id	sid	tid	token	lemma	pos
ap-10625	1	1	acta	acta	PROPN
ap-10625	1	2	polytechnica	polytechnica	PROPN
ap-10625	1	3	https://doi.org/10.14311/ap.2025.65.0546	https://doi.org/10.14311/ap.2025.65.0546	PROPN
ap-10625	1	4	acta	acta	PROPN
ap-10625	1	5	polytechnica	polytechnica	PROPN
ap-10625	1	6	65(5):546–553	65(5):546–553	PROPN
ap-10625	1	7	,	,	PUNCT
ap-10625	1	8	2025	2025	NUM
ap-10625	1	9	©	©	ADP
ap-10625	1	10	2025	2025	NUM
ap-10625	1	11	the	the	DET
ap-10625	1	12	author(s	author(s	NOUN
ap-10625	1	13	)	)	PUNCT
ap-10625	1	14	.	.	PUNCT
ap-10625	2	1	licensed	license	VERB
ap-10625	2	2	under	under	ADP
ap-10625	2	3	a	a	DET
ap-10625	2	4	cc	cc	NOUN
ap-10625	2	5	-	-	PUNCT
ap-10625	2	6	by	by	ADP
ap-10625	2	7	4.0	4.0	NUM
ap-10625	2	8	licence	licence	NOUN
ap-10625	2	9	published	publish	VERB
ap-10625	2	10	by	by	ADP
ap-10625	2	11	the	the	DET
ap-10625	2	12	czech	czech	PROPN
ap-10625	2	13	technical	technical	PROPN
ap-10625	2	14	university	university	PROPN
ap-10625	2	15	in	in	ADP
ap-10625	2	16	prague	prague	PROPN
ap-10625	2	17	dirac	dirac	PROPN
ap-10625	2	18	fermion	fermion	PROPN
ap-10625	2	19	in	in	ADP
ap-10625	2	20	a	a	DET
ap-10625	2	21	time	time	NOUN
ap-10625	2	22	-	-	PUNCT
ap-10625	2	23	dependent	dependent	ADJ
ap-10625	2	24	spherical	spherical	ADJ
ap-10625	2	25	box	box	PROPN
ap-10625	2	26	kuvonchbek	kuvonchbek	PROPN
ap-10625	2	27	matchonova	matchonova	PROPN
ap-10625	2	28	,	,	PUNCT
ap-10625	2	29	davron	davron	PROPN
ap-10625	2	30	matrasulovb	matrasulovb	PROPN
ap-10625	2	31	,	,	PUNCT
ap-10625	2	32	c	c	NOUN
ap-10625	2	33	,	,	PUNCT
ap-10625	2	34	jaroslav	jaroslav	PROPN
ap-10625	2	35	dittrichd,∗	dittrichd,∗	AUX
ap-10625	2	36	a	a	DET
ap-10625	2	37	national	national	ADJ
ap-10625	2	38	university	university	PROPN
ap-10625	2	39	of	of	ADP
ap-10625	2	40	uzbekistan	uzbekistan	PROPN
ap-10625	2	41	,	,	PUNCT
ap-10625	2	42	4	4	NUM
ap-10625	2	43	university	university	NOUN
ap-10625	2	44	str	str	NOUN
ap-10625	2	45	.	.	PUNCT
ap-10625	3	1	,	,	PUNCT
ap-10625	3	2	100174	100174	NUM
ap-10625	3	3	tashkent	tashkent	NOUN
ap-10625	3	4	,	,	PUNCT
ap-10625	3	5	uzbekistan	uzbekistan	PROPN
ap-10625	3	6	b	b	PROPN
ap-10625	3	7	turin	turin	PROPN
ap-10625	3	8	polytechnic	polytechnic	PROPN
ap-10625	3	9	university	university	PROPN
ap-10625	3	10	in	in	ADP
ap-10625	3	11	tashkent	tashkent	NOUN
ap-10625	3	12	,	,	PUNCT
ap-10625	3	13	17	17	NUM
ap-10625	3	14	niyazov	niyazov	NOUN
ap-10625	3	15	str	str	NOUN
ap-10625	3	16	.	.	PUNCT
ap-10625	3	17	,	,	PUNCT
ap-10625	3	18	100095	100095	NUM
ap-10625	3	19	tashkent	tashkent	NOUN
ap-10625	3	20	,	,	PUNCT
ap-10625	3	21	uzbekistan	uzbekistan	PROPN
ap-10625	3	22	c	c	PROPN
ap-10625	3	23	tashkent	tashkent	PROPN
ap-10625	3	24	university	university	PROPN
ap-10625	3	25	of	of	ADP
ap-10625	3	26	architecture	architecture	NOUN
ap-10625	3	27	and	and	CCONJ
ap-10625	3	28	civil	civil	ADJ
ap-10625	3	29	engineering	engineering	NOUN
ap-10625	3	30	,	,	PUNCT
ap-10625	3	31	yangishahar	yangishahar	PROPN
ap-10625	3	32	str	str	NOUN
ap-10625	3	33	.	.	PUNCT
ap-10625	4	1	9a	9a	NOUN
ap-10625	4	2	,	,	PUNCT
ap-10625	4	3	100095	100095	NUM
ap-10625	4	4	tashkent	tashkent	NOUN
ap-10625	4	5	,	,	PUNCT
ap-10625	4	6	uzbekistan	uzbekistan	PROPN
ap-10625	4	7	d	d	PROPN
ap-10625	4	8	czech	czech	PROPN
ap-10625	4	9	academy	academy	PROPN
ap-10625	4	10	of	of	ADP
ap-10625	4	11	sciences	sciences	PROPN
ap-10625	4	12	,	,	PUNCT
ap-10625	4	13	nuclear	nuclear	PROPN
ap-10625	4	14	physics	physics	PROPN
ap-10625	4	15	institute	institute	PROPN
ap-10625	4	16	,	,	PUNCT
ap-10625	4	17	25068	25068	NUM
ap-10625	4	18	řež	řež	PROPN
ap-10625	4	19	,	,	PUNCT
ap-10625	4	20	czech	czech	PROPN
ap-10625	4	21	republic	republic	NOUN
ap-10625	4	22	∗	∗	NOUN
ap-10625	4	23	corresponding	correspond	VERB
ap-10625	4	24	author	author	NOUN
ap-10625	4	25	:	:	PUNCT
ap-10625	4	26	dittrich@ujf.cas.cz	dittrich@ujf.cas.cz	NOUN
ap-10625	4	27	abstract	abstract	NOUN
ap-10625	4	28	.	.	PUNCT
ap-10625	5	1	we	we	PRON
ap-10625	5	2	consider	consider	VERB
ap-10625	5	3	a	a	DET
ap-10625	5	4	dirac	dirac	NOUN
ap-10625	5	5	particle	particle	NOUN
ap-10625	5	6	in	in	ADP
ap-10625	5	7	a	a	DET
ap-10625	5	8	spherical	spherical	ADJ
ap-10625	5	9	box	box	NOUN
ap-10625	5	10	with	with	ADP
ap-10625	5	11	a	a	DET
ap-10625	5	12	time	time	NOUN
ap-10625	5	13	-	-	PUNCT
ap-10625	5	14	dependent	dependent	ADJ
ap-10625	5	15	radius	radius	NOUN
ap-10625	5	16	.	.	PUNCT
ap-10625	6	1	analytical	analytical	ADJ
ap-10625	6	2	and	and	CCONJ
ap-10625	6	3	numerical	numerical	ADJ
ap-10625	6	4	solutions	solution	NOUN
ap-10625	6	5	of	of	ADP
ap-10625	6	6	the	the	DET
ap-10625	6	7	time	time	NOUN
ap-10625	6	8	-	-	PUNCT
ap-10625	6	9	dependent	dependent	ADJ
ap-10625	6	10	dirac	dirac	NOUN
ap-10625	6	11	equation	equation	NOUN
ap-10625	6	12	with	with	ADP
ap-10625	6	13	time	time	NOUN
ap-10625	6	14	-	-	PUNCT
ap-10625	6	15	dependent	dependent	ADJ
ap-10625	6	16	boundary	boundary	NOUN
ap-10625	6	17	(	(	PUNCT
ap-10625	6	18	dirichlet	dirichlet	NOUN
ap-10625	6	19	)	)	PUNCT
ap-10625	6	20	conditions	condition	NOUN
ap-10625	6	21	are	be	AUX
ap-10625	6	22	obtained	obtain	VERB
ap-10625	6	23	.	.	PUNCT
ap-10625	7	1	using	use	VERB
ap-10625	7	2	the	the	DET
ap-10625	7	3	obtained	obtain	VERB
ap-10625	7	4	solutions	solution	NOUN
ap-10625	7	5	,	,	PUNCT
ap-10625	7	6	physically	physically	ADV
ap-10625	7	7	observable	observable	ADJ
ap-10625	7	8	characteristics	characteristic	NOUN
ap-10625	7	9	of	of	ADP
ap-10625	7	10	the	the	DET
ap-10625	7	11	dynamical	dynamical	ADJ
ap-10625	7	12	confinement	confinement	NOUN
ap-10625	7	13	,	,	PUNCT
ap-10625	7	14	such	such	ADJ
ap-10625	7	15	as	as	ADP
ap-10625	7	16	the	the	DET
ap-10625	7	17	average	average	ADJ
ap-10625	7	18	kinetic	kinetic	ADJ
ap-10625	7	19	energy	energy	NOUN
ap-10625	7	20	(	(	PUNCT
ap-10625	7	21	as	as	ADP
ap-10625	7	22	a	a	DET
ap-10625	7	23	function	function	NOUN
ap-10625	7	24	of	of	ADP
ap-10625	7	25	time	time	NOUN
ap-10625	7	26	)	)	PUNCT
ap-10625	7	27	and	and	CCONJ
ap-10625	7	28	average	average	ADJ
ap-10625	7	29	quantum	quantum	ADJ
ap-10625	7	30	force	force	NOUN
ap-10625	7	31	acting	act	VERB
ap-10625	7	32	on	on	ADP
ap-10625	7	33	the	the	DET
ap-10625	7	34	particle	particle	NOUN
ap-10625	7	35	by	by	ADP
ap-10625	7	36	the	the	DET
ap-10625	7	37	moving	move	VERB
ap-10625	7	38	wall	wall	NOUN
ap-10625	7	39	,	,	PUNCT
ap-10625	7	40	are	be	AUX
ap-10625	7	41	calculated	calculate	VERB
ap-10625	7	42	.	.	PUNCT
ap-10625	8	1	the	the	DET
ap-10625	8	2	trembling	tremble	VERB
ap-10625	8	3	motion	motion	NOUN
ap-10625	8	4	is	be	AUX
ap-10625	8	5	analysed	analyse	VERB
ap-10625	8	6	by	by	ADP
ap-10625	8	7	computing	compute	VERB
ap-10625	8	8	the	the	DET
ap-10625	8	9	average	average	ADJ
ap-10625	8	10	coordinate	coordinate	NOUN
ap-10625	8	11	of	of	ADP
ap-10625	8	12	the	the	DET
ap-10625	8	13	dirac	dirac	NOUN
ap-10625	8	14	particle	particle	NOUN
ap-10625	8	15	as	as	ADP
ap-10625	8	16	a	a	DET
ap-10625	8	17	function	function	NOUN
ap-10625	8	18	of	of	ADP
ap-10625	8	19	time	time	NOUN
ap-10625	8	20	.	.	PUNCT
ap-10625	9	1	the	the	DET
ap-10625	9	2	absence	absence	NOUN
ap-10625	9	3	of	of	ADP
ap-10625	9	4	the	the	DET
ap-10625	9	5	geometric	geometric	ADJ
ap-10625	9	6	phase	phase	NOUN
ap-10625	9	7	is	be	AUX
ap-10625	9	8	shown	show	VERB
ap-10625	9	9	by	by	ADP
ap-10625	9	10	direct	direct	ADJ
ap-10625	9	11	calculation	calculation	NOUN
ap-10625	9	12	.	.	PUNCT
ap-10625	10	1	keywords	keyword	NOUN
ap-10625	10	2	:	:	PUNCT
ap-10625	10	3	dirac	dirac	NOUN
ap-10625	10	4	equation	equation	NOUN
ap-10625	10	5	,	,	PUNCT
ap-10625	10	6	ball	ball	NOUN
ap-10625	10	7	with	with	ADP
ap-10625	10	8	time	time	NOUN
ap-10625	10	9	-	-	PUNCT
ap-10625	10	10	dependent	dependent	ADJ
ap-10625	10	11	radius	radius	NOUN
ap-10625	10	12	,	,	PUNCT
ap-10625	10	13	dynamical	dynamical	ADJ
ap-10625	10	14	confinement	confinement	NOUN
ap-10625	10	15	,	,	PUNCT
ap-10625	10	16	dirichlet	dirichlet	PROPN
ap-10625	10	17	boundary	boundary	ADJ
ap-10625	10	18	condition	condition	NOUN
ap-10625	10	19	.	.	PUNCT
ap-10625	11	1	1	1	X
ap-10625	11	2	.	.	X
ap-10625	11	3	introduction	introduction	NOUN
ap-10625	11	4	dirac	dirac	PROPN
ap-10625	11	5	fermions	fermion	NOUN
ap-10625	11	6	appear	appear	VERB
ap-10625	11	7	in	in	ADP
ap-10625	11	8	various	various	ADJ
ap-10625	11	9	topics	topic	NOUN
ap-10625	11	10	of	of	ADP
ap-10625	11	11	the	the	DET
ap-10625	11	12	contemporary	contemporary	ADJ
ap-10625	11	13	physics	physics	PROPN
ap-10625	11	14	.	.	PUNCT
ap-10625	12	1	in	in	ADP
ap-10625	12	2	early	early	ADJ
ap-10625	12	3	stages	stage	NOUN
ap-10625	12	4	of	of	ADP
ap-10625	12	5	quantum	quantum	ADJ
ap-10625	12	6	mechanics	mechanic	NOUN
ap-10625	12	7	,	,	PUNCT
ap-10625	12	8	they	they	PRON
ap-10625	12	9	have	have	AUX
ap-10625	12	10	been	be	AUX
ap-10625	12	11	considered	consider	VERB
ap-10625	12	12	in	in	ADP
ap-10625	12	13	the	the	DET
ap-10625	12	14	context	context	NOUN
ap-10625	12	15	of	of	ADP
ap-10625	12	16	high	high	ADJ
ap-10625	12	17	energy	energy	NOUN
ap-10625	12	18	physics	physics	NOUN
ap-10625	12	19	and	and	CCONJ
ap-10625	12	20	quantum	quantum	ADJ
ap-10625	12	21	field	field	NOUN
ap-10625	12	22	theory	theory	NOUN
ap-10625	12	23	,	,	PUNCT
ap-10625	12	24	however	however	ADV
ap-10625	12	25	,	,	PUNCT
ap-10625	12	26	during	during	ADP
ap-10625	12	27	past	past	ADJ
ap-10625	12	28	two	two	NUM
ap-10625	12	29	decades	decade	NOUN
ap-10625	12	30	,	,	PUNCT
ap-10625	12	31	quasiparticles	quasiparticle	NOUN
ap-10625	12	32	described	describe	VERB
ap-10625	12	33	in	in	ADP
ap-10625	12	34	terms	term	NOUN
ap-10625	12	35	of	of	ADP
ap-10625	12	36	the	the	DET
ap-10625	12	37	dirac	dirac	NOUN
ap-10625	12	38	equation	equation	NOUN
ap-10625	12	39	attracted	attract	VERB
ap-10625	12	40	significant	significant	ADJ
ap-10625	12	41	attention	attention	NOUN
ap-10625	12	42	in	in	ADP
ap-10625	12	43	condensed	condense	VERB
ap-10625	12	44	matter	matter	NOUN
ap-10625	12	45	physics	physics	NOUN
ap-10625	12	46	[	[	X
ap-10625	12	47	1–5	1–5	X
ap-10625	12	48	]	]	X
ap-10625	12	49	.	.	PUNCT
ap-10625	13	1	this	this	PRON
ap-10625	13	2	happened	happen	VERB
ap-10625	13	3	due	due	ADP
ap-10625	13	4	to	to	ADP
ap-10625	13	5	the	the	DET
ap-10625	13	6	fact	fact	NOUN
ap-10625	13	7	that	that	SCONJ
ap-10625	13	8	in	in	ADP
ap-10625	13	9	materials	material	NOUN
ap-10625	13	10	,	,	PUNCT
ap-10625	13	11	such	such	ADJ
ap-10625	13	12	as	as	ADP
ap-10625	13	13	graphene	graphene	NOUN
ap-10625	13	14	,	,	PUNCT
ap-10625	13	15	topological	topological	ADJ
ap-10625	13	16	insulators	insulator	NOUN
ap-10625	13	17	and	and	CCONJ
ap-10625	13	18	weyl	weyl	VERB
ap-10625	13	19	semimetals	semimetal	NOUN
ap-10625	13	20	,	,	PUNCT
ap-10625	13	21	quasiparticles	quasiparticle	NOUN
ap-10625	13	22	(	(	PUNCT
ap-10625	13	23	electrons	electron	NOUN
ap-10625	13	24	and	and	CCONJ
ap-10625	13	25	holes	hole	NOUN
ap-10625	13	26	)	)	PUNCT
ap-10625	13	27	,	,	PUNCT
ap-10625	13	28	can	can	AUX
ap-10625	13	29	“	"	PUNCT
ap-10625	13	30	mimic	mimic	VERB
ap-10625	13	31	”	"	PUNCT
ap-10625	13	32	relativistic	relativistic	ADJ
ap-10625	13	33	behaviour	behaviour	NOUN
ap-10625	13	34	being	be	AUX
ap-10625	13	35	described	describe	VERB
ap-10625	13	36	in	in	ADP
ap-10625	13	37	terms	term	NOUN
ap-10625	13	38	of	of	ADP
ap-10625	13	39	dirac	dirac	NOUN
ap-10625	13	40	equation	equation	NOUN
ap-10625	13	41	.	.	PUNCT
ap-10625	14	1	therefore	therefore	ADV
ap-10625	14	2	,	,	PUNCT
ap-10625	14	3	these	these	DET
ap-10625	14	4	materials	material	NOUN
ap-10625	14	5	are	be	AUX
ap-10625	14	6	unified	unify	VERB
ap-10625	14	7	under	under	ADP
ap-10625	14	8	the	the	DET
ap-10625	14	9	general	general	ADJ
ap-10625	14	10	term	term	NOUN
ap-10625	14	11	,	,	PUNCT
ap-10625	14	12	“	"	PUNCT
ap-10625	14	13	dirac	dirac	NOUN
ap-10625	14	14	materials	material	NOUN
ap-10625	14	15	”	"	PUNCT
ap-10625	15	1	[	[	X
ap-10625	15	2	1–5	1–5	X
ap-10625	15	3	]	]	X
ap-10625	15	4	.	.	PUNCT
ap-10625	16	1	besides	besides	SCONJ
ap-10625	16	2	the	the	DET
ap-10625	16	3	dirac	dirac	NOUN
ap-10625	16	4	materials	material	NOUN
ap-10625	16	5	,	,	PUNCT
ap-10625	16	6	relativistic	relativistic	ADJ
ap-10625	16	7	quasiparticles	quasiparticle	NOUN
ap-10625	16	8	described	describe	VERB
ap-10625	16	9	in	in	ADP
ap-10625	16	10	terms	term	NOUN
ap-10625	16	11	of	of	ADP
ap-10625	16	12	the	the	DET
ap-10625	16	13	dirac	dirac	NOUN
ap-10625	16	14	equation	equation	NOUN
ap-10625	16	15	appear	appear	VERB
ap-10625	16	16	in	in	ADP
ap-10625	16	17	some	some	DET
ap-10625	16	18	optical	optical	ADJ
ap-10625	16	19	systems	system	NOUN
ap-10625	16	20	[	[	X
ap-10625	16	21	6	6	NUM
ap-10625	16	22	,	,	PUNCT
ap-10625	16	23	7	7	NUM
ap-10625	16	24	]	]	PUNCT
ap-10625	16	25	.	.	PUNCT
ap-10625	17	1	in	in	ADP
ap-10625	17	2	most	most	ADJ
ap-10625	17	3	of	of	ADP
ap-10625	17	4	the	the	DET
ap-10625	17	5	cases	case	NOUN
ap-10625	17	6	,	,	PUNCT
ap-10625	17	7	dirac	dirac	NOUN
ap-10625	17	8	fermions	fermion	NOUN
ap-10625	17	9	appear	appear	VERB
ap-10625	17	10	in	in	ADP
ap-10625	17	11	confined	confine	VERB
ap-10625	17	12	form	form	NOUN
ap-10625	17	13	and	and	CCONJ
ap-10625	17	14	the	the	DET
ap-10625	17	15	boundary	boundary	NOUN
ap-10625	17	16	of	of	ADP
ap-10625	17	17	the	the	DET
ap-10625	17	18	confining	confine	VERB
ap-10625	17	19	domain	domain	NOUN
ap-10625	17	20	is	be	AUX
ap-10625	17	21	not	not	PART
ap-10625	17	22	always	always	ADV
ap-10625	17	23	static	static	ADJ
ap-10625	17	24	,	,	PUNCT
ap-10625	17	25	i.e.	i.e.	X
ap-10625	17	26	changes	change	NOUN
ap-10625	17	27	in	in	ADP
ap-10625	17	28	time	time	NOUN
ap-10625	17	29	.	.	PUNCT
ap-10625	18	1	such	such	ADJ
ap-10625	18	2	changes	change	NOUN
ap-10625	18	3	/	/	SYM
ap-10625	18	4	fluctuations	fluctuation	NOUN
ap-10625	18	5	of	of	ADP
ap-10625	18	6	the	the	DET
ap-10625	18	7	confinement	confinement	ADJ
ap-10625	18	8	boundary	boundary	NOUN
ap-10625	18	9	can	can	AUX
ap-10625	18	10	affect	affect	VERB
ap-10625	18	11	the	the	DET
ap-10625	18	12	physical	physical	ADJ
ap-10625	18	13	properties	property	NOUN
ap-10625	18	14	of	of	ADP
ap-10625	18	15	system	system	NOUN
ap-10625	18	16	under	under	ADP
ap-10625	18	17	consideration	consideration	NOUN
ap-10625	18	18	,	,	PUNCT
ap-10625	18	19	as	as	SCONJ
ap-10625	18	20	they	they	PRON
ap-10625	18	21	cause	cause	VERB
ap-10625	18	22	changes	change	NOUN
ap-10625	18	23	in	in	ADP
ap-10625	18	24	the	the	DET
ap-10625	18	25	boundary	boundary	ADJ
ap-10625	18	26	conditions	condition	NOUN
ap-10625	18	27	for	for	ADP
ap-10625	18	28	the	the	DET
ap-10625	18	29	quantum	quantum	ADJ
ap-10625	18	30	mechanical	mechanical	ADJ
ap-10625	18	31	wave	wave	NOUN
ap-10625	18	32	(	(	PUNCT
ap-10625	18	33	e.g.	e.g.	ADV
ap-10625	18	34	schrödinger	schrödinger	ADJ
ap-10625	18	35	,	,	PUNCT
ap-10625	18	36	dirac	dirac	NOUN
ap-10625	18	37	,	,	PUNCT
ap-10625	18	38	etc	etc	X
ap-10625	18	39	.	.	X
ap-10625	18	40	)	)	PUNCT
ap-10625	18	41	equations	equation	NOUN
ap-10625	18	42	.	.	PUNCT
ap-10625	19	1	such	such	DET
ap-10625	19	2	an	an	DET
ap-10625	19	3	effect	effect	NOUN
ap-10625	19	4	leads	lead	VERB
ap-10625	19	5	to	to	ADP
ap-10625	19	6	the	the	DET
ap-10625	19	7	important	important	ADJ
ap-10625	19	8	mathematical	mathematical	ADJ
ap-10625	19	9	problem	problem	NOUN
ap-10625	19	10	,	,	PUNCT
ap-10625	19	11	solving	solve	VERB
ap-10625	19	12	the	the	DET
ap-10625	19	13	quantum	quantum	ADJ
ap-10625	19	14	evolution	evolution	NOUN
ap-10625	19	15	equations	equation	NOUN
ap-10625	19	16	with	with	ADP
ap-10625	19	17	time	time	NOUN
ap-10625	19	18	-	-	PUNCT
ap-10625	19	19	dependent	dependent	ADJ
ap-10625	19	20	boundary	boundary	ADJ
ap-10625	19	21	conditions	condition	NOUN
ap-10625	19	22	.	.	PUNCT
ap-10625	20	1	in	in	ADP
ap-10625	20	2	physics	physics	PROPN
ap-10625	20	3	,	,	PUNCT
ap-10625	20	4	this	this	DET
ap-10625	20	5	problem	problem	NOUN
ap-10625	20	6	is	be	AUX
ap-10625	20	7	called	call	VERB
ap-10625	20	8	“	"	PUNCT
ap-10625	20	9	dynamical	dynamical	ADJ
ap-10625	20	10	quantum	quantum	NOUN
ap-10625	20	11	confinement	confinement	NOUN
ap-10625	20	12	”	"	PUNCT
ap-10625	20	13	.	.	PUNCT
ap-10625	21	1	earlier	early	ADV
ap-10625	21	2	dynamical	dynamical	ADJ
ap-10625	21	3	confinement	confinement	NOUN
ap-10625	21	4	attracted	attract	VERB
ap-10625	21	5	much	much	ADJ
ap-10625	21	6	attention	attention	NOUN
ap-10625	21	7	in	in	ADP
ap-10625	21	8	the	the	DET
ap-10625	21	9	context	context	NOUN
ap-10625	21	10	of	of	ADP
ap-10625	21	11	nonrelativistic	nonrelativistic	ADJ
ap-10625	21	12	quantum	quantum	ADJ
ap-10625	21	13	mechanics	mechanic	NOUN
ap-10625	21	14	described	describe	VERB
ap-10625	21	15	by	by	ADP
ap-10625	21	16	schrödinger	schrödinger	ADJ
ap-10625	21	17	equation	equation	NOUN
ap-10625	21	18	(	(	PUNCT
ap-10625	21	19	see	see	VERB
ap-10625	21	20	,	,	PUNCT
ap-10625	21	21	for	for	ADP
ap-10625	21	22	example	example	NOUN
ap-10625	21	23	,	,	PUNCT
ap-10625	21	24	the	the	DET
ap-10625	21	25	[	[	X
ap-10625	21	26	8	8	NUM
ap-10625	21	27	,	,	PUNCT
ap-10625	21	28	9	9	NUM
ap-10625	21	29	]	]	PUNCT
ap-10625	21	30	,	,	PUNCT
ap-10625	21	31	for	for	ADP
ap-10625	21	32	review	review	NOUN
ap-10625	21	33	)	)	PUNCT
ap-10625	21	34	.	.	PUNCT
ap-10625	22	1	despite	despite	SCONJ
ap-10625	22	2	the	the	DET
ap-10625	22	3	considerable	considerable	ADJ
ap-10625	22	4	progress	progress	NOUN
ap-10625	22	5	made	make	VERB
ap-10625	22	6	in	in	ADP
ap-10625	22	7	the	the	DET
ap-10625	22	8	study	study	NOUN
ap-10625	22	9	of	of	ADP
ap-10625	22	10	dynamical	dynamical	ADJ
ap-10625	22	11	confinement	confinement	NOUN
ap-10625	22	12	in	in	ADP
ap-10625	22	13	nonrelativistic	nonrelativistic	ADJ
ap-10625	22	14	quantum	quantum	ADJ
ap-10625	22	15	mechanics	mechanic	NOUN
ap-10625	22	16	,	,	PUNCT
ap-10625	22	17	relativistic	relativistic	ADJ
ap-10625	22	18	cases	case	NOUN
ap-10625	22	19	,	,	PUNCT
ap-10625	22	20	especially	especially	ADV
ap-10625	22	21	the	the	DET
ap-10625	22	22	case	case	NOUN
ap-10625	22	23	of	of	ADP
ap-10625	22	24	relativistic	relativistic	ADJ
ap-10625	22	25	spin	spin	NOUN
ap-10625	22	26	-	-	PUNCT
ap-10625	22	27	half	half	NOUN
ap-10625	22	28	particles	particle	NOUN
ap-10625	22	29	,	,	PUNCT
ap-10625	22	30	are	be	AUX
ap-10625	22	31	still	still	ADV
ap-10625	22	32	not	not	PART
ap-10625	22	33	the	the	DET
ap-10625	22	34	focus	focus	NOUN
ap-10625	22	35	of	of	ADP
ap-10625	22	36	many	many	ADJ
ap-10625	22	37	studies	study	NOUN
ap-10625	22	38	.	.	PUNCT
ap-10625	23	1	we	we	PRON
ap-10625	23	2	note	note	VERB
ap-10625	23	3	that	that	SCONJ
ap-10625	23	4	dynamical	dynamical	ADJ
ap-10625	23	5	confinement	confinement	NOUN
ap-10625	23	6	for	for	ADP
ap-10625	23	7	relativistic	relativistic	ADJ
ap-10625	23	8	scalar	scalar	ADJ
ap-10625	23	9	particles	particle	NOUN
ap-10625	23	10	have	have	AUX
ap-10625	23	11	been	be	AUX
ap-10625	23	12	studied	study	VERB
ap-10625	23	13	in	in	ADP
ap-10625	23	14	the	the	DET
ap-10625	23	15	context	context	NOUN
ap-10625	23	16	of	of	ADP
ap-10625	23	17	dynamical	dynamical	ADJ
ap-10625	23	18	casimir	casimir	NOUN
ap-10625	23	19	effect	effect	NOUN
ap-10625	23	20	[	[	X
ap-10625	23	21	10	10	NUM
ap-10625	23	22	]	]	PUNCT
ap-10625	23	23	.	.	PUNCT
ap-10625	24	1	in	in	ADP
ap-10625	24	2	this	this	DET
ap-10625	24	3	paper	paper	NOUN
ap-10625	24	4	,	,	PUNCT
ap-10625	24	5	we	we	PRON
ap-10625	24	6	address	address	VERB
ap-10625	24	7	the	the	DET
ap-10625	24	8	problem	problem	NOUN
ap-10625	24	9	of	of	ADP
ap-10625	24	10	dynamical	dynamical	ADJ
ap-10625	24	11	confinement	confinement	NOUN
ap-10625	24	12	for	for	ADP
ap-10625	24	13	spin	spin	NOUN
ap-10625	24	14	-	-	PUNCT
ap-10625	24	15	half	half	NOUN
ap-10625	24	16	dirac	dirac	NOUN
ap-10625	24	17	fermions	fermion	NOUN
ap-10625	24	18	by	by	ADP
ap-10625	24	19	considering	consider	VERB
ap-10625	24	20	a	a	DET
ap-10625	24	21	spherical	spherical	ADJ
ap-10625	24	22	confining	confining	NOUN
ap-10625	24	23	domain	domain	NOUN
ap-10625	24	24	,	,	PUNCT
ap-10625	24	25	where	where	SCONJ
ap-10625	24	26	the	the	DET
ap-10625	24	27	time	time	NOUN
ap-10625	24	28	dependence	dependence	NOUN
ap-10625	24	29	of	of	ADP
ap-10625	24	30	the	the	DET
ap-10625	24	31	boundary	boundary	NOUN
ap-10625	24	32	does	do	AUX
ap-10625	24	33	not	not	PART
ap-10625	24	34	break	break	VERB
ap-10625	24	35	the	the	DET
ap-10625	24	36	spherical	spherical	ADJ
ap-10625	24	37	symmetry	symmetry	NOUN
ap-10625	24	38	,	,	PUNCT
ap-10625	24	39	so	so	SCONJ
ap-10625	24	40	that	that	SCONJ
ap-10625	24	41	the	the	DET
ap-10625	24	42	system	system	NOUN
ap-10625	24	43	is	be	AUX
ap-10625	24	44	described	describe	VERB
ap-10625	24	45	in	in	ADP
ap-10625	24	46	terms	term	NOUN
ap-10625	24	47	of	of	ADP
ap-10625	24	48	the	the	DET
ap-10625	24	49	radial	radial	ADJ
ap-10625	24	50	dirac	dirac	NOUN
ap-10625	24	51	equation	equation	NOUN
ap-10625	24	52	.	.	PUNCT
ap-10625	25	1	we	we	PRON
ap-10625	25	2	note	note	VERB
ap-10625	25	3	that	that	SCONJ
ap-10625	25	4	recently	recently	ADV
ap-10625	25	5	,	,	PUNCT
ap-10625	25	6	an	an	DET
ap-10625	25	7	one	one	NUM
ap-10625	25	8	-	-	PUNCT
ap-10625	25	9	dimensional	dimensional	ADJ
ap-10625	25	10	counterpart	counterpart	NOUN
ap-10625	25	11	of	of	ADP
ap-10625	25	12	such	such	DET
ap-10625	25	13	a	a	DET
ap-10625	25	14	problem	problem	NOUN
ap-10625	25	15	was	be	AUX
ap-10625	25	16	considered	consider	VERB
ap-10625	25	17	in	in	ADP
ap-10625	25	18	the	the	PRON
ap-10625	25	19	[	[	X
ap-10625	25	20	9	9	NUM
ap-10625	25	21	]	]	SYM
ap-10625	25	22	.	.	PUNCT
ap-10625	26	1	2	2	X
ap-10625	26	2	.	.	X
ap-10625	26	3	dirac	dirac	NOUN
ap-10625	26	4	particle	particle	NOUN
ap-10625	26	5	in	in	ADP
ap-10625	26	6	a	a	DET
ap-10625	26	7	spherical	spherical	ADJ
ap-10625	26	8	box	box	NOUN
ap-10625	26	9	the	the	DET
ap-10625	26	10	dirac	dirac	NOUN
ap-10625	26	11	equation	equation	NOUN
ap-10625	26	12	on	on	ADP
ap-10625	26	13	confined	confine	VERB
ap-10625	26	14	domains	domain	NOUN
ap-10625	26	15	has	have	AUX
ap-10625	26	16	been	be	AUX
ap-10625	26	17	studied	study	VERB
ap-10625	26	18	in	in	ADP
ap-10625	26	19	[	[	X
ap-10625	26	20	11–16	11–16	NUM
ap-10625	26	21	]	]	X
ap-10625	26	22	.	.	PUNCT
ap-10625	27	1	[	[	X
ap-10625	27	2	11	11	NUM
ap-10625	27	3	]	]	PUNCT
ap-10625	27	4	presents	present	VERB
ap-10625	27	5	a	a	DET
ap-10625	27	6	pioneering	pioneer	VERB
ap-10625	27	7	study	study	NOUN
ap-10625	27	8	of	of	ADP
ap-10625	27	9	the	the	DET
ap-10625	27	10	dirac	dirac	NOUN
ap-10625	27	11	equation	equation	NOUN
ap-10625	27	12	in	in	ADP
ap-10625	27	13	a	a	DET
ap-10625	27	14	hard	hard	ADJ
ap-10625	27	15	-	-	PUNCT
ap-10625	27	16	wall	wall	NOUN
ap-10625	27	17	box	box	PROPN
ap-10625	27	18	,	,	PUNCT
ap-10625	27	19	where	where	SCONJ
ap-10625	27	20	physically	physically	ADV
ap-10625	27	21	relevant	relevant	ADJ
ap-10625	27	22	self	self	NOUN
ap-10625	27	23	-	-	PUNCT
ap-10625	27	24	adjoint	adjoint	NOUN
ap-10625	27	25	general	general	ADJ
ap-10625	27	26	boundary	boundary	ADJ
ap-10625	27	27	conditions	condition	NOUN
ap-10625	27	28	were	be	AUX
ap-10625	27	29	derived	derive	VERB
ap-10625	27	30	.	.	PUNCT
ap-10625	28	1	one	one	NUM
ap-10625	28	2	-	-	PUNCT
ap-10625	28	3	dimensional	dimensional	ADJ
ap-10625	28	4	dirac	dirac	NOUN
ap-10625	28	5	equation	equation	NOUN
ap-10625	28	6	in	in	ADP
ap-10625	28	7	a	a	DET
ap-10625	28	8	quantum	quantum	NOUN
ap-10625	28	9	box	box	NOUN
ap-10625	28	10	has	have	AUX
ap-10625	28	11	been	be	AUX
ap-10625	28	12	studied	study	VERB
ap-10625	28	13	in	in	ADP
ap-10625	28	14	details	detail	NOUN
ap-10625	28	15	in	in	ADP
ap-10625	28	16	[	[	X
ap-10625	28	17	12	12	NUM
ap-10625	28	18	,	,	PUNCT
ap-10625	28	19	13	13	NUM
ap-10625	28	20	]	]	PUNCT
ap-10625	28	21	.	.	PUNCT
ap-10625	29	1	the	the	DET
ap-10625	29	2	one	one	NUM
ap-10625	29	3	-	-	PUNCT
ap-10625	29	4	dimensional	dimensional	ADJ
ap-10625	29	5	dirac	dirac	NOUN
ap-10625	29	6	equation	equation	NOUN
ap-10625	29	7	in	in	ADP
ap-10625	29	8	time	time	NOUN
ap-10625	29	9	-	-	PUNCT
ap-10625	29	10	varying	vary	VERB
ap-10625	29	11	domains	domain	NOUN
ap-10625	29	12	was	be	AUX
ap-10625	29	13	studied	study	VERB
ap-10625	29	14	in	in	ADP
ap-10625	29	15	[	[	X
ap-10625	29	16	14	14	NUM
ap-10625	29	17	]	]	PUNCT
ap-10625	29	18	,	,	PUNCT
ap-10625	29	19	by	by	ADP
ap-10625	29	20	considering	consider	VERB
ap-10625	29	21	special	special	ADJ
ap-10625	29	22	cases	case	NOUN
ap-10625	29	23	of	of	ADP
ap-10625	29	24	the	the	DET
ap-10625	29	25	dynamical	dynamical	ADJ
ap-10625	29	26	confinement	confinement	NOUN
ap-10625	29	27	and	and	CCONJ
ap-10625	29	28	deriving	derive	VERB
ap-10625	29	29	an	an	DET
ap-10625	29	30	analytical	analytical	ADJ
ap-10625	29	31	solution	solution	NOUN
ap-10625	29	32	to	to	ADP
ap-10625	29	33	the	the	DET
ap-10625	29	34	problem	problem	NOUN
ap-10625	29	35	.	.	PUNCT
ap-10625	30	1	practical	practical	ADJ
ap-10625	30	2	applications	application	NOUN
ap-10625	30	3	of	of	ADP
ap-10625	30	4	the	the	DET
ap-10625	30	5	dirac	dirac	NOUN
ap-10625	30	6	equation	equation	NOUN
ap-10625	30	7	to	to	PART
ap-10625	30	8	graphene	graphene	VERB
ap-10625	30	9	quantum	quantum	NOUN
ap-10625	30	10	dots	dot	NOUN
ap-10625	30	11	were	be	AUX
ap-10625	30	12	considered	consider	VERB
ap-10625	30	13	in	in	ADP
ap-10625	30	14	[	[	X
ap-10625	30	15	16	16	NUM
ap-10625	30	16	]	]	PUNCT
ap-10625	30	17	.	.	PUNCT
ap-10625	31	1	the	the	DET
ap-10625	31	2	dynamics	dynamic	NOUN
ap-10625	31	3	of	of	ADP
ap-10625	31	4	a	a	DET
ap-10625	31	5	dirac	dirac	NOUN
ap-10625	31	6	particle	particle	NOUN
ap-10625	31	7	under	under	ADP
ap-10625	31	8	an	an	DET
ap-10625	31	9	one	one	NUM
ap-10625	31	10	-	-	PUNCT
ap-10625	31	11	dimensional	dimensional	ADJ
ap-10625	31	12	dynamical	dynamical	ADJ
ap-10625	31	13	confinement	confinement	NOUN
ap-10625	31	14	was	be	AUX
ap-10625	31	15	studied	study	VERB
ap-10625	31	16	in	in	ADP
ap-10625	31	17	a	a	DET
ap-10625	31	18	recent	recent	ADJ
ap-10625	31	19	paper	paper	NOUN
ap-10625	31	20	[	[	X
ap-10625	31	21	9	9	NUM
ap-10625	31	22	]	]	PUNCT
ap-10625	31	23	.	.	PUNCT
ap-10625	32	1	here	here	ADV
ap-10625	32	2	,	,	PUNCT
ap-10625	32	3	we	we	PRON
ap-10625	32	4	consider	consider	VERB
ap-10625	32	5	dynamical	dynamical	ADJ
ap-10625	32	6	confinement	confinement	NOUN
ap-10625	32	7	caused	cause	VERB
ap-10625	32	8	by	by	ADP
ap-10625	32	9	a	a	DET
ap-10625	32	10	spherical	spherical	ADJ
ap-10625	32	11	box	box	NOUN
ap-10625	32	12	with	with	ADP
ap-10625	32	13	a	a	DET
ap-10625	32	14	timevarying	timevarying	NOUN
ap-10625	32	15	radius	radius	NOUN
ap-10625	32	16	,	,	PUNCT
ap-10625	32	17	described	describe	VERB
ap-10625	32	18	in	in	ADP
ap-10625	32	19	terms	term	NOUN
ap-10625	32	20	of	of	ADP
ap-10625	32	21	the	the	DET
ap-10625	32	22	radial	radial	ADJ
ap-10625	32	23	dirac	dirac	NOUN
ap-10625	32	24	equation	equation	NOUN
ap-10625	32	25	with	with	ADP
ap-10625	32	26	time	time	NOUN
ap-10625	32	27	-	-	PUNCT
ap-10625	32	28	dependent	dependent	ADJ
ap-10625	32	29	boundary	boundary	ADJ
ap-10625	32	30	conditions	condition	NOUN
ap-10625	32	31	.	.	PUNCT
ap-10625	33	1	we	we	PRON
ap-10625	33	2	choose	choose	VERB
ap-10625	33	3	standard	standard	ADJ
ap-10625	33	4	representation	representation	NOUN
ap-10625	33	5	of	of	ADP
ap-10625	33	6	the	the	DET
ap-10625	33	7	dirac	dirac	NOUN
ap-10625	33	8	matrices	matrix	NOUN
ap-10625	33	9	according	accord	VERB
ap-10625	33	10	to	to	ADP
ap-10625	33	11	[	[	X
ap-10625	33	12	17	17	NUM
ap-10625	33	13	]	]	PUNCT
ap-10625	33	14	and	and	CCONJ
ap-10625	33	15	follow	follow	VERB
ap-10625	33	16	the	the	DET
ap-10625	33	17	conventions	convention	NOUN
ap-10625	33	18	for	for	ADP
ap-10625	33	19	the	the	DET
ap-10625	33	20	spherical	spherical	ADJ
ap-10625	33	21	spinors	spinor	NOUN
ap-10625	33	22	used	use	VERB
ap-10625	33	23	there	there	ADV
ap-10625	33	24	.	.	PUNCT
ap-10625	34	1	for	for	ADP
ap-10625	34	2	the	the	DET
ap-10625	34	3	spherically	spherically	NOUN
ap-10625	34	4	symmetric	symmetric	ADJ
ap-10625	34	5	situations	situation	NOUN
ap-10625	34	6	,	,	PUNCT
ap-10625	34	7	the	the	DET
ap-10625	34	8	hamiltonian	hamiltonian	NOUN
ap-10625	34	9	can	can	AUX
ap-10625	34	10	be	be	AUX
ap-10625	34	11	decom546	decom546	PROPN
ap-10625	34	12	https://doi.org/10.14311/ap.2025.65.0546	https://doi.org/10.14311/ap.2025.65.0546	PROPN
ap-10625	34	13	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-10625	34	14	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-10625	34	15	vol	vol	NOUN
ap-10625	34	16	.	.	PROPN
ap-10625	35	1	65	65	NUM
ap-10625	35	2	no	no	NOUN
ap-10625	35	3	.	.	PUNCT
ap-10625	36	1	5/2025	5/2025	NUM
ap-10625	36	2	dirac	dirac	NOUN
ap-10625	36	3	fermion	fermion	NOUN
ap-10625	36	4	in	in	ADP
ap-10625	36	5	a	a	DET
ap-10625	36	6	time	time	NOUN
ap-10625	36	7	-	-	PUNCT
ap-10625	36	8	dependent	dependent	ADJ
ap-10625	36	9	spherical	spherical	ADJ
ap-10625	36	10	box	box	NOUN
ap-10625	36	11	posed	pose	VERB
ap-10625	36	12	into	into	ADP
ap-10625	36	13	a	a	DET
ap-10625	36	14	direct	direct	ADJ
ap-10625	36	15	sum	sum	NOUN
ap-10625	36	16	of	of	ADP
ap-10625	36	17	parts	part	NOUN
ap-10625	36	18	with	with	ADP
ap-10625	36	19	a	a	DET
ap-10625	36	20	given	give	VERB
ap-10625	36	21	value	value	NOUN
ap-10625	36	22	of	of	ADP
ap-10625	36	23	the	the	DET
ap-10625	36	24	total	total	ADJ
ap-10625	36	25	momentum	momentum	NOUN
ap-10625	36	26	j	j	PROPN
ap-10625	36	27	,	,	PUNCT
ap-10625	36	28	its	its	PRON
ap-10625	36	29	third	third	ADJ
ap-10625	36	30	component	component	NOUN
ap-10625	36	31	j3	j3	PROPN
ap-10625	36	32	,	,	PUNCT
ap-10625	36	33	and	and	CCONJ
ap-10625	36	34	parity	parity	NOUN
ap-10625	36	35	(	(	PUNCT
ap-10625	36	36	−1)l	−1)l	X
ap-10625	36	37	(	(	PUNCT
ap-10625	36	38	[	[	X
ap-10625	36	39	17	17	NUM
ap-10625	36	40	]	]	PUNCT
ap-10625	36	41	,	,	PUNCT
ap-10625	36	42	see	see	VERB
ap-10625	36	43	,	,	PUNCT
ap-10625	36	44	e.g.	e.g.	ADV
ap-10625	36	45	,	,	PUNCT
ap-10625	36	46	[	[	X
ap-10625	36	47	18	18	NUM
ap-10625	36	48	]	]	PUNCT
ap-10625	36	49	for	for	ADP
ap-10625	36	50	more	more	ADJ
ap-10625	36	51	details	detail	NOUN
ap-10625	36	52	)	)	PUNCT
ap-10625	36	53	.	.	PUNCT
ap-10625	37	1	let	let	VERB
ap-10625	37	2	us	we	PRON
ap-10625	37	3	remind	remind	VERB
ap-10625	37	4	here	here	ADV
ap-10625	37	5	only	only	ADV
ap-10625	37	6	the	the	DET
ap-10625	37	7	basic	basic	ADJ
ap-10625	37	8	formula	formula	NOUN
ap-10625	37	9	:	:	PUNCT
ap-10625	37	10	ψ(t	ψ(t	PROPN
ap-10625	37	11	,	,	PUNCT
ap-10625	37	12	x⃗	x⃗	PROPN
ap-10625	37	13	)	)	PUNCT
ap-10625	38	1	=	=	SYM
ap-10625	38	2	(	(	PUNCT
ap-10625	38	3	rf(t	rf(t	NOUN
ap-10625	38	4	,	,	PUNCT
ap-10625	38	5	r)ωjlj3(n⃗	r)ωjlj3(n⃗	NOUN
ap-10625	38	6	)	)	PUNCT
ap-10625	38	7	(	(	PUNCT
ap-10625	38	8	−1	−1	NOUN
ap-10625	38	9	)	)	PUNCT
ap-10625	38	10	1+l−l′	1+l−l′	NUM
ap-10625	38	11	2	2	NUM
ap-10625	38	12	rg(t	rg(t	ADJ
ap-10625	38	13	,	,	PUNCT
ap-10625	38	14	r)ωjl′j3(n⃗	r)ωjl′j3(n⃗	PROPN
ap-10625	38	15	)	)	PUNCT
ap-10625	38	16	)	)	PUNCT
ap-10625	38	17	,	,	PUNCT
ap-10625	38	18	r	r	NOUN
ap-10625	38	19	=	=	SYM
ap-10625	38	20	|x⃗|	|x⃗|	PROPN
ap-10625	38	21	,	,	PUNCT
ap-10625	38	22	n⃗	n⃗	PROPN
ap-10625	38	23	=	=	PUNCT
ap-10625	38	24	x⃗	x⃗	PROPN
ap-10625	39	1	r	r	NOUN
ap-10625	39	2	.	.	PUNCT
ap-10625	40	1	further	far	ADV
ap-10625	40	2	,	,	PUNCT
ap-10625	40	3	notations	notation	NOUN
ap-10625	40	4	l	l	NOUN
ap-10625	40	5	=	=	PUNCT
ap-10625	40	6	j	j	PROPN
ap-10625	40	7	+	+	CCONJ
ap-10625	40	8	1	1	NUM
ap-10625	40	9	2µ	2µ	NOUN
ap-10625	40	10	,	,	PUNCT
ap-10625	40	11	l′	l′	PUNCT
ap-10625	40	12	=	=	PUNCT
ap-10625	40	13	j	j	PROPN
ap-10625	40	14	−	−	NUM
ap-10625	40	15	1	1	NUM
ap-10625	40	16	2µ	2µ	NOUN
ap-10625	40	17	,	,	PUNCT
ap-10625	40	18	µ	µ	X
ap-10625	40	19	=	=	SYM
ap-10625	40	20	±1	±1	VERB
ap-10625	40	21	,	,	PUNCT
ap-10625	40	22	κ	κ	X
ap-10625	40	23	=	=	PUNCT
ap-10625	40	24	µ(j	µ(j	PROPN
ap-10625	40	25	+	+	PROPN
ap-10625	40	26	1	1	NUM
ap-10625	40	27	2	2	NUM
ap-10625	40	28	)	)	PUNCT
ap-10625	40	29	,	,	PUNCT
ap-10625	40	30	ν	ν	X
ap-10625	40	31	=	=	PUNCT
ap-10625	40	32	l	l	NOUN
ap-10625	40	33	+	+	NOUN
ap-10625	40	34	1	1	NUM
ap-10625	40	35	2	2	NUM
ap-10625	40	36	,	,	PUNCT
ap-10625	40	37	ν′	ν′	NOUN
ap-10625	40	38	=	=	SYM
ap-10625	40	39	l′	l′	X
ap-10625	40	40	+	+	CCONJ
ap-10625	40	41	1	1	NUM
ap-10625	40	42	2	2	NUM
ap-10625	40	43	are	be	AUX
ap-10625	40	44	used	use	VERB
ap-10625	40	45	.	.	PUNCT
ap-10625	41	1	notice	notice	NOUN
ap-10625	41	2	,	,	PUNCT
ap-10625	41	3	that	that	PRON
ap-10625	41	4	κ	κ	NOUN
ap-10625	41	5	=	=	PUNCT
ap-10625	41	6	±1,±2	±1,±2	PROPN
ap-10625	41	7	,	,	PUNCT
ap-10625	41	8	.	.	PUNCT
ap-10625	41	9	.	.	PUNCT
ap-10625	41	10	.	.	PUNCT
ap-10625	41	11	.	.	PUNCT
ap-10625	42	1	we	we	PRON
ap-10625	42	2	consider	consider	VERB
ap-10625	42	3	the	the	DET
ap-10625	42	4	dirac	dirac	NOUN
ap-10625	42	5	operator	operator	NOUN
ap-10625	42	6	on	on	ADP
ap-10625	42	7	the	the	DET
ap-10625	42	8	threedimensional	threedimensional	ADJ
ap-10625	42	9	sphere	sphere	NOUN
ap-10625	42	10	of	of	ADP
ap-10625	42	11	time	time	NOUN
ap-10625	42	12	dependent	dependent	ADJ
ap-10625	42	13	radius	radius	NOUN
ap-10625	42	14	r0(t	r0(t	PROPN
ap-10625	42	15	)	)	PUNCT
ap-10625	42	16	,	,	PUNCT
ap-10625	42	17	let	let	VERB
ap-10625	42	18	us	we	PRON
ap-10625	42	19	assume	assume	VERB
ap-10625	42	20	that	that	SCONJ
ap-10625	42	21	r0	r0	NOUN
ap-10625	42	22	is	be	AUX
ap-10625	42	23	c2	c2	PROPN
ap-10625	42	24	-	-	PUNCT
ap-10625	42	25	smooth	smooth	PROPN
ap-10625	42	26	.	.	PUNCT
ap-10625	43	1	to	to	PART
ap-10625	43	2	assure	assure	VERB
ap-10625	43	3	a	a	DET
ap-10625	43	4	unitary	unitary	ADJ
ap-10625	43	5	evolution	evolution	NOUN
ap-10625	43	6	of	of	ADP
ap-10625	43	7	the	the	DET
ap-10625	43	8	system	system	NOUN
ap-10625	43	9	,	,	PUNCT
ap-10625	43	10	we	we	PRON
ap-10625	43	11	replace	replace	VERB
ap-10625	43	12	the	the	DET
ap-10625	43	13	time	time	NOUN
ap-10625	43	14	derivative	derivative	ADJ
ap-10625	43	15	with	with	ADP
ap-10625	43	16	the	the	DET
ap-10625	43	17	modified	modify	VERB
ap-10625	43	18	one	one	NOUN
ap-10625	43	19	given	give	VERB
ap-10625	43	20	as	as	ADP
ap-10625	43	21	(	(	PUNCT
ap-10625	43	22	cf	cf	NOUN
ap-10625	43	23	.	.	PUNCT
ap-10625	44	1	[	[	X
ap-10625	44	2	19	19	NUM
ap-10625	44	3	]	]	SYM
ap-10625	44	4	):	):	PUNCT
ap-10625	44	5	∇t	∇t	PROPN
ap-10625	44	6	=	=	PUNCT
ap-10625	44	7	∂t	∂t	PROPN
ap-10625	44	8	+	+	CCONJ
ap-10625	44	9	ṙ0(t	ṙ0(t	PROPN
ap-10625	44	10	)	)	PUNCT
ap-10625	44	11	2r0(t	2r0(t	NUM
ap-10625	44	12	)	)	PUNCT
ap-10625	44	13	(	(	PUNCT
ap-10625	44	14	r∂r	r∂r	VERB
ap-10625	44	15	+	+	CCONJ
ap-10625	44	16	∂rr	∂rr	PROPN
ap-10625	44	17	)	)	PUNCT
ap-10625	44	18	.	.	PUNCT
ap-10625	45	1	(	(	PUNCT
ap-10625	45	2	1	1	X
ap-10625	45	3	)	)	PUNCT
ap-10625	45	4	the	the	DET
ap-10625	45	5	modified	modify	VERB
ap-10625	45	6	radial	radial	ADJ
ap-10625	45	7	dirac	dirac	NOUN
ap-10625	45	8	equation	equation	NOUN
ap-10625	45	9	now	now	ADV
ap-10625	45	10	reads	read	VERB
ap-10625	45	11	as	as	SCONJ
ap-10625	45	12	follows	follow	VERB
ap-10625	45	13	:	:	PUNCT
ap-10625	45	14	i∇tψ	i∇tψ	X
ap-10625	45	15	=	=	SYM
ap-10625	45	16	(	(	PUNCT
ap-10625	45	17	−iα∂r	−iα∂r	PROPN
ap-10625	45	18	+	+	NUM
ap-10625	45	19	α1	α1	PROPN
ap-10625	45	20	κ	κ	NOUN
ap-10625	45	21	r	r	NOUN
ap-10625	45	22	+	+	CCONJ
ap-10625	45	23	βm	βm	ADJ
ap-10625	45	24	)	)	PUNCT
ap-10625	46	1	ψ	ψ	PROPN
ap-10625	46	2	,	,	PUNCT
ap-10625	46	3	(	(	PUNCT
ap-10625	46	4	2	2	NUM
ap-10625	46	5	)	)	PUNCT
ap-10625	47	1	where	where	SCONJ
ap-10625	47	2	:	:	PUNCT
ap-10625	47	3	α	α	X
ap-10625	47	4	=	=	SYM
ap-10625	47	5	(	(	PUNCT
ap-10625	47	6	0	0	NUM
ap-10625	47	7	−i	−i	NOUN
ap-10625	47	8	i	i	INTJ
ap-10625	47	9	0	0	NUM
ap-10625	47	10	)	)	PUNCT
ap-10625	47	11	,	,	PUNCT
ap-10625	47	12	α1	α1	PROPN
ap-10625	47	13	=	=	SYM
ap-10625	47	14	(	(	PUNCT
ap-10625	47	15	0	0	NUM
ap-10625	47	16	1	1	NUM
ap-10625	47	17	1	1	NUM
ap-10625	47	18	0	0	NUM
ap-10625	47	19	)	)	PUNCT
ap-10625	47	20	,	,	PUNCT
ap-10625	47	21	β	β	X
ap-10625	47	22	=	=	PUNCT
ap-10625	47	23	(	(	PUNCT
ap-10625	47	24	1	1	NUM
ap-10625	47	25	0	0	NUM
ap-10625	47	26	0	0	NUM
ap-10625	47	27	−1	−1	NOUN
ap-10625	47	28	)	)	PUNCT
ap-10625	47	29	.	.	PUNCT
ap-10625	48	1	it	it	PRON
ap-10625	48	2	is	be	AUX
ap-10625	48	3	easy	easy	ADJ
ap-10625	48	4	to	to	PART
ap-10625	48	5	check	check	VERB
ap-10625	48	6	that	that	DET
ap-10625	48	7	equation	equation	NOUN
ap-10625	48	8	(	(	PUNCT
ap-10625	48	9	2	2	X
ap-10625	48	10	)	)	PUNCT
ap-10625	48	11	provides	provide	VERB
ap-10625	48	12	the	the	DET
ap-10625	48	13	conservation	conservation	NOUN
ap-10625	48	14	of	of	ADP
ap-10625	48	15	probability	probability	NOUN
ap-10625	48	16	:	:	PUNCT
ap-10625	49	1	d	d	X
ap-10625	49	2	dt	dt	X
ap-10625	49	3	∫	∫	PROPN
ap-10625	49	4	r0(t	r0(t	NOUN
ap-10625	49	5	)	)	PUNCT
ap-10625	49	6	0	0	PUNCT
ap-10625	50	1	ψ(r	ψ(r	NOUN
ap-10625	50	2	,	,	PUNCT
ap-10625	50	3	t)†ψ(r	t)†ψ(r	ADV
ap-10625	50	4	,	,	PUNCT
ap-10625	50	5	t)dr	t)dr	NOUN
ap-10625	50	6	=	=	SYM
ap-10625	50	7	0	0	X
ap-10625	50	8	.	.	PUNCT
ap-10625	51	1	we	we	PRON
ap-10625	51	2	use	use	VERB
ap-10625	51	3	the	the	DET
ap-10625	51	4	following	follow	VERB
ap-10625	51	5	transformations	transformation	NOUN
ap-10625	51	6	of	of	ADP
ap-10625	51	7	distance	distance	NOUN
ap-10625	51	8	,	,	PUNCT
ap-10625	51	9	time	time	NOUN
ap-10625	51	10	and	and	CCONJ
ap-10625	51	11	the	the	DET
ap-10625	51	12	wave	wave	NOUN
ap-10625	51	13	function	function	NOUN
ap-10625	51	14	:	:	PUNCT
ap-10625	52	1	y	y	NOUN
ap-10625	52	2	=	=	PUNCT
ap-10625	52	3	r	r	X
ap-10625	52	4	r0(t	r0(t	NOUN
ap-10625	52	5	)	)	PUNCT
ap-10625	52	6	,	,	PUNCT
ap-10625	52	7	τ	τ	PROPN
ap-10625	52	8	=	=	SYM
ap-10625	52	9	∫	∫	PROPN
ap-10625	52	10	t	t	PROPN
ap-10625	52	11	0	0	NUM
ap-10625	52	12	1	1	NUM
ap-10625	52	13	r0(ξ	r0(ξ	NOUN
ap-10625	52	14	)	)	PUNCT
ap-10625	52	15	dξ	dξ	PROPN
ap-10625	52	16	,	,	PUNCT
ap-10625	52	17	ψ(r	ψ(r	PROPN
ap-10625	52	18	,	,	PUNCT
ap-10625	52	19	t	t	PROPN
ap-10625	52	20	)	)	PUNCT
ap-10625	52	21	=	=	SYM
ap-10625	52	22	1√	1√	NUM
ap-10625	52	23	r0(t	r0(t	NOUN
ap-10625	52	24	)	)	PUNCT
ap-10625	52	25	φ(y	φ(y	ADJ
ap-10625	52	26	,	,	PUNCT
ap-10625	52	27	τ(t	τ(t	NOUN
ap-10625	52	28	)	)	PUNCT
ap-10625	52	29	)	)	PUNCT
ap-10625	52	30	,	,	PUNCT
ap-10625	52	31	(	(	PUNCT
ap-10625	52	32	3	3	X
ap-10625	52	33	)	)	PUNCT
ap-10625	52	34	with	with	ADP
ap-10625	52	35	φ	φ	PROPN
ap-10625	52	36	=	=	SYM
ap-10625	52	37	(	(	PUNCT
ap-10625	52	38	φ1	φ1	PROPN
ap-10625	52	39	φ2	φ2	PROPN
ap-10625	52	40	)	)	PUNCT
ap-10625	53	1	∈	∈	PROPN
ap-10625	53	2	l2((0	l2((0	PROPN
ap-10625	53	3	,	,	PUNCT
ap-10625	53	4	1),c2	1),c2	NUM
ap-10625	53	5	)	)	PUNCT
ap-10625	53	6	.	.	PUNCT
ap-10625	54	1	then	then	ADV
ap-10625	54	2	,	,	PUNCT
ap-10625	54	3	from	from	ADP
ap-10625	54	4	the	the	DET
ap-10625	54	5	equation	equation	NOUN
ap-10625	54	6	(	(	PUNCT
ap-10625	54	7	2	2	NUM
ap-10625	54	8	)	)	PUNCT
ap-10625	54	9	,	,	PUNCT
ap-10625	54	10	we	we	PRON
ap-10625	54	11	obtain	obtain	VERB
ap-10625	54	12	:	:	PUNCT
ap-10625	54	13	i∂τφ(y	i∂τφ(y	PROPN
ap-10625	54	14	,	,	PUNCT
ap-10625	54	15	τ	τ	X
ap-10625	54	16	)	)	PUNCT
ap-10625	54	17	=	=	SYM
ap-10625	54	18	(	(	PUNCT
ap-10625	54	19	−iα∂y	−iα∂y	INTJ
ap-10625	54	20	+	+	CCONJ
ap-10625	54	21	α1	α1	PROPN
ap-10625	54	22	κ	κ	X
ap-10625	54	23	y	y	PROPN
ap-10625	54	24	+	+	PROPN
ap-10625	54	25	mr0(t(τ))β	mr0(t(τ))β	ADJ
ap-10625	54	26	)	)	PUNCT
ap-10625	54	27	φ(y	φ(y	PROPN
ap-10625	54	28	,	,	PUNCT
ap-10625	54	29	τ	τ	PROPN
ap-10625	54	30	)	)	PUNCT
ap-10625	54	31	,	,	PUNCT
ap-10625	54	32	(	(	PUNCT
ap-10625	54	33	4	4	X
ap-10625	54	34	)	)	PUNCT
ap-10625	54	35	where	where	SCONJ
ap-10625	54	36	y	y	PROPN
ap-10625	54	37	∈	∈	PROPN
ap-10625	54	38	(	(	PUNCT
ap-10625	54	39	0	0	NUM
ap-10625	54	40	,	,	PUNCT
ap-10625	54	41	1	1	NUM
ap-10625	54	42	)	)	PUNCT
ap-10625	54	43	and	and	CCONJ
ap-10625	54	44	φ1(0	φ1(0	PROPN
ap-10625	54	45	,	,	PUNCT
ap-10625	54	46	τ)=φ2(0	τ)=φ2(0	PROPN
ap-10625	54	47	,	,	PUNCT
ap-10625	54	48	τ	τ	X
ap-10625	54	49	)	)	PUNCT
ap-10625	54	50	=	=	SYM
ap-10625	54	51	0	0	X
ap-10625	54	52	.	.	PUNCT
ap-10625	54	53	thus	thus	ADV
ap-10625	54	54	,	,	PUNCT
ap-10625	54	55	we	we	PRON
ap-10625	54	56	“	"	PUNCT
ap-10625	54	57	mapped	map	VERB
ap-10625	54	58	”	"	PUNCT
ap-10625	54	59	the	the	DET
ap-10625	54	60	problem	problem	NOUN
ap-10625	54	61	onto	onto	ADP
ap-10625	54	62	the	the	DET
ap-10625	54	63	dirac	dirac	NOUN
ap-10625	54	64	equation	equation	NOUN
ap-10625	54	65	on	on	ADP
ap-10625	54	66	a	a	DET
ap-10625	54	67	fixed	fix	VERB
ap-10625	54	68	interval	interval	NOUN
ap-10625	54	69	but	but	CCONJ
ap-10625	54	70	with	with	ADP
ap-10625	54	71	a	a	DET
ap-10625	54	72	time	time	NOUN
ap-10625	54	73	-	-	PUNCT
ap-10625	54	74	dependent	dependent	ADJ
ap-10625	54	75	mass	mass	NOUN
ap-10625	54	76	m(τ	m(τ	PROPN
ap-10625	54	77	)	)	PUNCT
ap-10625	54	78	=	=	SYM
ap-10625	54	79	mr0(t(τ	mr0(t(τ	NOUN
ap-10625	54	80	)	)	PUNCT
ap-10625	54	81	)	)	PUNCT
ap-10625	54	82	.	.	PUNCT
ap-10625	55	1	2.1	2.1	NUM
ap-10625	55	2	.	.	PUNCT
ap-10625	55	3	radial	radial	ADJ
ap-10625	55	4	operator	operator	NOUN
ap-10625	55	5	domain	domain	VERB
ap-10625	55	6	the	the	DET
ap-10625	55	7	self	self	NOUN
ap-10625	55	8	-	-	PUNCT
ap-10625	55	9	adjointness	adjointness	NOUN
ap-10625	55	10	and	and	CCONJ
ap-10625	55	11	the	the	DET
ap-10625	55	12	basic	basic	ADJ
ap-10625	55	13	spectral	spectral	ADJ
ap-10625	55	14	properties	property	NOUN
ap-10625	55	15	of	of	ADP
ap-10625	55	16	the	the	DET
ap-10625	55	17	considered	consider	VERB
ap-10625	55	18	dirac	dirac	NOUN
ap-10625	55	19	operator	operator	NOUN
ap-10625	55	20	in	in	ADP
ap-10625	55	21	three	three	NUM
ap-10625	55	22	dimensions	dimension	NOUN
ap-10625	55	23	were	be	AUX
ap-10625	55	24	established	establish	VERB
ap-10625	55	25	in	in	ADP
ap-10625	55	26	[	[	X
ap-10625	55	27	20	20	NUM
ap-10625	55	28	]	]	PUNCT
ap-10625	55	29	.	.	PUNCT
ap-10625	56	1	a	a	DET
ap-10625	56	2	simple	simple	ADJ
ap-10625	56	3	example	example	NOUN
ap-10625	56	4	given	give	VERB
ap-10625	56	5	there	there	PRON
ap-10625	56	6	shows	show	VERB
ap-10625	56	7	that	that	SCONJ
ap-10625	56	8	the	the	DET
ap-10625	56	9	operator	operator	NOUN
ap-10625	56	10	domain	domain	NOUN
ap-10625	56	11	is	be	AUX
ap-10625	56	12	not	not	PART
ap-10625	56	13	contained	contain	VERB
ap-10625	56	14	in	in	ADP
ap-10625	56	15	the	the	DET
ap-10625	56	16	sobolev	sobolev	NOUN
ap-10625	56	17	space	space	NOUN
ap-10625	56	18	h1	h1	PROPN
ap-10625	56	19	.	.	PUNCT
ap-10625	57	1	however	however	ADV
ap-10625	57	2	,	,	PUNCT
ap-10625	57	3	the	the	DET
ap-10625	57	4	domains	domain	NOUN
ap-10625	57	5	of	of	ADP
ap-10625	57	6	the	the	DET
ap-10625	57	7	corresponding	corresponding	ADJ
ap-10625	57	8	radial	radial	ADJ
ap-10625	57	9	operators	operator	NOUN
ap-10625	57	10	,	,	PUNCT
ap-10625	57	11	and	and	CCONJ
ap-10625	57	12	consequently	consequently	ADV
ap-10625	57	13	those	those	PRON
ap-10625	57	14	on	on	ADP
ap-10625	57	15	the	the	DET
ap-10625	57	16	right	right	ADJ
ap-10625	57	17	hand	hand	NOUN
ap-10625	57	18	side	side	NOUN
ap-10625	57	19	of	of	ADP
ap-10625	57	20	equation	equation	NOUN
ap-10625	57	21	(	(	PUNCT
ap-10625	57	22	4	4	NUM
ap-10625	57	23	)	)	PUNCT
ap-10625	57	24	,	,	PUNCT
ap-10625	57	25	are	be	AUX
ap-10625	57	26	contained	contain	VERB
ap-10625	57	27	in	in	ADP
ap-10625	57	28	h1	h1	PROPN
ap-10625	57	29	.	.	PUNCT
ap-10625	58	1	this	this	PRON
ap-10625	58	2	was	be	AUX
ap-10625	58	3	observed	observe	VERB
ap-10625	58	4	already	already	ADV
ap-10625	58	5	in	in	ADP
ap-10625	58	6	[	[	X
ap-10625	58	7	18	18	NUM
ap-10625	58	8	]	]	PUNCT
ap-10625	58	9	on	on	ADP
ap-10625	58	10	the	the	DET
ap-10625	58	11	basis	basis	NOUN
ap-10625	58	12	that	that	SCONJ
ap-10625	58	13	the	the	DET
ap-10625	58	14	full	full	ADJ
ap-10625	58	15	dirac	dirac	NOUN
ap-10625	58	16	operator	operator	NOUN
ap-10625	58	17	has	have	AUX
ap-10625	58	18	the	the	DET
ap-10625	58	19	domain	domain	NOUN
ap-10625	58	20	inside	inside	ADP
ap-10625	58	21	h1	h1	PROPN
ap-10625	58	22	loc(r3,c4	loc(r3,c4	PROPN
ap-10625	58	23	)	)	PUNCT
ap-10625	58	24	and	and	CCONJ
ap-10625	58	25	the	the	DET
ap-10625	58	26	radial	radial	ADJ
ap-10625	58	27	operators	operator	NOUN
ap-10625	58	28	contain	contain	VERB
ap-10625	58	29	only	only	ADV
ap-10625	58	30	terms	term	NOUN
ap-10625	58	31	regular	regular	ADV
ap-10625	58	32	at	at	ADP
ap-10625	58	33	the	the	DET
ap-10625	58	34	bag	bag	NOUN
ap-10625	58	35	surface	surface	NOUN
ap-10625	58	36	.	.	PUNCT
ap-10625	59	1	we	we	PRON
ap-10625	59	2	give	give	VERB
ap-10625	59	3	here	here	ADV
ap-10625	59	4	an	an	DET
ap-10625	59	5	independent	independent	ADJ
ap-10625	59	6	proof	proof	NOUN
ap-10625	59	7	based	base	VERB
ap-10625	59	8	on	on	ADP
ap-10625	59	9	the	the	DET
ap-10625	59	10	form	form	NOUN
ap-10625	59	11	of	of	ADP
ap-10625	59	12	the	the	DET
ap-10625	59	13	radial	radial	ADJ
ap-10625	59	14	operator	operator	NOUN
ap-10625	59	15	itself	itself	PRON
ap-10625	59	16	only	only	ADV
ap-10625	59	17	,	,	PUNCT
ap-10625	59	18	without	without	ADP
ap-10625	59	19	the	the	DET
ap-10625	59	20	reference	reference	NOUN
ap-10625	59	21	to	to	ADP
ap-10625	59	22	its	its	PRON
ap-10625	59	23	origin	origin	NOUN
ap-10625	59	24	.	.	PUNCT
ap-10625	60	1	in	in	ADP
ap-10625	60	2	equation	equation	NOUN
ap-10625	60	3	(	(	PUNCT
ap-10625	60	4	4	4	NUM
ap-10625	60	5	)	)	PUNCT
ap-10625	60	6	,	,	PUNCT
ap-10625	60	7	the	the	DET
ap-10625	60	8	formal	formal	ADJ
ap-10625	60	9	differential	differential	NOUN
ap-10625	60	10	operator	operator	NOUN
ap-10625	60	11	:	:	PUNCT
ap-10625	60	12	t	t	NOUN
ap-10625	60	13	=	=	PUNCT
ap-10625	60	14	−iα∂y	−iα∂y	PROPN
ap-10625	60	15	+	+	NUM
ap-10625	60	16	α1	α1	PROPN
ap-10625	60	17	κ	κ	X
ap-10625	60	18	y	y	PROPN
ap-10625	60	19	+	+	PROPN
ap-10625	60	20	mβ	mβ	PROPN
ap-10625	60	21	appears	appear	VERB
ap-10625	60	22	.	.	PUNCT
ap-10625	61	1	the	the	DET
ap-10625	61	2	maximal	maximal	ADJ
ap-10625	61	3	operator	operator	NOUN
ap-10625	61	4	tmax	tmax	ADP
ap-10625	61	5	domain	domain	NOUN
ap-10625	61	6	consists	consist	VERB
ap-10625	61	7	of	of	ADP
ap-10625	61	8	functions	function	NOUN
ap-10625	61	9	φ	φ	X
ap-10625	61	10	∈	∈	PROPN
ap-10625	61	11	l2((0	l2((0	PROPN
ap-10625	61	12	,	,	PUNCT
ap-10625	61	13	1),c2	1),c2	NUM
ap-10625	61	14	)	)	PUNCT
ap-10625	61	15	such	such	ADJ
ap-10625	61	16	that	that	SCONJ
ap-10625	61	17	tφ	tφ	PROPN
ap-10625	61	18	∈	∈	PROPN
ap-10625	61	19	l2((0	l2((0	PROPN
ap-10625	61	20	,	,	PUNCT
ap-10625	61	21	1),c2	1),c2	NUM
ap-10625	61	22	)	)	PUNCT
ap-10625	61	23	.	.	PUNCT
ap-10625	62	1	proposition	proposition	NOUN
ap-10625	62	2	1	1	NUM
ap-10625	62	3	.	.	PUNCT
ap-10625	63	1	for	for	ADP
ap-10625	63	2	κ	κ	NOUN
ap-10625	63	3	=	=	SYM
ap-10625	63	4	±1,±2	±1,±2	PROPN
ap-10625	63	5	,	,	PUNCT
ap-10625	63	6	.	.	PUNCT
ap-10625	63	7	.	.	PUNCT
ap-10625	63	8	.	.	PUNCT
ap-10625	64	1	,	,	PUNCT
ap-10625	64	2	the	the	DET
ap-10625	64	3	domain	domain	NOUN
ap-10625	64	4	:	:	PUNCT
ap-10625	64	5	d(tmax	d(tmax	NOUN
ap-10625	64	6	)	)	PUNCT
ap-10625	65	1	=	=	PRON
ap-10625	65	2	{	{	PUNCT
ap-10625	65	3	φ	φ	PROPN
ap-10625	65	4	∈	∈	PROPN
ap-10625	65	5	h1((0	h1((0	PROPN
ap-10625	65	6	,	,	PUNCT
ap-10625	65	7	1),c2	1),c2	NUM
ap-10625	65	8	)	)	PUNCT
ap-10625	65	9	|φ(0	|φ(0	NOUN
ap-10625	65	10	)	)	PUNCT
ap-10625	65	11	=	=	SYM
ap-10625	65	12	0	0	NUM
ap-10625	65	13	}	}	PUNCT
ap-10625	65	14	,	,	PUNCT
ap-10625	65	15	(	(	PUNCT
ap-10625	65	16	5	5	X
ap-10625	65	17	)	)	PUNCT
ap-10625	65	18	where	where	SCONJ
ap-10625	65	19	φ(0	φ(0	ADJ
ap-10625	65	20	)	)	PUNCT
ap-10625	65	21	is	be	AUX
ap-10625	65	22	the	the	DET
ap-10625	65	23	trace	trace	NOUN
ap-10625	65	24	of	of	ADP
ap-10625	65	25	φ	φ	PROPN
ap-10625	65	26	at	at	ADP
ap-10625	65	27	0	0	NUM
ap-10625	65	28	.	.	PUNCT
ap-10625	66	1	proof	proof	NOUN
ap-10625	66	2	.	.	PUNCT
ap-10625	67	1	let	let	VERB
ap-10625	67	2	φ	φ	PROPN
ap-10625	67	3	∈	∈	PROPN
ap-10625	67	4	d(tmax	d(tmax	NOUN
ap-10625	67	5	)	)	PUNCT
ap-10625	67	6	.	.	PUNCT
ap-10625	68	1	evidently	evidently	ADV
ap-10625	68	2	,	,	PUNCT
ap-10625	68	3	φ	φ	PROPN
ap-10625	68	4	∈	∈	PROPN
ap-10625	68	5	h1((ε	h1((ε	PROPN
ap-10625	68	6	,	,	PUNCT
ap-10625	68	7	1	1	NUM
ap-10625	68	8	)	)	PUNCT
ap-10625	68	9	)	)	PUNCT
ap-10625	68	10	for	for	ADP
ap-10625	68	11	any	any	PRON
ap-10625	68	12	0	0	PUNCT
ap-10625	68	13	<	<	X
ap-10625	68	14	ε	ε	X
ap-10625	68	15	<	<	X
ap-10625	68	16	1	1	NUM
ap-10625	68	17	as	as	SCONJ
ap-10625	68	18	α	α	NOUN
ap-10625	68	19	is	be	AUX
ap-10625	68	20	constant	constant	ADJ
ap-10625	68	21	and	and	CCONJ
ap-10625	68	22	invertible	invertible	ADJ
ap-10625	68	23	and	and	CCONJ
ap-10625	68	24	(	(	PUNCT
ap-10625	68	25	α1	α1	PROPN
ap-10625	68	26	κ	κ	X
ap-10625	68	27	y	y	PROPN
ap-10625	68	28	+	+	PROPN
ap-10625	68	29	mβ)φ	mβ)φ	PROPN
ap-10625	68	30	∈	∈	PROPN
ap-10625	68	31	l2((ε	l2((ε	NOUN
ap-10625	68	32	,	,	PUNCT
ap-10625	68	33	1	1	NUM
ap-10625	68	34	)	)	PUNCT
ap-10625	68	35	)	)	PUNCT
ap-10625	68	36	.	.	PUNCT
ap-10625	69	1	let	let	VERB
ap-10625	69	2	f	f	PRON
ap-10625	69	3	be	be	AUX
ap-10625	69	4	the	the	DET
ap-10625	69	5	upper	upper	ADJ
ap-10625	69	6	/	/	SYM
ap-10625	69	7	lower	low	ADJ
ap-10625	69	8	component	component	NOUN
ap-10625	69	9	of	of	ADP
ap-10625	69	10	φ	φ	PROPN
ap-10625	69	11	.	.	PUNCT
ap-10625	70	1	then	then	ADV
ap-10625	70	2	:	:	PUNCT
ap-10625	70	3	f	f	PROPN
ap-10625	70	4	′(y	′(y	PROPN
ap-10625	70	5	)	)	PUNCT
ap-10625	70	6	±	±	PROPN
ap-10625	70	7	κ	κ	PROPN
ap-10625	70	8	y	y	PROPN
ap-10625	70	9	f(y	f(y	PROPN
ap-10625	70	10	)	)	PUNCT
ap-10625	71	1	=	=	SYM
ap-10625	71	2	f	f	PROPN
ap-10625	71	3	(	(	PUNCT
ap-10625	71	4	y	y	NOUN
ap-10625	71	5	)	)	PUNCT
ap-10625	71	6	,	,	PUNCT
ap-10625	71	7	(	(	PUNCT
ap-10625	71	8	6	6	NUM
ap-10625	71	9	)	)	PUNCT
ap-10625	71	10	with	with	ADP
ap-10625	71	11	a	a	DET
ap-10625	71	12	function	function	NOUN
ap-10625	71	13	f	f	PROPN
ap-10625	71	14	∈	∈	PROPN
ap-10625	71	15	l2((0	l2((0	PROPN
ap-10625	71	16	,	,	PUNCT
ap-10625	71	17	1	1	NUM
ap-10625	71	18	)	)	PUNCT
ap-10625	71	19	)	)	PUNCT
ap-10625	71	20	according	accord	VERB
ap-10625	71	21	to	to	ADP
ap-10625	71	22	the	the	DET
ap-10625	71	23	form	form	NOUN
ap-10625	71	24	of	of	ADP
ap-10625	71	25	t	t	PROPN
ap-10625	71	26	.	.	PUNCT
ap-10625	72	1	consider	consider	VERB
ap-10625	72	2	first	first	ADV
ap-10625	72	3	the	the	DET
ap-10625	72	4	case	case	NOUN
ap-10625	72	5	of	of	ADP
ap-10625	72	6	upper	upper	ADJ
ap-10625	72	7	sign	sign	NOUN
ap-10625	72	8	and	and	CCONJ
ap-10625	72	9	κ	κ	X
ap-10625	72	10	≥	≥	NUM
ap-10625	72	11	1	1	NUM
ap-10625	72	12	.	.	PUNCT
ap-10625	73	1	the	the	DET
ap-10625	73	2	above	above	ADJ
ap-10625	73	3	equation	equation	NOUN
ap-10625	73	4	has	have	VERB
ap-10625	73	5	the	the	DET
ap-10625	73	6	solution	solution	NOUN
ap-10625	73	7	:	:	PUNCT
ap-10625	73	8	f(y	f(y	NOUN
ap-10625	73	9	)	)	PUNCT
ap-10625	73	10	=	=	PUNCT
ap-10625	74	1	y−κ	y−κ	VERB
ap-10625	74	2	∫	∫	PROPN
ap-10625	74	3	y	y	PROPN
ap-10625	74	4	0	0	NUM
ap-10625	74	5	ξκf	ξκf	PROPN
ap-10625	74	6	(	(	PUNCT
ap-10625	74	7	ξ	ξ	NOUN
ap-10625	74	8	)	)	PUNCT
ap-10625	74	9	dξ	dξ	PROPN
ap-10625	74	10	+	+	CCONJ
ap-10625	74	11	cy−κ	cy−κ	ADJ
ap-10625	74	12	,	,	PUNCT
ap-10625	74	13	(	(	PUNCT
ap-10625	74	14	7	7	NUM
ap-10625	74	15	)	)	PUNCT
ap-10625	74	16	with	with	ADP
ap-10625	74	17	a	a	DET
ap-10625	74	18	constant	constant	ADJ
ap-10625	74	19	c	c	NOUN
ap-10625	74	20	provided	provide	VERB
ap-10625	74	21	that	that	SCONJ
ap-10625	74	22	the	the	DET
ap-10625	74	23	integral	integral	ADJ
ap-10625	74	24	is	be	AUX
ap-10625	74	25	convergent	convergent	NOUN
ap-10625	74	26	.	.	PUNCT
ap-10625	75	1	however:∣∣∣∣∫	however:∣∣∣∣∫	VERB
ap-10625	75	2	y	y	PROPN
ap-10625	75	3	0	0	NUM
ap-10625	75	4	ξκf	ξκf	PROPN
ap-10625	75	5	(	(	PUNCT
ap-10625	75	6	ξ	ξ	NOUN
ap-10625	75	7	)	)	PUNCT
ap-10625	75	8	dξ	dξ	PROPN
ap-10625	75	9	∣∣∣∣	∣∣∣∣	NOUN
ap-10625	75	10	≤	≤	PROPN
ap-10625	75	11	1√	1√	PROPN
ap-10625	75	12	2κ+	2κ+	NUM
ap-10625	75	13	1	1	NUM
ap-10625	75	14	yκ+	yκ+	NOUN
ap-10625	75	15	1	1	NUM
ap-10625	75	16	2	2	NUM
ap-10625	75	17	∥f∥l2	∥f∥l2	NOUN
ap-10625	75	18	,	,	PUNCT
ap-10625	75	19	by	by	ADP
ap-10625	75	20	the	the	DET
ap-10625	75	21	schwarz	schwarz	PROPN
ap-10625	75	22	inequality	inequality	NOUN
ap-10625	75	23	,	,	PUNCT
ap-10625	75	24	so	so	SCONJ
ap-10625	75	25	c	c	NOUN
ap-10625	75	26	=	=	SYM
ap-10625	75	27	0	0	NUM
ap-10625	75	28	,	,	PUNCT
ap-10625	75	29	and	and	CCONJ
ap-10625	75	30	f(0	f(0	NOUN
ap-10625	75	31	)	)	PUNCT
ap-10625	75	32	=	=	SYM
ap-10625	76	1	0	0	X
ap-10625	76	2	.	.	PUNCT
ap-10625	76	3	let	let	VERB
ap-10625	76	4	us	we	PRON
ap-10625	76	5	now	now	ADV
ap-10625	76	6	consider	consider	VERB
ap-10625	76	7	the	the	DET
ap-10625	76	8	case	case	NOUN
ap-10625	76	9	of	of	ADP
ap-10625	76	10	lower	low	ADJ
ap-10625	76	11	sign	sign	NOUN
ap-10625	76	12	and	and	CCONJ
ap-10625	76	13	κ	κ	X
ap-10625	76	14	≥	≥	NOUN
ap-10625	76	15	1	1	NUM
ap-10625	76	16	.	.	PUNCT
ap-10625	77	1	the	the	DET
ap-10625	77	2	solution	solution	NOUN
ap-10625	77	3	is	be	AUX
ap-10625	77	4	now	now	ADV
ap-10625	77	5	:	:	PUNCT
ap-10625	77	6	f(y	f(y	NOUN
ap-10625	77	7	)	)	PUNCT
ap-10625	78	1	=	=	SYM
ap-10625	78	2	−yκ	−yκ	NOUN
ap-10625	78	3	∫	∫	PROPN
ap-10625	78	4	1	1	NUM
ap-10625	78	5	y	y	PROPN
ap-10625	78	6	ξ−κf	ξ−κf	PROPN
ap-10625	78	7	(	(	PUNCT
ap-10625	78	8	ξ	ξ	PROPN
ap-10625	78	9	)	)	PUNCT
ap-10625	78	10	dξ	dξ	PROPN
ap-10625	79	1	+	+	CCONJ
ap-10625	79	2	c1y	c1y	NOUN
ap-10625	79	3	κ	κ	NOUN
ap-10625	79	4	,	,	PUNCT
ap-10625	79	5	(	(	PUNCT
ap-10625	79	6	8)	8)	NUM
ap-10625	79	7	with	with	ADP
ap-10625	79	8	a	a	DET
ap-10625	79	9	constant	constant	ADJ
ap-10625	79	10	c1	c1	NOUN
ap-10625	79	11	.	.	PUNCT
ap-10625	80	1	as:∣∣∣∣yκ	as:∣∣∣∣yκ	PROPN
ap-10625	80	2	∫	∫	PROPN
ap-10625	80	3	1	1	NUM
ap-10625	80	4	y	y	PROPN
ap-10625	80	5	ξ−κf	ξ−κf	PROPN
ap-10625	80	6	(	(	PUNCT
ap-10625	80	7	ξ	ξ	NOUN
ap-10625	80	8	)	)	PUNCT
ap-10625	80	9	dξ	dξ	PROPN
ap-10625	80	10	∣∣∣∣	∣∣∣∣	NOUN
ap-10625	80	11	≤	≤	PUNCT
ap-10625	80	12	1√	1√	NOUN
ap-10625	80	13	2κ−	2κ−	NUM
ap-10625	80	14	1	1	NUM
ap-10625	80	15	√	√	NUM
ap-10625	80	16	y	y	PROPN
ap-10625	80	17	−	−	PROPN
ap-10625	80	18	y2κ∥f∥l2	y2κ∥f∥l2	PROPN
ap-10625	80	19	,	,	PUNCT
ap-10625	80	20	we	we	PRON
ap-10625	80	21	obtain	obtain	VERB
ap-10625	80	22	,	,	PUNCT
ap-10625	80	23	again	again	ADV
ap-10625	80	24	,	,	PUNCT
ap-10625	80	25	f(0	f(0	NOUN
ap-10625	80	26	)	)	PUNCT
ap-10625	80	27	=	=	SYM
ap-10625	81	1	0	0	X
ap-10625	81	2	.	.	PUNCT
ap-10625	82	1	the	the	DET
ap-10625	82	2	cases	case	NOUN
ap-10625	82	3	of	of	ADP
ap-10625	82	4	κ	κ	PROPN
ap-10625	82	5	≤	≤	NUM
ap-10625	82	6	−1	−1	NOUN
ap-10625	82	7	are	be	AUX
ap-10625	82	8	also	also	ADV
ap-10625	82	9	included	include	VERB
ap-10625	82	10	due	due	ADP
ap-10625	82	11	to	to	ADP
ap-10625	82	12	the	the	DET
ap-10625	82	13	different	different	ADJ
ap-10625	82	14	signs	sign	NOUN
ap-10625	82	15	in	in	ADP
ap-10625	82	16	the	the	DET
ap-10625	82	17	equation	equation	NOUN
ap-10625	82	18	above	above	ADV
ap-10625	82	19	.	.	PUNCT
ap-10625	83	1	we	we	PRON
ap-10625	83	2	need	need	VERB
ap-10625	83	3	further	far	ADV
ap-10625	83	4	to	to	PART
ap-10625	83	5	refine	refine	VERB
ap-10625	83	6	our	our	PRON
ap-10625	83	7	estimates	estimate	NOUN
ap-10625	83	8	to	to	PART
ap-10625	83	9	prove	prove	VERB
ap-10625	83	10	that	that	SCONJ
ap-10625	83	11	f	f	PROPN
ap-10625	83	12	∈	∈	PROPN
ap-10625	83	13	h1	h1	PROPN
ap-10625	83	14	.	.	PUNCT
ap-10625	84	1	let	let	VERB
ap-10625	84	2	us	we	PRON
ap-10625	84	3	start	start	VERB
ap-10625	84	4	with	with	ADP
ap-10625	84	5	equation	equation	NOUN
ap-10625	84	6	(	(	PUNCT
ap-10625	84	7	7	7	NUM
ap-10625	84	8	)	)	PUNCT
ap-10625	84	9	(	(	PUNCT
ap-10625	84	10	c	c	NOUN
ap-10625	84	11	=	=	SYM
ap-10625	84	12	0	0	NUM
ap-10625	84	13	)	)	PUNCT
ap-10625	84	14	.	.	PUNCT
ap-10625	85	1	here	here	ADV
ap-10625	85	2	:	:	PUNCT
ap-10625	85	3	f	f	PROPN
ap-10625	85	4	′(y	′(y	NOUN
ap-10625	85	5	)	)	PUNCT
ap-10625	85	6	=	=	PUNCT
ap-10625	86	1	−κy−κ−1	−κy−κ−1	NUM
ap-10625	86	2	∫	∫	PROPN
ap-10625	86	3	y	y	PROPN
ap-10625	86	4	0	0	NUM
ap-10625	86	5	ξκf	ξκf	PROPN
ap-10625	86	6	(	(	PUNCT
ap-10625	86	7	ξ	ξ	NOUN
ap-10625	86	8	)	)	PUNCT
ap-10625	86	9	dξ	dξ	PROPN
ap-10625	87	1	+	+	CCONJ
ap-10625	87	2	f	f	PROPN
ap-10625	87	3	(	(	PUNCT
ap-10625	87	4	y	y	PROPN
ap-10625	87	5	)	)	PUNCT
ap-10625	87	6	.	.	PUNCT
ap-10625	88	1	547	547	NUM
ap-10625	88	2	k.	k.	NOUN
ap-10625	88	3	matchonov	matchonov	PROPN
ap-10625	88	4	,	,	PUNCT
ap-10625	88	5	d.	d.	PROPN
ap-10625	88	6	matrasulov	matrasulov	PROPN
ap-10625	88	7	,	,	PUNCT
ap-10625	88	8	j.	j.	PROPN
ap-10625	88	9	dittrich	dittrich	PROPN
ap-10625	88	10	acta	acta	PROPN
ap-10625	88	11	polytechnica	polytechnica	PROPN
ap-10625	88	12	as	as	ADP
ap-10625	88	13	f	f	PROPN
ap-10625	88	14	∈	∈	PROPN
ap-10625	88	15	l2	l2	NOUN
ap-10625	88	16	,	,	PUNCT
ap-10625	88	17	we	we	PRON
ap-10625	88	18	have	have	VERB
ap-10625	88	19	to	to	PART
ap-10625	88	20	prove	prove	VERB
ap-10625	88	21	the	the	DET
ap-10625	88	22	square	square	ADJ
ap-10625	88	23	integrability	integrability	NOUN
ap-10625	88	24	of	of	ADP
ap-10625	88	25	the	the	DET
ap-10625	88	26	first	first	ADJ
ap-10625	88	27	term	term	NOUN
ap-10625	88	28	.	.	PUNCT
ap-10625	89	1	let	let	VERB
ap-10625	89	2	us	we	PRON
ap-10625	89	3	calculate:∫	calculate:∫	NOUN
ap-10625	89	4	1	1	NUM
ap-10625	89	5	0	0	NUM
ap-10625	89	6	∣∣∣∣y−κ−1	∣∣∣∣y−κ−1	X
ap-10625	89	7	∫	∫	PROPN
ap-10625	89	8	y	y	PROPN
ap-10625	89	9	0	0	NUM
ap-10625	89	10	ξκf	ξκf	PROPN
ap-10625	89	11	(	(	PUNCT
ap-10625	89	12	ξ	ξ	NOUN
ap-10625	89	13	)	)	PUNCT
ap-10625	89	14	dξ	dξ	PROPN
ap-10625	89	15	∣∣∣∣2dy	∣∣∣∣2dy	PROPN
ap-10625	89	16	≤	≤	ADV
ap-10625	89	17	∫	∫	PROPN
ap-10625	90	1	1	1	NUM
ap-10625	90	2	0	0	NUM
ap-10625	90	3	y−2κ−2	y−2κ−2	PROPN
ap-10625	90	4	(	(	PUNCT
ap-10625	90	5	∫	∫	PROPN
ap-10625	90	6	y	y	PROPN
ap-10625	90	7	0	0	NUM
ap-10625	91	1	ξκ|f	ξκ|f	CCONJ
ap-10625	91	2	(	(	PUNCT
ap-10625	91	3	ξ)|dξ	ξ)|dξ	PROPN
ap-10625	91	4	)	)	PUNCT
ap-10625	91	5	2	2	NUM
ap-10625	91	6	dy	dy	X
ap-10625	91	7	=	=	SYM
ap-10625	91	8	∫	∫	PROPN
ap-10625	91	9	1	1	NUM
ap-10625	91	10	0	0	NUM
ap-10625	91	11	y−2κ−2	y−2κ−2	PROPN
ap-10625	91	12	(	(	PUNCT
ap-10625	91	13	∫	∫	PROPN
ap-10625	91	14	y	y	PROPN
ap-10625	91	15	0	0	NUM
ap-10625	92	1	ξκ|f	ξκ|f	CCONJ
ap-10625	92	2	(	(	PUNCT
ap-10625	92	3	ξ)|dξ	ξ)|dξ	PROPN
ap-10625	92	4	)	)	PUNCT
ap-10625	92	5	(	(	PUNCT
ap-10625	92	6	∫	∫	PROPN
ap-10625	92	7	y	y	PROPN
ap-10625	92	8	0	0	NUM
ap-10625	92	9	ηκ|f	ηκ|f	NOUN
ap-10625	92	10	(	(	PUNCT
ap-10625	92	11	η)|dη	η)|dη	PROPN
ap-10625	92	12	)	)	PUNCT
ap-10625	93	1	dy	dy	NOUN
ap-10625	93	2	=	=	SYM
ap-10625	93	3	2	2	NUM
ap-10625	93	4	∫	∫	NOUN
ap-10625	93	5	0	0	NUM
ap-10625	93	6	<	<	X
ap-10625	93	7	ξ	ξ	X
ap-10625	93	8	<	<	X
ap-10625	93	9	η	η	X
ap-10625	93	10	<	<	X
ap-10625	93	11	y<1	y<1	NOUN
ap-10625	93	12	y−2κ−2ξκηκ|f	y−2κ−2ξκηκ|f	PROPN
ap-10625	93	13	(	(	PUNCT
ap-10625	93	14	ξ)|	ξ)|	INTJ
ap-10625	93	15	|f	|f	PROPN
ap-10625	93	16	(	(	PUNCT
ap-10625	93	17	η)|dy	η)|dy	PROPN
ap-10625	93	18	dξ	dξ	PROPN
ap-10625	93	19	dη	dη	NOUN
ap-10625	94	1	=	=	SYM
ap-10625	94	2	2	2	NUM
ap-10625	94	3	∫	∫	NOUN
ap-10625	94	4	0	0	NUM
ap-10625	94	5	<	<	X
ap-10625	94	6	ξ	ξ	X
ap-10625	94	7	<	<	X
ap-10625	94	8	η<1	η<1	NOUN
ap-10625	94	9	1	1	NUM
ap-10625	94	10	2κ+	2κ+	NUM
ap-10625	94	11	1(η−2κ−1	1(η−2κ−1	NUM
ap-10625	94	12	−	−	PROPN
ap-10625	94	13	1)ξκηκ|f	1)ξκηκ|f	NUM
ap-10625	94	14	(	(	PUNCT
ap-10625	94	15	ξ)|	ξ)|	INTJ
ap-10625	94	16	|f	|f	PROPN
ap-10625	94	17	(	(	PUNCT
ap-10625	94	18	η)|dξ	η)|dξ	PROPN
ap-10625	94	19	dη	dη	ADV
ap-10625	94	20	≤	≤	NUM
ap-10625	94	21	2	2	NUM
ap-10625	94	22	2κ+	2κ+	NUM
ap-10625	94	23	1	1	NUM
ap-10625	94	24	∫	∫	NOUN
ap-10625	94	25	0	0	NUM
ap-10625	94	26	<	<	X
ap-10625	94	27	ξ	ξ	X
ap-10625	94	28	<	<	X
ap-10625	94	29	η<1	η<1	PROPN
ap-10625	94	30	ξκη−κ−1|f	ξκη−κ−1|f	NOUN
ap-10625	94	31	(	(	PUNCT
ap-10625	94	32	ξ)|	ξ)|	INTJ
ap-10625	94	33	|f	|f	PROPN
ap-10625	94	34	(	(	PUNCT
ap-10625	94	35	η)|dξ	η)|dξ	VERB
ap-10625	94	36	dη	dη	NOUN
ap-10625	94	37	=	=	SYM
ap-10625	94	38	2	2	NUM
ap-10625	94	39	2κ+	2κ+	NUM
ap-10625	94	40	1	1	NUM
ap-10625	94	41	∫	∫	NOUN
ap-10625	94	42	1	1	NUM
ap-10625	94	43	0	0	NUM
ap-10625	94	44	η−κ−1	η−κ−1	PROPN
ap-10625	94	45	(	(	PUNCT
ap-10625	94	46	∫	∫	PROPN
ap-10625	94	47	η	η	PROPN
ap-10625	94	48	0	0	PROPN
ap-10625	94	49	ξκ|f	ξκ|f	PROPN
ap-10625	94	50	(	(	PUNCT
ap-10625	94	51	ξ)|dξ	ξ)|dξ	PROPN
ap-10625	94	52	)	)	PUNCT
ap-10625	94	53	|f	|f	PROPN
ap-10625	94	54	(	(	PUNCT
ap-10625	94	55	η)|dη	η)|dη	PROPN
ap-10625	94	56	≤	≤	ADJ
ap-10625	94	57	2	2	NUM
ap-10625	94	58	2κ+	2κ+	NUM
ap-10625	94	59	1∥f∥l2((0,1	1∥f∥l2((0,1	NOUN
ap-10625	94	60	)	)	PUNCT
ap-10625	94	61	)	)	PUNCT
ap-10625	95	1	(	(	PUNCT
ap-10625	95	2	∫	∫	PROPN
ap-10625	95	3	1	1	NUM
ap-10625	95	4	0	0	NUM
ap-10625	95	5	η−2κ−2	η−2κ−2	PROPN
ap-10625	95	6	(	(	PUNCT
ap-10625	95	7	∫	∫	PROPN
ap-10625	95	8	η	η	PROPN
ap-10625	95	9	0	0	PROPN
ap-10625	95	10	ξκ|f	ξκ|f	ADP
ap-10625	95	11	(	(	PUNCT
ap-10625	95	12	ξ)|	ξ)|	INTJ
ap-10625	95	13	dξ	dξ	PROPN
ap-10625	95	14	)	)	PUNCT
ap-10625	95	15	2	2	NUM
ap-10625	95	16	)	)	PUNCT
ap-10625	95	17	1	1	NUM
ap-10625	95	18	2	2	NUM
ap-10625	95	19	.	.	PUNCT
ap-10625	96	1	if	if	SCONJ
ap-10625	96	2	the	the	DET
ap-10625	96	3	last	last	ADJ
ap-10625	96	4	integral	integral	ADJ
ap-10625	96	5	converges	converge	NOUN
ap-10625	96	6	we	we	PRON
ap-10625	96	7	can	can	AUX
ap-10625	96	8	divide	divide	VERB
ap-10625	96	9	by	by	ADP
ap-10625	96	10	its	its	PRON
ap-10625	96	11	square	square	ADJ
ap-10625	96	12	root	root	NOUN
ap-10625	96	13	and	and	CCONJ
ap-10625	96	14	obtain:(∫	obtain:(∫	PROPN
ap-10625	97	1	1	1	NUM
ap-10625	97	2	0	0	NUM
ap-10625	98	1	y−2κ−2	y−2κ−2	NOUN
ap-10625	99	1	(	(	PUNCT
ap-10625	99	2	∫	∫	PROPN
ap-10625	99	3	y	y	PROPN
ap-10625	99	4	0	0	NUM
ap-10625	99	5	ξκ|f	ξκ|f	CCONJ
ap-10625	99	6	(	(	PUNCT
ap-10625	99	7	ξ)|	ξ)|	INTJ
ap-10625	99	8	dξ	dξ	PROPN
ap-10625	99	9	)	)	PUNCT
ap-10625	99	10	2	2	NUM
ap-10625	99	11	)	)	SYM
ap-10625	99	12	1	1	NUM
ap-10625	99	13	2	2	NUM
ap-10625	99	14	≤	≤	NUM
ap-10625	99	15	2	2	NUM
ap-10625	99	16	2κ+	2κ+	NUM
ap-10625	99	17	1∥f∥l2((0,1	1∥f∥l2((0,1	NOUN
ap-10625	99	18	)	)	PUNCT
ap-10625	99	19	)	)	PUNCT
ap-10625	99	20	.	.	PUNCT
ap-10625	100	1	(	(	PUNCT
ap-10625	100	2	9	9	X
ap-10625	100	3	)	)	PUNCT
ap-10625	100	4	in	in	ADP
ap-10625	100	5	the	the	DET
ap-10625	100	6	general	general	ADJ
ap-10625	100	7	case	case	NOUN
ap-10625	100	8	,	,	PUNCT
ap-10625	100	9	|f	|f	PROPN
ap-10625	101	1	|	|	ADV
ap-10625	101	2	is	be	AUX
ap-10625	101	3	an	an	DET
ap-10625	101	4	almost	almost	ADV
ap-10625	101	5	everywhere	everywhere	ADV
ap-10625	101	6	non	non	ADJ
ap-10625	101	7	-	-	ADJ
ap-10625	101	8	negative	negative	ADJ
ap-10625	101	9	,	,	PUNCT
ap-10625	101	10	integrable	integrable	ADJ
ap-10625	101	11	and	and	CCONJ
ap-10625	101	12	square	square	ADJ
ap-10625	101	13	-	-	PUNCT
ap-10625	101	14	integrable	integrable	ADJ
ap-10625	101	15	function	function	NOUN
ap-10625	101	16	.	.	PUNCT
ap-10625	102	1	so	so	ADV
ap-10625	102	2	it	it	PRON
ap-10625	102	3	can	can	AUX
ap-10625	102	4	be	be	AUX
ap-10625	102	5	approximated	approximate	VERB
ap-10625	102	6	by	by	ADP
ap-10625	102	7	an	an	DET
ap-10625	102	8	almost	almost	ADV
ap-10625	102	9	everywhere	everywhere	ADV
ap-10625	102	10	non	non	ADJ
ap-10625	102	11	-	-	ADJ
ap-10625	102	12	decreasing	decrease	VERB
ap-10625	102	13	sequence	sequence	NOUN
ap-10625	102	14	of	of	ADP
ap-10625	102	15	bounded	bounded	ADJ
ap-10625	102	16	functions	function	NOUN
ap-10625	102	17	fn	fn	PROPN
ap-10625	102	18	↗	↗	PROPN
ap-10625	102	19	|f	|f	PROPN
ap-10625	103	1	|	|	ADV
ap-10625	103	2	,	,	PUNCT
ap-10625	103	3	e.g.	e.g.	ADV
ap-10625	103	4	fn	fn	NOUN
ap-10625	103	5	=	=	SYM
ap-10625	103	6	min(n	min(n	PROPN
ap-10625	103	7	,	,	PUNCT
ap-10625	103	8	|f	|f	PROPN
ap-10625	103	9	|	|	NOUN
ap-10625	103	10	)	)	PUNCT
ap-10625	103	11	.	.	PUNCT
ap-10625	104	1	the	the	DET
ap-10625	104	2	above	above	ADJ
ap-10625	104	3	derivation	derivation	NOUN
ap-10625	104	4	of	of	ADP
ap-10625	104	5	the	the	DET
ap-10625	104	6	estimate	estimate	NOUN
ap-10625	104	7	(	(	PUNCT
ap-10625	104	8	9	9	X
ap-10625	104	9	)	)	PUNCT
ap-10625	104	10	passes	pass	VERB
ap-10625	104	11	for	for	ADP
ap-10625	104	12	fn	fn	NOUN
ap-10625	104	13	,	,	PUNCT
ap-10625	104	14	and	and	CCONJ
ap-10625	104	15	then	then	ADV
ap-10625	104	16	we	we	PRON
ap-10625	104	17	obtain	obtain	VERB
ap-10625	104	18	the	the	DET
ap-10625	104	19	general	general	ADJ
ap-10625	104	20	case	case	NOUN
ap-10625	104	21	in	in	ADP
ap-10625	104	22	the	the	DET
ap-10625	104	23	limit	limit	NOUN
ap-10625	104	24	.	.	PUNCT
ap-10625	105	1	so	so	ADV
ap-10625	105	2	f	f	NOUN
ap-10625	105	3	′	′	NOUN
ap-10625	105	4	∈	∈	PROPN
ap-10625	105	5	l2	l2	NOUN
ap-10625	105	6	and	and	CCONJ
ap-10625	105	7	f	f	PROPN
ap-10625	105	8	∈	∈	PROPN
ap-10625	105	9	h1	h1	NOUN
ap-10625	105	10	in	in	ADP
ap-10625	105	11	the	the	DET
ap-10625	105	12	considered	consider	VERB
ap-10625	105	13	case	case	NOUN
ap-10625	105	14	(	(	PUNCT
ap-10625	105	15	7	7	NUM
ap-10625	105	16	)	)	PUNCT
ap-10625	105	17	.	.	PUNCT
ap-10625	106	1	let	let	VERB
ap-10625	106	2	us	we	PRON
ap-10625	106	3	now	now	ADV
ap-10625	106	4	turn	turn	VERB
ap-10625	106	5	to	to	ADP
ap-10625	106	6	the	the	DET
ap-10625	106	7	case	case	NOUN
ap-10625	106	8	(	(	PUNCT
ap-10625	106	9	8)	8)	NUM
ap-10625	106	10	.	.	PUNCT
ap-10625	107	1	then	then	ADV
ap-10625	107	2	:	:	PUNCT
ap-10625	107	3	f	f	PROPN
ap-10625	107	4	′(y	′(y	NOUN
ap-10625	107	5	)	)	PUNCT
ap-10625	108	1	=	=	SYM
ap-10625	108	2	−κyκ−1	−κyκ−1	PROPN
ap-10625	108	3	∫	∫	PROPN
ap-10625	108	4	1	1	NUM
ap-10625	108	5	y	y	PROPN
ap-10625	108	6	ξ−κf	ξ−κf	PROPN
ap-10625	108	7	(	(	PUNCT
ap-10625	108	8	ξ	ξ	PROPN
ap-10625	108	9	)	)	PUNCT
ap-10625	109	1	dξ	dξ	PROPN
ap-10625	110	1	+	+	CCONJ
ap-10625	110	2	f	f	PROPN
ap-10625	110	3	(	(	PUNCT
ap-10625	110	4	y	y	NOUN
ap-10625	110	5	)	)	PUNCT
ap-10625	110	6	+	+	CCONJ
ap-10625	110	7	c1κy	c1κy	PROPN
ap-10625	110	8	κ−1	κ−1	PROPN
ap-10625	110	9	,	,	PUNCT
ap-10625	110	10	where	where	SCONJ
ap-10625	110	11	the	the	DET
ap-10625	110	12	last	last	ADJ
ap-10625	110	13	two	two	NUM
ap-10625	110	14	terms	term	NOUN
ap-10625	110	15	are	be	AUX
ap-10625	110	16	apparently	apparently	ADV
ap-10625	110	17	in	in	ADP
ap-10625	110	18	l2	l2	NOUN
ap-10625	110	19	.	.	PUNCT
ap-10625	111	1	we	we	PRON
ap-10625	111	2	treat	treat	VERB
ap-10625	111	3	the	the	DET
ap-10625	111	4	first	first	ADJ
ap-10625	111	5	term	term	NOUN
ap-10625	111	6	similarly	similarly	ADV
ap-10625	111	7	as	as	ADP
ap-10625	111	8	above:∫	above:∫	PROPN
ap-10625	111	9	1	1	NUM
ap-10625	111	10	0	0	NUM
ap-10625	111	11	∣∣∣∣yκ−1	∣∣∣∣yκ−1	X
ap-10625	111	12	∫	∫	PROPN
ap-10625	111	13	1	1	NUM
ap-10625	111	14	y	y	PROPN
ap-10625	111	15	ξ−κf	ξ−κf	PROPN
ap-10625	111	16	(	(	PUNCT
ap-10625	111	17	ξ	ξ	PROPN
ap-10625	111	18	)	)	PUNCT
ap-10625	111	19	dξ	dξ	PROPN
ap-10625	111	20	∣∣∣∣2dy	∣∣∣∣2dy	PROPN
ap-10625	111	21	≤	≤	ADV
ap-10625	111	22	∫	∫	PROPN
ap-10625	111	23	1	1	NUM
ap-10625	111	24	0	0	NUM
ap-10625	112	1	(	(	PUNCT
ap-10625	112	2	yκ−1	yκ−1	PROPN
ap-10625	112	3	∫	∫	PROPN
ap-10625	112	4	1	1	NUM
ap-10625	112	5	y	y	PROPN
ap-10625	112	6	ξ−κ|f	ξ−κ|f	PROPN
ap-10625	112	7	(	(	PUNCT
ap-10625	112	8	ξ)|	ξ)|	INTJ
ap-10625	112	9	dξ	dξ	PROPN
ap-10625	112	10	)	)	PUNCT
ap-10625	112	11	2	2	NUM
ap-10625	112	12	dy	dy	NOUN
ap-10625	112	13	=	=	SYM
ap-10625	112	14	2	2	NUM
ap-10625	112	15	∫	∫	NOUN
ap-10625	112	16	0	0	NUM
ap-10625	112	17	<	<	X
ap-10625	112	18	y	y	X
ap-10625	112	19	<	<	X
ap-10625	112	20	ξ	ξ	X
ap-10625	112	21	<	<	X
ap-10625	112	22	η<1	η<1	PROPN
ap-10625	112	23	y2κ−2ξ−κη−κ|f	y2κ−2ξ−κη−κ|f	PROPN
ap-10625	112	24	(	(	PUNCT
ap-10625	112	25	ξ)|	ξ)|	INTJ
ap-10625	112	26	|f	|f	PROPN
ap-10625	112	27	(	(	PUNCT
ap-10625	112	28	η)|	η)|	PROPN
ap-10625	112	29	dy	dy	X
ap-10625	112	30	dξ	dξ	PROPN
ap-10625	112	31	dη	dη	NOUN
ap-10625	112	32	=	=	NOUN
ap-10625	112	33	2	2	NUM
ap-10625	112	34	2κ−	2κ−	PRON
ap-10625	112	35	1	1	NUM
ap-10625	112	36	∫	∫	NOUN
ap-10625	112	37	0	0	NUM
ap-10625	112	38	<	<	X
ap-10625	112	39	ξ	ξ	X
ap-10625	112	40	<	<	X
ap-10625	112	41	η<1	η<1	PROPN
ap-10625	112	42	ξκ−1η−κ|f	ξκ−1η−κ|f	PROPN
ap-10625	112	43	(	(	PUNCT
ap-10625	112	44	ξ)|	ξ)|	INTJ
ap-10625	112	45	|f	|f	PROPN
ap-10625	112	46	(	(	PUNCT
ap-10625	112	47	η)|	η)|	PROPN
ap-10625	112	48	dξ	dξ	PROPN
ap-10625	112	49	dη	dη	NOUN
ap-10625	112	50	=	=	NOUN
ap-10625	112	51	2	2	NUM
ap-10625	112	52	2κ−	2κ−	PRON
ap-10625	112	53	1	1	NUM
ap-10625	112	54	∫	∫	NOUN
ap-10625	112	55	1	1	NUM
ap-10625	112	56	0	0	NUM
ap-10625	112	57	(	(	PUNCT
ap-10625	112	58	ξκ−1	ξκ−1	PROPN
ap-10625	112	59	∫	∫	PROPN
ap-10625	112	60	1	1	NUM
ap-10625	112	61	ξ	ξ	PROPN
ap-10625	112	62	η−κ|f	η−κ|f	PROPN
ap-10625	112	63	(	(	PUNCT
ap-10625	112	64	η)|	η)|	PROPN
ap-10625	112	65	dη	dη	ADP
ap-10625	112	66	|f	|f	PROPN
ap-10625	112	67	(	(	PUNCT
ap-10625	112	68	ξ)|	ξ)|	INTJ
ap-10625	112	69	)	)	PUNCT
ap-10625	112	70	dξ	dξ	PROPN
ap-10625	112	71	≤	≤	NUM
ap-10625	112	72	2	2	NUM
ap-10625	112	73	2κ−	2κ−	NUM
ap-10625	112	74	1∥f∥l2((0,1	1∥f∥l2((0,1	NOUN
ap-10625	112	75	)	)	PUNCT
ap-10625	112	76	)	)	PUNCT
ap-10625	113	1	(	(	PUNCT
ap-10625	113	2	∫	∫	PROPN
ap-10625	113	3	1	1	NUM
ap-10625	113	4	0	0	NUM
ap-10625	113	5	(	(	PUNCT
ap-10625	113	6	yκ−1	yκ−1	PROPN
ap-10625	113	7	∫	∫	PROPN
ap-10625	113	8	1	1	NUM
ap-10625	113	9	y	y	PROPN
ap-10625	113	10	ξ−κ|f	ξ−κ|f	PROPN
ap-10625	113	11	(	(	PUNCT
ap-10625	113	12	ξ)|	ξ)|	INTJ
ap-10625	113	13	dξ	dξ	PROPN
ap-10625	113	14	)	)	PUNCT
ap-10625	113	15	2	2	NUM
ap-10625	113	16	dy	dy	NOUN
ap-10625	113	17	)	)	PUNCT
ap-10625	113	18	1	1	NUM
ap-10625	113	19	2	2	NUM
ap-10625	113	20	.	.	PUNCT
ap-10625	114	1	if	if	SCONJ
ap-10625	114	2	the	the	DET
ap-10625	114	3	last	last	ADJ
ap-10625	114	4	integral	integral	ADJ
ap-10625	114	5	converges	converge	NOUN
ap-10625	114	6	,	,	PUNCT
ap-10625	114	7	we	we	PRON
ap-10625	114	8	obtain:(∫	obtain:(∫	VERB
ap-10625	114	9	1	1	NUM
ap-10625	114	10	0	0	NUM
ap-10625	114	11	(	(	PUNCT
ap-10625	114	12	yκ−1	yκ−1	PROPN
ap-10625	114	13	∫	∫	PROPN
ap-10625	114	14	1	1	NUM
ap-10625	114	15	y	y	PROPN
ap-10625	114	16	ξ−κ|f	ξ−κ|f	PROPN
ap-10625	114	17	(	(	PUNCT
ap-10625	114	18	ξ)|	ξ)|	INTJ
ap-10625	114	19	dξ	dξ	PROPN
ap-10625	114	20	)	)	PUNCT
ap-10625	114	21	2	2	NUM
ap-10625	114	22	dy	dy	NOUN
ap-10625	114	23	)	)	PUNCT
ap-10625	114	24	1	1	NUM
ap-10625	114	25	2	2	NUM
ap-10625	114	26	≤	≤	NUM
ap-10625	114	27	2	2	NUM
ap-10625	114	28	2κ−	2κ−	NUM
ap-10625	114	29	1∥f∥l2((0,1	1∥f∥l2((0,1	NOUN
ap-10625	114	30	)	)	PUNCT
ap-10625	114	31	)	)	PUNCT
ap-10625	114	32	.	.	PUNCT
ap-10625	115	1	(	(	PUNCT
ap-10625	115	2	10	10	X
ap-10625	115	3	)	)	PUNCT
ap-10625	115	4	approximating	approximate	VERB
ap-10625	115	5	general	general	ADJ
ap-10625	115	6	f	f	PROPN
ap-10625	115	7	∈	∈	PROPN
ap-10625	115	8	l2	l2	NOUN
ap-10625	115	9	by	by	ADP
ap-10625	115	10	bounded	bounded	ADJ
ap-10625	115	11	functions	function	NOUN
ap-10625	115	12	,	,	PUNCT
ap-10625	115	13	we	we	PRON
ap-10625	115	14	obtain	obtain	VERB
ap-10625	115	15	equation	equation	NOUN
ap-10625	115	16	(	(	PUNCT
ap-10625	115	17	10	10	NUM
ap-10625	115	18	)	)	PUNCT
ap-10625	115	19	in	in	ADP
ap-10625	115	20	the	the	DET
ap-10625	115	21	limit	limit	NOUN
ap-10625	115	22	.	.	PUNCT
ap-10625	116	1	so	so	ADV
ap-10625	116	2	f	f	NOUN
ap-10625	116	3	′	′	NOUN
ap-10625	116	4	∈	∈	PROPN
ap-10625	116	5	l2	l2	NOUN
ap-10625	116	6	and	and	CCONJ
ap-10625	116	7	f	f	PROPN
ap-10625	116	8	∈	∈	PROPN
ap-10625	116	9	h1	h1	PROPN
ap-10625	116	10	.	.	PUNCT
ap-10625	117	1	all	all	DET
ap-10625	117	2	possibilities	possibility	NOUN
ap-10625	117	3	of	of	ADP
ap-10625	117	4	signs	sign	NOUN
ap-10625	117	5	in	in	ADP
ap-10625	117	6	equation	equation	NOUN
ap-10625	117	7	(	(	PUNCT
ap-10625	117	8	6	6	NUM
ap-10625	117	9	)	)	PUNCT
ap-10625	117	10	are	be	AUX
ap-10625	117	11	covered	cover	VERB
ap-10625	117	12	.	.	PUNCT
ap-10625	118	1	it	it	PRON
ap-10625	118	2	remains	remain	VERB
ap-10625	118	3	to	to	PART
ap-10625	118	4	prove	prove	VERB
ap-10625	118	5	that	that	SCONJ
ap-10625	118	6	functions	function	NOUN
ap-10625	118	7	satisfying	satisfy	VERB
ap-10625	118	8	conditions	condition	NOUN
ap-10625	118	9	in	in	ADP
ap-10625	118	10	equation	equation	NOUN
ap-10625	118	11	(	(	PUNCT
ap-10625	118	12	5	5	X
ap-10625	118	13	)	)	PUNCT
ap-10625	118	14	belong	belong	VERB
ap-10625	118	15	to	to	ADP
ap-10625	118	16	d(tmax	d(tmax	NOUN
ap-10625	118	17	)	)	PUNCT
ap-10625	118	18	,	,	PUNCT
ap-10625	118	19	i.e.	i.e.	X
ap-10625	118	20	that	that	SCONJ
ap-10625	118	21	y−1φ	y−1φ	PROPN
ap-10625	118	22	∈	∈	PROPN
ap-10625	118	23	l2	l2	NOUN
ap-10625	118	24	.	.	PUNCT
ap-10625	119	1	as	as	ADP
ap-10625	119	2	now	now	ADV
ap-10625	119	3	:	:	PUNCT
ap-10625	119	4	φ(y	φ(y	ADJ
ap-10625	119	5	)	)	PUNCT
ap-10625	119	6	=	=	SYM
ap-10625	120	1	∫	∫	PROPN
ap-10625	120	2	y	y	PROPN
ap-10625	120	3	0	0	NUM
ap-10625	120	4	φ′(y	φ′(y	NOUN
ap-10625	120	5	)	)	PUNCT
ap-10625	120	6	dy	dy	NOUN
ap-10625	120	7	,	,	PUNCT
ap-10625	120	8	the	the	DET
ap-10625	120	9	required	require	VERB
ap-10625	120	10	integrability	integrability	NOUN
ap-10625	120	11	follows	follow	VERB
ap-10625	120	12	from	from	ADP
ap-10625	120	13	equation	equation	NOUN
ap-10625	120	14	(	(	PUNCT
ap-10625	120	15	9	9	NUM
ap-10625	120	16	)	)	PUNCT
ap-10625	120	17	,	,	PUNCT
ap-10625	120	18	which	which	PRON
ap-10625	120	19	holds	hold	VERB
ap-10625	120	20	for	for	ADP
ap-10625	120	21	κ	κ	NOUN
ap-10625	120	22	=	=	SYM
ap-10625	120	23	0	0	PROPN
ap-10625	120	24	as	as	ADV
ap-10625	120	25	well	well	ADV
ap-10625	120	26	.	.	PUNCT
ap-10625	121	1	in	in	ADP
ap-10625	121	2	fact	fact	NOUN
ap-10625	121	3	,	,	PUNCT
ap-10625	121	4	equation	equation	NOUN
ap-10625	121	5	(	(	PUNCT
ap-10625	121	6	9	9	NUM
ap-10625	121	7	)	)	PUNCT
ap-10625	121	8	reduces	reduce	VERB
ap-10625	121	9	to	to	ADP
ap-10625	121	10	the	the	DET
ap-10625	121	11	usual	usual	ADJ
ap-10625	121	12	hardy	hardy	ADJ
ap-10625	121	13	inequality	inequality	NOUN
ap-10625	121	14	for	for	ADP
ap-10625	121	15	κ	κ	NOUN
ap-10625	121	16	=	=	SYM
ap-10625	121	17	0	0	PROPN
ap-10625	121	18	.	.	PUNCT
ap-10625	122	1	the	the	DET
ap-10625	122	2	proposition	proposition	NOUN
ap-10625	122	3	is	be	AUX
ap-10625	122	4	completely	completely	ADV
ap-10625	122	5	proved	prove	VERB
ap-10625	122	6	now	now	ADV
ap-10625	122	7	.	.	PUNCT
ap-10625	123	1	proposition	proposition	NOUN
ap-10625	123	2	2	2	NUM
ap-10625	123	3	.	.	X
ap-10625	123	4	operator	operator	NOUN
ap-10625	123	5	h	h	PROPN
ap-10625	124	1	⊂	⊂	PROPN
ap-10625	124	2	tmax	tmax	PROPN
ap-10625	124	3	is	be	AUX
ap-10625	124	4	self	self	NOUN
ap-10625	124	5	-	-	PUNCT
ap-10625	124	6	adjoint	adjoint	NOUN
ap-10625	124	7	,	,	PUNCT
ap-10625	124	8	h	h	NOUN
ap-10625	124	9	=	=	SYM
ap-10625	124	10	h∗	h∗	PROPN
ap-10625	124	11	,	,	PUNCT
ap-10625	124	12	if	if	SCONJ
ap-10625	124	13	and	and	CCONJ
ap-10625	124	14	only	only	ADV
ap-10625	124	15	if	if	SCONJ
ap-10625	124	16	:	:	PUNCT
ap-10625	124	17	d(h	d(h	PROPN
ap-10625	124	18	)	)	PUNCT
ap-10625	124	19	=	=	PRON
ap-10625	124	20	{	{	PUNCT
ap-10625	124	21	φ	φ	PROPN
ap-10625	124	22	∈	∈	PROPN
ap-10625	124	23	h1((0	h1((0	PROPN
ap-10625	124	24	,	,	PUNCT
ap-10625	124	25	1),c2	1),c2	NUM
ap-10625	124	26	)	)	PUNCT
ap-10625	124	27	|φ(0	|φ(0	NOUN
ap-10625	124	28	)	)	PUNCT
ap-10625	124	29	=	=	SYM
ap-10625	124	30	0	0	NUM
ap-10625	124	31	,	,	PUNCT
ap-10625	124	32	cφ1(1	cφ1(1	NOUN
ap-10625	124	33	)	)	PUNCT
ap-10625	124	34	+	+	NUM
ap-10625	124	35	dφ2(1	dφ2(1	NOUN
ap-10625	124	36	)	)	PUNCT
ap-10625	124	37	=	=	SYM
ap-10625	124	38	0	0	NUM
ap-10625	124	39	}	}	PUNCT
ap-10625	124	40	,	,	PUNCT
ap-10625	124	41	(	(	PUNCT
ap-10625	124	42	11	11	NUM
ap-10625	124	43	)	)	PUNCT
ap-10625	124	44	where	where	SCONJ
ap-10625	124	45	c	c	X
ap-10625	124	46	,	,	PUNCT
ap-10625	124	47	d	d	X
ap-10625	124	48	are	be	AUX
ap-10625	124	49	real	real	ADJ
ap-10625	124	50	numbers	number	NOUN
ap-10625	124	51	,	,	PUNCT
ap-10625	124	52	which	which	PRON
ap-10625	124	53	are	be	AUX
ap-10625	124	54	not	not	PART
ap-10625	124	55	simultaneously	simultaneously	ADV
ap-10625	124	56	zero	zero	NUM
ap-10625	124	57	(	(	PUNCT
ap-10625	124	58	c2	c2	PROPN
ap-10625	124	59	+	+	CCONJ
ap-10625	124	60	d2	d2	PROPN
ap-10625	124	61	=	=	SYM
ap-10625	124	62	1	1	NUM
ap-10625	124	63	may	may	AUX
ap-10625	124	64	be	be	AUX
ap-10625	124	65	required	require	VERB
ap-10625	124	66	)	)	PUNCT
ap-10625	124	67	.	.	PUNCT
ap-10625	125	1	proof	proof	NOUN
ap-10625	125	2	.	.	PUNCT
ap-10625	126	1	by	by	ADP
ap-10625	126	2	proposition	proposition	NOUN
ap-10625	126	3	1	1	NUM
ap-10625	126	4	,	,	PUNCT
ap-10625	126	5	the	the	DET
ap-10625	126	6	only	only	ADJ
ap-10625	126	7	non	non	ADJ
ap-10625	126	8	-	-	ADJ
ap-10625	126	9	trivial	trivial	ADJ
ap-10625	126	10	boundary	boundary	ADJ
ap-10625	126	11	values	value	NOUN
ap-10625	126	12	are	be	AUX
ap-10625	126	13	the	the	DET
ap-10625	126	14	two	two	NUM
ap-10625	126	15	components	component	NOUN
ap-10625	126	16	of	of	ADP
ap-10625	126	17	φ(1	φ(1	PROPN
ap-10625	126	18	)	)	PUNCT
ap-10625	126	19	.	.	PUNCT
ap-10625	127	1	the	the	DET
ap-10625	127	2	boundary	boundary	ADJ
ap-10625	127	3	condition	condition	NOUN
ap-10625	127	4	defining	define	VERB
ap-10625	127	5	self	self	NOUN
ap-10625	127	6	-	-	PUNCT
ap-10625	127	7	adjoint	adjoint	NOUN
ap-10625	127	8	h	h	NOUN
ap-10625	127	9	reads	read	VERB
ap-10625	127	10	that	that	SCONJ
ap-10625	127	11	the	the	DET
ap-10625	127	12	boundary	boundary	ADJ
ap-10625	127	13	value	value	NOUN
ap-10625	127	14	φ(1	φ(1	PROPN
ap-10625	127	15	)	)	PUNCT
ap-10625	127	16	lies	lie	VERB
ap-10625	127	17	in	in	ADP
ap-10625	127	18	a	a	DET
ap-10625	127	19	linear	linear	ADJ
ap-10625	127	20	subspace	subspace	NOUN
ap-10625	127	21	l	l	PROPN
ap-10625	127	22	of	of	ADP
ap-10625	127	23	c2	c2	PROPN
ap-10625	127	24	,	,	PUNCT
ap-10625	127	25	which	which	PRON
ap-10625	127	26	can	can	AUX
ap-10625	127	27	be	be	AUX
ap-10625	127	28	specified	specify	VERB
ap-10625	127	29	by	by	ADP
ap-10625	127	30	its	its	PRON
ap-10625	127	31	orthogonal	orthogonal	ADJ
ap-10625	127	32	projector	projector	NOUN
ap-10625	127	33	r.	r.	PROPN
ap-10625	128	1	so	so	ADV
ap-10625	128	2	r	r	NOUN
ap-10625	128	3	=	=	PUNCT
ap-10625	128	4	r+	r+	NOUN
ap-10625	128	5	is	be	AUX
ap-10625	128	6	a	a	DET
ap-10625	128	7	hermitian	hermitian	ADJ
ap-10625	128	8	matrix	matrix	NOUN
ap-10625	128	9	satisfying	satisfy	VERB
ap-10625	128	10	the	the	DET
ap-10625	128	11	relation	relation	NOUN
ap-10625	128	12	r2	r2	PROPN
ap-10625	128	13	=	=	PUNCT
ap-10625	128	14	r.	r.	PROPN
ap-10625	128	15	it	it	PRON
ap-10625	128	16	has	have	VERB
ap-10625	128	17	the	the	DET
ap-10625	128	18	form	form	NOUN
ap-10625	128	19	:	:	PUNCT
ap-10625	128	20	r	r	NOUN
ap-10625	128	21	=	=	PUNCT
ap-10625	128	22	(	(	PUNCT
ap-10625	128	23	r1	r1	PROPN
ap-10625	128	24	r2	r2	PROPN
ap-10625	128	25	r2	r2	PROPN
ap-10625	128	26	r4	r4	PROPN
ap-10625	128	27	)	)	PUNCT
ap-10625	128	28	,	,	PUNCT
ap-10625	128	29	with	with	ADP
ap-10625	128	30	real	real	ADJ
ap-10625	128	31	r1	r1	NOUN
ap-10625	128	32	and	and	CCONJ
ap-10625	128	33	r4	r4	PROPN
ap-10625	128	34	.	.	PUNCT
ap-10625	129	1	the	the	DET
ap-10625	129	2	symmetry	symmetry	NOUN
ap-10625	129	3	condition	condition	NOUN
ap-10625	129	4	for	for	ADP
ap-10625	129	5	h	h	NOUN
ap-10625	129	6	:	:	SYM
ap-10625	129	7	0	0	NUM
ap-10625	129	8	=	=	SYM
ap-10625	129	9	(	(	PUNCT
ap-10625	129	10	φ	φ	PROPN
ap-10625	129	11	,	,	PUNCT
ap-10625	129	12	hψ	hψ	NOUN
ap-10625	129	13	)	)	PUNCT
ap-10625	129	14	−	−	PROPN
ap-10625	129	15	(	(	PUNCT
ap-10625	129	16	hφ	hφ	PROPN
ap-10625	129	17	,	,	PUNCT
ap-10625	129	18	ψ	ψ	NOUN
ap-10625	129	19	)	)	PUNCT
ap-10625	129	20	=	=	SYM
ap-10625	129	21	φ(1)+	φ(1)+	PROPN
ap-10625	129	22	(	(	PUNCT
ap-10625	129	23	0	0	NUM
ap-10625	129	24	−1	−1	NOUN
ap-10625	129	25	1	1	NUM
ap-10625	129	26	0	0	NUM
ap-10625	129	27	)	)	PUNCT
ap-10625	129	28	ψ(1	ψ(1	PROPN
ap-10625	129	29	)	)	PUNCT
ap-10625	129	30	,	,	PUNCT
ap-10625	129	31	for	for	ADP
ap-10625	129	32	every	every	DET
ap-10625	129	33	φ	φ	PROPN
ap-10625	129	34	,	,	PUNCT
ap-10625	129	35	ψ	ψ	X
ap-10625	129	36	∈	∈	PROPN
ap-10625	129	37	d(h	d(h	PROPN
ap-10625	129	38	)	)	PUNCT
ap-10625	129	39	,	,	PUNCT
ap-10625	129	40	reads	read	VERB
ap-10625	129	41	:	:	PUNCT
ap-10625	129	42	r+	r+	NOUN
ap-10625	129	43	(	(	PUNCT
ap-10625	129	44	0	0	NUM
ap-10625	129	45	−1	−1	NOUN
ap-10625	129	46	1	1	NUM
ap-10625	129	47	0	0	NUM
ap-10625	129	48	)	)	PUNCT
ap-10625	129	49	r	r	NOUN
ap-10625	129	50	=	=	SYM
ap-10625	129	51	0	0	NUM
ap-10625	129	52	.	.	PUNCT
ap-10625	130	1	when	when	SCONJ
ap-10625	130	2	analysing	analyse	VERB
ap-10625	130	3	the	the	DET
ap-10625	130	4	obtained	obtain	VERB
ap-10625	130	5	conditions	condition	NOUN
ap-10625	130	6	on	on	ADP
ap-10625	130	7	r	r	NOUN
ap-10625	130	8	,	,	PUNCT
ap-10625	130	9	one	one	PRON
ap-10625	130	10	can	can	AUX
ap-10625	130	11	see	see	VERB
ap-10625	130	12	that	that	DET
ap-10625	130	13	r2	r2	PROPN
ap-10625	130	14	must	must	AUX
ap-10625	130	15	be	be	AUX
ap-10625	130	16	real	real	ADJ
ap-10625	130	17	and	and	CCONJ
ap-10625	130	18	the	the	DET
ap-10625	130	19	boundary	boundary	ADJ
ap-10625	130	20	conditions	condition	NOUN
ap-10625	130	21	leading	lead	VERB
ap-10625	130	22	to	to	ADP
ap-10625	130	23	the	the	DET
ap-10625	130	24	maximal	maximal	ADJ
ap-10625	130	25	symmetric	symmetric	ADJ
ap-10625	130	26	operators	operator	NOUN
ap-10625	130	27	h	h	NOUN
ap-10625	130	28	are	be	AUX
ap-10625	130	29	just	just	ADV
ap-10625	130	30	(	(	PUNCT
ap-10625	130	31	11	11	NUM
ap-10625	130	32	)	)	PUNCT
ap-10625	130	33	.	.	PUNCT
ap-10625	131	1	remark	remark	PROPN
ap-10625	131	2	.	.	PUNCT
ap-10625	132	1	the	the	DET
ap-10625	132	2	self	self	NOUN
ap-10625	132	3	-	-	PUNCT
ap-10625	132	4	adjointness	adjointness	NOUN
ap-10625	132	5	conditions	condition	NOUN
ap-10625	132	6	(	(	PUNCT
ap-10625	132	7	11	11	NUM
ap-10625	132	8	)	)	PUNCT
ap-10625	132	9	are	be	AUX
ap-10625	132	10	just	just	ADV
ap-10625	132	11	those	those	PRON
ap-10625	132	12	found	find	VERB
ap-10625	132	13	in	in	ADP
ap-10625	132	14	[	[	X
ap-10625	132	15	18	18	NUM
ap-10625	132	16	]	]	PUNCT
ap-10625	132	17	for	for	ADP
ap-10625	132	18	the	the	DET
ap-10625	132	19	impenetrable	impenetrable	ADJ
ap-10625	132	20	spherical	spherical	ADJ
ap-10625	132	21	shell	shell	NOUN
ap-10625	132	22	.	.	PUNCT
ap-10625	133	1	the	the	DET
ap-10625	133	2	dirichlet	dirichlet	PROPN
ap-10625	133	3	boundary	boundary	PROPN
ap-10625	133	4	condition	condition	NOUN
ap-10625	133	5	considered	consider	VERB
ap-10625	133	6	by	by	ADP
ap-10625	133	7	us	we	PRON
ap-10625	133	8	corresponds	correspond	VERB
ap-10625	133	9	to	to	ADP
ap-10625	133	10	c	c	NOUN
ap-10625	133	11	=	=	SYM
ap-10625	133	12	1	1	NUM
ap-10625	133	13	,	,	PUNCT
ap-10625	133	14	d	d	NOUN
ap-10625	133	15	=	=	SYM
ap-10625	133	16	0	0	NUM
ap-10625	133	17	,	,	PUNCT
ap-10625	133	18	and	and	CCONJ
ap-10625	133	19	the	the	DET
ap-10625	133	20	known	know	VERB
ap-10625	133	21	mit	mit	NOUN
ap-10625	133	22	bag	bag	NOUN
ap-10625	133	23	boundary	boundary	ADJ
ap-10625	133	24	condition	condition	NOUN
ap-10625	133	25	to	to	ADP
ap-10625	133	26	c	c	NOUN
ap-10625	133	27	=	=	SYM
ap-10625	133	28	d	d	NOUN
ap-10625	133	29	=	=	SYM
ap-10625	133	30	1	1	NUM
ap-10625	133	31	.	.	NOUN
ap-10625	133	32	548	548	NUM
ap-10625	133	33	vol	vol	NOUN
ap-10625	133	34	.	.	PUNCT
ap-10625	134	1	65	65	NUM
ap-10625	134	2	no	no	NOUN
ap-10625	134	3	.	.	PUNCT
ap-10625	135	1	5/2025	5/2025	NUM
ap-10625	135	2	dirac	dirac	NOUN
ap-10625	135	3	fermion	fermion	NOUN
ap-10625	135	4	in	in	ADP
ap-10625	135	5	a	a	DET
ap-10625	135	6	time	time	NOUN
ap-10625	135	7	-	-	PUNCT
ap-10625	135	8	dependent	dependent	ADJ
ap-10625	135	9	spherical	spherical	ADJ
ap-10625	135	10	box	box	NOUN
ap-10625	135	11	as	as	ADP
ap-10625	135	12	h1((0	h1((0	PROPN
ap-10625	135	13	,	,	PUNCT
ap-10625	135	14	1),c2	1),c2	NUM
ap-10625	135	15	)	)	PUNCT
ap-10625	135	16	is	be	AUX
ap-10625	135	17	compactly	compactly	ADV
ap-10625	135	18	embedded	embed	VERB
ap-10625	135	19	in	in	ADP
ap-10625	135	20	l2((0	l2((0	PROPN
ap-10625	135	21	,	,	PUNCT
ap-10625	135	22	1),c2	1),c2	NUM
ap-10625	135	23	)	)	PUNCT
ap-10625	135	24	by	by	ADP
ap-10625	135	25	the	the	DET
ap-10625	135	26	rellich	rellich	NOUN
ap-10625	135	27	-	-	PUNCT
ap-10625	135	28	kondrachov	kondrachov	NOUN
ap-10625	135	29	theorem	theorem	NOUN
ap-10625	135	30	,	,	PUNCT
ap-10625	135	31	h	h	NOUN
ap-10625	135	32	has	have	VERB
ap-10625	135	33	a	a	DET
ap-10625	135	34	compact	compact	ADJ
ap-10625	135	35	resolvent	resolvent	NOUN
ap-10625	135	36	,	,	PUNCT
ap-10625	135	37	and	and	CCONJ
ap-10625	135	38	therefore	therefore	ADV
ap-10625	135	39	a	a	DET
ap-10625	135	40	discrete	discrete	ADJ
ap-10625	135	41	spectrum	spectrum	NOUN
ap-10625	135	42	due	due	ADP
ap-10625	135	43	to	to	ADP
ap-10625	135	44	the	the	DET
ap-10625	135	45	riesz	riesz	NOUN
ap-10625	135	46	-	-	PUNCT
ap-10625	135	47	schauder	schauder	NOUN
ap-10625	135	48	theorem	theorem	NOUN
ap-10625	135	49	.	.	PUNCT
ap-10625	136	1	in	in	ADP
ap-10625	136	2	particular	particular	ADJ
ap-10625	136	3	,	,	PUNCT
ap-10625	136	4	h	h	NOUN
ap-10625	136	5	has	have	VERB
ap-10625	136	6	a	a	DET
ap-10625	136	7	countable	countable	ADJ
ap-10625	136	8	complete	complete	ADJ
ap-10625	136	9	set	set	NOUN
ap-10625	136	10	of	of	ADP
ap-10625	136	11	eigenstates	eigenstate	NOUN
ap-10625	136	12	.	.	PUNCT
ap-10625	137	1	2.2	2.2	NUM
ap-10625	137	2	.	.	PUNCT
ap-10625	137	3	solution	solution	NOUN
ap-10625	137	4	of	of	ADP
ap-10625	137	5	the	the	DET
ap-10625	137	6	dirac	dirac	NOUN
ap-10625	137	7	equation	equation	NOUN
ap-10625	137	8	on	on	ADP
ap-10625	137	9	time	time	NOUN
ap-10625	137	10	-	-	PUNCT
ap-10625	137	11	dependent	dependent	ADJ
ap-10625	137	12	spherical	spherical	ADJ
ap-10625	137	13	box	box	NOUN
ap-10625	137	14	the	the	DET
ap-10625	137	15	solutions	solution	NOUN
ap-10625	137	16	of	of	ADP
ap-10625	137	17	equation	equation	NOUN
ap-10625	137	18	(	(	PUNCT
ap-10625	137	19	4	4	X
ap-10625	137	20	)	)	PUNCT
ap-10625	137	21	can	can	AUX
ap-10625	137	22	be	be	AUX
ap-10625	137	23	written	write	VERB
ap-10625	137	24	in	in	ADP
ap-10625	137	25	terms	term	NOUN
ap-10625	137	26	of	of	ADP
ap-10625	137	27	the	the	DET
ap-10625	137	28	complete	complete	ADJ
ap-10625	137	29	set	set	NOUN
ap-10625	137	30	of	of	ADP
ap-10625	137	31	the	the	DET
ap-10625	137	32	eigenfunctions	eigenfunction	NOUN
ap-10625	137	33	of	of	ADP
ap-10625	137	34	the	the	DET
ap-10625	137	35	massless	massless	NOUN
ap-10625	137	36	dirac	dirac	NOUN
ap-10625	137	37	equation	equation	NOUN
ap-10625	137	38	given	give	VERB
ap-10625	137	39	by	by	ADP
ap-10625	137	40	(	(	PUNCT
ap-10625	137	41	n	n	X
ap-10625	137	42	∈	∈	PROPN
ap-10625	137	43	z	z	PROPN
ap-10625	137	44	):	):	PUNCT
ap-10625	137	45	(	(	PUNCT
ap-10625	137	46	−iα∂y	−iα∂y	NOUN
ap-10625	137	47	+	+	NUM
ap-10625	137	48	α1	α1	PROPN
ap-10625	137	49	κ	κ	PROPN
ap-10625	137	50	y	y	PROPN
ap-10625	137	51	)	)	PUNCT
ap-10625	137	52	ψn	ψn	PROPN
ap-10625	138	1	=	=	SYM
ap-10625	138	2	εnψn	εnψn	PROPN
ap-10625	138	3	,	,	PUNCT
ap-10625	138	4	ψn,1(0	ψn,1(0	PROPN
ap-10625	138	5	)	)	PUNCT
ap-10625	138	6	=	=	SYM
ap-10625	138	7	ψn,2(0	ψn,2(0	NOUN
ap-10625	138	8	)	)	PUNCT
ap-10625	138	9	=	=	PUNCT
ap-10625	138	10	ψn,1(1	ψn,1(1	PROPN
ap-10625	138	11	)	)	PUNCT
ap-10625	138	12	=	=	SYM
ap-10625	138	13	0	0	NUM
ap-10625	138	14	,	,	PUNCT
ap-10625	138	15	(	(	PUNCT
ap-10625	138	16	12	12	NUM
ap-10625	138	17	)	)	PUNCT
ap-10625	138	18	the	the	DET
ap-10625	138	19	eigenvalues	eigenvalue	NOUN
ap-10625	138	20	can	can	AUX
ap-10625	138	21	be	be	AUX
ap-10625	138	22	numbered	number	VERB
ap-10625	138	23	in	in	ADP
ap-10625	138	24	such	such	DET
ap-10625	138	25	a	a	DET
ap-10625	138	26	way	way	NOUN
ap-10625	138	27	that	that	PRON
ap-10625	138	28	εn	εn	ADP
ap-10625	138	29	>	>	X
ap-10625	138	30	0	0	PUNCT
ap-10625	138	31	for	for	ADP
ap-10625	138	32	n	n	X
ap-10625	138	33	>	>	SYM
ap-10625	138	34	0	0	PUNCT
ap-10625	138	35	and	and	CCONJ
ap-10625	138	36	εn	εn	ADP
ap-10625	138	37	<	<	X
ap-10625	138	38	0	0	NUM
ap-10625	138	39	for	for	ADP
ap-10625	138	40	n	n	X
ap-10625	138	41	<	<	X
ap-10625	138	42	0	0	NUM
ap-10625	138	43	.	.	PUNCT
ap-10625	139	1	let	let	VERB
ap-10625	139	2	us	we	PRON
ap-10625	139	3	denote	denote	VERB
ap-10625	139	4	kn	kn	PROPN
ap-10625	139	5	=	=	SYM
ap-10625	139	6	|εn|	|εn|	PROPN
ap-10625	139	7	.	.	PUNCT
ap-10625	140	1	the	the	DET
ap-10625	140	2	solution	solution	NOUN
ap-10625	140	3	of	of	ADP
ap-10625	140	4	equation	equation	NOUN
ap-10625	140	5	(	(	PUNCT
ap-10625	140	6	12	12	NUM
ap-10625	140	7	)	)	PUNCT
ap-10625	140	8	can	can	AUX
ap-10625	140	9	be	be	AUX
ap-10625	140	10	written	write	VERB
ap-10625	140	11	as	as	ADP
ap-10625	140	12	:	:	PUNCT
ap-10625	140	13	ψn(y	ψn(y	NUM
ap-10625	140	14	)	)	PUNCT
ap-10625	140	15	=	=	SYM
ap-10625	140	16	an	an	DET
ap-10625	140	17	(	(	PUNCT
ap-10625	140	18	sgn(n)√yjν(kny	sgn(n)√yjν(kny	NOUN
ap-10625	140	19	)	)	PUNCT
ap-10625	140	20	µ	µ	PRON
ap-10625	140	21	√	√	NUM
ap-10625	140	22	yjν′(kny	yjν′(kny	PROPN
ap-10625	140	23	)	)	PUNCT
ap-10625	140	24	)	)	PUNCT
ap-10625	141	1	,	,	PUNCT
ap-10625	141	2	(	(	PUNCT
ap-10625	141	3	ψn	ψn	INTJ
ap-10625	141	4	,	,	PUNCT
ap-10625	141	5	ψk	ψk	NOUN
ap-10625	141	6	)	)	PUNCT
ap-10625	141	7	=	=	SYM
ap-10625	141	8	δn	δn	PROPN
ap-10625	141	9	,	,	PUNCT
ap-10625	141	10	k	k	NOUN
ap-10625	141	11	,	,	PUNCT
ap-10625	141	12	(	(	PUNCT
ap-10625	141	13	13	13	NUM
ap-10625	141	14	)	)	PUNCT
ap-10625	141	15	where	where	SCONJ
ap-10625	141	16	an	an	DET
ap-10625	141	17	=	=	X
ap-10625	141	18	[	[	PUNCT
ap-10625	141	19	1	1	NUM
ap-10625	141	20	2	2	NUM
ap-10625	141	21	(	(	PUNCT
ap-10625	141	22	jν′(kn)2	jν′(kn)2	ADP
ap-10625	141	23	−	−	PROPN
ap-10625	141	24	jν+1(kn)jν−1(kn	jν+1(kn)jν−1(kn	NOUN
ap-10625	141	25	)	)	PUNCT
ap-10625	141	26	)	)	PUNCT
ap-10625	142	1	]	]	PUNCT
ap-10625	142	2	−	−	PROPN
ap-10625	142	3	1	1	NUM
ap-10625	142	4	2	2	NUM
ap-10625	142	5	.	.	PUNCT
ap-10625	143	1	using	use	VERB
ap-10625	143	2	the	the	DET
ap-10625	143	3	boundary	boundary	ADJ
ap-10625	143	4	conditions	condition	NOUN
ap-10625	143	5	given	give	VERB
ap-10625	143	6	in	in	ADP
ap-10625	143	7	equation	equation	NOUN
ap-10625	143	8	(	(	PUNCT
ap-10625	143	9	12	12	NUM
ap-10625	143	10	):	):	PUNCT
ap-10625	143	11	jν(kn	jν(kn	PROPN
ap-10625	143	12	)	)	PUNCT
ap-10625	144	1	=	=	PUNCT
ap-10625	144	2	0	0	NUM
ap-10625	144	3	,	,	PUNCT
ap-10625	144	4	(	(	PUNCT
ap-10625	144	5	14	14	NUM
ap-10625	144	6	)	)	PUNCT
ap-10625	144	7	and	and	CCONJ
ap-10625	144	8	kn	kn	PROPN
ap-10625	144	9	=	=	PROPN
ap-10625	144	10	k−n	k−n	PROPN
ap-10625	144	11	is	be	AUX
ap-10625	144	12	chosen	choose	VERB
ap-10625	144	13	as	as	ADP
ap-10625	144	14	the	the	DET
ap-10625	144	15	|n|th	|n|th	PRON
ap-10625	144	16	positive	positive	ADJ
ap-10625	144	17	root	root	NOUN
ap-10625	144	18	of	of	ADP
ap-10625	144	19	jν	jν	NOUN
ap-10625	144	20	.	.	PUNCT
ap-10625	145	1	the	the	DET
ap-10625	145	2	equation	equation	NOUN
ap-10625	145	3	(	(	PUNCT
ap-10625	145	4	13	13	NUM
ap-10625	145	5	)	)	PUNCT
ap-10625	145	6	holds	hold	VERB
ap-10625	145	7	for	for	ADP
ap-10625	145	8	n	n	NOUN
ap-10625	145	9	=	=	NOUN
ap-10625	145	10	̸	̸	NUM
ap-10625	145	11	0	0	NUM
ap-10625	145	12	,	,	PUNCT
ap-10625	145	13	the	the	DET
ap-10625	145	14	trivial	trivial	ADJ
ap-10625	145	15	case	case	NOUN
ap-10625	145	16	of	of	ADP
ap-10625	145	17	n	n	NOUN
ap-10625	145	18	=	=	SYM
ap-10625	145	19	0	0	NUM
ap-10625	145	20	,	,	PUNCT
ap-10625	145	21	ε0	ε0	NOUN
ap-10625	145	22	=	=	SYM
ap-10625	145	23	0	0	PROPN
ap-10625	145	24	,	,	PUNCT
ap-10625	145	25	which	which	PRON
ap-10625	145	26	occurs	occur	VERB
ap-10625	145	27	for	for	ADP
ap-10625	145	28	κ	κ	PROPN
ap-10625	145	29	>	>	X
ap-10625	145	30	0	0	PROPN
ap-10625	145	31	,	,	PUNCT
ap-10625	145	32	having	have	VERB
ap-10625	145	33	the	the	DET
ap-10625	145	34	form	form	NOUN
ap-10625	145	35	ψ01(y	ψ01(y	ADJ
ap-10625	145	36	)	)	PUNCT
ap-10625	146	1	=	=	SYM
ap-10625	146	2	0	0	X
ap-10625	146	3	.	.	PUNCT
ap-10625	146	4	ψ02(y	ψ02(y	ADJ
ap-10625	146	5	)	)	PUNCT
ap-10625	147	1	=	=	SYM
ap-10625	148	1	a0y	a0y	PROPN
ap-10625	148	2	κ	κ	X
ap-10625	148	3	.	.	PUNCT
ap-10625	148	4	inserting	insert	VERB
ap-10625	148	5	the	the	DET
ap-10625	148	6	expansion	expansion	NOUN
ap-10625	148	7	:	:	PUNCT
ap-10625	148	8	φ(y	φ(y	PROPN
ap-10625	148	9	,	,	PUNCT
ap-10625	148	10	τ	τ	X
ap-10625	148	11	)	)	PUNCT
ap-10625	148	12	=	=	PUNCT
ap-10625	149	1	+	+	PUNCT
ap-10625	149	2	∞∑	∞∑	NUM
ap-10625	149	3	n=−∞	n=−∞	NUM
ap-10625	149	4	an(τ)ψn(y	an(τ)ψn(y	NOUN
ap-10625	149	5	)	)	PUNCT
ap-10625	149	6	(	(	PUNCT
ap-10625	149	7	15	15	NUM
ap-10625	149	8	)	)	PUNCT
ap-10625	149	9	into	into	ADP
ap-10625	149	10	equation	equation	NOUN
ap-10625	149	11	(	(	PUNCT
ap-10625	149	12	4	4	NUM
ap-10625	149	13	)	)	PUNCT
ap-10625	149	14	and	and	CCONJ
ap-10625	149	15	projecting	project	VERB
ap-10625	149	16	onto	onto	ADP
ap-10625	149	17	ψn	ψn	ADP
ap-10625	149	18	,	,	PUNCT
ap-10625	149	19	we	we	PRON
ap-10625	149	20	obtain	obtain	VERB
ap-10625	149	21	:	:	PUNCT
ap-10625	149	22	iȧn(τ	iȧn(τ	ADJ
ap-10625	149	23	)	)	PUNCT
ap-10625	149	24	=	=	PUNCT
ap-10625	150	1	εnan(τ	εnan(τ	PROPN
ap-10625	150	2	)	)	PUNCT
ap-10625	150	3	−mr0(t(τ))a−n(τ	−mr0(t(τ))a−n(τ	ADV
ap-10625	150	4	)	)	PUNCT
ap-10625	150	5	,	,	PUNCT
ap-10625	150	6	n	n	PROPN
ap-10625	150	7	∈	∈	PROPN
ap-10625	150	8	z	z	NOUN
ap-10625	150	9	,	,	PUNCT
ap-10625	150	10	i.e.	i.e.	X
ap-10625	150	11	the	the	DET
ap-10625	150	12	system	system	NOUN
ap-10625	150	13	of	of	ADP
ap-10625	150	14	ordinary	ordinary	ADJ
ap-10625	150	15	differential	differential	ADJ
ap-10625	150	16	equations	equation	NOUN
ap-10625	150	17	for	for	ADP
ap-10625	150	18	an	an	DET
ap-10625	150	19	,	,	PUNCT
ap-10625	150	20	a−n	a−n	PROPN
ap-10625	150	21	:	:	PUNCT
ap-10625	150	22	iȧn(τ	iȧn(τ	NOUN
ap-10625	150	23	)	)	PUNCT
ap-10625	151	1	=	=	PUNCT
ap-10625	151	2	knan(τ	knan(τ	PROPN
ap-10625	151	3	)	)	PUNCT
ap-10625	151	4	−mr0(t(τ))a−n(τ	−mr0(t(τ))a−n(τ	ADV
ap-10625	151	5	)	)	PUNCT
ap-10625	151	6	,	,	PUNCT
ap-10625	151	7	iȧ−n(τ	iȧ−n(τ	PROPN
ap-10625	151	8	)	)	PUNCT
ap-10625	151	9	=	=	SYM
ap-10625	152	1	−kna−n(τ	−kna−n(τ	VERB
ap-10625	152	2	)	)	PUNCT
ap-10625	152	3	−mr0(t(τ))an(τ	−mr0(t(τ))an(τ	NUM
ap-10625	152	4	)	)	PUNCT
ap-10625	152	5	,	,	PUNCT
ap-10625	152	6	n	n	PROPN
ap-10625	152	7	∈	∈	PROPN
ap-10625	152	8	n	n	CCONJ
ap-10625	152	9	,	,	PUNCT
ap-10625	152	10	(	(	PUNCT
ap-10625	152	11	16	16	NUM
ap-10625	152	12	)	)	PUNCT
ap-10625	152	13	which	which	PRON
ap-10625	152	14	can	can	AUX
ap-10625	152	15	be	be	AUX
ap-10625	152	16	written	write	VERB
ap-10625	152	17	in	in	ADP
ap-10625	152	18	a	a	DET
ap-10625	152	19	matrix	matrix	NOUN
ap-10625	152	20	form	form	NOUN
ap-10625	152	21	as	as	SCONJ
ap-10625	152	22	follows	follow	VERB
ap-10625	152	23	:	:	PUNCT
ap-10625	152	24	iȧ(n)(τ	iȧ(n)(τ	VERB
ap-10625	152	25	)	)	PUNCT
ap-10625	152	26	=	=	PRON
ap-10625	153	1	(	(	PUNCT
ap-10625	153	2	kn	kn	PROPN
ap-10625	153	3	−mr0(t(τ	−mr0(t(τ	PROPN
ap-10625	153	4	)	)	PUNCT
ap-10625	153	5	)	)	PUNCT
ap-10625	153	6	−mr0(t(τ	−mr0(t(τ	NOUN
ap-10625	153	7	)	)	PUNCT
ap-10625	153	8	)	)	PUNCT
ap-10625	153	9	−kn	−kn	PROPN
ap-10625	153	10	)	)	PUNCT
ap-10625	153	11	a(n)(τ	a(n)(τ	NUM
ap-10625	153	12	)	)	PUNCT
ap-10625	153	13	,	,	PUNCT
ap-10625	153	14	a(n)(τ	a(n)(τ	X
ap-10625	153	15	)	)	PUNCT
ap-10625	153	16	=	=	SYM
ap-10625	153	17	(	(	PUNCT
ap-10625	153	18	an(τ	an(τ	ADJ
ap-10625	153	19	)	)	PUNCT
ap-10625	153	20	a−n(τ	a−n(τ	NOUN
ap-10625	153	21	)	)	PUNCT
ap-10625	153	22	)	)	PUNCT
ap-10625	153	23	,	,	PUNCT
ap-10625	153	24	n	n	PROPN
ap-10625	153	25	∈	∈	PROPN
ap-10625	153	26	n.	n.	NOUN
ap-10625	153	27	(	(	PUNCT
ap-10625	153	28	17	17	NUM
ap-10625	153	29	)	)	PUNCT
ap-10625	153	30	in	in	ADP
ap-10625	153	31	particular	particular	ADJ
ap-10625	153	32	,	,	PUNCT
ap-10625	153	33	coefficients	coefficient	NOUN
ap-10625	153	34	a±n	a±n	PROPN
ap-10625	153	35	remain	remain	VERB
ap-10625	153	36	bounded	bounded	ADJ
ap-10625	153	37	in	in	ADP
ap-10625	153	38	τ	τ	PROPN
ap-10625	153	39	for	for	ADP
ap-10625	153	40	every	every	DET
ap-10625	153	41	n	n	CCONJ
ap-10625	153	42	∈	∈	PROPN
ap-10625	153	43	n.	n.	NOUN
ap-10625	153	44	for	for	ADP
ap-10625	153	45	the	the	DET
ap-10625	153	46	special	special	ADJ
ap-10625	153	47	case	case	NOUN
ap-10625	153	48	of	of	ADP
ap-10625	153	49	a	a	DET
ap-10625	153	50	massless	massless	ADJ
ap-10625	153	51	dirac	dirac	NOUN
ap-10625	153	52	particle	particle	NOUN
ap-10625	153	53	,	,	PUNCT
ap-10625	153	54	i.e.	i.e.	X
ap-10625	153	55	for	for	ADP
ap-10625	153	56	m	m	PROPN
ap-10625	153	57	=	=	SYM
ap-10625	153	58	0	0	NUM
ap-10625	153	59	,	,	PUNCT
ap-10625	153	60	the	the	DET
ap-10625	153	61	system	system	NOUN
ap-10625	153	62	(	(	PUNCT
ap-10625	153	63	16	16	NUM
ap-10625	153	64	)	)	PUNCT
ap-10625	153	65	splits	split	VERB
ap-10625	153	66	into	into	ADP
ap-10625	153	67	two	two	NUM
ap-10625	153	68	uncoupled	uncoupled	ADJ
ap-10625	153	69	equations	equation	NOUN
ap-10625	153	70	,	,	PUNCT
ap-10625	153	71	whose	whose	DET
ap-10625	153	72	solutions	solution	NOUN
ap-10625	153	73	are	be	AUX
ap-10625	153	74	given	give	VERB
ap-10625	153	75	as	as	ADP
ap-10625	153	76	:	:	PUNCT
ap-10625	153	77	a±n(τ	a±n(τ	NOUN
ap-10625	153	78	)	)	PUNCT
ap-10625	153	79	=	=	NOUN
ap-10625	153	80	a±n(0)e∓iknτ	a±n(0)e∓iknτ	NOUN
ap-10625	153	81	.	.	PUNCT
ap-10625	154	1	(	(	PUNCT
ap-10625	154	2	18	18	NUM
ap-10625	154	3	)	)	PUNCT
ap-10625	154	4	for	for	ADP
ap-10625	154	5	a	a	DET
ap-10625	154	6	linearly	linearly	ADV
ap-10625	154	7	moving	move	VERB
ap-10625	154	8	wall	wall	NOUN
ap-10625	154	9	of	of	ADP
ap-10625	154	10	the	the	DET
ap-10625	154	11	sphere	sphere	NOUN
ap-10625	154	12	,	,	PUNCT
ap-10625	154	13	given	give	VERB
ap-10625	154	14	by	by	ADP
ap-10625	154	15	r0(t	r0(t	PROPN
ap-10625	154	16	)	)	PUNCT
ap-10625	154	17	=	=	SYM
ap-10625	154	18	a+	a+	PUNCT
ap-10625	154	19	bt	bt	NOUN
ap-10625	154	20	,	,	PUNCT
ap-10625	154	21	by	by	ADP
ap-10625	154	22	taking	take	VERB
ap-10625	154	23	into	into	ADP
ap-10625	154	24	account	account	NOUN
ap-10625	154	25	relation	relation	NOUN
ap-10625	154	26	between	between	ADP
ap-10625	154	27	τ	τ	PROPN
ap-10625	154	28	and	and	CCONJ
ap-10625	154	29	t	t	PROPN
ap-10625	154	30	given	give	VERB
ap-10625	154	31	in	in	ADP
ap-10625	154	32	equation	equation	NOUN
ap-10625	154	33	(	(	PUNCT
ap-10625	154	34	3	3	NUM
ap-10625	154	35	)	)	PUNCT
ap-10625	154	36	,	,	PUNCT
ap-10625	154	37	one	one	PRON
ap-10625	154	38	can	can	AUX
ap-10625	154	39	obtain	obtain	VERB
ap-10625	154	40	the	the	DET
ap-10625	154	41	exact	exact	ADJ
ap-10625	154	42	solution	solution	NOUN
ap-10625	154	43	for	for	ADP
ap-10625	154	44	a	a	DET
ap-10625	154	45	massless	massless	ADJ
ap-10625	154	46	dirac	dirac	NOUN
ap-10625	154	47	particle	particle	NOUN
ap-10625	154	48	as	as	ADP
ap-10625	154	49	:	:	PUNCT
ap-10625	154	50	a±n(τ	a±n(τ	NOUN
ap-10625	154	51	)	)	PUNCT
ap-10625	154	52	=	=	VERB
ap-10625	155	1	a±n(0)e∓i	a±n(0)e∓i	ADJ
ap-10625	155	2	kn	kn	NOUN
ap-10625	155	3	b	b	PROPN
ap-10625	155	4	ln(1	ln(1	PROPN
ap-10625	155	5	+	+	PROPN
ap-10625	155	6	b	b	PROPN
ap-10625	155	7	a	a	DET
ap-10625	155	8	t	t	NOUN
ap-10625	155	9	)	)	PUNCT
ap-10625	155	10	.	.	PUNCT
ap-10625	156	1	(	(	PUNCT
ap-10625	156	2	19	19	NUM
ap-10625	156	3	)	)	PUNCT
ap-10625	156	4	the	the	DET
ap-10625	156	5	solution	solution	NOUN
ap-10625	156	6	of	of	ADP
ap-10625	156	7	the	the	DET
ap-10625	156	8	original	original	ADJ
ap-10625	156	9	dirac	dirac	NOUN
ap-10625	156	10	equation	equation	NOUN
ap-10625	156	11	for	for	ADP
ap-10625	156	12	timedependent	timedependent	NOUN
ap-10625	156	13	box	box	NOUN
ap-10625	156	14	given	give	VERB
ap-10625	156	15	by	by	ADP
ap-10625	156	16	equation	equation	NOUN
ap-10625	156	17	(	(	PUNCT
ap-10625	156	18	2	2	X
ap-10625	156	19	)	)	PUNCT
ap-10625	156	20	can	can	AUX
ap-10625	156	21	be	be	AUX
ap-10625	156	22	found	find	VERB
ap-10625	156	23	using	use	VERB
ap-10625	156	24	the	the	DET
ap-10625	156	25	relation	relation	NOUN
ap-10625	156	26	between	between	ADP
ap-10625	156	27	ψ	ψ	PROPN
ap-10625	156	28	and	and	CCONJ
ap-10625	156	29	φ	φ	NUM
ap-10625	156	30	in	in	ADP
ap-10625	156	31	equation	equation	NOUN
ap-10625	156	32	(	(	PUNCT
ap-10625	156	33	3	3	NUM
ap-10625	156	34	)	)	PUNCT
ap-10625	156	35	that	that	PRON
ap-10625	156	36	yields	yield	VERB
ap-10625	156	37	:	:	PUNCT
ap-10625	156	38	ψ(r	ψ(r	PROPN
ap-10625	156	39	,	,	PUNCT
ap-10625	156	40	t	t	NOUN
ap-10625	156	41	)	)	PUNCT
ap-10625	156	42	=	=	SYM
ap-10625	157	1	1√	1√	NUM
ap-10625	157	2	r0(t	r0(t	NOUN
ap-10625	157	3	)	)	PUNCT
ap-10625	157	4	+	+	ADJ
ap-10625	157	5	∞∑	∞∑	NUM
ap-10625	157	6	n=−∞	n=−∞	PRON
ap-10625	157	7	an(0)e−i	an(0)e−i	NOUN
ap-10625	157	8	εn	εn	VERB
ap-10625	157	9	b	b	PROPN
ap-10625	157	10	ln(1	ln(1	NOUN
ap-10625	157	11	+	+	NOUN
ap-10625	157	12	b	b	NOUN
ap-10625	157	13	a	a	DET
ap-10625	157	14	t)ψn	t)ψn	PROPN
ap-10625	157	15	(	(	PUNCT
ap-10625	157	16	r	r	NOUN
ap-10625	157	17	r0(t	r0(t	NOUN
ap-10625	157	18	)	)	PUNCT
ap-10625	157	19	)	)	PUNCT
ap-10625	157	20	,	,	PUNCT
ap-10625	157	21	where	where	SCONJ
ap-10625	157	22	ψn	ψn	PRON
ap-10625	157	23	are	be	AUX
ap-10625	157	24	given	give	VERB
ap-10625	157	25	by	by	ADP
ap-10625	157	26	equation	equation	NOUN
ap-10625	157	27	(	(	PUNCT
ap-10625	157	28	13	13	NUM
ap-10625	157	29	)	)	PUNCT
ap-10625	157	30	and	and	CCONJ
ap-10625	157	31	a±n	a±n	PROPN
ap-10625	157	32	fulfill	fulfill	VERB
ap-10625	157	33	the	the	DET
ap-10625	157	34	relation	relation	NOUN
ap-10625	157	35	following	follow	VERB
ap-10625	157	36	from	from	ADP
ap-10625	157	37	the	the	DET
ap-10625	157	38	norm	norm	NOUN
ap-10625	157	39	conservation	conservation	NOUN
ap-10625	157	40	:	:	PUNCT
ap-10625	158	1	+	+	SCONJ
ap-10625	158	2	∞∑	∞∑	NUM
ap-10625	158	3	n=−∞	n=−∞	X
ap-10625	158	4	|an(0)|2	|an(0)|2	PUNCT
ap-10625	158	5	=	=	SYM
ap-10625	159	1	1	1	X
ap-10625	159	2	.	.	X
ap-10625	159	3	for	for	ADP
ap-10625	159	4	the	the	DET
ap-10625	159	5	general	general	ADJ
ap-10625	159	6	case	case	NOUN
ap-10625	159	7	,	,	PUNCT
ap-10625	159	8	we	we	PRON
ap-10625	159	9	are	be	AUX
ap-10625	159	10	able	able	ADJ
ap-10625	159	11	to	to	PART
ap-10625	159	12	solve	solve	VERB
ap-10625	159	13	the	the	DET
ap-10625	159	14	system	system	NOUN
ap-10625	159	15	(	(	PUNCT
ap-10625	159	16	17	17	NUM
ap-10625	159	17	)	)	PUNCT
ap-10625	159	18	only	only	ADV
ap-10625	159	19	numerically	numerically	ADV
ap-10625	159	20	,	,	PUNCT
ap-10625	159	21	starting	start	VERB
ap-10625	159	22	from	from	ADP
ap-10625	159	23	the	the	DET
ap-10625	159	24	initial	initial	ADJ
ap-10625	159	25	values	value	NOUN
ap-10625	160	1	:	:	PUNCT
ap-10625	160	2	an(0	an(0	NUM
ap-10625	160	3	)	)	PUNCT
ap-10625	160	4	=	=	SYM
ap-10625	160	5	1√	1√	PROPN
ap-10625	160	6	r0(0	r0(0	PROPN
ap-10625	160	7	)	)	PUNCT
ap-10625	160	8	∫	∫	PROPN
ap-10625	160	9	r0(0	r0(0	PROPN
ap-10625	160	10	)	)	PUNCT
ap-10625	160	11	0	0	NUM
ap-10625	161	1	ψ†	ψ†	NOUN
ap-10625	162	1	n	n	CCONJ
ap-10625	162	2	r	r	NOUN
ap-10625	162	3	r0(0)ψ(r	r0(0)ψ(r	PROPN
ap-10625	162	4	,	,	PUNCT
ap-10625	162	5	0)dr	0)dr	PROPN
ap-10625	162	6	,	,	PUNCT
ap-10625	162	7	(	(	PUNCT
ap-10625	162	8	20	20	NUM
ap-10625	162	9	)	)	PUNCT
ap-10625	162	10	where	where	SCONJ
ap-10625	162	11	ψn	ψn	PRON
ap-10625	162	12	are	be	AUX
ap-10625	162	13	given	give	VERB
ap-10625	162	14	by	by	ADP
ap-10625	162	15	equation	equation	NOUN
ap-10625	162	16	(	(	PUNCT
ap-10625	162	17	13	13	NUM
ap-10625	162	18	)	)	PUNCT
ap-10625	162	19	.	.	PUNCT
ap-10625	163	1	for	for	ADP
ap-10625	163	2	the	the	DET
ap-10625	163	3	illustrative	illustrative	ADJ
ap-10625	163	4	purposes	purpose	NOUN
ap-10625	163	5	,	,	PUNCT
ap-10625	163	6	we	we	PRON
ap-10625	163	7	choose	choose	VERB
ap-10625	163	8	the	the	DET
ap-10625	163	9	initial	initial	ADJ
ap-10625	163	10	condition	condition	NOUN
ap-10625	163	11	,	,	PUNCT
ap-10625	163	12	e.g.	e.g.	ADV
ap-10625	163	13	as	as	ADP
ap-10625	163	14	a	a	DET
ap-10625	163	15	gaussian	gaussian	ADJ
ap-10625	163	16	wave	wave	NOUN
ap-10625	163	17	packet	packet	NOUN
ap-10625	163	18	given	give	VERB
ap-10625	163	19	by	by	ADP
ap-10625	163	20	:	:	PUNCT
ap-10625	163	21	ψ(r	ψ(r	PROPN
ap-10625	163	22	,	,	PUNCT
ap-10625	163	23	0	0	NUM
ap-10625	163	24	)	)	PUNCT
ap-10625	163	25	=	=	SYM
ap-10625	163	26	f(r)√	f(r)√	NOUN
ap-10625	163	27	s2	s2	NOUN
ap-10625	163	28	1	1	NUM
ap-10625	163	29	+	+	CCONJ
ap-10625	163	30	s2	s2	X
ap-10625	163	31	2	2	NUM
ap-10625	163	32	(	(	PUNCT
ap-10625	163	33	s1	s1	PROPN
ap-10625	163	34	s2	s2	PROPN
ap-10625	163	35	)	)	PUNCT
ap-10625	163	36	,	,	PUNCT
ap-10625	163	37	with	with	ADP
ap-10625	163	38	s1	s1	NOUN
ap-10625	163	39	and	and	CCONJ
ap-10625	163	40	s2	s2	NOUN
ap-10625	163	41	being	be	AUX
ap-10625	163	42	the	the	DET
ap-10625	163	43	initial	initial	ADJ
ap-10625	163	44	spin	spin	NOUN
ap-10625	163	45	polarisation	polarisation	NOUN
ap-10625	163	46	and	and	CCONJ
ap-10625	163	47	:	:	PUNCT
ap-10625	163	48	f(r	f(r	X
ap-10625	163	49	)	)	PUNCT
ap-10625	164	1	=	=	SYM
ap-10625	164	2	1√	1√	NUM
ap-10625	164	3	d	d	NOUN
ap-10625	164	4	√	√	PROPN
ap-10625	164	5	2π	2π	NUM
ap-10625	164	6	r(r0(0	r(r0(0	NOUN
ap-10625	164	7	)	)	PUNCT
ap-10625	164	8	−	−	ADP
ap-10625	164	9	r	r	X
ap-10625	164	10	)	)	PUNCT
ap-10625	164	11	exp	exp	NOUN
ap-10625	164	12	[	[	PUNCT
ap-10625	164	13	−	−	PROPN
ap-10625	164	14	(	(	PUNCT
ap-10625	164	15	r	r	NOUN
ap-10625	164	16	−	−	PROPN
ap-10625	164	17	r0)2	r0)2	NUM
ap-10625	164	18	4d2	4d2	NUM
ap-10625	165	1	+	+	CCONJ
ap-10625	165	2	iv0r	iv0r	PROPN
ap-10625	165	3	]	]	PUNCT
ap-10625	165	4	,	,	PUNCT
ap-10625	165	5	(	(	PUNCT
ap-10625	165	6	21	21	NUM
ap-10625	165	7	)	)	PUNCT
ap-10625	165	8	where	where	SCONJ
ap-10625	165	9	,	,	PUNCT
ap-10625	165	10	d	d	NOUN
ap-10625	165	11	,	,	PUNCT
ap-10625	165	12	r0	r0	NOUN
ap-10625	165	13	and	and	CCONJ
ap-10625	165	14	v0	v0	NOUN
ap-10625	165	15	are	be	AUX
ap-10625	165	16	the	the	DET
ap-10625	165	17	packet	packet	NOUN
ap-10625	165	18	’s	’s	PART
ap-10625	165	19	width	width	NOUN
ap-10625	165	20	,	,	PUNCT
ap-10625	165	21	initial	initial	ADJ
ap-10625	165	22	position	position	NOUN
ap-10625	165	23	of	of	ADP
ap-10625	165	24	the	the	DET
ap-10625	165	25	centre	centre	NOUN
ap-10625	165	26	of	of	ADP
ap-10625	165	27	mass	mass	NOUN
ap-10625	165	28	,	,	PUNCT
ap-10625	165	29	and	and	CCONJ
ap-10625	165	30	initial	initial	ADJ
ap-10625	165	31	velocity	velocity	NOUN
ap-10625	165	32	,	,	PUNCT
ap-10625	165	33	respectively	respectively	ADV
ap-10625	165	34	.	.	PUNCT
ap-10625	166	1	3	3	X
ap-10625	166	2	.	.	X
ap-10625	166	3	quantum	quantum	ADJ
ap-10625	166	4	dynamics	dynamic	NOUN
ap-10625	166	5	under	under	ADP
ap-10625	166	6	the	the	DET
ap-10625	166	7	dynamical	dynamical	ADJ
ap-10625	166	8	confinement	confinement	NOUN
ap-10625	166	9	3.1	3.1	NUM
ap-10625	166	10	.	.	PUNCT
ap-10625	167	1	fermi	fermi	NOUN
ap-10625	167	2	acceleration	acceleration	NOUN
ap-10625	167	3	one	one	NUM
ap-10625	167	4	of	of	ADP
ap-10625	167	5	the	the	DET
ap-10625	167	6	features	feature	NOUN
ap-10625	167	7	of	of	ADP
ap-10625	167	8	the	the	DET
ap-10625	167	9	time	time	NOUN
ap-10625	167	10	-	-	PUNCT
ap-10625	167	11	dependent	dependent	ADJ
ap-10625	167	12	box	box	NOUN
ap-10625	167	13	is	be	AUX
ap-10625	167	14	the	the	DET
ap-10625	167	15	so	so	ADV
ap-10625	167	16	-	-	PUNCT
ap-10625	167	17	called	call	VERB
ap-10625	167	18	fermi	fermi	NOUN
ap-10625	167	19	acceleration	acceleration	NOUN
ap-10625	167	20	,	,	PUNCT
ap-10625	167	21	which	which	PRON
ap-10625	167	22	implies	imply	VERB
ap-10625	167	23	an	an	DET
ap-10625	167	24	increase	increase	NOUN
ap-10625	167	25	of	of	ADP
ap-10625	167	26	the	the	DET
ap-10625	167	27	particle	particle	NOUN
ap-10625	167	28	velocity	velocity	NOUN
ap-10625	167	29	caused	cause	VERB
ap-10625	167	30	by	by	ADP
ap-10625	167	31	its	its	PRON
ap-10625	167	32	interaction	interaction	NOUN
ap-10625	167	33	with	with	ADP
ap-10625	167	34	the	the	DET
ap-10625	167	35	periodically	periodically	ADV
ap-10625	167	36	oscillating	oscillate	VERB
ap-10625	167	37	wall	wall	NOUN
ap-10625	167	38	of	of	ADP
ap-10625	167	39	the	the	DET
ap-10625	167	40	box	box	NOUN
ap-10625	167	41	.	.	PUNCT
ap-10625	168	1	an	an	DET
ap-10625	168	2	important	important	ADJ
ap-10625	168	3	physically	physically	ADV
ap-10625	168	4	observable	observable	ADJ
ap-10625	168	5	characteristics	characteristic	NOUN
ap-10625	168	6	of	of	ADP
ap-10625	168	7	the	the	DET
ap-10625	168	8	fermi	fermi	NOUN
ap-10625	168	9	acceleration	acceleration	NOUN
ap-10625	168	10	in	in	ADP
ap-10625	168	11	quantum	quantum	ADJ
ap-10625	168	12	regime	regime	NOUN
ap-10625	168	13	is	be	AUX
ap-10625	168	14	the	the	DET
ap-10625	168	15	average	average	ADJ
ap-10625	168	16	kinetic	kinetic	ADJ
ap-10625	168	17	energy	energy	NOUN
ap-10625	168	18	of	of	ADP
ap-10625	168	19	the	the	DET
ap-10625	168	20	particle	particle	NOUN
ap-10625	168	21	,	,	PUNCT
ap-10625	168	22	which	which	PRON
ap-10625	168	23	is	be	AUX
ap-10625	168	24	determined	determine	VERB
ap-10625	168	25	as	as	ADP
ap-10625	168	26	:	:	PUNCT
ap-10625	168	27	⟨e(t)⟩	⟨e(t)⟩	NOUN
ap-10625	168	28	=	=	SYM
ap-10625	168	29	∫	∫	PROPN
ap-10625	169	1	r0(t	r0(t	NOUN
ap-10625	169	2	)	)	PUNCT
ap-10625	169	3	0	0	PUNCT
ap-10625	170	1	ψ(r	ψ(r	PROPN
ap-10625	170	2	,	,	PUNCT
ap-10625	170	3	t)†hψ(r	t)†hψ(r	PROPN
ap-10625	170	4	,	,	PUNCT
ap-10625	170	5	t	t	PROPN
ap-10625	170	6	)	)	PUNCT
ap-10625	170	7	dr	dr	PROPN
ap-10625	170	8	.	.	PROPN
ap-10625	170	9	549	549	NUM
ap-10625	170	10	k.	k.	PROPN
ap-10625	170	11	matchonov	matchonov	PROPN
ap-10625	170	12	,	,	PUNCT
ap-10625	170	13	d.	d.	PROPN
ap-10625	170	14	matrasulov	matrasulov	PROPN
ap-10625	170	15	,	,	PUNCT
ap-10625	170	16	j.	j.	PROPN
ap-10625	170	17	dittrich	dittrich	PROPN
ap-10625	170	18	acta	acta	PROPN
ap-10625	170	19	polytechnica	polytechnica	PROPN
ap-10625	170	20	0	0	NUM
ap-10625	170	21	20	20	NUM
ap-10625	170	22	40	40	NUM
ap-10625	170	23	60	60	NUM
ap-10625	170	24	80	80	NUM
ap-10625	170	25	100	100	NUM
ap-10625	170	26	t	t	NOUN
ap-10625	170	27	20	20	NUM
ap-10625	170	28	40	40	NUM
ap-10625	170	29	60	60	NUM
ap-10625	170	30	80	80	NUM
ap-10625	170	31	100	100	NUM
ap-10625	170	32	120	120	NUM
ap-10625	170	33	140	140	NUM
ap-10625	170	34	160	160	NUM
ap-10625	170	35	<	<	X
ap-10625	170	36	e	e	X
ap-10625	170	37	(	(	PUNCT
ap-10625	170	38	t	t	PROPN
ap-10625	170	39	)	)	PUNCT
ap-10625	170	40	>	>	X
ap-10625	170	41	b	b	X
ap-10625	171	1	=	=	SYM
ap-10625	171	2	0.1	0.1	NUM
ap-10625	171	3	b	b	X
ap-10625	171	4	=	=	NOUN
ap-10625	171	5	0.2	0.2	NUM
ap-10625	171	6	b	b	X
ap-10625	171	7	=	=	SYM
ap-10625	171	8	0.3	0.3	NUM
ap-10625	171	9	(	(	PUNCT
ap-10625	171	10	a	a	NOUN
ap-10625	171	11	)	)	PUNCT
ap-10625	171	12	.	.	PUNCT
ap-10625	172	1	the	the	DET
ap-10625	172	2	average	average	ADJ
ap-10625	172	3	kinetic	kinetic	ADJ
ap-10625	172	4	energy	energy	NOUN
ap-10625	172	5	of	of	ADP
ap-10625	172	6	a	a	DET
ap-10625	172	7	dirac	dirac	NOUN
ap-10625	172	8	particle	particle	NOUN
ap-10625	172	9	confined	confine	VERB
ap-10625	172	10	in	in	ADP
ap-10625	172	11	an	an	DET
ap-10625	172	12	expanding	expand	VERB
ap-10625	172	13	spherical	spherical	ADJ
ap-10625	172	14	box	box	NOUN
ap-10625	172	15	(	(	PUNCT
ap-10625	172	16	r0(t	r0(t	PROPN
ap-10625	172	17	)	)	PUNCT
ap-10625	172	18	=	=	SYM
ap-10625	172	19	a	a	PRON
ap-10625	173	1	+	+	X
ap-10625	173	2	bt	bt	PROPN
ap-10625	173	3	,	,	PUNCT
ap-10625	173	4	a	a	DET
ap-10625	173	5	=	=	NOUN
ap-10625	173	6	5	5	NUM
ap-10625	173	7	)	)	PUNCT
ap-10625	173	8	as	as	ADP
ap-10625	173	9	a	a	DET
ap-10625	173	10	function	function	NOUN
ap-10625	173	11	of	of	ADP
ap-10625	173	12	time	time	NOUN
ap-10625	173	13	at	at	ADP
ap-10625	173	14	different	different	ADJ
ap-10625	173	15	values	value	NOUN
ap-10625	173	16	of	of	ADP
ap-10625	173	17	b	b	PROPN
ap-10625	173	18	for	for	ADP
ap-10625	173	19	m	m	PROPN
ap-10625	173	20	=	=	NOUN
ap-10625	173	21	1	1	NUM
ap-10625	173	22	.	.	PUNCT
ap-10625	174	1	the	the	DET
ap-10625	174	2	wave	wave	NOUN
ap-10625	174	3	packet	packet	NOUN
ap-10625	174	4	’s	’s	PART
ap-10625	174	5	width	width	NOUN
ap-10625	174	6	,	,	PUNCT
ap-10625	174	7	initial	initial	ADJ
ap-10625	174	8	position	position	NOUN
ap-10625	174	9	of	of	ADP
ap-10625	174	10	the	the	DET
ap-10625	174	11	center	center	NOUN
ap-10625	174	12	of	of	ADP
ap-10625	174	13	mass	mass	PROPN
ap-10625	174	14	,	,	PUNCT
ap-10625	174	15	initial	initial	ADJ
ap-10625	174	16	velocity	velocity	NOUN
ap-10625	174	17	and	and	CCONJ
ap-10625	174	18	the	the	DET
ap-10625	174	19	initial	initial	ADJ
ap-10625	174	20	spin	spin	NOUN
ap-10625	174	21	polarization	polarization	NOUN
ap-10625	174	22	are	be	AUX
ap-10625	174	23	chosen	choose	VERB
ap-10625	174	24	as	as	ADP
ap-10625	174	25	d	d	PROPN
ap-10625	174	26	=	=	SYM
ap-10625	174	27	0.1	0.1	NUM
ap-10625	174	28	,	,	PUNCT
ap-10625	174	29	r0	r0	NOUN
ap-10625	174	30	=	=	SYM
ap-10625	174	31	r0(0	r0(0	PROPN
ap-10625	174	32	)	)	PUNCT
ap-10625	174	33	2	2	NUM
ap-10625	174	34	,	,	PUNCT
ap-10625	174	35	v0	v0	NOUN
ap-10625	174	36	=	=	SYM
ap-10625	174	37	0	0	NUM
ap-10625	174	38	,	,	PUNCT
ap-10625	174	39	s1	s1	NOUN
ap-10625	174	40	=	=	SYM
ap-10625	174	41	1	1	NUM
ap-10625	174	42	and	and	CCONJ
ap-10625	174	43	s2	s2	VERB
ap-10625	174	44	=	=	SYM
ap-10625	174	45	0	0	NUM
ap-10625	174	46	,	,	PUNCT
ap-10625	174	47	respectively	respectively	ADV
ap-10625	174	48	.	.	PUNCT
ap-10625	175	1	0	0	NUM
ap-10625	176	1	20	20	NUM
ap-10625	176	2	40	40	NUM
ap-10625	176	3	60	60	NUM
ap-10625	176	4	80	80	NUM
ap-10625	176	5	100	100	NUM
ap-10625	176	6	t	t	NOUN
ap-10625	176	7	100	100	NUM
ap-10625	176	8	200	200	NUM
ap-10625	176	9	300	300	NUM
ap-10625	176	10	400	400	NUM
ap-10625	176	11	500	500	NUM
ap-10625	176	12	600	600	NUM
ap-10625	176	13	700	700	NUM
ap-10625	176	14	800	800	NUM
ap-10625	176	15	<	<	X
ap-10625	176	16	e	e	X
ap-10625	176	17	(	(	PUNCT
ap-10625	176	18	t	t	PROPN
ap-10625	176	19	)	)	PUNCT
ap-10625	176	20	>	>	X
ap-10625	176	21	b	b	X
ap-10625	176	22	=	=	SYM
ap-10625	176	23	-0.02	-0.02	NUM
ap-10625	176	24	b	b	NOUN
ap-10625	176	25	=	=	SYM
ap-10625	176	26	-0.03	-0.03	NUM
ap-10625	176	27	b	b	NOUN
ap-10625	176	28	=	=	SYM
ap-10625	176	29	-0.04	-0.04	NUM
ap-10625	176	30	(	(	PUNCT
ap-10625	176	31	b	b	NOUN
ap-10625	176	32	)	)	PUNCT
ap-10625	176	33	.	.	PUNCT
ap-10625	177	1	the	the	DET
ap-10625	177	2	average	average	ADJ
ap-10625	177	3	kinetic	kinetic	ADJ
ap-10625	177	4	energy	energy	NOUN
ap-10625	177	5	of	of	ADP
ap-10625	177	6	a	a	DET
ap-10625	177	7	dirac	dirac	NOUN
ap-10625	177	8	particle	particle	NOUN
ap-10625	177	9	confined	confine	VERB
ap-10625	177	10	in	in	ADP
ap-10625	177	11	a	a	DET
ap-10625	177	12	contracting	contracting	NOUN
ap-10625	177	13	box	box	NOUN
ap-10625	177	14	(	(	PUNCT
ap-10625	177	15	r0(t	r0(t	PROPN
ap-10625	177	16	)	)	PUNCT
ap-10625	177	17	=	=	SYM
ap-10625	177	18	a	a	PRON
ap-10625	178	1	+	+	X
ap-10625	178	2	bt	bt	PROPN
ap-10625	178	3	,	,	PUNCT
ap-10625	178	4	a	a	DET
ap-10625	178	5	=	=	NOUN
ap-10625	178	6	5	5	NUM
ap-10625	178	7	)	)	PUNCT
ap-10625	178	8	as	as	ADP
ap-10625	178	9	a	a	DET
ap-10625	178	10	function	function	NOUN
ap-10625	178	11	of	of	ADP
ap-10625	178	12	time	time	NOUN
ap-10625	178	13	at	at	ADP
ap-10625	178	14	different	different	ADJ
ap-10625	178	15	values	value	NOUN
ap-10625	178	16	of	of	ADP
ap-10625	178	17	b.	b.	PROPN
ap-10625	178	18	the	the	DET
ap-10625	178	19	other	other	ADJ
ap-10625	178	20	parameters	parameter	NOUN
ap-10625	178	21	are	be	AUX
ap-10625	178	22	as	as	ADP
ap-10625	178	23	in	in	ADP
ap-10625	178	24	figure	figure	NOUN
ap-10625	178	25	1a	1a	NOUN
ap-10625	178	26	.	.	PUNCT
ap-10625	179	1	figure	figure	NOUN
ap-10625	179	2	1	1	NUM
ap-10625	179	3	.	.	PUNCT
ap-10625	180	1	the	the	DET
ap-10625	180	2	average	average	ADJ
ap-10625	180	3	kinetic	kinetic	ADJ
ap-10625	180	4	energy	energy	NOUN
ap-10625	180	5	of	of	ADP
ap-10625	180	6	a	a	DET
ap-10625	180	7	dirac	dirac	NOUN
ap-10625	180	8	particle	particle	NOUN
ap-10625	180	9	confined	confine	VERB
ap-10625	180	10	in	in	ADP
ap-10625	180	11	an	an	DET
ap-10625	180	12	expanding	expanding	NOUN
ap-10625	180	13	and	and	CCONJ
ap-10625	180	14	a	a	DET
ap-10625	180	15	contracting	contracting	NOUN
ap-10625	180	16	box	box	NOUN
ap-10625	180	17	.	.	PUNCT
ap-10625	181	1	0	0	NUM
ap-10625	182	1	20	20	NUM
ap-10625	182	2	40	40	NUM
ap-10625	182	3	60	60	NUM
ap-10625	182	4	80	80	NUM
ap-10625	182	5	100	100	NUM
ap-10625	182	6	t	t	NOUN
ap-10625	182	7	140	140	NUM
ap-10625	182	8	145	145	NUM
ap-10625	182	9	150	150	NUM
ap-10625	182	10	155	155	NUM
ap-10625	182	11	160	160	NUM
ap-10625	182	12	<	<	X
ap-10625	182	13	e	e	X
ap-10625	182	14	(	(	PUNCT
ap-10625	182	15	t	t	PROPN
ap-10625	182	16	)	)	PUNCT
ap-10625	182	17	>	>	X
ap-10625	182	18	b	b	X
ap-10625	183	1	=	=	SYM
ap-10625	183	2	0.1	0.1	NUM
ap-10625	183	3	b	b	X
ap-10625	183	4	=	=	NOUN
ap-10625	183	5	0.2	0.2	NUM
ap-10625	183	6	b	b	X
ap-10625	183	7	=	=	SYM
ap-10625	183	8	0.3	0.3	NUM
ap-10625	183	9	(	(	PUNCT
ap-10625	183	10	a	a	NOUN
ap-10625	183	11	)	)	PUNCT
ap-10625	183	12	.	.	PUNCT
ap-10625	184	1	time	time	NOUN
ap-10625	184	2	-	-	PUNCT
ap-10625	184	3	dependence	dependence	NOUN
ap-10625	184	4	of	of	ADP
ap-10625	184	5	the	the	DET
ap-10625	184	6	average	average	ADJ
ap-10625	184	7	kinetic	kinetic	ADJ
ap-10625	184	8	energy	energy	NOUN
ap-10625	184	9	of	of	ADP
ap-10625	184	10	a	a	DET
ap-10625	184	11	dirac	dirac	NOUN
ap-10625	184	12	particle	particle	NOUN
ap-10625	184	13	in	in	ADP
ap-10625	184	14	a	a	DET
ap-10625	184	15	spherical	spherical	ADJ
ap-10625	184	16	box	box	NOUN
ap-10625	184	17	(	(	PUNCT
ap-10625	184	18	r0(t	r0(t	PROPN
ap-10625	184	19	)	)	PUNCT
ap-10625	184	20	=	=	PUNCT
ap-10625	184	21	a	a	DET
ap-10625	184	22	+	+	NUM
ap-10625	184	23	b	b	NOUN
ap-10625	184	24	sin	sin	NOUN
ap-10625	184	25	ωt	ωt	NOUN
ap-10625	184	26	)	)	PUNCT
ap-10625	184	27	at	at	ADP
ap-10625	184	28	different	different	ADJ
ap-10625	184	29	values	value	NOUN
ap-10625	184	30	of	of	ADP
ap-10625	184	31	amplitude	amplitude	NOUN
ap-10625	184	32	for	for	ADP
ap-10625	184	33	fixed	fix	VERB
ap-10625	184	34	a	a	DET
ap-10625	184	35	=	=	SYM
ap-10625	184	36	5	5	NUM
ap-10625	184	37	,	,	PUNCT
ap-10625	184	38	ω	ω	NOUN
ap-10625	184	39	=	=	SYM
ap-10625	184	40	2	2	NUM
ap-10625	184	41	and	and	CCONJ
ap-10625	184	42	m	m	NOUN
ap-10625	184	43	=	=	ADJ
ap-10625	184	44	1	1	X
ap-10625	184	45	.	.	PUNCT
ap-10625	185	1	the	the	DET
ap-10625	185	2	wave	wave	NOUN
ap-10625	185	3	packet	packet	NOUN
ap-10625	185	4	’s	’s	PART
ap-10625	185	5	width	width	NOUN
ap-10625	185	6	,	,	PUNCT
ap-10625	185	7	initial	initial	ADJ
ap-10625	185	8	position	position	NOUN
ap-10625	185	9	of	of	ADP
ap-10625	185	10	the	the	DET
ap-10625	185	11	center	center	NOUN
ap-10625	185	12	of	of	ADP
ap-10625	185	13	mass	mass	PROPN
ap-10625	185	14	,	,	PUNCT
ap-10625	185	15	initial	initial	ADJ
ap-10625	185	16	velocity	velocity	NOUN
ap-10625	185	17	and	and	CCONJ
ap-10625	185	18	the	the	DET
ap-10625	185	19	initial	initial	ADJ
ap-10625	185	20	spin	spin	NOUN
ap-10625	185	21	polarization	polarization	NOUN
ap-10625	185	22	are	be	AUX
ap-10625	185	23	chosen	choose	VERB
ap-10625	185	24	as	as	ADP
ap-10625	185	25	d	d	PROPN
ap-10625	185	26	=	=	SYM
ap-10625	185	27	0.1	0.1	NUM
ap-10625	185	28	,	,	PUNCT
ap-10625	185	29	r0	r0	NOUN
ap-10625	185	30	=	=	SYM
ap-10625	185	31	r0(0	r0(0	PROPN
ap-10625	185	32	)	)	PUNCT
ap-10625	185	33	2	2	NUM
ap-10625	185	34	,	,	PUNCT
ap-10625	185	35	v0	v0	NOUN
ap-10625	185	36	=	=	SYM
ap-10625	185	37	0	0	NUM
ap-10625	185	38	,	,	PUNCT
ap-10625	185	39	s1	s1	NOUN
ap-10625	185	40	=	=	SYM
ap-10625	185	41	1	1	NUM
ap-10625	185	42	and	and	CCONJ
ap-10625	185	43	s2	s2	VERB
ap-10625	185	44	=	=	SYM
ap-10625	185	45	0	0	NUM
ap-10625	185	46	,	,	PUNCT
ap-10625	185	47	respectively	respectively	ADV
ap-10625	185	48	.	.	PUNCT
ap-10625	186	1	0	0	NUM
ap-10625	187	1	20	20	NUM
ap-10625	187	2	40	40	NUM
ap-10625	187	3	60	60	NUM
ap-10625	187	4	80	80	NUM
ap-10625	187	5	100	100	NUM
ap-10625	187	6	t	t	NOUN
ap-10625	187	7	148	148	NUM
ap-10625	187	8	150	150	NUM
ap-10625	187	9	152	152	NUM
ap-10625	187	10	154	154	NUM
ap-10625	187	11	<	<	X
ap-10625	187	12	e	e	X
ap-10625	187	13	(	(	PUNCT
ap-10625	187	14	t	t	PROPN
ap-10625	187	15	)	)	PUNCT
ap-10625	187	16	>	>	X
ap-10625	187	17	=	=	PUNCT
ap-10625	187	18	0.5	0.5	NUM
ap-10625	187	19	=	=	SYM
ap-10625	187	20	1	1	NUM
ap-10625	187	21	=	=	SYM
ap-10625	187	22	2	2	NUM
ap-10625	187	23	(	(	PUNCT
ap-10625	187	24	b	b	NOUN
ap-10625	187	25	)	)	PUNCT
ap-10625	187	26	.	.	PUNCT
ap-10625	188	1	time	time	NOUN
ap-10625	188	2	-	-	PUNCT
ap-10625	188	3	dependence	dependence	NOUN
ap-10625	188	4	of	of	ADP
ap-10625	188	5	the	the	DET
ap-10625	188	6	average	average	ADJ
ap-10625	188	7	kinetic	kinetic	ADJ
ap-10625	188	8	energy	energy	NOUN
ap-10625	188	9	of	of	ADP
ap-10625	188	10	a	a	DET
ap-10625	188	11	dirac	dirac	NOUN
ap-10625	188	12	particle	particle	NOUN
ap-10625	188	13	in	in	ADP
ap-10625	188	14	a	a	DET
ap-10625	188	15	spherical	spherical	ADJ
ap-10625	188	16	box	box	NOUN
ap-10625	188	17	(	(	PUNCT
ap-10625	188	18	r0(t	r0(t	PROPN
ap-10625	188	19	)	)	PUNCT
ap-10625	188	20	=	=	SYM
ap-10625	188	21	a+b	a+b	NUM
ap-10625	188	22	sin	sin	NOUN
ap-10625	188	23	ωt	ωt	NOUN
ap-10625	188	24	)	)	PUNCT
ap-10625	188	25	at	at	ADP
ap-10625	188	26	different	different	ADJ
ap-10625	188	27	values	value	NOUN
ap-10625	188	28	of	of	ADP
ap-10625	188	29	frequency	frequency	NOUN
ap-10625	188	30	for	for	ADP
ap-10625	188	31	fixed	fix	VERB
ap-10625	188	32	b	b	NOUN
ap-10625	188	33	=	=	SYM
ap-10625	188	34	0.1	0.1	NUM
ap-10625	188	35	.	.	PUNCT
ap-10625	189	1	the	the	DET
ap-10625	189	2	other	other	ADJ
ap-10625	189	3	parameters	parameter	NOUN
ap-10625	189	4	are	be	AUX
ap-10625	189	5	as	as	ADP
ap-10625	189	6	in	in	ADP
ap-10625	189	7	figure	figure	NOUN
ap-10625	189	8	2a	2a	NUM
ap-10625	189	9	.	.	PUNCT
ap-10625	190	1	figure	figure	NOUN
ap-10625	190	2	2	2	NUM
ap-10625	190	3	.	.	NOUN
ap-10625	190	4	time	time	NOUN
ap-10625	190	5	-	-	PUNCT
ap-10625	190	6	dependence	dependence	NOUN
ap-10625	190	7	of	of	ADP
ap-10625	190	8	the	the	DET
ap-10625	190	9	average	average	ADJ
ap-10625	190	10	kinetic	kinetic	ADJ
ap-10625	190	11	energy	energy	NOUN
ap-10625	190	12	of	of	ADP
ap-10625	190	13	a	a	DET
ap-10625	190	14	dirac	dirac	NOUN
ap-10625	190	15	particle	particle	NOUN
ap-10625	190	16	in	in	ADP
ap-10625	190	17	a	a	DET
ap-10625	190	18	spherical	spherical	ADJ
ap-10625	190	19	box	box	NOUN
ap-10625	190	20	at	at	ADP
ap-10625	190	21	different	different	ADJ
ap-10625	190	22	values	value	NOUN
ap-10625	190	23	of	of	ADP
ap-10625	190	24	amplitude	amplitude	NOUN
ap-10625	190	25	and	and	CCONJ
ap-10625	190	26	frequency	frequency	NOUN
ap-10625	190	27	.	.	PUNCT
ap-10625	191	1	using	use	VERB
ap-10625	191	2	equations	equation	NOUN
ap-10625	191	3	(	(	PUNCT
ap-10625	191	4	3	3	NUM
ap-10625	191	5	)	)	PUNCT
ap-10625	191	6	and	and	CCONJ
ap-10625	191	7	(	(	PUNCT
ap-10625	191	8	15	15	NUM
ap-10625	191	9	)	)	PUNCT
ap-10625	191	10	for	for	ADP
ap-10625	191	11	the	the	DET
ap-10625	191	12	average	average	ADJ
ap-10625	191	13	kinetic	kinetic	ADJ
ap-10625	191	14	energy	energy	NOUN
ap-10625	191	15	we	we	PRON
ap-10625	191	16	have	have	VERB
ap-10625	191	17	:	:	PUNCT
ap-10625	191	18	⟨e(t)⟩	⟨e(t)⟩	NUM
ap-10625	191	19	=	=	SYM
ap-10625	191	20	∞∑	∞∑	PRON
ap-10625	191	21	n=0	n=0	NUM
ap-10625	191	22	en(t	en(t	NUM
ap-10625	191	23	)	)	PUNCT
ap-10625	191	24	,	,	PUNCT
ap-10625	191	25	e0(t	e0(t	X
ap-10625	191	26	)	)	PUNCT
ap-10625	191	27	=	=	SYM
ap-10625	191	28	−m|a0(τ(t))|2	−m|a0(τ(t))|2	X
ap-10625	191	29	,	,	PUNCT
ap-10625	191	30	en(t	en(t	PRON
ap-10625	191	31	)	)	PUNCT
ap-10625	191	32	=	=	SYM
ap-10625	191	33	εn	εn	ADJ
ap-10625	191	34	r0(t	r0(t	PROPN
ap-10625	191	35	)	)	PUNCT
ap-10625	191	36	(	(	PUNCT
ap-10625	191	37	|an(τ(t))|2	|an(τ(t))|2	X
ap-10625	191	38	−	−	NOUN
ap-10625	191	39	|a−n(τ(t))|2	|a−n(τ(t))|2	NOUN
ap-10625	191	40	)	)	PUNCT
ap-10625	192	1	−	−	PROPN
ap-10625	193	1	2mℜ	2mℜ	NUM
ap-10625	193	2	(	(	PUNCT
ap-10625	193	3	an(τ(t))a−n(τ(t	an(τ(t))a−n(τ(t	ADJ
ap-10625	193	4	)	)	PUNCT
ap-10625	193	5	)	)	PUNCT
ap-10625	193	6	)	)	PUNCT
ap-10625	193	7	,	,	PUNCT
ap-10625	193	8	for	for	ADP
ap-10625	193	9	n	n	DET
ap-10625	193	10	∈	∈	PROPN
ap-10625	193	11	n.	n.	NOUN
ap-10625	193	12	(	(	PUNCT
ap-10625	193	13	22	22	NUM
ap-10625	193	14	)	)	PUNCT
ap-10625	193	15	for	for	ADP
ap-10625	193	16	the	the	DET
ap-10625	193	17	massless	massless	NOUN
ap-10625	193	18	particle	particle	NOUN
ap-10625	193	19	,	,	PUNCT
ap-10625	193	20	equations	equation	NOUN
ap-10625	193	21	(	(	PUNCT
ap-10625	193	22	22	22	NUM
ap-10625	193	23	)	)	PUNCT
ap-10625	193	24	and	and	CCONJ
ap-10625	193	25	(	(	PUNCT
ap-10625	193	26	18	18	NUM
ap-10625	193	27	)	)	PUNCT
ap-10625	193	28	lead	lead	VERB
ap-10625	193	29	to	to	ADP
ap-10625	193	30	:	:	PUNCT
ap-10625	193	31	en(t	en(t	X
ap-10625	193	32	)	)	PUNCT
ap-10625	194	1	=	=	SYM
ap-10625	194	2	kn	kn	PROPN
ap-10625	194	3	r0(t	r0(t	PROPN
ap-10625	194	4	)	)	PUNCT
ap-10625	194	5	(	(	PUNCT
ap-10625	194	6	|an(τ(t))|2	|an(τ(t))|2	X
ap-10625	194	7	−	−	ADP
ap-10625	194	8	|a−n(τ(t))|2	|a−n(τ(t))|2	NOUN
ap-10625	194	9	)	)	PUNCT
ap-10625	194	10	=	=	SYM
ap-10625	195	1	kn	kn	PROPN
ap-10625	195	2	r0(t	r0(t	PROPN
ap-10625	195	3	)	)	PUNCT
ap-10625	195	4	(	(	PUNCT
ap-10625	195	5	|an(0)|2	|an(0)|2	ADP
ap-10625	195	6	−	−	NOUN
ap-10625	195	7	|a−n(0)|2	|a−n(0)|2	NOUN
ap-10625	195	8	)	)	PUNCT
ap-10625	195	9	,	,	PUNCT
ap-10625	195	10	for	for	ADP
ap-10625	195	11	n	n	PRON
ap-10625	195	12	∈	∈	PROPN
ap-10625	195	13	n.	n.	NOUN
ap-10625	195	14	for	for	ADP
ap-10625	195	15	the	the	DET
ap-10625	195	16	massive	massive	ADJ
ap-10625	195	17	case	case	NOUN
ap-10625	195	18	(	(	PUNCT
ap-10625	195	19	m	m	VERB
ap-10625	195	20	̸=	̸=	PROPN
ap-10625	195	21	0	0	NUM
ap-10625	195	22	)	)	PUNCT
ap-10625	195	23	,	,	PUNCT
ap-10625	195	24	the	the	DET
ap-10625	195	25	average	average	ADJ
ap-10625	195	26	energy	energy	NOUN
ap-10625	195	27	should	should	AUX
ap-10625	195	28	be	be	AUX
ap-10625	195	29	computed	compute	VERB
ap-10625	195	30	numerically	numerically	ADV
ap-10625	195	31	.	.	PUNCT
ap-10625	196	1	in	in	ADP
ap-10625	196	2	figure	figure	NOUN
ap-10625	196	3	1	1	NUM
ap-10625	196	4	the	the	DET
ap-10625	196	5	average	average	ADJ
ap-10625	196	6	kinetic	kinetic	ADJ
ap-10625	196	7	energy	energy	NOUN
ap-10625	196	8	is	be	AUX
ap-10625	196	9	plotted	plot	VERB
ap-10625	196	10	as	as	ADP
ap-10625	196	11	a	a	DET
ap-10625	196	12	function	function	NOUN
ap-10625	196	13	of	of	ADP
ap-10625	196	14	time	time	NOUN
ap-10625	196	15	for	for	ADP
ap-10625	196	16	linearly	linearly	ADV
ap-10625	196	17	expanding	expand	VERB
ap-10625	196	18	(	(	PUNCT
ap-10625	196	19	figure	figure	NOUN
ap-10625	196	20	1a	1a	NOUN
ap-10625	196	21	)	)	PUNCT
ap-10625	196	22	and	and	CCONJ
ap-10625	196	23	contracting	contracting	NOUN
ap-10625	196	24	(	(	PUNCT
ap-10625	196	25	figure	figure	NOUN
ap-10625	196	26	1b	1b	NUM
ap-10625	196	27	)	)	PUNCT
ap-10625	196	28	sphere	sphere	ADV
ap-10625	196	29	at	at	ADP
ap-10625	196	30	different	different	ADJ
ap-10625	196	31	values	value	NOUN
ap-10625	196	32	of	of	ADP
ap-10625	196	33	the	the	DET
ap-10625	196	34	wall	wall	NOUN
ap-10625	196	35	’s	’s	PART
ap-10625	196	36	velocity	velocity	NOUN
ap-10625	196	37	.	.	PUNCT
ap-10625	197	1	figure	figure	NOUN
ap-10625	197	2	2	2	NUM
ap-10625	197	3	compares	compare	NOUN
ap-10625	197	4	⟨e(t)⟩	⟨e(t)⟩	NOUN
ap-10625	197	5	for	for	SCONJ
ap-10625	197	6	the	the	DET
ap-10625	197	7	dirac	dirac	NOUN
ap-10625	197	8	particle	particle	NOUN
ap-10625	197	9	confined	confine	VERB
ap-10625	197	10	in	in	ADP
ap-10625	197	11	a	a	DET
ap-10625	197	12	spherical	spherical	ADJ
ap-10625	197	13	box	box	NOUN
ap-10625	197	14	with	with	ADP
ap-10625	197	15	harmonically	harmonically	ADV
ap-10625	197	16	oscillating	oscillate	VERB
ap-10625	197	17	radius	radius	NOUN
ap-10625	197	18	at	at	ADP
ap-10625	197	19	different	different	ADJ
ap-10625	197	20	values	value	NOUN
ap-10625	197	21	of	of	ADP
ap-10625	197	22	the	the	DET
ap-10625	197	23	oscillation	oscillation	NOUN
ap-10625	197	24	amplitude	amplitude	NOUN
ap-10625	197	25	(	(	PUNCT
ap-10625	197	26	figure	figure	NOUN
ap-10625	197	27	2a	2a	NUM
ap-10625	197	28	)	)	PUNCT
ap-10625	197	29	and	and	CCONJ
ap-10625	197	30	frequency	frequency	NOUN
ap-10625	197	31	(	(	PUNCT
ap-10625	197	32	figure	figure	NOUN
ap-10625	197	33	2b	2b	NOUN
ap-10625	197	34	)	)	PUNCT
ap-10625	197	35	.	.	PUNCT
ap-10625	198	1	in	in	ADP
ap-10625	198	2	both	both	DET
ap-10625	198	3	cases	case	NOUN
ap-10625	198	4	,	,	PUNCT
ap-10625	198	5	⟨e(t)⟩	⟨e(t)⟩	NOUN
ap-10625	198	6	is	be	AUX
ap-10625	198	7	periodic	periodic	ADJ
ap-10625	198	8	in	in	ADP
ap-10625	198	9	time	time	NOUN
ap-10625	198	10	and	and	CCONJ
ap-10625	198	11	the	the	DET
ap-10625	198	12	larger	large	ADJ
ap-10625	198	13	the	the	DET
ap-10625	198	14	oscillation	oscillation	NOUN
ap-10625	198	15	amplitude	amplitude	NOUN
ap-10625	198	16	of	of	ADP
ap-10625	198	17	the	the	DET
ap-10625	198	18	wall	wall	NOUN
ap-10625	198	19	is	be	AUX
ap-10625	198	20	,	,	PUNCT
ap-10625	198	21	the	the	PRON
ap-10625	198	22	larger	large	ADJ
ap-10625	198	23	the	the	DET
ap-10625	198	24	amplitude	amplitude	NOUN
ap-10625	198	25	of	of	ADP
ap-10625	198	26	⟨e(t)⟩	⟨e(t)⟩	NOUN
ap-10625	198	27	is	be	AUX
ap-10625	198	28	.	.	PUNCT
ap-10625	199	1	as	as	ADP
ap-10625	199	2	the	the	DET
ap-10625	199	3	wall	wall	NOUN
ap-10625	199	4	’s	’s	PART
ap-10625	199	5	oscillation	oscillation	NOUN
ap-10625	199	6	frequency	frequency	NOUN
ap-10625	199	7	increses	increse	NOUN
ap-10625	199	8	,	,	PUNCT
ap-10625	199	9	the	the	DET
ap-10625	199	10	period	period	NOUN
ap-10625	199	11	of	of	ADP
ap-10625	199	12	⟨e(t)⟩	⟨e(t)⟩	NOUN
ap-10625	199	13	decreases	decrease	NOUN
ap-10625	199	14	.	.	PUNCT
ap-10625	200	1	thus	thus	ADV
ap-10625	200	2	,	,	PUNCT
ap-10625	200	3	no	no	DET
ap-10625	200	4	monotonic	monotonic	ADJ
ap-10625	200	5	growth	growth	NOUN
ap-10625	200	6	of	of	ADP
ap-10625	200	7	average	average	ADJ
ap-10625	200	8	kinetic	kinetic	ADJ
ap-10625	200	9	energy	energy	NOUN
ap-10625	200	10	is	be	AUX
ap-10625	200	11	possible	possible	ADJ
ap-10625	200	12	for	for	ADP
ap-10625	200	13	a	a	DET
ap-10625	200	14	dirac	dirac	NOUN
ap-10625	200	15	particle	particle	NOUN
ap-10625	200	16	in	in	ADP
ap-10625	200	17	a	a	DET
ap-10625	200	18	harmonically	harmonically	ADV
ap-10625	200	19	oscillating	oscillate	VERB
ap-10625	200	20	box	box	NOUN
ap-10625	200	21	,	,	PUNCT
ap-10625	200	22	i.e.	i.e.	X
ap-10625	200	23	no	no	DET
ap-10625	200	24	fermi	fermi	NOUN
ap-10625	200	25	acceleration	acceleration	NOUN
ap-10625	200	26	can	can	AUX
ap-10625	200	27	be	be	AUX
ap-10625	200	28	observed	observe	VERB
ap-10625	200	29	.	.	PUNCT
ap-10625	201	1	3.2	3.2	NUM
ap-10625	201	2	.	.	PUNCT
ap-10625	201	3	zitterbewegung	zitterbewegung	NOUN
ap-10625	201	4	one	one	NUM
ap-10625	201	5	of	of	ADP
ap-10625	201	6	the	the	DET
ap-10625	201	7	unusual	unusual	ADJ
ap-10625	201	8	effects	effect	NOUN
ap-10625	201	9	in	in	ADP
ap-10625	201	10	the	the	DET
ap-10625	201	11	dirac	dirac	NOUN
ap-10625	201	12	particle	particle	NOUN
ap-10625	201	13	’s	’s	PART
ap-10625	201	14	dynamics	dynamic	NOUN
ap-10625	201	15	is	be	AUX
ap-10625	201	16	the	the	DET
ap-10625	201	17	so	so	ADV
ap-10625	201	18	-	-	PUNCT
ap-10625	201	19	called	call	VERB
ap-10625	201	20	“	"	PUNCT
ap-10625	201	21	zitterbewegung	zitterbewegung	NOUN
ap-10625	201	22	”	"	PUNCT
ap-10625	201	23	,	,	PUNCT
ap-10625	201	24	i.e.	i.e.	X
ap-10625	201	25	the	the	DET
ap-10625	201	26	manifestation	manifestation	NOUN
ap-10625	201	27	of	of	ADP
ap-10625	201	28	the	the	DET
ap-10625	201	29	trembling	tremble	VERB
ap-10625	201	30	motion	motion	NOUN
ap-10625	201	31	of	of	ADP
ap-10625	201	32	the	the	DET
ap-10625	201	33	particle	particle	NOUN
ap-10625	201	34	.	.	PUNCT
ap-10625	202	1	it	it	PRON
ap-10625	202	2	550	550	NUM
ap-10625	202	3	vol	vol	NOUN
ap-10625	202	4	.	.	PUNCT
ap-10625	203	1	65	65	NUM
ap-10625	203	2	no	no	NOUN
ap-10625	203	3	.	.	PUNCT
ap-10625	204	1	5/2025	5/2025	NUM
ap-10625	204	2	dirac	dirac	NOUN
ap-10625	204	3	fermion	fermion	NOUN
ap-10625	204	4	in	in	ADP
ap-10625	204	5	a	a	DET
ap-10625	204	6	time	time	NOUN
ap-10625	204	7	-	-	PUNCT
ap-10625	204	8	dependent	dependent	ADJ
ap-10625	204	9	spherical	spherical	ADJ
ap-10625	204	10	box	box	NOUN
ap-10625	204	11	was	be	AUX
ap-10625	204	12	found	find	VERB
ap-10625	204	13	,	,	PUNCT
ap-10625	204	14	by	by	ADP
ap-10625	204	15	considering	consider	VERB
ap-10625	204	16	the	the	DET
ap-10625	204	17	wave	wave	NOUN
ap-10625	204	18	packet	packet	NOUN
ap-10625	204	19	motion	motion	NOUN
ap-10625	204	20	described	describe	VERB
ap-10625	204	21	by	by	ADP
ap-10625	204	22	the	the	DET
ap-10625	204	23	time	time	NOUN
ap-10625	204	24	-	-	PUNCT
ap-10625	204	25	dependent	dependent	ADJ
ap-10625	204	26	dirac	dirac	NOUN
ap-10625	204	27	equation	equation	NOUN
ap-10625	204	28	,	,	PUNCT
ap-10625	204	29	that	that	SCONJ
ap-10625	204	30	the	the	DET
ap-10625	204	31	average	average	ADJ
ap-10625	204	32	coordinate	coordinate	NOUN
ap-10625	204	33	oscillates	oscillate	NOUN
ap-10625	204	34	as	as	ADP
ap-10625	204	35	a	a	DET
ap-10625	204	36	function	function	NOUN
ap-10625	204	37	of	of	ADP
ap-10625	204	38	time	time	NOUN
ap-10625	204	39	.	.	PUNCT
ap-10625	205	1	here	here	ADV
ap-10625	205	2	,	,	PUNCT
ap-10625	205	3	we	we	PRON
ap-10625	205	4	consider	consider	VERB
ap-10625	205	5	this	this	DET
ap-10625	205	6	phenomenon	phenomenon	NOUN
ap-10625	205	7	for	for	ADP
ap-10625	205	8	a	a	DET
ap-10625	205	9	dirac	dirac	NOUN
ap-10625	205	10	particle	particle	NOUN
ap-10625	205	11	under	under	ADP
ap-10625	205	12	dynamical	dynamical	ADJ
ap-10625	205	13	confinement	confinement	NOUN
ap-10625	205	14	provided	provide	VERB
ap-10625	205	15	by	by	ADP
ap-10625	205	16	a	a	DET
ap-10625	205	17	timedependent	timedependent	NOUN
ap-10625	205	18	box	box	NOUN
ap-10625	205	19	.	.	PUNCT
ap-10625	206	1	the	the	DET
ap-10625	206	2	main	main	ADJ
ap-10625	206	3	characteristics	characteristic	NOUN
ap-10625	206	4	of	of	ADP
ap-10625	206	5	zitterbewegung	zitterbewegung	PROPN
ap-10625	206	6	,	,	PUNCT
ap-10625	206	7	the	the	DET
ap-10625	206	8	average	average	ADJ
ap-10625	206	9	position	position	NOUN
ap-10625	206	10	,	,	PUNCT
ap-10625	206	11	is	be	AUX
ap-10625	206	12	determined	determine	VERB
ap-10625	206	13	as	as	ADP
ap-10625	206	14	:	:	PUNCT
ap-10625	206	15	⟨r(t)⟩	⟨r(t)⟩	NOUN
ap-10625	206	16	=	=	SYM
ap-10625	206	17	⟨ψ(r	⟨ψ(r	PROPN
ap-10625	206	18	,	,	PUNCT
ap-10625	206	19	t)|r|ψ(r	t)|r|ψ(r	NUM
ap-10625	206	20	,	,	PUNCT
ap-10625	206	21	t)⟩.	t)⟩.	NOUN
ap-10625	206	22	(	(	PUNCT
ap-10625	206	23	23	23	NUM
ap-10625	206	24	)	)	PUNCT
ap-10625	206	25	using	use	VERB
ap-10625	206	26	equation	equation	NOUN
ap-10625	206	27	(	(	PUNCT
ap-10625	206	28	15	15	NUM
ap-10625	206	29	)	)	PUNCT
ap-10625	206	30	⟨r(t)⟩	⟨r(t)⟩	NOUN
ap-10625	206	31	can	can	AUX
ap-10625	206	32	be	be	AUX
ap-10625	206	33	written	write	VERB
ap-10625	206	34	as	as	SCONJ
ap-10625	206	35	follows	follow	VERB
ap-10625	206	36	:	:	PUNCT
ap-10625	206	37	⟨r(t)⟩	⟨r(t)⟩	NOUN
ap-10625	206	38	=	=	SYM
ap-10625	207	1	r0(t	r0(t	VERB
ap-10625	207	2	)	)	PUNCT
ap-10625	207	3	∑	∑	NUM
ap-10625	207	4	n	n	CCONJ
ap-10625	207	5	,	,	PUNCT
ap-10625	207	6	m	m	VERB
ap-10625	207	7	a∗	a∗	ADJ
ap-10625	207	8	n(τ(t))am(τ(t))vnm	n(τ(t))am(τ(t))vnm	ADJ
ap-10625	207	9	,	,	PUNCT
ap-10625	207	10	(	(	PUNCT
ap-10625	207	11	24	24	NUM
ap-10625	207	12	)	)	PUNCT
ap-10625	207	13	where	where	SCONJ
ap-10625	207	14	the	the	DET
ap-10625	207	15	matrix	matrix	NOUN
ap-10625	207	16	elements	element	NOUN
ap-10625	207	17	:	:	PUNCT
ap-10625	208	1	vnm	vnm	PROPN
ap-10625	208	2	=	=	SYM
ap-10625	208	3	∫	∫	PROPN
ap-10625	208	4	1	1	NUM
ap-10625	208	5	0	0	NUM
ap-10625	208	6	ψn(y)†yψm(y	ψn(y)†yψm(y	NOUN
ap-10625	208	7	)	)	PUNCT
ap-10625	208	8	dy	dy	NOUN
ap-10625	208	9	were	be	AUX
ap-10625	208	10	computed	compute	VERB
ap-10625	208	11	numerically	numerically	ADV
ap-10625	208	12	.	.	PUNCT
ap-10625	209	1	for	for	ADP
ap-10625	209	2	a	a	DET
ap-10625	209	3	massless	massless	ADJ
ap-10625	209	4	dirac	dirac	NOUN
ap-10625	209	5	particle	particle	NOUN
ap-10625	209	6	,	,	PUNCT
ap-10625	209	7	i.e.	i.e.	X
ap-10625	209	8	for	for	ADP
ap-10625	209	9	m	m	PROPN
ap-10625	209	10	=	=	SYM
ap-10625	209	11	0	0	NUM
ap-10625	209	12	,	,	PUNCT
ap-10625	209	13	the	the	DET
ap-10625	209	14	average	average	ADJ
ap-10625	209	15	coordinate	coordinate	NOUN
ap-10625	209	16	can	can	AUX
ap-10625	209	17	be	be	AUX
ap-10625	209	18	defined	define	VERB
ap-10625	209	19	using	use	VERB
ap-10625	209	20	(	(	PUNCT
ap-10625	209	21	18	18	NUM
ap-10625	209	22	)	)	PUNCT
ap-10625	209	23	for	for	ADP
ap-10625	209	24	r0(t	r0(t	NOUN
ap-10625	209	25	)	)	PUNCT
ap-10625	209	26	=	=	SYM
ap-10625	209	27	a+bt	a+bt	ADJ
ap-10625	209	28	as	as	SCONJ
ap-10625	209	29	follows	follow	VERB
ap-10625	209	30	:	:	PUNCT
ap-10625	209	31	⟨r(t)⟩	⟨r(t)⟩	NOUN
ap-10625	209	32	=	=	SYM
ap-10625	209	33	(	(	PUNCT
ap-10625	209	34	a+bt	a+bt	ADJ
ap-10625	209	35	)	)	PUNCT
ap-10625	209	36	∑	∑	DET
ap-10625	209	37	n	n	CCONJ
ap-10625	209	38	,	,	PUNCT
ap-10625	209	39	m	m	PROPN
ap-10625	209	40	a∗	a∗	PROPN
ap-10625	209	41	n(0)am(0	n(0)am(0	NOUN
ap-10625	209	42	)	)	PUNCT
ap-10625	210	1	ei	ei	NOUN
ap-10625	210	2	π(n−m	π(n−m	PROPN
ap-10625	210	3	)	)	PUNCT
ap-10625	210	4	b	b	PROPN
ap-10625	211	1	ln(1	ln(1	NOUN
ap-10625	211	2	+	+	NOUN
ap-10625	211	3	b	b	NOUN
ap-10625	211	4	a	a	DET
ap-10625	211	5	t)vnm	t)vnm	PROPN
ap-10625	211	6	.	.	PUNCT
ap-10625	212	1	(	(	PUNCT
ap-10625	212	2	25	25	NUM
ap-10625	212	3	)	)	PUNCT
ap-10625	212	4	in	in	ADP
ap-10625	212	5	figure	figure	NOUN
ap-10625	212	6	3	3	NUM
ap-10625	212	7	,	,	PUNCT
ap-10625	212	8	the	the	DET
ap-10625	212	9	average	average	ADJ
ap-10625	212	10	position	position	NOUN
ap-10625	212	11	is	be	AUX
ap-10625	212	12	plotted	plot	VERB
ap-10625	212	13	as	as	ADP
ap-10625	212	14	a	a	DET
ap-10625	212	15	function	function	NOUN
ap-10625	212	16	of	of	ADP
ap-10625	212	17	time	time	NOUN
ap-10625	212	18	for	for	ADP
ap-10625	212	19	three	three	NUM
ap-10625	212	20	regimes	regime	NOUN
ap-10625	212	21	of	of	ADP
ap-10625	212	22	the	the	DET
ap-10625	212	23	wall	wall	NOUN
ap-10625	212	24	’s	’s	PART
ap-10625	212	25	motion	motion	NOUN
ap-10625	212	26	,	,	PUNCT
ap-10625	212	27	for	for	ADP
ap-10625	212	28	linearly	linearly	ADV
ap-10625	212	29	expanding	expand	VERB
ap-10625	212	30	,	,	PUNCT
ap-10625	212	31	contracting	contracting	NOUN
ap-10625	212	32	,	,	PUNCT
ap-10625	212	33	and	and	CCONJ
ap-10625	212	34	harmonically	harmonically	ADV
ap-10625	212	35	oscillating	oscillate	VERB
ap-10625	212	36	walls	wall	NOUN
ap-10625	212	37	.	.	PUNCT
ap-10625	213	1	one	one	PRON
ap-10625	213	2	can	can	AUX
ap-10625	213	3	clearly	clearly	ADV
ap-10625	213	4	see	see	VERB
ap-10625	213	5	that	that	DET
ap-10625	213	6	zitterbewegung	zitterbewegung	NOUN
ap-10625	213	7	can	can	AUX
ap-10625	213	8	be	be	AUX
ap-10625	213	9	observed	observe	VERB
ap-10625	213	10	for	for	ADP
ap-10625	213	11	all	all	DET
ap-10625	213	12	three	three	NUM
ap-10625	213	13	regimes	regime	NOUN
ap-10625	213	14	.	.	PUNCT
ap-10625	214	1	3.3	3.3	NUM
ap-10625	214	2	.	.	PUNCT
ap-10625	214	3	quantum	quantum	NOUN
ap-10625	214	4	force	force	NOUN
ap-10625	214	5	the	the	DET
ap-10625	214	6	expectation	expectation	NOUN
ap-10625	214	7	value	value	NOUN
ap-10625	214	8	of	of	ADP
ap-10625	214	9	the	the	DET
ap-10625	214	10	force	force	NOUN
ap-10625	214	11	,	,	PUNCT
ap-10625	214	12	⟨f	⟨f	PUNCT
ap-10625	214	13	(	(	PUNCT
ap-10625	214	14	t)⟩	t)⟩	NOUN
ap-10625	214	15	acting	act	VERB
ap-10625	214	16	on	on	ADP
ap-10625	214	17	a	a	DET
ap-10625	214	18	dirac	dirac	NOUN
ap-10625	214	19	particle	particle	NOUN
ap-10625	214	20	can	can	AUX
ap-10625	214	21	be	be	AUX
ap-10625	214	22	determined	determine	VERB
ap-10625	214	23	as	as	ADP
ap-10625	214	24	:	:	PUNCT
ap-10625	214	25	⟨f	⟨f	PUNCT
ap-10625	214	26	(	(	PUNCT
ap-10625	214	27	t)⟩	t)⟩	NOUN
ap-10625	214	28	=	=	SYM
ap-10625	214	29	−	−	PROPN
ap-10625	214	30	〈	〈	PROPN
ap-10625	214	31	ψ	ψ	NOUN
ap-10625	214	32	∣∣∣∣	∣∣∣∣	NOUN
ap-10625	214	33	∂h	∂h	PROPN
ap-10625	214	34	∂r0(t	∂r0(t	PROPN
ap-10625	214	35	)	)	PUNCT
ap-10625	214	36	∣∣∣∣ψ	∣∣∣∣ψ	NOUN
ap-10625	214	37	〉	〉	NOUN
ap-10625	214	38	=	=	SYM
ap-10625	214	39	−	−	PROPN
ap-10625	214	40	∂	∂	NUM
ap-10625	214	41	∂r0(t	∂r0(t	PROPN
ap-10625	214	42	)	)	PUNCT
ap-10625	214	43	⟨e(t)⟩	⟨e(t)⟩	PROPN
ap-10625	214	44	,	,	PUNCT
ap-10625	214	45	(	(	PUNCT
ap-10625	214	46	26	26	NUM
ap-10625	214	47	)	)	PUNCT
ap-10625	214	48	where	where	SCONJ
ap-10625	214	49	⟨e(t)⟩	⟨e(t)⟩	NOUN
ap-10625	214	50	is	be	AUX
ap-10625	214	51	the	the	DET
ap-10625	214	52	average	average	ADJ
ap-10625	214	53	kinetic	kinetic	ADJ
ap-10625	214	54	energy	energy	NOUN
ap-10625	214	55	of	of	ADP
ap-10625	214	56	the	the	DET
ap-10625	214	57	particle	particle	NOUN
ap-10625	214	58	.	.	PUNCT
ap-10625	215	1	using	use	VERB
ap-10625	215	2	the	the	DET
ap-10625	215	3	expansion	expansion	NOUN
ap-10625	215	4	(	(	PUNCT
ap-10625	215	5	22	22	NUM
ap-10625	215	6	)	)	PUNCT
ap-10625	215	7	and	and	CCONJ
ap-10625	215	8	equations	equation	NOUN
ap-10625	215	9	(	(	PUNCT
ap-10625	215	10	16	16	NUM
ap-10625	215	11	):	):	PUNCT
ap-10625	215	12	⟨f	⟨f	PUNCT
ap-10625	215	13	(	(	PUNCT
ap-10625	215	14	t)⟩	t)⟩	NOUN
ap-10625	215	15	=	=	SYM
ap-10625	215	16	−	−	PROPN
ap-10625	215	17	1	1	NUM
ap-10625	215	18	ṙ0	ṙ0	PROPN
ap-10625	215	19	∂	∂	NUM
ap-10625	215	20	∂t	∂t	PROPN
ap-10625	215	21	⟨e(t)⟩	⟨e(t)⟩	NOUN
ap-10625	215	22	=	=	SYM
ap-10625	215	23	∞∑	∞∑	PRON
ap-10625	215	24	n=0	n=0	NUM
ap-10625	215	25	fn(t	fn(t	NUM
ap-10625	215	26	)	)	PUNCT
ap-10625	215	27	,	,	PUNCT
ap-10625	216	1	(	(	PUNCT
ap-10625	216	2	27	27	NUM
ap-10625	216	3	)	)	PUNCT
ap-10625	216	4	where	where	SCONJ
ap-10625	216	5	:	:	PUNCT
ap-10625	216	6	fn(t	fn(t	NUM
ap-10625	216	7	)	)	PUNCT
ap-10625	216	8	=	=	SYM
ap-10625	216	9	1	1	NUM
ap-10625	216	10	r0(t)2	r0(t)2	PROPN
ap-10625	216	11	(	(	PUNCT
ap-10625	216	12	|an(τ(t))|2	|an(τ(t))|2	X
ap-10625	216	13	−	−	ADP
ap-10625	216	14	|a−n(τ(t))|2	|a−n(τ(t))|2	NOUN
ap-10625	216	15	)	)	PUNCT
ap-10625	216	16	(	(	PUNCT
ap-10625	216	17	28	28	NUM
ap-10625	216	18	)	)	PUNCT
ap-10625	216	19	n	n	PRON
ap-10625	216	20	∈	∈	PROPN
ap-10625	216	21	n.	n.	NOUN
ap-10625	216	22	apparently	apparently	ADV
ap-10625	216	23	,	,	PUNCT
ap-10625	216	24	f0(t	f0(t	PROPN
ap-10625	216	25	)	)	PUNCT
ap-10625	216	26	=	=	NOUN
ap-10625	217	1	0	0	X
ap-10625	217	2	.	.	PUNCT
ap-10625	218	1	the	the	DET
ap-10625	218	2	signs	sign	NOUN
ap-10625	218	3	in	in	ADP
ap-10625	218	4	equation	equation	NOUN
ap-10625	218	5	(	(	PUNCT
ap-10625	218	6	28	28	NUM
ap-10625	218	7	)	)	PUNCT
ap-10625	218	8	suggest	suggest	VERB
ap-10625	218	9	that	that	SCONJ
ap-10625	218	10	an	an	DET
ap-10625	218	11	increase	increase	NOUN
ap-10625	218	12	in	in	ADP
ap-10625	218	13	the	the	DET
ap-10625	218	14	positive	positive	ADJ
ap-10625	218	15	energy	energy	NOUN
ap-10625	218	16	components	component	NOUN
ap-10625	218	17	of	of	ADP
ap-10625	218	18	the	the	DET
ap-10625	218	19	particle	particle	NOUN
ap-10625	218	20	state	state	NOUN
ap-10625	218	21	requires	require	VERB
ap-10625	218	22	a	a	DET
ap-10625	218	23	positive	positive	ADJ
ap-10625	218	24	force	force	NOUN
ap-10625	218	25	and	and	CCONJ
ap-10625	218	26	its	its	PRON
ap-10625	218	27	work	work	NOUN
ap-10625	218	28	,	,	PUNCT
ap-10625	218	29	whereas	whereas	SCONJ
ap-10625	218	30	an	an	DET
ap-10625	218	31	increase	increase	NOUN
ap-10625	218	32	in	in	ADP
ap-10625	218	33	the	the	DET
ap-10625	218	34	negative	negative	ADJ
ap-10625	218	35	energy	energy	NOUN
ap-10625	218	36	components	component	NOUN
ap-10625	218	37	requires	require	VERB
ap-10625	218	38	a	a	DET
ap-10625	218	39	negative	negative	ADJ
ap-10625	218	40	force	force	NOUN
ap-10625	218	41	.	.	PUNCT
ap-10625	219	1	figure	figure	VERB
ap-10625	219	2	4	4	NUM
ap-10625	219	3	presents	present	VERB
ap-10625	219	4	the	the	DET
ap-10625	219	5	plots	plot	NOUN
ap-10625	219	6	of	of	ADP
ap-10625	219	7	the	the	DET
ap-10625	219	8	average	average	ADJ
ap-10625	219	9	quantum	quantum	ADJ
ap-10625	219	10	force	force	NOUN
ap-10625	219	11	,	,	PUNCT
ap-10625	219	12	⟨f	⟨f	X
ap-10625	219	13	(	(	PUNCT
ap-10625	219	14	t)⟩	t)⟩	NOUN
ap-10625	219	15	as	as	ADP
ap-10625	219	16	a	a	DET
ap-10625	219	17	function	function	NOUN
ap-10625	219	18	of	of	ADP
ap-10625	219	19	time	time	NOUN
ap-10625	219	20	for	for	ADP
ap-10625	219	21	three	three	NUM
ap-10625	219	22	regimes	regime	NOUN
ap-10625	219	23	of	of	ADP
ap-10625	219	24	time	time	NOUN
ap-10625	219	25	-	-	PUNCT
ap-10625	219	26	dependence	dependence	NOUN
ap-10625	219	27	of	of	ADP
ap-10625	219	28	the	the	DET
ap-10625	219	29	radius	radius	NOUN
ap-10625	219	30	,	,	PUNCT
ap-10625	219	31	linearly	linearly	ADV
ap-10625	219	32	expanding	expand	VERB
ap-10625	219	33	,	,	PUNCT
ap-10625	219	34	contracting	contracting	NOUN
ap-10625	219	35	,	,	PUNCT
ap-10625	219	36	and	and	CCONJ
ap-10625	219	37	harmonically	harmonically	ADV
ap-10625	219	38	oscillating	oscillate	VERB
ap-10625	219	39	ones	one	NOUN
ap-10625	219	40	.	.	PUNCT
ap-10625	220	1	the	the	DET
ap-10625	220	2	force	force	NOUN
ap-10625	220	3	grows	grow	VERB
ap-10625	220	4	as	as	ADP
ap-10625	220	5	a	a	DET
ap-10625	220	6	function	function	NOUN
ap-10625	220	7	of	of	ADP
ap-10625	220	8	time	time	NOUN
ap-10625	220	9	for	for	ADP
ap-10625	220	10	the	the	DET
ap-10625	220	11	contracting	contracting	NOUN
ap-10625	220	12	box	box	NOUN
ap-10625	220	13	,	,	PUNCT
ap-10625	220	14	while	while	SCONJ
ap-10625	220	15	it	it	PRON
ap-10625	220	16	is	be	AUX
ap-10625	220	17	observed	observe	VERB
ap-10625	220	18	to	to	PART
ap-10625	220	19	decay	decay	VERB
ap-10625	220	20	for	for	ADP
ap-10625	220	21	the	the	DET
ap-10625	220	22	expanding	expand	VERB
ap-10625	220	23	box	box	NOUN
ap-10625	220	24	.	.	PUNCT
ap-10625	221	1	it	it	PRON
ap-10625	221	2	oscillates	oscillate	VERB
ap-10625	221	3	for	for	ADP
ap-10625	221	4	the	the	DET
ap-10625	221	5	oscillating	oscillate	VERB
ap-10625	221	6	wall	wall	NOUN
ap-10625	221	7	.	.	PUNCT
ap-10625	222	1	0	0	NUM
ap-10625	223	1	10	10	NUM
ap-10625	223	2	20	20	NUM
ap-10625	223	3	30	30	NUM
ap-10625	223	4	40	40	NUM
ap-10625	223	5	50	50	NUM
ap-10625	223	6	t	t	NOUN
ap-10625	223	7	0.04	0.04	NUM
ap-10625	223	8	0.06	0.06	NUM
ap-10625	223	9	0.08	0.08	NUM
ap-10625	223	10	0.1	0.1	NUM
ap-10625	223	11	0.12	0.12	NUM
ap-10625	223	12	0.14	0.14	NUM
ap-10625	223	13	0.16	0.16	NUM
ap-10625	223	14	<	<	X
ap-10625	223	15	r	r	X
ap-10625	223	16	(	(	PUNCT
ap-10625	223	17	t	t	PROPN
ap-10625	223	18	)	)	PUNCT
ap-10625	223	19	>	>	PUNCT
ap-10625	224	1	r	r	NOUN
ap-10625	224	2	0	0	NUM
ap-10625	224	3	(	(	PUNCT
ap-10625	224	4	t)=5	t)=5	ADP
ap-10625	224	5	+	+	SYM
ap-10625	224	6	0.1	0.1	NUM
ap-10625	224	7	t	t	NOUN
ap-10625	224	8	r	r	NOUN
ap-10625	224	9	0	0	NUM
ap-10625	224	10	(	(	PUNCT
ap-10625	224	11	t)=5	t)=5	PROPN
ap-10625	224	12	-	-	PUNCT
ap-10625	224	13	0.05	0.05	NUM
ap-10625	224	14	t	t	NOUN
ap-10625	224	15	r	r	NOUN
ap-10625	224	16	0	0	NUM
ap-10625	224	17	(	(	PUNCT
ap-10625	224	18	t)=5	t)=5	PROPN
ap-10625	224	19	+	+	SYM
ap-10625	224	20	0.1sin(2	0.1sin(2	ADJ
ap-10625	224	21	t	t	NOUN
ap-10625	224	22	)	)	PUNCT
ap-10625	224	23	figure	figure	NOUN
ap-10625	224	24	3	3	NUM
ap-10625	224	25	.	.	NOUN
ap-10625	224	26	time	time	NOUN
ap-10625	224	27	-	-	PUNCT
ap-10625	224	28	dependence	dependence	NOUN
ap-10625	224	29	of	of	ADP
ap-10625	224	30	the	the	DET
ap-10625	224	31	average	average	ADJ
ap-10625	224	32	position	position	NOUN
ap-10625	224	33	of	of	ADP
ap-10625	224	34	a	a	DET
ap-10625	224	35	dirac	dirac	NOUN
ap-10625	224	36	particle	particle	NOUN
ap-10625	224	37	in	in	ADP
ap-10625	224	38	a	a	DET
ap-10625	224	39	box	box	NOUN
ap-10625	224	40	with	with	ADP
ap-10625	224	41	three	three	NUM
ap-10625	224	42	regimes	regime	NOUN
ap-10625	224	43	of	of	ADP
ap-10625	224	44	wall	wall	NOUN
ap-10625	224	45	’s	’s	PART
ap-10625	224	46	motion	motion	NOUN
ap-10625	224	47	(	(	PUNCT
ap-10625	224	48	r0(t	r0(t	NOUN
ap-10625	224	49	)	)	PUNCT
ap-10625	224	50	=	=	SYM
ap-10625	224	51	5	5	NUM
ap-10625	225	1	+	+	NUM
ap-10625	225	2	0.1	0.1	NUM
ap-10625	225	3	t	t	NOUN
ap-10625	225	4	,	,	PUNCT
ap-10625	225	5	r0(t	r0(t	PROPN
ap-10625	225	6	)	)	PUNCT
ap-10625	225	7	=	=	SYM
ap-10625	225	8	5	5	NUM
ap-10625	225	9	−	−	NOUN
ap-10625	225	10	0.05	0.05	NUM
ap-10625	225	11	t	t	NOUN
ap-10625	225	12	and	and	CCONJ
ap-10625	225	13	r0(t	r0(t	PROPN
ap-10625	225	14	)	)	PUNCT
ap-10625	225	15	=	=	SYM
ap-10625	225	16	5	5	NUM
ap-10625	225	17	+	+	NUM
ap-10625	225	18	0.1	0.1	NUM
ap-10625	225	19	sin	sin	NOUN
ap-10625	225	20	2	2	NUM
ap-10625	225	21	t	t	NOUN
ap-10625	225	22	)	)	PUNCT
ap-10625	225	23	for	for	ADP
ap-10625	225	24	m	m	PROPN
ap-10625	225	25	=	=	NOUN
ap-10625	225	26	1	1	X
ap-10625	225	27	.	.	PUNCT
ap-10625	226	1	the	the	DET
ap-10625	226	2	wave	wave	NOUN
ap-10625	226	3	packet	packet	NOUN
ap-10625	226	4	’s	’s	PART
ap-10625	226	5	width	width	NOUN
ap-10625	226	6	,	,	PUNCT
ap-10625	226	7	initial	initial	ADJ
ap-10625	226	8	position	position	NOUN
ap-10625	226	9	of	of	ADP
ap-10625	226	10	the	the	DET
ap-10625	226	11	centre	centre	NOUN
ap-10625	226	12	of	of	ADP
ap-10625	226	13	mass	mass	PROPN
ap-10625	226	14	,	,	PUNCT
ap-10625	226	15	initial	initial	ADJ
ap-10625	226	16	velocity	velocity	NOUN
ap-10625	226	17	and	and	CCONJ
ap-10625	226	18	the	the	DET
ap-10625	226	19	initial	initial	ADJ
ap-10625	226	20	spin	spin	NOUN
ap-10625	226	21	polarisation	polarisation	NOUN
ap-10625	226	22	are	be	AUX
ap-10625	226	23	chosen	choose	VERB
ap-10625	226	24	as	as	ADP
ap-10625	226	25	d	d	PROPN
ap-10625	226	26	=	=	SYM
ap-10625	226	27	0.1	0.1	NUM
ap-10625	226	28	,	,	PUNCT
ap-10625	226	29	r0	r0	NOUN
ap-10625	226	30	=	=	SYM
ap-10625	226	31	r0(0	r0(0	PROPN
ap-10625	226	32	)	)	PUNCT
ap-10625	226	33	2	2	NUM
ap-10625	226	34	,	,	PUNCT
ap-10625	226	35	v0	v0	NOUN
ap-10625	226	36	=	=	SYM
ap-10625	226	37	0	0	NUM
ap-10625	226	38	,	,	PUNCT
ap-10625	226	39	s1	s1	NOUN
ap-10625	226	40	=	=	SYM
ap-10625	226	41	1	1	NUM
ap-10625	226	42	and	and	CCONJ
ap-10625	226	43	s2	s2	VERB
ap-10625	226	44	=	=	SYM
ap-10625	226	45	0	0	NUM
ap-10625	226	46	,	,	PUNCT
ap-10625	226	47	respectively	respectively	ADV
ap-10625	226	48	.	.	PUNCT
ap-10625	227	1	0	0	NUM
ap-10625	228	1	10	10	NUM
ap-10625	228	2	20	20	NUM
ap-10625	228	3	30	30	NUM
ap-10625	228	4	40	40	NUM
ap-10625	228	5	50	50	NUM
ap-10625	228	6	t	t	NOUN
ap-10625	228	7	0	0	NUM
ap-10625	228	8	10	10	NUM
ap-10625	228	9	20	20	NUM
ap-10625	228	10	30	30	NUM
ap-10625	228	11	40	40	NUM
ap-10625	228	12	50	50	NUM
ap-10625	228	13	60	60	NUM
ap-10625	228	14	<	<	X
ap-10625	228	15	f	f	X
ap-10625	228	16	(	(	PUNCT
ap-10625	228	17	t	t	PROPN
ap-10625	228	18	)	)	PUNCT
ap-10625	228	19	>	>	X
ap-10625	229	1	r	r	NOUN
ap-10625	229	2	0	0	NUM
ap-10625	229	3	(	(	PUNCT
ap-10625	229	4	t)=5	t)=5	NUM
ap-10625	229	5	+	+	SYM
ap-10625	229	6	0.05	0.05	NUM
ap-10625	229	7	t	t	NOUN
ap-10625	229	8	r	r	NOUN
ap-10625	229	9	0	0	NUM
ap-10625	229	10	(	(	PUNCT
ap-10625	229	11	t)=5	t)=5	PROPN
ap-10625	229	12	-	-	PUNCT
ap-10625	229	13	0.05	0.05	NUM
ap-10625	229	14	t	t	NOUN
ap-10625	229	15	r	r	NOUN
ap-10625	229	16	0	0	NUM
ap-10625	229	17	(	(	PUNCT
ap-10625	229	18	t)=5	t)=5	PROPN
ap-10625	229	19	+	+	SYM
ap-10625	229	20	0.1sin(0.5	0.1sin(0.5	PROPN
ap-10625	229	21	t	t	NOUN
ap-10625	229	22	)	)	PUNCT
ap-10625	229	23	figure	figure	NOUN
ap-10625	229	24	4	4	NUM
ap-10625	229	25	.	.	NOUN
ap-10625	229	26	time	time	NOUN
ap-10625	229	27	-	-	PUNCT
ap-10625	229	28	dependence	dependence	NOUN
ap-10625	229	29	of	of	ADP
ap-10625	229	30	the	the	DET
ap-10625	229	31	average	average	ADJ
ap-10625	229	32	force	force	NOUN
ap-10625	229	33	of	of	ADP
ap-10625	229	34	a	a	DET
ap-10625	229	35	dirac	dirac	NOUN
ap-10625	229	36	particle	particle	NOUN
ap-10625	229	37	in	in	ADP
ap-10625	229	38	a	a	DET
ap-10625	229	39	box	box	NOUN
ap-10625	229	40	with	with	ADP
ap-10625	229	41	three	three	NUM
ap-10625	229	42	regimes	regime	NOUN
ap-10625	229	43	of	of	ADP
ap-10625	229	44	the	the	DET
ap-10625	229	45	wall	wall	NOUN
ap-10625	229	46	’s	’s	PART
ap-10625	229	47	motion	motion	NOUN
ap-10625	229	48	(	(	PUNCT
ap-10625	229	49	r0(t	r0(t	NOUN
ap-10625	229	50	)	)	PUNCT
ap-10625	229	51	=	=	SYM
ap-10625	229	52	5	5	NUM
ap-10625	230	1	+	+	NUM
ap-10625	230	2	0.05	0.05	NUM
ap-10625	230	3	t	t	NOUN
ap-10625	230	4	,	,	PUNCT
ap-10625	230	5	r0(t	r0(t	PROPN
ap-10625	230	6	)	)	PUNCT
ap-10625	230	7	=	=	SYM
ap-10625	230	8	5	5	NUM
ap-10625	230	9	−	−	NOUN
ap-10625	230	10	0.05	0.05	NUM
ap-10625	230	11	t	t	NOUN
ap-10625	230	12	and	and	CCONJ
ap-10625	230	13	r0(t	r0(t	PROPN
ap-10625	230	14	)	)	PUNCT
ap-10625	230	15	=	=	SYM
ap-10625	230	16	5	5	NUM
ap-10625	230	17	+	+	SYM
ap-10625	230	18	0.1	0.1	NUM
ap-10625	230	19	sin	sin	NOUN
ap-10625	230	20	0.5	0.5	NUM
ap-10625	230	21	t	t	NOUN
ap-10625	230	22	)	)	PUNCT
ap-10625	230	23	for	for	ADP
ap-10625	230	24	m	m	PROPN
ap-10625	230	25	=	=	NOUN
ap-10625	230	26	1	1	X
ap-10625	230	27	.	.	PUNCT
ap-10625	231	1	the	the	DET
ap-10625	231	2	wave	wave	NOUN
ap-10625	231	3	packet	packet	NOUN
ap-10625	231	4	’s	’s	PART
ap-10625	231	5	width	width	NOUN
ap-10625	231	6	,	,	PUNCT
ap-10625	231	7	initial	initial	ADJ
ap-10625	231	8	position	position	NOUN
ap-10625	231	9	of	of	ADP
ap-10625	231	10	the	the	DET
ap-10625	231	11	centre	centre	NOUN
ap-10625	231	12	of	of	ADP
ap-10625	231	13	mass	mass	PROPN
ap-10625	231	14	,	,	PUNCT
ap-10625	231	15	initial	initial	ADJ
ap-10625	231	16	velocity	velocity	NOUN
ap-10625	231	17	,	,	PUNCT
ap-10625	231	18	and	and	CCONJ
ap-10625	231	19	the	the	DET
ap-10625	231	20	initial	initial	ADJ
ap-10625	231	21	spin	spin	NOUN
ap-10625	231	22	polarisation	polarisation	NOUN
ap-10625	231	23	are	be	AUX
ap-10625	231	24	chosen	choose	VERB
ap-10625	231	25	as	as	ADP
ap-10625	231	26	d	d	PROPN
ap-10625	231	27	=	=	SYM
ap-10625	231	28	0.1	0.1	NUM
ap-10625	231	29	,	,	PUNCT
ap-10625	231	30	r0	r0	NOUN
ap-10625	231	31	=	=	SYM
ap-10625	231	32	r0(0	r0(0	PROPN
ap-10625	231	33	)	)	PUNCT
ap-10625	231	34	2	2	NUM
ap-10625	231	35	,	,	PUNCT
ap-10625	231	36	v0	v0	NOUN
ap-10625	231	37	=	=	SYM
ap-10625	231	38	0	0	NUM
ap-10625	231	39	,	,	PUNCT
ap-10625	231	40	s1	s1	NOUN
ap-10625	231	41	=	=	SYM
ap-10625	231	42	1	1	NUM
ap-10625	231	43	and	and	CCONJ
ap-10625	231	44	s2	s2	VERB
ap-10625	231	45	=	=	SYM
ap-10625	231	46	0	0	NUM
ap-10625	231	47	,	,	PUNCT
ap-10625	231	48	respectively	respectively	ADV
ap-10625	231	49	.	.	PUNCT
ap-10625	232	1	3.4	3.4	NUM
ap-10625	232	2	.	.	PUNCT
ap-10625	232	3	berry	berry	NOUN
ap-10625	232	4	phase	phase	NOUN
ap-10625	232	5	during	during	ADP
ap-10625	232	6	an	an	DET
ap-10625	232	7	adiabatic	adiabatic	ADJ
ap-10625	232	8	change	change	NOUN
ap-10625	232	9	of	of	ADP
ap-10625	232	10	the	the	DET
ap-10625	232	11	radius	radius	NOUN
ap-10625	232	12	r0	r0	NOUN
ap-10625	232	13	,	,	PUNCT
ap-10625	232	14	and	and	CCONJ
ap-10625	232	15	consequently	consequently	ADV
ap-10625	232	16	the	the	DET
ap-10625	232	17	effective	effective	ADJ
ap-10625	232	18	mass	mass	NOUN
ap-10625	232	19	m	m	VERB
ap-10625	232	20	,	,	PUNCT
ap-10625	232	21	along	along	ADP
ap-10625	232	22	a	a	DET
ap-10625	232	23	closed	closed	ADJ
ap-10625	232	24	curve	curve	NOUN
ap-10625	232	25	c	c	NOUN
ap-10625	232	26	,	,	PUNCT
ap-10625	232	27	the	the	DET
ap-10625	232	28	eigenfunctions	eigenfunction	NOUN
ap-10625	232	29	can	can	AUX
ap-10625	232	30	aquire	aquire	VERB
ap-10625	232	31	a	a	DET
ap-10625	232	32	geometric	geometric	ADJ
ap-10625	232	33	(	(	PUNCT
ap-10625	232	34	berry	berry	NOUN
ap-10625	232	35	)	)	PUNCT
ap-10625	232	36	phase	phase	NOUN
ap-10625	232	37	[	[	X
ap-10625	232	38	21	21	NUM
ap-10625	232	39	]	]	PUNCT
ap-10625	232	40	.	.	PUNCT
ap-10625	233	1	self	self	NOUN
ap-10625	233	2	-	-	PUNCT
ap-10625	233	3	adjoint	adjoint	NOUN
ap-10625	233	4	hamiltonians	hamiltonian	NOUN
ap-10625	233	5	corresponding	correspond	VERB
ap-10625	233	6	to	to	ADP
ap-10625	233	7	t	t	PROPN
ap-10625	233	8	form	form	VERB
ap-10625	233	9	a	a	DET
ap-10625	233	10	trivial	trivial	ADJ
ap-10625	233	11	analytic	analytic	ADJ
ap-10625	233	12	family	family	NOUN
ap-10625	233	13	of	of	ADP
ap-10625	233	14	the	the	DET
ap-10625	233	15	type	type	NOUN
ap-10625	233	16	a	a	DET
ap-10625	233	17	(	(	PUNCT
ap-10625	233	18	e.g.	e.g.	ADV
ap-10625	233	19	[	[	X
ap-10625	233	20	22	22	NUM
ap-10625	233	21	,	,	PUNCT
ap-10625	233	22	par	par	NOUN
ap-10625	233	23	.	.	PUNCT
ap-10625	234	1	xii.2	xii.2	PROPN
ap-10625	234	2	]	]	PUNCT
ap-10625	234	3	)	)	PUNCT
ap-10625	235	1	with	with	ADP
ap-10625	235	2	respect	respect	NOUN
ap-10625	235	3	to	to	ADP
ap-10625	235	4	the	the	DET
ap-10625	235	5	parameter	parameter	NOUN
ap-10625	235	6	m	m	PROPN
ap-10625	235	7	.	.	PUNCT
ap-10625	236	1	therefore	therefore	ADV
ap-10625	236	2	,	,	PUNCT
ap-10625	236	3	the	the	DET
ap-10625	236	4	eigenfunctions	eigenfunction	NOUN
ap-10625	236	5	ϕn	ϕn	PRON
ap-10625	236	6	are	be	AUX
ap-10625	236	7	analytic	analytic	ADJ
ap-10625	236	8	in	in	ADP
ap-10625	236	9	m	m	PROPN
ap-10625	236	10	by	by	ADP
ap-10625	236	11	the	the	DET
ap-10625	236	12	kato	kato	PROPN
ap-10625	236	13	-	-	PUNCT
ap-10625	236	14	rellich	rellich	PROPN
ap-10625	236	15	theorem	theorem	VERB
ap-10625	236	16	,	,	PUNCT
ap-10625	236	17	which	which	PRON
ap-10625	236	18	justifies	justify	VERB
ap-10625	236	19	the	the	DET
ap-10625	236	20	interchange	interchange	NOUN
ap-10625	236	21	of	of	ADP
ap-10625	236	22	differentiation	differentiation	NOUN
ap-10625	236	23	and	and	CCONJ
ap-10625	236	24	integration	integration	NOUN
ap-10625	236	25	in	in	ADP
ap-10625	236	26	the	the	DET
ap-10625	236	27	formula	formula	NOUN
ap-10625	236	28	for	for	ADP
ap-10625	236	29	the	the	DET
ap-10625	236	30	berry	berry	NOUN
ap-10625	236	31	phase	phase	NOUN
ap-10625	236	32	[	[	X
ap-10625	236	33	21	21	NUM
ap-10625	236	34	]	]	PUNCT
ap-10625	236	35	.	.	PUNCT
ap-10625	237	1	taking	take	VERB
ap-10625	237	2	551	551	NUM
ap-10625	237	3	k.	k.	NOUN
ap-10625	237	4	matchonov	matchonov	PROPN
ap-10625	237	5	,	,	PUNCT
ap-10625	237	6	d.	d.	PROPN
ap-10625	237	7	matrasulov	matrasulov	PROPN
ap-10625	237	8	,	,	PUNCT
ap-10625	237	9	j.	j.	PROPN
ap-10625	237	10	dittrich	dittrich	PROPN
ap-10625	237	11	acta	acta	PROPN
ap-10625	237	12	polytechnica	polytechnica	PROPN
ap-10625	237	13	into	into	ADP
ap-10625	237	14	account	account	NOUN
ap-10625	237	15	that	that	SCONJ
ap-10625	237	16	the	the	DET
ap-10625	237	17	components	component	NOUN
ap-10625	237	18	of	of	ADP
ap-10625	237	19	eigenfunctions	eigenfunction	NOUN
ap-10625	237	20	ϕn	ϕn	AUX
ap-10625	237	21	have	have	AUX
ap-10625	237	22	constant	constant	ADJ
ap-10625	237	23	phases	phase	NOUN
ap-10625	237	24	and	and	CCONJ
ap-10625	237	25	their	their	PRON
ap-10625	237	26	normalisation	normalisation	NOUN
ap-10625	237	27	,	,	PUNCT
ap-10625	237	28	we	we	PRON
ap-10625	237	29	obtain	obtain	VERB
ap-10625	237	30	:	:	PUNCT
ap-10625	237	31	γn(c	γn(c	NUM
ap-10625	237	32	)	)	PUNCT
ap-10625	238	1	=	=	PUNCT
ap-10625	238	2	i	i	PRON
ap-10625	238	3	∮	∮	VERB
ap-10625	238	4	c	c	VERB
ap-10625	239	1	(	(	PUNCT
ap-10625	239	2	∫	∫	PROPN
ap-10625	239	3	1	1	NUM
ap-10625	239	4	0	0	NUM
ap-10625	239	5	ϕn(m	ϕn(m	PROPN
ap-10625	239	6	,	,	PUNCT
ap-10625	239	7	y)†∂mϕn(m	y)†∂mϕn(m	PROPN
ap-10625	239	8	,	,	PUNCT
ap-10625	239	9	z	z	NOUN
ap-10625	239	10	)	)	PUNCT
ap-10625	239	11	dy	dy	NOUN
ap-10625	239	12	)	)	PUNCT
ap-10625	240	1	dm	dm	PROPN
ap-10625	240	2	=	=	SYM
ap-10625	240	3	i	i	NOUN
ap-10625	240	4	2	2	NUM
ap-10625	240	5	∮	∮	NUM
ap-10625	241	1	c	c	NOUN
ap-10625	241	2	(	(	PUNCT
ap-10625	241	3	∂m	∂m	X
ap-10625	241	4	∫	∫	PROPN
ap-10625	241	5	1	1	NUM
ap-10625	241	6	0	0	NUM
ap-10625	241	7	ϕn(m	ϕn(m	PROPN
ap-10625	241	8	,	,	PUNCT
ap-10625	241	9	y)tϕn(m	y)tϕn(m	NOUN
ap-10625	241	10	,	,	PUNCT
ap-10625	241	11	z	z	NOUN
ap-10625	241	12	)	)	PUNCT
ap-10625	241	13	dy	dy	NOUN
ap-10625	241	14	)	)	PUNCT
ap-10625	241	15	dm	dm	PROPN
ap-10625	241	16	=	=	SYM
ap-10625	241	17	0	0	NUM
ap-10625	241	18	,	,	PUNCT
ap-10625	241	19	i.e.	i.e.	X
ap-10625	241	20	there	there	PRON
ap-10625	241	21	is	be	VERB
ap-10625	241	22	no	no	DET
ap-10625	241	23	berry	berry	NOUN
ap-10625	241	24	phase	phase	NOUN
ap-10625	241	25	for	for	ADP
ap-10625	241	26	a	a	DET
ap-10625	241	27	dirac	dirac	NOUN
ap-10625	241	28	particle	particle	NOUN
ap-10625	241	29	with	with	ADP
ap-10625	241	30	time	time	NOUN
ap-10625	241	31	-	-	PUNCT
ap-10625	241	32	dependent	dependent	ADJ
ap-10625	241	33	mass	mass	NOUN
ap-10625	241	34	in	in	ADP
ap-10625	241	35	a	a	DET
ap-10625	241	36	spherical	spherical	ADJ
ap-10625	241	37	box	box	NOUN
ap-10625	241	38	.	.	PUNCT
ap-10625	242	1	4	4	X
ap-10625	242	2	.	.	X
ap-10625	242	3	conclusion	conclusion	NOUN
ap-10625	242	4	we	we	PRON
ap-10625	242	5	studied	study	VERB
ap-10625	242	6	the	the	DET
ap-10625	242	7	dynamics	dynamic	NOUN
ap-10625	242	8	of	of	ADP
ap-10625	242	9	a	a	DET
ap-10625	242	10	dirac	dirac	NOUN
ap-10625	242	11	particle	particle	NOUN
ap-10625	242	12	under	under	ADP
ap-10625	242	13	dynamical	dynamical	ADJ
ap-10625	242	14	confinement	confinement	NOUN
ap-10625	242	15	.	.	PUNCT
ap-10625	243	1	the	the	DET
ap-10625	243	2	latter	latter	ADJ
ap-10625	243	3	is	be	AUX
ap-10625	243	4	assumed	assume	VERB
ap-10625	243	5	to	to	PART
ap-10625	243	6	be	be	AUX
ap-10625	243	7	caused	cause	VERB
ap-10625	243	8	by	by	ADP
ap-10625	243	9	a	a	DET
ap-10625	243	10	hard	hard	ADJ
ap-10625	243	11	-	-	PUNCT
ap-10625	243	12	wall	wall	NOUN
ap-10625	243	13	sphere	sphere	NOUN
ap-10625	243	14	with	with	ADP
ap-10625	243	15	a	a	DET
ap-10625	243	16	time	time	NOUN
ap-10625	243	17	-	-	PUNCT
ap-10625	243	18	varying	vary	VERB
ap-10625	243	19	radius	radius	NOUN
ap-10625	243	20	that	that	PRON
ap-10625	243	21	ensures	ensure	VERB
ap-10625	243	22	the	the	DET
ap-10625	243	23	spherical	spherical	ADJ
ap-10625	243	24	symmetry	symmetry	NOUN
ap-10625	243	25	of	of	ADP
ap-10625	243	26	the	the	DET
ap-10625	243	27	system	system	NOUN
ap-10625	243	28	.	.	PUNCT
ap-10625	244	1	the	the	DET
ap-10625	244	2	system	system	NOUN
ap-10625	244	3	is	be	AUX
ap-10625	244	4	modelled	model	VERB
ap-10625	244	5	in	in	ADP
ap-10625	244	6	terms	term	NOUN
ap-10625	244	7	of	of	ADP
ap-10625	244	8	the	the	DET
ap-10625	244	9	radial	radial	ADJ
ap-10625	244	10	dirac	dirac	NOUN
ap-10625	244	11	equation	equation	NOUN
ap-10625	244	12	with	with	ADP
ap-10625	244	13	time	time	NOUN
ap-10625	244	14	-	-	PUNCT
ap-10625	244	15	dependent	dependent	ADJ
ap-10625	244	16	boundary	boundary	ADJ
ap-10625	244	17	conditions	condition	NOUN
ap-10625	244	18	.	.	PUNCT
ap-10625	245	1	analytical	analytical	ADJ
ap-10625	245	2	solutions	solution	NOUN
ap-10625	245	3	of	of	ADP
ap-10625	245	4	the	the	DET
ap-10625	245	5	problem	problem	NOUN
ap-10625	245	6	are	be	AUX
ap-10625	245	7	obtained	obtain	VERB
ap-10625	245	8	for	for	ADP
ap-10625	245	9	some	some	DET
ap-10625	245	10	special	special	ADJ
ap-10625	245	11	cases	case	NOUN
ap-10625	245	12	of	of	ADP
ap-10625	245	13	the	the	DET
ap-10625	245	14	time	time	NOUN
ap-10625	245	15	-	-	PUNCT
ap-10625	245	16	dependence	dependence	NOUN
ap-10625	245	17	of	of	ADP
ap-10625	245	18	the	the	DET
ap-10625	245	19	sphere	sphere	NOUN
ap-10625	245	20	radius	radius	NOUN
ap-10625	245	21	,	,	PUNCT
ap-10625	245	22	while	while	SCONJ
ap-10625	245	23	the	the	DET
ap-10625	245	24	for	for	ADP
ap-10625	245	25	general	general	ADJ
ap-10625	245	26	case	case	NOUN
ap-10625	245	27	,	,	PUNCT
ap-10625	245	28	the	the	DET
ap-10625	245	29	problem	problem	NOUN
ap-10625	245	30	is	be	AUX
ap-10625	245	31	solved	solve	VERB
ap-10625	245	32	numerically	numerically	ADV
ap-10625	245	33	.	.	PUNCT
ap-10625	246	1	physically	physically	ADV
ap-10625	246	2	observable	observable	ADJ
ap-10625	246	3	characteristics	characteristic	NOUN
ap-10625	246	4	,	,	PUNCT
ap-10625	246	5	such	such	ADJ
ap-10625	246	6	as	as	ADP
ap-10625	246	7	average	average	ADJ
ap-10625	246	8	kinetic	kinetic	ADJ
ap-10625	246	9	energy	energy	NOUN
ap-10625	246	10	,	,	PUNCT
ap-10625	246	11	average	average	ADJ
ap-10625	246	12	coordinate	coordinate	NOUN
ap-10625	246	13	,	,	PUNCT
ap-10625	246	14	and	and	CCONJ
ap-10625	246	15	the	the	DET
ap-10625	246	16	average	average	ADJ
ap-10625	246	17	quantum	quantum	ADJ
ap-10625	246	18	force	force	NOUN
ap-10625	246	19	,	,	PUNCT
ap-10625	246	20	are	be	AUX
ap-10625	246	21	computed	compute	VERB
ap-10625	246	22	as	as	ADP
ap-10625	246	23	functions	function	NOUN
ap-10625	246	24	of	of	ADP
ap-10625	246	25	time	time	NOUN
ap-10625	246	26	for	for	ADP
ap-10625	246	27	different	different	ADJ
ap-10625	246	28	regimes	regime	NOUN
ap-10625	246	29	of	of	ADP
ap-10625	246	30	the	the	DET
ap-10625	246	31	wall	wall	NOUN
ap-10625	246	32	’s	’s	PART
ap-10625	246	33	motion	motion	NOUN
ap-10625	246	34	.	.	PUNCT
ap-10625	247	1	it	it	PRON
ap-10625	247	2	is	be	AUX
ap-10625	247	3	shown	show	VERB
ap-10625	247	4	that	that	SCONJ
ap-10625	247	5	for	for	ADP
ap-10625	247	6	a	a	DET
ap-10625	247	7	harmonically	harmonically	ADV
ap-10625	247	8	breathing	breathing	NOUN
ap-10625	247	9	sphere	sphere	NOUN
ap-10625	247	10	,	,	PUNCT
ap-10625	247	11	the	the	DET
ap-10625	247	12	average	average	ADJ
ap-10625	247	13	kinetic	kinetic	ADJ
ap-10625	247	14	energy	energy	NOUN
ap-10625	247	15	oscillates	oscillate	NOUN
ap-10625	247	16	in	in	ADP
ap-10625	247	17	time	time	NOUN
ap-10625	247	18	without	without	ADP
ap-10625	247	19	a	a	DET
ap-10625	247	20	monotonic	monotonic	ADJ
ap-10625	247	21	growth	growth	NOUN
ap-10625	247	22	,	,	PUNCT
ap-10625	247	23	which	which	PRON
ap-10625	247	24	implies	imply	VERB
ap-10625	247	25	the	the	DET
ap-10625	247	26	absence	absence	NOUN
ap-10625	247	27	of	of	ADP
ap-10625	247	28	the	the	DET
ap-10625	247	29	fermi	fermi	NOUN
ap-10625	247	30	acceleration	acceleration	NOUN
ap-10625	247	31	.	.	PUNCT
ap-10625	248	1	the	the	DET
ap-10625	248	2	absence	absence	NOUN
ap-10625	248	3	of	of	ADP
ap-10625	248	4	the	the	DET
ap-10625	248	5	berry	berry	NOUN
ap-10625	248	6	phase	phase	NOUN
ap-10625	248	7	is	be	AUX
ap-10625	248	8	shown	show	VERB
ap-10625	248	9	by	by	ADP
ap-10625	248	10	the	the	DET
ap-10625	248	11	direct	direct	ADJ
ap-10625	248	12	calculation	calculation	NOUN
ap-10625	248	13	of	of	ADP
ap-10625	248	14	the	the	DET
ap-10625	248	15	geometric	geometric	ADJ
ap-10625	248	16	phase	phase	NOUN
ap-10625	248	17	.	.	PUNCT
ap-10625	249	1	acknowledgements	acknowledgement	NOUN
ap-10625	249	2	the	the	DET
ap-10625	249	3	work	work	NOUN
ap-10625	249	4	is	be	AUX
ap-10625	249	5	dedicated	dedicate	VERB
ap-10625	249	6	to	to	ADP
ap-10625	249	7	the	the	DET
ap-10625	249	8	memory	memory	NOUN
ap-10625	249	9	of	of	ADP
ap-10625	249	10	professor	professor	NOUN
ap-10625	249	11	miloslav	miloslav	PROPN
ap-10625	249	12	havlíček	havlíček	PROPN
ap-10625	249	13	,	,	PUNCT
ap-10625	249	14	an	an	DET
ap-10625	249	15	outstanding	outstanding	ADJ
ap-10625	249	16	czech	czech	ADJ
ap-10625	249	17	mathematical	mathematical	ADJ
ap-10625	249	18	physicist	physicist	NOUN
ap-10625	249	19	.	.	PUNCT
ap-10625	250	1	this	this	DET
ap-10625	250	2	paper	paper	NOUN
ap-10625	250	3	is	be	AUX
ap-10625	250	4	supported	support	VERB
ap-10625	250	5	by	by	ADP
ap-10625	250	6	european	european	PROPN
ap-10625	250	7	union	union	PROPN
ap-10625	250	8	’s	’s	PART
ap-10625	250	9	horizon	horizon	NOUN
ap-10625	250	10	2020	2020	NUM
ap-10625	250	11	research	research	NOUN
ap-10625	250	12	and	and	CCONJ
ap-10625	250	13	innovation	innovation	NOUN
ap-10625	250	14	programme	programme	NOUN
ap-10625	250	15	under	under	ADP
ap-10625	250	16	the	the	DET
ap-10625	250	17	marie	marie	PROPN
ap-10625	250	18	sklodowska	sklodowska	PROPN
ap-10625	250	19	-	-	PUNCT
ap-10625	250	20	curie	curie	PROPN
ap-10625	250	21	grant	grant	NOUN
ap-10625	250	22	agreement	agreement	NOUN
ap-10625	250	23	i	i	PROPN
ap-10625	250	24	d	d	PROPN
ap-10625	250	25	:	:	PUNCT
ap-10625	250	26	873071	873071	NUM
ap-10625	250	27	,	,	PUNCT
ap-10625	250	28	project	project	NOUN
ap-10625	250	29	sompaty	sompaty	NOUN
ap-10625	250	30	(	(	PUNCT
ap-10625	250	31	spectral	spectral	ADJ
ap-10625	250	32	optimization	optimization	NOUN
ap-10625	250	33	:	:	PUNCT
ap-10625	250	34	from	from	ADP
ap-10625	250	35	mathematics	mathematics	PROPN
ap-10625	250	36	to	to	ADP
ap-10625	250	37	physics	physics	NOUN
ap-10625	250	38	and	and	CCONJ
ap-10625	250	39	advanced	advanced	ADJ
ap-10625	250	40	technology	technology	NOUN
ap-10625	250	41	)	)	PUNCT
ap-10625	250	42	.	.	PUNCT
ap-10625	251	1	references	reference	NOUN
ap-10625	251	2	[	[	X
ap-10625	251	3	1	1	X
ap-10625	251	4	]	]	PUNCT
ap-10625	251	5	t.	t.	PROPN
ap-10625	251	6	o.	o.	PROPN
ap-10625	251	7	wehling	wehling	PROPN
ap-10625	251	8	,	,	PUNCT
ap-10625	251	9	a.	a.	NOUN
ap-10625	251	10	m.	m.	NOUN
ap-10625	251	11	black	black	PROPN
ap-10625	251	12	-	-	PUNCT
ap-10625	251	13	schaffer	schaffer	PROPN
ap-10625	251	14	,	,	PUNCT
ap-10625	251	15	a.	a.	PROPN
ap-10625	251	16	v.	v.	ADP
ap-10625	251	17	balatsky	balatsky	PROPN
ap-10625	251	18	.	.	PUNCT
ap-10625	252	1	dirac	dirac	NOUN
ap-10625	252	2	materials	material	NOUN
ap-10625	252	3	.	.	PUNCT
ap-10625	253	1	advances	advance	NOUN
ap-10625	253	2	in	in	ADP
ap-10625	253	3	physics	physics	NOUN
ap-10625	253	4	63(1):1–76	63(1):1–76	NOUN
ap-10625	253	5	,	,	PUNCT
ap-10625	253	6	2014	2014	NUM
ap-10625	253	7	.	.	PUNCT
ap-10625	254	1	https://doi.org/10.1080/00018732.2014.927109	https://doi.org/10.1080/00018732.2014.927109	X
ap-10625	255	1	[	[	X
ap-10625	255	2	2	2	X
ap-10625	255	3	]	]	PUNCT
ap-10625	255	4	j.	j.	PROPN
ap-10625	255	5	cayssol	cayssol	PROPN
ap-10625	255	6	.	.	PUNCT
ap-10625	256	1	introduction	introduction	NOUN
ap-10625	256	2	to	to	PART
ap-10625	256	3	dirac	dirac	VERB
ap-10625	256	4	materials	material	NOUN
ap-10625	256	5	and	and	CCONJ
ap-10625	256	6	topological	topological	ADJ
ap-10625	256	7	insulators	insulator	NOUN
ap-10625	256	8	.	.	PUNCT
ap-10625	257	1	comptes	compte	VERB
ap-10625	257	2	rendus	rendus	PROPN
ap-10625	257	3	physique	physique	PROPN
ap-10625	257	4	14(9–10):760–778	14(9–10):760–778	NUM
ap-10625	257	5	,	,	PUNCT
ap-10625	257	6	2013	2013	NUM
ap-10625	257	7	.	.	PUNCT
ap-10625	258	1	https://doi.org/10.1016/j.crhy.2013.09.012	https://doi.org/10.1016/j.crhy.2013.09.012	PROPN
ap-10625	258	2	[	[	X
ap-10625	258	3	3	3	X
ap-10625	258	4	]	]	PUNCT
ap-10625	258	5	m.	m.	NOUN
ap-10625	258	6	z.	z.	PROPN
ap-10625	258	7	hasan	hasan	PROPN
ap-10625	258	8	,	,	PUNCT
ap-10625	258	9	c.	c.	PROPN
ap-10625	258	10	l.	l.	PROPN
ap-10625	258	11	kane	kane	PROPN
ap-10625	258	12	.	.	PUNCT
ap-10625	259	1	colloquium	colloquium	NOUN
ap-10625	259	2	:	:	PUNCT
ap-10625	259	3	topological	topological	ADJ
ap-10625	259	4	insulators	insulator	NOUN
ap-10625	259	5	.	.	PUNCT
ap-10625	260	1	reviews	review	NOUN
ap-10625	260	2	of	of	ADP
ap-10625	260	3	modern	modern	ADJ
ap-10625	260	4	physics	physic	NOUN
ap-10625	260	5	82(4):3045–3067	82(4):3045–3067	NUM
ap-10625	260	6	,	,	PUNCT
ap-10625	260	7	2010	2010	NUM
ap-10625	260	8	.	.	PUNCT
ap-10625	261	1	https://doi.org/10.1103/revmodphys.82.3045	https://doi.org/10.1103/revmodphys.82.3045	PROPN
ap-10625	262	1	[	[	X
ap-10625	262	2	4	4	X
ap-10625	262	3	]	]	PUNCT
ap-10625	262	4	x.-l	x.-l	PROPN
ap-10625	262	5	.	.	PUNCT
ap-10625	263	1	qi	qi	PROPN
ap-10625	263	2	,	,	PUNCT
ap-10625	263	3	s.-c	s.-c	NOUN
ap-10625	263	4	.	.	PUNCT
ap-10625	264	1	zhang	zhang	PROPN
ap-10625	264	2	.	.	PUNCT
ap-10625	265	1	topological	topological	ADJ
ap-10625	265	2	insulators	insulator	NOUN
ap-10625	265	3	and	and	CCONJ
ap-10625	265	4	superconductors	superconductor	NOUN
ap-10625	265	5	.	.	PUNCT
ap-10625	266	1	reviews	review	NOUN
ap-10625	266	2	of	of	ADP
ap-10625	266	3	modern	modern	ADJ
ap-10625	266	4	physics	physics	PROPN
ap-10625	266	5	83(4):1057–1110	83(4):1057–1110	NUM
ap-10625	266	6	,	,	PUNCT
ap-10625	266	7	2011	2011	NUM
ap-10625	266	8	.	.	PUNCT
ap-10625	267	1	https://doi.org/10.1103/revmodphys.83.1057	https://doi.org/10.1103/revmodphys.83.1057	VERB
ap-10625	268	1	[	[	X
ap-10625	268	2	5	5	NUM
ap-10625	268	3	]	]	PUNCT
ap-10625	268	4	c.	c.	PROPN
ap-10625	268	5	w.	w.	PROPN
ap-10625	268	6	j.	j.	PROPN
ap-10625	268	7	beenakker	beenakker	PROPN
ap-10625	268	8	.	.	PUNCT
ap-10625	269	1	colloquium	colloquium	NOUN
ap-10625	269	2	:	:	PUNCT
ap-10625	269	3	andreev	andreev	PROPN
ap-10625	269	4	reflection	reflection	NOUN
ap-10625	269	5	and	and	CCONJ
ap-10625	269	6	klein	klein	PROPN
ap-10625	269	7	tunneling	tunnel	VERB
ap-10625	269	8	in	in	ADP
ap-10625	269	9	graphene	graphene	NOUN
ap-10625	269	10	.	.	PUNCT
ap-10625	270	1	reviews	review	NOUN
ap-10625	270	2	of	of	ADP
ap-10625	270	3	modern	modern	ADJ
ap-10625	270	4	physics	physic	NOUN
ap-10625	270	5	80(4):1337–1354	80(4):1337–1354	NUM
ap-10625	270	6	,	,	PUNCT
ap-10625	270	7	2008	2008	NUM
ap-10625	270	8	.	.	PUNCT
ap-10625	271	1	https://doi.org/10.1103/revmodphys.80.1337	https://doi.org/10.1103/revmodphys.80.1337	NOUN
ap-10625	272	1	[	[	X
ap-10625	272	2	6	6	NUM
ap-10625	272	3	]	]	PUNCT
ap-10625	272	4	j.	j.	PROPN
ap-10625	272	5	m.	m.	PROPN
ap-10625	272	6	zeuner	zeuner	PROPN
ap-10625	272	7	,	,	PUNCT
ap-10625	272	8	n.	n.	PROPN
ap-10625	272	9	k.	k.	PROPN
ap-10625	272	10	efremidis	efremidis	PROPN
ap-10625	272	11	,	,	PUNCT
ap-10625	272	12	r.	r.	PROPN
ap-10625	272	13	keil	keil	PROPN
ap-10625	272	14	,	,	PUNCT
ap-10625	272	15	et	et	PROPN
ap-10625	272	16	al	al	PROPN
ap-10625	272	17	.	.	PROPN
ap-10625	272	18	optical	optical	ADJ
ap-10625	272	19	analogues	analogue	NOUN
ap-10625	272	20	for	for	ADP
ap-10625	272	21	massless	massless	ADJ
ap-10625	272	22	dirac	dirac	NOUN
ap-10625	272	23	particles	particle	NOUN
ap-10625	272	24	and	and	CCONJ
ap-10625	272	25	conical	conical	NOUN
ap-10625	272	26	diffraction	diffraction	NOUN
ap-10625	272	27	in	in	ADP
ap-10625	272	28	one	one	NUM
ap-10625	272	29	dimension	dimension	NOUN
ap-10625	272	30	.	.	PUNCT
ap-10625	273	1	reviews	review	NOUN
ap-10625	273	2	of	of	ADP
ap-10625	273	3	modern	modern	ADJ
ap-10625	273	4	physics	physic	NOUN
ap-10625	273	5	109(2):023602	109(2):023602	NUM
ap-10625	273	6	,	,	PUNCT
ap-10625	273	7	2012	2012	NUM
ap-10625	273	8	.	.	PUNCT
ap-10625	274	1	https://doi.org/10.1103/physrevlett.109.023602	https://doi.org/10.1103/physrevlett.109.023602	VERB
ap-10625	275	1	[	[	X
ap-10625	275	2	7	7	X
ap-10625	275	3	]	]	PUNCT
ap-10625	275	4	s.	s.	PROPN
ap-10625	275	5	m.	m.	PROPN
ap-10625	275	6	barnett	barnett	PROPN
ap-10625	275	7	.	.	PUNCT
ap-10625	276	1	optical	optical	ADJ
ap-10625	276	2	dirac	dirac	NOUN
ap-10625	276	3	equation	equation	NOUN
ap-10625	276	4	.	.	PUNCT
ap-10625	277	1	new	new	ADJ
ap-10625	277	2	journal	journal	PROPN
ap-10625	277	3	of	of	ADP
ap-10625	277	4	physics	physics	PROPN
ap-10625	277	5	16(9):093008	16(9):093008	PROPN
ap-10625	277	6	,	,	PUNCT
ap-10625	277	7	2014	2014	NUM
ap-10625	277	8	.	.	PUNCT
ap-10625	278	1	https://doi.org/10.1088/1367-2630/16/9/093008	https://doi.org/10.1088/1367-2630/16/9/093008	PUNCT
ap-10625	279	1	[	[	X
ap-10625	279	2	8	8	X
ap-10625	279	3	]	]	PUNCT
ap-10625	279	4	s.	s.	PROPN
ap-10625	279	5	w.	w.	PROPN
ap-10625	279	6	doescher	doescher	PROPN
ap-10625	279	7	,	,	PUNCT
ap-10625	279	8	m.	m.	PROPN
ap-10625	279	9	h.	h.	PROPN
ap-10625	279	10	rice	rice	PROPN
ap-10625	279	11	.	.	PUNCT
ap-10625	280	1	infinite	infinite	ADJ
ap-10625	280	2	square	square	ADJ
ap-10625	280	3	-	-	PUNCT
ap-10625	280	4	well	well	NOUN
ap-10625	280	5	potential	potential	NOUN
ap-10625	280	6	with	with	ADP
ap-10625	280	7	a	a	DET
ap-10625	280	8	moving	move	VERB
ap-10625	280	9	wall	wall	NOUN
ap-10625	280	10	.	.	PUNCT
ap-10625	281	1	american	american	PROPN
ap-10625	281	2	journal	journal	PROPN
ap-10625	281	3	of	of	ADP
ap-10625	281	4	physics	physics	PROPN
ap-10625	281	5	37(12):1246–1249	37(12):1246–1249	NUM
ap-10625	281	6	,	,	PUNCT
ap-10625	281	7	1969	1969	NUM
ap-10625	281	8	.	.	PUNCT
ap-10625	282	1	https://doi.org/10.1119/1.1975291	https://doi.org/10.1119/1.1975291	PROPN
ap-10625	283	1	[	[	X
ap-10625	283	2	9	9	NUM
ap-10625	283	3	]	]	X
ap-10625	283	4	j.	j.	PROPN
ap-10625	283	5	dittrich	dittrich	PROPN
ap-10625	283	6	,	,	PUNCT
ap-10625	283	7	s.	s.	PROPN
ap-10625	283	8	rakhmanov	rakhmanov	PROPN
ap-10625	283	9	,	,	PUNCT
ap-10625	283	10	d.	d.	PROPN
ap-10625	283	11	matrasulov	matrasulov	PROPN
ap-10625	283	12	.	.	PUNCT
ap-10625	284	1	dirac	dirac	NOUN
ap-10625	284	2	particle	particle	NOUN
ap-10625	284	3	under	under	ADP
ap-10625	284	4	dynamical	dynamical	ADJ
ap-10625	284	5	confinement	confinement	NOUN
ap-10625	284	6	:	:	PUNCT
ap-10625	284	7	fermi	fermi	NOUN
ap-10625	284	8	acceleration	acceleration	NOUN
ap-10625	284	9	,	,	PUNCT
ap-10625	284	10	trembling	tremble	VERB
ap-10625	284	11	motion	motion	NOUN
ap-10625	284	12	and	and	CCONJ
ap-10625	284	13	quantum	quantum	NOUN
ap-10625	284	14	force	force	NOUN
ap-10625	284	15	.	.	PUNCT
ap-10625	285	1	physics	physics	NOUN
ap-10625	285	2	letters	letter	NOUN
ap-10625	285	3	a	a	DET
ap-10625	285	4	503:129408	503:129408	NUM
ap-10625	285	5	,	,	PUNCT
ap-10625	285	6	2024	2024	NUM
ap-10625	285	7	.	.	PUNCT
ap-10625	286	1	https://doi.org/10.1016/j.physleta.2024.129408	https://doi.org/10.1016/j.physleta.2024.129408	VERB
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ap-10625	287	3	]	]	X
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ap-10625	287	5	v.	v.	CCONJ
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ap-10625	287	8	v.	v.	PROPN
ap-10625	287	9	i.	i.	PROPN
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ap-10625	287	11	,	,	PUNCT
ap-10625	287	12	d.	d.	PROPN
ap-10625	287	13	e.	e.	PROPN
ap-10625	287	14	nikonov	nikonov	PROPN
ap-10625	287	15	.	.	PUNCT
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ap-10625	288	2	propagators	propagator	NOUN
ap-10625	288	3	for	for	ADP
ap-10625	288	4	time	time	NOUN
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ap-10625	288	6	dependent	dependent	ADJ
ap-10625	288	7	coulomb	coulomb	NOUN
ap-10625	288	8	,	,	PUNCT
ap-10625	288	9	delta	delta	NOUN
ap-10625	288	10	and	and	CCONJ
ap-10625	288	11	other	other	ADJ
ap-10625	288	12	potentials	potential	NOUN
ap-10625	288	13	.	.	PUNCT
ap-10625	289	1	physics	physics	NOUN
ap-10625	289	2	letters	letter	NOUN
ap-10625	289	3	a	a	DET
ap-10625	289	4	162(5):359–364	162(5):359–364	NUM
ap-10625	289	5	,	,	PUNCT
ap-10625	289	6	1992	1992	NUM
ap-10625	289	7	.	.	PUNCT
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ap-10625	291	2	11	11	NUM
ap-10625	291	3	]	]	PUNCT
ap-10625	291	4	m.	m.	NOUN
ap-10625	291	5	v.	v.	ADP
ap-10625	291	6	berry	berry	PROPN
ap-10625	291	7	,	,	PUNCT
ap-10625	291	8	r.	r.	PROPN
ap-10625	291	9	j.	j.	PROPN
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ap-10625	291	11	.	.	PUNCT
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ap-10625	292	5	-	-	PUNCT
ap-10625	292	6	reversal	reversal	NOUN
ap-10625	292	7	symmetry	symmetry	NOUN
ap-10625	292	8	-	-	PUNCT
ap-10625	292	9	breaking	breaking	NOUN
ap-10625	292	10	without	without	ADP
ap-10625	292	11	magnetic	magnetic	ADJ
ap-10625	292	12	fields	field	NOUN
ap-10625	292	13	.	.	PUNCT
ap-10625	293	1	proceedings	proceeding	NOUN
ap-10625	293	2	of	of	ADP
ap-10625	293	3	the	the	DET
ap-10625	293	4	royal	royal	ADJ
ap-10625	293	5	society	society	NOUN
ap-10625	293	6	of	of	ADP
ap-10625	293	7	london	london	PROPN
ap-10625	293	8	a.	a.	PROPN
ap-10625	293	9	mathematical	mathematical	PROPN
ap-10625	293	10	and	and	CCONJ
ap-10625	293	11	physical	physical	ADJ
ap-10625	293	12	sciences	science	NOUN
ap-10625	293	13	412(1842):53–74	412(1842):53–74	NUM
ap-10625	293	14	,	,	PUNCT
ap-10625	293	15	1987	1987	NUM
ap-10625	293	16	.	.	PUNCT
ap-10625	294	1	https://doi.org/10.1098/rspa.1987.0080	https://doi.org/10.1098/rspa.1987.0080	PROPN
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ap-10625	295	2	12	12	NUM
ap-10625	295	3	]	]	X
ap-10625	295	4	v.	v.	ADP
ap-10625	295	5	alonso	alonso	PROPN
ap-10625	295	6	,	,	PUNCT
ap-10625	295	7	s.	s.	PROPN
ap-10625	295	8	d.	d.	PROPN
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ap-10625	295	10	,	,	PUNCT
ap-10625	295	11	l.	l.	PROPN
ap-10625	295	12	mondino	mondino	PROPN
ap-10625	295	13	.	.	PUNCT
ap-10625	296	1	on	on	ADP
ap-10625	296	2	the	the	DET
ap-10625	296	3	boundary	boundary	ADJ
ap-10625	296	4	conditions	condition	NOUN
ap-10625	296	5	for	for	ADP
ap-10625	296	6	the	the	DET
ap-10625	296	7	dirac	dirac	NOUN
ap-10625	296	8	equation	equation	NOUN
ap-10625	296	9	.	.	PUNCT
ap-10625	297	1	european	european	PROPN
ap-10625	297	2	journal	journal	PROPN
ap-10625	297	3	of	of	ADP
ap-10625	297	4	physics	physics	PROPN
ap-10625	297	5	18(5):315	18(5):315	NUM
ap-10625	297	6	,	,	PUNCT
ap-10625	297	7	1997	1997	NUM
ap-10625	297	8	.	.	PUNCT
ap-10625	298	1	https://doi.org/10.1088/0143-0807/18/5/001	https://doi.org/10.1088/0143-0807/18/5/001	PROPN
ap-10625	299	1	[	[	X
ap-10625	299	2	13	13	NUM
ap-10625	299	3	]	]	PUNCT
ap-10625	299	4	v.	v.	ADP
ap-10625	299	5	alonso	alonso	PROPN
ap-10625	299	6	,	,	PUNCT
ap-10625	299	7	s.	s.	PROPN
ap-10625	299	8	d.	d.	PROPN
ap-10625	299	9	vincenzo	vincenzo	PROPN
ap-10625	299	10	.	.	PUNCT
ap-10625	300	1	general	general	ADJ
ap-10625	300	2	boundary	boundary	ADJ
ap-10625	300	3	conditions	condition	NOUN
ap-10625	300	4	for	for	ADP
ap-10625	300	5	a	a	DET
ap-10625	300	6	dirac	dirac	NOUN
ap-10625	300	7	particle	particle	NOUN
ap-10625	300	8	in	in	ADP
ap-10625	300	9	a	a	DET
ap-10625	300	10	box	box	NOUN
ap-10625	300	11	and	and	CCONJ
ap-10625	300	12	their	their	PRON
ap-10625	300	13	non	non	ADJ
ap-10625	300	14	-	-	ADJ
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ap-10625	300	17	.	.	PUNCT
ap-10625	301	1	journal	journal	PROPN
ap-10625	301	2	of	of	ADP
ap-10625	301	3	physics	physics	PROPN
ap-10625	301	4	a	a	PRON
ap-10625	301	5	:	:	PUNCT
ap-10625	301	6	mathematical	mathematical	ADJ
ap-10625	301	7	and	and	CCONJ
ap-10625	301	8	general	general	ADJ
ap-10625	301	9	30(24):8573	30(24):8573	NUM
ap-10625	301	10	,	,	PUNCT
ap-10625	301	11	1997	1997	NUM
ap-10625	301	12	.	.	PUNCT
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ap-10625	303	1	[	[	X
ap-10625	303	2	14	14	NUM
ap-10625	303	3	]	]	PUNCT
ap-10625	303	4	z.	z.	PROPN
ap-10625	303	5	a.	a.	PROPN
ap-10625	303	6	sobirov	sobirov	PROPN
ap-10625	303	7	,	,	PUNCT
ap-10625	303	8	d.	d.	PROPN
ap-10625	303	9	matrasulov	matrasulov	PROPN
ap-10625	303	10	,	,	PUNCT
ap-10625	303	11	s.	s.	PROPN
ap-10625	303	12	ataev	ataev	PROPN
ap-10625	303	13	,	,	PUNCT
ap-10625	303	14	h.	h.	PROPN
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ap-10625	303	16	.	.	PUNCT
ap-10625	303	17	time	time	NOUN
ap-10625	303	18	dependent	dependent	ADJ
ap-10625	303	19	neutrino	neutrino	NOUN
ap-10625	303	20	billiards	billiard	NOUN
ap-10625	303	21	.	.	PUNCT
ap-10625	304	1	in	in	ADP
ap-10625	304	2	g.	g.	PROPN
ap-10625	304	3	casati	casati	PROPN
ap-10625	304	4	,	,	PUNCT
ap-10625	304	5	d.	d.	PROPN
ap-10625	304	6	matrasulov	matrasulov	PROPN
ap-10625	304	7	(	(	PUNCT
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ap-10625	304	9	.	.	PUNCT
ap-10625	304	10	)	)	PUNCT
ap-10625	304	11	,	,	PUNCT
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ap-10625	304	14	in	in	ADP
ap-10625	304	15	nanoscale	nanoscale	NOUN
ap-10625	304	16	systems	system	NOUN
ap-10625	304	17	,	,	PUNCT
ap-10625	304	18	pp	pp	ADJ
ap-10625	304	19	.	.	PUNCT
ap-10625	305	1	215–221	215–221	NUM
ap-10625	305	2	.	.	PUNCT
ap-10625	305	3	springer	springer	PROPN
ap-10625	305	4	netherlands	netherlands	PROPN
ap-10625	305	5	,	,	PUNCT
ap-10625	305	6	dordrecht	dordrecht	PROPN
ap-10625	305	7	,	,	PUNCT
ap-10625	305	8	2009	2009	NUM
ap-10625	305	9	.	.	PUNCT
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ap-10625	307	1	[	[	X
ap-10625	307	2	15	15	NUM
ap-10625	307	3	]	]	X
ap-10625	307	4	s.	s.	PROPN
ap-10625	307	5	rakhmanov	rakhmanov	PROPN
ap-10625	307	6	,	,	PUNCT
ap-10625	307	7	d.	d.	PROPN
ap-10625	307	8	matrasulov	matrasulov	PROPN
ap-10625	307	9	,	,	PUNCT
ap-10625	307	10	v.	v.	PROPN
ap-10625	307	11	i.	i.	PROPN
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ap-10625	308	2	dynamics	dynamic	NOUN
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ap-10625	308	4	a	a	DET
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ap-10625	308	6	-	-	PUNCT
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ap-10625	308	8	atom	atom	NOUN
ap-10625	308	9	in	in	ADP
ap-10625	308	10	a	a	DET
ap-10625	308	11	time	time	NOUN
ap-10625	308	12	-	-	PUNCT
ap-10625	308	13	dependent	dependent	ADJ
ap-10625	308	14	box	box	NOUN
ap-10625	308	15	:	:	PUNCT
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ap-10625	308	17	-	-	ADJ
ap-10625	308	18	adiabatic	adiabatic	ADJ
ap-10625	308	19	regime	regime	NOUN
ap-10625	308	20	.	.	PUNCT
ap-10625	309	1	the	the	DET
ap-10625	309	2	european	european	PROPN
ap-10625	309	3	physical	physical	PROPN
ap-10625	309	4	journal	journal	PROPN
ap-10625	309	5	d	d	PROPN
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ap-10625	309	7	,	,	PUNCT
ap-10625	309	8	2018	2018	NUM
ap-10625	309	9	.	.	PUNCT
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ap-10625	311	2	16	16	NUM
ap-10625	311	3	]	]	PUNCT
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ap-10625	311	5	.	.	PUNCT
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ap-10625	313	4	.	.	PUNCT
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ap-10625	314	17	chiral	chiral	ADJ
ap-10625	314	18	quantum	quantum	ADJ
ap-10625	314	19	scars	scar	NOUN
ap-10625	314	20	.	.	PUNCT
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ap-10625	315	5	,	,	PUNCT
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ap-10625	315	7	.	.	PUNCT
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ap-10625	316	20	.	.	PUNCT
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ap-10625	320	6	.	.	PUNCT
ap-10625	321	1	552	552	NUM
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ap-10625	325	8	-	-	PUNCT
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ap-10625	326	6	,	,	PUNCT
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ap-10625	328	4	p.	p.	NOUN
ap-10625	328	5	pereshogin	pereshogin	NOUN
ap-10625	328	6	,	,	PUNCT
ap-10625	328	7	p.	p.	PROPN
ap-10625	328	8	pronin	pronin	PROPN
ap-10625	328	9	.	.	PUNCT
ap-10625	329	1	effective	effective	ADJ
ap-10625	329	2	hamiltonian	hamiltonian	NOUN
ap-10625	329	3	and	and	CCONJ
ap-10625	329	4	berry	berry	NOUN
ap-10625	329	5	phase	phase	NOUN
ap-10625	329	6	in	in	ADP
ap-10625	329	7	a	a	DET
ap-10625	329	8	quantum	quantum	ADJ
ap-10625	329	9	mechanical	mechanical	ADJ
ap-10625	329	10	system	system	NOUN
ap-10625	329	11	with	with	ADP
ap-10625	329	12	time	time	NOUN
ap-10625	329	13	dependent	dependent	ADJ
ap-10625	329	14	boundary	boundary	ADJ
ap-10625	329	15	conditions	condition	NOUN
ap-10625	329	16	.	.	PUNCT
ap-10625	330	1	physics	physics	NOUN
ap-10625	330	2	letters	letter	NOUN
ap-10625	330	3	a	a	DET
ap-10625	330	4	156(1):12–16	156(1):12–16	NOUN
ap-10625	330	5	,	,	PUNCT
ap-10625	330	6	1991	1991	NUM
ap-10625	330	7	.	.	PUNCT
ap-10625	331	1	https://doi.org/10.1016/0375-9601(91)90117-q	https://doi.org/10.1016/0375-9601(91)90117-q	PROPN
ap-10625	331	2	[	[	X
ap-10625	331	3	20	20	NUM
ap-10625	331	4	]	]	PUNCT
ap-10625	331	5	m.	m.	NOUN
ap-10625	331	6	holzmann	holzmann	PROPN
ap-10625	331	7	.	.	PUNCT
ap-10625	332	1	a	a	DET
ap-10625	332	2	note	note	NOUN
ap-10625	332	3	on	on	ADP
ap-10625	332	4	the	the	DET
ap-10625	332	5	three	three	NUM
ap-10625	332	6	dimensional	dimensional	ADJ
ap-10625	332	7	dirac	dirac	NOUN
ap-10625	332	8	operator	operator	NOUN
ap-10625	332	9	with	with	ADP
ap-10625	332	10	zigzag	zigzag	NOUN
ap-10625	332	11	type	type	NOUN
ap-10625	332	12	boundary	boundary	ADJ
ap-10625	332	13	conditions	condition	NOUN
ap-10625	332	14	.	.	PUNCT
ap-10625	333	1	complex	complex	ADJ
ap-10625	333	2	analysis	analysis	NOUN
ap-10625	333	3	and	and	CCONJ
ap-10625	333	4	operator	operator	NOUN
ap-10625	333	5	theory	theory	NOUN
ap-10625	333	6	15(3):47	15(3):47	NUM
ap-10625	333	7	,	,	PUNCT
ap-10625	333	8	2021	2021	NUM
ap-10625	333	9	.	.	PUNCT
ap-10625	334	1	https://doi.org/10.1007/s11785-021-01090-x	https://doi.org/10.1007/s11785-021-01090-x	PROPN
ap-10625	335	1	[	[	X
ap-10625	335	2	21	21	NUM
ap-10625	335	3	]	]	X
ap-10625	335	4	m.	m.	NOUN
ap-10625	335	5	v.	v.	ADP
ap-10625	335	6	berry	berry	PROPN
ap-10625	335	7	.	.	PUNCT
ap-10625	336	1	quantal	quantal	ADJ
ap-10625	336	2	phase	phase	NOUN
ap-10625	336	3	factors	factor	NOUN
ap-10625	336	4	accompanying	accompany	VERB
ap-10625	336	5	adiabatic	adiabatic	ADJ
ap-10625	336	6	changes	change	NOUN
ap-10625	336	7	.	.	PUNCT
ap-10625	337	1	proceedings	proceeding	NOUN
ap-10625	337	2	of	of	ADP
ap-10625	337	3	the	the	DET
ap-10625	337	4	royal	royal	ADJ
ap-10625	337	5	society	society	NOUN
ap-10625	337	6	of	of	ADP
ap-10625	337	7	london	london	PROPN
ap-10625	337	8	a.	a.	PROPN
ap-10625	337	9	mathematical	mathematical	PROPN
ap-10625	337	10	and	and	CCONJ
ap-10625	337	11	physical	physical	ADJ
ap-10625	337	12	sciences	science	NOUN
ap-10625	337	13	392(1802):45–57	392(1802):45–57	NUM
ap-10625	337	14	,	,	PUNCT
ap-10625	337	15	1984	1984	NUM
ap-10625	337	16	.	.	PUNCT
ap-10625	338	1	https://doi.org/10.1098/rspa.1984.0023	https://doi.org/10.1098/rspa.1984.0023	PROPN
ap-10625	338	2	[	[	X
ap-10625	338	3	22	22	NUM
ap-10625	338	4	]	]	PUNCT
ap-10625	338	5	m.	m.	NOUN
ap-10625	338	6	reed	reed	PROPN
ap-10625	338	7	,	,	PUNCT
ap-10625	338	8	b.	b.	PROPN
ap-10625	338	9	simon	simon	PROPN
ap-10625	338	10	.	.	PUNCT
ap-10625	339	1	methods	method	NOUN
ap-10625	339	2	of	of	ADP
ap-10625	339	3	modern	modern	ADJ
ap-10625	339	4	mathematical	mathematical	ADJ
ap-10625	339	5	physics	physics	NOUN
ap-10625	339	6	.	.	PUNCT
ap-10625	340	1	iv	iv	X
ap-10625	340	2	:	:	PUNCT
ap-10625	340	3	analysis	analysis	NOUN
ap-10625	340	4	of	of	ADP
ap-10625	340	5	operators	operator	NOUN
ap-10625	340	6	.	.	PUNCT
ap-10625	341	1	academic	academic	ADJ
ap-10625	341	2	press	press	NOUN
ap-10625	341	3	,	,	PUNCT
ap-10625	341	4	san	san	PROPN
ap-10625	341	5	diego	diego	PROPN
ap-10625	341	6	,	,	PUNCT
ap-10625	341	7	1978	1978	NUM
ap-10625	341	8	.	.	PUNCT
ap-10625	342	1	553	553	NUM
ap-10625	342	2	https://doi.org/10.1063/1.528469	https://doi.org/10.1063/1.528469	ADJ
ap-10625	342	3	https://doi.org/10.1016/0375-9601(91)90117-q	https://doi.org/10.1016/0375-9601(91)90117-q	PROPN
ap-10625	342	4	https://doi.org/10.1007/s11785-021-01090-x	https://doi.org/10.1007/s11785-021-01090-x	NOUN
ap-10625	342	5	https://doi.org/10.1098/rspa.1984.0023	https://doi.org/10.1098/rspa.1984.0023	PROPN
ap-10625	342	6	acta	acta	PROPN
ap-10625	342	7	polytechnica	polytechnica	PROPN
ap-10625	342	8	65(5):546–553	65(5):546–553	PROPN
ap-10625	342	9	,	,	PUNCT
ap-10625	342	10	2025	2025	NUM
ap-10625	342	11	1	1	NUM
ap-10625	342	12	introduction	introduction	NOUN
ap-10625	342	13	2	2	NUM
ap-10625	342	14	dirac	dirac	NOUN
ap-10625	342	15	particle	particle	NOUN
ap-10625	342	16	in	in	ADP
ap-10625	342	17	a	a	DET
ap-10625	342	18	spherical	spherical	ADJ
ap-10625	342	19	box	box	NOUN
ap-10625	342	20	2.1	2.1	NUM
ap-10625	342	21	radial	radial	ADJ
ap-10625	342	22	operator	operator	NOUN
ap-10625	342	23	domain	domain	NOUN
ap-10625	342	24	2.2	2.2	NUM
ap-10625	342	25	solution	solution	NOUN
ap-10625	342	26	of	of	ADP
ap-10625	342	27	the	the	DET
ap-10625	342	28	dirac	dirac	NOUN
ap-10625	342	29	equation	equation	NOUN
ap-10625	342	30	on	on	ADP
ap-10625	342	31	time	time	NOUN
ap-10625	342	32	-	-	PUNCT
ap-10625	342	33	dependent	dependent	ADJ
ap-10625	342	34	spherical	spherical	ADJ
ap-10625	342	35	box	box	NOUN
ap-10625	342	36	3	3	NUM
ap-10625	342	37	quantum	quantum	NOUN
ap-10625	342	38	dynamics	dynamic	NOUN
ap-10625	342	39	under	under	ADP
ap-10625	342	40	the	the	DET
ap-10625	342	41	dynamical	dynamical	ADJ
ap-10625	342	42	confinement	confinement	NOUN
ap-10625	342	43	3.1	3.1	NUM
ap-10625	342	44	fermi	fermi	NOUN
ap-10625	342	45	acceleration	acceleration	NOUN
ap-10625	342	46	3.2	3.2	NUM
ap-10625	342	47	zitterbewegung	zitterbewegung	NOUN
ap-10625	342	48	3.3	3.3	NUM
ap-10625	342	49	quantum	quantum	NOUN
ap-10625	342	50	force	force	NOUN
ap-10625	342	51	3.4	3.4	NUM
ap-10625	342	52	berry	berry	NOUN
ap-10625	342	53	phase	phase	NOUN
ap-10625	342	54	4	4	NUM
ap-10625	342	55	conclusion	conclusion	NOUN
ap-10625	342	56	acknowledgements	acknowledgement	NOUN
ap-10625	342	57	references	reference	NOUN