNCT
ap-8348	226	4	m.	m.	NOUN
ap-8348	226	5	maamache	maamache	PROPN
ap-8348	226	6	,	,	PUNCT
ap-8348	226	7	o.	o.	PROPN
ap-8348	226	8	djeghiour	djeghiour	NOUN
ap-8348	226	9	,	,	PUNCT
ap-8348	226	10	n.	n.	PROPN
ap-8348	226	11	mana	mana	PROPN
ap-8348	226	12	,	,	PUNCT
ap-8348	226	13	w.	w.	PROPN
ap-8348	226	14	koussa	koussa	PROPN
ap-8348	226	15	.	.	PUNCT
ap-8348	227	1	pseudo	pseudo	NOUN
ap-8348	227	2	-	-	PUNCT
ap-8348	227	3	invariants	invariant	NOUN
ap-8348	227	4	theory	theory	NOUN
ap-8348	227	5	and	and	CCONJ
ap-8348	227	6	real	real	ADJ
ap-8348	227	7	phases	phase	NOUN
ap-8348	227	8	for	for	ADP
ap-8348	227	9	systems	system	NOUN
ap-8348	227	10	with	with	ADP
ap-8348	227	11	non	non	ADJ
ap-8348	227	12	-	-	ADJ
ap-8348	227	13	hermitian	hermitian	ADJ
ap-8348	227	14	time	time	NOUN
ap-8348	227	15	-	-	PUNCT
ap-8348	227	16	dependent	dependent	ADJ
ap-8348	227	17	hamiltonians	hamiltonian	NOUN
ap-8348	227	18	.	.	PUNCT
ap-8348	228	1	the	the	DET
ap-8348	228	2	european	european	PROPN
ap-8348	228	3	physical	physical	PROPN
ap-8348	228	4	journal	journal	PROPN
ap-8348	228	5	plus	plus	CCONJ
ap-8348	228	6	132(9):383	132(9):383	NOUN
ap-8348	228	7	,	,	PUNCT
ap-8348	228	8	2017	2017	NUM
ap-8348	228	9	.	.	PUNCT
ap-8348	229	1	https://doi.org/10.1140/epjp/i2017-11678-2	https://doi.org/10.1140/epjp/i2017-11678-2	VERB
ap-8348	229	2	[	[	X
ap-8348	229	3	19	19	NUM
ap-8348	229	4	]	]	PUNCT
ap-8348	229	5	m.	m.	NOUN
ap-8348	229	6	maamache	maamache	PROPN
ap-8348	229	7	.	.	PUNCT
ap-8348	230	1	non	non	ADJ
ap-8348	230	2	-	-	ADJ
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ap-8348	230	4	transformation	transformation	NOUN
ap-8348	230	5	of	of	ADP
ap-8348	230	6	quantum	quantum	ADJ
ap-8348	230	7	time	time	NOUN
ap-8348	230	8	-	-	PUNCT
ap-8348	230	9	dependent	dependent	ADJ
ap-8348	230	10	non	non	ADJ
ap-8348	230	11	-	-	ADJ
ap-8348	230	12	hermitian	hermitian	ADJ
ap-8348	230	13	systems	system	NOUN
ap-8348	230	14	.	.	PUNCT
ap-8348	231	1	acta	acta	PROPN
ap-8348	231	2	polytechnica	polytechnica	PROPN
ap-8348	231	3	57(6):424	57(6):424	NUM
ap-8348	231	4	,	,	PUNCT
ap-8348	231	5	2017	2017	NUM
ap-8348	231	6	.	.	PUNCT
ap-8348	232	1	https://doi.org/10.14311/ap.2017.57.0424	https://doi.org/10.14311/ap.2017.57.0424	PART
ap-8348	233	1	[	[	X
ap-8348	233	2	20	20	NUM
ap-8348	233	3	]	]	PUNCT
ap-8348	233	4	b.	b.	PROPN
ap-8348	233	5	bagchi	bagchi	PROPN
ap-8348	233	6	.	.	PUNCT
ap-8348	234	1	evolution	evolution	NOUN
ap-8348	234	2	operator	operator	NOUN
ap-8348	234	3	for	for	ADP
ap-8348	234	4	time	time	NOUN
ap-8348	234	5	-	-	PUNCT
ap-8348	234	6	dependent	dependent	ADJ
ap-8348	234	7	non	non	ADJ
ap-8348	234	8	-	-	ADJ
ap-8348	234	9	hermitian	hermitian	ADJ
ap-8348	234	10	hamiltonians	hamiltonian	NOUN
ap-8348	234	11	.	.	PUNCT
ap-8348	235	1	letters	letter	NOUN
ap-8348	235	2	in	in	ADP
ap-8348	235	3	high	high	ADJ
ap-8348	235	4	energy	energy	NOUN
ap-8348	235	5	physics	physics	NOUN
ap-8348	235	6	1(3):4–8	1(3):4–8	NUM
ap-8348	235	7	,	,	PUNCT
ap-8348	235	8	2018	2018	NUM
ap-8348	235	9	.	.	PUNCT
ap-8348	236	1	https://doi.org/10.31526/lhep.3.2018.02	https://doi.org/10.31526/lhep.3.2018.02	PROPN
ap-8348	237	1	[	[	X
ap-8348	237	2	21	21	NUM
ap-8348	237	3	]	]	X
ap-8348	237	4	b.	b.	PROPN
ap-8348	237	5	ramos	ramos	PROPN
ap-8348	237	6	,	,	PUNCT
ap-8348	237	7	i.	i.	PROPN
ap-8348	237	8	pedrosa	pedrosa	PROPN
ap-8348	237	9	,	,	PUNCT
ap-8348	237	10	a.	a.	PROPN
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ap-8348	237	12	de	de	X
ap-8348	237	13	lima	lima	PROPN
ap-8348	237	14	.	.	PUNCT
ap-8348	238	1	lewis	lewis	PROPN
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ap-8348	238	3	riesenfeld	riesenfeld	VERB
ap-8348	238	4	approach	approach	NOUN
ap-8348	238	5	to	to	ADP
ap-8348	238	6	time	time	NOUN
ap-8348	238	7	-	-	PUNCT
ap-8348	238	8	dependent	dependent	ADJ
ap-8348	238	9	non	non	ADJ
ap-8348	238	10	-	-	ADJ
ap-8348	238	11	hermitian	hermitian	ADJ
ap-8348	238	12	hamiltonians	hamiltonian	NOUN
ap-8348	238	13	having	have	VERB
ap-8348	238	14	pt	pt	PRON
ap-8348	238	15	symmetry	symmetry	NOUN
ap-8348	238	16	.	.	PUNCT
ap-8348	239	1	the	the	DET
ap-8348	239	2	european	european	PROPN
ap-8348	239	3	physical	physical	PROPN
ap-8348	239	4	journal	journal	PROPN
ap-8348	239	5	plus	plus	CCONJ
ap-8348	239	6	133(11):449	133(11):449	NUM
ap-8348	239	7	,	,	PUNCT
ap-8348	239	8	2018	2018	NUM
ap-8348	239	9	.	.	PUNCT
ap-8348	240	1	https://doi.org/10.1140/epjp/i2018-12251-3	https://doi.org/10.1140/epjp/i2018-12251-3	NOUN
ap-8348	241	1	[	[	X
ap-8348	241	2	22	22	NUM
ap-8348	241	3	]	]	X
ap-8348	241	4	w.	w.	PROPN
ap-8348	241	5	koussa	koussa	PROPN
ap-8348	241	6	,	,	PUNCT
ap-8348	241	7	n.	n.	PROPN
ap-8348	241	8	mana	mana	PROPN
ap-8348	241	9	,	,	PUNCT
ap-8348	241	10	o.	o.	PROPN
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ap-8348	241	12	,	,	PUNCT
ap-8348	241	13	m.	m.	NOUN
ap-8348	241	14	maamache	maamache	PROPN
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ap-8348	242	1	the	the	DET
ap-8348	242	2	pseudo	pseudo	NOUN
ap-8348	242	3	hermitian	hermitian	ADJ
ap-8348	242	4	invariant	invariant	ADJ
ap-8348	242	5	operator	operator	NOUN
ap-8348	242	6	and	and	CCONJ
ap-8348	242	7	time	time	NOUN
ap-8348	242	8	-	-	PUNCT
ap-8348	242	9	dependent	dependent	ADJ
ap-8348	242	10	non	non	ADJ
ap-8348	242	11	-	-	ADJ
ap-8348	242	12	hermitian	hermitian	ADJ
ap-8348	242	13	hamiltonian	hamiltonian	NOUN
ap-8348	242	14	exhibiting	exhibit	VERB
ap-8348	242	15	a	a	DET
ap-8348	242	16	su(1,1	su(1,1	NOUN
ap-8348	242	17	)	)	PUNCT
ap-8348	242	18	and	and	CCONJ
ap-8348	242	19	su(2	su(2	NOUN
ap-8348	242	20	)	)	PUNCT
ap-8348	242	21	dynamical	dynamical	ADJ
ap-8348	242	22	symmetry	symmetry	NOUN
ap-8348	242	23	.	.	PUNCT
ap-8348	243	1	journal	journal	PROPN
ap-8348	243	2	of	of	ADP
ap-8348	243	3	mathematical	mathematical	ADJ
ap-8348	243	4	physics	physics	NOUN
ap-8348	243	5	59(7):072103	59(7):072103	NUM
ap-8348	243	6	,	,	PUNCT
ap-8348	243	7	2018	2018	NUM
ap-8348	243	8	.	.	PUNCT
ap-8348	244	1	https://doi.org/10.1063/1.5041718	https://doi.org/10.1063/1.5041718	PROPN
ap-8348	245	1	[	[	X
ap-8348	245	2	23	23	NUM
ap-8348	245	3	]	]	PUNCT
ap-8348	245	4	h.	h.	PROPN
ap-8348	245	5	wang	wang	PROPN
ap-8348	245	6	,	,	PUNCT
ap-8348	245	7	l.	l.	PROPN
ap-8348	245	8	lang	lang	PROPN
ap-8348	245	9	,	,	PUNCT
ap-8348	245	10	y.	y.	PROPN
ap-8348	245	11	chong	chong	PROPN
ap-8348	245	12	.	.	PUNCT
ap-8348	246	1	non	non	ADJ
ap-8348	246	2	-	-	ADJ
ap-8348	246	3	hermitian	hermitian	ADJ
ap-8348	246	4	dynamics	dynamic	NOUN
ap-8348	246	5	of	of	ADP
ap-8348	246	6	slowly	slowly	ADV
ap-8348	246	7	varying	vary	VERB
ap-8348	246	8	hamiltonians	hamiltonian	NOUN
ap-8348	246	9	.	.	PUNCT
ap-8348	247	1	physical	physical	ADJ
ap-8348	247	2	review	review	NOUN
ap-8348	247	3	a	a	DET
ap-8348	247	4	98(1):012119	98(1):012119	NUM
ap-8348	247	5	,	,	PUNCT
ap-8348	247	6	2018	2018	NUM
ap-8348	247	7	.	.	PUNCT
ap-8348	248	1	https://doi.org/10.1103/physreva.98.012119	https://doi.org/10.1103/physreva.98.012119	NOUN
ap-8348	249	1	[	[	X
ap-8348	249	2	24	24	NUM
ap-8348	249	3	]	]	X
ap-8348	249	4	s.	s.	PROPN
ap-8348	249	5	cheniti	cheniti	PROPN
ap-8348	249	6	,	,	PUNCT
ap-8348	249	7	w.	w.	PROPN
ap-8348	249	8	koussa	koussa	PROPN
ap-8348	249	9	,	,	PUNCT
ap-8348	249	10	a.	a.	PROPN
ap-8348	249	11	medjber	medjber	PROPN
ap-8348	249	12	,	,	PUNCT
ap-8348	249	13	m.	m.	PROPN
ap-8348	249	14	maamache	maamache	PROPN
ap-8348	249	15	.	.	PUNCT
ap-8348	250	1	adiabatic	adiabatic	ADJ
ap-8348	250	2	theorem	theorem	NOUN
ap-8348	250	3	and	and	CCONJ
ap-8348	250	4	generalized	generalize	VERB
ap-8348	250	5	geometrical	geometrical	ADJ
ap-8348	250	6	phase	phase	NOUN
ap-8348	250	7	in	in	ADP
ap-8348	250	8	the	the	DET
ap-8348	250	9	case	case	NOUN
ap-8348	250	10	of	of	ADP
ap-8348	250	11	pseudo	pseudo	NOUN
ap-8348	250	12	-	-	ADJ
ap-8348	250	13	hermitian	hermitian	ADJ
ap-8348	250	14	systems	system	NOUN
ap-8348	250	15	.	.	PUNCT
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ap-8348	251	2	of	of	ADP
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ap-8348	251	5	:	:	PUNCT
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ap-8348	251	7	and	and	CCONJ
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ap-8348	251	9	53(40):405302	53(40):405302	NUM
ap-8348	251	10	,	,	PUNCT
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ap-8348	251	12	.	.	PUNCT
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ap-8348	253	2	25	25	NUM
ap-8348	253	3	]	]	PUNCT
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ap-8348	253	5	bishop	bishop	PROPN
ap-8348	253	6	,	,	PUNCT
ap-8348	253	7	m.	m.	NOUN
ap-8348	253	8	znojil	znojil	PROPN
ap-8348	253	9	.	.	PUNCT
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ap-8348	254	2	-	-	ADJ
ap-8348	254	3	hermitian	hermitian	ADJ
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ap-8348	254	9	-	-	ADJ
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ap-8348	254	11	systems	system	NOUN
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ap-8348	254	14	interaction	interaction	NOUN
ap-8348	254	15	-	-	PUNCT
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ap-8348	255	3	physical	physical	PROPN
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ap-8348	255	7	,	,	PUNCT
ap-8348	255	8	2020	2020	NUM
ap-8348	255	9	.	.	PUNCT
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ap-8348	256	7	s13360	s13360	NOUN
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ap-8348	256	9	020	020	NUM
ap-8348	256	10	-	-	PUNCT
ap-8348	256	11	00374	00374	NUM
ap-8348	256	12	-	-	SYM
ap-8348	256	13	z	z	NOUN
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ap-8348	257	2	26	26	NUM
ap-8348	257	3	]	]	PUNCT
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ap-8348	257	8	ighezou	ighezou	PROPN
ap-8348	257	9	,	,	PUNCT
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ap-8348	257	11	cherbal	cherbal	PROPN
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ap-8348	257	14	maamache	maamache	PROPN
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ap-8348	258	1	ladder	ladder	NOUN
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ap-8348	258	3	and	and	CCONJ
ap-8348	258	4	coherent	coherent	ADJ
ap-8348	258	5	states	state	NOUN
ap-8348	258	6	for	for	ADP
ap-8348	258	7	timedependent	timedependent	NOUN
ap-8348	258	8	non	non	ADJ
ap-8348	258	9	-	-	ADJ
ap-8348	258	10	hermitian	hermitian	ADJ
ap-8348	258	11	hamiltonians	hamiltonian	NOUN
ap-8348	258	12	.	.	PUNCT
ap-8348	259	1	international	international	ADJ
ap-8348	259	2	journal	journal	PROPN
ap-8348	259	3	of	of	ADP
ap-8348	259	4	theoretical	theoretical	ADJ
ap-8348	259	5	physics	physics	NOUN
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ap-8348	259	7	,	,	PUNCT
ap-8348	259	8	2020	2020	NUM
ap-8348	259	9	.	.	PUNCT
ap-8348	260	1	https://doi.org/10.1007/s10773-020-04401-8	https://doi.org/10.1007/s10773-020-04401-8	X
ap-8348	261	1	[	[	X
ap-8348	261	2	27	27	NUM
ap-8348	261	3	]	]	PUNCT
ap-8348	261	4	j.	j.	PROPN
ap-8348	261	5	choi	choi	PROPN
ap-8348	261	6	.	.	PUNCT
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ap-8348	262	2	theory	theory	NOUN
ap-8348	262	3	for	for	ADP
ap-8348	262	4	time	time	NOUN
ap-8348	262	5	-	-	PUNCT
ap-8348	262	6	dependent	dependent	ADJ
ap-8348	262	7	quantum	quantum	NOUN
ap-8348	262	8	systems	system	NOUN
ap-8348	262	9	involving	involve	VERB
ap-8348	262	10	complex	complex	ADJ
ap-8348	262	11	potentials	potential	NOUN
ap-8348	262	12	.	.	PUNCT
ap-8348	263	1	frontiers	frontier	NOUN
ap-8348	263	2	in	in	ADP
ap-8348	263	3	physics	physics	NOUN
ap-8348	263	4	8	8	NUM
ap-8348	263	5	,	,	PUNCT
ap-8348	263	6	2020	2020	NUM
ap-8348	263	7	.	.	PUNCT
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ap-8348	266	3	the	the	DET
ap-8348	266	4	time	time	NOUN
ap-8348	266	5	-	-	PUNCT
ap-8348	266	6	evolution	evolution	NOUN
ap-8348	266	7	and	and	CCONJ
ap-8348	266	8	observability	observability	NOUN
ap-8348	266	9	of	of	ADP
ap-8348	266	10	non	non	ADJ
ap-8348	266	11	-	-	ADJ
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ap-8348	266	13	hamiltonians	hamiltonian	NOUN
ap-8348	266	14	for	for	ADP
ap-8348	266	15	time	time	NOUN
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ap-8348	266	18	dyson	dyson	NOUN
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ap-8348	266	20	.	.	PUNCT
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ap-8348	267	2	scripta	scripta	PROPN
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ap-8348	267	6	.	.	PUNCT
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ap-8348	270	1	time	time	NOUN
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ap-8348	270	4	pseudo	pseudo	NOUN
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ap-8348	270	9	a	a	DET
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ap-8348	270	15	mechanics	mechanic	NOUN
ap-8348	270	16	.	.	PUNCT
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ap-8348	271	4	2020	2020	NUM
ap-8348	271	5	.	.	PUNCT
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ap-8348	272	2	[	[	X
ap-8348	272	3	30	30	NUM
ap-8348	272	4	]	]	PUNCT
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ap-8348	272	6	alves	alves	PROPN
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ap-8348	272	9	,	,	PUNCT
ap-8348	272	10	r.	r.	PROPN
ap-8348	272	11	dourado	dourado	PROPN
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ap-8348	273	5	:	:	PUNCT
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ap-8348	273	9	-	-	PUNCT
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ap-8348	273	14	-	-	PUNCT
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ap-8348	273	17	-	-	ADJ
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ap-8348	274	3	core	core	PROPN
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ap-8348	274	5	,	,	PUNCT
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ap-8348	274	7	.	.	PUNCT
ap-8348	275	1	https	https	NOUN
ap-8348	275	2	:	:	PUNCT
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ap-8348	275	7	31	31	NUM
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ap-8348	275	20	.	.	PUNCT
ap-8348	276	1	pt	pt	PROPN
ap-8348	276	2	-	-	PUNCT
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ap-8348	276	5	-	-	ADJ
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ap-8348	276	10	operator	operator	NOUN
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ap-8348	276	17	.	.	PUNCT
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ap-8348	277	2	in	in	ADP
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ap-8348	277	5	,	,	PUNCT
ap-8348	277	6	2022	2022	NUM
ap-8348	277	7	.	.	PUNCT
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ap-8348	279	2	32	32	NUM
ap-8348	279	3	]	]	PUNCT
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ap-8348	280	2	-	-	PUNCT
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ap-8348	281	1	applicable	applicable	ADJ
ap-8348	281	2	analysis	analysis	NOUN
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ap-8348	281	5	mathematics	mathematic	NOUN
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ap-8348	281	7	,	,	PUNCT
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ap-8348	281	9	.	.	PUNCT
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ap-8348	283	2	33	33	NUM
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ap-8348	285	2	,	,	PUNCT
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ap-8348	286	2	34	34	NUM
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ap-8348	287	8	hermitian	hermitian	ADJ
ap-8348	287	9	hamiltonian	hamiltonian	ADJ
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ap-8348	287	15	-	-	ADJ
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ap-8348	288	4	95(1):010102	95(1):010102	NUM
ap-8348	288	5	,	,	PUNCT
ap-8348	288	6	2017	2017	NUM
ap-8348	288	7	.	.	PUNCT
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ap-8348	290	4	approach	approach	NOUN
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ap-8348	296	6	,	,	PUNCT
ap-8348	296	7	o.	o.	PROPN
ap-8348	296	8	rosas	rosas	PROPN
ap-8348	296	9	-	-	PUNCT
ap-8348	296	10	ortiz	ortiz	PROPN
ap-8348	296	11	.	.	PUNCT
ap-8348	297	1	exact	exact	ADJ
ap-8348	297	2	solutions	solution	NOUN
ap-8348	297	3	for	for	ADP
ap-8348	297	4	time	time	NOUN
ap-8348	297	5	-	-	PUNCT
ap-8348	297	6	dependent	dependent	ADJ
ap-8348	297	7	non	non	ADJ
ap-8348	297	8	-	-	ADJ
ap-8348	297	9	hermitian	hermitian	ADJ
ap-8348	297	10	oscillators	oscillator	NOUN
ap-8348	297	11	:	:	PUNCT
ap-8348	297	12	classical	classical	ADJ
ap-8348	297	13	and	and	CCONJ
ap-8348	297	14	quantum	quantum	ADJ
ap-8348	297	15	pictures	picture	NOUN
ap-8348	297	16	.	.	PUNCT
ap-8348	298	1	quantum	quantum	ADJ
ap-8348	298	2	reports	report	NOUN
ap-8348	298	3	3(3):458–472	3(3):458–472	NUM
ap-8348	298	4	,	,	PUNCT
ap-8348	298	5	2021	2021	NUM
ap-8348	298	6	.	.	PUNCT
ap-8348	299	1	https://doi.org/10.3390/quantum3030030	https://doi.org/10.3390/quantum3030030	PROPN
ap-8348	300	1	[	[	X
ap-8348	300	2	38	38	NUM
ap-8348	300	3	]	]	PUNCT
ap-8348	300	4	m.	m.	PROPN
ap-8348	300	5	huang	huang	PROPN
ap-8348	300	6	,	,	PUNCT
ap-8348	300	7	r.	r.	PROPN
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ap-8348	300	9	,	,	PUNCT
ap-8348	300	10	q.	q.	PROPN
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ap-8348	300	12	,	,	PUNCT
ap-8348	300	13	et	et	PROPN
ap-8348	300	14	al	al	PROPN
ap-8348	300	15	.	.	PUNCT
ap-8348	301	1	solvable	solvable	ADJ
ap-8348	301	2	dilation	dilation	NOUN
ap-8348	301	3	model	model	NOUN
ap-8348	301	4	of	of	ADP
ap-8348	301	5	time	time	NOUN
ap-8348	301	6	-	-	PUNCT
ap-8348	301	7	dependent	dependent	ADJ
ap-8348	301	8	pt	pt	ADJ
ap-8348	301	9	-	-	PUNCT
ap-8348	301	10	symmetric	symmetric	ADJ
ap-8348	301	11	systems	system	NOUN
ap-8348	301	12	.	.	PUNCT
ap-8348	302	1	physical	physical	ADJ
ap-8348	302	2	review	review	VERB
ap-8348	302	3	a	a	DET
ap-8348	302	4	105(6):062205	105(6):062205	NUM
ap-8348	302	5	,	,	PUNCT
ap-8348	302	6	2022	2022	NUM
ap-8348	302	7	.	.	PUNCT
ap-8348	303	1	https://doi.org/10.1103/physreva.105.062205	https://doi.org/10.1103/physreva.105.062205	NOUN
ap-8348	303	2	138	138	NUM
ap-8348	303	3	https://doi.org/10.1016/j.physletb.2007.04.064	https://doi.org/10.1016/j.physletb.2007.04.064	NOUN
ap-8348	303	4	http://arxiv.org/abs/0710.5653	http://arxiv.org/abs/0710.5653	X
ap-8348	303	5	https://doi.org/10.1103/physrevd.78.085003	https://doi.org/10.1103/physrevd.78.085003	NOUN
ap-8348	303	6	https://doi.org/10.1088/1751-8113/46/48/485302	https://doi.org/10.1088/1751-8113/46/48/485302	PROPN
ap-8348	303	7	https://doi.org/10.1103/physreva.93.042114	https://doi.org/10.1103/physreva.93.042114	NOUN
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ap-8348	303	10	https://doi.org/10.1140/epjp/i2017-11678-2	https://doi.org/10.1140/epjp/i2017-11678-2	NOUN
ap-8348	303	11	https://doi.org/10.14311/ap.2017.57.0424	https://doi.org/10.14311/ap.2017.57.0424	NOUN
ap-8348	303	12	https://doi.org/10.31526/lhep.3.2018.02	https://doi.org/10.31526/lhep.3.2018.02	PROPN
ap-8348	303	13	https://doi.org/10.1140/epjp/i2018-12251-3	https://doi.org/10.1140/epjp/i2018-12251-3	PROPN
ap-8348	303	14	https://doi.org/10.1063/1.5041718	https://doi.org/10.1063/1.5041718	PROPN
ap-8348	303	15	https://doi.org/10.1103/physreva.98.012119	https://doi.org/10.1103/physreva.98.012119	PROPN
ap-8348	303	16	https://doi.org/10.1088/1751-8121/abad79	https://doi.org/10.1088/1751-8121/abad79	PART
ap-8348	303	17	https://doi.org/10.1140/epjp/s13360-020-00374-z	https://doi.org/10.1140/epjp/s13360-020-00374-z	PROPN
ap-8348	303	18	https://doi.org/10.1140/epjp/s13360-020-00374-z	https://doi.org/10.1140/epjp/s13360-020-00374-z	PROPN
ap-8348	303	19	https://doi.org/10.1007/s10773-020-04401-8	https://doi.org/10.1007/s10773-020-04401-8	NOUN
ap-8348	303	20	https://doi.org/10.3389/fphy.2020.00189	https://doi.org/10.3389/fphy.2020.00189	PROPN
ap-8348	303	21	https://doi.org/10.1088/1402-4896/ab80e5	https://doi.org/10.1088/1402-4896/ab80e5	NOUN
ap-8348	303	22	https://doi.org/10.3390/e22040471	https://doi.org/10.3390/e22040471	PROPN
ap-8348	303	23	https://doi.org/10.21468/scipostphyscore.5.1.012	https://doi.org/10.21468/scipostphyscore.5.1.012	PROPN
ap-8348	303	24	https://doi.org/10.21468/scipostphyscore.5.1.012	https://doi.org/10.21468/scipostphyscore.5.1.012	PROPN
ap-8348	303	25	https://doi.org/10.1016/j.rinp.2022.105561	https://doi.org/10.1016/j.rinp.2022.105561	PROPN
ap-8348	303	26	https://doi.org/10.2298/aadm0802123e	https://doi.org/10.2298/aadm0802123e	VERB
ap-8348	303	27	https://doi.org/10.1103/physreva.95.010102	https://doi.org/10.1103/physreva.95.010102	ADJ
ap-8348	303	28	https://doi.org/10.1007/s10773-020-04417-0	https://doi.org/10.1007/s10773-020-04417-0	NUM
ap-8348	303	29	https://doi.org/10.1016/j.physleta.2021.127548	https://doi.org/10.1016/j.physleta.2021.127548	PROPN
ap-8348	303	30	https://doi.org/10.3390/quantum3030030	https://doi.org/10.3390/quantum3030030	NOUN
ap-8348	303	31	https://doi.org/10.1103/physreva.105.062205	https://doi.org/10.1103/physreva.105.062205	NOUN
ap-8348	303	32	vol	vol	NOUN
ap-8348	303	33	.	.	PROPN
ap-8348	304	1	63	63	NUM
ap-8348	304	2	no	no	NOUN
ap-8348	304	3	.	.	PUNCT
ap-8348	305	1	2/2023	2/2023	NUM
ap-8348	305	2	exact	exact	ADJ
ap-8348	305	3	solutions	solution	NOUN
ap-8348	305	4	for	for	ADP
ap-8348	305	5	time	time	NOUN
ap-8348	305	6	-	-	PUNCT
ap-8348	305	7	dependent	dependent	ADJ
ap-8348	305	8	complex	complex	ADJ
ap-8348	305	9	symmetric	symmetric	ADJ
ap-8348	305	10	potential	potential	NOUN
ap-8348	306	1	well	well	INTJ
ap-8348	307	1	[	[	X
ap-8348	307	2	39	39	NUM
ap-8348	307	3	]	]	PUNCT
ap-8348	307	4	f.	f.	PROPN
ap-8348	307	5	kecita	kecita	PROPN
ap-8348	307	6	,	,	PUNCT
ap-8348	307	7	a.	a.	NOUN
ap-8348	307	8	bounames	bouname	NOUN
ap-8348	307	9	,	,	PUNCT
ap-8348	307	10	m.	m.	NOUN
ap-8348	307	11	maamache	maamache	PROPN
ap-8348	307	12	.	.	PUNCT
ap-8348	308	1	a	a	DET
ap-8348	308	2	real	real	ADJ
ap-8348	308	3	expectation	expectation	NOUN
ap-8348	308	4	value	value	NOUN
ap-8348	308	5	of	of	ADP
ap-8348	308	6	the	the	DET
ap-8348	308	7	time	time	NOUN
ap-8348	308	8	-	-	PUNCT
ap-8348	308	9	dependent	dependent	ADJ
ap-8348	308	10	non	non	ADJ
ap-8348	308	11	-	-	ADJ
ap-8348	308	12	hermitian	hermitian	ADJ
ap-8348	308	13	hamiltonians	hamiltonian	NOUN
ap-8348	308	14	.	.	PUNCT
ap-8348	309	1	physica	physica	PROPN
ap-8348	309	2	scripta	scripta	PROPN
ap-8348	309	3	96(12):125265	96(12):125265	PROPN
ap-8348	309	4	,	,	PUNCT
ap-8348	309	5	2021	2021	NUM
ap-8348	309	6	.	.	PUNCT
ap-8348	310	1	https://doi.org/10.1088/1402-4896/ac3dbd	https://doi.org/10.1088/1402-4896/ac3dbd	X
ap-8348	311	1	[	[	X
ap-8348	311	2	40	40	NUM
ap-8348	311	3	]	]	PUNCT
ap-8348	311	4	b.	b.	PROPN
ap-8348	311	5	villegas	villegas	PROPN
ap-8348	311	6	-	-	PUNCT
ap-8348	311	7	martinez	martinez	PROPN
ap-8348	311	8	,	,	PUNCT
ap-8348	311	9	h.	h.	PROPN
ap-8348	311	10	moya	moya	PROPN
ap-8348	311	11	-	-	PUNCT
ap-8348	311	12	cessa	cessa	PROPN
ap-8348	311	13	,	,	PUNCT
ap-8348	311	14	f.	f.	PROPN
ap-8348	311	15	soto	soto	PROPN
ap-8348	311	16	-	-	PUNCT
ap-8348	311	17	eguibar	eguibar	NOUN
ap-8348	311	18	.	.	PUNCT
ap-8348	312	1	exact	exact	ADJ
ap-8348	312	2	solution	solution	NOUN
ap-8348	312	3	for	for	ADP
ap-8348	312	4	the	the	DET
ap-8348	312	5	time	time	NOUN
ap-8348	312	6	dependent	dependent	ADJ
ap-8348	312	7	non	non	ADJ
ap-8348	312	8	-	-	ADJ
ap-8348	312	9	hermitian	hermitian	ADJ
ap-8348	312	10	generalized	generalized	ADJ
ap-8348	312	11	swanson	swanson	PROPN
ap-8348	312	12	oscillator	oscillator	NOUN
ap-8348	312	13	,	,	PUNCT
ap-8348	312	14	2022	2022	NUM
ap-8348	312	15	.	.	PUNCT
ap-8348	313	1	arxiv:2205.05741	arxiv:2205.05741	VERB
ap-8348	314	1	[	[	X
ap-8348	314	2	41	41	NUM
ap-8348	314	3	]	]	PUNCT
ap-8348	314	4	p.	p.	NOUN
ap-8348	314	5	caldirola	caldirola	PROPN
ap-8348	314	6	.	.	PUNCT
ap-8348	315	1	forze	forze	PROPN
ap-8348	315	2	non	non	PROPN
ap-8348	315	3	conservative	conservative	ADJ
ap-8348	315	4	nella	nella	PROPN
ap-8348	315	5	meccanica	meccanica	PROPN
ap-8348	315	6	quantistica	quantistica	PROPN
ap-8348	315	7	.	.	PUNCT
ap-8348	316	1	il	il	PROPN
ap-8348	316	2	nuovo	nuovo	PROPN
ap-8348	316	3	cimento	cimento	PROPN
ap-8348	316	4	18(9):393–400	18(9):393–400	PROPN
ap-8348	316	5	,	,	PUNCT
ap-8348	316	6	1941	1941	NUM
ap-8348	316	7	.	.	PUNCT
ap-8348	317	1	https://doi.org/10.1007/bf02960144	https://doi.org/10.1007/bf02960144	X
ap-8348	318	1	[	[	X
ap-8348	318	2	42	42	NUM
ap-8348	318	3	]	]	X
ap-8348	318	4	e.	e.	PROPN
ap-8348	318	5	kanai	kanai	PROPN
ap-8348	318	6	.	.	PROPN
ap-8348	319	1	on	on	ADP
ap-8348	319	2	the	the	DET
ap-8348	319	3	quantization	quantization	NOUN
ap-8348	319	4	of	of	ADP
ap-8348	319	5	the	the	DET
ap-8348	319	6	dissipative	dissipative	NOUN
ap-8348	319	7	systems	system	NOUN
ap-8348	319	8	.	.	PUNCT
ap-8348	320	1	progress	progress	NOUN
ap-8348	320	2	of	of	ADP
ap-8348	320	3	theoretical	theoretical	ADJ
ap-8348	320	4	physics	physics	NOUN
ap-8348	320	5	3(4):440–442	3(4):440–442	NUM
ap-8348	320	6	,	,	PUNCT
ap-8348	320	7	1948	1948	NUM
ap-8348	320	8	.	.	PUNCT
ap-8348	321	1	https://doi.org/10.1143/ptp/3.4.440	https://doi.org/10.1143/ptp/3.4.440	NOUN
ap-8348	322	1	[	[	X
ap-8348	322	2	43	43	NUM
ap-8348	322	3	]	]	PUNCT
ap-8348	322	4	m.	m.	NOUN
ap-8348	322	5	abdalla	abdalla	PROPN
ap-8348	322	6	.	.	PUNCT
ap-8348	323	1	canonical	canonical	ADJ
ap-8348	323	2	treatment	treatment	NOUN
ap-8348	323	3	of	of	ADP
ap-8348	323	4	harmonic	harmonic	ADJ
ap-8348	323	5	oscillator	oscillator	NOUN
ap-8348	323	6	with	with	ADP
ap-8348	323	7	variable	variable	ADJ
ap-8348	323	8	mass	mass	PROPN
ap-8348	323	9	.	.	PUNCT
ap-8348	324	1	physical	physical	ADJ
ap-8348	324	2	review	review	NOUN
ap-8348	324	3	a	a	DET
ap-8348	324	4	33(5):2870–2876	33(5):2870–2876	NUM
ap-8348	324	5	,	,	PUNCT
ap-8348	324	6	1986	1986	NUM
ap-8348	324	7	.	.	PUNCT
ap-8348	325	1	https://doi.org/10.1103/physreva.33.2870	https://doi.org/10.1103/physreva.33.2870	NOUN
ap-8348	326	1	[	[	X
ap-8348	326	2	44	44	NUM
ap-8348	326	3	]	]	PUNCT
ap-8348	326	4	i.	i.	PROPN
ap-8348	326	5	ramos	ramos	PROPN
ap-8348	326	6	-	-	PROPN
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ap-8348	326	8	,	,	PUNCT
ap-8348	326	9	a.	a.	PROPN
ap-8348	326	10	espinosa	espinosa	PROPN
ap-8348	326	11	-	-	PUNCT
ap-8348	326	12	zuñiga	zuñiga	PROPN
ap-8348	326	13	,	,	PUNCT
ap-8348	326	14	m.	m.	NOUN
ap-8348	326	15	fernández	fernández	PROPN
ap-8348	326	16	-	-	PUNCT
ap-8348	326	17	guasti	guasti	PROPN
ap-8348	326	18	,	,	PUNCT
ap-8348	326	19	h.	h.	PROPN
ap-8348	326	20	moya	moya	PROPN
ap-8348	326	21	-	-	PUNCT
ap-8348	326	22	cessa	cessa	NOUN
ap-8348	326	23	.	.	PUNCT
ap-8348	327	1	quantum	quantum	PROPN
ap-8348	327	2	harmonic	harmonic	NOUN
ap-8348	327	3	oscillator	oscillator	NOUN
ap-8348	327	4	with	with	ADP
ap-8348	327	5	time	time	NOUN
ap-8348	327	6	-	-	PUNCT
ap-8348	327	7	dependent	dependent	ADJ
ap-8348	327	8	mass	mass	NOUN
ap-8348	327	9	.	.	PUNCT
ap-8348	328	1	modern	modern	ADJ
ap-8348	328	2	physics	physics	PROPN
ap-8348	328	3	letters	letters	PROPN
ap-8348	328	4	b	b	PROPN
ap-8348	328	5	32(20):1850235	32(20):1850235	NUM
ap-8348	328	6	,	,	PUNCT
ap-8348	328	7	2018	2018	NUM
ap-8348	328	8	.	.	PUNCT
ap-8348	329	1	https://doi.org/10.1142/s0217984918502354	https://doi.org/10.1142/s0217984918502354	NUM
ap-8348	329	2	[	[	X
ap-8348	329	3	45	45	NUM
ap-8348	329	4	]	]	PUNCT
ap-8348	329	5	k.	k.	PROPN
ap-8348	329	6	zelaya	zelaya	PROPN
ap-8348	329	7	.	.	PUNCT
ap-8348	329	8	time	time	NOUN
ap-8348	329	9	-	-	PUNCT
ap-8348	329	10	dependent	dependent	ADJ
ap-8348	329	11	mass	mass	NOUN
ap-8348	329	12	oscillators	oscillator	NOUN
ap-8348	329	13	:	:	PUNCT
ap-8348	329	14	constants	constant	NOUN
ap-8348	329	15	of	of	ADP
ap-8348	329	16	motion	motion	NOUN
ap-8348	329	17	and	and	CCONJ
ap-8348	329	18	semiclasical	semiclasical	ADJ
ap-8348	329	19	states	state	NOUN
ap-8348	329	20	.	.	PUNCT
ap-8348	330	1	acta	acta	PROPN
ap-8348	330	2	polytechnica	polytechnica	PROPN
ap-8348	330	3	62(1):211–221	62(1):211–221	PROPN
ap-8348	330	4	,	,	PUNCT
ap-8348	330	5	2022	2022	NUM
ap-8348	330	6	.	.	PUNCT
ap-8348	331	1	https://doi.org/10.14311/ap.2022.62.0211	https://doi.org/10.14311/ap.2022.62.0211	X
ap-8348	332	1	[	[	X
ap-8348	332	2	46	46	NUM
ap-8348	332	3	]	]	X
ap-8348	332	4	h.	h.	PROPN
ap-8348	332	5	lewis	lewis	PROPN
ap-8348	332	6	,	,	PUNCT
ap-8348	332	7	w.	w.	PROPN
ap-8348	332	8	riesenfeld	riesenfeld	PROPN
ap-8348	332	9	.	.	PUNCT
ap-8348	333	1	an	an	DET
ap-8348	333	2	exact	exact	ADJ
ap-8348	333	3	quantum	quantum	NOUN
ap-8348	333	4	theory	theory	NOUN
ap-8348	333	5	of	of	ADP
ap-8348	333	6	the	the	DET
ap-8348	333	7	time	time	NOUN
ap-8348	333	8	-	-	PUNCT
ap-8348	333	9	dependent	dependent	ADJ
ap-8348	333	10	harmonic	harmonic	ADJ
ap-8348	333	11	oscillator	oscillator	NOUN
ap-8348	333	12	and	and	CCONJ
ap-8348	333	13	of	of	ADP
ap-8348	333	14	a	a	DET
ap-8348	333	15	charged	charge	VERB
ap-8348	333	16	particle	particle	NOUN
ap-8348	333	17	in	in	ADP
ap-8348	333	18	a	a	DET
ap-8348	333	19	time	time	NOUN
ap-8348	333	20	-	-	PUNCT
ap-8348	333	21	dependent	dependent	ADJ
ap-8348	333	22	electromagnetic	electromagnetic	ADJ
ap-8348	333	23	field	field	NOUN
ap-8348	333	24	.	.	PUNCT
ap-8348	334	1	journal	journal	PROPN
ap-8348	334	2	of	of	ADP
ap-8348	334	3	mathematical	mathematical	ADJ
ap-8348	334	4	physics	physics	NOUN
ap-8348	334	5	10(8):1458–1473	10(8):1458–1473	NUM
ap-8348	334	6	,	,	PUNCT
ap-8348	334	7	1969	1969	NUM
ap-8348	334	8	.	.	PUNCT
ap-8348	335	1	https://doi.org/10.1063/1.1664991	https://doi.org/10.1063/1.1664991	PUNCT
ap-8348	336	1	[	[	X
ap-8348	336	2	47	47	NUM
ap-8348	336	3	]	]	PUNCT
ap-8348	336	4	j.	j.	PROPN
ap-8348	336	5	schwinger	schwinger	PROPN
ap-8348	336	6	.	.	PUNCT
ap-8348	336	7	symbolism	symbolism	NOUN
ap-8348	336	8	of	of	ADP
ap-8348	336	9	atomic	atomic	ADJ
ap-8348	336	10	measurements	measurement	NOUN
ap-8348	336	11	.	.	PUNCT
ap-8348	337	1	springer	springer	NOUN
ap-8348	337	2	,	,	PUNCT
ap-8348	337	3	2001	2001	NUM
ap-8348	337	4	.	.	PUNCT
ap-8348	338	1	[	[	X
ap-8348	338	2	48	48	NUM
ap-8348	338	3	]	]	PUNCT
ap-8348	338	4	o.	o.	NOUN
ap-8348	338	5	vallée	vallée	NOUN
ap-8348	338	6	,	,	PUNCT
ap-8348	338	7	m.	m.	NOUN
ap-8348	338	8	soares	soares	PROPN
ap-8348	338	9	.	.	PUNCT
ap-8348	338	10	airy	airy	ADJ
ap-8348	338	11	functions	function	NOUN
ap-8348	338	12	and	and	CCONJ
ap-8348	338	13	applications	application	NOUN
ap-8348	338	14	to	to	ADP
ap-8348	338	15	physics	physics	PROPN
ap-8348	338	16	.	.	PUNCT
ap-8348	339	1	imperial	imperial	ADJ
ap-8348	339	2	college	college	PROPN
ap-8348	339	3	press	press	NOUN
ap-8348	339	4	,	,	PUNCT
ap-8348	339	5	2004	2004	NUM
ap-8348	339	6	.	.	PUNCT
ap-8348	340	1	[	[	X
ap-8348	340	2	49	49	NUM
ap-8348	340	3	]	]	PUNCT
ap-8348	340	4	f.	f.	PROPN
ap-8348	340	5	olver	olver	PROPN
ap-8348	340	6	,	,	PUNCT
ap-8348	340	7	d.	d.	PROPN
ap-8348	340	8	lozier	lozier	PROPN
ap-8348	340	9	,	,	PUNCT
ap-8348	340	10	r.	r.	PROPN
ap-8348	340	11	boisvert	boisvert	PROPN
ap-8348	340	12	,	,	PUNCT
ap-8348	340	13	c.	c.	PROPN
ap-8348	340	14	clark	clark	PROPN
ap-8348	340	15	.	.	PUNCT
ap-8348	341	1	nist	nist	PROPN
ap-8348	341	2	handbook	handbook	PROPN
ap-8348	341	3	of	of	ADP
ap-8348	341	4	mathematical	mathematical	ADJ
ap-8348	341	5	functions	function	NOUN
ap-8348	341	6	,	,	PUNCT
ap-8348	341	7	chap	chap	NOUN
ap-8348	341	8	.	.	PUNCT
ap-8348	342	1	9	9	X
ap-8348	342	2	.	.	X
ap-8348	342	3	cambridge	cambridge	PROPN
ap-8348	342	4	university	university	PROPN
ap-8348	342	5	press	press	NOUN
ap-8348	342	6	,	,	PUNCT
ap-8348	342	7	2010	2010	NUM
ap-8348	342	8	.	.	PUNCT
ap-8348	343	1	http://dlmf.nist.gov/9	http://dlmf.nist.gov/9	NOUN
ap-8348	343	2	139	139	NUM
ap-8348	343	3	https://doi.org/10.1088/1402-4896/ac3dbd	https://doi.org/10.1088/1402-4896/ac3dbd	PROPN
ap-8348	343	4	http://arxiv.org/abs/2205.05741	http://arxiv.org/abs/2205.05741	PROPN
ap-8348	343	5	https://doi.org/10.1007/bf02960144	https://doi.org/10.1007/bf02960144	X
ap-8348	343	6	https://doi.org/10.1143/ptp/3.4.440	https://doi.org/10.1143/ptp/3.4.440	X
ap-8348	343	7	https://doi.org/10.1103/physreva.33.2870	https://doi.org/10.1103/physreva.33.2870	NOUN
ap-8348	343	8	https://doi.org/10.1142/s0217984918502354	https://doi.org/10.1142/s0217984918502354	X
ap-8348	343	9	https://doi.org/10.14311/ap.2022.62.0211	https://doi.org/10.14311/ap.2022.62.0211	NOUN
ap-8348	343	10	https://doi.org/10.1063/1.1664991	https://doi.org/10.1063/1.1664991	PUNCT
ap-8348	343	11	http://dlmf.nist.gov/9	http://dlmf.nist.gov/9	NOUN
ap-8348	343	12	acta	acta	PROPN
ap-8348	343	13	polytechnica	polytechnica	PROPN
ap-8348	343	14	63(2):132–138	63(2):132–138	PROPN
ap-8348	343	15	,	,	PUNCT
ap-8348	343	16	2023	2023	NUM
ap-8348	343	17	1	1	NUM
ap-8348	343	18	introduction	introduction	NOUN
ap-8348	343	19	2	2	NUM
ap-8348	343	20	td	td	NOUN
ap-8348	343	21	non	non	ADJ
ap-8348	343	22	-	-	ADJ
ap-8348	343	23	hermitian	hermitian	ADJ
ap-8348	343	24	hamiltonian	hamiltonian	NOUN
ap-8348	343	25	with	with	ADP
ap-8348	343	26	td	td	NOUN
ap-8348	343	27	metric	metric	ADJ
ap-8348	343	28	3	3	NUM
ap-8348	343	29	pseudo	pseudo	NOUN
ap-8348	343	30	-	-	ADJ
ap-8348	343	31	invariant	invariant	ADJ
ap-8348	343	32	operator	operator	NOUN
ap-8348	343	33	method	method	NOUN
ap-8348	343	34	4	4	NUM
ap-8348	343	35	particle	particle	NOUN
ap-8348	343	36	in	in	ADP
ap-8348	343	37	td	td	NOUN
ap-8348	343	38	complex	complex	ADJ
ap-8348	343	39	symmetric	symmetric	ADJ
ap-8348	343	40	potential	potential	ADJ
ap-8348	343	41	well	well	NOUN
ap-8348	343	42	5	5	NUM
ap-8348	343	43	conclusion	conclusion	NOUN
ap-8348	343	44	references	reference	NOUN