id	sid	tid	token	lemma	pos
ejpam-5828	1	1	european	european	PROPN
ejpam-5828	1	2	journal	journal	PROPN
ejpam-5828	1	3	of	of	ADP
ejpam-5828	1	4	pure	pure	ADJ
ejpam-5828	1	5	and	and	CCONJ
ejpam-5828	1	6	applied	applied	ADJ
ejpam-5828	1	7	mathematics	mathematic	NOUN
ejpam-5828	1	8	2025	2025	NUM
ejpam-5828	1	9	,	,	PUNCT
ejpam-5828	1	10	vol	vol	NOUN
ejpam-5828	1	11	.	.	PROPN
ejpam-5828	1	12	18	18	NUM
ejpam-5828	1	13	,	,	PUNCT
ejpam-5828	1	14	issue	issue	NOUN
ejpam-5828	1	15	2	2	NUM
ejpam-5828	1	16	,	,	PUNCT
ejpam-5828	1	17	article	article	NOUN
ejpam-5828	1	18	number	number	NOUN
ejpam-5828	1	19	5828	5828	NUM
ejpam-5828	1	20	issn	issn	VERB
ejpam-5828	1	21	1307	1307	NUM
ejpam-5828	1	22	-	-	SYM
ejpam-5828	1	23	5543	5543	NUM
ejpam-5828	1	24	–	–	PUNCT
ejpam-5828	1	25	ejpam.com	ejpam.com	X
ejpam-5828	1	26	published	publish	VERB
ejpam-5828	1	27	by	by	ADP
ejpam-5828	1	28	new	new	PROPN
ejpam-5828	1	29	york	york	PROPN
ejpam-5828	1	30	business	business	PROPN
ejpam-5828	1	31	global	global	ADJ
ejpam-5828	1	32	quantization	quantization	NOUN
ejpam-5828	1	33	of	of	ADP
ejpam-5828	1	34	dissipative	dissipative	ADJ
ejpam-5828	1	35	anisotropic	anisotropic	NOUN
ejpam-5828	1	36	harmonic	harmonic	ADJ
ejpam-5828	1	37	oscillators	oscillator	NOUN
ejpam-5828	1	38	bashar	bashar	PROPN
ejpam-5828	1	39	.	.	PUNCT
ejpam-5828	2	1	m.	m.	PROPN
ejpam-5828	2	2	al	al	PROPN
ejpam-5828	2	3	-	-	PUNCT
ejpam-5828	2	4	khamiseh1	khamiseh1	PROPN
ejpam-5828	2	5	,	,	PUNCT
ejpam-5828	2	6	yazen	yazen	NOUN
ejpam-5828	2	7	.	.	PUNCT
ejpam-5828	2	8	m.	m.	PROPN
ejpam-5828	2	9	alawaideh1,∗	alawaideh1,∗	PROPN
ejpam-5828	2	10	,	,	PUNCT
ejpam-5828	2	11	hayat	hayat	PROPN
ejpam-5828	2	12	issaadi2	issaadi2	PROPN
ejpam-5828	2	13	,	,	PUNCT
ejpam-5828	2	14	muhammad	muhammad	PROPN
ejpam-5828	2	15	bilal3	bilal3	NOUN
ejpam-5828	2	16	,	,	PUNCT
ejpam-5828	2	17	shajar	shajar	PROPN
ejpam-5828	2	18	abbas4	abbas4	PROPN
ejpam-5828	2	19	,	,	PUNCT
ejpam-5828	2	20	hala	hala	PROPN
ejpam-5828	2	21	ghannam5	ghannam5	PROPN
ejpam-5828	2	22	,	,	PUNCT
ejpam-5828	2	23	dumitru	dumitru	PROPN
ejpam-5828	2	24	baleanu6,7	baleanu6,7	PROPN
ejpam-5828	2	25	1	1	NUM
ejpam-5828	2	26	meu	meu	NOUN
ejpam-5828	2	27	research	research	NOUN
ejpam-5828	2	28	unit	unit	NOUN
ejpam-5828	2	29	,	,	PUNCT
ejpam-5828	2	30	middle	middle	PROPN
ejpam-5828	2	31	east	east	PROPN
ejpam-5828	2	32	university	university	PROPN
ejpam-5828	2	33	,	,	PUNCT
ejpam-5828	2	34	amman	amman	PROPN
ejpam-5828	2	35	,	,	PUNCT
ejpam-5828	2	36	jordan	jordan	PROPN
ejpam-5828	2	37	2	2	NUM
ejpam-5828	2	38	usthb	usthb	ADJ
ejpam-5828	2	39	university	university	NOUN
ejpam-5828	2	40	,	,	PUNCT
ejpam-5828	2	41	operational	operational	ADJ
ejpam-5828	2	42	research	research	NOUN
ejpam-5828	2	43	department	department	PROPN
ejpam-5828	2	44	,	,	PUNCT
ejpam-5828	2	45	bp	bp	PROPN
ejpam-5828	2	46	32	32	NUM
ejpam-5828	2	47	el	el	PROPN
ejpam-5828	2	48	-	-	PUNCT
ejpam-5828	2	49	alia	alia	PROPN
ejpam-5828	2	50	,	,	PUNCT
ejpam-5828	2	51	bab	bab	PROPN
ejpam-5828	2	52	-	-	PUNCT
ejpam-5828	2	53	ezzouar	ezzouar	ADJ
ejpam-5828	2	54	,	,	PUNCT
ejpam-5828	2	55	16111	16111	NUM
ejpam-5828	2	56	,	,	PUNCT
ejpam-5828	2	57	algeria	algeria	PROPN
ejpam-5828	2	58	3	3	PROPN
ejpam-5828	2	59	department	department	PROPN
ejpam-5828	2	60	of	of	ADP
ejpam-5828	2	61	physics	physics	PROPN
ejpam-5828	2	62	,	,	PUNCT
ejpam-5828	2	63	shanghai	shanghai	PROPN
ejpam-5828	2	64	university	university	PROPN
ejpam-5828	2	65	,	,	PUNCT
ejpam-5828	2	66	shanghai	shanghai	PROPN
ejpam-5828	2	67	200444	200444	NUM
ejpam-5828	2	68	,	,	PUNCT
ejpam-5828	2	69	china	china	PROPN
ejpam-5828	2	70	4	4	NUM
ejpam-5828	2	71	as	as	ADP
ejpam-5828	2	72	(	(	PUNCT
ejpam-5828	2	73	ayub	ayub	NOUN
ejpam-5828	2	74	shah	shah	PROPN
ejpam-5828	2	75	)	)	PUNCT
ejpam-5828	2	76	,	,	PUNCT
ejpam-5828	2	77	institute	institute	NOUN
ejpam-5828	2	78	of	of	ADP
ejpam-5828	2	79	mathematics	mathematics	PROPN
ejpam-5828	2	80	and	and	CCONJ
ejpam-5828	2	81	research	research	NOUN
ejpam-5828	2	82	centre	centre	NOUN
ejpam-5828	2	83	,	,	PUNCT
ejpam-5828	2	84	multan	multan	PROPN
ejpam-5828	2	85	,	,	PUNCT
ejpam-5828	2	86	pakistan	pakistan	PROPN
ejpam-5828	2	87	5	5	NUM
ejpam-5828	2	88	department	department	NOUN
ejpam-5828	2	89	of	of	ADP
ejpam-5828	2	90	basic	basic	ADJ
ejpam-5828	2	91	sciences	science	NOUN
ejpam-5828	2	92	,	,	PUNCT
ejpam-5828	2	93	middle	middle	PROPN
ejpam-5828	2	94	east	east	PROPN
ejpam-5828	2	95	university	university	PROPN
ejpam-5828	2	96	,	,	PUNCT
ejpam-5828	2	97	amman	amman	PROPN
ejpam-5828	2	98	11831	11831	NUM
ejpam-5828	2	99	,	,	PUNCT
ejpam-5828	2	100	jordan	jordan	PROPN
ejpam-5828	2	101	6	6	NUM
ejpam-5828	2	102	department	department	NOUN
ejpam-5828	2	103	of	of	ADP
ejpam-5828	2	104	computer	computer	NOUN
ejpam-5828	2	105	science	science	NOUN
ejpam-5828	2	106	and	and	CCONJ
ejpam-5828	2	107	mathematics	mathematic	NOUN
ejpam-5828	2	108	,	,	PUNCT
ejpam-5828	2	109	lebanese	lebanese	ADJ
ejpam-5828	2	110	american	american	PROPN
ejpam-5828	2	111	university	university	PROPN
ejpam-5828	2	112	,	,	PUNCT
ejpam-5828	2	113	beirut	beirut	PROPN
ejpam-5828	2	114	,	,	PUNCT
ejpam-5828	2	115	lebanon	lebanon	PROPN
ejpam-5828	2	116	7	7	NUM
ejpam-5828	2	117	institute	institute	PROPN
ejpam-5828	2	118	of	of	ADP
ejpam-5828	2	119	space	space	NOUN
ejpam-5828	2	120	sciences	sciences	PROPN
ejpam-5828	2	121	–	–	PUNCT
ejpam-5828	2	122	inflpr	inflpr	ADP
ejpam-5828	2	123	subsidiary	subsidiary	NOUN
ejpam-5828	2	124	,	,	PUNCT
ejpam-5828	2	125	magurele	magurele	PROPN
ejpam-5828	2	126	-	-	PUNCT
ejpam-5828	2	127	bucharest	bucharest	PROPN
ejpam-5828	2	128	,	,	PUNCT
ejpam-5828	2	129	romania	romania	PROPN
ejpam-5828	2	130	abstract	abstract	NOUN
ejpam-5828	2	131	.	.	PUNCT
ejpam-5828	3	1	in	in	ADP
ejpam-5828	3	2	this	this	DET
ejpam-5828	3	3	study	study	NOUN
ejpam-5828	3	4	,	,	PUNCT
ejpam-5828	3	5	we	we	PRON
ejpam-5828	3	6	developed	develop	VERB
ejpam-5828	3	7	a	a	DET
ejpam-5828	3	8	hamiltonian	hamiltonian	ADJ
ejpam-5828	3	9	framework	framework	NOUN
ejpam-5828	3	10	for	for	ADP
ejpam-5828	3	11	the	the	DET
ejpam-5828	3	12	anisotropic	anisotropic	NOUN
ejpam-5828	3	13	harmonic	harmonic	ADJ
ejpam-5828	3	14	oscillator	oscillator	NOUN
ejpam-5828	3	15	and	and	CCONJ
ejpam-5828	3	16	applied	apply	VERB
ejpam-5828	3	17	the	the	DET
ejpam-5828	3	18	hamilton	hamilton	PROPN
ejpam-5828	3	19	-	-	PUNCT
ejpam-5828	3	20	jacobi	jacobi	PROPN
ejpam-5828	3	21	equations	equation	NOUN
ejpam-5828	3	22	to	to	PART
ejpam-5828	3	23	analyze	analyze	VERB
ejpam-5828	3	24	a	a	DET
ejpam-5828	3	25	dissipative	dissipative	ADJ
ejpam-5828	3	26	system	system	NOUN
ejpam-5828	3	27	.	.	PUNCT
ejpam-5828	4	1	by	by	ADP
ejpam-5828	4	2	incorporating	incorporate	VERB
ejpam-5828	4	3	boundary	boundary	ADJ
ejpam-5828	4	4	conditions	condition	NOUN
ejpam-5828	4	5	,	,	PUNCT
ejpam-5828	4	6	we	we	PRON
ejpam-5828	4	7	derived	derive	VERB
ejpam-5828	4	8	the	the	DET
ejpam-5828	4	9	action	action	NOUN
ejpam-5828	4	10	function	function	NOUN
ejpam-5828	4	11	.	.	PUNCT
ejpam-5828	5	1	the	the	DET
ejpam-5828	5	2	system	system	NOUN
ejpam-5828	5	3	was	be	AUX
ejpam-5828	5	4	quantized	quantize	VERB
ejpam-5828	5	5	using	use	VERB
ejpam-5828	5	6	three	three	NUM
ejpam-5828	5	7	methods	method	NOUN
ejpam-5828	5	8	:	:	PUNCT
ejpam-5828	5	9	the	the	DET
ejpam-5828	5	10	wkb	wkb	PROPN
ejpam-5828	5	11	approximation	approximation	NOUN
ejpam-5828	5	12	,	,	PUNCT
ejpam-5828	5	13	canonical	canonical	ADJ
ejpam-5828	5	14	quantization	quantization	NOUN
ejpam-5828	5	15	,	,	PUNCT
ejpam-5828	5	16	and	and	CCONJ
ejpam-5828	5	17	creation	creation	NOUN
ejpam-5828	5	18	-	-	PUNCT
ejpam-5828	5	19	annihilation	annihilation	NOUN
ejpam-5828	5	20	operators	operator	NOUN
ejpam-5828	5	21	.	.	PUNCT
ejpam-5828	6	1	the	the	DET
ejpam-5828	6	2	heisenberg	heisenberg	PROPN
ejpam-5828	6	3	equations	equation	NOUN
ejpam-5828	6	4	were	be	AUX
ejpam-5828	6	5	reformulated	reformulate	VERB
ejpam-5828	6	6	using	use	VERB
ejpam-5828	6	7	poisson	poisson	NOUN
ejpam-5828	6	8	bracket	bracket	ADJ
ejpam-5828	6	9	quantum	quantum	ADJ
ejpam-5828	6	10	variables	variable	NOUN
ejpam-5828	6	11	,	,	PUNCT
ejpam-5828	6	12	and	and	CCONJ
ejpam-5828	6	13	energy	energy	NOUN
ejpam-5828	6	14	levels	level	NOUN
ejpam-5828	6	15	and	and	CCONJ
ejpam-5828	6	16	quantum	quantum	NOUN
ejpam-5828	6	17	states	state	NOUN
ejpam-5828	6	18	were	be	AUX
ejpam-5828	6	19	obtained	obtain	VERB
ejpam-5828	6	20	.	.	PUNCT
ejpam-5828	7	1	all	all	DET
ejpam-5828	7	2	methods	method	NOUN
ejpam-5828	7	3	yielded	yield	VERB
ejpam-5828	7	4	consistent	consistent	ADJ
ejpam-5828	7	5	results	result	NOUN
ejpam-5828	7	6	,	,	PUNCT
ejpam-5828	7	7	demonstrating	demonstrate	VERB
ejpam-5828	7	8	the	the	DET
ejpam-5828	7	9	model	model	NOUN
ejpam-5828	7	10	’s	’s	PART
ejpam-5828	7	11	robustness	robustness	NOUN
ejpam-5828	7	12	and	and	CCONJ
ejpam-5828	7	13	its	its	PRON
ejpam-5828	7	14	significance	significance	NOUN
ejpam-5828	7	15	for	for	ADP
ejpam-5828	7	16	understanding	understand	VERB
ejpam-5828	7	17	dissipative	dissipative	ADJ
ejpam-5828	7	18	quantum	quantum	NOUN
ejpam-5828	7	19	systems	system	NOUN
ejpam-5828	7	20	.	.	PUNCT
ejpam-5828	8	1	2020	2020	NUM
ejpam-5828	8	2	mathematics	mathematic	NOUN
ejpam-5828	8	3	subject	subject	NOUN
ejpam-5828	8	4	classifications	classification	NOUN
ejpam-5828	8	5	:	:	PUNCT
ejpam-5828	8	6	54c08	54c08	NUM
ejpam-5828	8	7	,	,	PUNCT
ejpam-5828	8	8	54c60	54c60	NUM
ejpam-5828	8	9	key	key	ADJ
ejpam-5828	8	10	words	word	NOUN
ejpam-5828	8	11	and	and	CCONJ
ejpam-5828	8	12	phrases	phrase	NOUN
ejpam-5828	8	13	:	:	PUNCT
ejpam-5828	8	14	poisson	poisson	PROPN
ejpam-5828	8	15	bracket	bracket	NOUN
ejpam-5828	8	16	,	,	PUNCT
ejpam-5828	8	17	creation	creation	NOUN
ejpam-5828	8	18	and	and	CCONJ
ejpam-5828	8	19	annihilation	annihilation	NOUN
ejpam-5828	8	20	operators	operator	NOUN
ejpam-5828	8	21	,	,	PUNCT
ejpam-5828	8	22	wkb	wkb	NOUN
ejpam-5828	8	23	approximation	approximation	NOUN
ejpam-5828	8	24	,	,	PUNCT
ejpam-5828	8	25	staeckel	staeckel	ADP
ejpam-5828	8	26	boundary	boundary	ADJ
ejpam-5828	8	27	conditions	condition	NOUN
ejpam-5828	8	28	,	,	PUNCT
ejpam-5828	8	29	two	two	NUM
ejpam-5828	8	30	-	-	PUNCT
ejpam-5828	8	31	dimensional	dimensional	ADJ
ejpam-5828	8	32	anisotropic	anisotropic	NOUN
ejpam-5828	8	33	,	,	PUNCT
ejpam-5828	8	34	harmonic	harmonic	ADJ
ejpam-5828	8	35	oscillator	oscillator	NOUN
ejpam-5828	8	36	dissipative	dissipative	NOUN
ejpam-5828	8	37	.	.	PUNCT
ejpam-5828	9	1	1	1	X
ejpam-5828	9	2	.	.	X
ejpam-5828	9	3	introduction	introduction	NOUN
ejpam-5828	9	4	describing	describe	VERB
ejpam-5828	9	5	microscopic	microscopic	ADJ
ejpam-5828	9	6	systems	system	NOUN
ejpam-5828	9	7	presents	present	VERB
ejpam-5828	9	8	a	a	DET
ejpam-5828	9	9	significant	significant	ADJ
ejpam-5828	9	10	challenge	challenge	NOUN
ejpam-5828	9	11	,	,	PUNCT
ejpam-5828	9	12	particularly	particularly	ADV
ejpam-5828	9	13	in	in	ADP
ejpam-5828	9	14	bridging	bridge	VERB
ejpam-5828	9	15	classical	classical	ADJ
ejpam-5828	9	16	and	and	CCONJ
ejpam-5828	9	17	quantum	quantum	ADJ
ejpam-5828	9	18	representations	representation	NOUN
ejpam-5828	9	19	through	through	ADP
ejpam-5828	9	20	hamiltonian	hamiltonian	ADJ
ejpam-5828	9	21	operator	operator	NOUN
ejpam-5828	9	22	quantization	quantization	NOUN
ejpam-5828	9	23	.	.	PUNCT
ejpam-5828	10	1	among	among	ADP
ejpam-5828	10	2	these	these	DET
ejpam-5828	10	3	systems	system	NOUN
ejpam-5828	10	4	,	,	PUNCT
ejpam-5828	10	5	the	the	DET
ejpam-5828	10	6	damped	damped	ADJ
ejpam-5828	10	7	harmonic	harmonic	ADJ
ejpam-5828	10	8	oscillator	oscillator	NOUN
ejpam-5828	10	9	is	be	AUX
ejpam-5828	10	10	of	of	ADP
ejpam-5828	10	11	particular	particular	ADJ
ejpam-5828	10	12	interest	interest	NOUN
ejpam-5828	10	13	due	due	ADP
ejpam-5828	10	14	to	to	ADP
ejpam-5828	10	15	its	its	PRON
ejpam-5828	10	16	inherent	inherent	ADJ
ejpam-5828	10	17	dissipative	dissipative	NOUN
ejpam-5828	10	18	nature	nature	NOUN
ejpam-5828	10	19	,	,	PUNCT
ejpam-5828	10	20	which	which	PRON
ejpam-5828	10	21	complicates	complicate	VERB
ejpam-5828	10	22	its	its	PRON
ejpam-5828	10	23	quantization	quantization	NOUN
ejpam-5828	10	24	.	.	PUNCT
ejpam-5828	11	1	canonical	canonical	ADJ
ejpam-5828	11	2	quantization	quantization	NOUN
ejpam-5828	11	3	methods	method	NOUN
ejpam-5828	11	4	,	,	PUNCT
ejpam-5828	11	5	including	include	VERB
ejpam-5828	11	6	coherent	coherent	ADJ
ejpam-5828	11	7	states	state	NOUN
ejpam-5828	11	8	and	and	CCONJ
ejpam-5828	11	9	time	time	NOUN
ejpam-5828	11	10	-	-	PUNCT
ejpam-5828	11	11	dependent	dependent	ADJ
ejpam-5828	11	12	creation	creation	NOUN
ejpam-5828	11	13	-	-	PUNCT
ejpam-5828	11	14	annihilation	annihilation	NOUN
ejpam-5828	11	15	operators	operator	NOUN
ejpam-5828	11	16	,	,	PUNCT
ejpam-5828	11	17	∗corresponding	∗corresponde	VERB
ejpam-5828	11	18	author	author	NOUN
ejpam-5828	11	19	.	.	PUNCT
ejpam-5828	12	1	doi	doi	NOUN
ejpam-5828	12	2	:	:	PUNCT
ejpam-5828	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5828	https://doi.org/10.29020/nybg.ejpam.v18i2.5828	PROPN
ejpam-5828	12	4	email	email	NOUN
ejpam-5828	12	5	addresses	address	NOUN
ejpam-5828	12	6	:	:	PUNCT
ejpam-5828	12	7	yazen.awaida@yahoo.com	yazen.awaida@yahoo.com	X
ejpam-5828	12	8	(	(	PUNCT
ejpam-5828	12	9	y.	y.	PROPN
ejpam-5828	12	10	m.	m.	PROPN
ejpam-5828	12	11	alawaideh	alawaideh	PROPN
ejpam-5828	12	12	)	)	PUNCT
ejpam-5828	12	13	,	,	PUNCT
ejpam-5828	12	14	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5828	12	15	1	1	NUM
ejpam-5828	12	16	copyright	copyright	NOUN
ejpam-5828	12	17	:	:	PUNCT
ejpam-5828	13	1	©	©	PROPN
ejpam-5828	13	2	2025	2025	NUM
ejpam-5828	13	3	the	the	DET
ejpam-5828	13	4	author(s	author(s	NOUN
ejpam-5828	13	5	)	)	PUNCT
ejpam-5828	13	6	.	.	PUNCT
ejpam-5828	14	1	(	(	PUNCT
ejpam-5828	14	2	cc	cc	NOUN
ejpam-5828	14	3	by	by	ADP
ejpam-5828	14	4	-	-	PUNCT
ejpam-5828	14	5	nc	nc	PROPN
ejpam-5828	14	6	4.0	4.0	NUM
ejpam-5828	14	7	)	)	PUNCT
ejpam-5828	14	8	b.	b.	PROPN
ejpam-5828	14	9	m.	m.	PROPN
ejpam-5828	14	10	al	al	PROPN
ejpam-5828	14	11	-	-	PUNCT
ejpam-5828	14	12	khamiseh	khamiseh	PROPN
ejpam-5828	14	13	et	et	PROPN
ejpam-5828	14	14	al	al	PROPN
ejpam-5828	14	15	.	.	PUNCT
ejpam-5828	14	16	/	/	SYM
ejpam-5828	14	17	eur	eur	PROPN
ejpam-5828	14	18	.	.	PUNCT
ejpam-5828	15	1	j.	j.	PROPN
ejpam-5828	15	2	pure	pure	PROPN
ejpam-5828	15	3	appl	appl	PROPN
ejpam-5828	15	4	.	.	PROPN
ejpam-5828	15	5	math	math	PROPN
ejpam-5828	15	6	,	,	PUNCT
ejpam-5828	15	7	18	18	NUM
ejpam-5828	15	8	(	(	PUNCT
ejpam-5828	15	9	2	2	NUM
ejpam-5828	15	10	)	)	PUNCT
ejpam-5828	15	11	(	(	PUNCT
ejpam-5828	15	12	2025	2025	NUM
ejpam-5828	15	13	)	)	PUNCT
ejpam-5828	15	14	,	,	PUNCT
ejpam-5828	15	15	5828	5828	NUM
ejpam-5828	15	16	2	2	NUM
ejpam-5828	15	17	of	of	ADP
ejpam-5828	15	18	25	25	NUM
ejpam-5828	15	19	have	have	AUX
ejpam-5828	15	20	been	be	AUX
ejpam-5828	15	21	widely	widely	ADV
ejpam-5828	15	22	explored	explore	VERB
ejpam-5828	15	23	to	to	PART
ejpam-5828	15	24	address	address	VERB
ejpam-5828	15	25	such	such	ADJ
ejpam-5828	15	26	systems	system	NOUN
ejpam-5828	16	1	[	[	X
ejpam-5828	16	2	1	1	NUM
ejpam-5828	16	3	,	,	PUNCT
ejpam-5828	16	4	2	2	NUM
ejpam-5828	16	5	]	]	PUNCT
ejpam-5828	16	6	.	.	PUNCT
ejpam-5828	17	1	the	the	DET
ejpam-5828	17	2	quantum	quantum	PROPN
ejpam-5828	17	3	bateman	bateman	NOUN
ejpam-5828	17	4	method	method	NOUN
ejpam-5828	17	5	has	have	AUX
ejpam-5828	17	6	also	also	ADV
ejpam-5828	17	7	been	be	AUX
ejpam-5828	17	8	extensively	extensively	ADV
ejpam-5828	17	9	studied	study	VERB
ejpam-5828	17	10	for	for	ADP
ejpam-5828	17	11	dissipative	dissipative	ADJ
ejpam-5828	17	12	systems	system	NOUN
ejpam-5828	17	13	,	,	PUNCT
ejpam-5828	17	14	offering	offer	VERB
ejpam-5828	17	15	valuable	valuable	ADJ
ejpam-5828	17	16	insights	insight	NOUN
ejpam-5828	17	17	[	[	X
ejpam-5828	17	18	3	3	NUM
ejpam-5828	17	19	–	–	PUNCT
ejpam-5828	17	20	5	5	NUM
ejpam-5828	17	21	]	]	PUNCT
ejpam-5828	17	22	.	.	PUNCT
ejpam-5828	18	1	additionally	additionally	ADV
ejpam-5828	18	2	,	,	PUNCT
ejpam-5828	18	3	fractional	fractional	ADJ
ejpam-5828	18	4	calculus	calculus	NOUN
ejpam-5828	18	5	techniques	technique	NOUN
ejpam-5828	18	6	have	have	AUX
ejpam-5828	18	7	been	be	AUX
ejpam-5828	18	8	employed	employ	VERB
ejpam-5828	18	9	to	to	PART
ejpam-5828	18	10	derive	derive	VERB
ejpam-5828	18	11	lagrangians	lagrangian	NOUN
ejpam-5828	18	12	and	and	CCONJ
ejpam-5828	18	13	hamiltonians	hamiltonian	NOUN
ejpam-5828	18	14	for	for	ADP
ejpam-5828	18	15	non	non	ADJ
ejpam-5828	18	16	-	-	ADJ
ejpam-5828	18	17	conservative	conservative	ADJ
ejpam-5828	18	18	systems	system	NOUN
ejpam-5828	18	19	,	,	PUNCT
ejpam-5828	18	20	further	far	ADV
ejpam-5828	18	21	advancing	advance	VERB
ejpam-5828	18	22	the	the	DET
ejpam-5828	18	23	field	field	NOUN
ejpam-5828	18	24	[	[	X
ejpam-5828	18	25	6	6	NUM
ejpam-5828	18	26	?	?	PUNCT
ejpam-5828	18	27	]	]	PUNCT
ejpam-5828	18	28	.	.	PUNCT
ejpam-5828	19	1	recent	recent	ADJ
ejpam-5828	19	2	studies	study	NOUN
ejpam-5828	19	3	have	have	AUX
ejpam-5828	19	4	focused	focus	VERB
ejpam-5828	19	5	on	on	ADP
ejpam-5828	19	6	time	time	NOUN
ejpam-5828	19	7	-	-	PUNCT
ejpam-5828	19	8	dependent	dependent	ADJ
ejpam-5828	19	9	harmonic	harmonic	ADJ
ejpam-5828	19	10	oscillators	oscillator	NOUN
ejpam-5828	19	11	and	and	CCONJ
ejpam-5828	19	12	particles	particle	NOUN
ejpam-5828	19	13	under	under	ADP
ejpam-5828	19	14	specific	specific	ADJ
ejpam-5828	19	15	potentials	potential	NOUN
ejpam-5828	19	16	,	,	PUNCT
ejpam-5828	19	17	emphasizing	emphasize	VERB
ejpam-5828	19	18	time	time	NOUN
ejpam-5828	19	19	-	-	PUNCT
ejpam-5828	19	20	dependent	dependent	ADJ
ejpam-5828	19	21	invariants	invariant	NOUN
ejpam-5828	19	22	[	[	X
ejpam-5828	19	23	7	7	NUM
ejpam-5828	19	24	]	]	PUNCT
ejpam-5828	19	25	.	.	PUNCT
ejpam-5828	20	1	efforts	effort	NOUN
ejpam-5828	20	2	to	to	PART
ejpam-5828	20	3	address	address	VERB
ejpam-5828	20	4	hamilton	hamilton	PROPN
ejpam-5828	20	5	-	-	PUNCT
ejpam-5828	20	6	jacobi	jacobi	PROPN
ejpam-5828	20	7	equations	equation	NOUN
ejpam-5828	20	8	using	use	VERB
ejpam-5828	20	9	electromagnetic	electromagnetic	ADJ
ejpam-5828	20	10	field	field	NOUN
ejpam-5828	20	11	techniques	technique	NOUN
ejpam-5828	20	12	have	have	AUX
ejpam-5828	20	13	also	also	ADV
ejpam-5828	20	14	been	be	AUX
ejpam-5828	20	15	made	make	VERB
ejpam-5828	20	16	,	,	PUNCT
ejpam-5828	20	17	with	with	ADP
ejpam-5828	20	18	methods	method	NOUN
ejpam-5828	20	19	such	such	ADJ
ejpam-5828	20	20	as	as	ADP
ejpam-5828	20	21	variable	variable	ADJ
ejpam-5828	20	22	separation	separation	NOUN
ejpam-5828	20	23	under	under	ADP
ejpam-5828	20	24	staeckel	staeckel	NOUN
ejpam-5828	20	25	conditions	condition	NOUN
ejpam-5828	20	26	and	and	CCONJ
ejpam-5828	20	27	newtonian	newtonian	ADJ
ejpam-5828	20	28	formalism	formalism	NOUN
ejpam-5828	20	29	being	be	AUX
ejpam-5828	20	30	applied	apply	VERB
ejpam-5828	20	31	[	[	PUNCT
ejpam-5828	20	32	8	8	NUM
ejpam-5828	20	33	]	]	PUNCT
ejpam-5828	20	34	.	.	PUNCT
ejpam-5828	21	1	despite	despite	SCONJ
ejpam-5828	21	2	these	these	DET
ejpam-5828	21	3	advancements	advancement	NOUN
ejpam-5828	21	4	,	,	PUNCT
ejpam-5828	21	5	challenges	challenge	NOUN
ejpam-5828	21	6	remain	remain	VERB
ejpam-5828	21	7	in	in	ADP
ejpam-5828	21	8	quantifying	quantify	VERB
ejpam-5828	21	9	dissipative	dissipative	ADJ
ejpam-5828	21	10	systems	system	NOUN
ejpam-5828	21	11	,	,	PUNCT
ejpam-5828	21	12	particularly	particularly	ADV
ejpam-5828	21	13	when	when	SCONJ
ejpam-5828	21	14	dissipation	dissipation	NOUN
ejpam-5828	21	15	depends	depend	VERB
ejpam-5828	21	16	solely	solely	ADV
ejpam-5828	21	17	on	on	ADP
ejpam-5828	21	18	coordinates	coordinate	NOUN
ejpam-5828	21	19	[	[	X
ejpam-5828	21	20	9	9	NUM
ejpam-5828	21	21	]	]	PUNCT
ejpam-5828	21	22	.	.	PUNCT
ejpam-5828	22	1	this	this	DET
ejpam-5828	22	2	highlights	highlight	VERB
ejpam-5828	22	3	the	the	DET
ejpam-5828	22	4	need	need	NOUN
ejpam-5828	22	5	for	for	ADP
ejpam-5828	22	6	innovative	innovative	ADJ
ejpam-5828	22	7	approaches	approach	NOUN
ejpam-5828	22	8	to	to	PART
ejpam-5828	22	9	better	well	ADV
ejpam-5828	22	10	understand	understand	VERB
ejpam-5828	22	11	and	and	CCONJ
ejpam-5828	22	12	model	model	VERB
ejpam-5828	22	13	such	such	ADJ
ejpam-5828	22	14	systems	system	NOUN
ejpam-5828	22	15	.	.	PUNCT
ejpam-5828	23	1	in	in	ADP
ejpam-5828	23	2	this	this	DET
ejpam-5828	23	3	context	context	NOUN
ejpam-5828	23	4	,	,	PUNCT
ejpam-5828	23	5	recent	recent	ADJ
ejpam-5828	23	6	research	research	NOUN
ejpam-5828	23	7	has	have	AUX
ejpam-5828	23	8	explored	explore	VERB
ejpam-5828	23	9	the	the	DET
ejpam-5828	23	10	application	application	NOUN
ejpam-5828	23	11	of	of	ADP
ejpam-5828	23	12	fractional	fractional	ADJ
ejpam-5828	23	13	calculus	calculus	NOUN
ejpam-5828	23	14	in	in	ADP
ejpam-5828	23	15	modeling	model	VERB
ejpam-5828	23	16	complex	complex	ADJ
ejpam-5828	23	17	dynamical	dynamical	ADJ
ejpam-5828	23	18	systems	system	NOUN
ejpam-5828	23	19	,	,	PUNCT
ejpam-5828	23	20	such	such	ADJ
ejpam-5828	23	21	as	as	ADP
ejpam-5828	23	22	the	the	DET
ejpam-5828	23	23	immune	immune	ADJ
ejpam-5828	23	24	system	system	NOUN
ejpam-5828	23	25	’s	’s	PART
ejpam-5828	23	26	response	response	NOUN
ejpam-5828	23	27	to	to	ADP
ejpam-5828	23	28	hiv	hiv	PROPN
ejpam-5828	23	29	-	-	PUNCT
ejpam-5828	23	30	tumor	tumor	NOUN
ejpam-5828	23	31	interactions	interaction	NOUN
ejpam-5828	23	32	,	,	PUNCT
ejpam-5828	23	33	providing	provide	VERB
ejpam-5828	23	34	a	a	DET
ejpam-5828	23	35	fractional	fractional	ADJ
ejpam-5828	23	36	framework	framework	NOUN
ejpam-5828	23	37	to	to	PART
ejpam-5828	23	38	understand	understand	VERB
ejpam-5828	23	39	these	these	DET
ejpam-5828	23	40	interactions	interaction	NOUN
ejpam-5828	23	41	.	.	PUNCT
ejpam-5828	24	1	similarly	similarly	ADV
ejpam-5828	24	2	,	,	PUNCT
ejpam-5828	24	3	numerical	numerical	ADJ
ejpam-5828	24	4	investigations	investigation	NOUN
ejpam-5828	24	5	using	use	VERB
ejpam-5828	24	6	caputo	caputo	PROPN
ejpam-5828	24	7	-	-	PUNCT
ejpam-5828	24	8	fabrizio	fabrizio	PROPN
ejpam-5828	24	9	fractional	fractional	ADJ
ejpam-5828	24	10	derivatives	derivative	NOUN
ejpam-5828	24	11	have	have	AUX
ejpam-5828	24	12	been	be	AUX
ejpam-5828	24	13	employed	employ	VERB
ejpam-5828	24	14	to	to	PART
ejpam-5828	24	15	study	study	VERB
ejpam-5828	24	16	the	the	DET
ejpam-5828	24	17	dynamical	dynamical	ADJ
ejpam-5828	24	18	behavior	behavior	NOUN
ejpam-5828	24	19	of	of	ADP
ejpam-5828	24	20	the	the	DET
ejpam-5828	24	21	hepatitis	hepatitis	PROPN
ejpam-5828	24	22	b	b	PROPN
ejpam-5828	24	23	virus	virus	NOUN
ejpam-5828	24	24	,	,	PUNCT
ejpam-5828	24	25	offering	offer	VERB
ejpam-5828	24	26	insights	insight	NOUN
ejpam-5828	24	27	into	into	ADP
ejpam-5828	24	28	the	the	DET
ejpam-5828	24	29	complex	complex	ADJ
ejpam-5828	24	30	dynamics	dynamic	NOUN
ejpam-5828	24	31	of	of	ADP
ejpam-5828	24	32	viral	viral	ADJ
ejpam-5828	24	33	infections	infection	NOUN
ejpam-5828	24	34	.	.	PUNCT
ejpam-5828	25	1	these	these	DET
ejpam-5828	25	2	studies	study	NOUN
ejpam-5828	25	3	demonstrate	demonstrate	VERB
ejpam-5828	25	4	the	the	DET
ejpam-5828	25	5	versatility	versatility	NOUN
ejpam-5828	25	6	of	of	ADP
ejpam-5828	25	7	fractional	fractional	ADJ
ejpam-5828	25	8	calculus	calculus	NOUN
ejpam-5828	25	9	in	in	ADP
ejpam-5828	25	10	addressing	address	VERB
ejpam-5828	25	11	real	real	ADJ
ejpam-5828	25	12	-	-	PUNCT
ejpam-5828	25	13	world	world	NOUN
ejpam-5828	25	14	dynamical	dynamical	ADJ
ejpam-5828	25	15	systems	system	NOUN
ejpam-5828	25	16	,	,	PUNCT
ejpam-5828	25	17	which	which	PRON
ejpam-5828	25	18	aligns	align	VERB
ejpam-5828	25	19	with	with	ADP
ejpam-5828	25	20	the	the	DET
ejpam-5828	25	21	challenges	challenge	NOUN
ejpam-5828	25	22	faced	face	VERB
ejpam-5828	25	23	in	in	ADP
ejpam-5828	25	24	quantizing	quantize	VERB
ejpam-5828	25	25	dissipative	dissipative	ADJ
ejpam-5828	25	26	systems	system	NOUN
ejpam-5828	25	27	.	.	PUNCT
ejpam-5828	26	1	for	for	ADP
ejpam-5828	26	2	instance	instance	NOUN
ejpam-5828	26	3	,	,	PUNCT
ejpam-5828	26	4	the	the	DET
ejpam-5828	26	5	fractional	fractional	ADJ
ejpam-5828	26	6	quantization	quantization	NOUN
ejpam-5828	26	7	of	of	ADP
ejpam-5828	26	8	podolsky	podolsky	ADJ
ejpam-5828	26	9	electrodynamics	electrodynamic	NOUN
ejpam-5828	26	10	using	use	VERB
ejpam-5828	26	11	the	the	DET
ejpam-5828	26	12	fractional	fractional	PROPN
ejpam-5828	26	13	hamilton	hamilton	PROPN
ejpam-5828	26	14	-	-	PUNCT
ejpam-5828	26	15	jacobi	jacobi	PROPN
ejpam-5828	26	16	formulation	formulation	NOUN
ejpam-5828	26	17	highlights	highlight	VERB
ejpam-5828	26	18	the	the	DET
ejpam-5828	26	19	potential	potential	NOUN
ejpam-5828	26	20	of	of	ADP
ejpam-5828	26	21	fractional	fractional	ADJ
ejpam-5828	26	22	calculus	calculus	NOUN
ejpam-5828	26	23	in	in	ADP
ejpam-5828	26	24	extending	extend	VERB
ejpam-5828	26	25	classical	classical	ADJ
ejpam-5828	26	26	and	and	CCONJ
ejpam-5828	26	27	quantum	quantum	NOUN
ejpam-5828	26	28	theories	theory	NOUN
ejpam-5828	26	29	to	to	ADP
ejpam-5828	26	30	systems	system	NOUN
ejpam-5828	26	31	with	with	ADP
ejpam-5828	26	32	nonlocal	nonlocal	ADJ
ejpam-5828	26	33	and	and	CCONJ
ejpam-5828	26	34	memory	memory	NOUN
ejpam-5828	26	35	dependent	dependent	ADJ
ejpam-5828	26	36	behaviors	behavior	NOUN
ejpam-5828	26	37	.	.	PUNCT
ejpam-5828	27	1	this	this	DET
ejpam-5828	27	2	approach	approach	NOUN
ejpam-5828	27	3	not	not	PART
ejpam-5828	27	4	only	only	ADV
ejpam-5828	27	5	bridges	bridge	VERB
ejpam-5828	27	6	the	the	DET
ejpam-5828	27	7	gap	gap	NOUN
ejpam-5828	27	8	between	between	ADP
ejpam-5828	27	9	classical	classical	ADJ
ejpam-5828	27	10	and	and	CCONJ
ejpam-5828	27	11	quantum	quantum	ADJ
ejpam-5828	27	12	descriptions	description	NOUN
ejpam-5828	27	13	but	but	CCONJ
ejpam-5828	27	14	also	also	ADV
ejpam-5828	27	15	provides	provide	VERB
ejpam-5828	27	16	a	a	DET
ejpam-5828	27	17	robust	robust	ADJ
ejpam-5828	27	18	framework	framework	NOUN
ejpam-5828	27	19	for	for	ADP
ejpam-5828	27	20	analyzing	analyze	VERB
ejpam-5828	27	21	systems	system	NOUN
ejpam-5828	27	22	with	with	ADP
ejpam-5828	27	23	fractional	fractional	ADJ
ejpam-5828	27	24	dynamics	dynamic	NOUN
ejpam-5828	27	25	,	,	PUNCT
ejpam-5828	27	26	such	such	ADJ
ejpam-5828	27	27	as	as	ADP
ejpam-5828	27	28	those	those	PRON
ejpam-5828	27	29	encountered	encounter	VERB
ejpam-5828	27	30	in	in	ADP
ejpam-5828	27	31	biological	biological	ADJ
ejpam-5828	27	32	and	and	CCONJ
ejpam-5828	27	33	physical	physical	ADJ
ejpam-5828	27	34	systems	system	NOUN
ejpam-5828	27	35	[	[	X
ejpam-5828	27	36	10–12	10–12	NUM
ejpam-5828	27	37	]	]	PUNCT
ejpam-5828	27	38	.	.	PUNCT
ejpam-5828	28	1	furthermore	furthermore	ADV
ejpam-5828	28	2	,	,	PUNCT
ejpam-5828	28	3	the	the	DET
ejpam-5828	28	4	madelung	madelung	ADJ
ejpam-5828	28	5	formalism	formalism	NOUN
ejpam-5828	28	6	has	have	AUX
ejpam-5828	28	7	been	be	AUX
ejpam-5828	28	8	applied	apply	VERB
ejpam-5828	28	9	to	to	ADP
ejpam-5828	28	10	dissipating	dissipate	VERB
ejpam-5828	28	11	and	and	CCONJ
ejpam-5828	28	12	decaying	decay	VERB
ejpam-5828	28	13	systems	system	NOUN
ejpam-5828	28	14	,	,	PUNCT
ejpam-5828	28	15	providing	provide	VERB
ejpam-5828	28	16	a	a	DET
ejpam-5828	28	17	deeper	deep	ADJ
ejpam-5828	28	18	understanding	understanding	NOUN
ejpam-5828	28	19	of	of	ADP
ejpam-5828	28	20	the	the	DET
ejpam-5828	28	21	quantum	quantum	ADJ
ejpam-5828	28	22	dynamics	dynamic	NOUN
ejpam-5828	28	23	of	of	ADP
ejpam-5828	28	24	such	such	ADJ
ejpam-5828	28	25	systems	system	NOUN
ejpam-5828	28	26	[	[	X
ejpam-5828	28	27	13	13	NUM
ejpam-5828	28	28	]	]	PUNCT
ejpam-5828	28	29	.	.	PUNCT
ejpam-5828	29	1	the	the	DET
ejpam-5828	29	2	quantum	quantum	PROPN
ejpam-5828	29	3	hamilton	hamilton	PROPN
ejpam-5828	29	4	-	-	PUNCT
ejpam-5828	29	5	jacobi	jacobi	PROPN
ejpam-5828	29	6	formalism	formalism	NOUN
ejpam-5828	29	7	has	have	AUX
ejpam-5828	29	8	also	also	ADV
ejpam-5828	29	9	been	be	AUX
ejpam-5828	29	10	extensively	extensively	ADV
ejpam-5828	29	11	studied	study	VERB
ejpam-5828	29	12	,	,	PUNCT
ejpam-5828	29	13	offering	offer	VERB
ejpam-5828	29	14	a	a	DET
ejpam-5828	29	15	robust	robust	ADJ
ejpam-5828	29	16	framework	framework	NOUN
ejpam-5828	29	17	for	for	ADP
ejpam-5828	29	18	analyzing	analyze	VERB
ejpam-5828	29	19	quantum	quantum	ADJ
ejpam-5828	29	20	systems	system	NOUN
ejpam-5828	29	21	with	with	ADP
ejpam-5828	29	22	dissipation[14	dissipation[14	PROPN
ejpam-5828	29	23	]	]	PUNCT
ejpam-5828	29	24	.	.	PUNCT
ejpam-5828	30	1	additionally	additionally	ADV
ejpam-5828	30	2	,	,	PUNCT
ejpam-5828	30	3	generalized	generalized	ADJ
ejpam-5828	30	4	creation	creation	NOUN
ejpam-5828	30	5	and	and	CCONJ
ejpam-5828	30	6	annihilation	annihilation	NOUN
ejpam-5828	30	7	operators	operator	NOUN
ejpam-5828	30	8	have	have	AUX
ejpam-5828	30	9	been	be	AUX
ejpam-5828	30	10	developed	develop	VERB
ejpam-5828	30	11	using	use	VERB
ejpam-5828	30	12	complex	complex	ADJ
ejpam-5828	30	13	nonlinear	nonlinear	ADJ
ejpam-5828	30	14	riccati	riccati	PROPN
ejpam-5828	30	15	equations	equation	NOUN
ejpam-5828	30	16	,	,	PUNCT
ejpam-5828	30	17	which	which	PRON
ejpam-5828	30	18	are	be	AUX
ejpam-5828	30	19	crucial	crucial	ADJ
ejpam-5828	30	20	for	for	ADP
ejpam-5828	30	21	understanding	understand	VERB
ejpam-5828	30	22	the	the	DET
ejpam-5828	30	23	quantization	quantization	NOUN
ejpam-5828	30	24	of	of	ADP
ejpam-5828	30	25	dissipative	dissipative	ADJ
ejpam-5828	30	26	systems	system	NOUN
ejpam-5828	30	27	[	[	X
ejpam-5828	30	28	15	15	NUM
ejpam-5828	30	29	]	]	PUNCT
ejpam-5828	30	30	.	.	PUNCT
ejpam-5828	31	1	recent	recent	ADJ
ejpam-5828	31	2	advancements	advancement	NOUN
ejpam-5828	31	3	in	in	ADP
ejpam-5828	31	4	dissipative	dissipative	ADJ
ejpam-5828	31	5	fuzzy	fuzzy	ADJ
ejpam-5828	31	6	tracking	tracking	NOUN
ejpam-5828	31	7	control	control	NOUN
ejpam-5828	31	8	for	for	ADP
ejpam-5828	31	9	nonlinear	nonlinear	ADJ
ejpam-5828	31	10	networked	networked	ADJ
ejpam-5828	31	11	systems	system	NOUN
ejpam-5828	31	12	with	with	ADP
ejpam-5828	31	13	quantization	quantization	NOUN
ejpam-5828	31	14	have	have	AUX
ejpam-5828	31	15	also	also	ADV
ejpam-5828	31	16	contributed	contribute	VERB
ejpam-5828	31	17	to	to	ADP
ejpam-5828	31	18	the	the	DET
ejpam-5828	31	19	field	field	NOUN
ejpam-5828	31	20	,	,	PUNCT
ejpam-5828	31	21	particularly	particularly	ADV
ejpam-5828	31	22	in	in	ADP
ejpam-5828	31	23	understanding	understand	VERB
ejpam-5828	31	24	the	the	DET
ejpam-5828	31	25	effects	effect	NOUN
ejpam-5828	31	26	of	of	ADP
ejpam-5828	31	27	quantization	quantization	NOUN
ejpam-5828	31	28	on	on	ADP
ejpam-5828	31	29	dissipative	dissipative	ADJ
ejpam-5828	31	30	systems	system	NOUN
ejpam-5828	31	31	[	[	X
ejpam-5828	31	32	16	16	NUM
ejpam-5828	31	33	]	]	PUNCT
ejpam-5828	31	34	.	.	PUNCT
ejpam-5828	32	1	recent	recent	ADJ
ejpam-5828	32	2	advancements	advancement	NOUN
ejpam-5828	32	3	in	in	ADP
ejpam-5828	32	4	dissipative	dissipative	ADJ
ejpam-5828	32	5	fuzzy	fuzzy	ADJ
ejpam-5828	32	6	tracking	tracking	NOUN
ejpam-5828	32	7	control	control	NOUN
ejpam-5828	32	8	for	for	ADP
ejpam-5828	32	9	nonlinear	nonlinear	ADJ
ejpam-5828	32	10	networked	networked	ADJ
ejpam-5828	32	11	systems	system	NOUN
ejpam-5828	32	12	with	with	ADP
ejpam-5828	32	13	quantization	quantization	NOUN
ejpam-5828	32	14	have	have	AUX
ejpam-5828	32	15	also	also	ADV
ejpam-5828	32	16	contributed	contribute	VERB
ejpam-5828	32	17	to	to	ADP
ejpam-5828	32	18	the	the	DET
ejpam-5828	32	19	field	field	NOUN
ejpam-5828	32	20	,	,	PUNCT
ejpam-5828	32	21	particularly	particularly	ADV
ejpam-5828	32	22	in	in	ADP
ejpam-5828	32	23	understanding	understand	VERB
ejpam-5828	32	24	the	the	DET
ejpam-5828	32	25	effects	effect	NOUN
ejpam-5828	32	26	of	of	ADP
ejpam-5828	32	27	quantization	quantization	NOUN
ejpam-5828	32	28	on	on	ADP
ejpam-5828	32	29	dissipative	dissipative	ADJ
ejpam-5828	32	30	systems	system	NOUN
ejpam-5828	32	31	[	[	X
ejpam-5828	32	32	17	17	NUM
ejpam-5828	32	33	]	]	PUNCT
ejpam-5828	32	34	.	.	PUNCT
ejpam-5828	33	1	this	this	DET
ejpam-5828	33	2	research	research	NOUN
ejpam-5828	33	3	aims	aim	VERB
ejpam-5828	33	4	to	to	PART
ejpam-5828	33	5	develop	develop	VERB
ejpam-5828	33	6	a	a	DET
ejpam-5828	33	7	hamiltonian	hamiltonian	ADJ
ejpam-5828	33	8	framework	framework	NOUN
ejpam-5828	33	9	to	to	PART
ejpam-5828	33	10	describe	describe	VERB
ejpam-5828	33	11	the	the	DET
ejpam-5828	33	12	two	two	NUM
ejpam-5828	33	13	-	-	PUNCT
ejpam-5828	33	14	dimensional	dimensional	ADJ
ejpam-5828	33	15	anisotropic	anisotropic	NOUN
ejpam-5828	33	16	harmonic	harmonic	ADJ
ejpam-5828	33	17	oscillator	oscillator	NOUN
ejpam-5828	33	18	with	with	ADP
ejpam-5828	33	19	damping	damp	VERB
ejpam-5828	33	20	effects	effect	NOUN
ejpam-5828	33	21	by	by	ADP
ejpam-5828	33	22	utilizing	utilize	VERB
ejpam-5828	33	23	the	the	DET
ejpam-5828	33	24	hamilton	hamilton	PROPN
ejpam-5828	33	25	-	-	PUNCT
ejpam-5828	33	26	jacobi	jacobi	PROPN
ejpam-5828	33	27	equations	equation	NOUN
ejpam-5828	33	28	to	to	PART
ejpam-5828	33	29	analyze	analyze	VERB
ejpam-5828	33	30	the	the	DET
ejpam-5828	33	31	dissipative	dissipative	ADJ
ejpam-5828	33	32	system	system	NOUN
ejpam-5828	33	33	.	.	PUNCT
ejpam-5828	34	1	to	to	PART
ejpam-5828	34	2	achieve	achieve	VERB
ejpam-5828	34	3	this	this	PRON
ejpam-5828	34	4	,	,	PUNCT
ejpam-5828	34	5	the	the	DET
ejpam-5828	34	6	researchers	researcher	NOUN
ejpam-5828	34	7	employed	employ	VERB
ejpam-5828	34	8	three	three	NUM
ejpam-5828	34	9	different	different	ADJ
ejpam-5828	34	10	quantization	quantization	NOUN
ejpam-5828	34	11	methods	method	NOUN
ejpam-5828	34	12	:	:	PUNCT
ejpam-5828	34	13	the	the	DET
ejpam-5828	34	14	wkb	wkb	PROPN
ejpam-5828	34	15	approximation	approximation	NOUN
ejpam-5828	34	16	and	and	CCONJ
ejpam-5828	34	17	creation	creation	NOUN
ejpam-5828	34	18	and	and	CCONJ
ejpam-5828	34	19	annihilation	annihilation	NOUN
ejpam-5828	34	20	operators	operator	NOUN
ejpam-5828	34	21	,	,	PUNCT
ejpam-5828	34	22	and	and	CCONJ
ejpam-5828	34	23	canonical	canonical	ADJ
ejpam-5828	34	24	quantization	quantization	NOUN
ejpam-5828	34	25	.	.	PUNCT
ejpam-5828	35	1	b.	b.	PROPN
ejpam-5828	35	2	m.	m.	PROPN
ejpam-5828	35	3	al	al	PROPN
ejpam-5828	35	4	-	-	PUNCT
ejpam-5828	35	5	khamiseh	khamiseh	PROPN
ejpam-5828	35	6	et	et	PROPN
ejpam-5828	35	7	al	al	PROPN
ejpam-5828	35	8	.	.	PUNCT
ejpam-5828	35	9	/	/	SYM
ejpam-5828	35	10	eur	eur	PROPN
ejpam-5828	35	11	.	.	PUNCT
ejpam-5828	36	1	j.	j.	PROPN
ejpam-5828	36	2	pure	pure	PROPN
ejpam-5828	36	3	appl	appl	PROPN
ejpam-5828	36	4	.	.	PROPN
ejpam-5828	36	5	math	math	PROPN
ejpam-5828	36	6	,	,	PUNCT
ejpam-5828	36	7	18	18	NUM
ejpam-5828	36	8	(	(	PUNCT
ejpam-5828	36	9	2	2	NUM
ejpam-5828	36	10	)	)	PUNCT
ejpam-5828	36	11	(	(	PUNCT
ejpam-5828	36	12	2025	2025	NUM
ejpam-5828	36	13	)	)	PUNCT
ejpam-5828	36	14	,	,	PUNCT
ejpam-5828	36	15	5828	5828	NUM
ejpam-5828	36	16	3	3	NUM
ejpam-5828	36	17	of	of	ADP
ejpam-5828	36	18	25	25	NUM
ejpam-5828	36	19	the	the	DET
ejpam-5828	36	20	paper	paper	NOUN
ejpam-5828	36	21	follows	follow	VERB
ejpam-5828	36	22	a	a	DET
ejpam-5828	36	23	structured	structured	ADJ
ejpam-5828	36	24	approach	approach	NOUN
ejpam-5828	36	25	,	,	PUNCT
ejpam-5828	36	26	beginning	begin	VERB
ejpam-5828	36	27	with	with	ADP
ejpam-5828	36	28	an	an	DET
ejpam-5828	36	29	introduction	introduction	NOUN
ejpam-5828	36	30	that	that	PRON
ejpam-5828	36	31	discusses	discuss	VERB
ejpam-5828	36	32	the	the	DET
ejpam-5828	36	33	challenges	challenge	NOUN
ejpam-5828	36	34	of	of	ADP
ejpam-5828	36	35	quantizing	quantize	VERB
ejpam-5828	36	36	dissipative	dissipative	ADJ
ejpam-5828	36	37	systems	system	NOUN
ejpam-5828	36	38	and	and	CCONJ
ejpam-5828	36	39	reviews	review	VERB
ejpam-5828	36	40	existing	exist	VERB
ejpam-5828	36	41	methods	method	NOUN
ejpam-5828	36	42	such	such	ADJ
ejpam-5828	36	43	as	as	ADP
ejpam-5828	36	44	canonical	canonical	ADJ
ejpam-5828	36	45	quantization	quantization	NOUN
ejpam-5828	36	46	,	,	PUNCT
ejpam-5828	36	47	fractional	fractional	ADJ
ejpam-5828	36	48	calculus	calculus	NOUN
ejpam-5828	36	49	,	,	PUNCT
ejpam-5828	36	50	and	and	CCONJ
ejpam-5828	36	51	hamilto	hamilto	VERB
ejpam-5828	36	52	jacobi	jacobi	PROPN
ejpam-5828	36	53	approaches	approach	VERB
ejpam-5828	36	54	.	.	PUNCT
ejpam-5828	37	1	it	it	PRON
ejpam-5828	37	2	then	then	ADV
ejpam-5828	37	3	develops	develop	VERB
ejpam-5828	37	4	the	the	DET
ejpam-5828	37	5	hamiltonian	hamiltonian	ADJ
ejpam-5828	37	6	and	and	CCONJ
ejpam-5828	37	7	lagrangian	lagrangian	ADJ
ejpam-5828	37	8	formulations	formulation	NOUN
ejpam-5828	37	9	for	for	ADP
ejpam-5828	37	10	the	the	DET
ejpam-5828	37	11	two	two	NUM
ejpam-5828	37	12	-	-	PUNCT
ejpam-5828	37	13	dimensional	dimensional	ADJ
ejpam-5828	37	14	dissipative	dissipative	ADJ
ejpam-5828	37	15	harmonic	harmonic	ADJ
ejpam-5828	37	16	oscillator	oscillator	NOUN
ejpam-5828	37	17	,	,	PUNCT
ejpam-5828	37	18	based	base	VERB
ejpam-5828	37	19	on	on	ADP
ejpam-5828	37	20	bateman	bateman	PROPN
ejpam-5828	37	21	’s	’s	PART
ejpam-5828	37	22	approach	approach	NOUN
ejpam-5828	37	23	.	.	PUNCT
ejpam-5828	38	1	the	the	DET
ejpam-5828	38	2	study	study	NOUN
ejpam-5828	38	3	applies	apply	VERB
ejpam-5828	38	4	the	the	DET
ejpam-5828	38	5	wkb	wkb	PROPN
ejpam-5828	38	6	approximation	approximation	NOUN
ejpam-5828	38	7	to	to	PART
ejpam-5828	38	8	quantize	quantize	VERB
ejpam-5828	38	9	the	the	DET
ejpam-5828	38	10	system	system	NOUN
ejpam-5828	38	11	and	and	CCONJ
ejpam-5828	38	12	analyze	analyze	VERB
ejpam-5828	38	13	its	its	PRON
ejpam-5828	38	14	energy	energy	NOUN
ejpam-5828	38	15	levels	level	NOUN
ejpam-5828	38	16	,	,	PUNCT
ejpam-5828	38	17	followed	follow	VERB
ejpam-5828	38	18	by	by	ADP
ejpam-5828	38	19	canonical	canonical	ADJ
ejpam-5828	38	20	quantization	quantization	NOUN
ejpam-5828	38	21	using	use	VERB
ejpam-5828	38	22	the	the	DET
ejpam-5828	38	23	nikiforov	nikiforov	NOUN
ejpam-5828	38	24	-	-	PUNCT
ejpam-5828	38	25	uvarov	uvarov	ADJ
ejpam-5828	38	26	method	method	NOUN
ejpam-5828	38	27	,	,	PUNCT
ejpam-5828	38	28	which	which	PRON
ejpam-5828	38	29	solves	solve	VERB
ejpam-5828	38	30	the	the	DET
ejpam-5828	38	31	schrödinger	schrödinger	NOUN
ejpam-5828	38	32	equation	equation	NOUN
ejpam-5828	38	33	to	to	PART
ejpam-5828	38	34	derive	derive	VERB
ejpam-5828	38	35	energy	energy	NOUN
ejpam-5828	38	36	eigenvalues	eigenvalue	NOUN
ejpam-5828	38	37	and	and	CCONJ
ejpam-5828	38	38	wave	wave	NOUN
ejpam-5828	38	39	functions	function	NOUN
ejpam-5828	38	40	.	.	PUNCT
ejpam-5828	39	1	the	the	DET
ejpam-5828	39	2	separation	separation	NOUN
ejpam-5828	39	3	of	of	ADP
ejpam-5828	39	4	variables	variable	NOUN
ejpam-5828	39	5	in	in	ADP
ejpam-5828	39	6	the	the	DET
ejpam-5828	39	7	hamilton	hamilton	PROPN
ejpam-5828	39	8	-	-	PUNCT
ejpam-5828	39	9	jacobi	jacobi	PROPN
ejpam-5828	39	10	equation	equation	NOUN
ejpam-5828	39	11	is	be	AUX
ejpam-5828	39	12	examined	examine	VERB
ejpam-5828	39	13	using	use	VERB
ejpam-5828	39	14	staeckel	staeckel	NOUN
ejpam-5828	39	15	boundary	boundary	ADJ
ejpam-5828	39	16	conditions	condition	NOUN
ejpam-5828	39	17	to	to	PART
ejpam-5828	39	18	facilitate	facilitate	VERB
ejpam-5828	39	19	the	the	DET
ejpam-5828	39	20	quantization	quantization	NOUN
ejpam-5828	39	21	process	process	NOUN
ejpam-5828	39	22	.	.	PUNCT
ejpam-5828	40	1	additionally	additionally	ADV
ejpam-5828	40	2	,	,	PUNCT
ejpam-5828	40	3	the	the	DET
ejpam-5828	40	4	paper	paper	NOUN
ejpam-5828	40	5	reformulates	reformulate	VERB
ejpam-5828	40	6	the	the	DET
ejpam-5828	40	7	dissipative	dissipative	ADJ
ejpam-5828	40	8	system	system	NOUN
ejpam-5828	40	9	through	through	ADP
ejpam-5828	40	10	poisson	poisson	NOUN
ejpam-5828	40	11	brackets	bracket	NOUN
ejpam-5828	40	12	,	,	PUNCT
ejpam-5828	40	13	applying	apply	VERB
ejpam-5828	40	14	standard	standard	ADJ
ejpam-5828	40	15	quantization	quantization	NOUN
ejpam-5828	40	16	rules	rule	NOUN
ejpam-5828	40	17	to	to	PART
ejpam-5828	40	18	obtain	obtain	VERB
ejpam-5828	40	19	heisenberg	heisenberg	PROPN
ejpam-5828	40	20	equations	equation	NOUN
ejpam-5828	40	21	and	and	CCONJ
ejpam-5828	40	22	expectation	expectation	NOUN
ejpam-5828	40	23	values	value	NOUN
ejpam-5828	40	24	.	.	PUNCT
ejpam-5828	41	1	the	the	DET
ejpam-5828	41	2	study	study	NOUN
ejpam-5828	41	3	further	far	ADV
ejpam-5828	41	4	explores	explore	VERB
ejpam-5828	41	5	the	the	DET
ejpam-5828	41	6	applications	application	NOUN
ejpam-5828	41	7	of	of	ADP
ejpam-5828	41	8	the	the	DET
ejpam-5828	41	9	hamilton	hamilton	PROPN
ejpam-5828	41	10	-	-	PUNCT
ejpam-5828	41	11	jacobi	jacobi	PROPN
ejpam-5828	41	12	technique	technique	NOUN
ejpam-5828	41	13	,	,	PUNCT
ejpam-5828	41	14	demonstrating	demonstrate	VERB
ejpam-5828	41	15	its	its	PRON
ejpam-5828	41	16	use	use	NOUN
ejpam-5828	41	17	in	in	ADP
ejpam-5828	41	18	understanding	understand	VERB
ejpam-5828	41	19	oscillatory	oscillatory	ADJ
ejpam-5828	41	20	dynamics	dynamic	NOUN
ejpam-5828	41	21	,	,	PUNCT
ejpam-5828	41	22	dissipative	dissipative	ADJ
ejpam-5828	41	23	effects	effect	NOUN
ejpam-5828	41	24	,	,	PUNCT
ejpam-5828	41	25	and	and	CCONJ
ejpam-5828	41	26	chaos	chaos	NOUN
ejpam-5828	41	27	in	in	ADP
ejpam-5828	41	28	quantum	quantum	NOUN
ejpam-5828	41	29	and	and	CCONJ
ejpam-5828	41	30	relativistic	relativistic	ADJ
ejpam-5828	41	31	systems	system	NOUN
ejpam-5828	41	32	.	.	PUNCT
ejpam-5828	42	1	to	to	PART
ejpam-5828	42	2	illustrate	illustrate	VERB
ejpam-5828	42	3	the	the	DET
ejpam-5828	42	4	effects	effect	NOUN
ejpam-5828	42	5	of	of	ADP
ejpam-5828	42	6	dissipation	dissipation	NOUN
ejpam-5828	42	7	on	on	ADP
ejpam-5828	42	8	quantum	quantum	ADJ
ejpam-5828	42	9	states	state	NOUN
ejpam-5828	42	10	,	,	PUNCT
ejpam-5828	42	11	the	the	DET
ejpam-5828	42	12	paper	paper	NOUN
ejpam-5828	42	13	presents	present	VERB
ejpam-5828	42	14	graphical	graphical	ADJ
ejpam-5828	42	15	representations	representation	NOUN
ejpam-5828	42	16	of	of	ADP
ejpam-5828	42	17	energy	energy	NOUN
ejpam-5828	42	18	levels	level	NOUN
ejpam-5828	42	19	and	and	CCONJ
ejpam-5828	42	20	probability	probability	NOUN
ejpam-5828	42	21	distributions	distribution	NOUN
ejpam-5828	42	22	.	.	PUNCT
ejpam-5828	43	1	in	in	ADP
ejpam-5828	43	2	the	the	DET
ejpam-5828	43	3	future	future	ADJ
ejpam-5828	43	4	directions	direction	NOUN
ejpam-5828	43	5	,	,	PUNCT
ejpam-5828	43	6	it	it	PRON
ejpam-5828	43	7	proposes	propose	VERB
ejpam-5828	43	8	extending	extend	VERB
ejpam-5828	43	9	the	the	DET
ejpam-5828	43	10	model	model	NOUN
ejpam-5828	43	11	to	to	ADP
ejpam-5828	43	12	three	three	NUM
ejpam-5828	43	13	dimensions	dimension	NOUN
ejpam-5828	43	14	and	and	CCONJ
ejpam-5828	43	15	incorporating	incorporate	VERB
ejpam-5828	43	16	additional	additional	ADJ
ejpam-5828	43	17	coupling	coupling	NOUN
ejpam-5828	43	18	terms	term	NOUN
ejpam-5828	43	19	to	to	PART
ejpam-5828	43	20	enhance	enhance	VERB
ejpam-5828	43	21	the	the	DET
ejpam-5828	43	22	understanding	understanding	NOUN
ejpam-5828	43	23	of	of	ADP
ejpam-5828	43	24	anisotropic	anisotropic	NOUN
ejpam-5828	43	25	and	and	CCONJ
ejpam-5828	43	26	dissipative	dissipative	ADJ
ejpam-5828	43	27	quantum	quantum	NOUN
ejpam-5828	43	28	systems	system	NOUN
ejpam-5828	43	29	.	.	PUNCT
ejpam-5828	44	1	the	the	DET
ejpam-5828	44	2	study	study	NOUN
ejpam-5828	44	3	also	also	ADV
ejpam-5828	44	4	compares	compare	VERB
ejpam-5828	44	5	its	its	PRON
ejpam-5828	44	6	findings	finding	NOUN
ejpam-5828	44	7	with	with	ADP
ejpam-5828	44	8	previous	previous	ADJ
ejpam-5828	44	9	research	research	NOUN
ejpam-5828	44	10	,	,	PUNCT
ejpam-5828	44	11	emphasizing	emphasize	VERB
ejpam-5828	44	12	improvements	improvement	NOUN
ejpam-5828	44	13	in	in	ADP
ejpam-5828	44	14	quantization	quantization	NOUN
ejpam-5828	44	15	techniques	technique	NOUN
ejpam-5828	44	16	and	and	CCONJ
ejpam-5828	44	17	theoretical	theoretical	ADJ
ejpam-5828	44	18	modeling	modeling	NOUN
ejpam-5828	44	19	.	.	PUNCT
ejpam-5828	45	1	finally	finally	ADV
ejpam-5828	45	2	,	,	PUNCT
ejpam-5828	45	3	the	the	DET
ejpam-5828	45	4	conclusions	conclusion	NOUN
ejpam-5828	45	5	summarize	summarize	VERB
ejpam-5828	45	6	key	key	ADJ
ejpam-5828	45	7	findings	finding	NOUN
ejpam-5828	45	8	,	,	PUNCT
ejpam-5828	45	9	including	include	VERB
ejpam-5828	45	10	the	the	DET
ejpam-5828	45	11	consistency	consistency	NOUN
ejpam-5828	45	12	of	of	ADP
ejpam-5828	45	13	different	different	ADJ
ejpam-5828	45	14	quantization	quantization	NOUN
ejpam-5828	45	15	methods	method	NOUN
ejpam-5828	45	16	,	,	PUNCT
ejpam-5828	45	17	the	the	DET
ejpam-5828	45	18	validation	validation	NOUN
ejpam-5828	45	19	of	of	ADP
ejpam-5828	45	20	the	the	DET
ejpam-5828	45	21	hamilton	hamilton	PROPN
ejpam-5828	45	22	-	-	PUNCT
ejpam-5828	45	23	jacobi	jacobi	PROPN
ejpam-5828	45	24	formalism	formalism	NOUN
ejpam-5828	45	25	,	,	PUNCT
ejpam-5828	45	26	and	and	CCONJ
ejpam-5828	45	27	the	the	DET
ejpam-5828	45	28	significance	significance	NOUN
ejpam-5828	45	29	of	of	ADP
ejpam-5828	45	30	dissipation	dissipation	NOUN
ejpam-5828	45	31	in	in	ADP
ejpam-5828	45	32	quantum	quantum	ADJ
ejpam-5828	45	33	mechanics	mechanic	NOUN
ejpam-5828	45	34	.	.	PUNCT
ejpam-5828	46	1	2	2	X
ejpam-5828	46	2	.	.	X
ejpam-5828	46	3	dissipative	dissipative	ADJ
ejpam-5828	46	4	anisotropic	anisotropic	NOUN
ejpam-5828	46	5	harmonic	harmonic	ADJ
ejpam-5828	46	6	oscillators	oscillator	NOUN
ejpam-5828	46	7	:	:	PUNCT
ejpam-5828	46	8	hamiltonian	hamiltonian	ADJ
ejpam-5828	46	9	and	and	CCONJ
ejpam-5828	46	10	lagrangian	lagrangian	ADJ
ejpam-5828	46	11	formalis	formali	NOUN
ejpam-5828	46	12	in	in	ADP
ejpam-5828	46	13	this	this	DET
ejpam-5828	46	14	section	section	NOUN
ejpam-5828	47	1	,	,	PUNCT
ejpam-5828	47	2	we	we	PRON
ejpam-5828	47	3	use	use	VERB
ejpam-5828	47	4	the	the	DET
ejpam-5828	47	5	lagrangian	lagrangian	NOUN
ejpam-5828	47	6	proposed	propose	VERB
ejpam-5828	47	7	by	by	ADP
ejpam-5828	47	8	bateman	bateman	NOUN
ejpam-5828	47	9	to	to	PART
ejpam-5828	47	10	describe	describe	VERB
ejpam-5828	47	11	the	the	DET
ejpam-5828	47	12	twodimensional	twodimensional	ADJ
ejpam-5828	47	13	dissipative	dissipative	ADJ
ejpam-5828	47	14	system	system	NOUN
ejpam-5828	47	15	.	.	PUNCT
ejpam-5828	48	1	this	this	DET
ejpam-5828	48	2	lagrangian	lagrangian	NOUN
ejpam-5828	48	3	provides	provide	VERB
ejpam-5828	48	4	a	a	DET
ejpam-5828	48	5	framework	framework	NOUN
ejpam-5828	48	6	for	for	ADP
ejpam-5828	48	7	describing	describe	VERB
ejpam-5828	48	8	dissipation	dissipation	NOUN
ejpam-5828	48	9	in	in	ADP
ejpam-5828	48	10	the	the	DET
ejpam-5828	48	11	system	system	NOUN
ejpam-5828	48	12	,	,	PUNCT
ejpam-5828	48	13	but	but	CCONJ
ejpam-5828	48	14	quantization	quantization	NOUN
ejpam-5828	48	15	is	be	AUX
ejpam-5828	48	16	carried	carry	VERB
ejpam-5828	48	17	out	out	ADP
ejpam-5828	48	18	using	use	VERB
ejpam-5828	48	19	other	other	ADJ
ejpam-5828	48	20	methods	method	NOUN
ejpam-5828	48	21	such	such	ADJ
ejpam-5828	48	22	as	as	ADP
ejpam-5828	48	23	the	the	DET
ejpam-5828	48	24	wkb	wkb	NOUN
ejpam-5828	48	25	approximation	approximation	NOUN
ejpam-5828	48	26	and	and	CCONJ
ejpam-5828	48	27	canonical	canonical	ADJ
ejpam-5828	48	28	quantization	quantization	NOUN
ejpam-5828	49	1	.the	.the	DET
ejpam-5828	49	2	lagrangian	lagrangian	ADJ
ejpam-5828	49	3	used	use	VERB
ejpam-5828	49	4	in	in	ADP
ejpam-5828	49	5	eq	eq	ADP
ejpam-5828	49	6	.	.	PUNCT
ejpam-5828	50	1	(	(	PUNCT
ejpam-5828	50	2	1	1	X
ejpam-5828	50	3	)	)	PUNCT
ejpam-5828	50	4	was	be	AUX
ejpam-5828	50	5	originally	originally	ADV
ejpam-5828	50	6	proposed	propose	VERB
ejpam-5828	50	7	by	by	ADP
ejpam-5828	50	8	bateman	bateman	NOUN
ejpam-5828	50	9	[	[	X
ejpam-5828	50	10	18	18	NUM
ejpam-5828	50	11	]	]	PUNCT
ejpam-5828	50	12	and	and	CCONJ
ejpam-5828	50	13	later	later	ADV
ejpam-5828	50	14	utilized	utilize	VERB
ejpam-5828	50	15	in	in	ADP
ejpam-5828	50	16	various	various	ADJ
ejpam-5828	50	17	studies	study	NOUN
ejpam-5828	50	18	,	,	PUNCT
ejpam-5828	50	19	including	include	VERB
ejpam-5828	50	20	[	[	X
ejpam-5828	50	21	19	19	NUM
ejpam-5828	50	22	]	]	PUNCT
ejpam-5828	50	23	,	,	PUNCT
ejpam-5828	50	24	to	to	PART
ejpam-5828	50	25	model	model	VERB
ejpam-5828	50	26	dissipative	dissipative	NOUN
ejpam-5828	50	27	two	two	NUM
ejpam-5828	50	28	dimensional	dimensional	ADJ
ejpam-5828	50	29	anisotropic	anisotropic	NOUN
ejpam-5828	50	30	harmonic	harmonic	ADJ
ejpam-5828	50	31	oscillators	oscillator	NOUN
ejpam-5828	50	32	l	l	NOUN
ejpam-5828	51	1	=	=	PUNCT
ejpam-5828	51	2	2∑	2∑	NUM
ejpam-5828	51	3	i=1	i=1	PROPN
ejpam-5828	51	4	(	(	PUNCT
ejpam-5828	51	5	1	1	NUM
ejpam-5828	51	6	2	2	NUM
ejpam-5828	51	7	mq2i	mq2i	NOUN
ejpam-5828	51	8	−	−	NOUN
ejpam-5828	51	9	2π2mv2i	2π2mv2i	NUM
ejpam-5828	51	10	q	q	NOUN
ejpam-5828	51	11	2	2	NUM
ejpam-5828	51	12	i	i	NOUN
ejpam-5828	51	13	)	)	PUNCT
ejpam-5828	51	14	e	e	X
ejpam-5828	51	15	λit	λit	VERB
ejpam-5828	51	16	(	(	PUNCT
ejpam-5828	51	17	1	1	X
ejpam-5828	51	18	)	)	PUNCT
ejpam-5828	51	19	in	in	ADP
ejpam-5828	51	20	accordance	accordance	NOUN
ejpam-5828	51	21	with	with	ADP
ejpam-5828	51	22	(	(	PUNCT
ejpam-5828	51	23	1	1	NUM
ejpam-5828	51	24	)	)	PUNCT
ejpam-5828	51	25	,	,	PUNCT
ejpam-5828	51	26	the	the	DET
ejpam-5828	51	27	equations	equation	NOUN
ejpam-5828	51	28	of	of	ADP
ejpam-5828	51	29	motion	motion	NOUN
ejpam-5828	51	30	can	can	AUX
ejpam-5828	51	31	be	be	AUX
ejpam-5828	51	32	expressed	express	VERB
ejpam-5828	51	33	as	as	ADP
ejpam-5828	51	34	:	:	PUNCT
ejpam-5828	51	35	q̈1	q̈1	NOUN
ejpam-5828	51	36	+	+	CCONJ
ejpam-5828	51	37	λ1q1	λ1q1	PUNCT
ejpam-5828	52	1	+	+	SYM
ejpam-5828	52	2	4π2v21q1	4π2v21q1	NUM
ejpam-5828	52	3	=	=	SYM
ejpam-5828	52	4	0	0	NUM
ejpam-5828	52	5	q̈2	q̈2	VERB
ejpam-5828	53	1	+	+	CCONJ
ejpam-5828	53	2	λ2q1	λ2q1	PROPN
ejpam-5828	53	3	+	+	NUM
ejpam-5828	53	4	4π2v22q2	4π2v22q2	NOUN
ejpam-5828	53	5	=	=	SYM
ejpam-5828	53	6	0	0	PROPN
ejpam-5828	53	7	b.	b.	PROPN
ejpam-5828	53	8	m.	m.	PROPN
ejpam-5828	54	1	al	al	PROPN
ejpam-5828	54	2	-	-	PUNCT
ejpam-5828	54	3	khamiseh	khamiseh	PROPN
ejpam-5828	54	4	et	et	PROPN
ejpam-5828	54	5	al	al	PROPN
ejpam-5828	54	6	.	.	PUNCT
ejpam-5828	54	7	/	/	SYM
ejpam-5828	54	8	eur	eur	PROPN
ejpam-5828	54	9	.	.	PUNCT
ejpam-5828	55	1	j.	j.	PROPN
ejpam-5828	55	2	pure	pure	PROPN
ejpam-5828	55	3	appl	appl	PROPN
ejpam-5828	55	4	.	.	PROPN
ejpam-5828	55	5	math	math	PROPN
ejpam-5828	55	6	,	,	PUNCT
ejpam-5828	55	7	18	18	NUM
ejpam-5828	55	8	(	(	PUNCT
ejpam-5828	55	9	2	2	NUM
ejpam-5828	55	10	)	)	PUNCT
ejpam-5828	55	11	(	(	PUNCT
ejpam-5828	55	12	2025	2025	NUM
ejpam-5828	55	13	)	)	PUNCT
ejpam-5828	55	14	,	,	PUNCT
ejpam-5828	55	15	5828	5828	NUM
ejpam-5828	55	16	4	4	NUM
ejpam-5828	55	17	of	of	ADP
ejpam-5828	55	18	25	25	NUM
ejpam-5828	55	19	this	this	DET
ejpam-5828	55	20	transformation	transformation	NOUN
ejpam-5828	55	21	clearly	clearly	ADV
ejpam-5828	55	22	delineates	delineate	VERB
ejpam-5828	55	23	the	the	DET
ejpam-5828	55	24	dissipative	dissipative	ADJ
ejpam-5828	55	25	nature	nature	NOUN
ejpam-5828	55	26	of	of	ADP
ejpam-5828	55	27	the	the	DET
ejpam-5828	55	28	two	two	NUM
ejpam-5828	55	29	-	-	PUNCT
ejpam-5828	55	30	dimensional	dimensional	ADJ
ejpam-5828	55	31	anisotropic	anisotropic	NOUN
ejpam-5828	55	32	harmonic	harmonic	ADJ
ejpam-5828	55	33	oscillator	oscillator	NOUN
ejpam-5828	55	34	.	.	PUNCT
ejpam-5828	56	1	xi	xi	X
ejpam-5828	57	1	=	=	NOUN
ejpam-5828	57	2	2∑	2∑	NUM
ejpam-5828	57	3	i=1	i=1	PROPN
ejpam-5828	57	4	qie	qie	PROPN
ejpam-5828	57	5	λit	λit	VERB
ejpam-5828	57	6	2	2	NUM
ejpam-5828	57	7	for	for	ADP
ejpam-5828	57	8	i	i	PRON
ejpam-5828	57	9	=	=	NOUN
ejpam-5828	57	10	1	1	NUM
ejpam-5828	57	11	,	,	PUNCT
ejpam-5828	57	12	2	2	NUM
ejpam-5828	57	13	,	,	PUNCT
ejpam-5828	57	14	the	the	DET
ejpam-5828	57	15	lagrangian	lagrangian	NOUN
ejpam-5828	57	16	is	be	AUX
ejpam-5828	57	17	transformed	transform	VERB
ejpam-5828	57	18	as	as	ADP
ejpam-5828	57	19	follows	follow	NOUN
ejpam-5828	57	20	based	base	VERB
ejpam-5828	57	21	on	on	ADP
ejpam-5828	57	22	the	the	DET
ejpam-5828	57	23	preceding	precede	VERB
ejpam-5828	57	24	equation	equation	NOUN
ejpam-5828	57	25	:	:	PUNCT
ejpam-5828	58	1	l	l	X
ejpam-5828	58	2	=	=	PUNCT
ejpam-5828	59	1	2∑	2∑	NUM
ejpam-5828	59	2	i=1	i=1	SYM
ejpam-5828	59	3	1	1	NUM
ejpam-5828	59	4	2	2	NUM
ejpam-5828	59	5	mx2i	mx2i	NOUN
ejpam-5828	59	6	+	+	CCONJ
ejpam-5828	59	7	1	1	NUM
ejpam-5828	59	8	8	8	NUM
ejpam-5828	59	9	mλ2ix	mλ2ix	NOUN
ejpam-5828	59	10	2	2	NUM
ejpam-5828	60	1	i	i	PRON
ejpam-5828	60	2	−	−	VERB
ejpam-5828	60	3	1	1	NUM
ejpam-5828	60	4	4	4	NUM
ejpam-5828	60	5	mλiẋixi	mλiẋixi	NOUN
ejpam-5828	60	6	−	−	NUM
ejpam-5828	60	7	2π2mv2i	2π2mv2i	NUM
ejpam-5828	60	8	x	x	SYM
ejpam-5828	60	9	2	2	NUM
ejpam-5828	60	10	i	i	PRON
ejpam-5828	60	11	when	when	SCONJ
ejpam-5828	60	12	the	the	DET
ejpam-5828	60	13	terms	term	NOUN
ejpam-5828	60	14	ẋi	ẋi	PROPN
ejpam-5828	60	15	and	and	CCONJ
ejpam-5828	60	16	xi	xi	X
ejpam-5828	60	17	in	in	ADP
ejpam-5828	60	18	the	the	DET
ejpam-5828	60	19	lagrangian	lagrangian	ADJ
ejpam-5828	60	20	do	do	AUX
ejpam-5828	60	21	n’t	not	PART
ejpam-5828	60	22	affect	affect	VERB
ejpam-5828	60	23	the	the	DET
ejpam-5828	60	24	equations	equation	NOUN
ejpam-5828	60	25	of	of	ADP
ejpam-5828	60	26	motion	motion	NOUN
ejpam-5828	60	27	fi	fi	NOUN
ejpam-5828	60	28	(	(	PUNCT
ejpam-5828	60	29	where	where	SCONJ
ejpam-5828	60	30	(	(	PUNCT
ejpam-5828	60	31	dfi	dfi	PROPN
ejpam-5828	60	32	dt	dt	PROPN
ejpam-5828	60	33	=	=	SYM
ejpam-5828	60	34	0	0	PUNCT
ejpam-5828	60	35	=	=	SYM
ejpam-5828	60	36	ẋixi	ẋixi	NOUN
ejpam-5828	60	37	)	)	PUNCT
ejpam-5828	60	38	)	)	PUNCT
ejpam-5828	61	1	it	it	PRON
ejpam-5828	61	2	suggests	suggest	VERB
ejpam-5828	61	3	fi	fi	NOUN
ejpam-5828	62	1	=	=	NOUN
ejpam-5828	62	2	x2i	x2i	PROPN
ejpam-5828	62	3	2	2	NUM
ejpam-5828	62	4	.	.	PUNCT
ejpam-5828	63	1	consequently	consequently	ADV
ejpam-5828	63	2	,	,	PUNCT
ejpam-5828	63	3	we	we	PRON
ejpam-5828	63	4	obtain	obtain	VERB
ejpam-5828	63	5	the	the	DET
ejpam-5828	63	6	following	follow	VERB
ejpam-5828	63	7	equivalent	equivalent	ADJ
ejpam-5828	63	8	lagrangian	lagrangian	NOUN
ejpam-5828	63	9	:	:	PUNCT
ejpam-5828	63	10	l	l	X
ejpam-5828	64	1	=	=	PUNCT
ejpam-5828	65	1	2∑	2∑	NUM
ejpam-5828	65	2	i=1	i=1	SYM
ejpam-5828	65	3	1	1	NUM
ejpam-5828	65	4	2	2	NUM
ejpam-5828	65	5	mx2i	mx2i	NOUN
ejpam-5828	65	6	+	+	CCONJ
ejpam-5828	65	7	1	1	NUM
ejpam-5828	65	8	8	8	NUM
ejpam-5828	65	9	mλ2ix	mλ2ix	NOUN
ejpam-5828	65	10	2	2	NUM
ejpam-5828	65	11	i	i	PRON
ejpam-5828	65	12	−	−	NOUN
ejpam-5828	65	13	2π2mv2i	2π2mv2i	NUM
ejpam-5828	65	14	x	x	SYM
ejpam-5828	65	15	2	2	NUM
ejpam-5828	65	16	i	i	PRON
ejpam-5828	65	17	here	here	ADV
ejpam-5828	65	18	,	,	PUNCT
ejpam-5828	65	19	the	the	DET
ejpam-5828	65	20	subscript	subscript	NOUN
ejpam-5828	65	21	(	(	PUNCT
ejpam-5828	65	22	i	i	NOUN
ejpam-5828	65	23	)	)	PUNCT
ejpam-5828	65	24	means	mean	VERB
ejpam-5828	65	25	sum	sum	NOUN
ejpam-5828	65	26	over	over	ADP
ejpam-5828	65	27	(	(	PUNCT
ejpam-5828	65	28	x1	x1	PROPN
ejpam-5828	65	29	=	=	SYM
ejpam-5828	65	30	x	x	NOUN
ejpam-5828	65	31	,	,	PUNCT
ejpam-5828	65	32	x2	x2	PROPN
ejpam-5828	65	33	=	=	SYM
ejpam-5828	65	34	y	y	PROPN
ejpam-5828	65	35	)	)	PUNCT
ejpam-5828	65	36	.	.	PUNCT
ejpam-5828	66	1	the	the	DET
ejpam-5828	66	2	lagrangian	lagrangian	ADJ
ejpam-5828	66	3	describes	describe	VERB
ejpam-5828	66	4	the	the	DET
ejpam-5828	66	5	dissipative	dissipative	NOUN
ejpam-5828	66	6	,	,	PUNCT
ejpam-5828	66	7	two	two	NUM
ejpam-5828	66	8	-	-	PUNCT
ejpam-5828	66	9	dimensional	dimensional	ADJ
ejpam-5828	66	10	anisotropic	anisotropic	NOUN
ejpam-5828	66	11	harmonic	harmonic	ADJ
ejpam-5828	66	12	oscillator	oscillator	NOUN
ejpam-5828	66	13	.	.	PUNCT
ejpam-5828	67	1	the	the	DET
ejpam-5828	67	2	equations	equation	NOUN
ejpam-5828	67	3	of	of	ADP
ejpam-5828	67	4	motion	motion	NOUN
ejpam-5828	67	5	can	can	AUX
ejpam-5828	67	6	be	be	AUX
ejpam-5828	67	7	derived	derive	VERB
ejpam-5828	67	8	from	from	ADP
ejpam-5828	67	9	this	this	DET
ejpam-5828	67	10	lagrangian	lagrangian	NOUN
ejpam-5828	67	11	.	.	PUNCT
ejpam-5828	68	1	ẍ+	ẍ+	PROPN
ejpam-5828	68	2	(	(	PUNCT
ejpam-5828	68	3	w2	w2	NOUN
ejpam-5828	68	4	x	x	X
ejpam-5828	68	5	−	−	PROPN
ejpam-5828	68	6	λ2x	λ2x	PRON
ejpam-5828	68	7	4	4	NUM
ejpam-5828	68	8	)	)	PUNCT
ejpam-5828	68	9	x	x	SYM
ejpam-5828	69	1	=	=	SYM
ejpam-5828	69	2	0	0	NUM
ejpam-5828	69	3	(	(	PUNCT
ejpam-5828	69	4	2	2	NUM
ejpam-5828	69	5	)	)	PUNCT
ejpam-5828	69	6	ÿ	ÿ	PROPN
ejpam-5828	69	7	+	+	CCONJ
ejpam-5828	69	8	(	(	PUNCT
ejpam-5828	69	9	w2	w2	NOUN
ejpam-5828	69	10	y	y	PROPN
ejpam-5828	69	11	−	−	PROPN
ejpam-5828	69	12	λ2y	λ2y	PUNCT
ejpam-5828	69	13	4	4	NUM
ejpam-5828	69	14	)	)	PUNCT
ejpam-5828	69	15	y	y	NOUN
ejpam-5828	69	16	=	=	SYM
ejpam-5828	69	17	0	0	PUNCT
ejpam-5828	69	18	(	(	PUNCT
ejpam-5828	69	19	3	3	X
ejpam-5828	69	20	)	)	PUNCT
ejpam-5828	69	21	a	a	DET
ejpam-5828	69	22	significant	significant	ADJ
ejpam-5828	69	23	finding	finding	NOUN
ejpam-5828	69	24	is	be	AUX
ejpam-5828	69	25	that	that	SCONJ
ejpam-5828	69	26	the	the	DET
ejpam-5828	69	27	damped	damped	NOUN
ejpam-5828	69	28	oscillator	oscillator	NOUN
ejpam-5828	69	29	’s	’s	PART
ejpam-5828	69	30	angular	angular	ADJ
ejpam-5828	69	31	frequency	frequency	NOUN
ejpam-5828	69	32	assumes	assume	VERB
ejpam-5828	69	33	values√	values√	NOUN
ejpam-5828	69	34	(	(	PUNCT
ejpam-5828	69	35	w2	w2	NOUN
ejpam-5828	69	36	x	x	X
ejpam-5828	69	37	−	−	PROPN
ejpam-5828	69	38	λ2x	λ2x	PRON
ejpam-5828	69	39	4	4	NUM
ejpam-5828	69	40	)	)	PUNCT
ejpam-5828	69	41	and	and	CCONJ
ejpam-5828	69	42	√	√	PROPN
ejpam-5828	69	43	(	(	PUNCT
ejpam-5828	69	44	w2	w2	NOUN
ejpam-5828	69	45	y	y	PROPN
ejpam-5828	69	46	−	−	PROPN
ejpam-5828	69	47	λ2y	λ2y	PROPN
ejpam-5828	69	48	4	4	NUM
ejpam-5828	69	49	)	)	PUNCT
ejpam-5828	69	50	where	where	SCONJ
ejpam-5828	69	51	(	(	PUNCT
ejpam-5828	69	52	wx	wx	PROPN
ejpam-5828	69	53	,	,	PUNCT
ejpam-5828	69	54	wy	wy	PROPN
ejpam-5828	69	55	)	)	PUNCT
ejpam-5828	69	56	represents	represent	VERB
ejpam-5828	69	57	the	the	DET
ejpam-5828	69	58	angular	angular	ADJ
ejpam-5828	69	59	frequencies	frequency	NOUN
ejpam-5828	69	60	of	of	ADP
ejpam-5828	69	61	the	the	DET
ejpam-5828	69	62	conservative	conservative	ADJ
ejpam-5828	69	63	system	system	NOUN
ejpam-5828	69	64	.	.	PUNCT
ejpam-5828	70	1	to	to	PART
ejpam-5828	70	2	revert	revert	VERB
ejpam-5828	70	3	to	to	ADP
ejpam-5828	70	4	the	the	DET
ejpam-5828	70	5	basic	basic	ADJ
ejpam-5828	70	6	harmonic	harmonic	ADJ
ejpam-5828	70	7	oscillator	oscillator	NOUN
ejpam-5828	70	8	,	,	PUNCT
ejpam-5828	70	9	one	one	PRON
ejpam-5828	70	10	sets	set	VERB
ejpam-5828	70	11	the	the	DET
ejpam-5828	70	12	damping	damp	VERB
ejpam-5828	70	13	coefficient	coefficient	NOUN
ejpam-5828	70	14	(	(	PUNCT
ejpam-5828	70	15	λy	λy	PROPN
ejpam-5828	70	16	,	,	PUNCT
ejpam-5828	70	17	λx	λx	PROPN
ejpam-5828	70	18	)	)	PUNCT
ejpam-5828	70	19	to	to	ADP
ejpam-5828	70	20	zero	zero	NUM
ejpam-5828	70	21	in	in	ADP
ejpam-5828	70	22	the	the	DET
ejpam-5828	70	23	equations	equation	NOUN
ejpam-5828	70	24	.	.	PUNCT
ejpam-5828	71	1	the	the	DET
ejpam-5828	71	2	hamiltonian	hamiltonian	NOUN
ejpam-5828	71	3	(	(	PUNCT
ejpam-5828	71	4	h	h	NOUN
ejpam-5828	71	5	)	)	PUNCT
ejpam-5828	71	6	can	can	AUX
ejpam-5828	71	7	be	be	AUX
ejpam-5828	71	8	expressed	express	VERB
ejpam-5828	71	9	as	as	ADP
ejpam-5828	71	10	a	a	DET
ejpam-5828	71	11	function	function	NOUN
ejpam-5828	71	12	of	of	ADP
ejpam-5828	71	13	coordinates	coordinate	NOUN
ejpam-5828	71	14	(	(	PUNCT
ejpam-5828	71	15	x	x	X
ejpam-5828	71	16	,	,	PUNCT
ejpam-5828	71	17	y	y	PROPN
ejpam-5828	71	18	)	)	PUNCT
ejpam-5828	71	19	and	and	CCONJ
ejpam-5828	71	20	conjugate	conjugate	ADJ
ejpam-5828	71	21	momenta	momenta	NOUN
ejpam-5828	71	22	(	(	PUNCT
ejpam-5828	71	23	px	px	PROPN
ejpam-5828	71	24	,	,	PUNCT
ejpam-5828	71	25	py	py	PROPN
ejpam-5828	71	26	)	)	PUNCT
ejpam-5828	71	27	.	.	PUNCT
ejpam-5828	72	1	h	h	NOUN
ejpam-5828	73	1	=	=	NOUN
ejpam-5828	73	2	pxẋ+	pxẋ+	NUM
ejpam-5828	74	1	pyẏ	pyẏ	PROPN
ejpam-5828	74	2	−	−	PROPN
ejpam-5828	74	3	l	l	NOUN
ejpam-5828	74	4	the	the	DET
ejpam-5828	74	5	generalized	generalized	ADJ
ejpam-5828	74	6	momenta	momenta	NOUN
ejpam-5828	74	7	are	be	AUX
ejpam-5828	74	8	defined	define	VERB
ejpam-5828	74	9	as	as	SCONJ
ejpam-5828	74	10	follows	follow	VERB
ejpam-5828	74	11	[	[	X
ejpam-5828	74	12	20	20	NUM
ejpam-5828	74	13	]	]	SYM
ejpam-5828	74	14	:	:	PUNCT
ejpam-5828	75	1	px	px	X
ejpam-5828	75	2	=	=	PUNCT
ejpam-5828	75	3	∂l	∂l	PROPN
ejpam-5828	75	4	∂x	∂x	PROPN
ejpam-5828	75	5	=	=	SYM
ejpam-5828	75	6	mẋ	mẋ	PROPN
ejpam-5828	75	7	and	and	CCONJ
ejpam-5828	75	8	py	py	NOUN
ejpam-5828	76	1	=	=	SYM
ejpam-5828	76	2	∂l	∂l	PROPN
ejpam-5828	76	3	∂y	∂y	X
ejpam-5828	76	4	=	=	PUNCT
ejpam-5828	76	5	mẏ	mẏ	X
ejpam-5828	77	1	the	the	DET
ejpam-5828	77	2	following	follow	VERB
ejpam-5828	77	3	is	be	AUX
ejpam-5828	77	4	the	the	DET
ejpam-5828	77	5	hamiltonian	hamiltonian	NOUN
ejpam-5828	77	6	’s	’s	PART
ejpam-5828	77	7	expression	expression	NOUN
ejpam-5828	77	8	in	in	ADP
ejpam-5828	77	9	terms	term	NOUN
ejpam-5828	77	10	of	of	ADP
ejpam-5828	77	11	the	the	DET
ejpam-5828	77	12	time	time	NOUN
ejpam-5828	77	13	derivatives	derivative	NOUN
ejpam-5828	77	14	:	:	PUNCT
ejpam-5828	77	15	h	h	NOUN
ejpam-5828	77	16	=	=	PUNCT
ejpam-5828	78	1	p	p	X
ejpam-5828	78	2	2	2	NUM
ejpam-5828	78	3	x	x	SYM
ejpam-5828	78	4	2	2	NUM
ejpam-5828	78	5	m	m	NOUN
ejpam-5828	78	6	+	+	NOUN
ejpam-5828	78	7	p	p	X
ejpam-5828	78	8	2	2	NUM
ejpam-5828	78	9	y	y	PROPN
ejpam-5828	78	10	2	2	NUM
ejpam-5828	78	11	m	m	NOUN
ejpam-5828	78	12	−	−	NUM
ejpam-5828	78	13	1	1	NUM
ejpam-5828	78	14	4	4	NUM
ejpam-5828	78	15	mλ2xx	mλ2xx	NOUN
ejpam-5828	78	16	2	2	NUM
ejpam-5828	78	17	−	−	NOUN
ejpam-5828	78	18	1	1	NUM
ejpam-5828	78	19	4	4	NUM
ejpam-5828	78	20	mλ2yy	mλ2yy	NOUN
ejpam-5828	78	21	2	2	NUM
ejpam-5828	78	22	+	+	CCONJ
ejpam-5828	78	23	2π2mv2xx	2π2mv2xx	NOUN
ejpam-5828	78	24	2	2	NUM
ejpam-5828	78	25	+	+	NOUN
ejpam-5828	78	26	+2π2mv2yy	+2π2mv2yy	NOUN
ejpam-5828	78	27	2	2	NUM
ejpam-5828	78	28	the	the	DET
ejpam-5828	78	29	current	current	ADJ
ejpam-5828	78	30	study	study	NOUN
ejpam-5828	78	31	’s	’s	PART
ejpam-5828	78	32	conclusions	conclusion	NOUN
ejpam-5828	78	33	and	and	CCONJ
ejpam-5828	78	34	rabei	rabei	VERB
ejpam-5828	78	35	et	et	PROPN
ejpam-5828	78	36	al	al	PROPN
ejpam-5828	78	37	.	.	PROPN
ejpam-5828	78	38	’s	’s	PART
ejpam-5828	78	39	analysis	analysis	NOUN
ejpam-5828	78	40	differ	differ	VERB
ejpam-5828	78	41	for	for	ADP
ejpam-5828	78	42	a	a	DET
ejpam-5828	78	43	number	number	NOUN
ejpam-5828	78	44	of	of	ADP
ejpam-5828	78	45	reasons	reason	NOUN
ejpam-5828	78	46	.	.	PUNCT
ejpam-5828	79	1	firstly	firstly	ADV
ejpam-5828	79	2	,	,	PUNCT
ejpam-5828	79	3	the	the	DET
ejpam-5828	79	4	current	current	ADJ
ejpam-5828	79	5	work	work	NOUN
ejpam-5828	79	6	focused	focus	VERB
ejpam-5828	79	7	on	on	ADP
ejpam-5828	79	8	scattering	scatter	VERB
ejpam-5828	79	9	using	use	VERB
ejpam-5828	79	10	a	a	DET
ejpam-5828	79	11	number	number	NOUN
ejpam-5828	79	12	of	of	ADP
ejpam-5828	79	13	approaches	approach	NOUN
ejpam-5828	79	14	,	,	PUNCT
ejpam-5828	79	15	including	include	VERB
ejpam-5828	79	16	hamilton	hamilton	PROPN
ejpam-5828	79	17	-	-	PUNCT
ejpam-5828	79	18	jacobi	jacobi	PROPN
ejpam-5828	79	19	and	and	CCONJ
ejpam-5828	79	20	variable	variable	ADJ
ejpam-5828	79	21	separation	separation	NOUN
ejpam-5828	79	22	,	,	PUNCT
ejpam-5828	79	23	with	with	ADP
ejpam-5828	79	24	a	a	DET
ejpam-5828	79	25	focus	focus	NOUN
ejpam-5828	79	26	on	on	ADP
ejpam-5828	79	27	dissipative	dissipative	NOUN
ejpam-5828	79	28	.	.	PUNCT
ejpam-5828	80	1	secondly	secondly	ADV
ejpam-5828	80	2	,	,	PUNCT
ejpam-5828	80	3	rabei	rabei	VERB
ejpam-5828	80	4	et	et	PROPN
ejpam-5828	80	5	b.	b.	PROPN
ejpam-5828	80	6	m.	m.	PROPN
ejpam-5828	81	1	al	al	PROPN
ejpam-5828	81	2	-	-	PUNCT
ejpam-5828	81	3	khamiseh	khamiseh	PROPN
ejpam-5828	81	4	et	et	PROPN
ejpam-5828	81	5	al	al	PROPN
ejpam-5828	81	6	.	.	PUNCT
ejpam-5828	81	7	/	/	SYM
ejpam-5828	81	8	eur	eur	PROPN
ejpam-5828	81	9	.	.	PUNCT
ejpam-5828	82	1	j.	j.	PROPN
ejpam-5828	82	2	pure	pure	PROPN
ejpam-5828	82	3	appl	appl	PROPN
ejpam-5828	82	4	.	.	PROPN
ejpam-5828	82	5	math	math	PROPN
ejpam-5828	82	6	,	,	PUNCT
ejpam-5828	82	7	18	18	NUM
ejpam-5828	82	8	(	(	PUNCT
ejpam-5828	82	9	2	2	NUM
ejpam-5828	82	10	)	)	PUNCT
ejpam-5828	82	11	(	(	PUNCT
ejpam-5828	82	12	2025	2025	NUM
ejpam-5828	82	13	)	)	PUNCT
ejpam-5828	82	14	,	,	PUNCT
ejpam-5828	82	15	5828	5828	NUM
ejpam-5828	82	16	5	5	NUM
ejpam-5828	82	17	of	of	ADP
ejpam-5828	82	18	25	25	NUM
ejpam-5828	82	19	al	al	PROPN
ejpam-5828	82	20	.	.	PUNCT
ejpam-5828	83	1	[	[	X
ejpam-5828	83	2	21	21	NUM
ejpam-5828	83	3	]	]	X
ejpam-5828	83	4	utilized	utilize	VERB
ejpam-5828	83	5	the	the	DET
ejpam-5828	83	6	wkb	wkb	NOUN
ejpam-5828	83	7	for	for	ADP
ejpam-5828	83	8	constrained	constrained	ADJ
ejpam-5828	83	9	systems	system	NOUN
ejpam-5828	83	10	.	.	PUNCT
ejpam-5828	84	1	hence	hence	ADV
ejpam-5828	84	2	,	,	PUNCT
ejpam-5828	84	3	the	the	DET
ejpam-5828	84	4	hamilton	hamilton	PROPN
ejpam-5828	84	5	–	–	PUNCT
ejpam-5828	84	6	jacobi	jacobi	PROPN
ejpam-5828	84	7	equation	equation	NOUN
ejpam-5828	84	8	assumes	assume	VERB
ejpam-5828	84	9	the	the	DET
ejpam-5828	84	10	form	form	NOUN
ejpam-5828	84	11	1	1	NUM
ejpam-5828	84	12	2	2	NUM
ejpam-5828	84	13	m	m	VERB
ejpam-5828	84	14	(	(	PUNCT
ejpam-5828	84	15	(	(	PUNCT
ejpam-5828	84	16	∂s	∂s	PROPN
ejpam-5828	84	17	∂x	∂x	PROPN
ejpam-5828	84	18	)	)	PUNCT
ejpam-5828	84	19	2	2	NUM
ejpam-5828	84	20	+	+	SYM
ejpam-5828	84	21	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	84	22	2	2	NUM
ejpam-5828	84	23	−	−	NOUN
ejpam-5828	84	24	1	1	NUM
ejpam-5828	84	25	2	2	NUM
ejpam-5828	84	26	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	84	27	2	2	NUM
ejpam-5828	84	28	+	+	CCONJ
ejpam-5828	84	29	(	(	PUNCT
ejpam-5828	84	30	∂s	∂s	PROPN
ejpam-5828	84	31	∂y	∂y	PROPN
ejpam-5828	84	32	)	)	PUNCT
ejpam-5828	84	33	2	2	NUM
ejpam-5828	85	1	+	+	NUM
ejpam-5828	85	2	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	85	3	2	2	NUM
ejpam-5828	85	4	−	−	NOUN
ejpam-5828	85	5	1	1	NUM
ejpam-5828	85	6	2	2	NUM
ejpam-5828	85	7	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	85	8	2	2	NUM
ejpam-5828	85	9	)	)	PUNCT
ejpam-5828	85	10	+	+	NUM
ejpam-5828	86	1	∂s	∂s	PROPN
ejpam-5828	86	2	∂t	∂t	PROPN
ejpam-5828	87	1	=	=	SYM
ejpam-5828	87	2	0	0	PROPN
ejpam-5828	88	1	(	(	PUNCT
ejpam-5828	88	2	4	4	NUM
ejpam-5828	88	3	)	)	PUNCT
ejpam-5828	88	4	where	where	SCONJ
ejpam-5828	88	5	∂s	∂s	PROPN
ejpam-5828	88	6	∂x	∂x	PROPN
ejpam-5828	88	7	and	and	CCONJ
ejpam-5828	88	8	∂s	∂s	PROPN
ejpam-5828	88	9	∂y	∂y	PRON
ejpam-5828	88	10	represent	represent	VERB
ejpam-5828	88	11	the	the	DET
ejpam-5828	88	12	canonical	canonical	ADJ
ejpam-5828	88	13	momenta	momenta	NOUN
ejpam-5828	88	14	px	px	PROPN
ejpam-5828	88	15	and	and	CCONJ
ejpam-5828	88	16	py	py	INTJ
ejpam-5828	88	17	,	,	PUNCT
ejpam-5828	88	18	respectively	respectively	ADV
ejpam-5828	88	19	.	.	PUNCT
ejpam-5828	89	1	by	by	ADP
ejpam-5828	89	2	substituting	substitute	VERB
ejpam-5828	89	3	these	these	PRON
ejpam-5828	89	4	into	into	ADP
ejpam-5828	89	5	the	the	DET
ejpam-5828	89	6	equation	equation	NOUN
ejpam-5828	89	7	,	,	PUNCT
ejpam-5828	89	8	it	it	PRON
ejpam-5828	89	9	can	can	AUX
ejpam-5828	89	10	be	be	AUX
ejpam-5828	89	11	rewritten	rewrite	VERB
ejpam-5828	89	12	as	as	SCONJ
ejpam-5828	89	13	follows	follow	VERB
ejpam-5828	89	14	:	:	PUNCT
ejpam-5828	89	15	1	1	NUM
ejpam-5828	89	16	2	2	NUM
ejpam-5828	89	17	m	m	VERB
ejpam-5828	89	18	(	(	PUNCT
ejpam-5828	89	19	(	(	PUNCT
ejpam-5828	89	20	px	px	NOUN
ejpam-5828	89	21	)	)	PUNCT
ejpam-5828	89	22	2	2	NUM
ejpam-5828	90	1	+	+	SYM
ejpam-5828	90	2	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	90	3	2	2	NUM
ejpam-5828	90	4	−	−	NOUN
ejpam-5828	90	5	1	1	NUM
ejpam-5828	90	6	2	2	NUM
ejpam-5828	90	7	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	90	8	2	2	NUM
ejpam-5828	90	9	+	+	CCONJ
ejpam-5828	90	10	(	(	PUNCT
ejpam-5828	90	11	py	py	INTJ
ejpam-5828	90	12	)	)	PUNCT
ejpam-5828	90	13	2	2	NUM
ejpam-5828	91	1	+	+	NUM
ejpam-5828	91	2	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	91	3	2	2	NUM
ejpam-5828	91	4	−	−	NOUN
ejpam-5828	91	5	1	1	NUM
ejpam-5828	91	6	2	2	NUM
ejpam-5828	91	7	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	91	8	2	2	NUM
ejpam-5828	91	9	)	)	PUNCT
ejpam-5828	91	10	+	+	NUM
ejpam-5828	91	11	∂s	∂s	PROPN
ejpam-5828	91	12	∂t	∂t	PROPN
ejpam-5828	91	13	=	=	PUNCT
ejpam-5828	91	14	0	0	PROPN
ejpam-5828	92	1	the	the	DET
ejpam-5828	92	2	given	give	VERB
ejpam-5828	92	3	hamiltonian	hamiltonian	NOUN
ejpam-5828	92	4	is	be	AUX
ejpam-5828	92	5	expressed	express	VERB
ejpam-5828	92	6	as	as	ADP
ejpam-5828	92	7	:	:	PUNCT
ejpam-5828	92	8	h	h	NOUN
ejpam-5828	92	9	=	=	NOUN
ejpam-5828	92	10	1	1	NUM
ejpam-5828	92	11	2	2	NUM
ejpam-5828	92	12	m	m	PROPN
ejpam-5828	92	13	(	(	PUNCT
ejpam-5828	92	14	px	px	PROPN
ejpam-5828	92	15	)	)	PUNCT
ejpam-5828	92	16	2	2	NUM
ejpam-5828	93	1	+	+	SYM
ejpam-5828	93	2	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	93	3	2	2	NUM
ejpam-5828	93	4	−	−	NOUN
ejpam-5828	93	5	1	1	NUM
ejpam-5828	93	6	2	2	NUM
ejpam-5828	93	7	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	93	8	2	2	NUM
ejpam-5828	93	9	+	+	CCONJ
ejpam-5828	93	10	1	1	NUM
ejpam-5828	93	11	2	2	NUM
ejpam-5828	93	12	m	m	PROPN
ejpam-5828	93	13	(	(	PUNCT
ejpam-5828	93	14	py	py	NOUN
ejpam-5828	93	15	)	)	PUNCT
ejpam-5828	93	16	2	2	NUM
ejpam-5828	94	1	+	+	NUM
ejpam-5828	94	2	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	94	3	2	2	NUM
ejpam-5828	94	4	−	−	NOUN
ejpam-5828	94	5	1	1	NUM
ejpam-5828	94	6	2	2	NUM
ejpam-5828	94	7	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	94	8	2	2	NUM
ejpam-5828	94	9	by	by	ADP
ejpam-5828	94	10	comparing	compare	VERB
ejpam-5828	94	11	the	the	DET
ejpam-5828	94	12	two	two	NUM
ejpam-5828	94	13	expressions	expression	NOUN
ejpam-5828	94	14	,	,	PUNCT
ejpam-5828	94	15	we	we	PRON
ejpam-5828	94	16	observe	observe	VERB
ejpam-5828	94	17	that	that	SCONJ
ejpam-5828	94	18	the	the	DET
ejpam-5828	94	19	kinetic	kinetic	ADJ
ejpam-5828	94	20	energy	energy	NOUN
ejpam-5828	94	21	terms	term	NOUN
ejpam-5828	94	22	(	(	PUNCT
ejpam-5828	94	23	px)2	px)2	NOUN
ejpam-5828	94	24	2	2	NUM
ejpam-5828	94	25	m	m	NOUN
ejpam-5828	94	26	+	+	NOUN
ejpam-5828	94	27	(	(	PUNCT
ejpam-5828	94	28	py)2	py)2	NOUN
ejpam-5828	94	29	2	2	NUM
ejpam-5828	94	30	m	m	NOUN
ejpam-5828	94	31	are	be	AUX
ejpam-5828	94	32	identical	identical	ADJ
ejpam-5828	94	33	in	in	ADP
ejpam-5828	94	34	both	both	DET
ejpam-5828	94	35	equations	equation	NOUN
ejpam-5828	94	36	.	.	PUNCT
ejpam-5828	95	1	for	for	ADP
ejpam-5828	95	2	the	the	DET
ejpam-5828	95	3	potential	potential	ADJ
ejpam-5828	95	4	energy	energy	NOUN
ejpam-5828	95	5	terms	term	NOUN
ejpam-5828	95	6	,	,	PUNCT
ejpam-5828	95	7	dividing	divide	VERB
ejpam-5828	95	8	the	the	DET
ejpam-5828	95	9	terms	term	NOUN
ejpam-5828	95	10	in	in	ADP
ejpam-5828	95	11	the	the	DET
ejpam-5828	95	12	hamilton	hamilton	PROPN
ejpam-5828	95	13	-	-	PUNCT
ejpam-5828	95	14	jacobi	jacobi	PROPN
ejpam-5828	95	15	equation	equation	NOUN
ejpam-5828	95	16	by	by	ADP
ejpam-5828	95	17	2	2	NUM
ejpam-5828	95	18	m	m	PROPN
ejpam-5828	95	19	results	result	NOUN
ejpam-5828	95	20	in	in	ADP
ejpam-5828	95	21	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	95	22	2−	2−	NUM
ejpam-5828	95	23	1	1	NUM
ejpam-5828	95	24	2	2	NUM
ejpam-5828	95	25	m	m	NUM
ejpam-5828	95	26	2λ2xx	2λ2xx	NUM
ejpam-5828	95	27	2	2	NUM
ejpam-5828	95	28	+	+	NOUN
ejpam-5828	95	29	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	95	30	2−	2−	NUM
ejpam-5828	95	31	1	1	NUM
ejpam-5828	95	32	2	2	NUM
ejpam-5828	95	33	m	m	NUM
ejpam-5828	95	34	2λ2yy	2λ2yy	NUM
ejpam-5828	95	35	2	2	NUM
ejpam-5828	95	36	,	,	PUNCT
ejpam-5828	95	37	which	which	PRON
ejpam-5828	95	38	matches	match	VERB
ejpam-5828	95	39	the	the	DET
ejpam-5828	95	40	corresponding	corresponding	ADJ
ejpam-5828	95	41	terms	term	NOUN
ejpam-5828	95	42	in	in	ADP
ejpam-5828	95	43	the	the	DET
ejpam-5828	95	44	hamiltonian	hamiltonian	NOUN
ejpam-5828	95	45	.	.	PUNCT
ejpam-5828	96	1	additionally	additionally	ADV
ejpam-5828	96	2	,	,	PUNCT
ejpam-5828	96	3	the	the	DET
ejpam-5828	96	4	timedependent	timedependent	NOUN
ejpam-5828	96	5	term	term	NOUN
ejpam-5828	96	6	∂s	∂s	PROPN
ejpam-5828	96	7	∂t	∂t	PROPN
ejpam-5828	96	8	in	in	ADP
ejpam-5828	96	9	the	the	DET
ejpam-5828	96	10	hamilton	hamilton	PROPN
ejpam-5828	96	11	-	-	PUNCT
ejpam-5828	96	12	jacobi	jacobi	PROPN
ejpam-5828	96	13	equation	equation	NOUN
ejpam-5828	96	14	is	be	AUX
ejpam-5828	96	15	consistent	consistent	ADJ
ejpam-5828	96	16	with	with	ADP
ejpam-5828	96	17	the	the	DET
ejpam-5828	96	18	role	role	NOUN
ejpam-5828	96	19	of	of	ADP
ejpam-5828	96	20	time	time	NOUN
ejpam-5828	96	21	in	in	ADP
ejpam-5828	96	22	classical	classical	ADJ
ejpam-5828	96	23	dynamics	dynamic	NOUN
ejpam-5828	96	24	,	,	PUNCT
ejpam-5828	96	25	even	even	ADV
ejpam-5828	96	26	though	though	SCONJ
ejpam-5828	96	27	it	it	PRON
ejpam-5828	96	28	does	do	AUX
ejpam-5828	96	29	not	not	PART
ejpam-5828	96	30	explicitly	explicitly	ADV
ejpam-5828	96	31	appear	appear	VERB
ejpam-5828	96	32	in	in	ADP
ejpam-5828	96	33	the	the	DET
ejpam-5828	96	34	hamiltonian	hamiltonian	NOUN
ejpam-5828	96	35	.	.	PUNCT
ejpam-5828	97	1	consequently	consequently	ADV
ejpam-5828	97	2	,	,	PUNCT
ejpam-5828	97	3	the	the	DET
ejpam-5828	97	4	hamilton	hamilton	PROPN
ejpam-5828	97	5	-	-	PUNCT
ejpam-5828	97	6	jacobi	jacobi	PROPN
ejpam-5828	97	7	equation	equation	NOUN
ejpam-5828	97	8	and	and	CCONJ
ejpam-5828	97	9	the	the	DET
ejpam-5828	97	10	given	give	VERB
ejpam-5828	97	11	hamiltonian	hamiltonian	NOUN
ejpam-5828	97	12	are	be	AUX
ejpam-5828	97	13	equivalent	equivalent	ADJ
ejpam-5828	97	14	,	,	PUNCT
ejpam-5828	97	15	as	as	SCONJ
ejpam-5828	97	16	their	their	PRON
ejpam-5828	97	17	kinetic	kinetic	NOUN
ejpam-5828	97	18	,	,	PUNCT
ejpam-5828	97	19	potential	potential	ADJ
ejpam-5828	97	20	,	,	PUNCT
ejpam-5828	97	21	and	and	CCONJ
ejpam-5828	97	22	temporal	temporal	ADJ
ejpam-5828	97	23	components	component	NOUN
ejpam-5828	97	24	align	align	VERB
ejpam-5828	97	25	perfectly	perfectly	ADV
ejpam-5828	97	26	.	.	PUNCT
ejpam-5828	98	1	the	the	DET
ejpam-5828	98	2	principal	principal	ADJ
ejpam-5828	98	3	hamiltonian	hamiltonian	ADJ
ejpam-5828	98	4	function	function	NOUN
ejpam-5828	98	5	s	s	PART
ejpam-5828	98	6	can	can	AUX
ejpam-5828	98	7	be	be	AUX
ejpam-5828	98	8	expressed	express	VERB
ejpam-5828	98	9	as	as	SCONJ
ejpam-5828	98	10	follows	follow	VERB
ejpam-5828	98	11	:	:	PUNCT
ejpam-5828	98	12	s(x	s(x	NOUN
ejpam-5828	98	13	,	,	PUNCT
ejpam-5828	98	14	y	y	PROPN
ejpam-5828	98	15	,	,	PUNCT
ejpam-5828	98	16	α	α	PROPN
ejpam-5828	98	17	,	,	PUNCT
ejpam-5828	98	18	αy	αy	NOUN
ejpam-5828	98	19	,	,	PUNCT
ejpam-5828	98	20	t	t	PROPN
ejpam-5828	98	21	)	)	PUNCT
ejpam-5828	99	1	=	=	NOUN
ejpam-5828	99	2	wx(x	wx(x	X
ejpam-5828	99	3	,	,	PUNCT
ejpam-5828	99	4	α	α	NOUN
ejpam-5828	99	5	,	,	PUNCT
ejpam-5828	99	6	αy	αy	NOUN
ejpam-5828	99	7	)	)	PUNCT
ejpam-5828	99	8	+	+	ADV
ejpam-5828	99	9	wy(y	wy(y	X
ejpam-5828	99	10	,	,	PUNCT
ejpam-5828	99	11	α	α	X
ejpam-5828	99	12	,	,	PUNCT
ejpam-5828	99	13	αy)−	αy)−	NOUN
ejpam-5828	99	14	αt	αt	NOUN
ejpam-5828	99	15	this	this	PRON
ejpam-5828	99	16	leads	lead	VERB
ejpam-5828	99	17	to	to	ADP
ejpam-5828	99	18	∂s	∂s	PROPN
ejpam-5828	99	19	∂t	∂t	PROPN
ejpam-5828	99	20	=	=	PUNCT
ejpam-5828	99	21	−α	−α	PROPN
ejpam-5828	99	22	(	(	PUNCT
ejpam-5828	99	23	5	5	NUM
ejpam-5828	99	24	)	)	PUNCT
ejpam-5828	99	25	the	the	DET
ejpam-5828	99	26	partial	partial	ADJ
ejpam-5828	99	27	derivatives	derivative	NOUN
ejpam-5828	99	28	of	of	ADP
ejpam-5828	99	29	the	the	DET
ejpam-5828	99	30	function	function	NOUN
ejpam-5828	99	31	w	w	NOUN
ejpam-5828	99	32	with	with	ADP
ejpam-5828	99	33	respect	respect	NOUN
ejpam-5828	99	34	to	to	ADP
ejpam-5828	99	35	x	x	PUNCT
ejpam-5828	99	36	and	and	CCONJ
ejpam-5828	99	37	y	y	PROPN
ejpam-5828	99	38	are	be	AUX
ejpam-5828	99	39	defined	define	VERB
ejpam-5828	99	40	by	by	ADP
ejpam-5828	99	41	the	the	DET
ejpam-5828	99	42	formulas	formula	NOUN
ejpam-5828	99	43	px	px	X
ejpam-5828	99	44	=	=	SYM
ejpam-5828	99	45	∂w	∂w	PROPN
ejpam-5828	99	46	∂x	∂x	PROPN
ejpam-5828	99	47	and	and	CCONJ
ejpam-5828	99	48	py	py	NOUN
ejpam-5828	99	49	=	=	NOUN
ejpam-5828	99	50	∂w	∂w	PROPN
ejpam-5828	99	51	∂y	∂y	PROPN
ejpam-5828	99	52	,	,	PUNCT
ejpam-5828	99	53	respectively	respectively	ADV
ejpam-5828	99	54	the	the	DET
ejpam-5828	99	55	hamilton	hamilton	PROPN
ejpam-5828	99	56	-	-	PUNCT
ejpam-5828	99	57	jacobi	jacobi	PROPN
ejpam-5828	99	58	equation	equation	NOUN
ejpam-5828	99	59	(	(	PUNCT
ejpam-5828	99	60	hje	hje	PROPN
ejpam-5828	99	61	)	)	PUNCT
ejpam-5828	99	62	is	be	AUX
ejpam-5828	99	63	rewritten	rewrite	VERB
ejpam-5828	99	64	in	in	ADP
ejpam-5828	99	65	terms	term	NOUN
ejpam-5828	99	66	of	of	ADP
ejpam-5828	99	67	the	the	DET
ejpam-5828	99	68	functions	function	NOUN
ejpam-5828	99	69	and	and	CCONJ
ejpam-5828	99	70	by	by	ADP
ejpam-5828	99	71	inserting	insert	VERB
ejpam-5828	99	72	equation	equation	NOUN
ejpam-5828	99	73	2	2	NUM
ejpam-5828	99	74	into	into	ADP
ejpam-5828	99	75	equation	equation	NOUN
ejpam-5828	99	76	3	3	NUM
ejpam-5828	99	77	:	:	SYM
ejpam-5828	99	78	1	1	NUM
ejpam-5828	99	79	2	2	NUM
ejpam-5828	99	80	m	m	VERB
ejpam-5828	99	81	(	(	PUNCT
ejpam-5828	99	82	[	[	PUNCT
ejpam-5828	99	83	∂wx	∂wx	PROPN
ejpam-5828	99	84	∂x	∂x	PROPN
ejpam-5828	99	85	]	]	SYM
ejpam-5828	99	86	2	2	NUM
ejpam-5828	99	87	+	+	NUM
ejpam-5828	99	88	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	99	89	2	2	NUM
ejpam-5828	99	90	−	−	NOUN
ejpam-5828	99	91	1	1	NUM
ejpam-5828	99	92	2	2	NUM
ejpam-5828	99	93	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	99	94	2	2	NUM
ejpam-5828	99	95	+	+	CCONJ
ejpam-5828	99	96	[	[	PUNCT
ejpam-5828	99	97	∂wy	∂wy	X
ejpam-5828	99	98	∂y	∂y	X
ejpam-5828	99	99	]	]	SYM
ejpam-5828	99	100	2	2	NUM
ejpam-5828	99	101	+	+	NUM
ejpam-5828	99	102	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	99	103	2	2	NUM
ejpam-5828	99	104	−	−	NOUN
ejpam-5828	99	105	1	1	NUM
ejpam-5828	99	106	2	2	NUM
ejpam-5828	99	107	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	99	108	2	2	NUM
ejpam-5828	99	109	)	)	PUNCT
ejpam-5828	99	110	=	=	PUNCT
ejpam-5828	99	111	α	α	NOUN
ejpam-5828	99	112	by	by	ADP
ejpam-5828	99	113	separating	separate	VERB
ejpam-5828	99	114	the	the	DET
ejpam-5828	99	115	variables	variable	NOUN
ejpam-5828	99	116	,	,	PUNCT
ejpam-5828	99	117	we	we	PRON
ejpam-5828	99	118	can	can	AUX
ejpam-5828	99	119	get	get	VERB
ejpam-5828	99	120	the	the	DET
ejpam-5828	99	121	following	follow	VERB
ejpam-5828	99	122	results	result	NOUN
ejpam-5828	99	123	:	:	PUNCT
ejpam-5828	99	124	1	1	NUM
ejpam-5828	99	125	2	2	NUM
ejpam-5828	99	126	m	m	VERB
ejpam-5828	99	127	(	(	PUNCT
ejpam-5828	99	128	[	[	PUNCT
ejpam-5828	99	129	∂wx	∂wx	PROPN
ejpam-5828	99	130	∂x	∂x	PROPN
ejpam-5828	99	131	]	]	SYM
ejpam-5828	99	132	2	2	NUM
ejpam-5828	99	133	+	+	NUM
ejpam-5828	99	134	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	99	135	2	2	NUM
ejpam-5828	99	136	−	−	NOUN
ejpam-5828	99	137	1	1	NUM
ejpam-5828	99	138	2	2	NUM
ejpam-5828	99	139	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	99	140	2	2	NUM
ejpam-5828	99	141	)	)	PUNCT
ejpam-5828	99	142	=	=	SYM
ejpam-5828	100	1	α	α	X
ejpam-5828	100	2	.	.	PUNCT
ejpam-5828	101	1	(	(	PUNCT
ejpam-5828	101	2	6	6	NUM
ejpam-5828	101	3	)	)	SYM
ejpam-5828	101	4	1	1	NUM
ejpam-5828	101	5	2	2	NUM
ejpam-5828	101	6	m	m	VERB
ejpam-5828	101	7	(	(	PUNCT
ejpam-5828	101	8	[	[	PUNCT
ejpam-5828	101	9	∂wy	∂wy	X
ejpam-5828	101	10	∂y	∂y	X
ejpam-5828	101	11	]	]	SYM
ejpam-5828	101	12	2	2	NUM
ejpam-5828	101	13	+	+	NUM
ejpam-5828	101	14	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	101	15	2	2	NUM
ejpam-5828	101	16	−	−	NOUN
ejpam-5828	101	17	1	1	NUM
ejpam-5828	101	18	2	2	NUM
ejpam-5828	101	19	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	101	20	2	2	NUM
ejpam-5828	101	21	)	)	PUNCT
ejpam-5828	101	22	=	=	PRON
ejpam-5828	101	23	αy	αy	PART
ejpam-5828	101	24	(	(	PUNCT
ejpam-5828	101	25	7	7	NUM
ejpam-5828	101	26	)	)	PUNCT
ejpam-5828	101	27	by	by	ADP
ejpam-5828	101	28	rewriting	rewrite	VERB
ejpam-5828	101	29	equations	equation	NOUN
ejpam-5828	101	30	4	4	NUM
ejpam-5828	101	31	and	and	CCONJ
ejpam-5828	101	32	5	5	NUM
ejpam-5828	101	33	,	,	PUNCT
ejpam-5828	101	34	we	we	PRON
ejpam-5828	101	35	get	get	VERB
ejpam-5828	101	36	:	:	PUNCT
ejpam-5828	101	37	∂wy	∂wy	PROPN
ejpam-5828	101	38	∂y	∂y	X
ejpam-5828	101	39	=	=	PUNCT
ejpam-5828	101	40	√	√	PROPN
ejpam-5828	101	41	2mαy	2mαy	NUM
ejpam-5828	101	42	−	−	NOUN
ejpam-5828	101	43	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	101	44	2	2	NUM
ejpam-5828	101	45	+	+	CCONJ
ejpam-5828	101	46	1	1	NUM
ejpam-5828	101	47	2	2	NUM
ejpam-5828	101	48	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	101	49	2	2	NUM
ejpam-5828	101	50	(	(	PUNCT
ejpam-5828	101	51	8)	8)	NUM
ejpam-5828	101	52	b.	b.	PROPN
ejpam-5828	101	53	m.	m.	PROPN
ejpam-5828	101	54	al	al	PROPN
ejpam-5828	101	55	-	-	PUNCT
ejpam-5828	101	56	khamiseh	khamiseh	PROPN
ejpam-5828	101	57	et	et	PROPN
ejpam-5828	101	58	al	al	PROPN
ejpam-5828	101	59	.	.	PUNCT
ejpam-5828	101	60	/	/	SYM
ejpam-5828	101	61	eur	eur	PROPN
ejpam-5828	101	62	.	.	PUNCT
ejpam-5828	102	1	j.	j.	PROPN
ejpam-5828	102	2	pure	pure	PROPN
ejpam-5828	102	3	appl	appl	PROPN
ejpam-5828	102	4	.	.	PROPN
ejpam-5828	102	5	math	math	PROPN
ejpam-5828	102	6	,	,	PUNCT
ejpam-5828	102	7	18	18	NUM
ejpam-5828	102	8	(	(	PUNCT
ejpam-5828	102	9	2	2	NUM
ejpam-5828	102	10	)	)	PUNCT
ejpam-5828	102	11	(	(	PUNCT
ejpam-5828	102	12	2025	2025	NUM
ejpam-5828	102	13	)	)	PUNCT
ejpam-5828	102	14	,	,	PUNCT
ejpam-5828	102	15	5828	5828	NUM
ejpam-5828	102	16	6	6	NUM
ejpam-5828	102	17	of	of	ADP
ejpam-5828	102	18	25	25	NUM
ejpam-5828	102	19	∂wx	∂wx	PROPN
ejpam-5828	102	20	∂x	∂x	PROPN
ejpam-5828	102	21	=	=	SYM
ejpam-5828	103	1	√	√	NUM
ejpam-5828	103	2	2mα−	2mα−	NUM
ejpam-5828	103	3	2mαy	2mαy	NUM
ejpam-5828	103	4	−	−	PROPN
ejpam-5828	103	5	4π2m2v2xy	4π2m2v2xy	NOUN
ejpam-5828	103	6	2	2	NUM
ejpam-5828	103	7	+	+	CCONJ
ejpam-5828	103	8	1	1	NUM
ejpam-5828	103	9	2	2	NUM
ejpam-5828	103	10	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	103	11	2	2	NUM
ejpam-5828	103	12	(	(	PUNCT
ejpam-5828	103	13	9	9	NUM
ejpam-5828	103	14	)	)	PUNCT
ejpam-5828	103	15	equations	equation	NOUN
ejpam-5828	103	16	6	6	NUM
ejpam-5828	103	17	and	and	CCONJ
ejpam-5828	103	18	7	7	NUM
ejpam-5828	103	19	can	can	AUX
ejpam-5828	103	20	be	be	AUX
ejpam-5828	103	21	solved	solve	VERB
ejpam-5828	103	22	by	by	ADP
ejpam-5828	103	23	integrating	integrate	VERB
ejpam-5828	103	24	the	the	DET
ejpam-5828	103	25	equation	equation	NOUN
ejpam-5828	103	26	to	to	PART
ejpam-5828	103	27	obtain	obtain	VERB
ejpam-5828	103	28	:	:	PUNCT
ejpam-5828	103	29	wy′	wy′	PROPN
ejpam-5828	103	30	=	=	SYM
ejpam-5828	103	31	∫	∫	PROPN
ejpam-5828	104	1	y	y	PROPN
ejpam-5828	105	1	′	′	NOUN
ejpam-5828	105	2	0	0	NUM
ejpam-5828	106	1	√	√	INTJ
ejpam-5828	107	1	(	(	PUNCT
ejpam-5828	107	2	2mαy	2mαy	PROPN
ejpam-5828	107	3	−	−	NOUN
ejpam-5828	107	4	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	107	5	2	2	NUM
ejpam-5828	108	1	+	+	CCONJ
ejpam-5828	108	2	1	1	NUM
ejpam-5828	108	3	2	2	NUM
ejpam-5828	108	4	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	108	5	2)dy	2)dy	NUM
ejpam-5828	108	6	(	(	PUNCT
ejpam-5828	108	7	10	10	NUM
ejpam-5828	108	8	)	)	PUNCT
ejpam-5828	108	9	wx′	wx′	NOUN
ejpam-5828	109	1	=	=	SYM
ejpam-5828	109	2	∫	∫	PROPN
ejpam-5828	109	3	x	x	PUNCT
ejpam-5828	110	1	′	′	NOUN
ejpam-5828	110	2	0	0	NUM
ejpam-5828	110	3	√	√	NUM
ejpam-5828	110	4	(	(	PUNCT
ejpam-5828	110	5	2mα−	2mα−	NUM
ejpam-5828	110	6	2mαy	2mαy	NUM
ejpam-5828	110	7	−	−	PROPN
ejpam-5828	110	8	4π2m2v2xy	4π2m2v2xy	NOUN
ejpam-5828	110	9	2	2	NUM
ejpam-5828	110	10	+	+	CCONJ
ejpam-5828	110	11	1	1	NUM
ejpam-5828	110	12	2	2	NUM
ejpam-5828	110	13	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	110	14	2)dx	2)dx	NOUN
ejpam-5828	110	15	(	(	PUNCT
ejpam-5828	110	16	11	11	NUM
ejpam-5828	110	17	)	)	PUNCT
ejpam-5828	110	18	substituting	substitute	VERB
ejpam-5828	110	19	equation	equation	NOUN
ejpam-5828	110	20	1	1	NUM
ejpam-5828	110	21	and	and	CCONJ
ejpam-5828	110	22	equation	equation	NOUN
ejpam-5828	110	23	11	11	NUM
ejpam-5828	110	24	in	in	ADP
ejpam-5828	110	25	equation	equation	NOUN
ejpam-5828	110	26	s(x	s(x	NOUN
ejpam-5828	110	27	,	,	PUNCT
ejpam-5828	110	28	y	y	PROPN
ejpam-5828	110	29	,	,	PUNCT
ejpam-5828	110	30	α	α	PROPN
ejpam-5828	110	31	,	,	PUNCT
ejpam-5828	110	32	αy	αy	NOUN
ejpam-5828	110	33	,	,	PUNCT
ejpam-5828	110	34	t	t	PROPN
ejpam-5828	110	35	)	)	PUNCT
ejpam-5828	110	36	=	=	NOUN
ejpam-5828	110	37	wx(x	wx(x	X
ejpam-5828	110	38	,	,	PUNCT
ejpam-5828	110	39	y	y	PROPN
ejpam-5828	110	40	,	,	PUNCT
ejpam-5828	110	41	α	α	NOUN
ejpam-5828	110	42	)	)	PUNCT
ejpam-5828	110	43	+	+	ADJ
ejpam-5828	110	44	wy(x	wy(x	X
ejpam-5828	110	45	,	,	PUNCT
ejpam-5828	110	46	y	y	PROPN
ejpam-5828	110	47	,	,	PUNCT
ejpam-5828	110	48	α)−	α)−	PROPN
ejpam-5828	110	49	αt	αt	NOUN
ejpam-5828	110	50	we	we	PRON
ejpam-5828	110	51	obtain	obtain	VERB
ejpam-5828	110	52	:	:	PUNCT
ejpam-5828	110	53	s(x	s(x	NOUN
ejpam-5828	110	54	,	,	PUNCT
ejpam-5828	110	55	y	y	PROPN
ejpam-5828	110	56	,	,	PUNCT
ejpam-5828	110	57	α	α	PROPN
ejpam-5828	110	58	,	,	PUNCT
ejpam-5828	110	59	αy	αy	NOUN
ejpam-5828	110	60	,	,	PUNCT
ejpam-5828	110	61	t	t	PROPN
ejpam-5828	110	62	)	)	PUNCT
ejpam-5828	110	63	=	=	SYM
ejpam-5828	111	1	∫	∫	PUNCT
ejpam-5828	111	2	x	x	X
ejpam-5828	112	1	′	′	NOUN
ejpam-5828	112	2	0	0	NUM
ejpam-5828	112	3	√	√	NUM
ejpam-5828	112	4	(	(	PUNCT
ejpam-5828	112	5	2mα−	2mα−	NUM
ejpam-5828	112	6	2mαy	2mαy	NUM
ejpam-5828	112	7	−	−	PROPN
ejpam-5828	112	8	4π2m2v2xy	4π2m2v2xy	NOUN
ejpam-5828	112	9	2	2	NUM
ejpam-5828	112	10	+	+	CCONJ
ejpam-5828	112	11	1	1	NUM
ejpam-5828	112	12	2	2	NUM
ejpam-5828	112	13	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	112	14	2)dx+	2)dx+	NUM
ejpam-5828	112	15	∫	∫	NOUN
ejpam-5828	112	16	y	y	PROPN
ejpam-5828	113	1	′	′	NOUN
ejpam-5828	113	2	0	0	NUM
ejpam-5828	114	1	√	√	INTJ
ejpam-5828	115	1	(	(	PUNCT
ejpam-5828	115	2	2mαy	2mαy	PROPN
ejpam-5828	115	3	−	−	NOUN
ejpam-5828	115	4	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	115	5	2	2	NUM
ejpam-5828	116	1	+	+	CCONJ
ejpam-5828	116	2	1	1	NUM
ejpam-5828	116	3	2	2	NUM
ejpam-5828	116	4	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	117	1	2)dy	2)dy	NUM
ejpam-5828	117	2	−	−	PROPN
ejpam-5828	117	3	αit	αit	NOUN
ejpam-5828	117	4	(	(	PUNCT
ejpam-5828	117	5	12	12	NUM
ejpam-5828	117	6	)	)	PUNCT
ejpam-5828	117	7	by	by	ADP
ejpam-5828	117	8	differentiating	differentiate	VERB
ejpam-5828	117	9	the	the	DET
ejpam-5828	117	10	previous	previous	ADJ
ejpam-5828	117	11	equation	equation	NOUN
ejpam-5828	117	12	with	with	ADP
ejpam-5828	117	13	respect	respect	NOUN
ejpam-5828	117	14	to	to	ADP
ejpam-5828	117	15	αi	αi	NOUN
ejpam-5828	117	16	,	,	PUNCT
ejpam-5828	117	17	we	we	PRON
ejpam-5828	117	18	obtain	obtain	VERB
ejpam-5828	117	19	:	:	PUNCT
ejpam-5828	117	20	by′	by′	NOUN
ejpam-5828	117	21	=	=	PUNCT
ejpam-5828	117	22	∂s	∂s	PROPN
ejpam-5828	117	23	∂αy′	∂αy′	PROPN
ejpam-5828	117	24	=	=	PUNCT
ejpam-5828	117	25	∫	∫	PROPN
ejpam-5828	118	1	y	y	PROPN
ejpam-5828	118	2	′	′	NUM
ejpam-5828	118	3	0	0	NUM
ejpam-5828	119	1	m	m	VERB
ejpam-5828	119	2	2mαy	2mαy	NUM
ejpam-5828	119	3	−	−	NOUN
ejpam-5828	119	4	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	119	5	2	2	NUM
ejpam-5828	120	1	+	+	CCONJ
ejpam-5828	120	2	1	1	NUM
ejpam-5828	120	3	2	2	NUM
ejpam-5828	120	4	m	m	NUM
ejpam-5828	120	5	2λ2yy	2λ2yy	NUM
ejpam-5828	120	6	2	2	NUM
ejpam-5828	120	7	)	)	PUNCT
ejpam-5828	120	8	dy−	dy−	NOUN
ejpam-5828	121	1	sin−1	sin−1	PROPN
ejpam-5828	121	2	(	(	PUNCT
ejpam-5828	121	3	√	√	PROPN
ejpam-5828	121	4	(	(	PUNCT
ejpam-5828	121	5	2mπ2v2	2mπ2v2	NUM
ejpam-5828	121	6	y	y	PROPN
ejpam-5828	121	7	′−	′−	PROPN
ejpam-5828	121	8	1	1	NUM
ejpam-5828	121	9	4	4	NUM
ejpam-5828	121	10	mλ2	mλ2	NOUN
ejpam-5828	121	11	y	y	NOUN
ejpam-5828	121	12	′	′	NUM
ejpam-5828	122	1	α	α	NOUN
ejpam-5828	122	2	y	y	NOUN
ejpam-5828	122	3	′	′	NUM
ejpam-5828	122	4	)	)	PUNCT
ejpam-5828	123	1	y	y	PROPN
ejpam-5828	123	2	′	′	NUM
ejpam-5828	123	3	)	)	PUNCT
ejpam-5828	124	1	√	√	NUM
ejpam-5828	125	1	4π2v2	4π2v2	NUM
ejpam-5828	125	2	y′	y′	NOUN
ejpam-5828	126	1	−	−	PROPN
ejpam-5828	126	2	sin−1	sin−1	PROPN
ejpam-5828	126	3	(	(	PUNCT
ejpam-5828	126	4	√	√	PROPN
ejpam-5828	126	5	(	(	PUNCT
ejpam-5828	126	6	2mπ2v2	2mπ2v2	NUM
ejpam-5828	126	7	x	x	SYM
ejpam-5828	126	8	′−	′−	NOUN
ejpam-5828	126	9	1	1	NUM
ejpam-5828	126	10	4	4	NUM
ejpam-5828	126	11	mλ2	mλ2	NOUN
ejpam-5828	126	12	x	x	NOUN
ejpam-5828	126	13	′	′	NUM
ejpam-5828	126	14	α−α	α−α	NUM
ejpam-5828	126	15	y	y	NOUN
ejpam-5828	126	16	′	′	NUM
ejpam-5828	126	17	)	)	PUNCT
ejpam-5828	127	1	x	x	SYM
ejpam-5828	127	2	′	′	NUM
ejpam-5828	127	3	)	)	PUNCT
ejpam-5828	128	1	√	√	PROPN
ejpam-5828	129	1	4π2v2	4π2v2	NUM
ejpam-5828	129	2	x′	x′	PROPN
ejpam-5828	129	3	(	(	PUNCT
ejpam-5828	129	4	13	13	NUM
ejpam-5828	129	5	)	)	PUNCT
ejpam-5828	129	6	βx′	βx′	NOUN
ejpam-5828	130	1	+	+	NUM
ejpam-5828	130	2	t	t	X
ejpam-5828	130	3	=	=	SYM
ejpam-5828	130	4	∫	∫	PROPN
ejpam-5828	130	5	x	x	PUNCT
ejpam-5828	131	1	′	′	NUM
ejpam-5828	131	2	0	0	NUM
ejpam-5828	132	1	m	m	VERB
ejpam-5828	132	2	2mα−	2mα−	NUM
ejpam-5828	133	1	2mαy	2mαy	NUM
ejpam-5828	133	2	−	−	NOUN
ejpam-5828	133	3	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	133	4	2	2	NUM
ejpam-5828	133	5	+	+	CCONJ
ejpam-5828	133	6	1	1	NUM
ejpam-5828	133	7	2	2	NUM
ejpam-5828	133	8	m	m	NUM
ejpam-5828	133	9	2λ2xx	2λ2xx	NUM
ejpam-5828	133	10	2	2	NUM
ejpam-5828	133	11	)	)	PUNCT
ejpam-5828	133	12	dx	dx	PROPN
ejpam-5828	134	1	=	=	SYM
ejpam-5828	134	2	sin−1	sin−1	PROPN
ejpam-5828	134	3	(	(	PUNCT
ejpam-5828	134	4	√	√	PROPN
ejpam-5828	134	5	(	(	PUNCT
ejpam-5828	134	6	2mπ2v2	2mπ2v2	NUM
ejpam-5828	134	7	x	x	SYM
ejpam-5828	134	8	′−	′−	NOUN
ejpam-5828	134	9	1	1	NUM
ejpam-5828	134	10	4	4	NUM
ejpam-5828	134	11	mλ2	mλ2	NOUN
ejpam-5828	134	12	x	x	NOUN
ejpam-5828	134	13	′	′	NUM
ejpam-5828	134	14	α−α	α−α	NUM
ejpam-5828	134	15	y	y	NOUN
ejpam-5828	134	16	′	′	NUM
ejpam-5828	134	17	)	)	PUNCT
ejpam-5828	134	18	x	x	SYM
ejpam-5828	134	19	′	′	NUM
ejpam-5828	134	20	)	)	PUNCT
ejpam-5828	135	1	√	√	PROPN
ejpam-5828	136	1	4π2v2	4π2v2	NUM
ejpam-5828	136	2	x′	x′	PROPN
ejpam-5828	136	3	(	(	PUNCT
ejpam-5828	136	4	14	14	NUM
ejpam-5828	136	5	)	)	PUNCT
ejpam-5828	136	6	after	after	ADP
ejpam-5828	136	7	integration	integration	NOUN
ejpam-5828	136	8	,	,	PUNCT
ejpam-5828	136	9	equation	equation	NOUN
ejpam-5828	136	10	14	14	NUM
ejpam-5828	136	11	was	be	AUX
ejpam-5828	136	12	subjected	subject	VERB
ejpam-5828	136	13	to	to	ADP
ejpam-5828	136	14	necessary	necessary	ADJ
ejpam-5828	136	15	algebraic	algebraic	ADJ
ejpam-5828	136	16	simplifications	simplification	NOUN
ejpam-5828	136	17	,	,	PUNCT
ejpam-5828	136	18	leading	lead	VERB
ejpam-5828	136	19	to	to	ADP
ejpam-5828	136	20	the	the	DET
ejpam-5828	136	21	expression	expression	NOUN
ejpam-5828	136	22	shown	show	VERB
ejpam-5828	136	23	in	in	ADP
ejpam-5828	136	24	equations	equation	NOUN
ejpam-5828	136	25	15	15	NUM
ejpam-5828	136	26	.	.	PUNCT
ejpam-5828	137	1	x	x	X
ejpam-5828	138	1	=	=	PUNCT
ejpam-5828	138	2	√√√√	√√√√	NOUN
ejpam-5828	138	3	(	(	PUNCT
ejpam-5828	138	4	α−	α−	ADP
ejpam-5828	138	5	αy	αy	ADP
ejpam-5828	138	6	2mπ2v2	2mπ2v2	NUM
ejpam-5828	138	7	x′	x′	PUNCT
ejpam-5828	138	8	−	−	NUM
ejpam-5828	138	9	1	1	NUM
ejpam-5828	138	10	4mλ	4mλ	NOUN
ejpam-5828	138	11	2	2	NUM
ejpam-5828	138	12	x′	x′	NUM
ejpam-5828	138	13	)	)	PUNCT
ejpam-5828	138	14	sin	sin	NOUN
ejpam-5828	139	1	[	[	X
ejpam-5828	139	2	√	√	NOUN
ejpam-5828	139	3	4π2v2	4π2v2	NUM
ejpam-5828	139	4	x′	x′	PROPN
ejpam-5828	140	1	(	(	PUNCT
ejpam-5828	140	2	βx′	βx′	PROPN
ejpam-5828	140	3	+	+	NUM
ejpam-5828	140	4	t	t	NOUN
ejpam-5828	140	5	)	)	PUNCT
ejpam-5828	140	6	]	]	PUNCT
ejpam-5828	140	7	(	(	PUNCT
ejpam-5828	140	8	15.a	15.a	NUM
ejpam-5828	140	9	)	)	PUNCT
ejpam-5828	140	10	b.	b.	PROPN
ejpam-5828	140	11	m.	m.	PROPN
ejpam-5828	140	12	al	al	PROPN
ejpam-5828	140	13	-	-	PUNCT
ejpam-5828	140	14	khamiseh	khamiseh	PROPN
ejpam-5828	140	15	et	et	PROPN
ejpam-5828	140	16	al	al	PROPN
ejpam-5828	140	17	.	.	PUNCT
ejpam-5828	140	18	/	/	SYM
ejpam-5828	140	19	eur	eur	PROPN
ejpam-5828	140	20	.	.	PUNCT
ejpam-5828	141	1	j.	j.	PROPN
ejpam-5828	141	2	pure	pure	PROPN
ejpam-5828	141	3	appl	appl	PROPN
ejpam-5828	141	4	.	.	PROPN
ejpam-5828	141	5	math	math	PROPN
ejpam-5828	141	6	,	,	PUNCT
ejpam-5828	141	7	18	18	NUM
ejpam-5828	141	8	(	(	PUNCT
ejpam-5828	141	9	2	2	NUM
ejpam-5828	141	10	)	)	PUNCT
ejpam-5828	141	11	(	(	PUNCT
ejpam-5828	141	12	2025	2025	NUM
ejpam-5828	141	13	)	)	PUNCT
ejpam-5828	141	14	,	,	PUNCT
ejpam-5828	141	15	5828	5828	NUM
ejpam-5828	141	16	7	7	NUM
ejpam-5828	141	17	of	of	ADP
ejpam-5828	141	18	25	25	NUM
ejpam-5828	141	19	y	y	NOUN
ejpam-5828	141	20	=	=	PUNCT
ejpam-5828	141	21	√√√√	√√√√	NOUN
ejpam-5828	141	22	(	(	PUNCT
ejpam-5828	141	23	α−	α−	ADP
ejpam-5828	141	24	αy	αy	ADP
ejpam-5828	141	25	2mπ2v2	2mπ2v2	NUM
ejpam-5828	141	26	y′	y′	NOUN
ejpam-5828	141	27	−	−	PROPN
ejpam-5828	141	28	1	1	NUM
ejpam-5828	141	29	4mλ	4mλ	NOUN
ejpam-5828	141	30	2	2	NUM
ejpam-5828	141	31	y′	y′	NOUN
ejpam-5828	141	32	)	)	PUNCT
ejpam-5828	141	33	sin	sin	NOUN
ejpam-5828	142	1	[	[	X
ejpam-5828	142	2	√	√	INTJ
ejpam-5828	142	3	4π2vy′2(βy′	4π2vy′2(βy′	NUM
ejpam-5828	142	4	+	+	NUM
ejpam-5828	142	5	t	t	NOUN
ejpam-5828	142	6	)	)	PUNCT
ejpam-5828	142	7	]	]	PUNCT
ejpam-5828	142	8	(	(	PUNCT
ejpam-5828	142	9	15.b	15.b	NUM
ejpam-5828	142	10	)	)	PUNCT
ejpam-5828	142	11	3	3	NUM
ejpam-5828	142	12	.	.	NOUN
ejpam-5828	142	13	quantization	quantization	NOUN
ejpam-5828	142	14	of	of	ADP
ejpam-5828	142	15	a	a	DET
ejpam-5828	142	16	dissipative	dissipative	ADJ
ejpam-5828	142	17	two	two	NUM
ejpam-5828	142	18	-	-	PUNCT
ejpam-5828	142	19	dimensional	dimensional	ADJ
ejpam-5828	142	20	anisotropic	anisotropic	NOUN
ejpam-5828	142	21	harmonic	harmonic	ADJ
ejpam-5828	142	22	oscillator	oscillator	NOUN
ejpam-5828	142	23	using	use	VERB
ejpam-5828	142	24	the	the	DET
ejpam-5828	142	25	wkb	wkb	NOUN
ejpam-5828	142	26	approximation	approximation	NOUN
ejpam-5828	142	27	we	we	PRON
ejpam-5828	142	28	start	start	VERB
ejpam-5828	142	29	our	our	PRON
ejpam-5828	142	30	formalism	formalism	NOUN
ejpam-5828	142	31	by	by	ADP
ejpam-5828	142	32	studying	study	VERB
ejpam-5828	142	33	the	the	DET
ejpam-5828	142	34	schrödinger	schrödinger	NOUN
ejpam-5828	142	35	equation	equation	NOUN
ejpam-5828	142	36	,	,	PUNCT
ejpam-5828	142	37	denoted	denote	VERB
ejpam-5828	142	38	as	as	ADP
ejpam-5828	142	39	:	:	PUNCT
ejpam-5828	142	40	hψ	hψ	X
ejpam-5828	142	41	=	=	PUNCT
ejpam-5828	142	42	ih	ih	PROPN
ejpam-5828	142	43	∂ψ	∂ψ	PROPN
ejpam-5828	142	44	∂t	∂t	PROPN
ejpam-5828	142	45	for	for	ADP
ejpam-5828	142	46	our	our	PRON
ejpam-5828	142	47	dissipative	dissipative	ADJ
ejpam-5828	142	48	two	two	NUM
ejpam-5828	142	49	-	-	PUNCT
ejpam-5828	142	50	dimensional	dimensional	ADJ
ejpam-5828	142	51	anisotropic	anisotropic	NOUN
ejpam-5828	142	52	harmonic	harmonic	ADJ
ejpam-5828	142	53	oscillator	oscillator	NOUN
ejpam-5828	142	54	,	,	PUNCT
ejpam-5828	142	55	the	the	DET
ejpam-5828	142	56	following	follow	VERB
ejpam-5828	142	57	formulation	formulation	NOUN
ejpam-5828	142	58	is	be	AUX
ejpam-5828	142	59	proposed	propose	VERB
ejpam-5828	142	60	.	.	PUNCT
ejpam-5828	143	1	(	(	PUNCT
ejpam-5828	143	2	h	h	NOUN
ejpam-5828	143	3	i	i	NOUN
ejpam-5828	143	4	∂	∂	VERB
ejpam-5828	143	5	t	t	NOUN
ejpam-5828	144	1	−	−	PROPN
ejpam-5828	144	2	p	p	NOUN
ejpam-5828	144	3	2	2	NUM
ejpam-5828	144	4	x	x	SYM
ejpam-5828	144	5	2	2	NUM
ejpam-5828	144	6	m	m	NOUN
ejpam-5828	144	7	−	−	NOUN
ejpam-5828	144	8	p	p	NOUN
ejpam-5828	144	9	2	2	NUM
ejpam-5828	144	10	y	y	PROPN
ejpam-5828	144	11	2	2	NUM
ejpam-5828	144	12	m	m	NOUN
ejpam-5828	144	13	−	−	NOUN
ejpam-5828	144	14	2π2mv2xx	2π2mv2xx	NOUN
ejpam-5828	144	15	2	2	NUM
ejpam-5828	144	16	−	−	NOUN
ejpam-5828	144	17	2π2mv2yy	2π2mv2yy	NOUN
ejpam-5828	144	18	2	2	NUM
ejpam-5828	144	19	+	+	CCONJ
ejpam-5828	144	20	1	1	NUM
ejpam-5828	144	21	4	4	NUM
ejpam-5828	144	22	mλ2xx	mλ2xx	NOUN
ejpam-5828	144	23	2	2	NUM
ejpam-5828	144	24	+	+	CCONJ
ejpam-5828	144	25	1	1	NUM
ejpam-5828	144	26	4	4	NUM
ejpam-5828	144	27	mλ2yy	mλ2yy	NOUN
ejpam-5828	144	28	2	2	NUM
ejpam-5828	144	29	)	)	PUNCT
ejpam-5828	144	30	=	=	SYM
ejpam-5828	144	31	0	0	NUM
ejpam-5828	145	1	where	where	SCONJ
ejpam-5828	145	2	{	{	PUNCT
ejpam-5828	145	3	p̂x	p̂x	NOUN
ejpam-5828	145	4	=	=	NOUN
ejpam-5828	146	1	h	h	NOUN
ejpam-5828	147	1	i	i	NOUN
ejpam-5828	147	2	∂	∂	NOUN
ejpam-5828	147	3	∂x	∂x	VERB
ejpam-5828	147	4	p̂y	p̂y	NOUN
ejpam-5828	147	5	=	=	SYM
ejpam-5828	147	6	h	h	NOUN
ejpam-5828	148	1	i	i	NOUN
ejpam-5828	148	2	∂	∂	ADV
ejpam-5828	148	3	∂y	∂y	NOUN
ejpam-5828	148	4	that	that	PRON
ejpam-5828	148	5	is	be	AUX
ejpam-5828	148	6	(	(	PUNCT
ejpam-5828	148	7	h	h	NOUN
ejpam-5828	148	8	i	i	NOUN
ejpam-5828	148	9	∂	∂	NOUN
ejpam-5828	148	10	∂t	∂t	PROPN
ejpam-5828	148	11	−	−	PROPN
ejpam-5828	148	12	h2	h2	PROPN
ejpam-5828	148	13	2	2	NUM
ejpam-5828	148	14	m	m	PROPN
ejpam-5828	148	15	∂2ψ	∂2ψ	PROPN
ejpam-5828	148	16	∂x2	∂x2	NOUN
ejpam-5828	148	17	−	−	PROPN
ejpam-5828	148	18	h2	h2	NOUN
ejpam-5828	148	19	2	2	NUM
ejpam-5828	148	20	m	m	NOUN
ejpam-5828	148	21	∂2ψ	∂2ψ	NOUN
ejpam-5828	148	22	∂y2	∂y2	VERB
ejpam-5828	148	23	−2π2mv2xx	−2π2mv2xx	ADJ
ejpam-5828	148	24	2ψ	2ψ	NOUN
ejpam-5828	149	1	−2π2mv2yy	−2π2mv2yy	PROPN
ejpam-5828	149	2	2ψ	2ψ	NOUN
ejpam-5828	150	1	+1	+1	NOUN
ejpam-5828	150	2	4mλ	4mλ	ADJ
ejpam-5828	150	3	2	2	NUM
ejpam-5828	150	4	xx	xx	NUM
ejpam-5828	150	5	2	2	NUM
ejpam-5828	150	6	+1	+1	NOUN
ejpam-5828	150	7	4mλ	4mλ	ADJ
ejpam-5828	150	8	2	2	NUM
ejpam-5828	150	9	yy	yy	NOUN
ejpam-5828	150	10	2	2	NUM
ejpam-5828	150	11	)	)	PUNCT
ejpam-5828	150	12	=	=	SYM
ejpam-5828	150	13	0	0	PUNCT
ejpam-5828	150	14	using	use	VERB
ejpam-5828	150	15	the	the	DET
ejpam-5828	150	16	wkb	wkb	NOUN
ejpam-5828	150	17	approximation	approximation	NOUN
ejpam-5828	150	18	,	,	PUNCT
ejpam-5828	150	19	we	we	PRON
ejpam-5828	150	20	take	take	VERB
ejpam-5828	150	21	ψ	ψ	NOUN
ejpam-5828	150	22	as	as	SCONJ
ejpam-5828	150	23	follows	follow	VERB
ejpam-5828	150	24	:	:	PUNCT
ejpam-5828	150	25	ψ	ψ	X
ejpam-5828	150	26	=	=	SYM
ejpam-5828	150	27	1√	1√	ADJ
ejpam-5828	150	28	pxpy	pxpy	NOUN
ejpam-5828	150	29	e	e	NOUN
ejpam-5828	150	30	is	be	AUX
ejpam-5828	150	31	h	h	NOUN
ejpam-5828	150	32	by	by	ADP
ejpam-5828	150	33	substituting	substitute	VERB
ejpam-5828	150	34	ψ	ψ	NOUN
ejpam-5828	150	35	and	and	CCONJ
ejpam-5828	150	36	performing	perform	VERB
ejpam-5828	150	37	the	the	DET
ejpam-5828	150	38	required	require	VERB
ejpam-5828	150	39	derivatives	derivative	NOUN
ejpam-5828	150	40	,	,	PUNCT
ejpam-5828	150	41	we	we	PRON
ejpam-5828	150	42	obtain:−α+	obtain:−α+	VERB
ejpam-5828	150	43	1	1	NUM
ejpam-5828	150	44	2	2	NUM
ejpam-5828	150	45	m	m	NOUN
ejpam-5828	150	46			NOUN
ejpam-5828	150	47	ih∂	ih∂	NUM
ejpam-5828	150	48	2s	2s	NUM
ejpam-5828	150	49	∂x2	∂x2	NOUN
ejpam-5828	150	50	+	+	NUM
ejpam-5828	150	51	∂s	∂s	PROPN
ejpam-5828	150	52	∂x	∂x	PROPN
ejpam-5828	150	53	∂s	∂s	PROPN
ejpam-5828	150	54	∂x+	∂x+	NOUN
ejpam-5828	150	55	ih∂	ih∂	VERB
ejpam-5828	151	1	2s	2s	PROPN
ejpam-5828	151	2	∂y2	∂y2	PROPN
ejpam-5828	151	3	+	+	NUM
ejpam-5828	152	1	∂s	∂s	PROPN
ejpam-5828	152	2	∂y	∂y	SYM
ejpam-5828	153	1	∂s	∂s	PROPN
ejpam-5828	153	2	∂y	∂y	SYM
ejpam-5828	154	1	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	154	2	2	2	NUM
ejpam-5828	154	3	+4π2m2v2yy	+4π2m2v2yy	SYM
ejpam-5828	154	4	2	2	NUM
ejpam-5828	154	5	+	+	NUM
ejpam-5828	154	6	y2	y2	NOUN
ejpam-5828	155	1	−1	−1	ADV
ejpam-5828	155	2	2mλ	2mλ	NOUN
ejpam-5828	155	3	2	2	NUM
ejpam-5828	155	4	xx	xx	NUM
ejpam-5828	155	5	2	2	NUM
ejpam-5828	155	6	−	−	NOUN
ejpam-5828	155	7	1	1	NUM
ejpam-5828	155	8	2mλ	2mλ	NOUN
ejpam-5828	155	9	2	2	NUM
ejpam-5828	155	10	yy	yy	NOUN
ejpam-5828	155	11	2	2	NUM
ejpam-5828	155	12			PROPN
ejpam-5828	155	13	ψ	ψ	PROPN
ejpam-5828	155	14	=	=	SYM
ejpam-5828	155	15	0	0	NUM
ejpam-5828	155	16	(	(	PUNCT
ejpam-5828	155	17	16	16	NUM
ejpam-5828	155	18	)	)	PUNCT
ejpam-5828	155	19	taking	take	VERB
ejpam-5828	155	20	the	the	DET
ejpam-5828	155	21	semi	semi	ADJ
ejpam-5828	155	22	-	-	ADJ
ejpam-5828	155	23	classical	classical	ADJ
ejpam-5828	155	24	limit	limit	NOUN
ejpam-5828	156	1	k	k	NOUN
ejpam-5828	156	2	−→	−→	NOUN
ejpam-5828	156	3	0	0	NUM
ejpam-5828	156	4	and	and	CCONJ
ejpam-5828	156	5	remembering	remember	VERB
ejpam-5828	156	6	that	that	SCONJ
ejpam-5828	156	7	px	px	PROPN
ejpam-5828	156	8	=	=	SYM
ejpam-5828	156	9	∂wx	∂wx	PROPN
ejpam-5828	156	10	∂x	∂x	PROPN
ejpam-5828	156	11	=	=	PUNCT
ejpam-5828	156	12	∂s	∂s	PROPN
ejpam-5828	156	13	∂x	∂x	PROPN
ejpam-5828	156	14	and	and	CCONJ
ejpam-5828	156	15	py	py	NOUN
ejpam-5828	156	16	=	=	PRON
ejpam-5828	157	1	∂wy	∂wy	PROPN
ejpam-5828	157	2	∂y	∂y	X
ejpam-5828	157	3	=	=	PUNCT
ejpam-5828	157	4	∂s	∂s	PROPN
ejpam-5828	157	5	∂y	∂y	NUM
ejpam-5828	157	6	,	,	PUNCT
ejpam-5828	157	7	we	we	PRON
ejpam-5828	157	8	get	get	VERB
ejpam-5828	157	9	:	:	PUNCT
ejpam-5828	157	10	1	1	NUM
ejpam-5828	157	11	2	2	NUM
ejpam-5828	157	12	m	m	VERB
ejpam-5828	157	13	(	(	PUNCT
ejpam-5828	157	14	(	(	PUNCT
ejpam-5828	157	15	∂wx	∂wx	PROPN
ejpam-5828	157	16	∂x	∂x	PROPN
ejpam-5828	157	17	)	)	PUNCT
ejpam-5828	157	18	2	2	NUM
ejpam-5828	158	1	+	+	CCONJ
ejpam-5828	158	2	(	(	PUNCT
ejpam-5828	158	3	∂wy	∂wy	PROPN
ejpam-5828	158	4	∂y	∂y	NUM
ejpam-5828	158	5	)	)	PUNCT
ejpam-5828	158	6	2	2	NUM
ejpam-5828	159	1	+	+	SYM
ejpam-5828	159	2	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	159	3	2	2	NUM
ejpam-5828	160	1	+	+	CCONJ
ejpam-5828	160	2	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	160	3	2	2	NUM
ejpam-5828	160	4	−	−	NOUN
ejpam-5828	160	5	1	1	NUM
ejpam-5828	160	6	2	2	NUM
ejpam-5828	160	7	mλ2xx	mλ2xx	NOUN
ejpam-5828	160	8	2	2	NUM
ejpam-5828	160	9	−	−	NOUN
ejpam-5828	160	10	1	1	NUM
ejpam-5828	160	11	2	2	NUM
ejpam-5828	160	12	mλ2yy	mλ2yy	NOUN
ejpam-5828	160	13	2	2	NUM
ejpam-5828	160	14	)	)	PUNCT
ejpam-5828	160	15	=	=	SYM
ejpam-5828	160	16	α	α	PROPN
ejpam-5828	160	17	(	(	PUNCT
ejpam-5828	160	18	17	17	NUM
ejpam-5828	160	19	)	)	PUNCT
ejpam-5828	160	20	which	which	PRON
ejpam-5828	160	21	is	be	AUX
ejpam-5828	160	22	the	the	DET
ejpam-5828	160	23	classical	classical	ADJ
ejpam-5828	160	24	hje	hje	NOUN
ejpam-5828	160	25	.	.	PUNCT
ejpam-5828	161	1	so	so	ADV
ejpam-5828	161	2	,	,	PUNCT
ejpam-5828	161	3	we	we	PRON
ejpam-5828	161	4	have	have	AUX
ejpam-5828	161	5	satisfied	satisfy	VERB
ejpam-5828	161	6	the	the	DET
ejpam-5828	161	7	schrodinger	schrodinger	ADJ
ejpam-5828	161	8	equation	equation	NOUN
ejpam-5828	161	9	and	and	CCONJ
ejpam-5828	161	10	quantized	quantize	VERB
ejpam-5828	161	11	the	the	DET
ejpam-5828	161	12	two	two	NUM
ejpam-5828	161	13	-	-	PUNCT
ejpam-5828	161	14	dimensional	dimensional	ADJ
ejpam-5828	161	15	anisotropic	anisotropic	NOUN
ejpam-5828	161	16	harmonic	harmonic	ADJ
ejpam-5828	161	17	oscillator	oscillator	NOUN
ejpam-5828	161	18	dissipative	dissipative	NOUN
ejpam-5828	161	19	.	.	PUNCT
ejpam-5828	162	1	the	the	DET
ejpam-5828	162	2	wkb	wkb	PROPN
ejpam-5828	162	3	method	method	NOUN
ejpam-5828	162	4	demonstrated	demonstrate	VERB
ejpam-5828	162	5	compatibility	compatibility	NOUN
ejpam-5828	162	6	between	between	ADP
ejpam-5828	162	7	quantum	quantum	ADJ
ejpam-5828	162	8	solutions	solution	NOUN
ejpam-5828	162	9	and	and	CCONJ
ejpam-5828	162	10	the	the	DET
ejpam-5828	162	11	classical	classical	ADJ
ejpam-5828	162	12	hamilton	hamilton	PROPN
ejpam-5828	162	13	-	-	PUNCT
ejpam-5828	162	14	jacobi	jacobi	PROPN
ejpam-5828	162	15	equation	equation	NOUN
ejpam-5828	162	16	,	,	PUNCT
ejpam-5828	162	17	confirming	confirm	VERB
ejpam-5828	162	18	the	the	DET
ejpam-5828	162	19	reliability	reliability	NOUN
ejpam-5828	162	20	of	of	ADP
ejpam-5828	162	21	the	the	DET
ejpam-5828	162	22	semiclassical	semiclassical	ADJ
ejpam-5828	162	23	approach	approach	NOUN
ejpam-5828	162	24	in	in	ADP
ejpam-5828	162	25	determining	determine	VERB
ejpam-5828	162	26	energy	energy	NOUN
ejpam-5828	162	27	levels	level	NOUN
ejpam-5828	162	28	.	.	PUNCT
ejpam-5828	163	1	b.	b.	PROPN
ejpam-5828	163	2	m.	m.	PROPN
ejpam-5828	163	3	al	al	PROPN
ejpam-5828	163	4	-	-	PUNCT
ejpam-5828	163	5	khamiseh	khamiseh	PROPN
ejpam-5828	163	6	et	et	PROPN
ejpam-5828	163	7	al	al	PROPN
ejpam-5828	163	8	.	.	PUNCT
ejpam-5828	163	9	/	/	SYM
ejpam-5828	163	10	eur	eur	PROPN
ejpam-5828	163	11	.	.	PUNCT
ejpam-5828	164	1	j.	j.	PROPN
ejpam-5828	164	2	pure	pure	PROPN
ejpam-5828	164	3	appl	appl	PROPN
ejpam-5828	164	4	.	.	PROPN
ejpam-5828	164	5	math	math	PROPN
ejpam-5828	164	6	,	,	PUNCT
ejpam-5828	164	7	18	18	NUM
ejpam-5828	164	8	(	(	PUNCT
ejpam-5828	164	9	2	2	NUM
ejpam-5828	164	10	)	)	PUNCT
ejpam-5828	164	11	(	(	PUNCT
ejpam-5828	164	12	2025	2025	NUM
ejpam-5828	164	13	)	)	PUNCT
ejpam-5828	164	14	,	,	PUNCT
ejpam-5828	164	15	5828	5828	NUM
ejpam-5828	164	16	8	8	NUM
ejpam-5828	164	17	of	of	ADP
ejpam-5828	164	18	25	25	NUM
ejpam-5828	164	19	4	4	NUM
ejpam-5828	164	20	.	.	PUNCT
ejpam-5828	165	1	canonical	canonical	ADJ
ejpam-5828	165	2	quantization	quantization	NOUN
ejpam-5828	165	3	of	of	ADP
ejpam-5828	165	4	a	a	DET
ejpam-5828	165	5	damped	damped	ADJ
ejpam-5828	165	6	two	two	NUM
ejpam-5828	165	7	-	-	PUNCT
ejpam-5828	165	8	dimensional	dimensional	ADJ
ejpam-5828	165	9	anisotropic	anisotropic	NOUN
ejpam-5828	165	10	harmonic	harmonic	ADJ
ejpam-5828	165	11	oscillator	oscillator	NOUN
ejpam-5828	165	12	with	with	ADP
ejpam-5828	165	13	the	the	DET
ejpam-5828	165	14	nikiforov	nikiforov	NOUN
ejpam-5828	165	15	-	-	PUNCT
ejpam-5828	165	16	uvarov	uvarov	ADJ
ejpam-5828	165	17	approach	approach	NOUN
ejpam-5828	165	18	the	the	DET
ejpam-5828	165	19	schrödinger	schrödinger	NOUN
ejpam-5828	165	20	equation	equation	NOUN
ejpam-5828	165	21	governing	govern	VERB
ejpam-5828	165	22	the	the	DET
ejpam-5828	165	23	wave	wave	NOUN
ejpam-5828	165	24	function	function	NOUN
ejpam-5828	165	25	,	,	PUNCT
ejpam-5828	165	26	for	for	ADP
ejpam-5828	165	27	a	a	DET
ejpam-5828	165	28	two	two	NUM
ejpam-5828	165	29	-	-	PUNCT
ejpam-5828	165	30	dimensional	dimensional	ADJ
ejpam-5828	165	31	anisotropic	anisotropic	NOUN
ejpam-5828	165	32	harmonic	harmonic	ADJ
ejpam-5828	165	33	oscillator	oscillator	NOUN
ejpam-5828	165	34	with	with	ADP
ejpam-5828	165	35	dissipation	dissipation	NOUN
ejpam-5828	165	36	is	be	AUX
ejpam-5828	165	37	given	give	VERB
ejpam-5828	165	38	by	by	ADP
ejpam-5828	165	39	2∑	2∑	NUM
ejpam-5828	165	40	i=1	i=1	PROPN
ejpam-5828	165	41	(	(	PUNCT
ejpam-5828	165	42	−	−	PROPN
ejpam-5828	165	43	h2	h2	NOUN
ejpam-5828	165	44	2	2	NUM
ejpam-5828	165	45	m	m	PROPN
ejpam-5828	165	46	∂2ψ	∂2ψ	NOUN
ejpam-5828	165	47	∂x2i	∂x2i	NOUN
ejpam-5828	165	48	)	)	PUNCT
ejpam-5828	165	49	−	−	NOUN
ejpam-5828	166	1	1	1	NUM
ejpam-5828	166	2	2	2	NUM
ejpam-5828	166	3	4π2m2v2i	4π2m2v2i	NOUN
ejpam-5828	166	4	ψ	ψ	NOUN
ejpam-5828	166	5	+	+	CCONJ
ejpam-5828	166	6	1	1	NUM
ejpam-5828	166	7	4	4	NUM
ejpam-5828	166	8	mλ2ix	mλ2ix	NOUN
ejpam-5828	166	9	2	2	NUM
ejpam-5828	166	10	iψ	iψ	NOUN
ejpam-5828	166	11	−	−	NOUN
ejpam-5828	166	12	eiψ	eiψ	NOUN
ejpam-5828	166	13	=	=	SYM
ejpam-5828	166	14	0	0	PUNCT
ejpam-5828	166	15	(	(	PUNCT
ejpam-5828	166	16	−∞	−∞	X
ejpam-5828	166	17	<	<	X
ejpam-5828	166	18	xi	xi	X
ejpam-5828	166	19	<	<	X
ejpam-5828	166	20	+	+	NOUN
ejpam-5828	166	21	∞	∞	NOUN
ejpam-5828	166	22	)	)	PUNCT
ejpam-5828	166	23	we	we	PRON
ejpam-5828	166	24	will	will	AUX
ejpam-5828	166	25	employ	employ	VERB
ejpam-5828	166	26	the	the	DET
ejpam-5828	166	27	nikiforov	nikiforov	NOUN
ejpam-5828	166	28	-	-	PUNCT
ejpam-5828	166	29	uvarov	uvarov	PROPN
ejpam-5828	166	30	(	(	PUNCT
ejpam-5828	166	31	nu	nu	NOUN
ejpam-5828	166	32	)	)	PUNCT
ejpam-5828	166	33	method	method	NOUN
ejpam-5828	166	34	to	to	PART
ejpam-5828	166	35	solve	solve	VERB
ejpam-5828	166	36	this	this	DET
ejpam-5828	166	37	eigenvalue	eigenvalue	NOUN
ejpam-5828	166	38	problem	problem	NOUN
ejpam-5828	166	39	,	,	PUNCT
ejpam-5828	166	40	as	as	SCONJ
ejpam-5828	166	41	outlined	outline	VERB
ejpam-5828	166	42	in	in	ADP
ejpam-5828	166	43	[	[	X
ejpam-5828	166	44	21	21	NUM
ejpam-5828	166	45	]	]	PUNCT
ejpam-5828	166	46	.	.	PUNCT
ejpam-5828	167	1	here	here	ADV
ejpam-5828	167	2	,	,	PUNCT
ejpam-5828	167	3	ψ(xi	ψ(xi	PROPN
ejpam-5828	167	4	)	)	PUNCT
ejpam-5828	167	5	must	must	AUX
ejpam-5828	167	6	be	be	AUX
ejpam-5828	167	7	bounded	bound	VERB
ejpam-5828	167	8	and	and	CCONJ
ejpam-5828	167	9	satisfy	satisfy	VERB
ejpam-5828	167	10	the	the	DET
ejpam-5828	167	11	normalization	normalization	NOUN
ejpam-5828	167	12	condition.∫	condition.∫	NOUN
ejpam-5828	167	13	+	+	NOUN
ejpam-5828	167	14	∞	∞	PROPN
ejpam-5828	167	15	−∞	−∞	ADP
ejpam-5828	167	16	|ψ(xi)|2dx	|ψ(xi)|2dx	PROPN
ejpam-5828	167	17	=	=	SYM
ejpam-5828	167	18	1	1	NUM
ejpam-5828	167	19	we	we	PRON
ejpam-5828	167	20	introduce	introduce	VERB
ejpam-5828	167	21	the	the	DET
ejpam-5828	167	22	dimensionless	dimensionless	NOUN
ejpam-5828	167	23	variables	variable	VERB
ejpam-5828	167	24	ζ	ζ	NOUN
ejpam-5828	167	25	and	and	CCONJ
ejpam-5828	167	26	ϵ	ϵ	NOUN
ejpam-5828	167	27	,	,	PUNCT
ejpam-5828	167	28	representing	represent	VERB
ejpam-5828	167	29	xi	xi	X
ejpam-5828	167	30	and	and	CCONJ
ejpam-5828	167	31	ei	ei	INTJ
ejpam-5828	167	32	,	,	PUNCT
ejpam-5828	167	33	respectively	respectively	ADV
ejpam-5828	167	34	.	.	PUNCT
ejpam-5828	168	1	this	this	DET
ejpam-5828	168	2	equation	equation	NOUN
ejpam-5828	168	3	describes	describe	VERB
ejpam-5828	168	4	a	a	DET
ejpam-5828	168	5	two	two	NUM
ejpam-5828	168	6	-	-	PUNCT
ejpam-5828	168	7	dimensional	dimensional	ADJ
ejpam-5828	168	8	anisotropic	anisotropic	NOUN
ejpam-5828	168	9	harmonic	harmonic	ADJ
ejpam-5828	168	10	oscillator	oscillator	NOUN
ejpam-5828	168	11	under	under	ADP
ejpam-5828	168	12	damping	damp	VERB
ejpam-5828	168	13	.	.	PUNCT
ejpam-5828	169	1	after	after	ADP
ejpam-5828	169	2	substituting	substitute	VERB
ejpam-5828	169	3	with	with	ADP
ejpam-5828	169	4	according	accord	VERB
ejpam-5828	169	5	to	to	ADP
ejpam-5828	169	6	the	the	DET
ejpam-5828	169	7	relation	relation	NOUN
ejpam-5828	169	8	;	;	PUNCT
ejpam-5828	169	9	2∑	2∑	X
ejpam-5828	169	10	i=1	i=1	X
ejpam-5828	169	11	ζi	ζi	PROPN
ejpam-5828	169	12	=	=	ADJ
ejpam-5828	169	13	2∑	2∑	NUM
ejpam-5828	169	14	i=1	i=1	PROPN
ejpam-5828	169	15	axi	axi	NOUN
ejpam-5828	169	16	where	where	SCONJ
ejpam-5828	169	17	ζi	ζi	PROPN
ejpam-5828	169	18	=	=	NOUN
ejpam-5828	169	19	√	√	PROPN
ejpam-5828	169	20	π	π	NOUN
ejpam-5828	169	21	mw	mw	VERB
ejpam-5828	169	22	xi	xi	X
ejpam-5828	169	23	and	and	CCONJ
ejpam-5828	169	24	replacing	replace	VERB
ejpam-5828	169	25	ei	ei	INTJ
ejpam-5828	169	26	with	with	ADP
ejpam-5828	169	27	;	;	PUNCT
ejpam-5828	169	28	ei	ei	X
ejpam-5828	169	29	=	=	SYM
ejpam-5828	170	1	2∑	2∑	NUM
ejpam-5828	170	2	i=1	i=1	X
ejpam-5828	170	3	hwϵi	hwϵi	PROPN
ejpam-5828	170	4	we	we	PRON
ejpam-5828	170	5	obtain	obtain	VERB
ejpam-5828	170	6	the	the	DET
ejpam-5828	170	7	following	follow	VERB
ejpam-5828	170	8	differential	differential	ADJ
ejpam-5828	170	9	equation	equation	NOUN
ejpam-5828	170	10	:	:	PUNCT
ejpam-5828	171	1	2∑	2∑	NUM
ejpam-5828	171	2	i=1	i=1	X
ejpam-5828	171	3	ψi	ψi	ADP
ejpam-5828	172	1	+	+	CCONJ
ejpam-5828	172	2	(	(	PUNCT
ejpam-5828	172	3	2ϵi	2ϵi	ADJ
ejpam-5828	172	4	−	−	PROPN
ejpam-5828	172	5	ζ2i	ζ2i	NOUN
ejpam-5828	172	6	)	)	PUNCT
ejpam-5828	172	7	ψi	ψi	ADP
ejpam-5828	173	1	=	=	SYM
ejpam-5828	173	2	0	0	NOUN
ejpam-5828	174	1	this	this	DET
ejpam-5828	174	2	equation	equation	NOUN
ejpam-5828	174	3	is	be	AUX
ejpam-5828	174	4	of	of	ADP
ejpam-5828	174	5	the	the	DET
ejpam-5828	174	6	hypergeometric	hypergeometric	ADJ
ejpam-5828	174	7	type	type	NOUN
ejpam-5828	174	8	,	,	PUNCT
ejpam-5828	174	9	denoted	denote	VERB
ejpam-5828	174	10	by	by	ADP
ejpam-5828	174	11	primes	prime	NOUN
ejpam-5828	174	12	to	to	PART
ejpam-5828	174	13	signify	signify	VERB
ejpam-5828	174	14	differentiation	differentiation	NOUN
ejpam-5828	174	15	with	with	ADP
ejpam-5828	174	16	respect	respect	NOUN
ejpam-5828	174	17	to	to	ADP
ejpam-5828	174	18	[	[	X
ejpam-5828	174	19	22	22	NUM
ejpam-5828	174	20	]	]	SYM
ejpam-5828	174	21	.	.	PUNCT
ejpam-5828	175	1	ζσ(ζi	ζσ(ζi	NOUN
ejpam-5828	175	2	)	)	PUNCT
ejpam-5828	176	1	=	=	SYM
ejpam-5828	176	2	1	1	NUM
ejpam-5828	176	3	to	to	PART
ejpam-5828	176	4	prove	prove	VERB
ejpam-5828	176	5	the	the	DET
ejpam-5828	176	6	equation	equation	NOUN
ejpam-5828	176	7	ζσ(ζi	ζσ(ζi	VERB
ejpam-5828	176	8	)	)	PUNCT
ejpam-5828	176	9	=	=	SYM
ejpam-5828	176	10	1	1	NUM
ejpam-5828	176	11	,	,	PUNCT
ejpam-5828	176	12	at	at	ADP
ejpam-5828	176	13	the	the	DET
ejpam-5828	176	14	point	point	NOUN
ejpam-5828	176	15	ζi	ζi	ADP
ejpam-5828	176	16	the	the	DET
ejpam-5828	176	17	equation	equation	NOUN
ejpam-5828	176	18	can	can	AUX
ejpam-5828	176	19	be	be	AUX
ejpam-5828	176	20	solved	solve	VERB
ejpam-5828	176	21	as	as	SCONJ
ejpam-5828	176	22	follows	follow	VERB
ejpam-5828	176	23	:	:	PUNCT
ejpam-5828	176	24	σ(ζi	σ(ζi	NOUN
ejpam-5828	176	25	)	)	PUNCT
ejpam-5828	176	26	=	=	SYM
ejpam-5828	177	1	1	1	NUM
ejpam-5828	177	2	ζi	ζi	ADP
ejpam-5828	177	3	thus	thus	ADV
ejpam-5828	177	4	,	,	PUNCT
ejpam-5828	177	5	σ(ζi	σ(ζi	PROPN
ejpam-5828	177	6	)	)	PUNCT
ejpam-5828	177	7	=	=	SYM
ejpam-5828	178	1	1	1	NUM
ejpam-5828	178	2	ζi	ζi	PROPN
ejpam-5828	178	3	,	,	PUNCT
ejpam-5828	178	4	the	the	DET
ejpam-5828	178	5	equation	equation	NOUN
ejpam-5828	178	6	becomes	become	VERB
ejpam-5828	178	7	:	:	PUNCT
ejpam-5828	178	8	ζi	ζi	NOUN
ejpam-5828	178	9	.	.	NOUN
ejpam-5828	178	10	1	1	NUM
ejpam-5828	178	11	ζi	ζi	NOUN
ejpam-5828	178	12	=	=	SYM
ejpam-5828	178	13	1	1	NUM
ejpam-5828	178	14	this	this	PRON
ejpam-5828	178	15	proves	prove	VERB
ejpam-5828	178	16	the	the	DET
ejpam-5828	178	17	validity	validity	NOUN
ejpam-5828	178	18	of	of	ADP
ejpam-5828	178	19	the	the	DET
ejpam-5828	178	20	equation	equation	NOUN
ejpam-5828	178	21	ζ.σ(ζi	ζ.σ(ζi	NOUN
ejpam-5828	178	22	)	)	PUNCT
ejpam-5828	178	23	=	=	SYM
ejpam-5828	179	1	1	1	NUM
ejpam-5828	179	2	additionally	additionally	ADV
ejpam-5828	179	3	,	,	PUNCT
ejpam-5828	179	4	the	the	DET
ejpam-5828	179	5	following	follow	VERB
ejpam-5828	179	6	relations	relation	NOUN
ejpam-5828	179	7	hold	hold	VERB
ejpam-5828	179	8	:	:	PUNCT
ejpam-5828	179	9	τ̂(ζi	τ̂(ζi	PROPN
ejpam-5828	179	10	)	)	PUNCT
ejpam-5828	179	11	=	=	SYM
ejpam-5828	179	12	0	0	NUM
ejpam-5828	179	13	,	,	PUNCT
ejpam-5828	179	14	and	and	CCONJ
ejpam-5828	179	15	σ̂(ζi	σ̂(ζi	X
ejpam-5828	179	16	)	)	PUNCT
ejpam-5828	179	17	=	=	SYM
ejpam-5828	180	1	2ϵi	2ϵi	NOUN
ejpam-5828	181	1	−	−	PROPN
ejpam-5828	181	2	ζ2i	ζ2i	PROPN
ejpam-5828	181	3	(	(	PUNCT
ejpam-5828	181	4	18	18	NUM
ejpam-5828	181	5	)	)	PUNCT
ejpam-5828	181	6	b.	b.	PROPN
ejpam-5828	181	7	m.	m.	PROPN
ejpam-5828	181	8	al	al	PROPN
ejpam-5828	181	9	-	-	PUNCT
ejpam-5828	181	10	khamiseh	khamiseh	PROPN
ejpam-5828	181	11	et	et	PROPN
ejpam-5828	181	12	al	al	PROPN
ejpam-5828	181	13	.	.	PUNCT
ejpam-5828	181	14	/	/	SYM
ejpam-5828	181	15	eur	eur	PROPN
ejpam-5828	181	16	.	.	PUNCT
ejpam-5828	182	1	j.	j.	PROPN
ejpam-5828	182	2	pure	pure	PROPN
ejpam-5828	182	3	appl	appl	PROPN
ejpam-5828	182	4	.	.	PROPN
ejpam-5828	182	5	math	math	PROPN
ejpam-5828	182	6	,	,	PUNCT
ejpam-5828	182	7	18	18	NUM
ejpam-5828	182	8	(	(	PUNCT
ejpam-5828	182	9	2	2	NUM
ejpam-5828	182	10	)	)	PUNCT
ejpam-5828	182	11	(	(	PUNCT
ejpam-5828	182	12	2025	2025	NUM
ejpam-5828	182	13	)	)	PUNCT
ejpam-5828	182	14	,	,	PUNCT
ejpam-5828	182	15	5828	5828	NUM
ejpam-5828	182	16	9	9	NUM
ejpam-5828	182	17	of	of	ADP
ejpam-5828	182	18	25	25	NUM
ejpam-5828	182	19	in	in	ADP
ejpam-5828	182	20	the	the	DET
ejpam-5828	182	21	given	give	VERB
ejpam-5828	182	22	situation	situation	NOUN
ejpam-5828	182	23	,	,	PUNCT
ejpam-5828	182	24	with	with	ADP
ejpam-5828	182	25	ρ̂(ζi	ρ̂(ζi	PRON
ejpam-5828	182	26	)	)	PUNCT
ejpam-5828	182	27	=	=	SYM
ejpam-5828	182	28	1	1	NUM
ejpam-5828	182	29	,	,	PUNCT
ejpam-5828	182	30	the	the	DET
ejpam-5828	182	31	requirement	requirement	NOUN
ejpam-5828	182	32	for	for	ADP
ejpam-5828	182	33	√	√	PROPN
ejpam-5828	182	34	ρ̂(ζi)ψ(ζi	ρ̂(ζi)ψ(ζi	NOUN
ejpam-5828	182	35	)	)	PUNCT
ejpam-5828	182	36	to	to	PART
ejpam-5828	182	37	be	be	AUX
ejpam-5828	182	38	integrable	integrable	ADJ
ejpam-5828	182	39	squares	square	NOUN
ejpam-5828	182	40	arises	arise	VERB
ejpam-5828	182	41	directly	directly	ADV
ejpam-5828	182	42	from	from	ADP
ejpam-5828	182	43	the	the	DET
ejpam-5828	182	44	normalization	normalization	NOUN
ejpam-5828	182	45	conditions	condition	NOUN
ejpam-5828	182	46	.	.	PUNCT
ejpam-5828	183	1	by	by	ADP
ejpam-5828	183	2	following	follow	VERB
ejpam-5828	183	3	the	the	DET
ejpam-5828	183	4	previously	previously	ADV
ejpam-5828	183	5	outlined	outline	VERB
ejpam-5828	183	6	method	method	NOUN
ejpam-5828	183	7	,	,	PUNCT
ejpam-5828	183	8	we	we	PRON
ejpam-5828	183	9	can	can	AUX
ejpam-5828	183	10	transform	transform	VERB
ejpam-5828	183	11	the	the	DET
ejpam-5828	183	12	equation	equation	NOUN
ejpam-5828	183	13	governing	govern	VERB
ejpam-5828	183	14	into	into	ADP
ejpam-5828	183	15	a	a	DET
ejpam-5828	183	16	hypergeometric	hypergeometric	ADJ
ejpam-5828	183	17	one	one	NOUN
ejpam-5828	183	18	,	,	PUNCT
ejpam-5828	183	19	and	and	CCONJ
ejpam-5828	183	20	thus	thus	ADV
ejpam-5828	183	21	we	we	PRON
ejpam-5828	183	22	get	get	VERB
ejpam-5828	183	23	:	:	PUNCT
ejpam-5828	183	24	σ(ζi)η	σ(ζi)η	PROPN
ejpam-5828	183	25	′′	′′	PROPN
ejpam-5828	183	26	i	i	PRON
ejpam-5828	184	1	+	+	NUM
ejpam-5828	184	2	η(ζi)η	η(ζi)η	PROPN
ejpam-5828	185	1	′	′	VERB
ejpam-5828	186	1	i	i	PRON
ejpam-5828	186	2	+	+	CCONJ
ejpam-5828	186	3	λiηi	λiηi	NOUN
ejpam-5828	187	1	=	=	SYM
ejpam-5828	187	2	0	0	NUM
ejpam-5828	187	3	(	(	PUNCT
ejpam-5828	187	4	19	19	NUM
ejpam-5828	187	5	)	)	PUNCT
ejpam-5828	187	6	from	from	ADP
ejpam-5828	187	7	the	the	DET
ejpam-5828	187	8	above	above	ADJ
ejpam-5828	187	9	equation	equation	NOUN
ejpam-5828	187	10	,	,	PUNCT
ejpam-5828	187	11	we	we	PRON
ejpam-5828	187	12	express	express	VERB
ejpam-5828	187	13	ψ(ζi	ψ(ζi	NOUN
ejpam-5828	187	14	)	)	PUNCT
ejpam-5828	187	15	=	=	SYM
ejpam-5828	188	1	∑2	∑2	NOUN
ejpam-5828	188	2	1	1	NUM
ejpam-5828	188	3	ϕ(ζi)η(ζi	ϕ(ζi)η(ζi	NOUN
ejpam-5828	188	4	)	)	PUNCT
ejpam-5828	188	5	as	as	ADP
ejpam-5828	188	6	a	a	DET
ejpam-5828	188	7	summation	summation	NOUN
ejpam-5828	188	8	.	.	PUNCT
ejpam-5828	189	1	to	to	PART
ejpam-5828	189	2	achieve	achieve	VERB
ejpam-5828	189	3	this	this	PRON
ejpam-5828	189	4	,	,	PUNCT
ejpam-5828	189	5	we	we	PRON
ejpam-5828	189	6	utilize	utilize	VERB
ejpam-5828	189	7	the	the	DET
ejpam-5828	189	8	condition	condition	NOUN
ejpam-5828	189	9	outlined	outline	VERB
ejpam-5828	189	10	in	in	ADP
ejpam-5828	189	11	equation	equation	NOUN
ejpam-5828	189	12	18	18	NUM
ejpam-5828	189	13	,	,	PUNCT
ejpam-5828	189	14	where	where	SCONJ
ejpam-5828	189	15	ϕ(ζi	ϕ(ζi	NOUN
ejpam-5828	189	16	)	)	PUNCT
ejpam-5828	189	17	satisfies	satisfy	VERB
ejpam-5828	189	18	the	the	DET
ejpam-5828	189	19	equation	equation	NOUN
ejpam-5828	189	20	.	.	PUNCT
ejpam-5828	190	1	ϕ	ϕ	NOUN
ejpam-5828	190	2	′	′	NUM
ejpam-5828	190	3	ϕ	ϕ	NOUN
ejpam-5828	190	4	=	=	PUNCT
ejpam-5828	190	5	π(ζi	π(ζi	NOUN
ejpam-5828	190	6	)	)	PUNCT
ejpam-5828	190	7	σ(ζi	σ(ζi	PROPN
ejpam-5828	190	8	)	)	PUNCT
ejpam-5828	190	9	(	(	PUNCT
ejpam-5828	190	10	20	20	NUM
ejpam-5828	190	11	)	)	PUNCT
ejpam-5828	190	12	the	the	DET
ejpam-5828	190	13	polynomial	polynomial	ADJ
ejpam-5828	190	14	π(ζi	π(ζi	NOUN
ejpam-5828	190	15	)	)	PUNCT
ejpam-5828	190	16	is	be	AUX
ejpam-5828	190	17	represented	represent	VERB
ejpam-5828	190	18	by	by	ADP
ejpam-5828	190	19	the	the	DET
ejpam-5828	190	20	expression	expression	NOUN
ejpam-5828	190	21	∑2	∑2	PROPN
ejpam-5828	191	1	1±	1±	NUM
ejpam-5828	191	2	√	√	ADJ
ejpam-5828	191	3	ki	ki	PROPN
ejpam-5828	192	1	−	−	PROPN
ejpam-5828	192	2	2ϵi	2ϵi	PROPN
ejpam-5828	193	1	+	+	CCONJ
ejpam-5828	193	2	ζ2i	ζ2i	NOUN
ejpam-5828	193	3	,	,	PUNCT
ejpam-5828	193	4	where	where	SCONJ
ejpam-5828	193	5	the	the	DET
ejpam-5828	193	6	constant	constant	ADJ
ejpam-5828	193	7	ki	ki	PROPN
ejpam-5828	193	8	is	be	AUX
ejpam-5828	193	9	chosen	choose	VERB
ejpam-5828	193	10	to	to	PART
ejpam-5828	193	11	result	result	VERB
ejpam-5828	193	12	in	in	ADP
ejpam-5828	193	13	a	a	DET
ejpam-5828	193	14	double	double	ADJ
ejpam-5828	193	15	zero	zero	NUM
ejpam-5828	193	16	,	,	PUNCT
ejpam-5828	193	17	specifically	specifically	ADV
ejpam-5828	193	18	set	set	VERB
ejpam-5828	193	19	as	as	ADP
ejpam-5828	193	20	ki	ki	PROPN
ejpam-5828	193	21	=	=	PROPN
ejpam-5828	193	22	2ϵi	2ϵi	PROPN
ejpam-5828	193	23	.	.	PUNCT
ejpam-5828	194	1	this	this	DET
ejpam-5828	194	2	expression	expression	NOUN
ejpam-5828	194	3	gives	give	VERB
ejpam-5828	194	4	rise	rise	NOUN
ejpam-5828	194	5	to	to	ADP
ejpam-5828	194	6	two	two	NUM
ejpam-5828	194	7	potential	potential	ADJ
ejpam-5828	194	8	polynomials	polynomial	NOUN
ejpam-5828	194	9	,	,	PUNCT
ejpam-5828	194	10	which	which	PRON
ejpam-5828	194	11	are	be	AUX
ejpam-5828	194	12	π(ζi	π(ζi	NOUN
ejpam-5828	194	13	)	)	PUNCT
ejpam-5828	194	14	=	=	SYM
ejpam-5828	194	15	±ζi	±ζi	NOUN
ejpam-5828	194	16	.	.	PUNCT
ejpam-5828	195	1	therefore	therefore	ADV
ejpam-5828	195	2	,	,	PUNCT
ejpam-5828	195	3	we	we	PRON
ejpam-5828	195	4	obtain	obtain	VERB
ejpam-5828	195	5	:	:	PUNCT
ejpam-5828	195	6	τ(ζi	τ(ζi	NOUN
ejpam-5828	195	7	)	)	PUNCT
ejpam-5828	195	8	=	=	SYM
ejpam-5828	195	9	τ̂(ζi	τ̂(ζi	PROPN
ejpam-5828	195	10	)	)	PUNCT
ejpam-5828	195	11	+	+	NUM
ejpam-5828	195	12	2π(ζi	2π(ζi	NUM
ejpam-5828	195	13	)	)	PUNCT
ejpam-5828	195	14	(	(	PUNCT
ejpam-5828	195	15	21	21	NUM
ejpam-5828	195	16	)	)	PUNCT
ejpam-5828	195	17	the	the	DET
ejpam-5828	195	18	existence	existence	NOUN
ejpam-5828	195	19	of	of	ADP
ejpam-5828	195	20	a	a	DET
ejpam-5828	195	21	negative	negative	ADJ
ejpam-5828	195	22	derivative	derivative	NOUN
ejpam-5828	195	23	indicates	indicate	VERB
ejpam-5828	195	24	that	that	SCONJ
ejpam-5828	195	25	certain	certain	ADJ
ejpam-5828	195	26	conditions	condition	NOUN
ejpam-5828	195	27	must	must	AUX
ejpam-5828	195	28	be	be	AUX
ejpam-5828	195	29	met	meet	VERB
ejpam-5828	195	30	for	for	ADP
ejpam-5828	195	31	the	the	DET
ejpam-5828	195	32	function	function	NOUN
ejpam-5828	195	33	τ(ζi	τ(ζi	NOUN
ejpam-5828	195	34	)	)	PUNCT
ejpam-5828	195	35	.	.	PUNCT
ejpam-5828	196	1	these	these	DET
ejpam-5828	196	2	conditions	condition	NOUN
ejpam-5828	196	3	are	be	AUX
ejpam-5828	196	4	satisfied	satisfied	ADJ
ejpam-5828	196	5	when	when	SCONJ
ejpam-5828	196	6	we	we	PRON
ejpam-5828	196	7	take	take	VERB
ejpam-5828	196	8	τ(ζi	τ(ζi	PRON
ejpam-5828	196	9	)	)	PUNCT
ejpam-5828	196	10	=	=	PUNCT
ejpam-5828	197	1	2ζi	2ζi	NOUN
ejpam-5828	197	2	.	.	PUNCT
ejpam-5828	198	1	under	under	ADP
ejpam-5828	198	2	these	these	DET
ejpam-5828	198	3	conditions	condition	NOUN
ejpam-5828	198	4	,	,	PUNCT
ejpam-5828	198	5	we	we	PRON
ejpam-5828	198	6	get	get	VERB
ejpam-5828	198	7	:	:	PUNCT
ejpam-5828	198	8	τ(ζi	τ(ζi	NOUN
ejpam-5828	198	9	)	)	PUNCT
ejpam-5828	198	10	=	=	SYM
ejpam-5828	198	11	−ζi	−ζi	PROPN
ejpam-5828	198	12	ϕ(ζi	ϕ(ζi	PROPN
ejpam-5828	198	13	)	)	PUNCT
ejpam-5828	198	14	=	=	PUNCT
ejpam-5828	198	15	e	e	NOUN
ejpam-5828	198	16	−ζ2i	−ζ2i	NUM
ejpam-5828	198	17	2	2	NUM
ejpam-5828	198	18	λi	λi	NOUN
ejpam-5828	198	19	=	=	NOUN
ejpam-5828	198	20	2ϵ2	2ϵ2	PROPN
ejpam-5828	198	21	−	−	PROPN
ejpam-5828	198	22	1	1	NUM
ejpam-5828	198	23	ρ(ζi	ρ(ζi	NUM
ejpam-5828	198	24	)	)	PUNCT
ejpam-5828	198	25	=	=	NOUN
ejpam-5828	198	26	e−ζ	e−ζ	ADP
ejpam-5828	198	27	2	2	NUM
ejpam-5828	198	28	i	i	PRON
ejpam-5828	198	29	the	the	DET
ejpam-5828	198	30	values	value	NOUN
ejpam-5828	198	31	of	of	ADP
ejpam-5828	198	32	the	the	DET
ejpam-5828	198	33	energy	energy	NOUN
ejpam-5828	198	34	eigenvalue	eigenvalue	NOUN
ejpam-5828	198	35	ϵ	ϵ	NOUN
ejpam-5828	198	36	=	=	PUNCT
ejpam-5828	198	37	ϵni	ϵni	PROPN
ejpam-5828	199	1	=	=	PUNCT
ejpam-5828	199	2	nx	nx	PROPN
ejpam-5828	200	1	+	+	CCONJ
ejpam-5828	200	2	ny	ny	X
ejpam-5828	201	1	+	+	CCONJ
ejpam-5828	201	2	1	1	NUM
ejpam-5828	201	3	2	2	NUM
ejpam-5828	201	4	hence	hence	ADV
ejpam-5828	201	5	s(λi	s(λi	ADV
ejpam-5828	201	6	)	)	PUNCT
ejpam-5828	201	7	are	be	AUX
ejpam-5828	201	8	determined	determine	VERB
ejpam-5828	201	9	by	by	ADP
ejpam-5828	201	10	an	an	DET
ejpam-5828	201	11	equation	equation	NOUN
ejpam-5828	201	12	based	base	VERB
ejpam-5828	201	13	on	on	ADP
ejpam-5828	201	14	τ	τ	PROPN
ejpam-5828	201	15	and	and	CCONJ
ejpam-5828	201	16	σ	σ	PROPN
ejpam-5828	201	17	,	,	PUNCT
ejpam-5828	201	18	which	which	PRON
ejpam-5828	201	19	is	be	AUX
ejpam-5828	201	20	used	use	VERB
ejpam-5828	201	21	to	to	PART
ejpam-5828	201	22	rearrange	rearrange	VERB
ejpam-5828	201	23	to	to	PART
ejpam-5828	201	24	achieve	achieve	VERB
ejpam-5828	201	25	equilibrium	equilibrium	NOUN
ejpam-5828	201	26	.	.	PUNCT
ejpam-5828	202	1	the	the	DET
ejpam-5828	202	2	expression	expression	NOUN
ejpam-5828	202	3	for	for	ADP
ejpam-5828	202	4	the	the	DET
ejpam-5828	202	5	energy	energy	NOUN
ejpam-5828	202	6	eigenvalues	eigenvalue	NOUN
ejpam-5828	202	7	(	(	PUNCT
ejpam-5828	202	8	ϵ	ϵ	X
ejpam-5828	202	9	)	)	PUNCT
ejpam-5828	202	10	is	be	AUX
ejpam-5828	202	11	:	:	PUNCT
ejpam-5828	202	12	enxny	enxny	X
ejpam-5828	202	13	=	=	PUNCT
ejpam-5828	202	14	ex	ex	X
ejpam-5828	203	1	+	+	NOUN
ejpam-5828	203	2	ey	ey	X
ejpam-5828	203	3	=	=	SYM
ejpam-5828	203	4	(	(	PUNCT
ejpam-5828	203	5	2πnxvx	2πnxvx	NUM
ejpam-5828	203	6	+	+	CCONJ
ejpam-5828	203	7	2πnyvy	2πnyvy	NUM
ejpam-5828	203	8	+	+	NUM
ejpam-5828	203	9	2π(vx	2π(vx	NUM
ejpam-5828	203	10	+	+	CCONJ
ejpam-5828	203	11	vy	vy	NOUN
ejpam-5828	203	12	)	)	PUNCT
ejpam-5828	203	13	2	2	NUM
ejpam-5828	203	14	)	)	PUNCT
ejpam-5828	203	15	h	h	NOUN
ejpam-5828	204	1	where	where	SCONJ
ejpam-5828	204	2	nx	nx	PROPN
ejpam-5828	204	3	=	=	SYM
ejpam-5828	204	4	0	0	PROPN
ejpam-5828	204	5	,	,	PUNCT
ejpam-5828	204	6	1	1	NUM
ejpam-5828	204	7	,	,	PUNCT
ejpam-5828	204	8	2	2	NUM
ejpam-5828	204	9	,	,	PUNCT
ejpam-5828	204	10	·	·	PUNCT
ejpam-5828	204	11	·	·	PUNCT
ejpam-5828	204	12	·	·	PUNCT
ejpam-5828	204	13	and	and	CCONJ
ejpam-5828	204	14	ny	ny	X
ejpam-5828	204	15	=	=	SYM
ejpam-5828	204	16	0	0	NUM
ejpam-5828	204	17	,	,	PUNCT
ejpam-5828	204	18	1	1	NUM
ejpam-5828	204	19	,	,	PUNCT
ejpam-5828	204	20	2	2	NUM
ejpam-5828	204	21	,	,	PUNCT
ejpam-5828	204	22	·	·	PUNCT
ejpam-5828	204	23	·	·	PUNCT
ejpam-5828	204	24	·	·	PUNCT
ejpam-5828	204	25	.	.	PUNCT
ejpam-5828	205	1	the	the	DET
ejpam-5828	205	2	eigenfunctions	eigenfunction	NOUN
ejpam-5828	205	3	ηnr(x	ηnr(x	PROPN
ejpam-5828	205	4	,	,	PUNCT
ejpam-5828	205	5	y	y	NOUN
ejpam-5828	205	6	)	)	PUNCT
ejpam-5828	205	7	are	be	AUX
ejpam-5828	205	8	defined	define	VERB
ejpam-5828	205	9	as	as	ADP
ejpam-5828	205	10	:	:	PUNCT
ejpam-5828	205	11	ηnr(x	ηnr(x	PROPN
ejpam-5828	205	12	,	,	PUNCT
ejpam-5828	205	13	y	y	NOUN
ejpam-5828	205	14	)	)	PUNCT
ejpam-5828	205	15	=	=	VERB
ejpam-5828	205	16	bnre	bnre	VERB
ejpam-5828	205	17	x2+y2(−1)n+r	x2+y2(−1)n+r	PROPN
ejpam-5828	205	18	∂	∂	X
ejpam-5828	205	19	n+r	n+r	X
ejpam-5828	205	20	∂r∂n	∂r∂n	VERB
ejpam-5828	205	21	e	e	AUX
ejpam-5828	205	22	−x2−y2	−x2−y2	NOUN
ejpam-5828	205	23	and	and	CCONJ
ejpam-5828	205	24	involve	involve	VERB
ejpam-5828	205	25	hermite	hermite	PROPN
ejpam-5828	205	26	functions	function	NOUN
ejpam-5828	205	27	hnr(x	hnr(x	PROPN
ejpam-5828	205	28	,	,	PUNCT
ejpam-5828	205	29	y	y	PROPN
ejpam-5828	205	30	)	)	PUNCT
ejpam-5828	205	31	.	.	PUNCT
ejpam-5828	206	1	similarly	similarly	ADV
ejpam-5828	206	2	,	,	PUNCT
ejpam-5828	206	3	the	the	DET
ejpam-5828	206	4	wave	wave	NOUN
ejpam-5828	206	5	functions	function	NOUN
ejpam-5828	206	6	ψnm(x	ψnm(x	PROPN
ejpam-5828	206	7	,	,	PUNCT
ejpam-5828	206	8	y	y	NOUN
ejpam-5828	206	9	)	)	PUNCT
ejpam-5828	206	10	are	be	AUX
ejpam-5828	206	11	derived	derive	VERB
ejpam-5828	206	12	from	from	ADP
ejpam-5828	206	13	the	the	DET
ejpam-5828	206	14	eigenfunctions	eigenfunction	NOUN
ejpam-5828	206	15	,	,	PUNCT
ejpam-5828	206	16	with	with	ADP
ejpam-5828	206	17	the	the	DET
ejpam-5828	206	18	form	form	NOUN
ejpam-5828	206	19	ψnm(x	ψnm(x	PROPN
ejpam-5828	206	20	,	,	PUNCT
ejpam-5828	206	21	y	y	NOUN
ejpam-5828	206	22	)	)	PUNCT
ejpam-5828	206	23	=	=	VERB
ejpam-5828	206	24	cnre	cnre	VERB
ejpam-5828	206	25	m(wxx2+wyy2	m(wxx2+wyy2	NOUN
ejpam-5828	206	26	)	)	PUNCT
ejpam-5828	206	27	2k	2k	NOUN
ejpam-5828	206	28	hnr	hnr	NOUN
ejpam-5828	206	29	(	(	PUNCT
ejpam-5828	206	30	mwx	mwx	NOUN
ejpam-5828	206	31	h	h	NOUN
ejpam-5828	206	32	x	x	NOUN
ejpam-5828	206	33	,	,	PUNCT
ejpam-5828	206	34	mwy	mwy	PROPN
ejpam-5828	206	35	h	h	PROPN
ejpam-5828	206	36	y	y	NOUN
ejpam-5828	206	37	)	)	PUNCT
ejpam-5828	207	1	=	=	PRON
ejpam-5828	207	2	(	(	PUNCT
ejpam-5828	207	3	m	m	VERB
ejpam-5828	207	4	πk	πk	NOUN
ejpam-5828	207	5	)	)	PUNCT
ejpam-5828	208	1	1	1	NUM
ejpam-5828	208	2	2	2	NUM
ejpam-5828	208	3	(	(	PUNCT
ejpam-5828	208	4	wx	wx	NOUN
ejpam-5828	208	5	)	)	PUNCT
ejpam-5828	208	6	1	1	NUM
ejpam-5828	208	7	2	2	NUM
ejpam-5828	208	8	(	(	PUNCT
ejpam-5828	208	9	wy	wy	PROPN
ejpam-5828	208	10	)	)	PUNCT
ejpam-5828	208	11	1	1	NUM
ejpam-5828	208	12	2	2	NUM
ejpam-5828	208	13	e−	e−	PROPN
ejpam-5828	208	14	m(wxx2+wyy2	m(wxx2+wyy2	NOUN
ejpam-5828	208	15	)	)	PUNCT
ejpam-5828	208	16	2k	2k	NOUN
ejpam-5828	208	17	hnr	hnr	NOUN
ejpam-5828	208	18	(	(	PUNCT
ejpam-5828	208	19	mwx	mwx	NOUN
ejpam-5828	208	20	h	h	NOUN
ejpam-5828	208	21	x	x	NOUN
ejpam-5828	208	22	,	,	PUNCT
ejpam-5828	208	23	mwy	mwy	PROPN
ejpam-5828	208	24	h	h	PROPN
ejpam-5828	208	25	y	y	PROPN
ejpam-5828	208	26	)	)	PUNCT
ejpam-5828	208	27	where	where	SCONJ
ejpam-5828	208	28	cnr	cnr	NOUN
ejpam-5828	208	29	=	=	SYM
ejpam-5828	208	30	(	(	PUNCT
ejpam-5828	208	31	mw	mw	X
ejpam-5828	208	32	πk	πk	PROPN
ejpam-5828	208	33	)	)	PUNCT
ejpam-5828	208	34	1	1	NUM
ejpam-5828	208	35	2	2	NUM
ejpam-5828	208	36	(	(	PUNCT
ejpam-5828	208	37	22	22	NUM
ejpam-5828	208	38	)	)	PUNCT
ejpam-5828	208	39	accurate	accurate	ADJ
ejpam-5828	208	40	energy	energy	NOUN
ejpam-5828	208	41	eigenvalues	eigenvalue	NOUN
ejpam-5828	208	42	were	be	AUX
ejpam-5828	208	43	derived	derive	VERB
ejpam-5828	208	44	using	use	VERB
ejpam-5828	208	45	the	the	DET
ejpam-5828	208	46	nu	nu	ADJ
ejpam-5828	208	47	method	method	NOUN
ejpam-5828	208	48	,	,	PUNCT
ejpam-5828	208	49	with	with	ADP
ejpam-5828	208	50	results	result	NOUN
ejpam-5828	208	51	consistent	consistent	ADJ
ejpam-5828	208	52	across	across	ADP
ejpam-5828	208	53	various	various	ADJ
ejpam-5828	208	54	approaches	approach	NOUN
ejpam-5828	208	55	,	,	PUNCT
ejpam-5828	208	56	demonstrating	demonstrate	VERB
ejpam-5828	208	57	the	the	DET
ejpam-5828	208	58	robustness	robustness	NOUN
ejpam-5828	208	59	of	of	ADP
ejpam-5828	208	60	the	the	DET
ejpam-5828	208	61	methodologies	methodology	NOUN
ejpam-5828	208	62	employed	employ	VERB
ejpam-5828	208	63	.	.	PUNCT
ejpam-5828	209	1	b.	b.	PROPN
ejpam-5828	209	2	m.	m.	PROPN
ejpam-5828	209	3	al	al	PROPN
ejpam-5828	209	4	-	-	PUNCT
ejpam-5828	209	5	khamiseh	khamiseh	PROPN
ejpam-5828	209	6	et	et	PROPN
ejpam-5828	209	7	al	al	PROPN
ejpam-5828	209	8	.	.	PUNCT
ejpam-5828	209	9	/	/	SYM
ejpam-5828	209	10	eur	eur	PROPN
ejpam-5828	209	11	.	.	PUNCT
ejpam-5828	210	1	j.	j.	PROPN
ejpam-5828	210	2	pure	pure	PROPN
ejpam-5828	210	3	appl	appl	PROPN
ejpam-5828	210	4	.	.	PROPN
ejpam-5828	210	5	math	math	PROPN
ejpam-5828	210	6	,	,	PUNCT
ejpam-5828	210	7	18	18	NUM
ejpam-5828	210	8	(	(	PUNCT
ejpam-5828	210	9	2	2	NUM
ejpam-5828	210	10	)	)	PUNCT
ejpam-5828	210	11	(	(	PUNCT
ejpam-5828	210	12	2025	2025	NUM
ejpam-5828	210	13	)	)	PUNCT
ejpam-5828	210	14	,	,	PUNCT
ejpam-5828	210	15	5828	5828	NUM
ejpam-5828	210	16	10	10	NUM
ejpam-5828	210	17	of	of	ADP
ejpam-5828	210	18	25	25	NUM
ejpam-5828	210	19	4.1	4.1	NUM
ejpam-5828	210	20	.	.	PUNCT
ejpam-5828	211	1	the	the	DET
ejpam-5828	211	2	continuity	continuity	NOUN
ejpam-5828	211	3	equation	equation	NOUN
ejpam-5828	211	4	and	and	CCONJ
ejpam-5828	211	5	the	the	DET
ejpam-5828	211	6	probability	probability	NOUN
ejpam-5828	211	7	current	current	ADJ
ejpam-5828	211	8	to	to	PART
ejpam-5828	211	9	derive	derive	VERB
ejpam-5828	211	10	the	the	DET
ejpam-5828	211	11	continuity	continuity	NOUN
ejpam-5828	211	12	equation	equation	NOUN
ejpam-5828	211	13	for	for	ADP
ejpam-5828	211	14	the	the	DET
ejpam-5828	211	15	dissipative	dissipative	ADJ
ejpam-5828	211	16	two	two	NUM
ejpam-5828	211	17	-	-	PUNCT
ejpam-5828	211	18	dimensional	dimensional	ADJ
ejpam-5828	211	19	anisotropic	anisotropic	NOUN
ejpam-5828	211	20	harmonic	harmonic	ADJ
ejpam-5828	211	21	oscillator	oscillator	NOUN
ejpam-5828	211	22	,	,	PUNCT
ejpam-5828	211	23	we	we	PRON
ejpam-5828	211	24	start	start	VERB
ejpam-5828	211	25	from	from	ADP
ejpam-5828	211	26	the	the	DET
ejpam-5828	211	27	schrödinger	schrödinger	NOUN
ejpam-5828	211	28	equation	equation	NOUN
ejpam-5828	211	29	of	of	ADP
ejpam-5828	211	30	the	the	DET
ejpam-5828	211	31	system	system	NOUN
ejpam-5828	211	32	,	,	PUNCT
ejpam-5828	211	33	taking	take	VERB
ejpam-5828	211	34	into	into	ADP
ejpam-5828	211	35	account	account	NOUN
ejpam-5828	211	36	the	the	DET
ejpam-5828	211	37	dissipation	dissipation	NOUN
ejpam-5828	211	38	effects	effect	NOUN
ejpam-5828	211	39	included	include	VERB
ejpam-5828	211	40	in	in	ADP
ejpam-5828	211	41	the	the	DET
ejpam-5828	211	42	hamiltonian	hamiltonian	NOUN
ejpam-5828	211	43	.	.	PUNCT
ejpam-5828	212	1	the	the	DET
ejpam-5828	212	2	continuity	continuity	NOUN
ejpam-5828	212	3	equation	equation	NOUN
ejpam-5828	212	4	expresses	express	VERB
ejpam-5828	212	5	the	the	DET
ejpam-5828	212	6	conservation	conservation	NOUN
ejpam-5828	212	7	of	of	ADP
ejpam-5828	212	8	probability	probability	NOUN
ejpam-5828	212	9	in	in	ADP
ejpam-5828	212	10	the	the	DET
ejpam-5828	212	11	quantum	quantum	ADJ
ejpam-5828	212	12	system	system	NOUN
ejpam-5828	212	13	,	,	PUNCT
ejpam-5828	212	14	linking	link	VERB
ejpam-5828	212	15	the	the	DET
ejpam-5828	212	16	change	change	NOUN
ejpam-5828	212	17	in	in	ADP
ejpam-5828	212	18	probability	probability	NOUN
ejpam-5828	212	19	density	density	NOUN
ejpam-5828	212	20	with	with	ADP
ejpam-5828	212	21	the	the	DET
ejpam-5828	212	22	probability	probability	NOUN
ejpam-5828	212	23	current	current	ADJ
ejpam-5828	212	24	.	.	PUNCT
ejpam-5828	213	1	the	the	DET
ejpam-5828	213	2	schrödinger	schrödinger	NOUN
ejpam-5828	213	3	equation	equation	NOUN
ejpam-5828	213	4	for	for	ADP
ejpam-5828	213	5	the	the	DET
ejpam-5828	213	6	system	system	NOUN
ejpam-5828	213	7	the	the	DET
ejpam-5828	213	8	schrödinger	schrödinger	NOUN
ejpam-5828	213	9	equation	equation	NOUN
ejpam-5828	213	10	for	for	ADP
ejpam-5828	213	11	the	the	DET
ejpam-5828	213	12	wave	wave	NOUN
ejpam-5828	213	13	function	function	PROPN
ejpam-5828	213	14	ψ(x	ψ(x	PROPN
ejpam-5828	213	15	,	,	PUNCT
ejpam-5828	213	16	y	y	PROPN
ejpam-5828	213	17	,	,	PUNCT
ejpam-5828	213	18	t	t	PROPN
ejpam-5828	213	19	)	)	PUNCT
ejpam-5828	213	20	is	be	AUX
ejpam-5828	213	21	given	give	VERB
ejpam-5828	213	22	as	as	SCONJ
ejpam-5828	213	23	follows	follow	VERB
ejpam-5828	213	24	:	:	PUNCT
ejpam-5828	214	1	i	i	PRON
ejpam-5828	214	2	h	h	NOUN
ejpam-5828	214	3	∂ψ	∂ψ	PROPN
ejpam-5828	215	1	∂t	∂t	PROPN
ejpam-5828	215	2	=	=	PUNCT
ejpam-5828	215	3	hψ	hψ	X
ejpam-5828	215	4	where	where	SCONJ
ejpam-5828	215	5	h	h	NOUN
ejpam-5828	215	6	is	be	AUX
ejpam-5828	215	7	the	the	DET
ejpam-5828	215	8	hamiltonian	hamiltonian	NOUN
ejpam-5828	215	9	of	of	ADP
ejpam-5828	215	10	the	the	DET
ejpam-5828	215	11	system	system	NOUN
ejpam-5828	215	12	.	.	PUNCT
ejpam-5828	216	1	in	in	ADP
ejpam-5828	216	2	our	our	PRON
ejpam-5828	216	3	case	case	NOUN
ejpam-5828	216	4	,	,	PUNCT
ejpam-5828	216	5	the	the	DET
ejpam-5828	216	6	hamiltonian	hamiltonian	NOUN
ejpam-5828	216	7	for	for	ADP
ejpam-5828	216	8	the	the	DET
ejpam-5828	216	9	twodimensional	twodimensional	ADJ
ejpam-5828	216	10	dissipative	dissipative	NOUN
ejpam-5828	216	11	system	system	NOUN
ejpam-5828	216	12	is	be	AUX
ejpam-5828	216	13	given	give	VERB
ejpam-5828	216	14	as	as	SCONJ
ejpam-5828	216	15	follows	follow	VERB
ejpam-5828	216	16	:	:	PUNCT
ejpam-5828	216	17	h	h	NOUN
ejpam-5828	216	18	=	=	PUNCT
ejpam-5828	217	1	p	p	X
ejpam-5828	217	2	2	2	NUM
ejpam-5828	217	3	x	x	SYM
ejpam-5828	217	4	2	2	NUM
ejpam-5828	217	5	m	m	NOUN
ejpam-5828	217	6	+	+	NOUN
ejpam-5828	217	7	p	p	X
ejpam-5828	217	8	2	2	NUM
ejpam-5828	217	9	y	y	PROPN
ejpam-5828	217	10	2	2	NUM
ejpam-5828	217	11	m	m	NOUN
ejpam-5828	217	12	+	+	NUM
ejpam-5828	217	13	v	v	ADJ
ejpam-5828	217	14	(	(	PUNCT
ejpam-5828	217	15	x	x	NOUN
ejpam-5828	217	16	,	,	PUNCT
ejpam-5828	217	17	y	y	PROPN
ejpam-5828	217	18	)	)	PUNCT
ejpam-5828	218	1	+	+	CCONJ
ejpam-5828	218	2	1	1	NUM
ejpam-5828	218	3	4	4	NUM
ejpam-5828	218	4	mλ2x	mλ2x	NOUN
ejpam-5828	218	5	+	+	CCONJ
ejpam-5828	218	6	1	1	NUM
ejpam-5828	218	7	4	4	NUM
ejpam-5828	218	8	mλ2y	mλ2y	NOUN
ejpam-5828	218	9	here	here	ADV
ejpam-5828	218	10	,	,	PUNCT
ejpam-5828	218	11	v	v	INTJ
ejpam-5828	218	12	(	(	PUNCT
ejpam-5828	218	13	x	x	NOUN
ejpam-5828	218	14	,	,	PUNCT
ejpam-5828	218	15	y	y	NOUN
ejpam-5828	218	16	)	)	PUNCT
ejpam-5828	218	17	=	=	SYM
ejpam-5828	219	1	2π2m(v2xx	2π2m(v2xx	NUM
ejpam-5828	219	2	2	2	NUM
ejpam-5828	219	3	−	−	NOUN
ejpam-5828	219	4	v2yy	v2yy	NOUN
ejpam-5828	219	5	2	2	NUM
ejpam-5828	219	6	)	)	PUNCT
ejpam-5828	219	7	represents	represent	VERB
ejpam-5828	219	8	the	the	DET
ejpam-5828	219	9	potential	potential	ADJ
ejpam-5828	219	10	energy	energy	NOUN
ejpam-5828	219	11	,	,	PUNCT
ejpam-5828	219	12	and	and	CCONJ
ejpam-5828	219	13	the	the	DET
ejpam-5828	219	14	terms	term	NOUN
ejpam-5828	219	15	1	1	NUM
ejpam-5828	219	16	4mλ	4mλ	ADJ
ejpam-5828	219	17	2	2	NUM
ejpam-5828	219	18	x	x	NOUN
ejpam-5828	219	19	and	and	CCONJ
ejpam-5828	219	20	1	1	NUM
ejpam-5828	219	21	4mλ	4mλ	ADJ
ejpam-5828	219	22	2	2	NUM
ejpam-5828	219	23	y	y	NOUN
ejpam-5828	219	24	account	account	VERB
ejpam-5828	219	25	for	for	ADP
ejpam-5828	219	26	the	the	DET
ejpam-5828	219	27	dissipation	dissipation	NOUN
ejpam-5828	219	28	effects	effect	NOUN
ejpam-5828	219	29	.	.	PUNCT
ejpam-5828	220	1	probability	probability	NOUN
ejpam-5828	220	2	density	density	NOUN
ejpam-5828	220	3	the	the	DET
ejpam-5828	220	4	probability	probability	NOUN
ejpam-5828	220	5	density	density	NOUN
ejpam-5828	220	6	ρ(x	ρ(x	PROPN
ejpam-5828	220	7	,	,	PUNCT
ejpam-5828	220	8	y	y	PROPN
ejpam-5828	220	9	,	,	PUNCT
ejpam-5828	220	10	t	t	PROPN
ejpam-5828	220	11	)	)	PUNCT
ejpam-5828	220	12	is	be	AUX
ejpam-5828	220	13	defined	define	VERB
ejpam-5828	220	14	as	as	ADP
ejpam-5828	220	15	:	:	PUNCT
ejpam-5828	220	16	ρ(x	ρ(x	PROPN
ejpam-5828	220	17	,	,	PUNCT
ejpam-5828	220	18	y	y	PROPN
ejpam-5828	220	19	,	,	PUNCT
ejpam-5828	220	20	t	t	PROPN
ejpam-5828	220	21	)	)	PUNCT
ejpam-5828	220	22	=	=	SYM
ejpam-5828	221	1	|ψ(x	|ψ(x	PROPN
ejpam-5828	221	2	,	,	PUNCT
ejpam-5828	221	3	y	y	PROPN
ejpam-5828	221	4	,	,	PUNCT
ejpam-5828	221	5	t)|2ψ(x	t)|2ψ(x	NOUN
ejpam-5828	221	6	,	,	PUNCT
ejpam-5828	221	7	y	y	PROPN
ejpam-5828	221	8	,	,	PUNCT
ejpam-5828	221	9	t	t	PROPN
ejpam-5828	221	10	)	)	PUNCT
ejpam-5828	221	11	∗	∗	PROPN
ejpam-5828	221	12	ψ(x	ψ(x	PROPN
ejpam-5828	221	13	,	,	PUNCT
ejpam-5828	221	14	y	y	PROPN
ejpam-5828	221	15	,	,	PUNCT
ejpam-5828	221	16	t	t	PROPN
ejpam-5828	221	17	)	)	PUNCT
ejpam-5828	221	18	where	where	SCONJ
ejpam-5828	221	19	ψ	ψ	NOUN
ejpam-5828	221	20	is	be	AUX
ejpam-5828	221	21	the	the	DET
ejpam-5828	221	22	complex	complex	ADJ
ejpam-5828	221	23	conjugate	conjugate	NOUN
ejpam-5828	221	24	of	of	ADP
ejpam-5828	221	25	the	the	DET
ejpam-5828	221	26	wave	wave	NOUN
ejpam-5828	221	27	function	function	NOUN
ejpam-5828	221	28	ψ∗.	ψ∗.	NOUN
ejpam-5828	221	29	derivation	derivation	NOUN
ejpam-5828	221	30	of	of	ADP
ejpam-5828	221	31	the	the	DET
ejpam-5828	221	32	continuity	continuity	NOUN
ejpam-5828	221	33	equation	equation	NOUN
ejpam-5828	221	34	with	with	ADP
ejpam-5828	221	35	dissipation	dissipation	NOUN
ejpam-5828	221	36	:	:	PUNCT
ejpam-5828	221	37	we	we	PRON
ejpam-5828	221	38	start	start	VERB
ejpam-5828	221	39	by	by	ADP
ejpam-5828	221	40	multiplying	multiply	VERB
ejpam-5828	221	41	the	the	DET
ejpam-5828	221	42	schrödinger	schrödinger	NOUN
ejpam-5828	221	43	equation	equation	NOUN
ejpam-5828	221	44	by	by	ADP
ejpam-5828	221	45	ψ∗	ψ∗	PROPN
ejpam-5828	221	46	and	and	CCONJ
ejpam-5828	221	47	subtracting	subtract	VERB
ejpam-5828	221	48	the	the	DET
ejpam-5828	221	49	complex	complex	ADJ
ejpam-5828	221	50	conjugate	conjugate	NOUN
ejpam-5828	221	51	of	of	ADP
ejpam-5828	221	52	the	the	DET
ejpam-5828	221	53	schrödinger	schrödinger	NOUN
ejpam-5828	221	54	equation	equation	NOUN
ejpam-5828	221	55	multiplied	multiply	VERB
ejpam-5828	221	56	by	by	ADP
ejpam-5828	221	57	ψ	ψ	X
ejpam-5828	221	58	:	:	PUNCT
ejpam-5828	221	59	ψ	ψ	X
ejpam-5828	221	60	∗	∗	NOUN
ejpam-5828	221	61	(	(	PUNCT
ejpam-5828	221	62	ih	ih	NOUN
ejpam-5828	221	63	∂ψ	∂ψ	PROPN
ejpam-5828	221	64	∂t	∂t	PROPN
ejpam-5828	221	65	)	)	PUNCT
ejpam-5828	222	1	−	−	PROPN
ejpam-5828	222	2	ψ	ψ	X
ejpam-5828	222	3	(	(	PUNCT
ejpam-5828	222	4	ih	ih	X
ejpam-5828	222	5	∂ψ∗	∂ψ∗	PROPN
ejpam-5828	222	6	∂t	∂t	PROPN
ejpam-5828	222	7	)	)	PUNCT
ejpam-5828	223	1	=	=	PUNCT
ejpam-5828	223	2	ψ	ψ	PART
ejpam-5828	223	3	∗hψ	∗hψ	NOUN
ejpam-5828	223	4	−	−	PROPN
ejpam-5828	223	5	ψhψ∗	ψhψ∗	NOUN
ejpam-5828	223	6	after	after	ADP
ejpam-5828	223	7	simplification	simplification	NOUN
ejpam-5828	223	8	,	,	PUNCT
ejpam-5828	223	9	we	we	PRON
ejpam-5828	223	10	obtain	obtain	VERB
ejpam-5828	223	11	:	:	PUNCT
ejpam-5828	223	12	ih	ih	PROPN
ejpam-5828	223	13	(	(	PUNCT
ejpam-5828	223	14	ψ	ψ	X
ejpam-5828	223	15	∗	∗	X
ejpam-5828	223	16	∂ψ	∂ψ	PROPN
ejpam-5828	224	1	∂t	∂t	PROPN
ejpam-5828	224	2	+	+	CCONJ
ejpam-5828	224	3	ψ	ψ	X
ejpam-5828	224	4	∂ψ∗	∂ψ∗	PROPN
ejpam-5828	224	5	∂t	∂t	PROPN
ejpam-5828	224	6	)	)	PUNCT
ejpam-5828	225	1	=	=	PUNCT
ejpam-5828	225	2	ψ	ψ	PART
ejpam-5828	225	3	∗hψ	∗hψ	NOUN
ejpam-5828	225	4	−	−	PROPN
ejpam-5828	225	5	ψhψ∗	ψhψ∗	VERB
ejpam-5828	225	6	the	the	DET
ejpam-5828	225	7	left	left	ADJ
ejpam-5828	225	8	-	-	PUNCT
ejpam-5828	225	9	hand	hand	NOUN
ejpam-5828	225	10	side	side	NOUN
ejpam-5828	225	11	can	can	AUX
ejpam-5828	225	12	be	be	AUX
ejpam-5828	225	13	written	write	VERB
ejpam-5828	225	14	as	as	ADP
ejpam-5828	225	15	:	:	PUNCT
ejpam-5828	225	16	ih	ih	PROPN
ejpam-5828	225	17	∂(ψ	∂(ψ	PROPN
ejpam-5828	225	18	∗	∗	PROPN
ejpam-5828	225	19	ψ	ψ	NOUN
ejpam-5828	225	20	)	)	PUNCT
ejpam-5828	225	21	∂t	∂t	PROPN
ejpam-5828	226	1	=	=	PUNCT
ejpam-5828	226	2	ih	ih	PROPN
ejpam-5828	226	3	∂ρ	∂ρ	PROPN
ejpam-5828	227	1	∂t	∂t	PROPN
ejpam-5828	228	1	the	the	DET
ejpam-5828	228	2	right	right	ADJ
ejpam-5828	228	3	-	-	PUNCT
ejpam-5828	228	4	hand	hand	NOUN
ejpam-5828	228	5	side	side	NOUN
ejpam-5828	228	6	can	can	AUX
ejpam-5828	228	7	be	be	AUX
ejpam-5828	228	8	simplified	simplify	VERB
ejpam-5828	228	9	using	use	VERB
ejpam-5828	228	10	the	the	DET
ejpam-5828	228	11	hamiltonian	hamiltonian	NOUN
ejpam-5828	228	12	:	:	PUNCT
ejpam-5828	228	13	ψ	ψ	X
ejpam-5828	228	14	∗hψ	∗hψ	NOUN
ejpam-5828	228	15	−	−	PROPN
ejpam-5828	228	16	ψhψ∗	ψhψ∗	NOUN
ejpam-5828	228	17	=	=	SYM
ejpam-5828	228	18	ψ	ψ	NOUN
ejpam-5828	228	19	∗	∗	NOUN
ejpam-5828	228	20	(	(	PUNCT
ejpam-5828	228	21	p	p	NOUN
ejpam-5828	228	22	2	2	NUM
ejpam-5828	228	23	x	x	SYM
ejpam-5828	228	24	2	2	NUM
ejpam-5828	228	25	m	m	NOUN
ejpam-5828	228	26	+	+	NOUN
ejpam-5828	228	27	p	p	X
ejpam-5828	228	28	2	2	NUM
ejpam-5828	228	29	y	y	PROPN
ejpam-5828	228	30	2m+	2m+	NUM
ejpam-5828	228	31	v	v	NOUN
ejpam-5828	228	32	(	(	PUNCT
ejpam-5828	228	33	x	x	NOUN
ejpam-5828	228	34	,	,	PUNCT
ejpam-5828	228	35	y	y	PROPN
ejpam-5828	228	36	)	)	PUNCT
ejpam-5828	229	1	+	+	CCONJ
ejpam-5828	229	2	1	1	NUM
ejpam-5828	229	3	4	4	NUM
ejpam-5828	229	4	mλ2x	mλ2x	NOUN
ejpam-5828	229	5	+	+	CCONJ
ejpam-5828	229	6	1	1	NUM
ejpam-5828	229	7	4	4	NUM
ejpam-5828	229	8	mλ2y	mλ2y	NOUN
ejpam-5828	229	9	)	)	PUNCT
ejpam-5828	230	1	ψ−	ψ−	PROPN
ejpam-5828	230	2	b.	b.	PROPN
ejpam-5828	230	3	m.	m.	PROPN
ejpam-5828	231	1	al	al	PROPN
ejpam-5828	231	2	-	-	PUNCT
ejpam-5828	231	3	khamiseh	khamiseh	PROPN
ejpam-5828	231	4	et	et	PROPN
ejpam-5828	231	5	al	al	PROPN
ejpam-5828	231	6	.	.	PUNCT
ejpam-5828	231	7	/	/	SYM
ejpam-5828	231	8	eur	eur	PROPN
ejpam-5828	231	9	.	.	PUNCT
ejpam-5828	232	1	j.	j.	PROPN
ejpam-5828	232	2	pure	pure	PROPN
ejpam-5828	232	3	appl	appl	PROPN
ejpam-5828	232	4	.	.	PROPN
ejpam-5828	232	5	math	math	PROPN
ejpam-5828	232	6	,	,	PUNCT
ejpam-5828	232	7	18	18	NUM
ejpam-5828	232	8	(	(	PUNCT
ejpam-5828	232	9	2	2	NUM
ejpam-5828	232	10	)	)	PUNCT
ejpam-5828	232	11	(	(	PUNCT
ejpam-5828	232	12	2025	2025	NUM
ejpam-5828	232	13	)	)	PUNCT
ejpam-5828	232	14	,	,	PUNCT
ejpam-5828	232	15	5828	5828	NUM
ejpam-5828	232	16	11	11	NUM
ejpam-5828	232	17	of	of	ADP
ejpam-5828	232	18	25	25	NUM
ejpam-5828	232	19	ψ	ψ	NOUN
ejpam-5828	232	20	(	(	PUNCT
ejpam-5828	232	21	p	p	PROPN
ejpam-5828	232	22	2	2	NUM
ejpam-5828	232	23	x	x	SYM
ejpam-5828	232	24	2	2	NUM
ejpam-5828	232	25	m	m	NOUN
ejpam-5828	232	26	+	+	NOUN
ejpam-5828	232	27	p	p	X
ejpam-5828	232	28	2	2	NUM
ejpam-5828	232	29	y	y	PROPN
ejpam-5828	232	30	2m+	2m+	NUM
ejpam-5828	232	31	v	v	NOUN
ejpam-5828	232	32	(	(	PUNCT
ejpam-5828	232	33	x	x	NOUN
ejpam-5828	232	34	,	,	PUNCT
ejpam-5828	232	35	y	y	PROPN
ejpam-5828	232	36	)	)	PUNCT
ejpam-5828	233	1	+	+	CCONJ
ejpam-5828	233	2	1	1	NUM
ejpam-5828	233	3	4	4	NUM
ejpam-5828	233	4	mλ2x	mλ2x	NOUN
ejpam-5828	233	5	+	+	CCONJ
ejpam-5828	233	6	1	1	NUM
ejpam-5828	233	7	4	4	NUM
ejpam-5828	233	8	mλ2y	mλ2y	NOUN
ejpam-5828	233	9	)	)	PUNCT
ejpam-5828	233	10	ψ∗	ψ∗	NOUN
ejpam-5828	233	11	since	since	SCONJ
ejpam-5828	233	12	v	v	NOUN
ejpam-5828	233	13	(	(	PUNCT
ejpam-5828	233	14	x	x	NOUN
ejpam-5828	233	15	,	,	PUNCT
ejpam-5828	233	16	y	y	NOUN
ejpam-5828	233	17	)	)	PUNCT
ejpam-5828	233	18	is	be	AUX
ejpam-5828	233	19	a	a	DET
ejpam-5828	233	20	real	real	ADJ
ejpam-5828	233	21	potential	potential	NOUN
ejpam-5828	233	22	,	,	PUNCT
ejpam-5828	233	23	it	it	PRON
ejpam-5828	233	24	cancels	cancel	VERB
ejpam-5828	233	25	out	out	ADP
ejpam-5828	233	26	,	,	PUNCT
ejpam-5828	233	27	leaving	leave	VERB
ejpam-5828	233	28	:	:	PUNCT
ejpam-5828	233	29	ψ∗	ψ∗	NOUN
ejpam-5828	233	30	(	(	PUNCT
ejpam-5828	233	31	p	p	NOUN
ejpam-5828	233	32	2	2	NUM
ejpam-5828	233	33	x	x	SYM
ejpam-5828	233	34	2	2	NUM
ejpam-5828	233	35	m	m	NOUN
ejpam-5828	233	36	+	+	NOUN
ejpam-5828	233	37	p	p	X
ejpam-5828	233	38	2	2	NUM
ejpam-5828	233	39	y	y	PROPN
ejpam-5828	233	40	2m+	2m+	NUM
ejpam-5828	233	41	v	v	NOUN
ejpam-5828	233	42	(	(	PUNCT
ejpam-5828	233	43	x	x	NOUN
ejpam-5828	233	44	,	,	PUNCT
ejpam-5828	233	45	y	y	PROPN
ejpam-5828	233	46	)	)	PUNCT
ejpam-5828	234	1	+	+	CCONJ
ejpam-5828	234	2	1	1	NUM
ejpam-5828	234	3	4mλ	4mλ	ADJ
ejpam-5828	234	4	2	2	NUM
ejpam-5828	234	5	x	x	SYM
ejpam-5828	234	6	+	+	NOUN
ejpam-5828	234	7	1	1	NUM
ejpam-5828	234	8	4mλ	4mλ	ADJ
ejpam-5828	234	9	2	2	NUM
ejpam-5828	234	10	y	y	NOUN
ejpam-5828	234	11	)	)	PUNCT
ejpam-5828	234	12	ψ−ψ	ψ−ψ	PROPN
ejpam-5828	234	13	(	(	PUNCT
ejpam-5828	234	14	p	p	PROPN
ejpam-5828	234	15	2	2	NUM
ejpam-5828	234	16	x	x	SYM
ejpam-5828	234	17	2	2	NUM
ejpam-5828	234	18	m	m	NOUN
ejpam-5828	234	19	+	+	NOUN
ejpam-5828	234	20	p	p	X
ejpam-5828	234	21	2	2	NUM
ejpam-5828	234	22	y	y	PROPN
ejpam-5828	234	23	2m+	2m+	NUM
ejpam-5828	234	24	v	v	NOUN
ejpam-5828	234	25	(	(	PUNCT
ejpam-5828	234	26	x	x	NOUN
ejpam-5828	234	27	,	,	PUNCT
ejpam-5828	234	28	y	y	PROPN
ejpam-5828	234	29	)	)	PUNCT
ejpam-5828	234	30	+	+	CCONJ
ejpam-5828	234	31	1	1	NUM
ejpam-5828	234	32	4mλ	4mλ	ADJ
ejpam-5828	234	33	2	2	NUM
ejpam-5828	234	34	x	x	SYM
ejpam-5828	234	35	+	+	NOUN
ejpam-5828	234	36	1	1	NUM
ejpam-5828	234	37	4mλ	4mλ	ADJ
ejpam-5828	234	38	2	2	NUM
ejpam-5828	234	39	y	y	NOUN
ejpam-5828	234	40	)	)	PUNCT
ejpam-5828	234	41	ψ∗	ψ∗	PROPN
ejpam-5828	234	42	using	use	VERB
ejpam-5828	234	43	the	the	DET
ejpam-5828	234	44	definition	definition	NOUN
ejpam-5828	234	45	of	of	ADP
ejpam-5828	234	46	the	the	DET
ejpam-5828	234	47	momentum	momentum	NOUN
ejpam-5828	234	48	operators	operator	NOUN
ejpam-5828	234	49	p̂x	p̂x	NOUN
ejpam-5828	234	50	=	=	NOUN
ejpam-5828	235	1	h	h	NOUN
ejpam-5828	235	2	i	i	NOUN
ejpam-5828	235	3	∂	∂	NOUN
ejpam-5828	235	4	∂x	∂x	PROPN
ejpam-5828	235	5	and	and	CCONJ
ejpam-5828	235	6	p̂y	p̂y	NOUN
ejpam-5828	235	7	=	=	SYM
ejpam-5828	235	8	h	h	NOUN
ejpam-5828	235	9	i	i	NOUN
ejpam-5828	235	10	∂	∂	ADV
ejpam-5828	235	11	∂y	∂y	NUM
ejpam-5828	235	12	,	,	PUNCT
ejpam-5828	235	13	we	we	PRON
ejpam-5828	235	14	get	get	VERB
ejpam-5828	235	15	:	:	PUNCT
ejpam-5828	235	16	ψ	ψ	X
ejpam-5828	235	17	∗	∗	NOUN
ejpam-5828	235	18	(	(	PUNCT
ejpam-5828	235	19	−	−	PROPN
ejpam-5828	235	20	h2	h2	NOUN
ejpam-5828	235	21	2	2	NUM
ejpam-5828	235	22	m	m	PROPN
ejpam-5828	235	23	∂2	∂2	ADJ
ejpam-5828	235	24	∂x2	∂x2	NOUN
ejpam-5828	235	25	−	−	PROPN
ejpam-5828	235	26	h2	h2	NOUN
ejpam-5828	235	27	2	2	NUM
ejpam-5828	235	28	m	m	NOUN
ejpam-5828	235	29	∂2	∂2	NOUN
ejpam-5828	235	30	∂y2	∂y2	NOUN
ejpam-5828	235	31	+	+	CCONJ
ejpam-5828	235	32	1	1	NUM
ejpam-5828	235	33	4mλ	4mλ	ADJ
ejpam-5828	235	34	2	2	NUM
ejpam-5828	235	35	x	x	SYM
ejpam-5828	235	36	+	+	NOUN
ejpam-5828	236	1	1	1	NUM
ejpam-5828	236	2	4mλ	4mλ	ADJ
ejpam-5828	236	3	2	2	NUM
ejpam-5828	236	4	y	y	NOUN
ejpam-5828	236	5	)	)	PUNCT
ejpam-5828	236	6	ψ	ψ	ADP
ejpam-5828	236	7	−	−	NOUN
ejpam-5828	236	8	ψ	ψ	X
ejpam-5828	236	9	(	(	PUNCT
ejpam-5828	236	10	−	−	PROPN
ejpam-5828	236	11	k2	k2	ADJ
ejpam-5828	236	12	2	2	NUM
ejpam-5828	236	13	m	m	NOUN
ejpam-5828	236	14	∂2	∂2	ADJ
ejpam-5828	236	15	∂x2	∂x2	NOUN
ejpam-5828	236	16	−	−	PROPN
ejpam-5828	236	17	k2	k2	ADJ
ejpam-5828	236	18	2	2	NUM
ejpam-5828	236	19	m	m	NOUN
ejpam-5828	236	20	∂2	∂2	NOUN
ejpam-5828	236	21	∂y2	∂y2	NOUN
ejpam-5828	236	22	+	+	CCONJ
ejpam-5828	236	23	1	1	NUM
ejpam-5828	236	24	4mλ	4mλ	ADJ
ejpam-5828	236	25	2	2	NUM
ejpam-5828	236	26	x	x	SYM
ejpam-5828	236	27	+	+	NOUN
ejpam-5828	236	28	1	1	NUM
ejpam-5828	236	29	4mλ	4mλ	ADJ
ejpam-5828	236	30	2	2	NUM
ejpam-5828	236	31	y	y	NOUN
ejpam-5828	236	32	)	)	PUNCT
ejpam-5828	236	33	ψ∗	ψ∗	NOUN
ejpam-5828	236	34	after	after	ADP
ejpam-5828	236	35	simplification	simplification	NOUN
ejpam-5828	236	36	,	,	PUNCT
ejpam-5828	236	37	we	we	PRON
ejpam-5828	236	38	obtain	obtain	VERB
ejpam-5828	236	39	:	:	PUNCT
ejpam-5828	236	40	−	−	PROPN
ejpam-5828	236	41	h2	h2	NOUN
ejpam-5828	236	42	2	2	NUM
ejpam-5828	236	43	m	m	NOUN
ejpam-5828	236	44	(	(	PUNCT
ejpam-5828	236	45	ψ	ψ	VERB
ejpam-5828	236	46	∗	∗	X
ejpam-5828	236	47	∂2ψ	∂2ψ	PROPN
ejpam-5828	236	48	∂x2	∂x2	NOUN
ejpam-5828	236	49	−	−	NOUN
ejpam-5828	236	50	ψ	ψ	NOUN
ejpam-5828	236	51	∂2ψ∗	∂2ψ∗	VERB
ejpam-5828	236	52	∂x2	∂x2	NOUN
ejpam-5828	236	53	)	)	PUNCT
ejpam-5828	236	54	−	−	PROPN
ejpam-5828	237	1	k2	k2	ADJ
ejpam-5828	237	2	2	2	NUM
ejpam-5828	237	3	m	m	NOUN
ejpam-5828	237	4	(	(	PUNCT
ejpam-5828	237	5	ψ	ψ	VERB
ejpam-5828	237	6	∗	∗	NOUN
ejpam-5828	237	7	∂2ψ	∂2ψ	NOUN
ejpam-5828	237	8	∂y2	∂y2	NOUN
ejpam-5828	237	9	−	−	NOUN
ejpam-5828	237	10	ψ	ψ	SYM
ejpam-5828	237	11	∂2ψ∗	∂2ψ∗	NOUN
ejpam-5828	237	12	∂y2	∂y2	ADV
ejpam-5828	237	13	)	)	PUNCT
ejpam-5828	238	1	+	+	CCONJ
ejpam-5828	238	2	1	1	NUM
ejpam-5828	238	3	4mλ	4mλ	ADJ
ejpam-5828	238	4	2	2	NUM
ejpam-5828	238	5	x(ψ∗ψ−ψψ∗)+	x(ψ∗ψ−ψψ∗)+	PROPN
ejpam-5828	238	6	1	1	NUM
ejpam-5828	238	7	4mλ	4mλ	ADJ
ejpam-5828	238	8	2	2	NUM
ejpam-5828	238	9	y(ψ∗ψ−ψψ∗	y(ψ∗ψ−ψψ∗	PROPN
ejpam-5828	238	10	)	)	PUNCT
ejpam-5828	238	11	the	the	DET
ejpam-5828	238	12	terms	term	NOUN
ejpam-5828	238	13	involving	involve	VERB
ejpam-5828	238	14	λx	λx	PROPN
ejpam-5828	238	15	and	and	CCONJ
ejpam-5828	238	16	λy	λy	PROPN
ejpam-5828	238	17	vanish	vanish	VERB
ejpam-5828	238	18	because	because	SCONJ
ejpam-5828	238	19	ψ	ψ	X
ejpam-5828	238	20	∗ψ	∗ψ	PROPN
ejpam-5828	238	21	=	=	SYM
ejpam-5828	238	22	ψψ∗.	ψψ∗.	PROPN
ejpam-5828	238	23	thus	thus	ADV
ejpam-5828	238	24	,	,	PUNCT
ejpam-5828	238	25	the	the	DET
ejpam-5828	238	26	equation	equation	NOUN
ejpam-5828	238	27	simplifies	simplify	VERB
ejpam-5828	238	28	to	to	PART
ejpam-5828	238	29	:	:	PUNCT
ejpam-5828	238	30	−	−	PROPN
ejpam-5828	238	31	h2	h2	NOUN
ejpam-5828	238	32	2	2	NUM
ejpam-5828	238	33	m	m	NOUN
ejpam-5828	238	34	∂	∂	NOUN
ejpam-5828	238	35	∂x	∂x	PROPN
ejpam-5828	238	36	(	(	PUNCT
ejpam-5828	238	37	ψ	ψ	NOUN
ejpam-5828	238	38	∗	∗	X
ejpam-5828	238	39	∂ψ	∂ψ	PROPN
ejpam-5828	239	1	∂x	∂x	PROPN
ejpam-5828	239	2	−	−	PROPN
ejpam-5828	239	3	ψ	ψ	ADP
ejpam-5828	239	4	∂ψ∗	∂ψ∗	PROPN
ejpam-5828	239	5	∂x	∂x	PROPN
ejpam-5828	239	6	)	)	PUNCT
ejpam-5828	239	7	−	−	PROPN
ejpam-5828	239	8	h2	h2	NOUN
ejpam-5828	239	9	2	2	NUM
ejpam-5828	239	10	m	m	NOUN
ejpam-5828	239	11	∂	∂	NUM
ejpam-5828	239	12	(	(	PUNCT
ejpam-5828	239	13	ψ	ψ	X
ejpam-5828	239	14	∗	∗	X
ejpam-5828	239	15	∂ψ	∂ψ	NOUN
ejpam-5828	239	16	∂y	∂y	NUM
ejpam-5828	239	17	−	−	NOUN
ejpam-5828	239	18	ψ	ψ	ADP
ejpam-5828	239	19	∂ψ∗	∂ψ∗	X
ejpam-5828	239	20	∂y	∂y	X
ejpam-5828	239	21	)	)	PUNCT
ejpam-5828	239	22	we	we	PRON
ejpam-5828	239	23	notice	notice	VERB
ejpam-5828	239	24	that	that	SCONJ
ejpam-5828	239	25	the	the	DET
ejpam-5828	239	26	expression	expression	NOUN
ejpam-5828	239	27	inside	inside	ADP
ejpam-5828	239	28	the	the	DET
ejpam-5828	239	29	parentheses	parenthesis	NOUN
ejpam-5828	239	30	is	be	AUX
ejpam-5828	239	31	the	the	DET
ejpam-5828	239	32	probability	probability	NOUN
ejpam-5828	239	33	current	current	ADJ
ejpam-5828	239	34	in	in	ADP
ejpam-5828	239	35	the	the	DET
ejpam-5828	239	36	x	x	NOUN
ejpam-5828	239	37	and	and	CCONJ
ejpam-5828	239	38	y	y	PROPN
ejpam-5828	239	39	directions	direction	NOUN
ejpam-5828	239	40	:	:	PUNCT
ejpam-5828	240	1	jx	jx	PROPN
ejpam-5828	240	2	=	=	PUNCT
ejpam-5828	240	3	h	h	PROPN
ejpam-5828	240	4	2mi	2mi	NOUN
ejpam-5828	240	5	(	(	PUNCT
ejpam-5828	240	6	ψ	ψ	X
ejpam-5828	240	7	∗	∗	X
ejpam-5828	240	8	∂ψ	∂ψ	PROPN
ejpam-5828	241	1	∂x	∂x	PROPN
ejpam-5828	241	2	−	−	PROPN
ejpam-5828	241	3	ψ	ψ	ADP
ejpam-5828	241	4	∂ψ∗	∂ψ∗	PROPN
ejpam-5828	241	5	∂x	∂x	PROPN
ejpam-5828	241	6	)	)	PUNCT
ejpam-5828	242	1	jy	jy	PROPN
ejpam-5828	242	2	=	=	PUNCT
ejpam-5828	242	3	h	h	PROPN
ejpam-5828	242	4	2mi	2mi	NOUN
ejpam-5828	242	5	(	(	PUNCT
ejpam-5828	242	6	ψ	ψ	X
ejpam-5828	242	7	∗	∗	X
ejpam-5828	242	8	∂ψ	∂ψ	NOUN
ejpam-5828	242	9	∂y	∂y	NUM
ejpam-5828	242	10	−	−	NOUN
ejpam-5828	242	11	ψ	ψ	ADP
ejpam-5828	242	12	∂ψ∗	∂ψ∗	PROPN
ejpam-5828	242	13	∂y	∂y	X
ejpam-5828	242	14	)	)	PUNCT
ejpam-5828	242	15	therefore	therefore	ADV
ejpam-5828	242	16	,	,	PUNCT
ejpam-5828	242	17	the	the	DET
ejpam-5828	242	18	equation	equation	NOUN
ejpam-5828	242	19	can	can	AUX
ejpam-5828	242	20	be	be	AUX
ejpam-5828	242	21	written	write	VERB
ejpam-5828	242	22	as	as	ADP
ejpam-5828	242	23	:	:	PUNCT
ejpam-5828	242	24	ih	ih	PROPN
ejpam-5828	242	25	∂ρ	∂ρ	PROPN
ejpam-5828	243	1	∂t	∂t	PROPN
ejpam-5828	243	2	=	=	PUNCT
ejpam-5828	244	1	−	−	PROPN
ejpam-5828	244	2	h2	h2	NOUN
ejpam-5828	244	3	2	2	NUM
ejpam-5828	244	4	m	m	NOUN
ejpam-5828	244	5	(	(	PUNCT
ejpam-5828	244	6	∂jx	∂jx	PROPN
ejpam-5828	244	7	∂x	∂x	PROPN
ejpam-5828	244	8	+	+	CCONJ
ejpam-5828	244	9	∂jy	∂jy	PROPN
ejpam-5828	244	10	∂y	∂y	NOUN
ejpam-5828	244	11	)	)	PUNCT
ejpam-5828	244	12	dividing	divide	VERB
ejpam-5828	244	13	both	both	DET
ejpam-5828	244	14	sides	side	NOUN
ejpam-5828	244	15	by	by	ADP
ejpam-5828	244	16	ih	ih	PRON
ejpam-5828	244	17	,	,	PUNCT
ejpam-5828	244	18	we	we	PRON
ejpam-5828	244	19	obtain	obtain	VERB
ejpam-5828	244	20	:	:	PUNCT
ejpam-5828	244	21	∂ρ	∂ρ	PROPN
ejpam-5828	244	22	∂t	∂t	PROPN
ejpam-5828	245	1	+	+	CCONJ
ejpam-5828	245	2	∂jx	∂jx	PROPN
ejpam-5828	245	3	∂x	∂x	PROPN
ejpam-5828	245	4	+	+	CCONJ
ejpam-5828	245	5	∂jy	∂jy	PROPN
ejpam-5828	245	6	∂y	∂y	NOUN
ejpam-5828	245	7	=	=	SYM
ejpam-5828	245	8	0	0	NUM
ejpam-5828	245	9	this	this	PRON
ejpam-5828	245	10	is	be	AUX
ejpam-5828	245	11	the	the	DET
ejpam-5828	245	12	continuity	continuity	NOUN
ejpam-5828	245	13	equation	equation	NOUN
ejpam-5828	245	14	,	,	PUNCT
ejpam-5828	245	15	which	which	PRON
ejpam-5828	245	16	expresses	express	VERB
ejpam-5828	245	17	the	the	DET
ejpam-5828	245	18	conservation	conservation	NOUN
ejpam-5828	245	19	of	of	ADP
ejpam-5828	245	20	probability	probability	NOUN
ejpam-5828	245	21	in	in	ADP
ejpam-5828	245	22	the	the	DET
ejpam-5828	245	23	quantum	quantum	ADJ
ejpam-5828	245	24	system	system	NOUN
ejpam-5828	245	25	,	,	PUNCT
ejpam-5828	245	26	even	even	ADV
ejpam-5828	245	27	in	in	ADP
ejpam-5828	245	28	the	the	DET
ejpam-5828	245	29	presence	presence	NOUN
ejpam-5828	245	30	of	of	ADP
ejpam-5828	245	31	dissipation	dissipation	NOUN
ejpam-5828	245	32	.	.	PUNCT
ejpam-5828	246	1	the	the	DET
ejpam-5828	246	2	inclusion	inclusion	NOUN
ejpam-5828	246	3	of	of	ADP
ejpam-5828	246	4	dissipative	dissipative	ADJ
ejpam-5828	246	5	terms	term	NOUN
ejpam-5828	246	6	in	in	ADP
ejpam-5828	246	7	the	the	DET
ejpam-5828	246	8	hamiltonian	hamiltonian	NOUN
ejpam-5828	246	9	,	,	PUNCT
ejpam-5828	246	10	as	as	SCONJ
ejpam-5828	246	11	demonstrated	demonstrate	VERB
ejpam-5828	246	12	by	by	ADP
ejpam-5828	246	13	serhan	serhan	PROPN
ejpam-5828	246	14	et	et	PROPN
ejpam-5828	246	15	al	al	PROPN
ejpam-5828	246	16	.	.	PUNCT
ejpam-5828	247	1	[	[	X
ejpam-5828	247	2	18	18	NUM
ejpam-5828	247	3	]	]	PUNCT
ejpam-5828	247	4	,	,	PUNCT
ejpam-5828	247	5	ensures	ensure	VERB
ejpam-5828	247	6	that	that	SCONJ
ejpam-5828	247	7	the	the	DET
ejpam-5828	247	8	continuity	continuity	NOUN
ejpam-5828	247	9	equation	equation	NOUN
ejpam-5828	247	10	remains	remain	VERB
ejpam-5828	247	11	valid	valid	ADJ
ejpam-5828	247	12	for	for	ADP
ejpam-5828	247	13	systems	system	NOUN
ejpam-5828	247	14	with	with	ADP
ejpam-5828	247	15	energy	energy	NOUN
ejpam-5828	247	16	loss	loss	NOUN
ejpam-5828	247	17	due	due	ADJ
ejpam-5828	247	18	to	to	ADP
ejpam-5828	247	19	damping	damp	VERB
ejpam-5828	247	20	or	or	CCONJ
ejpam-5828	247	21	environmental	environmental	ADJ
ejpam-5828	247	22	interactions	interaction	NOUN
ejpam-5828	247	23	.	.	PUNCT
ejpam-5828	248	1	probability	probability	NOUN
ejpam-5828	248	2	current	current	ADJ
ejpam-5828	248	3	the	the	DET
ejpam-5828	248	4	probability	probability	NOUN
ejpam-5828	248	5	current	current	ADJ
ejpam-5828	248	6	j	j	PROPN
ejpam-5828	248	7	is	be	AUX
ejpam-5828	248	8	given	give	VERB
ejpam-5828	248	9	by	by	ADP
ejpam-5828	248	10	:	:	PUNCT
ejpam-5828	248	11	j	j	PROPN
ejpam-5828	248	12	=	=	SYM
ejpam-5828	248	13	(	(	PUNCT
ejpam-5828	248	14	jx	jx	PROPN
ejpam-5828	248	15	,	,	PUNCT
ejpam-5828	248	16	jy	jy	PROPN
ejpam-5828	248	17	)	)	PUNCT
ejpam-5828	249	1	where	where	SCONJ
ejpam-5828	249	2	:	:	PUNCT
ejpam-5828	249	3	jx	jx	PROPN
ejpam-5828	249	4	=	=	PUNCT
ejpam-5828	249	5	h	h	PROPN
ejpam-5828	249	6	2mi	2mi	NOUN
ejpam-5828	249	7	(	(	PUNCT
ejpam-5828	249	8	ψ	ψ	X
ejpam-5828	249	9	∗	∗	X
ejpam-5828	249	10	∂ψ	∂ψ	PROPN
ejpam-5828	249	11	∂x	∂x	PROPN
ejpam-5828	249	12	−	−	PROPN
ejpam-5828	249	13	ψ	ψ	ADP
ejpam-5828	249	14	∂ψ∗	∂ψ∗	PROPN
ejpam-5828	249	15	∂x	∂x	PROPN
ejpam-5828	249	16	)	)	PUNCT
ejpam-5828	249	17	jy	jy	PROPN
ejpam-5828	249	18	=	=	PUNCT
ejpam-5828	249	19	h	h	PROPN
ejpam-5828	249	20	2mi	2mi	NOUN
ejpam-5828	249	21	(	(	PUNCT
ejpam-5828	249	22	ψ	ψ	X
ejpam-5828	249	23	∗	∗	X
ejpam-5828	249	24	∂ψ	∂ψ	NOUN
ejpam-5828	249	25	∂y	∂y	NUM
ejpam-5828	249	26	−	−	NOUN
ejpam-5828	249	27	ψ	ψ	ADP
ejpam-5828	249	28	∂ψ∗	∂ψ∗	PROPN
ejpam-5828	249	29	∂y	∂y	SYM
ejpam-5828	249	30	)	)	PUNCT
ejpam-5828	249	31	b.	b.	PROPN
ejpam-5828	249	32	m.	m.	PROPN
ejpam-5828	249	33	al	al	PROPN
ejpam-5828	249	34	-	-	PUNCT
ejpam-5828	249	35	khamiseh	khamiseh	PROPN
ejpam-5828	249	36	et	et	PROPN
ejpam-5828	249	37	al	al	PROPN
ejpam-5828	249	38	.	.	PUNCT
ejpam-5828	249	39	/	/	SYM
ejpam-5828	249	40	eur	eur	PROPN
ejpam-5828	249	41	.	.	PUNCT
ejpam-5828	250	1	j.	j.	PROPN
ejpam-5828	250	2	pure	pure	PROPN
ejpam-5828	250	3	appl	appl	PROPN
ejpam-5828	250	4	.	.	PROPN
ejpam-5828	250	5	math	math	PROPN
ejpam-5828	250	6	,	,	PUNCT
ejpam-5828	250	7	18	18	NUM
ejpam-5828	250	8	(	(	PUNCT
ejpam-5828	250	9	2	2	NUM
ejpam-5828	250	10	)	)	PUNCT
ejpam-5828	250	11	(	(	PUNCT
ejpam-5828	250	12	2025	2025	NUM
ejpam-5828	250	13	)	)	PUNCT
ejpam-5828	250	14	,	,	PUNCT
ejpam-5828	250	15	5828	5828	NUM
ejpam-5828	250	16	12	12	NUM
ejpam-5828	250	17	of	of	ADP
ejpam-5828	250	18	25	25	NUM
ejpam-5828	250	19	the	the	DET
ejpam-5828	250	20	continuity	continuity	NOUN
ejpam-5828	250	21	equation	equation	NOUN
ejpam-5828	250	22	expresses	express	VERB
ejpam-5828	250	23	the	the	DET
ejpam-5828	250	24	conservation	conservation	NOUN
ejpam-5828	250	25	of	of	ADP
ejpam-5828	250	26	probability	probability	NOUN
ejpam-5828	250	27	in	in	ADP
ejpam-5828	250	28	the	the	DET
ejpam-5828	250	29	quantum	quantum	ADJ
ejpam-5828	250	30	system	system	NOUN
ejpam-5828	250	31	,	,	PUNCT
ejpam-5828	250	32	linking	link	VERB
ejpam-5828	250	33	the	the	DET
ejpam-5828	250	34	change	change	NOUN
ejpam-5828	250	35	in	in	ADP
ejpam-5828	250	36	probability	probability	NOUN
ejpam-5828	250	37	density	density	NOUN
ejpam-5828	250	38	to	to	ADP
ejpam-5828	250	39	the	the	DET
ejpam-5828	250	40	probability	probability	NOUN
ejpam-5828	250	41	current	current	ADJ
ejpam-5828	250	42	.	.	PUNCT
ejpam-5828	251	1	for	for	ADP
ejpam-5828	251	2	the	the	DET
ejpam-5828	251	3	twodimensional	twodimensional	ADJ
ejpam-5828	251	4	system	system	NOUN
ejpam-5828	251	5	with	with	ADP
ejpam-5828	251	6	dissipation	dissipation	NOUN
ejpam-5828	251	7	,	,	PUNCT
ejpam-5828	251	8	the	the	DET
ejpam-5828	251	9	continuity	continuity	NOUN
ejpam-5828	251	10	equation	equation	NOUN
ejpam-5828	251	11	is	be	AUX
ejpam-5828	251	12	:	:	PUNCT
ejpam-5828	251	13	∂ρ	∂ρ	PROPN
ejpam-5828	251	14	∂t	∂t	PROPN
ejpam-5828	252	1	+	+	PROPN
ejpam-5828	252	2	▽	▽	PROPN
ejpam-5828	252	3	j	j	NOUN
ejpam-5828	252	4	=	=	SYM
ejpam-5828	252	5	0	0	PROPN
ejpam-5828	253	1	where	where	SCONJ
ejpam-5828	253	2	▽	▽	X
ejpam-5828	253	3	j	j	PROPN
ejpam-5828	253	4	=	=	SYM
ejpam-5828	253	5	∂jx	∂jx	PROPN
ejpam-5828	253	6	∂x	∂x	PROPN
ejpam-5828	253	7	+	+	CCONJ
ejpam-5828	253	8	∂jy	∂jy	PROPN
ejpam-5828	253	9	∂y	∂y	SYM
ejpam-5828	253	10	(	(	PUNCT
ejpam-5828	253	11	23	23	NUM
ejpam-5828	253	12	)	)	PUNCT
ejpam-5828	253	13	5	5	NUM
ejpam-5828	253	14	.	.	X
ejpam-5828	253	15	separation	separation	NOUN
ejpam-5828	253	16	of	of	ADP
ejpam-5828	253	17	variables	variable	NOUN
ejpam-5828	253	18	in	in	ADP
ejpam-5828	253	19	the	the	DET
ejpam-5828	253	20	hamilton	hamilton	PROPN
ejpam-5828	253	21	-	-	PUNCT
ejpam-5828	253	22	jacobi	jacobi	PROPN
ejpam-5828	253	23	equation	equation	NOUN
ejpam-5828	253	24	using	use	VERB
ejpam-5828	253	25	staeckel	staeckel	NOUN
ejpam-5828	253	26	boundary	boundary	ADJ
ejpam-5828	253	27	conditions	condition	NOUN
ejpam-5828	253	28	consider	consider	VERB
ejpam-5828	253	29	the	the	DET
ejpam-5828	253	30	motion	motion	NOUN
ejpam-5828	253	31	of	of	ADP
ejpam-5828	253	32	a	a	DET
ejpam-5828	253	33	two	two	NUM
ejpam-5828	253	34	-	-	PUNCT
ejpam-5828	253	35	dimensional	dimensional	ADJ
ejpam-5828	253	36	anisotropic	anisotropic	NOUN
ejpam-5828	253	37	harmonic	harmonic	ADJ
ejpam-5828	253	38	oscillator	oscillator	NOUN
ejpam-5828	253	39	with	with	ADP
ejpam-5828	253	40	a	a	DET
ejpam-5828	253	41	dissipative	dissipative	ADJ
ejpam-5828	253	42	potential	potential	NOUN
ejpam-5828	253	43	v	v	NOUN
ejpam-5828	253	44	=	=	SYM
ejpam-5828	253	45	2π2m(v2xx	2π2m(v2xx	NOUN
ejpam-5828	253	46	2	2	NUM
ejpam-5828	253	47	+	+	CCONJ
ejpam-5828	253	48	v2yy	v2yy	NOUN
ejpam-5828	253	49	2	2	NUM
ejpam-5828	253	50	)	)	PUNCT
ejpam-5828	253	51	.	.	PUNCT
ejpam-5828	254	1	the	the	DET
ejpam-5828	254	2	hamilton	hamilton	PROPN
ejpam-5828	254	3	-	-	PUNCT
ejpam-5828	254	4	jacobi	jacobi	PROPN
ejpam-5828	254	5	equation	equation	NOUN
ejpam-5828	254	6	is	be	AUX
ejpam-5828	254	7	given	give	VERB
ejpam-5828	254	8	by	by	ADP
ejpam-5828	254	9	:	:	PUNCT
ejpam-5828	254	10	h	h	PROPN
ejpam-5828	254	11	=	=	SYM
ejpam-5828	254	12	t	t	PROPN
ejpam-5828	254	13	+	+	CCONJ
ejpam-5828	254	14	v	v	NOUN
ejpam-5828	254	15	=	=	SYM
ejpam-5828	254	16	1	1	NUM
ejpam-5828	254	17	2	2	NUM
ejpam-5828	254	18	m	m	VERB
ejpam-5828	254	19	(	(	PUNCT
ejpam-5828	254	20	(	(	PUNCT
ejpam-5828	254	21	p	p	NOUN
ejpam-5828	254	22	2	2	NUM
ejpam-5828	254	23	x	x	SYM
ejpam-5828	254	24	+	+	NUM
ejpam-5828	254	25	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	254	26	2	2	NUM
ejpam-5828	254	27	−	−	NOUN
ejpam-5828	254	28	1	1	NUM
ejpam-5828	254	29	2	2	NUM
ejpam-5828	254	30	mλ2xx	mλ2xx	NOUN
ejpam-5828	254	31	2	2	NUM
ejpam-5828	254	32	)	)	PUNCT
ejpam-5828	254	33	+	+	CCONJ
ejpam-5828	255	1	(	(	PUNCT
ejpam-5828	255	2	p	p	PROPN
ejpam-5828	255	3	2	2	NUM
ejpam-5828	255	4	y	y	NOUN
ejpam-5828	255	5	+	+	NUM
ejpam-5828	255	6	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	255	7	2	2	NUM
ejpam-5828	255	8	−	−	NOUN
ejpam-5828	255	9	1	1	NUM
ejpam-5828	255	10	2	2	NUM
ejpam-5828	255	11	mλ2yy	mλ2yy	NOUN
ejpam-5828	255	12	2	2	NUM
ejpam-5828	255	13	)	)	PUNCT
ejpam-5828	255	14	)	)	PUNCT
ejpam-5828	255	15	(	(	PUNCT
ejpam-5828	255	16	24	24	NUM
ejpam-5828	255	17	)	)	PUNCT
ejpam-5828	255	18	comparing	compare	VERB
ejpam-5828	255	19	this	this	DET
ejpam-5828	255	20	equation	equation	NOUN
ejpam-5828	255	21	with	with	ADP
ejpam-5828	255	22	h	h	NOUN
ejpam-5828	255	23	=	=	NOUN
ejpam-5828	255	24	1	1	NUM
ejpam-5828	255	25	2(p	2(p	NUM
ejpam-5828	255	26	−	−	NOUN
ejpam-5828	255	27	a)t−1(p	a)t−1(p	NOUN
ejpam-5828	255	28	−	−	NOUN
ejpam-5828	255	29	a	a	NOUN
ejpam-5828	255	30	)	)	PUNCT
ejpam-5828	255	31	+	+	NUM
ejpam-5828	255	32	v	v	X
ejpam-5828	255	33	(	(	PUNCT
ejpam-5828	255	34	q	q	NOUN
ejpam-5828	255	35	)	)	PUNCT
ejpam-5828	255	36	,	,	PUNCT
ejpam-5828	255	37	we	we	PRON
ejpam-5828	255	38	obtain	obtain	VERB
ejpam-5828	255	39	:	:	PUNCT
ejpam-5828	255	40	t−1	t−1	PROPN
ejpam-5828	255	41	=	=	PUNCT
ejpam-5828	255	42	(	(	PUNCT
ejpam-5828	255	43	1	1	NUM
ejpam-5828	255	44	m	m	NOUN
ejpam-5828	255	45	0	0	NUM
ejpam-5828	255	46	0	0	NUM
ejpam-5828	255	47	1	1	NUM
ejpam-5828	255	48	m	m	NOUN
ejpam-5828	255	49	)	)	PUNCT
ejpam-5828	255	50	on	on	ADP
ejpam-5828	255	51	the	the	DET
ejpam-5828	255	52	other	other	ADJ
ejpam-5828	255	53	hand	hand	NOUN
ejpam-5828	255	54	,	,	PUNCT
ejpam-5828	255	55	the	the	DET
ejpam-5828	255	56	staeckel	staeckel	NOUN
ejpam-5828	255	57	conditions	condition	NOUN
ejpam-5828	255	58	require	require	VERB
ejpam-5828	255	59	the	the	DET
ejpam-5828	255	60	fulfillment	fulfillment	NOUN
ejpam-5828	255	61	of	of	ADP
ejpam-5828	255	62	two	two	NUM
ejpam-5828	255	63	main	main	ADJ
ejpam-5828	255	64	criteria	criterion	NOUN
ejpam-5828	255	65	:	:	PUNCT
ejpam-5828	255	66	(	(	PUNCT
ejpam-5828	255	67	i	i	NOUN
ejpam-5828	255	68	)	)	PUNCT
ejpam-5828	255	69	diagonal	diagonal	ADJ
ejpam-5828	255	70	matrix	matrix	NOUN
ejpam-5828	255	71	condition	condition	NOUN
ejpam-5828	255	72	:	:	PUNCT
ejpam-5828	255	73	the	the	DET
ejpam-5828	255	74	inverse	inverse	NOUN
ejpam-5828	255	75	of	of	ADP
ejpam-5828	255	76	the	the	DET
ejpam-5828	255	77	kinetic	kinetic	ADJ
ejpam-5828	255	78	energy	energy	NOUN
ejpam-5828	255	79	matrix	matrix	NOUN
ejpam-5828	255	80	t−1	t−1	PROPN
ejpam-5828	255	81	must	must	AUX
ejpam-5828	255	82	be	be	AUX
ejpam-5828	255	83	diagonal	diagonal	ADJ
ejpam-5828	255	84	.	.	PUNCT
ejpam-5828	256	1	in	in	ADP
ejpam-5828	256	2	this	this	DET
ejpam-5828	256	3	case	case	NOUN
ejpam-5828	256	4	,	,	PUNCT
ejpam-5828	256	5	this	this	DET
ejpam-5828	256	6	condition	condition	NOUN
ejpam-5828	256	7	is	be	AUX
ejpam-5828	256	8	satisfied	satisfied	ADJ
ejpam-5828	256	9	,	,	PUNCT
ejpam-5828	256	10	as	as	ADP
ejpam-5828	256	11	:	:	PUNCT
ejpam-5828	256	12	(	(	PUNCT
ejpam-5828	256	13	t−1)ii	t−1)ii	NOUN
ejpam-5828	256	14	=	=	SYM
ejpam-5828	256	15	1	1	NUM
ejpam-5828	256	16	tii	tii	NOUN
ejpam-5828	256	17	=	=	PUNCT
ejpam-5828	256	18	(	(	PUNCT
ejpam-5828	256	19	1	1	NUM
ejpam-5828	256	20	m	m	NOUN
ejpam-5828	256	21	0	0	NUM
ejpam-5828	256	22	0	0	NUM
ejpam-5828	256	23	1	1	NUM
ejpam-5828	256	24	m	m	NOUN
ejpam-5828	256	25	)	)	PUNCT
ejpam-5828	256	26	(	(	PUNCT
ejpam-5828	256	27	ii	ii	X
ejpam-5828	256	28	)	)	PUNCT
ejpam-5828	256	29	separable	separable	ADJ
ejpam-5828	256	30	potential	potential	ADJ
ejpam-5828	256	31	condition	condition	NOUN
ejpam-5828	256	32	:	:	PUNCT
ejpam-5828	256	33	the	the	DET
ejpam-5828	256	34	potential	potential	ADJ
ejpam-5828	256	35	v	v	X
ejpam-5828	256	36	(	(	PUNCT
ejpam-5828	256	37	q	q	NOUN
ejpam-5828	256	38	)	)	PUNCT
ejpam-5828	256	39	must	must	AUX
ejpam-5828	256	40	be	be	AUX
ejpam-5828	256	41	separable	separable	ADJ
ejpam-5828	256	42	in	in	ADP
ejpam-5828	256	43	the	the	DET
ejpam-5828	256	44	coordinates	coordinate	NOUN
ejpam-5828	256	45	x	x	PUNCT
ejpam-5828	256	46	and	and	CCONJ
ejpam-5828	256	47	y	y	PROPN
ejpam-5828	256	48	,	,	PUNCT
ejpam-5828	256	49	meaning	mean	VERB
ejpam-5828	256	50	it	it	PRON
ejpam-5828	256	51	can	can	AUX
ejpam-5828	256	52	be	be	AUX
ejpam-5828	256	53	expressed	express	VERB
ejpam-5828	256	54	as	as	ADP
ejpam-5828	256	55	:	:	PUNCT
ejpam-5828	256	56	(	(	PUNCT
ejpam-5828	256	57	ϕ−1)1j	ϕ−1)1j	NOUN
ejpam-5828	256	58	=	=	SYM
ejpam-5828	256	59	1	1	NUM
ejpam-5828	256	60	tjj	tjj	NOUN
ejpam-5828	256	61	=	=	PUNCT
ejpam-5828	256	62	(	(	PUNCT
ejpam-5828	256	63	1	1	NUM
ejpam-5828	256	64	m	m	NOUN
ejpam-5828	256	65	1	1	NUM
ejpam-5828	256	66	m	m	NOUN
ejpam-5828	256	67	0	0	NUM
ejpam-5828	256	68	1	1	NUM
ejpam-5828	256	69	m	m	NOUN
ejpam-5828	256	70	)	)	PUNCT
ejpam-5828	256	71	from	from	ADP
ejpam-5828	256	72	the	the	DET
ejpam-5828	256	73	given	give	VERB
ejpam-5828	256	74	potential	potential	NOUN
ejpam-5828	256	75	:	:	PUNCT
ejpam-5828	257	1	v	v	NOUN
ejpam-5828	257	2	(	(	PUNCT
ejpam-5828	257	3	q	q	NOUN
ejpam-5828	257	4	)	)	PUNCT
ejpam-5828	257	5	=	=	SYM
ejpam-5828	257	6	vi(qi	vi(qi	PROPN
ejpam-5828	257	7	)	)	PUNCT
ejpam-5828	257	8	tii	tii	PROPN
ejpam-5828	257	9	=	=	PUNCT
ejpam-5828	257	10	(	(	PUNCT
ejpam-5828	257	11	ψ1(x	ψ1(x	PROPN
ejpam-5828	257	12	)	)	PUNCT
ejpam-5828	257	13	m	m	PROPN
ejpam-5828	257	14	+	+	ADJ
ejpam-5828	257	15	ψ1(y)m	ψ1(y)m	NOUN
ejpam-5828	257	16	)	)	PUNCT
ejpam-5828	257	17	if	if	SCONJ
ejpam-5828	257	18	the	the	DET
ejpam-5828	257	19	staeckel	staeckel	NOUN
ejpam-5828	257	20	conditions	condition	NOUN
ejpam-5828	257	21	are	be	AUX
ejpam-5828	257	22	satisfied	satisfied	ADJ
ejpam-5828	257	23	,	,	PUNCT
ejpam-5828	257	24	then	then	ADV
ejpam-5828	257	25	hamilton	hamilton	PROPN
ejpam-5828	257	26	’s	’s	PART
ejpam-5828	257	27	characteristic	characteristic	ADJ
ejpam-5828	257	28	function	function	NOUN
ejpam-5828	257	29	is	be	AUX
ejpam-5828	257	30	completely	completely	ADV
ejpam-5828	257	31	separable	separable	ADJ
ejpam-5828	257	32	:	:	PUNCT
ejpam-5828	257	33	w	w	ADJ
ejpam-5828	257	34	(	(	PUNCT
ejpam-5828	257	35	q	q	X
ejpam-5828	257	36	)	)	PUNCT
ejpam-5828	257	37	=	=	PUNCT
ejpam-5828	258	1	∑	∑	PUNCT
ejpam-5828	258	2	i	i	PRON
ejpam-5828	258	3	wi(qi	wi(qi	PROPN
ejpam-5828	258	4	)	)	PUNCT
ejpam-5828	258	5	b.	b.	PROPN
ejpam-5828	258	6	m.	m.	PROPN
ejpam-5828	259	1	al	al	PROPN
ejpam-5828	259	2	-	-	PUNCT
ejpam-5828	259	3	khamiseh	khamiseh	PROPN
ejpam-5828	259	4	et	et	PROPN
ejpam-5828	259	5	al	al	PROPN
ejpam-5828	259	6	.	.	PUNCT
ejpam-5828	259	7	/	/	SYM
ejpam-5828	259	8	eur	eur	PROPN
ejpam-5828	259	9	.	.	PUNCT
ejpam-5828	260	1	j.	j.	PROPN
ejpam-5828	260	2	pure	pure	PROPN
ejpam-5828	260	3	appl	appl	PROPN
ejpam-5828	260	4	.	.	PROPN
ejpam-5828	260	5	math	math	PROPN
ejpam-5828	260	6	,	,	PUNCT
ejpam-5828	260	7	18	18	NUM
ejpam-5828	260	8	(	(	PUNCT
ejpam-5828	260	9	2	2	NUM
ejpam-5828	260	10	)	)	PUNCT
ejpam-5828	260	11	(	(	PUNCT
ejpam-5828	260	12	2025	2025	NUM
ejpam-5828	260	13	)	)	PUNCT
ejpam-5828	260	14	,	,	PUNCT
ejpam-5828	260	15	5828	5828	NUM
ejpam-5828	260	16	13	13	NUM
ejpam-5828	260	17	of	of	ADP
ejpam-5828	260	18	25	25	NUM
ejpam-5828	260	19	inserting	insert	VERB
ejpam-5828	260	20	from	from	ADP
ejpam-5828	260	21	equation	equation	NOUN
ejpam-5828	260	22	23	23	NUM
ejpam-5828	260	23	into	into	ADP
ejpam-5828	260	24	equation	equation	NOUN
ejpam-5828	260	25	(	(	PUNCT
ejpam-5828	260	26	h(q	h(q	ADV
ejpam-5828	260	27	,	,	PUNCT
ejpam-5828	260	28	∂w∂q	∂w∂q	PROPN
ejpam-5828	260	29	)	)	PUNCT
ejpam-5828	261	1	+	+	CCONJ
ejpam-5828	261	2	∂s0	∂s0	DET
ejpam-5828	261	3	∂t	∂t	PROPN
ejpam-5828	261	4	=	=	SYM
ejpam-5828	261	5	0	0	NUM
ejpam-5828	261	6	)	)	PUNCT
ejpam-5828	261	7	and	and	CCONJ
ejpam-5828	261	8	using	use	VERB
ejpam-5828	261	9	the	the	DET
ejpam-5828	261	10	definition	definition	NOUN
ejpam-5828	261	11	of	of	ADP
ejpam-5828	261	12	momentum	momentum	NOUN
ejpam-5828	261	13	p	p	NOUN
ejpam-5828	261	14	=	=	PUNCT
ejpam-5828	261	15	∂w	∂w	PROPN
ejpam-5828	261	16	∂q	∂q	NOUN
ejpam-5828	261	17	we	we	PRON
ejpam-5828	261	18	obtain	obtain	VERB
ejpam-5828	261	19	(	(	PUNCT
ejpam-5828	261	20	more	more	ADJ
ejpam-5828	261	21	details	detail	NOUN
ejpam-5828	261	22	see	see	VERB
ejpam-5828	261	23	appendix	appendix	NOUN
ejpam-5828	261	24	a	a	PRON
ejpam-5828	261	25	):	):	PUNCT
ejpam-5828	261	26	1	1	NUM
ejpam-5828	261	27	2	2	NUM
ejpam-5828	261	28	m	m	VERB
ejpam-5828	261	29	(	(	PUNCT
ejpam-5828	261	30	[	[	PUNCT
ejpam-5828	261	31	∂wx	∂wx	PROPN
ejpam-5828	261	32	∂x	∂x	PROPN
ejpam-5828	261	33	]	]	SYM
ejpam-5828	261	34	2	2	NUM
ejpam-5828	261	35	+	+	NUM
ejpam-5828	261	36	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	261	37	2	2	NUM
ejpam-5828	261	38	−	−	NOUN
ejpam-5828	261	39	1	1	NUM
ejpam-5828	261	40	2	2	NUM
ejpam-5828	261	41	λ2xx	λ2xx	X
ejpam-5828	261	42	2	2	NUM
ejpam-5828	261	43	+	+	CCONJ
ejpam-5828	261	44	[	[	PUNCT
ejpam-5828	261	45	∂wy	∂wy	X
ejpam-5828	261	46	∂y	∂y	X
ejpam-5828	261	47	]	]	SYM
ejpam-5828	261	48	2	2	NUM
ejpam-5828	261	49	+	+	NUM
ejpam-5828	261	50	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	261	51	2	2	NUM
ejpam-5828	261	52	−	−	NOUN
ejpam-5828	261	53	1	1	NUM
ejpam-5828	261	54	2	2	NUM
ejpam-5828	261	55	λ2yy	λ2yy	SYM
ejpam-5828	261	56	2	2	NUM
ejpam-5828	261	57	)	)	PUNCT
ejpam-5828	262	1	=	=	SYM
ejpam-5828	262	2	α	α	PROPN
ejpam-5828	262	3	(	(	PUNCT
ejpam-5828	262	4	25	25	NUM
ejpam-5828	262	5	)	)	PUNCT
ejpam-5828	262	6	6	6	NUM
ejpam-5828	262	7	.	.	PUNCT
ejpam-5828	263	1	hamiltonian	hamiltonian	ADJ
ejpam-5828	263	2	dynamics	dynamic	NOUN
ejpam-5828	263	3	of	of	ADP
ejpam-5828	263	4	a	a	DET
ejpam-5828	263	5	dissipative	dissipative	ADJ
ejpam-5828	263	6	two	two	NUM
ejpam-5828	263	7	-	-	PUNCT
ejpam-5828	263	8	dimensional	dimensional	ADJ
ejpam-5828	263	9	anisotropic	anisotropic	NOUN
ejpam-5828	263	10	oscillator	oscillator	NOUN
ejpam-5828	263	11	using	use	VERB
ejpam-5828	263	12	poisson	poisson	NOUN
ejpam-5828	263	13	brackets	bracket	NOUN
ejpam-5828	263	14	the	the	DET
ejpam-5828	263	15	formulation	formulation	NOUN
ejpam-5828	263	16	of	of	ADP
ejpam-5828	263	17	poisson	poisson	NOUN
ejpam-5828	263	18	brackets	bracket	NOUN
ejpam-5828	263	19	of	of	ADP
ejpam-5828	263	20	hamiltons	hamilton	NOUN
ejpam-5828	263	21	equations	equation	NOUN
ejpam-5828	263	22	of	of	ADP
ejpam-5828	263	23	motion	motion	NOUN
ejpam-5828	263	24	are	be	AUX
ejpam-5828	263	25	then	then	ADV
ejpam-5828	263	26	calculated	calculate	VERB
ejpam-5828	263	27	as	as	ADP
ejpam-5828	263	28	:	:	PUNCT
ejpam-5828	263	29	ẋ	ẋ	PROPN
ejpam-5828	263	30	=	=	PRON
ejpam-5828	263	31	{	{	PUNCT
ejpam-5828	263	32	x	x	NOUN
ejpam-5828	263	33	,	,	PUNCT
ejpam-5828	263	34	h	h	NOUN
ejpam-5828	263	35	}	}	PUNCT
ejpam-5828	263	36	=	=	SYM
ejpam-5828	264	1	x	x	ADJ
ejpam-5828	264	2	,	,	PUNCT
ejpam-5828	264	3	1	1	NUM
ejpam-5828	264	4	2	2	NUM
ejpam-5828	264	5	m	m	NOUN
ejpam-5828	264	6			PROPN
ejpam-5828	264	7	(	(	PUNCT
ejpam-5828	264	8	p	p	NOUN
ejpam-5828	264	9	2	2	NUM
ejpam-5828	264	10	x	x	SYM
ejpam-5828	264	11	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	264	12	2	2	NUM
ejpam-5828	264	13	−1	−1	NOUN
ejpam-5828	264	14	4mλ	4mλ	ADJ
ejpam-5828	264	15	2	2	NUM
ejpam-5828	264	16	xx	xx	NUM
ejpam-5828	264	17	2	2	NUM
ejpam-5828	264	18	)	)	PUNCT
ejpam-5828	264	19	+	+	CCONJ
ejpam-5828	264	20	(	(	PUNCT
ejpam-5828	264	21	p	p	PROPN
ejpam-5828	264	22	2	2	NUM
ejpam-5828	264	23	y	y	NOUN
ejpam-5828	264	24	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	264	25	2	2	NUM
ejpam-5828	264	26	−1	−1	NOUN
ejpam-5828	264	27	4mλ	4mλ	ADJ
ejpam-5828	264	28	2	2	NUM
ejpam-5828	264	29	yy	yy	NOUN
ejpam-5828	264	30	2	2	NUM
ejpam-5828	264	31	)	)	PUNCT
ejpam-5828	264	32			NOUN
ejpam-5828	264	33	=	=	PUNCT
ejpam-5828	264	34	{	{	PUNCT
ejpam-5828	264	35	x	x	NOUN
ejpam-5828	264	36	,	,	PUNCT
ejpam-5828	264	37	p	p	NOUN
ejpam-5828	264	38	2	2	NUM
ejpam-5828	264	39	x	x	SYM
ejpam-5828	264	40	2	2	NUM
ejpam-5828	264	41	m	m	NOUN
ejpam-5828	264	42	}	}	PUNCT
ejpam-5828	264	43	=	=	SYM
ejpam-5828	265	1	px	px	PART
ejpam-5828	265	2	m	m	PROPN
ejpam-5828	265	3	(	(	PUNCT
ejpam-5828	265	4	26	26	NUM
ejpam-5828	265	5	)	)	PUNCT
ejpam-5828	265	6	after	after	ADP
ejpam-5828	265	7	rewriting	rewrite	VERB
ejpam-5828	265	8	the	the	DET
ejpam-5828	265	9	previous	previous	ADJ
ejpam-5828	265	10	equation	equation	NOUN
ejpam-5828	265	11	in	in	ADP
ejpam-5828	265	12	terms	term	NOUN
ejpam-5828	265	13	of	of	ADP
ejpam-5828	265	14	ẏ,we	ẏ,we	PROPN
ejpam-5828	265	15	get	get	VERB
ejpam-5828	265	16	:	:	PUNCT
ejpam-5828	265	17	ẏ	ẏ	PROPN
ejpam-5828	265	18	=	=	PUNCT
ejpam-5828	265	19	{	{	PUNCT
ejpam-5828	265	20	y	y	PROPN
ejpam-5828	265	21	,	,	PUNCT
ejpam-5828	265	22	h	h	NOUN
ejpam-5828	265	23	}	}	PUNCT
ejpam-5828	265	24	=	=	SYM
ejpam-5828	265	25	y	y	VERB
ejpam-5828	265	26	,	,	PUNCT
ejpam-5828	265	27	1	1	NUM
ejpam-5828	265	28	2	2	NUM
ejpam-5828	265	29	m	m	NOUN
ejpam-5828	265	30			PROPN
ejpam-5828	265	31	(	(	PUNCT
ejpam-5828	265	32	p	p	NOUN
ejpam-5828	265	33	2	2	NUM
ejpam-5828	265	34	x	x	SYM
ejpam-5828	265	35	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	265	36	2	2	NUM
ejpam-5828	265	37	−1	−1	NOUN
ejpam-5828	265	38	4mλ	4mλ	ADJ
ejpam-5828	265	39	2	2	NUM
ejpam-5828	265	40	xx	xx	NUM
ejpam-5828	265	41	2	2	NUM
ejpam-5828	265	42	)	)	PUNCT
ejpam-5828	266	1	+	+	CCONJ
ejpam-5828	266	2	(	(	PUNCT
ejpam-5828	266	3	p	p	PROPN
ejpam-5828	266	4	2	2	NUM
ejpam-5828	266	5	y	y	NOUN
ejpam-5828	266	6	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	266	7	2	2	NUM
ejpam-5828	266	8	−1	−1	NOUN
ejpam-5828	266	9	4mλ	4mλ	ADJ
ejpam-5828	266	10	2	2	NUM
ejpam-5828	266	11	yy	yy	NOUN
ejpam-5828	266	12	2	2	NUM
ejpam-5828	266	13	)	)	PUNCT
ejpam-5828	266	14			NOUN
ejpam-5828	266	15	=	=	PUNCT
ejpam-5828	266	16	{	{	PUNCT
ejpam-5828	266	17	y	y	PROPN
ejpam-5828	266	18	,	,	PUNCT
ejpam-5828	266	19	p	p	NOUN
ejpam-5828	266	20	2	2	NUM
ejpam-5828	266	21	y	y	PROPN
ejpam-5828	266	22	2	2	NUM
ejpam-5828	266	23	m	m	NOUN
ejpam-5828	266	24	}	}	PUNCT
ejpam-5828	266	25	=	=	PUNCT
ejpam-5828	266	26	py	py	INTJ
ejpam-5828	266	27	m	m	PROPN
ejpam-5828	266	28	(	(	PUNCT
ejpam-5828	266	29	27	27	NUM
ejpam-5828	266	30	)	)	PUNCT
ejpam-5828	266	31	if	if	SCONJ
ejpam-5828	266	32	the	the	DET
ejpam-5828	266	33	poisson	poisson	NOUN
ejpam-5828	266	34	brackets	bracket	NOUN
ejpam-5828	266	35	satisfy	satisfy	VERB
ejpam-5828	266	36	the	the	DET
ejpam-5828	266	37	canonical	canonical	ADJ
ejpam-5828	266	38	relations	relation	NOUN
ejpam-5828	266	39	:	:	PUNCT
ejpam-5828	266	40	{	{	PUNCT
ejpam-5828	266	41	x	x	NOUN
ejpam-5828	266	42	,	,	PUNCT
ejpam-5828	266	43	px	px	PROPN
ejpam-5828	266	44	}	}	PUNCT
ejpam-5828	266	45	=	=	SYM
ejpam-5828	266	46	{	{	PUNCT
ejpam-5828	266	47	y	y	PROPN
ejpam-5828	266	48	,	,	PUNCT
ejpam-5828	266	49	py	py	X
ejpam-5828	266	50	}	}	PUNCT
ejpam-5828	266	51	=	=	SYM
ejpam-5828	267	1	1	1	NUM
ejpam-5828	267	2	then	then	ADV
ejpam-5828	267	3	the	the	DET
ejpam-5828	267	4	time	time	NOUN
ejpam-5828	267	5	evolution	evolution	NOUN
ejpam-5828	267	6	of	of	ADP
ejpam-5828	267	7	the	the	DET
ejpam-5828	267	8	momentum	momentum	NOUN
ejpam-5828	267	9	px	px	NOUN
ejpam-5828	267	10	is	be	AUX
ejpam-5828	267	11	derived	derive	VERB
ejpam-5828	267	12	as	as	ADP
ejpam-5828	267	13	:	:	PUNCT
ejpam-5828	267	14	ṗx	ṗx	NOUN
ejpam-5828	267	15	=	=	SYM
ejpam-5828	267	16	{	{	PUNCT
ejpam-5828	267	17	px	px	PROPN
ejpam-5828	267	18	,	,	PUNCT
ejpam-5828	267	19	h	h	NOUN
ejpam-5828	267	20	}	}	PUNCT
ejpam-5828	267	21	=	=	ADJ
ejpam-5828	267	22	px	px	NOUN
ejpam-5828	267	23	,	,	PUNCT
ejpam-5828	267	24	1	1	NUM
ejpam-5828	267	25	2	2	NUM
ejpam-5828	267	26	m	m	NOUN
ejpam-5828	267	27			PROPN
ejpam-5828	267	28	(	(	PUNCT
ejpam-5828	267	29	p	p	NOUN
ejpam-5828	267	30	2	2	NUM
ejpam-5828	267	31	x	x	SYM
ejpam-5828	267	32	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	267	33	2	2	NUM
ejpam-5828	267	34	−1	−1	NOUN
ejpam-5828	267	35	4mλ	4mλ	ADJ
ejpam-5828	267	36	2	2	NUM
ejpam-5828	267	37	xx	xx	NUM
ejpam-5828	267	38	2	2	NUM
ejpam-5828	267	39	)	)	PUNCT
ejpam-5828	267	40	+	+	CCONJ
ejpam-5828	267	41	(	(	PUNCT
ejpam-5828	267	42	p	p	PROPN
ejpam-5828	267	43	2	2	NUM
ejpam-5828	267	44	y	y	NOUN
ejpam-5828	267	45	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	267	46	2	2	NUM
ejpam-5828	267	47	−1	−1	NOUN
ejpam-5828	267	48	4mλ	4mλ	ADJ
ejpam-5828	267	49	2	2	NUM
ejpam-5828	267	50	yy	yy	NOUN
ejpam-5828	267	51	2	2	NUM
ejpam-5828	267	52	)	)	PUNCT
ejpam-5828	267	53			NOUN
ejpam-5828	267	54	=	=	PUNCT
ejpam-5828	267	55	{	{	PUNCT
ejpam-5828	267	56	px	px	PROPN
ejpam-5828	267	57	,	,	PUNCT
ejpam-5828	267	58	4π	4π	NUM
ejpam-5828	267	59	2m2v2xx	2m2v2xx	NUM
ejpam-5828	267	60	2	2	NUM
ejpam-5828	267	61	−	−	NOUN
ejpam-5828	267	62	1	1	NUM
ejpam-5828	267	63	4	4	NUM
ejpam-5828	267	64	mλ2xx	mλ2xx	NOUN
ejpam-5828	267	65	2	2	NUM
ejpam-5828	267	66	}	}	PUNCT
ejpam-5828	267	67	=	=	SYM
ejpam-5828	267	68	−4π2mv2xx+	−4π2mv2xx+	NOUN
ejpam-5828	267	69	1	1	NUM
ejpam-5828	267	70	4	4	NUM
ejpam-5828	267	71	mλ2xx	mλ2xx	NOUN
ejpam-5828	267	72	(	(	PUNCT
ejpam-5828	267	73	28	28	NUM
ejpam-5828	267	74	)	)	PUNCT
ejpam-5828	267	75	likewise	likewise	ADV
ejpam-5828	267	76	,	,	PUNCT
ejpam-5828	267	77	equation	equation	NOUN
ejpam-5828	267	78	(	(	PUNCT
ejpam-5828	267	79	34	34	NUM
ejpam-5828	267	80	)	)	PUNCT
ejpam-5828	267	81	may	may	AUX
ejpam-5828	267	82	be	be	AUX
ejpam-5828	267	83	expressed	express	VERB
ejpam-5828	267	84	in	in	ADP
ejpam-5828	267	85	ṗy	ṗy	PROPN
ejpam-5828	267	86	form	form	NOUN
ejpam-5828	267	87	as	as	SCONJ
ejpam-5828	267	88	follows	follow	VERB
ejpam-5828	267	89	:	:	PUNCT
ejpam-5828	268	1	ṗy	ṗy	PROPN
ejpam-5828	268	2	=	=	SYM
ejpam-5828	268	3	{	{	PUNCT
ejpam-5828	268	4	py	py	PROPN
ejpam-5828	268	5	,	,	PUNCT
ejpam-5828	268	6	h	h	NOUN
ejpam-5828	268	7	}	}	PUNCT
ejpam-5828	268	8	=	=	SYM
ejpam-5828	268	9	py	py	X
ejpam-5828	268	10	,	,	PUNCT
ejpam-5828	268	11	1	1	NUM
ejpam-5828	268	12	2	2	NUM
ejpam-5828	268	13	m	m	NOUN
ejpam-5828	268	14			PROPN
ejpam-5828	268	15	(	(	PUNCT
ejpam-5828	268	16	p	p	NOUN
ejpam-5828	268	17	2	2	NUM
ejpam-5828	268	18	x	x	SYM
ejpam-5828	268	19	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	268	20	2	2	NUM
ejpam-5828	268	21	−1	−1	NOUN
ejpam-5828	268	22	4mλ	4mλ	ADJ
ejpam-5828	268	23	2	2	NUM
ejpam-5828	268	24	xx	xx	NUM
ejpam-5828	268	25	2	2	NUM
ejpam-5828	268	26	)	)	PUNCT
ejpam-5828	268	27	+	+	CCONJ
ejpam-5828	269	1	(	(	PUNCT
ejpam-5828	269	2	p	p	PROPN
ejpam-5828	269	3	2	2	NUM
ejpam-5828	269	4	y	y	NOUN
ejpam-5828	269	5	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	269	6	2	2	NUM
ejpam-5828	269	7	−1	−1	NOUN
ejpam-5828	269	8	4mλ	4mλ	ADJ
ejpam-5828	269	9	2	2	NUM
ejpam-5828	269	10	yy	yy	NOUN
ejpam-5828	269	11	2	2	NUM
ejpam-5828	269	12	)	)	PUNCT
ejpam-5828	269	13			NOUN
ejpam-5828	270	1	=	=	CCONJ
ejpam-5828	270	2	{	{	PUNCT
ejpam-5828	270	3	py	py	PROPN
ejpam-5828	270	4	,	,	PUNCT
ejpam-5828	270	5	4π	4π	NUM
ejpam-5828	270	6	2m2v2yy	2m2v2yy	NUM
ejpam-5828	270	7	2	2	NUM
ejpam-5828	270	8	−	−	NOUN
ejpam-5828	270	9	1	1	NUM
ejpam-5828	270	10	4	4	NUM
ejpam-5828	270	11	mλ2yy	mλ2yy	NOUN
ejpam-5828	270	12	2	2	NUM
ejpam-5828	270	13	}	}	PUNCT
ejpam-5828	270	14	=	=	PUNCT
ejpam-5828	270	15	−4π2mv2yy	−4π2mv2yy	PROPN
ejpam-5828	270	16	+	+	CCONJ
ejpam-5828	270	17	1	1	NUM
ejpam-5828	270	18	4	4	NUM
ejpam-5828	270	19	mλ2yx	mλ2yx	NOUN
ejpam-5828	270	20	(	(	PUNCT
ejpam-5828	270	21	29	29	NUM
ejpam-5828	270	22	)	)	PUNCT
ejpam-5828	270	23	b.	b.	PROPN
ejpam-5828	270	24	m.	m.	PROPN
ejpam-5828	270	25	al	al	PROPN
ejpam-5828	270	26	-	-	PUNCT
ejpam-5828	270	27	khamiseh	khamiseh	PROPN
ejpam-5828	270	28	et	et	PROPN
ejpam-5828	270	29	al	al	PROPN
ejpam-5828	270	30	.	.	PUNCT
ejpam-5828	270	31	/	/	SYM
ejpam-5828	270	32	eur	eur	PROPN
ejpam-5828	270	33	.	.	PUNCT
ejpam-5828	271	1	j.	j.	PROPN
ejpam-5828	271	2	pure	pure	PROPN
ejpam-5828	271	3	appl	appl	PROPN
ejpam-5828	271	4	.	.	PROPN
ejpam-5828	271	5	math	math	PROPN
ejpam-5828	271	6	,	,	PUNCT
ejpam-5828	271	7	18	18	NUM
ejpam-5828	271	8	(	(	PUNCT
ejpam-5828	271	9	2	2	NUM
ejpam-5828	271	10	)	)	PUNCT
ejpam-5828	271	11	(	(	PUNCT
ejpam-5828	271	12	2025	2025	NUM
ejpam-5828	271	13	)	)	PUNCT
ejpam-5828	271	14	,	,	PUNCT
ejpam-5828	271	15	5828	5828	NUM
ejpam-5828	271	16	14	14	NUM
ejpam-5828	271	17	of	of	ADP
ejpam-5828	271	18	25	25	NUM
ejpam-5828	271	19	given	give	VERB
ejpam-5828	271	20	the	the	DET
ejpam-5828	271	21	complete	complete	ADJ
ejpam-5828	271	22	alignment	alignment	NOUN
ejpam-5828	271	23	with	with	ADP
ejpam-5828	271	24	equations	equation	NOUN
ejpam-5828	271	25	2	2	NUM
ejpam-5828	271	26	and	and	CCONJ
ejpam-5828	271	27	3	3	NUM
ejpam-5828	271	28	,	,	PUNCT
ejpam-5828	271	29	it	it	PRON
ejpam-5828	271	30	follows	follow	VERB
ejpam-5828	271	31	that	that	SCONJ
ejpam-5828	271	32	the	the	DET
ejpam-5828	271	33	poisson	poisson	NOUN
ejpam-5828	271	34	bracket	bracket	NOUN
ejpam-5828	271	35	relations	relation	NOUN
ejpam-5828	272	1	[	[	X
ejpam-5828	272	2	x	x	X
ejpam-5828	272	3	,	,	PUNCT
ejpam-5828	272	4	px	px	X
ejpam-5828	272	5	]	]	X
ejpam-5828	272	6	=	=	PUNCT
ejpam-5828	272	7	ih	ih	NOUN
ejpam-5828	272	8	imply	imply	VERB
ejpam-5828	272	9	the	the	DET
ejpam-5828	272	10	corresponding	corresponding	ADJ
ejpam-5828	272	11	commutation	commutation	NOUN
ejpam-5828	272	12	relations	relation	NOUN
ejpam-5828	273	1	[	[	X
ejpam-5828	273	2	x	x	X
ejpam-5828	273	3	,	,	PUNCT
ejpam-5828	273	4	x	x	X
ejpam-5828	273	5	]	]	X
ejpam-5828	273	6	=	=	PUNCT
ejpam-5828	274	1	[	[	X
ejpam-5828	274	2	y	y	PROPN
ejpam-5828	274	3	,	,	PUNCT
ejpam-5828	274	4	y	y	PROPN
ejpam-5828	274	5	]	]	X
ejpam-5828	274	6	=	=	PUNCT
ejpam-5828	275	1	[	[	X
ejpam-5828	275	2	px	px	PROPN
ejpam-5828	275	3	,	,	PUNCT
ejpam-5828	275	4	px	px	X
ejpam-5828	275	5	]	]	X
ejpam-5828	275	6	=	=	SYM
ejpam-5828	276	1	[	[	X
ejpam-5828	276	2	py	py	X
ejpam-5828	276	3	,	,	PUNCT
ejpam-5828	276	4	py	py	X
ejpam-5828	276	5	]	]	X
ejpam-5828	276	6	=	=	PUNCT
ejpam-5828	276	7	0	0	X
ejpam-5828	276	8	.	.	PUNCT
ejpam-5828	277	1	this	this	DET
ejpam-5828	277	2	alignment	alignment	NOUN
ejpam-5828	277	3	ensures	ensure	VERB
ejpam-5828	277	4	the	the	DET
ejpam-5828	277	5	consistency	consistency	NOUN
ejpam-5828	277	6	between	between	ADP
ejpam-5828	277	7	the	the	DET
ejpam-5828	277	8	classical	classical	ADJ
ejpam-5828	277	9	and	and	CCONJ
ejpam-5828	277	10	quantum	quantum	ADJ
ejpam-5828	277	11	descriptions	description	NOUN
ejpam-5828	277	12	of	of	ADP
ejpam-5828	277	13	the	the	DET
ejpam-5828	277	14	system	system	NOUN
ejpam-5828	277	15	.	.	PUNCT
ejpam-5828	278	1	building	build	VERB
ejpam-5828	278	2	on	on	ADP
ejpam-5828	278	3	this	this	DET
ejpam-5828	278	4	foundation	foundation	NOUN
ejpam-5828	278	5	.	.	PUNCT
ejpam-5828	279	1	this	this	DET
ejpam-5828	279	2	approach	approach	NOUN
ejpam-5828	279	3	is	be	AUX
ejpam-5828	279	4	consistent	consistent	ADJ
ejpam-5828	279	5	with	with	ADP
ejpam-5828	279	6	the	the	DET
ejpam-5828	279	7	methodology	methodology	NOUN
ejpam-5828	279	8	outlined	outline	VERB
ejpam-5828	279	9	in	in	ADP
ejpam-5828	279	10	[	[	X
ejpam-5828	279	11	23	23	NUM
ejpam-5828	279	12	]	]	PUNCT
ejpam-5828	279	13	,	,	PUNCT
ejpam-5828	279	14	where	where	SCONJ
ejpam-5828	279	15	similar	similar	ADJ
ejpam-5828	279	16	techniques	technique	NOUN
ejpam-5828	279	17	were	be	AUX
ejpam-5828	279	18	employed	employ	VERB
ejpam-5828	279	19	to	to	PART
ejpam-5828	279	20	analyze	analyze	VERB
ejpam-5828	279	21	dissipative	dissipative	ADJ
ejpam-5828	279	22	quantum	quantum	NOUN
ejpam-5828	279	23	systems	system	NOUN
ejpam-5828	280	1	d	d	NOUN
ejpam-5828	280	2	dt	dt	NOUN
ejpam-5828	281	1	⟨x⟩	⟨x⟩	PUNCT
ejpam-5828	282	1	=	=	PUNCT
ejpam-5828	283	1	i	i	PRON
ejpam-5828	283	2	h	h	VERB
ejpam-5828	283	3	〈	〈	NOUN
ejpam-5828	283	4			NOUN
ejpam-5828	283	5	1	1	NUM
ejpam-5828	283	6	2	2	NUM
ejpam-5828	283	7	m	m	PRON
ejpam-5828	283	8			PROPN
ejpam-5828	283	9	(	(	PUNCT
ejpam-5828	283	10	p	p	NOUN
ejpam-5828	283	11	2	2	NUM
ejpam-5828	283	12	x	x	SYM
ejpam-5828	283	13	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	283	14	2	2	NUM
ejpam-5828	283	15	−1	−1	NOUN
ejpam-5828	283	16	4mλ	4mλ	ADJ
ejpam-5828	283	17	2	2	NUM
ejpam-5828	283	18	xx	xx	NUM
ejpam-5828	283	19	2	2	NUM
ejpam-5828	283	20	)	)	PUNCT
ejpam-5828	283	21	+	+	CCONJ
ejpam-5828	283	22	(	(	PUNCT
ejpam-5828	283	23	p	p	PROPN
ejpam-5828	283	24	2	2	NUM
ejpam-5828	283	25	y	y	NOUN
ejpam-5828	283	26	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	283	27	2	2	NUM
ejpam-5828	283	28	−1	−1	NOUN
ejpam-5828	283	29	4mλ	4mλ	ADJ
ejpam-5828	283	30	2	2	NUM
ejpam-5828	283	31	yy	yy	NOUN
ejpam-5828	283	32	2	2	NUM
ejpam-5828	283	33	)	)	PUNCT
ejpam-5828	283	34			PROPN
ejpam-5828	283	35	,	,	PUNCT
ejpam-5828	283	36	x	x	SYM
ejpam-5828	283	37			VERB
ejpam-5828	283	38	〉	〉	NOUN
ejpam-5828	283	39	=	=	NOUN
ejpam-5828	284	1	i	i	PRON
ejpam-5828	284	2	h	h	VERB
ejpam-5828	284	3	〈	〈	PROPN
ejpam-5828	284	4	[	[	X
ejpam-5828	284	5	p	p	X
ejpam-5828	284	6	2	2	NUM
ejpam-5828	284	7	x	x	SYM
ejpam-5828	284	8	2	2	NUM
ejpam-5828	284	9	m	m	NOUN
ejpam-5828	284	10	,	,	PUNCT
ejpam-5828	284	11	x	x	X
ejpam-5828	284	12	]	]	X
ejpam-5828	284	13	〉	〉	X
ejpam-5828	284	14	=	=	SYM
ejpam-5828	284	15	〈	〈	PROPN
ejpam-5828	284	16	px	px	PROPN
ejpam-5828	284	17	m	m	VERB
ejpam-5828	284	18	〉	〉	NOUN
ejpam-5828	284	19	(	(	PUNCT
ejpam-5828	284	20	30	30	NUM
ejpam-5828	284	21	)	)	PUNCT
ejpam-5828	284	22	we	we	PRON
ejpam-5828	284	23	can	can	AUX
ejpam-5828	284	24	write	write	VERB
ejpam-5828	284	25	equation	equation	NOUN
ejpam-5828	284	26	26	26	NUM
ejpam-5828	284	27	in	in	ADP
ejpam-5828	284	28	terms	term	NOUN
ejpam-5828	284	29	of	of	ADP
ejpam-5828	284	30	,	,	PUNCT
ejpam-5828	284	31	we	we	PRON
ejpam-5828	284	32	get	get	VERB
ejpam-5828	284	33	:	:	PUNCT
ejpam-5828	285	1	d	d	X
ejpam-5828	285	2	dt	dt	X
ejpam-5828	286	1	⟨y⟩	⟨y⟩	NOUN
ejpam-5828	286	2	=	=	NOUN
ejpam-5828	287	1	i	i	PRON
ejpam-5828	287	2	h	h	VERB
ejpam-5828	287	3	〈	〈	NOUN
ejpam-5828	287	4			NOUN
ejpam-5828	287	5	1	1	NUM
ejpam-5828	287	6	2	2	NUM
ejpam-5828	287	7	m	m	PRON
ejpam-5828	287	8			PROPN
ejpam-5828	287	9	(	(	PUNCT
ejpam-5828	287	10	p	p	NOUN
ejpam-5828	287	11	2	2	NUM
ejpam-5828	287	12	x	x	SYM
ejpam-5828	287	13	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	287	14	2	2	NUM
ejpam-5828	287	15	−1	−1	NOUN
ejpam-5828	287	16	4mλ	4mλ	ADJ
ejpam-5828	287	17	2	2	NUM
ejpam-5828	287	18	xx	xx	NUM
ejpam-5828	287	19	2	2	NUM
ejpam-5828	287	20	)	)	PUNCT
ejpam-5828	287	21	+	+	CCONJ
ejpam-5828	287	22	(	(	PUNCT
ejpam-5828	287	23	p	p	PROPN
ejpam-5828	287	24	2	2	NUM
ejpam-5828	287	25	y	y	NOUN
ejpam-5828	287	26	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	287	27	2	2	NUM
ejpam-5828	287	28	−1	−1	NOUN
ejpam-5828	287	29	4mλ	4mλ	ADJ
ejpam-5828	287	30	2	2	NUM
ejpam-5828	287	31	yy	yy	NOUN
ejpam-5828	287	32	2	2	NUM
ejpam-5828	287	33	)	)	PUNCT
ejpam-5828	287	34			PROPN
ejpam-5828	287	35	,	,	PUNCT
ejpam-5828	287	36	x	x	SYM
ejpam-5828	287	37			VERB
ejpam-5828	287	38	〉	〉	NOUN
ejpam-5828	287	39	=	=	NOUN
ejpam-5828	288	1	i	i	PRON
ejpam-5828	288	2	h	h	VERB
ejpam-5828	288	3	〈	〈	PROPN
ejpam-5828	288	4	[	[	X
ejpam-5828	288	5	p	p	X
ejpam-5828	288	6	2	2	NUM
ejpam-5828	288	7	y	y	PROPN
ejpam-5828	288	8	2	2	NUM
ejpam-5828	288	9	m	m	NOUN
ejpam-5828	288	10	,	,	PUNCT
ejpam-5828	288	11	y	y	PROPN
ejpam-5828	288	12	]	]	PUNCT
ejpam-5828	288	13	〉	〉	X
ejpam-5828	288	14	=	=	SYM
ejpam-5828	288	15	〈	〈	PROPN
ejpam-5828	288	16	py	py	PROPN
ejpam-5828	288	17	m	m	PROPN
ejpam-5828	288	18	〉	〉	NOUN
ejpam-5828	288	19	(	(	PUNCT
ejpam-5828	288	20	31	31	NUM
ejpam-5828	288	21	)	)	PUNCT
ejpam-5828	288	22	the	the	DET
ejpam-5828	288	23	equation	equation	NOUN
ejpam-5828	288	24	31	31	NUM
ejpam-5828	288	25	agree	agree	VERB
ejpam-5828	288	26	with	with	ADP
ejpam-5828	288	27	equation	equation	NOUN
ejpam-5828	288	28	27	27	NUM
ejpam-5828	288	29	.	.	PUNCT
ejpam-5828	289	1	d	d	NOUN
ejpam-5828	289	2	dt	dt	X
ejpam-5828	289	3	⟨px⟩	⟨px⟩	PROPN
ejpam-5828	290	1	=	=	PUNCT
ejpam-5828	291	1	i	i	PRON
ejpam-5828	291	2	h	h	VERB
ejpam-5828	291	3	〈	〈	NOUN
ejpam-5828	291	4			NOUN
ejpam-5828	291	5	1	1	NUM
ejpam-5828	291	6	2	2	NUM
ejpam-5828	291	7	m	m	PRON
ejpam-5828	291	8			PROPN
ejpam-5828	291	9	(	(	PUNCT
ejpam-5828	291	10	p	p	NOUN
ejpam-5828	291	11	2	2	NUM
ejpam-5828	291	12	x	x	SYM
ejpam-5828	291	13	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	291	14	2	2	NUM
ejpam-5828	291	15	−1	−1	NOUN
ejpam-5828	291	16	4mλ	4mλ	ADJ
ejpam-5828	291	17	2	2	NUM
ejpam-5828	291	18	xx	xx	NUM
ejpam-5828	291	19	2	2	NUM
ejpam-5828	291	20	)	)	PUNCT
ejpam-5828	291	21	+	+	CCONJ
ejpam-5828	291	22	(	(	PUNCT
ejpam-5828	291	23	p	p	PROPN
ejpam-5828	291	24	2	2	NUM
ejpam-5828	291	25	y	y	NOUN
ejpam-5828	291	26	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	291	27	2	2	NUM
ejpam-5828	291	28	−1	−1	NOUN
ejpam-5828	291	29	4mλ	4mλ	ADJ
ejpam-5828	291	30	2	2	NUM
ejpam-5828	291	31	yy	yy	NOUN
ejpam-5828	291	32	2	2	NUM
ejpam-5828	291	33	)	)	PUNCT
ejpam-5828	291	34			PROPN
ejpam-5828	291	35	,	,	PUNCT
ejpam-5828	291	36	px	px	X
ejpam-5828	291	37			NOUN
ejpam-5828	291	38	〉	〉	NOUN
ejpam-5828	291	39	=	=	NOUN
ejpam-5828	292	1	i	i	PRON
ejpam-5828	292	2	h	h	NOUN
ejpam-5828	292	3	〈	〈	PROPN
ejpam-5828	292	4	[	[	PUNCT
ejpam-5828	292	5	2π2mv2xx	2π2mv2xx	NUM
ejpam-5828	292	6	2	2	NUM
ejpam-5828	292	7	,	,	PUNCT
ejpam-5828	292	8	px	px	X
ejpam-5828	292	9	]	]	PUNCT
ejpam-5828	292	10	〉	〉	X
ejpam-5828	292	11	=	=	PUNCT
ejpam-5828	292	12	−4π2mv2x	−4π2mv2x	X
ejpam-5828	292	13	⟨x⟩+	⟨x⟩+	PUNCT
ejpam-5828	293	1	1	1	NUM
ejpam-5828	293	2	4	4	NUM
ejpam-5828	293	3	mλ2x	mλ2x	PROPN
ejpam-5828	293	4	⟨x⟩	⟨x⟩	PROPN
ejpam-5828	293	5	(	(	PUNCT
ejpam-5828	293	6	32	32	NUM
ejpam-5828	293	7	)	)	PUNCT
ejpam-5828	293	8	and	and	CCONJ
ejpam-5828	293	9	d	d	NOUN
ejpam-5828	293	10	dt	dt	X
ejpam-5828	293	11	⟨py⟩	⟨py⟩	PROPN
ejpam-5828	294	1	=	=	SYM
ejpam-5828	295	1	i	i	PRON
ejpam-5828	295	2	h	h	VERB
ejpam-5828	295	3	〈	〈	NOUN
ejpam-5828	295	4			NOUN
ejpam-5828	295	5	1	1	NUM
ejpam-5828	295	6	2	2	NUM
ejpam-5828	295	7	m	m	PRON
ejpam-5828	295	8			PROPN
ejpam-5828	295	9	(	(	PUNCT
ejpam-5828	295	10	p	p	NOUN
ejpam-5828	295	11	2	2	NUM
ejpam-5828	295	12	x	x	SYM
ejpam-5828	295	13	+4π2m2v2xx	+4π2m2v2xx	PROPN
ejpam-5828	295	14	2	2	NUM
ejpam-5828	295	15	−1	−1	NOUN
ejpam-5828	295	16	4mλ	4mλ	ADJ
ejpam-5828	295	17	2	2	NUM
ejpam-5828	295	18	xx	xx	NUM
ejpam-5828	295	19	2	2	NUM
ejpam-5828	295	20	)	)	PUNCT
ejpam-5828	295	21	+	+	CCONJ
ejpam-5828	295	22	(	(	PUNCT
ejpam-5828	295	23	p	p	PROPN
ejpam-5828	295	24	2	2	NUM
ejpam-5828	295	25	y	y	NOUN
ejpam-5828	295	26	+4π2m2v2yy	+4π2m2v2yy	PROPN
ejpam-5828	295	27	2	2	NUM
ejpam-5828	295	28	−1	−1	NOUN
ejpam-5828	295	29	4mλ	4mλ	ADJ
ejpam-5828	295	30	2	2	NUM
ejpam-5828	295	31	yy	yy	NOUN
ejpam-5828	295	32	2	2	NUM
ejpam-5828	295	33	)	)	PUNCT
ejpam-5828	295	34			PROPN
ejpam-5828	295	35	,	,	PUNCT
ejpam-5828	295	36	py	py	PROPN
ejpam-5828	295	37			NOUN
ejpam-5828	295	38	〉	〉	NOUN
ejpam-5828	295	39	=	=	NOUN
ejpam-5828	296	1	i	i	PRON
ejpam-5828	296	2	h	h	NOUN
ejpam-5828	296	3	〈	〈	PROPN
ejpam-5828	296	4	[	[	PUNCT
ejpam-5828	296	5	2π2mv2yy	2π2mv2yy	NOUN
ejpam-5828	296	6	2	2	NUM
ejpam-5828	296	7	,	,	PUNCT
ejpam-5828	296	8	py	py	X
ejpam-5828	296	9	]	]	PUNCT
ejpam-5828	296	10	〉	〉	NOUN
ejpam-5828	296	11	=	=	PUNCT
ejpam-5828	297	1	−4π2mv2y	−4π2mv2y	ADJ
ejpam-5828	297	2	⟨x⟩+	⟨x⟩+	SYM
ejpam-5828	297	3	1	1	NUM
ejpam-5828	297	4	4	4	NUM
ejpam-5828	297	5	mλ2y	mλ2y	NOUN
ejpam-5828	297	6	⟨x⟩	⟨x⟩	X
ejpam-5828	297	7	(	(	PUNCT
ejpam-5828	297	8	33	33	NUM
ejpam-5828	297	9	)	)	PUNCT
ejpam-5828	297	10	ẍ	ẍ	X
ejpam-5828	298	1	=	=	SYM
ejpam-5828	298	2	ṗx	ṗx	PROPN
ejpam-5828	298	3	m	m	VERB
ejpam-5828	298	4	therefore	therefore	ADV
ejpam-5828	298	5	ẍ+	ẍ+	INTJ
ejpam-5828	298	6	(	(	PUNCT
ejpam-5828	298	7	42x	42x	X
ejpam-5828	298	8	−	−	ADP
ejpam-5828	298	9	1	1	NUM
ejpam-5828	298	10	4	4	NUM
ejpam-5828	298	11	λ2x)x	λ2x)x	NOUN
ejpam-5828	298	12	=	=	SYM
ejpam-5828	298	13	0	0	NUM
ejpam-5828	298	14	(	(	PUNCT
ejpam-5828	298	15	34	34	NUM
ejpam-5828	298	16	)	)	PUNCT
ejpam-5828	298	17	ÿ	ÿ	NOUN
ejpam-5828	298	18	=	=	SYM
ejpam-5828	298	19	ṗy	ṗy	PROPN
ejpam-5828	298	20	m	m	VERB
ejpam-5828	298	21	which	which	PRON
ejpam-5828	298	22	means	mean	VERB
ejpam-5828	298	23	that	that	SCONJ
ejpam-5828	298	24	ÿ	ÿ	PROPN
ejpam-5828	298	25	+	+	CCONJ
ejpam-5828	298	26	(	(	PUNCT
ejpam-5828	298	27	42y	42y	NOUN
ejpam-5828	298	28	−	−	NOUN
ejpam-5828	298	29	1	1	NUM
ejpam-5828	298	30	4	4	NUM
ejpam-5828	298	31	λ2y)y	λ2y)y	NOUN
ejpam-5828	298	32	=	=	SYM
ejpam-5828	298	33	0	0	NUM
ejpam-5828	298	34	(	(	PUNCT
ejpam-5828	298	35	35	35	NUM
ejpam-5828	298	36	)	)	PUNCT
ejpam-5828	298	37	these	these	DET
ejpam-5828	298	38	equations	equation	NOUN
ejpam-5828	298	39	align	align	VERB
ejpam-5828	298	40	with	with	ADP
ejpam-5828	298	41	the	the	DET
ejpam-5828	298	42	results	result	NOUN
ejpam-5828	298	43	obtained	obtain	VERB
ejpam-5828	298	44	through	through	ADP
ejpam-5828	298	45	other	other	ADJ
ejpam-5828	298	46	quantization	quantization	NOUN
ejpam-5828	298	47	methods	method	NOUN
ejpam-5828	298	48	.	.	PUNCT
ejpam-5828	299	1	the	the	DET
ejpam-5828	299	2	formulation	formulation	NOUN
ejpam-5828	299	3	is	be	AUX
ejpam-5828	299	4	further	far	ADV
ejpam-5828	299	5	extended	extend	VERB
ejpam-5828	299	6	using	use	VERB
ejpam-5828	299	7	creation	creation	NOUN
ejpam-5828	299	8	and	and	CCONJ
ejpam-5828	299	9	annihilation	annihilation	NOUN
ejpam-5828	299	10	operators	operator	NOUN
ejpam-5828	299	11	to	to	PART
ejpam-5828	299	12	derive	derive	VERB
ejpam-5828	299	13	the	the	DET
ejpam-5828	299	14	energy	energy	NOUN
ejpam-5828	299	15	eigenvalues	eigenvalue	NOUN
ejpam-5828	299	16	and	and	CCONJ
ejpam-5828	299	17	wave	wave	NOUN
ejpam-5828	299	18	functions	function	NOUN
ejpam-5828	299	19	,	,	PUNCT
ejpam-5828	299	20	as	as	SCONJ
ejpam-5828	299	21	detailed	detailed	ADJ
ejpam-5828	299	22	in	in	ADP
ejpam-5828	299	23	the	the	DET
ejpam-5828	299	24	appendix	appendix	PROPN
ejpam-5828	299	25	b.	b.	PROPN
ejpam-5828	299	26	b.	b.	PROPN
ejpam-5828	299	27	m.	m.	PROPN
ejpam-5828	299	28	al	al	PROPN
ejpam-5828	299	29	-	-	PUNCT
ejpam-5828	299	30	khamiseh	khamiseh	PROPN
ejpam-5828	299	31	et	et	PROPN
ejpam-5828	299	32	al	al	PROPN
ejpam-5828	299	33	.	.	PUNCT
ejpam-5828	299	34	/	/	SYM
ejpam-5828	299	35	eur	eur	PROPN
ejpam-5828	299	36	.	.	PUNCT
ejpam-5828	300	1	j.	j.	PROPN
ejpam-5828	300	2	pure	pure	PROPN
ejpam-5828	300	3	appl	appl	PROPN
ejpam-5828	300	4	.	.	PROPN
ejpam-5828	300	5	math	math	PROPN
ejpam-5828	300	6	,	,	PUNCT
ejpam-5828	300	7	18	18	NUM
ejpam-5828	300	8	(	(	PUNCT
ejpam-5828	300	9	2	2	NUM
ejpam-5828	300	10	)	)	PUNCT
ejpam-5828	300	11	(	(	PUNCT
ejpam-5828	300	12	2025	2025	NUM
ejpam-5828	300	13	)	)	PUNCT
ejpam-5828	300	14	,	,	PUNCT
ejpam-5828	300	15	5828	5828	NUM
ejpam-5828	300	16	15	15	NUM
ejpam-5828	300	17	of	of	ADP
ejpam-5828	300	18	25	25	NUM
ejpam-5828	300	19	7	7	NUM
ejpam-5828	300	20	.	.	PUNCT
ejpam-5828	301	1	applications	application	NOUN
ejpam-5828	301	2	of	of	ADP
ejpam-5828	301	3	the	the	DET
ejpam-5828	301	4	hamilton	hamilton	PROPN
ejpam-5828	301	5	-	-	PUNCT
ejpam-5828	301	6	jacobi	jacobi	PROPN
ejpam-5828	301	7	technique	technique	NOUN
ejpam-5828	301	8	in	in	ADP
ejpam-5828	301	9	analyzing	analyze	VERB
ejpam-5828	301	10	harmonic	harmonic	ADJ
ejpam-5828	301	11	oscillator	oscillator	NOUN
ejpam-5828	301	12	dynamics	dynamic	NOUN
ejpam-5828	301	13	this	this	DET
ejpam-5828	301	14	section	section	NOUN
ejpam-5828	301	15	discusses	discuss	VERB
ejpam-5828	301	16	how	how	SCONJ
ejpam-5828	301	17	we	we	PRON
ejpam-5828	301	18	can	can	AUX
ejpam-5828	301	19	use	use	VERB
ejpam-5828	301	20	the	the	DET
ejpam-5828	301	21	hamilton	hamilton	PROPN
ejpam-5828	301	22	-	-	PUNCT
ejpam-5828	301	23	jacobi	jacobi	PROPN
ejpam-5828	301	24	approach	approach	NOUN
ejpam-5828	301	25	to	to	PART
ejpam-5828	301	26	study	study	VERB
ejpam-5828	301	27	the	the	DET
ejpam-5828	301	28	harmonic	harmonic	ADJ
ejpam-5828	301	29	oscillator	oscillator	NOUN
ejpam-5828	301	30	,	,	PUNCT
ejpam-5828	301	31	showing	show	VERB
ejpam-5828	301	32	its	its	PRON
ejpam-5828	301	33	flexibility	flexibility	NOUN
ejpam-5828	301	34	and	and	CCONJ
ejpam-5828	301	35	effectiveness	effectiveness	NOUN
ejpam-5828	301	36	in	in	ADP
ejpam-5828	301	37	different	different	ADJ
ejpam-5828	301	38	situations	situation	NOUN
ejpam-5828	301	39	.	.	PUNCT
ejpam-5828	302	1	it	it	PRON
ejpam-5828	302	2	explains	explain	VERB
ejpam-5828	302	3	how	how	SCONJ
ejpam-5828	302	4	this	this	DET
ejpam-5828	302	5	method	method	NOUN
ejpam-5828	302	6	helps	help	VERB
ejpam-5828	302	7	us	we	PRON
ejpam-5828	302	8	understand	understand	VERB
ejpam-5828	302	9	the	the	DET
ejpam-5828	302	10	relationship	relationship	NOUN
ejpam-5828	302	11	between	between	ADP
ejpam-5828	302	12	the	the	DET
ejpam-5828	302	13	hamiltonjacobi	hamiltonjacobi	ADJ
ejpam-5828	302	14	equation	equation	NOUN
ejpam-5828	302	15	of	of	ADP
ejpam-5828	302	16	motion	motion	NOUN
ejpam-5828	302	17	and	and	CCONJ
ejpam-5828	302	18	the	the	DET
ejpam-5828	302	19	i	i	NOUN
ejpam-5828	302	20	-	-	PUNCT
ejpam-5828	302	21	factor	factor	NOUN
ejpam-5828	302	22	of	of	ADP
ejpam-5828	302	23	an	an	DET
ejpam-5828	302	24	oscillator	oscillator	NOUN
ejpam-5828	302	25	,	,	PUNCT
ejpam-5828	302	26	which	which	PRON
ejpam-5828	302	27	matches	match	VERB
ejpam-5828	302	28	the	the	DET
ejpam-5828	302	29	system	system	NOUN
ejpam-5828	302	30	’s	’s	PART
ejpam-5828	302	31	physical	physical	ADJ
ejpam-5828	302	32	features	feature	NOUN
ejpam-5828	302	33	well	well	ADV
ejpam-5828	302	34	.	.	PUNCT
ejpam-5828	303	1	this	this	PRON
ejpam-5828	303	2	confirms	confirm	VERB
ejpam-5828	303	3	that	that	SCONJ
ejpam-5828	303	4	the	the	DET
ejpam-5828	303	5	hamilton	hamilton	PROPN
ejpam-5828	303	6	-	-	PUNCT
ejpam-5828	303	7	jacobi	jacobi	PROPN
ejpam-5828	303	8	approach	approach	NOUN
ejpam-5828	303	9	works	work	VERB
ejpam-5828	303	10	well	well	ADV
ejpam-5828	303	11	and	and	CCONJ
ejpam-5828	303	12	proves	prove	VERB
ejpam-5828	303	13	that	that	SCONJ
ejpam-5828	303	14	the	the	DET
ejpam-5828	303	15	fractional	fractional	ADJ
ejpam-5828	303	16	oscillator	oscillator	NOUN
ejpam-5828	303	17	template	template	NOUN
ejpam-5828	303	18	is	be	AUX
ejpam-5828	303	19	useful	useful	ADJ
ejpam-5828	303	20	for	for	ADP
ejpam-5828	303	21	describing	describe	VERB
ejpam-5828	303	22	strongly	strongly	ADV
ejpam-5828	303	23	damped	damp	VERB
ejpam-5828	303	24	vibrations	vibration	NOUN
ejpam-5828	303	25	.	.	PUNCT
ejpam-5828	304	1	additionally	additionally	ADV
ejpam-5828	304	2	,	,	PUNCT
ejpam-5828	304	3	we	we	PRON
ejpam-5828	304	4	can	can	AUX
ejpam-5828	304	5	apply	apply	VERB
ejpam-5828	304	6	this	this	DET
ejpam-5828	304	7	approach	approach	NOUN
ejpam-5828	304	8	to	to	PART
ejpam-5828	304	9	see	see	VERB
ejpam-5828	304	10	how	how	SCONJ
ejpam-5828	304	11	dissipative	dissipative	ADJ
ejpam-5828	304	12	processes	process	NOUN
ejpam-5828	304	13	affect	affect	VERB
ejpam-5828	304	14	other	other	ADJ
ejpam-5828	304	15	oscillating	oscillate	VERB
ejpam-5828	304	16	physical	physical	ADJ
ejpam-5828	304	17	systems	system	NOUN
ejpam-5828	304	18	,	,	PUNCT
ejpam-5828	304	19	like	like	ADP
ejpam-5828	304	20	the	the	DET
ejpam-5828	304	21	ordered	order	VERB
ejpam-5828	304	22	hamilton	hamilton	PROPN
ejpam-5828	304	23	-	-	PUNCT
ejpam-5828	304	24	jacobi	jacobi	PROPN
ejpam-5828	304	25	harmonic	harmonic	PROPN
ejpam-5828	304	26	oscillator	oscillator	NOUN
ejpam-5828	304	27	.	.	PUNCT
ejpam-5828	305	1	another	another	DET
ejpam-5828	305	2	important	important	ADJ
ejpam-5828	305	3	point	point	NOUN
ejpam-5828	305	4	is	be	AUX
ejpam-5828	305	5	exploring	explore	VERB
ejpam-5828	305	6	how	how	SCONJ
ejpam-5828	305	7	classical	classical	ADJ
ejpam-5828	305	8	chaos	chaos	NOUN
ejpam-5828	305	9	affects	affect	VERB
ejpam-5828	305	10	the	the	DET
ejpam-5828	305	11	harmonic	harmonic	ADJ
ejpam-5828	305	12	oscillator	oscillator	NOUN
ejpam-5828	305	13	,	,	PUNCT
ejpam-5828	305	14	giving	give	VERB
ejpam-5828	305	15	us	we	PRON
ejpam-5828	305	16	insights	insight	NOUN
ejpam-5828	305	17	into	into	ADP
ejpam-5828	305	18	realistic	realistic	ADJ
ejpam-5828	305	19	systems	system	NOUN
ejpam-5828	305	20	in	in	ADP
ejpam-5828	305	21	classical	classical	ADJ
ejpam-5828	305	22	,	,	PUNCT
ejpam-5828	305	23	quantum	quantum	NOUN
ejpam-5828	305	24	,	,	PUNCT
ejpam-5828	305	25	and	and	CCONJ
ejpam-5828	305	26	relativistic	relativistic	ADJ
ejpam-5828	305	27	domains	domain	NOUN
ejpam-5828	305	28	.	.	PUNCT
ejpam-5828	306	1	while	while	SCONJ
ejpam-5828	306	2	newtonian	newtonian	ADJ
ejpam-5828	306	3	physics	physics	NOUN
ejpam-5828	306	4	suggests	suggest	VERB
ejpam-5828	306	5	the	the	DET
ejpam-5828	306	6	harmonic	harmonic	ADJ
ejpam-5828	306	7	oscillator	oscillator	NOUN
ejpam-5828	306	8	is	be	AUX
ejpam-5828	306	9	integrable	integrable	ADJ
ejpam-5828	306	10	no	no	ADV
ejpam-5828	306	11	matter	matter	ADV
ejpam-5828	306	12	what	what	PRON
ejpam-5828	306	13	,	,	PUNCT
ejpam-5828	306	14	this	this	DET
ejpam-5828	306	15	approach	approach	NOUN
ejpam-5828	306	16	lets	let	VERB
ejpam-5828	306	17	us	we	PRON
ejpam-5828	306	18	explore	explore	VERB
ejpam-5828	306	19	chaotic	chaotic	ADJ
ejpam-5828	306	20	behavior	behavior	NOUN
ejpam-5828	306	21	in	in	ADP
ejpam-5828	306	22	relativistic	relativistic	ADJ
ejpam-5828	306	23	,	,	PUNCT
ejpam-5828	306	24	one	one	NUM
ejpam-5828	306	25	dimensionally	dimensionally	ADV
ejpam-5828	306	26	driven	drive	VERB
ejpam-5828	306	27	oscillators	oscillator	NOUN
ejpam-5828	306	28	,	,	PUNCT
ejpam-5828	306	29	helping	help	VERB
ejpam-5828	306	30	us	we	PRON
ejpam-5828	306	31	understand	understand	VERB
ejpam-5828	306	32	complex	complex	ADJ
ejpam-5828	306	33	dynamical	dynamical	ADJ
ejpam-5828	306	34	systems	system	NOUN
ejpam-5828	306	35	better	well	ADV
ejpam-5828	306	36	.	.	PUNCT
ejpam-5828	307	1	8	8	X
ejpam-5828	307	2	.	.	X
ejpam-5828	307	3	discussion	discussion	NOUN
ejpam-5828	307	4	of	of	ADP
ejpam-5828	307	5	the	the	DET
ejpam-5828	307	6	figures	figure	NOUN
ejpam-5828	307	7	:	:	PUNCT
ejpam-5828	307	8	the	the	DET
ejpam-5828	307	9	impact	impact	NOUN
ejpam-5828	307	10	of	of	ADP
ejpam-5828	307	11	dissipation	dissipation	NOUN
ejpam-5828	307	12	on	on	ADP
ejpam-5828	307	13	the	the	DET
ejpam-5828	307	14	quantum	quantum	NOUN
ejpam-5828	307	15	oscillator	oscillator	NOUN
ejpam-5828	307	16	in	in	ADP
ejpam-5828	307	17	this	this	DET
ejpam-5828	307	18	section	section	NOUN
ejpam-5828	307	19	,	,	PUNCT
ejpam-5828	307	20	we	we	PRON
ejpam-5828	307	21	analyze	analyze	VERB
ejpam-5828	307	22	the	the	DET
ejpam-5828	307	23	effect	effect	NOUN
ejpam-5828	307	24	of	of	ADP
ejpam-5828	307	25	dissipation	dissipation	NOUN
ejpam-5828	307	26	on	on	ADP
ejpam-5828	307	27	the	the	DET
ejpam-5828	307	28	quantum	quantum	ADJ
ejpam-5828	307	29	two	two	NUM
ejpam-5828	307	30	-	-	PUNCT
ejpam-5828	307	31	dimensional	dimensional	ADJ
ejpam-5828	307	32	anisotropic	anisotropic	NOUN
ejpam-5828	307	33	oscillator	oscillator	NOUN
ejpam-5828	307	34	using	use	VERB
ejpam-5828	307	35	mathematical	mathematical	ADJ
ejpam-5828	307	36	analysis	analysis	NOUN
ejpam-5828	307	37	and	and	CCONJ
ejpam-5828	307	38	graphical	graphical	ADJ
ejpam-5828	307	39	representations	representation	NOUN
ejpam-5828	307	40	that	that	PRON
ejpam-5828	307	41	illustrate	illustrate	VERB
ejpam-5828	307	42	the	the	DET
ejpam-5828	307	43	relationship	relationship	NOUN
ejpam-5828	307	44	between	between	ADP
ejpam-5828	307	45	various	various	ADJ
ejpam-5828	307	46	dynamic	dynamic	ADJ
ejpam-5828	307	47	parameters	parameter	NOUN
ejpam-5828	307	48	.	.	PUNCT
ejpam-5828	308	1	graphical	graphical	ADJ
ejpam-5828	308	2	representations	representation	NOUN
ejpam-5828	308	3	have	have	AUX
ejpam-5828	308	4	been	be	AUX
ejpam-5828	308	5	provided	provide	VERB
ejpam-5828	308	6	to	to	PART
ejpam-5828	308	7	demonstrate	demonstrate	VERB
ejpam-5828	308	8	how	how	SCONJ
ejpam-5828	308	9	energy	energy	NOUN
ejpam-5828	308	10	and	and	CCONJ
ejpam-5828	308	11	probability	probability	NOUN
ejpam-5828	308	12	distributions	distribution	NOUN
ejpam-5828	308	13	are	be	AUX
ejpam-5828	308	14	influenced	influence	VERB
ejpam-5828	308	15	by	by	ADP
ejpam-5828	308	16	dissipation	dissipation	NOUN
ejpam-5828	308	17	.	.	PUNCT
ejpam-5828	309	1	the	the	DET
ejpam-5828	309	2	figures	figure	NOUN
ejpam-5828	309	3	have	have	AUX
ejpam-5828	309	4	been	be	AUX
ejpam-5828	309	5	plotted	plot	VERB
ejpam-5828	309	6	with	with	ADP
ejpam-5828	309	7	enhanced	enhanced	ADJ
ejpam-5828	309	8	clarity	clarity	NOUN
ejpam-5828	309	9	to	to	PART
ejpam-5828	309	10	ensure	ensure	VERB
ejpam-5828	309	11	a	a	DET
ejpam-5828	309	12	better	well	ADJ
ejpam-5828	309	13	understanding	understanding	NOUN
ejpam-5828	309	14	of	of	ADP
ejpam-5828	309	15	the	the	DET
ejpam-5828	309	16	results	result	NOUN
ejpam-5828	309	17	.	.	PUNCT
ejpam-5828	310	1	8.1	8.1	X
ejpam-5828	310	2	.	.	PUNCT
ejpam-5828	310	3	relationship	relationship	NOUN
ejpam-5828	310	4	between	between	ADP
ejpam-5828	310	5	energy	energy	NOUN
ejpam-5828	310	6	and	and	CCONJ
ejpam-5828	310	7	dynamic	dynamic	ADJ
ejpam-5828	310	8	parameters	parameter	NOUN
ejpam-5828	310	9	as	as	SCONJ
ejpam-5828	310	10	shown	show	VERB
ejpam-5828	310	11	in	in	ADP
ejpam-5828	310	12	figure	figure	NOUN
ejpam-5828	310	13	(	(	PUNCT
ejpam-5828	310	14	1	1	NUM
ejpam-5828	310	15	)	)	PUNCT
ejpam-5828	310	16	,	,	PUNCT
ejpam-5828	310	17	the	the	DET
ejpam-5828	310	18	total	total	ADJ
ejpam-5828	310	19	energy	energy	NOUN
ejpam-5828	310	20	of	of	ADP
ejpam-5828	310	21	the	the	DET
ejpam-5828	310	22	dissipative	dissipative	ADJ
ejpam-5828	310	23	quantum	quantum	NOUN
ejpam-5828	310	24	oscillator	oscillator	NOUN
ejpam-5828	310	25	is	be	AUX
ejpam-5828	310	26	analyzed	analyze	VERB
ejpam-5828	310	27	as	as	ADP
ejpam-5828	310	28	a	a	DET
ejpam-5828	310	29	function	function	NOUN
ejpam-5828	310	30	of	of	ADP
ejpam-5828	310	31	a	a	DET
ejpam-5828	310	32	key	key	ADJ
ejpam-5828	310	33	parameter	parameter	NOUN
ejpam-5828	310	34	related	relate	VERB
ejpam-5828	310	35	to	to	ADP
ejpam-5828	310	36	thermal	thermal	ADJ
ejpam-5828	310	37	and	and	CCONJ
ejpam-5828	310	38	quantum	quantum	ADJ
ejpam-5828	310	39	effects	effect	NOUN
ejpam-5828	310	40	.	.	PUNCT
ejpam-5828	311	1	the	the	DET
ejpam-5828	311	2	results	result	NOUN
ejpam-5828	311	3	indicate	indicate	VERB
ejpam-5828	311	4	that	that	SCONJ
ejpam-5828	311	5	increasing	increase	VERB
ejpam-5828	311	6	this	this	DET
ejpam-5828	311	7	parameter	parameter	NOUN
ejpam-5828	311	8	leads	lead	VERB
ejpam-5828	311	9	to	to	ADP
ejpam-5828	311	10	a	a	DET
ejpam-5828	311	11	rise	rise	NOUN
ejpam-5828	311	12	in	in	ADP
ejpam-5828	311	13	total	total	ADJ
ejpam-5828	311	14	energy	energy	NOUN
ejpam-5828	311	15	due	due	ADP
ejpam-5828	311	16	to	to	ADP
ejpam-5828	311	17	quantum	quantum	ADJ
ejpam-5828	311	18	contributions	contribution	NOUN
ejpam-5828	311	19	.	.	PUNCT
ejpam-5828	312	1	additionally	additionally	ADV
ejpam-5828	312	2	,	,	PUNCT
ejpam-5828	312	3	at	at	ADP
ejpam-5828	312	4	low	low	ADJ
ejpam-5828	312	5	temperatures	temperature	NOUN
ejpam-5828	312	6	,	,	PUNCT
ejpam-5828	312	7	the	the	DET
ejpam-5828	312	8	dissipation	dissipation	NOUN
ejpam-5828	312	9	effect	effect	NOUN
ejpam-5828	312	10	becomes	become	VERB
ejpam-5828	312	11	more	more	ADV
ejpam-5828	312	12	pronounced	pronounced	ADJ
ejpam-5828	312	13	,	,	PUNCT
ejpam-5828	312	14	causing	cause	VERB
ejpam-5828	312	15	a	a	DET
ejpam-5828	312	16	significant	significant	ADJ
ejpam-5828	312	17	deviation	deviation	NOUN
ejpam-5828	312	18	from	from	ADP
ejpam-5828	312	19	classical	classical	ADJ
ejpam-5828	312	20	behavior	behavior	NOUN
ejpam-5828	312	21	.	.	PUNCT
ejpam-5828	313	1	this	this	PRON
ejpam-5828	313	2	highlights	highlight	VERB
ejpam-5828	313	3	the	the	DET
ejpam-5828	313	4	fundamental	fundamental	ADJ
ejpam-5828	313	5	role	role	NOUN
ejpam-5828	313	6	of	of	ADP
ejpam-5828	313	7	dissipation	dissipation	NOUN
ejpam-5828	313	8	in	in	ADP
ejpam-5828	313	9	shaping	shape	VERB
ejpam-5828	313	10	the	the	DET
ejpam-5828	313	11	quantum	quantum	ADJ
ejpam-5828	313	12	dynamics	dynamic	NOUN
ejpam-5828	313	13	of	of	ADP
ejpam-5828	313	14	the	the	DET
ejpam-5828	313	15	system	system	NOUN
ejpam-5828	313	16	.	.	PUNCT
ejpam-5828	314	1	at	at	ADP
ejpam-5828	314	2	low	low	ADJ
ejpam-5828	314	3	temperatures	temperature	NOUN
ejpam-5828	314	4	,	,	PUNCT
ejpam-5828	314	5	the	the	DET
ejpam-5828	314	6	effect	effect	NOUN
ejpam-5828	314	7	of	of	ADP
ejpam-5828	314	8	dissipation	dissipation	NOUN
ejpam-5828	314	9	becomes	become	VERB
ejpam-5828	314	10	more	more	ADV
ejpam-5828	314	11	pronounced	pronounced	ADJ
ejpam-5828	314	12	,	,	PUNCT
ejpam-5828	314	13	leading	lead	VERB
ejpam-5828	314	14	to	to	ADP
ejpam-5828	314	15	a	a	DET
ejpam-5828	314	16	significant	significant	ADJ
ejpam-5828	314	17	deviation	deviation	NOUN
ejpam-5828	314	18	from	from	ADP
ejpam-5828	314	19	classical	classical	ADJ
ejpam-5828	314	20	behavior	behavior	NOUN
ejpam-5828	314	21	.	.	PUNCT
ejpam-5828	315	1	this	this	PRON
ejpam-5828	315	2	indicates	indicate	VERB
ejpam-5828	315	3	that	that	SCONJ
ejpam-5828	315	4	dissipation	dissipation	NOUN
ejpam-5828	315	5	plays	play	VERB
ejpam-5828	315	6	a	a	DET
ejpam-5828	315	7	fundamental	fundamental	ADJ
ejpam-5828	315	8	role	role	NOUN
ejpam-5828	315	9	in	in	ADP
ejpam-5828	315	10	shaping	shape	VERB
ejpam-5828	315	11	the	the	DET
ejpam-5828	315	12	quantum	quantum	ADJ
ejpam-5828	315	13	dynamics	dynamic	NOUN
ejpam-5828	315	14	of	of	ADP
ejpam-5828	315	15	the	the	DET
ejpam-5828	315	16	system	system	NOUN
ejpam-5828	315	17	,	,	PUNCT
ejpam-5828	315	18	especially	especially	ADV
ejpam-5828	315	19	under	under	ADP
ejpam-5828	315	20	conditions	condition	NOUN
ejpam-5828	315	21	where	where	SCONJ
ejpam-5828	315	22	quantum	quantum	NOUN
ejpam-5828	315	23	effects	effect	NOUN
ejpam-5828	315	24	dominate	dominate	VERB
ejpam-5828	315	25	.	.	PUNCT
ejpam-5828	316	1	this	this	DET
ejpam-5828	316	2	deviation	deviation	NOUN
ejpam-5828	316	3	can	can	AUX
ejpam-5828	316	4	be	be	AUX
ejpam-5828	316	5	explained	explain	VERB
ejpam-5828	316	6	by	by	ADP
ejpam-5828	316	7	the	the	DET
ejpam-5828	316	8	fact	fact	NOUN
ejpam-5828	316	9	that	that	SCONJ
ejpam-5828	316	10	dissipation	dissipation	NOUN
ejpam-5828	316	11	leads	lead	VERB
ejpam-5828	316	12	to	to	ADP
ejpam-5828	316	13	continuous	continuous	ADJ
ejpam-5828	316	14	energy	energy	NOUN
ejpam-5828	316	15	loss	loss	NOUN
ejpam-5828	316	16	,	,	PUNCT
ejpam-5828	316	17	affecting	affect	VERB
ejpam-5828	316	18	the	the	DET
ejpam-5828	316	19	quantum	quantum	ADJ
ejpam-5828	316	20	energy	energy	NOUN
ejpam-5828	316	21	distribution	distribution	NOUN
ejpam-5828	316	22	and	and	CCONJ
ejpam-5828	316	23	altering	alter	VERB
ejpam-5828	316	24	the	the	DET
ejpam-5828	316	25	system	system	NOUN
ejpam-5828	316	26	’s	’s	PART
ejpam-5828	316	27	states	state	NOUN
ejpam-5828	316	28	.	.	PUNCT
ejpam-5828	317	1	in	in	ADP
ejpam-5828	317	2	figure	figure	NOUN
ejpam-5828	317	3	b.	b.	PROPN
ejpam-5828	317	4	m.	m.	PROPN
ejpam-5828	317	5	al	al	PROPN
ejpam-5828	317	6	-	-	PUNCT
ejpam-5828	317	7	khamiseh	khamiseh	PROPN
ejpam-5828	317	8	et	et	PROPN
ejpam-5828	317	9	al	al	PROPN
ejpam-5828	317	10	.	.	PUNCT
ejpam-5828	317	11	/	/	SYM
ejpam-5828	317	12	eur	eur	PROPN
ejpam-5828	317	13	.	.	PUNCT
ejpam-5828	318	1	j.	j.	PROPN
ejpam-5828	318	2	pure	pure	PROPN
ejpam-5828	318	3	appl	appl	PROPN
ejpam-5828	318	4	.	.	PROPN
ejpam-5828	318	5	math	math	PROPN
ejpam-5828	318	6	,	,	PUNCT
ejpam-5828	318	7	18	18	NUM
ejpam-5828	318	8	(	(	PUNCT
ejpam-5828	318	9	2	2	NUM
ejpam-5828	318	10	)	)	PUNCT
ejpam-5828	318	11	(	(	PUNCT
ejpam-5828	318	12	2025	2025	NUM
ejpam-5828	318	13	)	)	PUNCT
ejpam-5828	318	14	,	,	PUNCT
ejpam-5828	318	15	5828	5828	NUM
ejpam-5828	318	16	16	16	NUM
ejpam-5828	318	17	of	of	ADP
ejpam-5828	318	18	25	25	NUM
ejpam-5828	318	19	0	0	NUM
ejpam-5828	318	20	2	2	NUM
ejpam-5828	318	21	4	4	NUM
ejpam-5828	318	22	6	6	NUM
ejpam-5828	318	23	8	8	NUM
ejpam-5828	318	24	10	10	NUM
ejpam-5828	318	25	0	0	NUM
ejpam-5828	318	26	2	2	NUM
ejpam-5828	318	27	4	4	NUM
ejpam-5828	318	28	6	6	NUM
ejpam-5828	318	29	8	8	NUM
ejpam-5828	318	30	10	10	NUM
ejpam-5828	318	31	α	α	PROPN
ejpam-5828	318	32	β	β	X
ejpam-5828	318	33	u	u	PROPN
ejpam-5828	318	34	,	,	PUNCT
ejpam-5828	318	35	β	β	X
ejpam-5828	318	36	e	e	NOUN
ejpam-5828	318	37	,	,	PUNCT
ejpam-5828	318	38	β	β	X
ejpam-5828	318	39	e	e	NOUN
ejpam-5828	318	40	figure	figure	NOUN
ejpam-5828	318	41	1	1	NUM
ejpam-5828	318	42	:	:	PUNCT
ejpam-5828	318	43	illustrates	illustrate	VERB
ejpam-5828	318	44	how	how	SCONJ
ejpam-5828	318	45	dissipation	dissipation	NOUN
ejpam-5828	318	46	affects	affect	VERB
ejpam-5828	318	47	the	the	DET
ejpam-5828	318	48	energy	energy	NOUN
ejpam-5828	318	49	probability	probability	NOUN
ejpam-5828	318	50	distribution	distribution	NOUN
ejpam-5828	318	51	in	in	ADP
ejpam-5828	318	52	a	a	DET
ejpam-5828	318	53	quantum	quantum	ADJ
ejpam-5828	318	54	system	system	NOUN
ejpam-5828	318	55	,	,	PUNCT
ejpam-5828	318	56	leading	lead	VERB
ejpam-5828	318	57	to	to	ADP
ejpam-5828	318	58	energy	energy	NOUN
ejpam-5828	318	59	transfer	transfer	NOUN
ejpam-5828	318	60	and	and	CCONJ
ejpam-5828	318	61	changes	change	NOUN
ejpam-5828	318	62	in	in	ADP
ejpam-5828	318	63	the	the	DET
ejpam-5828	318	64	system	system	NOUN
ejpam-5828	318	65	’s	’s	PART
ejpam-5828	318	66	states	state	NOUN
ejpam-5828	318	67	due	due	ADP
ejpam-5828	318	68	to	to	ADP
ejpam-5828	318	69	interaction	interaction	NOUN
ejpam-5828	318	70	with	with	ADP
ejpam-5828	318	71	the	the	DET
ejpam-5828	318	72	environment	environment	NOUN
ejpam-5828	318	73	.	.	PUNCT
ejpam-5828	319	1	(	(	PUNCT
ejpam-5828	319	2	2	2	NUM
ejpam-5828	319	3	)	)	PUNCT
ejpam-5828	319	4	,	,	PUNCT
ejpam-5828	319	5	we	we	PRON
ejpam-5828	319	6	analyze	analyze	VERB
ejpam-5828	319	7	the	the	DET
ejpam-5828	319	8	impact	impact	NOUN
ejpam-5828	319	9	of	of	ADP
ejpam-5828	319	10	the	the	DET
ejpam-5828	319	11	damping	damp	VERB
ejpam-5828	319	12	coefficient	coefficient	NOUN
ejpam-5828	319	13	on	on	ADP
ejpam-5828	319	14	energy	energy	NOUN
ejpam-5828	319	15	.	.	PUNCT
ejpam-5828	320	1	the	the	DET
ejpam-5828	320	2	graph	graph	NOUN
ejpam-5828	320	3	clearly	clearly	ADV
ejpam-5828	320	4	illustrates	illustrate	VERB
ejpam-5828	320	5	that	that	SCONJ
ejpam-5828	320	6	increasing	increase	VERB
ejpam-5828	320	7	the	the	DET
ejpam-5828	320	8	damping	damp	VERB
ejpam-5828	320	9	coefficient	coefficient	NOUN
ejpam-5828	320	10	results	result	NOUN
ejpam-5828	320	11	in	in	ADP
ejpam-5828	320	12	higher	high	ADJ
ejpam-5828	320	13	internal	internal	ADJ
ejpam-5828	320	14	energy	energy	NOUN
ejpam-5828	320	15	levels	level	NOUN
ejpam-5828	320	16	,	,	PUNCT
ejpam-5828	320	17	confirming	confirm	VERB
ejpam-5828	320	18	that	that	SCONJ
ejpam-5828	320	19	dissipation	dissipation	NOUN
ejpam-5828	320	20	directly	directly	ADV
ejpam-5828	320	21	influences	influence	VERB
ejpam-5828	320	22	the	the	DET
ejpam-5828	320	23	quantum	quantum	ADJ
ejpam-5828	320	24	energy	energy	NOUN
ejpam-5828	320	25	spectrum	spectrum	NOUN
ejpam-5828	320	26	and	and	CCONJ
ejpam-5828	320	27	alters	alter	VERB
ejpam-5828	320	28	the	the	DET
ejpam-5828	320	29	system	system	NOUN
ejpam-5828	320	30	’s	’s	PART
ejpam-5828	320	31	dynamics	dynamic	NOUN
ejpam-5828	320	32	.	.	PUNCT
ejpam-5828	321	1	0	0	NUM
ejpam-5828	321	2	0.5	0.5	NUM
ejpam-5828	321	3	1	1	NUM
ejpam-5828	321	4	1.5	1.5	NUM
ejpam-5828	321	5	2	2	NUM
ejpam-5828	321	6	0.5	0.5	NUM
ejpam-5828	321	7	1	1	NUM
ejpam-5828	321	8	1.5	1.5	NUM
ejpam-5828	321	9	γ	γ	NOUN
ejpam-5828	321	10	/	/	SYM
ejpam-5828	321	11	ωp	ωp	PROPN
ejpam-5828	321	12	β	β	PROPN
ejpam-5828	321	13	u	u	PROPN
ejpam-5828	321	14	,	,	PUNCT
ejpam-5828	321	15	β	β	X
ejpam-5828	321	16	e	e	NOUN
ejpam-5828	321	17	,	,	PUNCT
ejpam-5828	321	18	β	β	X
ejpam-5828	321	19	e	e	NOUN
ejpam-5828	321	20	figure	figure	NOUN
ejpam-5828	321	21	2	2	NUM
ejpam-5828	321	22	:	:	PUNCT
ejpam-5828	321	23	the	the	DET
ejpam-5828	321	24	dimensionless	dimensionless	NOUN
ejpam-5828	321	25	energy	energy	NOUN
ejpam-5828	321	26	this	this	DET
ejpam-5828	321	27	increase	increase	NOUN
ejpam-5828	321	28	in	in	ADP
ejpam-5828	321	29	energy	energy	NOUN
ejpam-5828	321	30	can	can	AUX
ejpam-5828	321	31	be	be	AUX
ejpam-5828	321	32	explained	explain	VERB
ejpam-5828	321	33	by	by	ADP
ejpam-5828	321	34	the	the	DET
ejpam-5828	321	35	fact	fact	NOUN
ejpam-5828	321	36	that	that	SCONJ
ejpam-5828	321	37	dissipation	dissipation	NOUN
ejpam-5828	321	38	leads	lead	VERB
ejpam-5828	321	39	to	to	ADP
ejpam-5828	321	40	additional	additional	ADJ
ejpam-5828	321	41	interactions	interaction	NOUN
ejpam-5828	321	42	between	between	ADP
ejpam-5828	321	43	the	the	DET
ejpam-5828	321	44	system	system	NOUN
ejpam-5828	321	45	and	and	CCONJ
ejpam-5828	321	46	its	its	PRON
ejpam-5828	321	47	surrounding	surround	VERB
ejpam-5828	321	48	environment	environment	NOUN
ejpam-5828	321	49	,	,	PUNCT
ejpam-5828	321	50	increasing	increase	VERB
ejpam-5828	321	51	the	the	DET
ejpam-5828	321	52	system	system	NOUN
ejpam-5828	321	53	’s	’s	PART
ejpam-5828	321	54	internal	internal	ADJ
ejpam-5828	321	55	energy	energy	NOUN
ejpam-5828	321	56	.	.	PUNCT
ejpam-5828	322	1	this	this	PRON
ejpam-5828	322	2	aligns	align	VERB
ejpam-5828	322	3	with	with	ADP
ejpam-5828	322	4	the	the	DET
ejpam-5828	322	5	theory	theory	NOUN
ejpam-5828	322	6	that	that	SCONJ
ejpam-5828	322	7	dissipation	dissipation	NOUN
ejpam-5828	322	8	alters	alter	VERB
ejpam-5828	322	9	the	the	DET
ejpam-5828	322	10	quantum	quantum	ADJ
ejpam-5828	322	11	energy	energy	NOUN
ejpam-5828	322	12	distribution	distribution	NOUN
ejpam-5828	322	13	and	and	CCONJ
ejpam-5828	322	14	leads	lead	VERB
ejpam-5828	322	15	to	to	ADP
ejpam-5828	322	16	the	the	DET
ejpam-5828	322	17	emergence	emergence	NOUN
ejpam-5828	322	18	of	of	ADP
ejpam-5828	322	19	new	new	ADJ
ejpam-5828	322	20	energy	energy	NOUN
ejpam-5828	322	21	states	state	NOUN
ejpam-5828	322	22	.	.	PUNCT
ejpam-5828	323	1	b.	b.	PROPN
ejpam-5828	323	2	m.	m.	PROPN
ejpam-5828	323	3	al	al	PROPN
ejpam-5828	323	4	-	-	PUNCT
ejpam-5828	323	5	khamiseh	khamiseh	PROPN
ejpam-5828	323	6	et	et	PROPN
ejpam-5828	323	7	al	al	PROPN
ejpam-5828	323	8	.	.	PUNCT
ejpam-5828	323	9	/	/	SYM
ejpam-5828	323	10	eur	eur	PROPN
ejpam-5828	323	11	.	.	PUNCT
ejpam-5828	324	1	j.	j.	PROPN
ejpam-5828	324	2	pure	pure	PROPN
ejpam-5828	324	3	appl	appl	PROPN
ejpam-5828	324	4	.	.	PROPN
ejpam-5828	324	5	math	math	PROPN
ejpam-5828	324	6	,	,	PUNCT
ejpam-5828	324	7	18	18	NUM
ejpam-5828	324	8	(	(	PUNCT
ejpam-5828	324	9	2	2	NUM
ejpam-5828	324	10	)	)	PUNCT
ejpam-5828	324	11	(	(	PUNCT
ejpam-5828	324	12	2025	2025	NUM
ejpam-5828	324	13	)	)	PUNCT
ejpam-5828	324	14	,	,	PUNCT
ejpam-5828	324	15	5828	5828	NUM
ejpam-5828	324	16	17	17	NUM
ejpam-5828	324	17	of	of	ADP
ejpam-5828	324	18	25	25	NUM
ejpam-5828	324	19	8.2	8.2	NUM
ejpam-5828	324	20	.	.	PUNCT
ejpam-5828	325	1	probability	probability	NOUN
ejpam-5828	325	2	distribution	distribution	NOUN
ejpam-5828	325	3	and	and	CCONJ
ejpam-5828	325	4	the	the	DET
ejpam-5828	325	5	effect	effect	NOUN
ejpam-5828	325	6	of	of	ADP
ejpam-5828	325	7	dissipation	dissipation	NOUN
ejpam-5828	325	8	figure	figure	NOUN
ejpam-5828	325	9	(	(	PUNCT
ejpam-5828	325	10	3	3	NUM
ejpam-5828	325	11	)	)	PUNCT
ejpam-5828	325	12	presents	present	VERB
ejpam-5828	325	13	the	the	DET
ejpam-5828	325	14	probability	probability	NOUN
ejpam-5828	325	15	distribution	distribution	NOUN
ejpam-5828	325	16	as	as	ADP
ejpam-5828	325	17	an	an	DET
ejpam-5828	325	18	indicator	indicator	NOUN
ejpam-5828	325	19	of	of	ADP
ejpam-5828	325	20	the	the	DET
ejpam-5828	325	21	quantum	quantum	NOUN
ejpam-5828	325	22	interaction	interaction	NOUN
ejpam-5828	325	23	with	with	ADP
ejpam-5828	325	24	the	the	DET
ejpam-5828	325	25	surrounding	surround	VERB
ejpam-5828	325	26	environment	environment	NOUN
ejpam-5828	325	27	.	.	PUNCT
ejpam-5828	326	1	it	it	PRON
ejpam-5828	326	2	is	be	AUX
ejpam-5828	326	3	observed	observe	VERB
ejpam-5828	326	4	that	that	SCONJ
ejpam-5828	326	5	dissipation	dissipation	NOUN
ejpam-5828	326	6	shifts	shift	NOUN
ejpam-5828	326	7	the	the	DET
ejpam-5828	326	8	probability	probability	NOUN
ejpam-5828	326	9	distribution	distribution	NOUN
ejpam-5828	326	10	towards	towards	ADP
ejpam-5828	326	11	higher	high	ADJ
ejpam-5828	326	12	energy	energy	NOUN
ejpam-5828	326	13	values	value	NOUN
ejpam-5828	326	14	,	,	PUNCT
ejpam-5828	326	15	reflecting	reflect	VERB
ejpam-5828	326	16	the	the	DET
ejpam-5828	326	17	energy	energy	NOUN
ejpam-5828	326	18	loss	loss	NOUN
ejpam-5828	326	19	induced	induce	VERB
ejpam-5828	326	20	by	by	ADP
ejpam-5828	326	21	system	system	NOUN
ejpam-5828	326	22	-	-	PUNCT
ejpam-5828	326	23	environment	environment	NOUN
ejpam-5828	326	24	interactions	interaction	NOUN
ejpam-5828	326	25	.	.	PUNCT
ejpam-5828	327	1	this	this	DET
ejpam-5828	327	2	shift	shift	NOUN
ejpam-5828	327	3	in	in	ADP
ejpam-5828	327	4	probability	probability	NOUN
ejpam-5828	327	5	distribution	distribution	NOUN
ejpam-5828	327	6	indicates	indicate	VERB
ejpam-5828	327	7	that	that	SCONJ
ejpam-5828	327	8	dissipation	dissipation	NOUN
ejpam-5828	327	9	not	not	PART
ejpam-5828	327	10	only	only	ADV
ejpam-5828	327	11	reduces	reduce	VERB
ejpam-5828	327	12	the	the	DET
ejpam-5828	327	13	total	total	ADJ
ejpam-5828	327	14	energy	energy	NOUN
ejpam-5828	327	15	of	of	ADP
ejpam-5828	327	16	the	the	DET
ejpam-5828	327	17	system	system	NOUN
ejpam-5828	327	18	but	but	CCONJ
ejpam-5828	327	19	also	also	ADV
ejpam-5828	327	20	alters	alter	VERB
ejpam-5828	327	21	the	the	DET
ejpam-5828	327	22	distribution	distribution	NOUN
ejpam-5828	327	23	of	of	ADP
ejpam-5828	327	24	quantum	quantum	ADJ
ejpam-5828	327	25	states	state	NOUN
ejpam-5828	327	26	.	.	PUNCT
ejpam-5828	328	1	this	this	PRON
ejpam-5828	328	2	can	can	AUX
ejpam-5828	328	3	be	be	AUX
ejpam-5828	328	4	explained	explain	VERB
ejpam-5828	328	5	by	by	ADP
ejpam-5828	328	6	the	the	DET
ejpam-5828	328	7	fact	fact	NOUN
ejpam-5828	328	8	that	that	SCONJ
ejpam-5828	328	9	dissipation	dissipation	NOUN
ejpam-5828	328	10	causes	cause	VERB
ejpam-5828	328	11	energy	energy	NOUN
ejpam-5828	328	12	to	to	PART
ejpam-5828	328	13	transfer	transfer	VERB
ejpam-5828	328	14	from	from	ADP
ejpam-5828	328	15	the	the	DET
ejpam-5828	328	16	system	system	NOUN
ejpam-5828	328	17	to	to	ADP
ejpam-5828	328	18	the	the	DET
ejpam-5828	328	19	surrounding	surround	VERB
ejpam-5828	328	20	environment	environment	NOUN
ejpam-5828	328	21	,	,	PUNCT
ejpam-5828	328	22	changing	change	VERB
ejpam-5828	328	23	the	the	DET
ejpam-5828	328	24	probability	probability	NOUN
ejpam-5828	328	25	distribution	distribution	NOUN
ejpam-5828	328	26	of	of	ADP
ejpam-5828	328	27	quantum	quantum	ADJ
ejpam-5828	328	28	states	state	NOUN
ejpam-5828	328	29	.	.	PUNCT
ejpam-5828	329	1	0	0	NUM
ejpam-5828	330	1	1	1	NUM
ejpam-5828	330	2	2	2	NUM
ejpam-5828	330	3	3	3	NUM
ejpam-5828	330	4	4	4	NUM
ejpam-5828	330	5	5	5	NUM
ejpam-5828	330	6	0	0	NUM
ejpam-5828	330	7	0.2	0.2	NUM
ejpam-5828	330	8	0.4	0.4	NUM
ejpam-5828	330	9	0.6	0.6	NUM
ejpam-5828	330	10	0.8	0.8	NUM
ejpam-5828	330	11	1	1	NUM
ejpam-5828	330	12	1.2	1.2	NUM
ejpam-5828	330	13	1.4	1.4	NUM
ejpam-5828	330	14	ω	ω	NOUN
ejpam-5828	330	15	/	/	SYM
ejpam-5828	330	16	ω0	ω0	PROPN
ejpam-5828	330	17	ω	ω	NOUN
ejpam-5828	330	18	0	0	PUNCT
ejpam-5828	331	1	p	p	X
ejpam-5828	331	2	i	i	NOUN
ejpam-5828	331	3	=	=	SYM
ejpam-5828	331	4	u	u	PROPN
ejpam-5828	331	5	,	,	PUNCT
ejpam-5828	331	6	e	e	PROPN
ejpam-5828	331	7	(	(	PUNCT
ejpam-5828	331	8	ω	ω	PROPN
ejpam-5828	331	9	/ω	/ω	NOUN
ejpam-5828	331	10	0	0	NUM
ejpam-5828	331	11	)	)	PUNCT
ejpam-5828	331	12	figure	figure	NOUN
ejpam-5828	331	13	3	3	NUM
ejpam-5828	331	14	:	:	PUNCT
ejpam-5828	331	15	the	the	DET
ejpam-5828	331	16	distribution	distribution	NOUN
ejpam-5828	331	17	functions	function	NOUN
ejpam-5828	331	18	for	for	ADP
ejpam-5828	331	19	the	the	DET
ejpam-5828	331	20	dissipative	dissipative	ADJ
ejpam-5828	331	21	oscillator	oscillator	NOUN
ejpam-5828	331	22	,	,	PUNCT
ejpam-5828	331	23	showing	show	VERB
ejpam-5828	331	24	the	the	DET
ejpam-5828	331	25	functions	function	NOUN
ejpam-5828	331	26	as	as	ADP
ejpam-5828	331	27	a	a	DET
ejpam-5828	331	28	function	function	NOUN
ejpam-5828	331	29	of	of	ADP
ejpam-5828	331	30	the	the	DET
ejpam-5828	331	31	rescaled	rescaled	ADJ
ejpam-5828	331	32	heat	heat	NOUN
ejpam-5828	331	33	-	-	PUNCT
ejpam-5828	331	34	bath	bath	NOUN
ejpam-5828	331	35	frequency	frequency	NOUN
ejpam-5828	331	36	.	.	PUNCT
ejpam-5828	332	1	the	the	DET
ejpam-5828	332	2	parameters	parameter	NOUN
ejpam-5828	332	3	are	be	AUX
ejpam-5828	332	4	set	set	VERB
ejpam-5828	332	5	to	to	ADP
ejpam-5828	332	6	specific	specific	ADJ
ejpam-5828	332	7	value	value	NOUN
ejpam-5828	332	8	moreover	moreover	ADV
ejpam-5828	332	9	,	,	PUNCT
ejpam-5828	332	10	figures	figure	NOUN
ejpam-5828	332	11	(	(	PUNCT
ejpam-5828	332	12	4a	4a	NUM
ejpam-5828	332	13	,	,	PUNCT
ejpam-5828	332	14	4b	4b	NOUN
ejpam-5828	332	15	,	,	PUNCT
ejpam-5828	332	16	4c	4c	NOUN
ejpam-5828	332	17	)	)	PUNCT
ejpam-5828	332	18	illustrate	illustrate	VERB
ejpam-5828	332	19	the	the	DET
ejpam-5828	332	20	effect	effect	NOUN
ejpam-5828	332	21	of	of	ADP
ejpam-5828	332	22	a	a	DET
ejpam-5828	332	23	magnetic	magnetic	ADJ
ejpam-5828	332	24	field	field	NOUN
ejpam-5828	332	25	on	on	ADP
ejpam-5828	332	26	the	the	DET
ejpam-5828	332	27	energy	energy	NOUN
ejpam-5828	332	28	distribution	distribution	NOUN
ejpam-5828	332	29	in	in	ADP
ejpam-5828	332	30	a	a	DET
ejpam-5828	332	31	three	three	NUM
ejpam-5828	332	32	dimensional	dimensional	ADJ
ejpam-5828	332	33	quantum	quantum	ADJ
ejpam-5828	332	34	oscillator	oscillator	NOUN
ejpam-5828	332	35	.	.	PUNCT
ejpam-5828	333	1	the	the	DET
ejpam-5828	333	2	interaction	interaction	NOUN
ejpam-5828	333	3	between	between	ADP
ejpam-5828	333	4	damping	damp	VERB
ejpam-5828	333	5	and	and	CCONJ
ejpam-5828	333	6	the	the	DET
ejpam-5828	333	7	magnetic	magnetic	ADJ
ejpam-5828	333	8	field	field	NOUN
ejpam-5828	333	9	leads	lead	VERB
ejpam-5828	333	10	to	to	ADP
ejpam-5828	333	11	the	the	DET
ejpam-5828	333	12	emergence	emergence	NOUN
ejpam-5828	333	13	of	of	ADP
ejpam-5828	333	14	multiple	multiple	ADJ
ejpam-5828	333	15	peaks	peak	NOUN
ejpam-5828	333	16	in	in	ADP
ejpam-5828	333	17	the	the	DET
ejpam-5828	333	18	probability	probability	NOUN
ejpam-5828	333	19	distribution	distribution	NOUN
ejpam-5828	333	20	,	,	PUNCT
ejpam-5828	333	21	indicating	indicate	VERB
ejpam-5828	333	22	resonance	resonance	NOUN
ejpam-5828	333	23	effects	effect	NOUN
ejpam-5828	333	24	caused	cause	VERB
ejpam-5828	333	25	by	by	ADP
ejpam-5828	333	26	the	the	DET
ejpam-5828	333	27	interplay	interplay	NOUN
ejpam-5828	333	28	between	between	ADP
ejpam-5828	333	29	quantum	quantum	ADJ
ejpam-5828	333	30	energy	energy	NOUN
ejpam-5828	333	31	levels	level	NOUN
ejpam-5828	333	32	and	and	CCONJ
ejpam-5828	333	33	dissipation	dissipation	NOUN
ejpam-5828	333	34	.	.	PUNCT
ejpam-5828	334	1	the	the	DET
ejpam-5828	334	2	appearance	appearance	NOUN
ejpam-5828	334	3	of	of	ADP
ejpam-5828	334	4	multiple	multiple	ADJ
ejpam-5828	334	5	peaks	peak	NOUN
ejpam-5828	334	6	in	in	ADP
ejpam-5828	334	7	the	the	DET
ejpam-5828	334	8	probability	probability	NOUN
ejpam-5828	334	9	distribution	distribution	NOUN
ejpam-5828	334	10	reflects	reflect	VERB
ejpam-5828	334	11	resonance	resonance	NOUN
ejpam-5828	334	12	effects	effect	NOUN
ejpam-5828	334	13	that	that	PRON
ejpam-5828	334	14	occur	occur	VERB
ejpam-5828	334	15	when	when	SCONJ
ejpam-5828	334	16	the	the	DET
ejpam-5828	334	17	system	system	NOUN
ejpam-5828	334	18	’s	’s	PART
ejpam-5828	334	19	frequencies	frequency	NOUN
ejpam-5828	334	20	match	match	VERB
ejpam-5828	334	21	those	those	PRON
ejpam-5828	334	22	of	of	ADP
ejpam-5828	334	23	the	the	DET
ejpam-5828	334	24	surrounding	surround	VERB
ejpam-5828	334	25	environment	environment	NOUN
ejpam-5828	334	26	.	.	PUNCT
ejpam-5828	335	1	this	this	PRON
ejpam-5828	335	2	suggests	suggest	VERB
ejpam-5828	335	3	that	that	SCONJ
ejpam-5828	335	4	dissipation	dissipation	NOUN
ejpam-5828	335	5	and	and	CCONJ
ejpam-5828	335	6	the	the	DET
ejpam-5828	335	7	magnetic	magnetic	ADJ
ejpam-5828	335	8	field	field	NOUN
ejpam-5828	335	9	work	work	VERB
ejpam-5828	335	10	together	together	ADV
ejpam-5828	335	11	to	to	PART
ejpam-5828	335	12	modify	modify	VERB
ejpam-5828	335	13	the	the	DET
ejpam-5828	335	14	quantum	quantum	ADJ
ejpam-5828	335	15	energy	energy	NOUN
ejpam-5828	335	16	distribution	distribution	NOUN
ejpam-5828	335	17	,	,	PUNCT
ejpam-5828	335	18	leading	lead	VERB
ejpam-5828	335	19	to	to	ADP
ejpam-5828	335	20	the	the	DET
ejpam-5828	335	21	emergence	emergence	NOUN
ejpam-5828	335	22	of	of	ADP
ejpam-5828	335	23	new	new	ADJ
ejpam-5828	335	24	energy	energy	NOUN
ejpam-5828	335	25	states	state	NOUN
ejpam-5828	335	26	and	and	CCONJ
ejpam-5828	335	27	changes	change	NOUN
ejpam-5828	335	28	in	in	ADP
ejpam-5828	335	29	the	the	DET
ejpam-5828	335	30	system	system	NOUN
ejpam-5828	335	31	’s	’s	PART
ejpam-5828	335	32	dynamics	dynamic	NOUN
ejpam-5828	335	33	.	.	PUNCT
ejpam-5828	336	1	9	9	X
ejpam-5828	336	2	.	.	X
ejpam-5828	336	3	future	future	ADJ
ejpam-5828	336	4	directions	direction	NOUN
ejpam-5828	336	5	in	in	ADP
ejpam-5828	336	6	the	the	DET
ejpam-5828	336	7	study	study	NOUN
ejpam-5828	336	8	of	of	ADP
ejpam-5828	336	9	dissipative	dissipative	ADJ
ejpam-5828	336	10	forces	force	NOUN
ejpam-5828	336	11	in	in	ADP
ejpam-5828	336	12	lagrangian	lagrangian	ADJ
ejpam-5828	336	13	mechanics	mechanic	NOUN
ejpam-5828	336	14	in	in	ADP
ejpam-5828	336	15	future	future	ADJ
ejpam-5828	336	16	studies	study	NOUN
ejpam-5828	336	17	,	,	PUNCT
ejpam-5828	336	18	this	this	DET
ejpam-5828	336	19	model	model	NOUN
ejpam-5828	336	20	can	can	AUX
ejpam-5828	336	21	be	be	AUX
ejpam-5828	336	22	expanded	expand	VERB
ejpam-5828	336	23	to	to	ADP
ejpam-5828	336	24	three	three	NUM
ejpam-5828	336	25	dimensions	dimension	NOUN
ejpam-5828	336	26	to	to	PART
ejpam-5828	336	27	investigate	investigate	VERB
ejpam-5828	336	28	the	the	DET
ejpam-5828	336	29	impact	impact	NOUN
ejpam-5828	336	30	of	of	ADP
ejpam-5828	336	31	the	the	DET
ejpam-5828	336	32	additional	additional	ADJ
ejpam-5828	336	33	dimension	dimension	NOUN
ejpam-5828	336	34	on	on	ADP
ejpam-5828	336	35	the	the	DET
ejpam-5828	336	36	dynamics	dynamic	NOUN
ejpam-5828	336	37	of	of	ADP
ejpam-5828	336	38	the	the	DET
ejpam-5828	336	39	dissipative	dissipative	ADJ
ejpam-5828	336	40	system	system	NOUN
ejpam-5828	336	41	.	.	PUNCT
ejpam-5828	337	1	furthermore	furthermore	ADV
ejpam-5828	337	2	,	,	PUNCT
ejpam-5828	337	3	a	a	DET
ejpam-5828	337	4	coupling	coupling	NOUN
ejpam-5828	337	5	term	term	NOUN
ejpam-5828	337	6	can	can	AUX
ejpam-5828	337	7	be	be	AUX
ejpam-5828	337	8	introduced	introduce	VERB
ejpam-5828	337	9	to	to	PART
ejpam-5828	337	10	analyze	analyze	VERB
ejpam-5828	337	11	its	its	PRON
ejpam-5828	337	12	effect	effect	NOUN
ejpam-5828	337	13	on	on	ADP
ejpam-5828	337	14	the	the	DET
ejpam-5828	337	15	system	system	NOUN
ejpam-5828	337	16	,	,	PUNCT
ejpam-5828	337	17	b.	b.	PROPN
ejpam-5828	337	18	m.	m.	PROPN
ejpam-5828	337	19	al	al	PROPN
ejpam-5828	337	20	-	-	PUNCT
ejpam-5828	337	21	khamiseh	khamiseh	PROPN
ejpam-5828	337	22	et	et	PROPN
ejpam-5828	337	23	al	al	PROPN
ejpam-5828	337	24	.	.	PUNCT
ejpam-5828	337	25	/	/	SYM
ejpam-5828	337	26	eur	eur	PROPN
ejpam-5828	337	27	.	.	PUNCT
ejpam-5828	338	1	j.	j.	PROPN
ejpam-5828	338	2	pure	pure	PROPN
ejpam-5828	338	3	appl	appl	PROPN
ejpam-5828	338	4	.	.	PROPN
ejpam-5828	338	5	math	math	PROPN
ejpam-5828	338	6	,	,	PUNCT
ejpam-5828	338	7	18	18	NUM
ejpam-5828	338	8	(	(	PUNCT
ejpam-5828	338	9	2	2	NUM
ejpam-5828	338	10	)	)	PUNCT
ejpam-5828	338	11	(	(	PUNCT
ejpam-5828	338	12	2025	2025	NUM
ejpam-5828	338	13	)	)	PUNCT
ejpam-5828	338	14	,	,	PUNCT
ejpam-5828	338	15	5828	5828	NUM
ejpam-5828	338	16	18	18	NUM
ejpam-5828	338	17	of	of	ADP
ejpam-5828	338	18	25	25	NUM
ejpam-5828	338	19	0	0	NUM
ejpam-5828	338	20	2	2	NUM
ejpam-5828	338	21	4	4	NUM
ejpam-5828	338	22	6	6	NUM
ejpam-5828	338	23	8	8	NUM
ejpam-5828	338	24	0	0	NUM
ejpam-5828	338	25	0.2	0.2	NUM
ejpam-5828	338	26	0.4	0.4	NUM
ejpam-5828	338	27	0.6	0.6	NUM
ejpam-5828	338	28	0.8	0.8	NUM
ejpam-5828	338	29	1	1	NUM
ejpam-5828	338	30	ω	ω	NUM
ejpam-5828	338	31	/	/	SYM
ejpam-5828	338	32	ω0	ω0	PROPN
ejpam-5828	338	33	ω	ω	NOUN
ejpam-5828	338	34	0	0	PUNCT
ejpam-5828	339	1	p	p	X
ejpam-5828	339	2	i	i	NOUN
ejpam-5828	339	3	=	=	SYM
ejpam-5828	339	4	u	u	PROPN
ejpam-5828	339	5	,	,	PUNCT
ejpam-5828	339	6	e	e	PROPN
ejpam-5828	339	7	(	(	PUNCT
ejpam-5828	339	8	ω	ω	PROPN
ejpam-5828	339	9	/ω	/ω	NOUN
ejpam-5828	339	10	0	0	NUM
ejpam-5828	339	11	)	)	PUNCT
ejpam-5828	339	12	figure	figure	NOUN
ejpam-5828	339	13	4	4	NUM
ejpam-5828	339	14	:	:	PUNCT
ejpam-5828	339	15	wc	wc	PROPN
ejpam-5828	339	16	=	=	PROPN
ejpam-5828	339	17	0.5w0	0.5w0	NUM
ejpam-5828	339	18	0	0	NUM
ejpam-5828	339	19	2	2	NUM
ejpam-5828	339	20	4	4	NUM
ejpam-5828	339	21	6	6	NUM
ejpam-5828	339	22	8	8	NUM
ejpam-5828	339	23	0	0	NUM
ejpam-5828	339	24	0.5	0.5	NUM
ejpam-5828	339	25	1	1	NUM
ejpam-5828	339	26	1.5	1.5	NUM
ejpam-5828	339	27	2	2	NUM
ejpam-5828	339	28	2.5	2.5	NUM
ejpam-5828	339	29	3	3	NUM
ejpam-5828	339	30	3.5	3.5	NUM
ejpam-5828	339	31	ω	ω	NOUN
ejpam-5828	339	32	/	/	SYM
ejpam-5828	339	33	ω0	ω0	PROPN
ejpam-5828	339	34	ω	ω	NOUN
ejpam-5828	339	35	0	0	PUNCT
ejpam-5828	340	1	p	p	X
ejpam-5828	340	2	i	i	NOUN
ejpam-5828	340	3	=	=	SYM
ejpam-5828	340	4	u	u	PROPN
ejpam-5828	340	5	,	,	PUNCT
ejpam-5828	340	6	e	e	PROPN
ejpam-5828	340	7	(	(	PUNCT
ejpam-5828	340	8	ω	ω	PROPN
ejpam-5828	340	9	/ω	/ω	NOUN
ejpam-5828	340	10	0	0	NUM
ejpam-5828	340	11	)	)	PUNCT
ejpam-5828	340	12	figure	figure	NOUN
ejpam-5828	340	13	5	5	NUM
ejpam-5828	340	14	:	:	PUNCT
ejpam-5828	340	15	wc	wc	PROPN
ejpam-5828	340	16	=	=	PROPN
ejpam-5828	340	17	0.5w0	0.5w0	NUM
ejpam-5828	340	18	particularly	particularly	ADV
ejpam-5828	340	19	in	in	ADP
ejpam-5828	340	20	cases	case	NOUN
ejpam-5828	340	21	where	where	SCONJ
ejpam-5828	340	22	the	the	DET
ejpam-5828	340	23	anisotropy	anisotropy	NOUN
ejpam-5828	340	24	is	be	AUX
ejpam-5828	340	25	strong	strong	ADJ
ejpam-5828	340	26	or	or	CCONJ
ejpam-5828	340	27	when	when	SCONJ
ejpam-5828	340	28	there	there	PRON
ejpam-5828	340	29	are	be	VERB
ejpam-5828	340	30	additional	additional	ADJ
ejpam-5828	340	31	interactions	interaction	NOUN
ejpam-5828	340	32	between	between	ADP
ejpam-5828	340	33	the	the	DET
ejpam-5828	340	34	dimensions	dimension	NOUN
ejpam-5828	340	35	.	.	PUNCT
ejpam-5828	341	1	while	while	SCONJ
ejpam-5828	341	2	the	the	DET
ejpam-5828	341	3	current	current	ADJ
ejpam-5828	341	4	study	study	NOUN
ejpam-5828	341	5	provides	provide	VERB
ejpam-5828	341	6	a	a	DET
ejpam-5828	341	7	comprehensive	comprehensive	ADJ
ejpam-5828	341	8	framework	framework	NOUN
ejpam-5828	341	9	for	for	ADP
ejpam-5828	341	10	understanding	understand	VERB
ejpam-5828	341	11	the	the	DET
ejpam-5828	341	12	two	two	NUM
ejpam-5828	341	13	dimensional	dimensional	ADJ
ejpam-5828	341	14	anisotropic	anisotropic	NOUN
ejpam-5828	341	15	harmonic	harmonic	ADJ
ejpam-5828	341	16	oscillator	oscillator	NOUN
ejpam-5828	341	17	under	under	ADP
ejpam-5828	341	18	dissipative	dissipative	ADJ
ejpam-5828	341	19	effects	effect	NOUN
ejpam-5828	341	20	,	,	PUNCT
ejpam-5828	341	21	there	there	PRON
ejpam-5828	341	22	remain	remain	VERB
ejpam-5828	341	23	opportunities	opportunity	NOUN
ejpam-5828	341	24	for	for	ADP
ejpam-5828	341	25	further	further	ADJ
ejpam-5828	341	26	exploration	exploration	NOUN
ejpam-5828	341	27	.	.	PUNCT
ejpam-5828	342	1	one	one	NUM
ejpam-5828	342	2	potential	potential	ADJ
ejpam-5828	342	3	avenue	avenue	NOUN
ejpam-5828	342	4	is	be	AUX
ejpam-5828	342	5	the	the	DET
ejpam-5828	342	6	extension	extension	NOUN
ejpam-5828	342	7	of	of	ADP
ejpam-5828	342	8	this	this	DET
ejpam-5828	342	9	model	model	NOUN
ejpam-5828	342	10	to	to	ADP
ejpam-5828	342	11	three	three	NUM
ejpam-5828	342	12	dimensions	dimension	NOUN
ejpam-5828	342	13	,	,	PUNCT
ejpam-5828	342	14	which	which	PRON
ejpam-5828	342	15	could	could	AUX
ejpam-5828	342	16	offer	offer	VERB
ejpam-5828	342	17	deeper	deep	ADJ
ejpam-5828	342	18	insights	insight	NOUN
ejpam-5828	342	19	into	into	ADP
ejpam-5828	342	20	the	the	DET
ejpam-5828	342	21	dynamics	dynamic	NOUN
ejpam-5828	342	22	of	of	ADP
ejpam-5828	342	23	dissipative	dissipative	ADJ
ejpam-5828	342	24	systems	system	NOUN
ejpam-5828	342	25	.	.	PUNCT
ejpam-5828	343	1	additionally	additionally	ADV
ejpam-5828	343	2	,	,	PUNCT
ejpam-5828	343	3	the	the	DET
ejpam-5828	343	4	inclusion	inclusion	NOUN
ejpam-5828	343	5	of	of	ADP
ejpam-5828	343	6	coupling	couple	VERB
ejpam-5828	343	7	terms	term	NOUN
ejpam-5828	343	8	,	,	PUNCT
ejpam-5828	343	9	particularly	particularly	ADV
ejpam-5828	343	10	in	in	ADP
ejpam-5828	343	11	the	the	DET
ejpam-5828	343	12	context	context	NOUN
ejpam-5828	343	13	of	of	ADP
ejpam-5828	343	14	anisotropic	anisotropic	NOUN
ejpam-5828	343	15	behavior	behavior	NOUN
ejpam-5828	343	16	,	,	PUNCT
ejpam-5828	343	17	represents	represent	VERB
ejpam-5828	343	18	an	an	DET
ejpam-5828	343	19	important	important	ADJ
ejpam-5828	343	20	area	area	NOUN
ejpam-5828	343	21	for	for	ADP
ejpam-5828	343	22	future	future	ADJ
ejpam-5828	343	23	investigation	investigation	NOUN
ejpam-5828	343	24	.	.	PUNCT
ejpam-5828	344	1	although	although	SCONJ
ejpam-5828	344	2	coupling	couple	VERB
ejpam-5828	344	3	terms	term	NOUN
ejpam-5828	344	4	were	be	AUX
ejpam-5828	344	5	excluded	exclude	VERB
ejpam-5828	344	6	in	in	ADP
ejpam-5828	344	7	the	the	DET
ejpam-5828	344	8	present	present	ADJ
ejpam-5828	344	9	work	work	NOUN
ejpam-5828	344	10	under	under	ADP
ejpam-5828	344	11	the	the	DET
ejpam-5828	344	12	assumption	assumption	NOUN
ejpam-5828	344	13	of	of	ADP
ejpam-5828	344	14	weak	weak	ADJ
ejpam-5828	344	15	anisotropy	anisotropy	NOUN
ejpam-5828	344	16	,	,	PUNCT
ejpam-5828	344	17	future	future	ADJ
ejpam-5828	344	18	studies	study	NOUN
ejpam-5828	344	19	could	could	AUX
ejpam-5828	344	20	examine	examine	VERB
ejpam-5828	344	21	their	their	PRON
ejpam-5828	344	22	impact	impact	NOUN
ejpam-5828	344	23	under	under	ADP
ejpam-5828	344	24	different	different	ADJ
ejpam-5828	344	25	conditions	condition	NOUN
ejpam-5828	344	26	and	and	CCONJ
ejpam-5828	344	27	assess	assess	VERB
ejpam-5828	344	28	their	their	PRON
ejpam-5828	344	29	role	role	NOUN
ejpam-5828	344	30	in	in	ADP
ejpam-5828	344	31	complex	complex	ADJ
ejpam-5828	344	32	dissipative	dissipative	ADJ
ejpam-5828	344	33	systems	system	NOUN
ejpam-5828	344	34	.	.	PUNCT
ejpam-5828	345	1	such	such	ADJ
ejpam-5828	345	2	developments	development	NOUN
ejpam-5828	345	3	would	would	AUX
ejpam-5828	345	4	enrich	enrich	VERB
ejpam-5828	345	5	the	the	DET
ejpam-5828	345	6	theoretical	theoretical	ADJ
ejpam-5828	345	7	understanding	understanding	NOUN
ejpam-5828	345	8	and	and	CCONJ
ejpam-5828	345	9	practical	practical	ADJ
ejpam-5828	345	10	applicability	applicability	NOUN
ejpam-5828	345	11	of	of	ADP
ejpam-5828	345	12	the	the	DET
ejpam-5828	345	13	proposed	propose	VERB
ejpam-5828	345	14	framework	framework	NOUN
ejpam-5828	345	15	.	.	PUNCT
ejpam-5828	346	1	b.	b.	PROPN
ejpam-5828	346	2	m.	m.	PROPN
ejpam-5828	346	3	al	al	PROPN
ejpam-5828	346	4	-	-	PUNCT
ejpam-5828	346	5	khamiseh	khamiseh	PROPN
ejpam-5828	346	6	et	et	PROPN
ejpam-5828	346	7	al	al	PROPN
ejpam-5828	346	8	.	.	PUNCT
ejpam-5828	346	9	/	/	SYM
ejpam-5828	346	10	eur	eur	PROPN
ejpam-5828	346	11	.	.	PUNCT
ejpam-5828	347	1	j.	j.	PROPN
ejpam-5828	347	2	pure	pure	PROPN
ejpam-5828	347	3	appl	appl	PROPN
ejpam-5828	347	4	.	.	PROPN
ejpam-5828	347	5	math	math	PROPN
ejpam-5828	347	6	,	,	PUNCT
ejpam-5828	347	7	18	18	NUM
ejpam-5828	347	8	(	(	PUNCT
ejpam-5828	347	9	2	2	NUM
ejpam-5828	347	10	)	)	PUNCT
ejpam-5828	347	11	(	(	PUNCT
ejpam-5828	347	12	2025	2025	NUM
ejpam-5828	347	13	)	)	PUNCT
ejpam-5828	347	14	,	,	PUNCT
ejpam-5828	347	15	5828	5828	NUM
ejpam-5828	347	16	19	19	NUM
ejpam-5828	347	17	of	of	ADP
ejpam-5828	347	18	25	25	NUM
ejpam-5828	347	19	10	10	NUM
ejpam-5828	347	20	.	.	PUNCT
ejpam-5828	348	1	current	current	ADJ
ejpam-5828	348	2	vs.	vs.	ADP
ejpam-5828	348	3	previous	previous	ADJ
ejpam-5828	348	4	research	research	NOUN
ejpam-5828	348	5	on	on	ADP
ejpam-5828	348	6	quantizing	quantize	VERB
ejpam-5828	348	7	dissipative	dissipative	NOUN
ejpam-5828	348	8	this	this	DET
ejpam-5828	348	9	study	study	NOUN
ejpam-5828	348	10	focuses	focus	VERB
ejpam-5828	348	11	on	on	ADP
ejpam-5828	348	12	the	the	DET
ejpam-5828	348	13	quantization	quantization	NOUN
ejpam-5828	348	14	of	of	ADP
ejpam-5828	348	15	dissipative	dissipative	ADJ
ejpam-5828	348	16	mechanical	mechanical	ADJ
ejpam-5828	348	17	systems	system	NOUN
ejpam-5828	348	18	using	use	VERB
ejpam-5828	348	19	methods	method	NOUN
ejpam-5828	348	20	such	such	ADJ
ejpam-5828	348	21	as	as	ADP
ejpam-5828	348	22	the	the	DET
ejpam-5828	348	23	wkb	wkb	NOUN
ejpam-5828	348	24	approximation	approximation	NOUN
ejpam-5828	348	25	,	,	PUNCT
ejpam-5828	348	26	the	the	DET
ejpam-5828	348	27	hamilton	hamilton	PROPN
ejpam-5828	348	28	-	-	PUNCT
ejpam-5828	348	29	jacobi	jacobi	PROPN
ejpam-5828	348	30	equation	equation	NOUN
ejpam-5828	348	31	,	,	PUNCT
ejpam-5828	348	32	the	the	DET
ejpam-5828	348	33	staeckel	staeckel	ADJ
ejpam-5828	348	34	boundary	boundary	ADJ
ejpam-5828	348	35	conditions	condition	NOUN
ejpam-5828	348	36	,	,	PUNCT
ejpam-5828	348	37	and	and	CCONJ
ejpam-5828	348	38	canonical	canonical	ADJ
ejpam-5828	348	39	quantization	quantization	NOUN
ejpam-5828	348	40	.	.	PUNCT
ejpam-5828	349	1	the	the	DET
ejpam-5828	349	2	following	follow	VERB
ejpam-5828	349	3	comparison	comparison	NOUN
ejpam-5828	349	4	highlights	highlight	VERB
ejpam-5828	349	5	the	the	DET
ejpam-5828	349	6	primary	primary	ADJ
ejpam-5828	349	7	differences	difference	NOUN
ejpam-5828	349	8	between	between	ADP
ejpam-5828	349	9	this	this	DET
ejpam-5828	349	10	study	study	NOUN
ejpam-5828	349	11	and	and	CCONJ
ejpam-5828	349	12	previous	previous	ADJ
ejpam-5828	349	13	research	research	NOUN
ejpam-5828	349	14	:	:	PUNCT
ejpam-5828	349	15	canonical	canonical	ADJ
ejpam-5828	349	16	quantization	quantization	NOUN
ejpam-5828	349	17	:	:	PUNCT
ejpam-5828	349	18	previous	previous	ADJ
ejpam-5828	349	19	studies	study	NOUN
ejpam-5828	349	20	,	,	PUNCT
ejpam-5828	349	21	including	include	VERB
ejpam-5828	349	22	those	those	PRON
ejpam-5828	349	23	by	by	ADP
ejpam-5828	349	24	dekker	dekker	PROPN
ejpam-5828	349	25	,	,	PUNCT
ejpam-5828	349	26	suzuki	suzuki	PROPN
ejpam-5828	349	27	,	,	PUNCT
ejpam-5828	349	28	and	and	CCONJ
ejpam-5828	349	29	majima	majima	PROPN
ejpam-5828	349	30	,	,	PUNCT
ejpam-5828	349	31	focused	focus	VERB
ejpam-5828	349	32	on	on	ADP
ejpam-5828	349	33	modeling	model	VERB
ejpam-5828	349	34	time	time	NOUN
ejpam-5828	349	35	-	-	PUNCT
ejpam-5828	349	36	dependent	dependent	ADJ
ejpam-5828	349	37	damping	damp	VERB
ejpam-5828	349	38	variables	variable	NOUN
ejpam-5828	349	39	.	.	PUNCT
ejpam-5828	350	1	in	in	ADP
ejpam-5828	350	2	contrast	contrast	NOUN
ejpam-5828	350	3	,	,	PUNCT
ejpam-5828	350	4	this	this	DET
ejpam-5828	350	5	study	study	NOUN
ejpam-5828	350	6	combines	combine	VERB
ejpam-5828	350	7	canonical	canonical	ADJ
ejpam-5828	350	8	quantization	quantization	NOUN
ejpam-5828	350	9	with	with	ADP
ejpam-5828	350	10	the	the	DET
ejpam-5828	350	11	wkb	wkb	NOUN
ejpam-5828	350	12	approximation	approximation	NOUN
ejpam-5828	350	13	,	,	PUNCT
ejpam-5828	350	14	resulting	result	VERB
ejpam-5828	350	15	in	in	ADP
ejpam-5828	350	16	a	a	DET
ejpam-5828	350	17	more	more	ADV
ejpam-5828	350	18	comprehensive	comprehensive	ADJ
ejpam-5828	350	19	and	and	CCONJ
ejpam-5828	350	20	accurate	accurate	ADJ
ejpam-5828	350	21	quantum	quantum	NOUN
ejpam-5828	350	22	model	model	NOUN
ejpam-5828	350	23	for	for	ADP
ejpam-5828	350	24	dissipative	dissipative	ADJ
ejpam-5828	350	25	systems	system	NOUN
ejpam-5828	350	26	.	.	PUNCT
ejpam-5828	351	1	non	non	ADJ
ejpam-5828	351	2	-	-	ADJ
ejpam-5828	351	3	conservative	conservative	ADJ
ejpam-5828	351	4	systems	system	NOUN
ejpam-5828	351	5	:	:	PUNCT
ejpam-5828	351	6	riewe	riewe	PROPN
ejpam-5828	351	7	’s	’s	PART
ejpam-5828	351	8	work	work	NOUN
ejpam-5828	351	9	with	with	ADP
ejpam-5828	351	10	fractional	fractional	ADJ
ejpam-5828	351	11	calculus	calculus	NOUN
ejpam-5828	351	12	helped	helped	AUX
ejpam-5828	351	13	develop	develop	VERB
ejpam-5828	351	14	new	new	ADJ
ejpam-5828	351	15	models	model	NOUN
ejpam-5828	351	16	for	for	ADP
ejpam-5828	351	17	non	non	X
ejpam-5828	351	18	conservative	conservative	ADJ
ejpam-5828	351	19	systems	system	NOUN
ejpam-5828	351	20	.	.	PUNCT
ejpam-5828	352	1	this	this	DET
ejpam-5828	352	2	study	study	NOUN
ejpam-5828	352	3	takes	take	VERB
ejpam-5828	352	4	these	these	DET
ejpam-5828	352	5	ideas	idea	NOUN
ejpam-5828	352	6	further	far	ADV
ejpam-5828	352	7	by	by	ADP
ejpam-5828	352	8	applying	apply	VERB
ejpam-5828	352	9	them	they	PRON
ejpam-5828	352	10	to	to	ADP
ejpam-5828	352	11	quantum	quantum	ADJ
ejpam-5828	352	12	dissipative	dissipative	NOUN
ejpam-5828	352	13	systems	system	NOUN
ejpam-5828	352	14	using	use	VERB
ejpam-5828	352	15	modern	modern	ADJ
ejpam-5828	352	16	techniques	technique	NOUN
ejpam-5828	352	17	,	,	PUNCT
ejpam-5828	352	18	such	such	ADJ
ejpam-5828	352	19	as	as	ADP
ejpam-5828	352	20	the	the	DET
ejpam-5828	352	21	hamilton	hamilton	PROPN
ejpam-5828	352	22	-	-	PUNCT
ejpam-5828	352	23	jacobi	jacobi	PROPN
ejpam-5828	352	24	equation	equation	NOUN
ejpam-5828	352	25	,	,	PUNCT
ejpam-5828	352	26	to	to	PART
ejpam-5828	352	27	provide	provide	VERB
ejpam-5828	352	28	a	a	DET
ejpam-5828	352	29	clearer	clear	ADJ
ejpam-5828	352	30	and	and	CCONJ
ejpam-5828	352	31	more	more	ADV
ejpam-5828	352	32	accurate	accurate	ADJ
ejpam-5828	352	33	quantum	quantum	ADJ
ejpam-5828	352	34	description	description	NOUN
ejpam-5828	352	35	.	.	PUNCT
ejpam-5828	353	1	wkb	wkb	PROPN
ejpam-5828	353	2	approximation	approximation	NOUN
ejpam-5828	353	3	:	:	PUNCT
ejpam-5828	353	4	the	the	DET
ejpam-5828	353	5	wkb	wkb	PROPN
ejpam-5828	353	6	approximation	approximation	NOUN
ejpam-5828	353	7	has	have	AUX
ejpam-5828	353	8	been	be	AUX
ejpam-5828	353	9	widely	widely	ADV
ejpam-5828	353	10	used	use	VERB
ejpam-5828	353	11	in	in	ADP
ejpam-5828	353	12	previous	previous	ADJ
ejpam-5828	353	13	studies	study	NOUN
ejpam-5828	353	14	to	to	PART
ejpam-5828	353	15	analyze	analyze	VERB
ejpam-5828	353	16	dissipative	dissipative	ADJ
ejpam-5828	353	17	systems	system	NOUN
ejpam-5828	353	18	.	.	PUNCT
ejpam-5828	354	1	this	this	DET
ejpam-5828	354	2	study	study	NOUN
ejpam-5828	354	3	extends	extend	VERB
ejpam-5828	354	4	its	its	PRON
ejpam-5828	354	5	use	use	NOUN
ejpam-5828	354	6	to	to	ADP
ejpam-5828	354	7	quantum	quantum	ADJ
ejpam-5828	354	8	dissipative	dissipative	NOUN
ejpam-5828	354	9	systems	system	NOUN
ejpam-5828	354	10	,	,	PUNCT
ejpam-5828	354	11	improving	improve	VERB
ejpam-5828	354	12	the	the	DET
ejpam-5828	354	13	precision	precision	NOUN
ejpam-5828	354	14	of	of	ADP
ejpam-5828	354	15	energy	energy	NOUN
ejpam-5828	354	16	level	level	NOUN
ejpam-5828	354	17	predictions	prediction	NOUN
ejpam-5828	354	18	and	and	CCONJ
ejpam-5828	354	19	the	the	DET
ejpam-5828	354	20	accuracy	accuracy	NOUN
ejpam-5828	354	21	of	of	ADP
ejpam-5828	354	22	state	state	NOUN
ejpam-5828	354	23	quantization	quantization	NOUN
ejpam-5828	354	24	.	.	PUNCT
ejpam-5828	355	1	creation	creation	NOUN
ejpam-5828	355	2	and	and	CCONJ
ejpam-5828	355	3	annihilation	annihilation	NOUN
ejpam-5828	355	4	operators	operator	NOUN
ejpam-5828	355	5	:	:	PUNCT
ejpam-5828	355	6	the	the	DET
ejpam-5828	355	7	integration	integration	NOUN
ejpam-5828	355	8	of	of	ADP
ejpam-5828	355	9	dissipation	dissipation	NOUN
ejpam-5828	355	10	into	into	ADP
ejpam-5828	355	11	the	the	DET
ejpam-5828	355	12	quantum	quantum	NOUN
ejpam-5828	355	13	framework	framework	NOUN
ejpam-5828	355	14	through	through	ADP
ejpam-5828	355	15	the	the	DET
ejpam-5828	355	16	use	use	NOUN
ejpam-5828	355	17	of	of	ADP
ejpam-5828	355	18	creation	creation	NOUN
ejpam-5828	355	19	and	and	CCONJ
ejpam-5828	355	20	annihilation	annihilation	NOUN
ejpam-5828	355	21	operators	operator	NOUN
ejpam-5828	355	22	results	result	VERB
ejpam-5828	355	23	in	in	ADP
ejpam-5828	355	24	more	more	ADV
ejpam-5828	355	25	accurate	accurate	ADJ
ejpam-5828	355	26	predictions	prediction	NOUN
ejpam-5828	355	27	for	for	ADP
ejpam-5828	355	28	energy	energy	NOUN
ejpam-5828	355	29	levels	level	NOUN
ejpam-5828	355	30	and	and	CCONJ
ejpam-5828	355	31	quantum	quantum	NOUN
ejpam-5828	355	32	states	state	NOUN
ejpam-5828	355	33	.	.	PUNCT
ejpam-5828	356	1	by	by	ADP
ejpam-5828	356	2	explicitly	explicitly	ADV
ejpam-5828	356	3	incorporating	incorporate	VERB
ejpam-5828	356	4	dissipative	dissipative	ADJ
ejpam-5828	356	5	effects	effect	NOUN
ejpam-5828	356	6	—	—	PUNCT
ejpam-5828	356	7	such	such	ADJ
ejpam-5828	356	8	as	as	ADP
ejpam-5828	356	9	energy	energy	NOUN
ejpam-5828	356	10	loss	loss	NOUN
ejpam-5828	356	11	due	due	ADJ
ejpam-5828	356	12	to	to	ADP
ejpam-5828	356	13	damping	damp	VERB
ejpam-5828	356	14	or	or	CCONJ
ejpam-5828	356	15	environmental	environmental	ADJ
ejpam-5828	356	16	interactions	interaction	NOUN
ejpam-5828	356	17	—	—	PUNCT
ejpam-5828	356	18	the	the	DET
ejpam-5828	356	19	model	model	NOUN
ejpam-5828	356	20	becomes	become	VERB
ejpam-5828	356	21	more	more	ADV
ejpam-5828	356	22	realistic	realistic	ADJ
ejpam-5828	356	23	,	,	PUNCT
ejpam-5828	356	24	closely	closely	ADV
ejpam-5828	356	25	reflecting	reflect	VERB
ejpam-5828	356	26	the	the	DET
ejpam-5828	356	27	physical	physical	ADJ
ejpam-5828	356	28	behavior	behavior	NOUN
ejpam-5828	356	29	of	of	ADP
ejpam-5828	356	30	the	the	DET
ejpam-5828	356	31	system	system	NOUN
ejpam-5828	356	32	.	.	PUNCT
ejpam-5828	357	1	this	this	DET
ejpam-5828	357	2	refinement	refinement	NOUN
ejpam-5828	357	3	ensures	ensure	VERB
ejpam-5828	357	4	that	that	SCONJ
ejpam-5828	357	5	the	the	DET
ejpam-5828	357	6	derived	derived	ADJ
ejpam-5828	357	7	energy	energy	NOUN
ejpam-5828	357	8	levels	level	NOUN
ejpam-5828	357	9	and	and	CCONJ
ejpam-5828	357	10	wave	wave	NOUN
ejpam-5828	357	11	functions	function	NOUN
ejpam-5828	357	12	are	be	AUX
ejpam-5828	357	13	more	more	ADV
ejpam-5828	357	14	precise	precise	ADJ
ejpam-5828	357	15	,	,	PUNCT
ejpam-5828	357	16	as	as	SCONJ
ejpam-5828	357	17	they	they	PRON
ejpam-5828	357	18	account	account	VERB
ejpam-5828	357	19	for	for	ADP
ejpam-5828	357	20	the	the	DET
ejpam-5828	357	21	impact	impact	NOUN
ejpam-5828	357	22	of	of	ADP
ejpam-5828	357	23	dissipation	dissipation	NOUN
ejpam-5828	357	24	on	on	ADP
ejpam-5828	357	25	the	the	DET
ejpam-5828	357	26	system	system	NOUN
ejpam-5828	357	27	’s	’s	PART
ejpam-5828	357	28	dynamics	dynamic	NOUN
ejpam-5828	357	29	.	.	PUNCT
ejpam-5828	358	1	as	as	ADP
ejpam-5828	358	2	a	a	DET
ejpam-5828	358	3	result	result	NOUN
ejpam-5828	358	4	,	,	PUNCT
ejpam-5828	358	5	the	the	DET
ejpam-5828	358	6	theoretical	theoretical	ADJ
ejpam-5828	358	7	predictions	prediction	NOUN
ejpam-5828	358	8	align	align	VERB
ejpam-5828	358	9	more	more	ADV
ejpam-5828	358	10	closely	closely	ADV
ejpam-5828	358	11	with	with	ADP
ejpam-5828	358	12	experimental	experimental	ADJ
ejpam-5828	358	13	observations	observation	NOUN
ejpam-5828	358	14	,	,	PUNCT
ejpam-5828	358	15	significantly	significantly	ADV
ejpam-5828	358	16	enhancing	enhance	VERB
ejpam-5828	358	17	the	the	DET
ejpam-5828	358	18	reliability	reliability	NOUN
ejpam-5828	358	19	and	and	CCONJ
ejpam-5828	358	20	applicability	applicability	NOUN
ejpam-5828	358	21	of	of	ADP
ejpam-5828	358	22	the	the	DET
ejpam-5828	358	23	framework	framework	NOUN
ejpam-5828	358	24	to	to	ADP
ejpam-5828	358	25	real	real	ADJ
ejpam-5828	358	26	-	-	PUNCT
ejpam-5828	358	27	world	world	NOUN
ejpam-5828	358	28	dissipative	dissipative	ADJ
ejpam-5828	358	29	quantum	quantum	NOUN
ejpam-5828	358	30	systems	system	NOUN
ejpam-5828	358	31	.	.	PUNCT
ejpam-5828	359	1	11	11	NUM
ejpam-5828	359	2	.	.	PUNCT
ejpam-5828	360	1	conclusions	conclusion	NOUN
ejpam-5828	360	2	in	in	ADP
ejpam-5828	360	3	this	this	DET
ejpam-5828	360	4	paper	paper	NOUN
ejpam-5828	360	5	,	,	PUNCT
ejpam-5828	360	6	we	we	PRON
ejpam-5828	360	7	investigated	investigate	VERB
ejpam-5828	360	8	the	the	DET
ejpam-5828	360	9	dissipative	dissipative	ADJ
ejpam-5828	360	10	two	two	NUM
ejpam-5828	360	11	-	-	PUNCT
ejpam-5828	360	12	dimensional	dimensional	ADJ
ejpam-5828	360	13	anisotropic	anisotropic	NOUN
ejpam-5828	360	14	harmonic	harmonic	ADJ
ejpam-5828	360	15	oscillator	oscillator	NOUN
ejpam-5828	360	16	using	use	VERB
ejpam-5828	360	17	the	the	DET
ejpam-5828	360	18	hamilton	hamilton	PROPN
ejpam-5828	360	19	jacobi	jacobi	PROPN
ejpam-5828	360	20	formalism	formalism	NOUN
ejpam-5828	360	21	.	.	PUNCT
ejpam-5828	361	1	we	we	PRON
ejpam-5828	361	2	obtained	obtain	VERB
ejpam-5828	361	3	the	the	DET
ejpam-5828	361	4	lagrangian	lagrangian	ADJ
ejpam-5828	361	5	and	and	CCONJ
ejpam-5828	361	6	hamiltonian	hamiltonian	ADJ
ejpam-5828	361	7	equations	equation	NOUN
ejpam-5828	361	8	,	,	PUNCT
ejpam-5828	361	9	solved	solve	VERB
ejpam-5828	361	10	the	the	DET
ejpam-5828	361	11	hamilton	hamilton	PROPN
ejpam-5828	361	12	-	-	PUNCT
ejpam-5828	361	13	jacobi	jacobi	PROPN
ejpam-5828	361	14	equation	equation	NOUN
ejpam-5828	361	15	,	,	PUNCT
ejpam-5828	361	16	and	and	CCONJ
ejpam-5828	361	17	quantified	quantify	VERB
ejpam-5828	361	18	the	the	DET
ejpam-5828	361	19	system	system	NOUN
ejpam-5828	361	20	using	use	VERB
ejpam-5828	361	21	the	the	DET
ejpam-5828	361	22	wkb	wkb	NOUN
ejpam-5828	361	23	approximation	approximation	NOUN
ejpam-5828	361	24	and	and	CCONJ
ejpam-5828	361	25	canonical	canonical	ADJ
ejpam-5828	361	26	quantization	quantization	NOUN
ejpam-5828	361	27	approaches	approach	NOUN
ejpam-5828	361	28	.	.	PUNCT
ejpam-5828	362	1	we	we	PRON
ejpam-5828	362	2	formulated	formulate	VERB
ejpam-5828	362	3	the	the	DET
ejpam-5828	362	4	equations	equation	NOUN
ejpam-5828	362	5	of	of	ADP
ejpam-5828	362	6	motion	motion	NOUN
ejpam-5828	362	7	and	and	CCONJ
ejpam-5828	362	8	the	the	DET
ejpam-5828	362	9	heisenberg	heisenberg	PROPN
ejpam-5828	362	10	equations	equation	NOUN
ejpam-5828	362	11	by	by	ADP
ejpam-5828	362	12	isolating	isolate	VERB
ejpam-5828	362	13	variables	variable	NOUN
ejpam-5828	362	14	and	and	CCONJ
ejpam-5828	362	15	using	use	VERB
ejpam-5828	362	16	poisson	poisson	NOUN
ejpam-5828	362	17	brackets	bracket	NOUN
ejpam-5828	362	18	and	and	CCONJ
ejpam-5828	362	19	commutation	commutation	NOUN
ejpam-5828	362	20	relations	relation	NOUN
ejpam-5828	362	21	.	.	PUNCT
ejpam-5828	363	1	using	use	VERB
ejpam-5828	363	2	creation	creation	NOUN
ejpam-5828	363	3	and	and	CCONJ
ejpam-5828	363	4	annihilation	annihilation	NOUN
ejpam-5828	363	5	operations	operation	NOUN
ejpam-5828	363	6	,	,	PUNCT
ejpam-5828	363	7	we	we	PRON
ejpam-5828	363	8	were	be	AUX
ejpam-5828	363	9	able	able	ADJ
ejpam-5828	363	10	to	to	PART
ejpam-5828	363	11	derive	derive	VERB
ejpam-5828	363	12	energy	energy	NOUN
ejpam-5828	363	13	levels	level	NOUN
ejpam-5828	363	14	and	and	CCONJ
ejpam-5828	363	15	eigenstates	eigenstate	NOUN
ejpam-5828	363	16	that	that	PRON
ejpam-5828	363	17	nearly	nearly	ADV
ejpam-5828	363	18	matched	match	VERB
ejpam-5828	363	19	the	the	DET
ejpam-5828	363	20	results	result	NOUN
ejpam-5828	363	21	of	of	ADP
ejpam-5828	363	22	canonical	canonical	ADJ
ejpam-5828	363	23	quantization	quantization	NOUN
ejpam-5828	363	24	.	.	PUNCT
ejpam-5828	364	1	in	in	ADP
ejpam-5828	364	2	exceptional	exceptional	ADJ
ejpam-5828	364	3	situations	situation	NOUN
ejpam-5828	364	4	,	,	PUNCT
ejpam-5828	364	5	for	for	ADP
ejpam-5828	364	6	one	one	NUM
ejpam-5828	364	7	dimension	dimension	NOUN
ejpam-5828	364	8	only	only	ADV
ejpam-5828	364	9	,	,	PUNCT
ejpam-5828	364	10	our	our	PRON
ejpam-5828	364	11	results	result	NOUN
ejpam-5828	364	12	are	be	AUX
ejpam-5828	364	13	in	in	ADP
ejpam-5828	364	14	precise	precise	ADJ
ejpam-5828	364	15	accord	accord	NOUN
ejpam-5828	364	16	with	with	ADP
ejpam-5828	364	17	other	other	ADJ
ejpam-5828	364	18	quantization	quantization	NOUN
ejpam-5828	364	19	schemes	scheme	NOUN
ejpam-5828	364	20	as	as	ADP
ejpam-5828	364	21	b.	b.	PROPN
ejpam-5828	364	22	m.	m.	PROPN
ejpam-5828	364	23	al	al	PROPN
ejpam-5828	364	24	-	-	PROPN
ejpam-5828	364	25	khamiseh	khamiseh	PROPN
ejpam-5828	364	26	et	et	PROPN
ejpam-5828	364	27	al	al	PROPN
ejpam-5828	364	28	.	.	PUNCT
ejpam-5828	364	29	/	/	SYM
ejpam-5828	364	30	eur	eur	PROPN
ejpam-5828	364	31	.	.	PUNCT
ejpam-5828	365	1	j.	j.	PROPN
ejpam-5828	365	2	pure	pure	PROPN
ejpam-5828	365	3	appl	appl	PROPN
ejpam-5828	365	4	.	.	PROPN
ejpam-5828	365	5	math	math	PROPN
ejpam-5828	365	6	,	,	PUNCT
ejpam-5828	365	7	18	18	NUM
ejpam-5828	365	8	(	(	PUNCT
ejpam-5828	365	9	2	2	NUM
ejpam-5828	365	10	)	)	PUNCT
ejpam-5828	365	11	(	(	PUNCT
ejpam-5828	365	12	2025	2025	NUM
ejpam-5828	365	13	)	)	PUNCT
ejpam-5828	365	14	,	,	PUNCT
ejpam-5828	365	15	5828	5828	NUM
ejpam-5828	365	16	20	20	NUM
ejpam-5828	365	17	of	of	ADP
ejpam-5828	365	18	25	25	NUM
ejpam-5828	365	19	described	describe	VERB
ejpam-5828	365	20	in	in	ADP
ejpam-5828	365	21	[	[	X
ejpam-5828	365	22	24	24	NUM
ejpam-5828	365	23	]	]	PUNCT
ejpam-5828	365	24	.	.	PUNCT
ejpam-5828	366	1	this	this	DET
ejpam-5828	366	2	study	study	NOUN
ejpam-5828	366	3	contributes	contribute	VERB
ejpam-5828	366	4	to	to	ADP
ejpam-5828	366	5	quantum	quantum	ADJ
ejpam-5828	366	6	mechanics	mechanic	NOUN
ejpam-5828	366	7	by	by	ADP
ejpam-5828	366	8	modeling	model	VERB
ejpam-5828	366	9	damped	damp	VERB
ejpam-5828	366	10	oscillatory	oscillatory	ADJ
ejpam-5828	366	11	systems	system	NOUN
ejpam-5828	366	12	,	,	PUNCT
ejpam-5828	366	13	an	an	DET
ejpam-5828	366	14	area	area	NOUN
ejpam-5828	366	15	that	that	PRON
ejpam-5828	366	16	has	have	AUX
ejpam-5828	366	17	been	be	AUX
ejpam-5828	366	18	insufficiently	insufficiently	ADV
ejpam-5828	366	19	studied	study	VERB
ejpam-5828	366	20	.	.	PUNCT
ejpam-5828	367	1	a	a	DET
ejpam-5828	367	2	new	new	ADJ
ejpam-5828	367	3	schrödinger	schrödinger	NOUN
ejpam-5828	367	4	equation	equation	NOUN
ejpam-5828	367	5	for	for	ADP
ejpam-5828	367	6	the	the	DET
ejpam-5828	367	7	two	two	NUM
ejpam-5828	367	8	-	-	PUNCT
ejpam-5828	367	9	dimensional	dimensional	ADJ
ejpam-5828	367	10	anisotropic	anisotropic	NOUN
ejpam-5828	367	11	oscillator	oscillator	NOUN
ejpam-5828	367	12	enhances	enhance	VERB
ejpam-5828	367	13	the	the	DET
ejpam-5828	367	14	understanding	understanding	NOUN
ejpam-5828	367	15	of	of	ADP
ejpam-5828	367	16	quantum	quantum	ADJ
ejpam-5828	367	17	dynamics	dynamic	NOUN
ejpam-5828	367	18	.	.	PUNCT
ejpam-5828	368	1	by	by	ADP
ejpam-5828	368	2	integrating	integrate	VERB
ejpam-5828	368	3	techniques	technique	NOUN
ejpam-5828	368	4	like	like	ADP
ejpam-5828	368	5	the	the	DET
ejpam-5828	368	6	wkb	wkb	NOUN
ejpam-5828	368	7	approximation	approximation	NOUN
ejpam-5828	368	8	and	and	CCONJ
ejpam-5828	368	9	canonical	canonical	ADJ
ejpam-5828	368	10	quantization	quantization	NOUN
ejpam-5828	368	11	,	,	PUNCT
ejpam-5828	368	12	the	the	DET
ejpam-5828	368	13	study	study	NOUN
ejpam-5828	368	14	consistently	consistently	ADV
ejpam-5828	368	15	derives	derive	VERB
ejpam-5828	368	16	energy	energy	NOUN
ejpam-5828	368	17	levels	level	NOUN
ejpam-5828	368	18	and	and	CCONJ
ejpam-5828	368	19	eigenstates	eigenstate	NOUN
ejpam-5828	368	20	,	,	PUNCT
ejpam-5828	368	21	providing	provide	VERB
ejpam-5828	368	22	insights	insight	NOUN
ejpam-5828	368	23	into	into	ADP
ejpam-5828	368	24	dissipative	dissipative	ADJ
ejpam-5828	368	25	effects	effect	NOUN
ejpam-5828	368	26	.	.	PUNCT
ejpam-5828	369	1	the	the	DET
ejpam-5828	369	2	results	result	NOUN
ejpam-5828	369	3	show	show	VERB
ejpam-5828	369	4	strong	strong	ADJ
ejpam-5828	369	5	consistency	consistency	NOUN
ejpam-5828	369	6	.	.	PUNCT
ejpam-5828	370	1	the	the	DET
ejpam-5828	370	2	results	result	NOUN
ejpam-5828	370	3	show	show	VERB
ejpam-5828	370	4	strong	strong	ADJ
ejpam-5828	370	5	consistency	consistency	NOUN
ejpam-5828	370	6	,	,	PUNCT
ejpam-5828	370	7	reinforcing	reinforce	VERB
ejpam-5828	370	8	the	the	DET
ejpam-5828	370	9	proposed	propose	VERB
ejpam-5828	370	10	model	model	NOUN
ejpam-5828	370	11	’s	’s	PART
ejpam-5828	370	12	credibility	credibility	NOUN
ejpam-5828	370	13	and	and	CCONJ
ejpam-5828	370	14	its	its	PRON
ejpam-5828	370	15	applicability	applicability	NOUN
ejpam-5828	370	16	to	to	ADP
ejpam-5828	370	17	similar	similar	ADJ
ejpam-5828	370	18	systems	system	NOUN
ejpam-5828	370	19	,	,	PUNCT
ejpam-5828	370	20	thus	thus	ADV
ejpam-5828	370	21	advancing	advance	VERB
ejpam-5828	370	22	the	the	DET
ejpam-5828	370	23	understanding	understanding	NOUN
ejpam-5828	370	24	of	of	ADP
ejpam-5828	370	25	dissipative	dissipative	ADJ
ejpam-5828	370	26	systems	system	NOUN
ejpam-5828	370	27	in	in	ADP
ejpam-5828	370	28	quantum	quantum	ADJ
ejpam-5828	370	29	mechanics	mechanic	NOUN
ejpam-5828	370	30	.	.	PUNCT
ejpam-5828	371	1	key	key	ADJ
ejpam-5828	371	2	findings	finding	NOUN
ejpam-5828	371	3	of	of	ADP
ejpam-5828	371	4	this	this	DET
ejpam-5828	371	5	study	study	NOUN
ejpam-5828	371	6	include	include	VERB
ejpam-5828	371	7	:	:	PUNCT
ejpam-5828	371	8	hamilton	hamilton	PROPN
ejpam-5828	371	9	-	-	PUNCT
ejpam-5828	371	10	jacobi	jacobi	PROPN
ejpam-5828	371	11	equation	equation	NOUN
ejpam-5828	371	12	solutions	solution	NOUN
ejpam-5828	371	13	:	:	PUNCT
ejpam-5828	371	14	the	the	DET
ejpam-5828	371	15	hamilton	hamilton	PROPN
ejpam-5828	371	16	-	-	PUNCT
ejpam-5828	371	17	jacobi	jacobi	PROPN
ejpam-5828	371	18	equation	equation	NOUN
ejpam-5828	371	19	was	be	AUX
ejpam-5828	371	20	solved	solve	VERB
ejpam-5828	371	21	using	use	VERB
ejpam-5828	371	22	the	the	DET
ejpam-5828	371	23	separation	separation	NOUN
ejpam-5828	371	24	of	of	ADP
ejpam-5828	371	25	variables	variable	NOUN
ejpam-5828	371	26	method	method	VERB
ejpam-5828	371	27	under	under	ADP
ejpam-5828	371	28	staeckel	staeckel	NOUN
ejpam-5828	371	29	boundary	boundary	ADJ
ejpam-5828	371	30	conditions	condition	NOUN
ejpam-5828	371	31	,	,	PUNCT
ejpam-5828	371	32	leading	lead	VERB
ejpam-5828	371	33	to	to	ADP
ejpam-5828	371	34	explicit	explicit	ADJ
ejpam-5828	371	35	expressions	expression	NOUN
ejpam-5828	371	36	for	for	ADP
ejpam-5828	371	37	the	the	DET
ejpam-5828	371	38	action	action	NOUN
ejpam-5828	371	39	function	function	NOUN
ejpam-5828	371	40	.	.	PUNCT
ejpam-5828	372	1	consistent	consistent	ADJ
ejpam-5828	372	2	quantization	quantization	NOUN
ejpam-5828	372	3	approaches	approach	NOUN
ejpam-5828	372	4	:	:	PUNCT
ejpam-5828	372	5	the	the	DET
ejpam-5828	372	6	system	system	NOUN
ejpam-5828	372	7	was	be	AUX
ejpam-5828	372	8	quantized	quantize	VERB
ejpam-5828	372	9	using	use	VERB
ejpam-5828	372	10	three	three	NUM
ejpam-5828	372	11	different	different	ADJ
ejpam-5828	372	12	methods	method	NOUN
ejpam-5828	372	13	—	—	PUNCT
ejpam-5828	372	14	wkb	wkb	NOUN
ejpam-5828	372	15	approximation	approximation	NOUN
ejpam-5828	372	16	,	,	PUNCT
ejpam-5828	372	17	canonical	canonical	ADJ
ejpam-5828	372	18	quantization	quantization	NOUN
ejpam-5828	372	19	,	,	PUNCT
ejpam-5828	372	20	and	and	CCONJ
ejpam-5828	372	21	creation	creation	NOUN
ejpam-5828	372	22	-	-	PUNCT
ejpam-5828	372	23	annihilation	annihilation	NOUN
ejpam-5828	372	24	operators	operator	NOUN
ejpam-5828	372	25	.	.	PUNCT
ejpam-5828	373	1	remarkably	remarkably	ADV
ejpam-5828	373	2	,	,	PUNCT
ejpam-5828	373	3	all	all	DET
ejpam-5828	373	4	three	three	NUM
ejpam-5828	373	5	methods	method	NOUN
ejpam-5828	373	6	yielded	yield	VERB
ejpam-5828	373	7	consistent	consistent	ADJ
ejpam-5828	373	8	results	result	NOUN
ejpam-5828	373	9	,	,	PUNCT
ejpam-5828	373	10	reinforcing	reinforce	VERB
ejpam-5828	373	11	the	the	DET
ejpam-5828	373	12	robustness	robustness	NOUN
ejpam-5828	373	13	of	of	ADP
ejpam-5828	373	14	the	the	DET
ejpam-5828	373	15	proposed	propose	VERB
ejpam-5828	373	16	model	model	NOUN
ejpam-5828	373	17	.	.	PUNCT
ejpam-5828	374	1	comparison	comparison	NOUN
ejpam-5828	374	2	with	with	ADP
ejpam-5828	374	3	classical	classical	ADJ
ejpam-5828	374	4	results	result	NOUN
ejpam-5828	374	5	:	:	PUNCT
ejpam-5828	374	6	in	in	ADP
ejpam-5828	374	7	the	the	DET
ejpam-5828	374	8	special	special	ADJ
ejpam-5828	374	9	case	case	NOUN
ejpam-5828	374	10	of	of	ADP
ejpam-5828	374	11	a	a	DET
ejpam-5828	374	12	one	one	NUM
ejpam-5828	374	13	-	-	PUNCT
ejpam-5828	374	14	dimensional	dimensional	ADJ
ejpam-5828	374	15	system	system	NOUN
ejpam-5828	374	16	,	,	PUNCT
ejpam-5828	374	17	the	the	DET
ejpam-5828	374	18	obtained	obtain	VERB
ejpam-5828	374	19	quantum	quantum	NOUN
ejpam-5828	374	20	results	result	NOUN
ejpam-5828	374	21	align	align	VERB
ejpam-5828	374	22	precisely	precisely	ADV
ejpam-5828	374	23	with	with	ADP
ejpam-5828	374	24	classical	classical	ADJ
ejpam-5828	374	25	predictions	prediction	NOUN
ejpam-5828	374	26	,	,	PUNCT
ejpam-5828	374	27	verifying	verify	VERB
ejpam-5828	374	28	the	the	DET
ejpam-5828	374	29	reliability	reliability	NOUN
ejpam-5828	374	30	of	of	ADP
ejpam-5828	374	31	the	the	DET
ejpam-5828	374	32	quantization	quantization	NOUN
ejpam-5828	374	33	framework	framework	NOUN
ejpam-5828	374	34	.	.	PUNCT
ejpam-5828	375	1	references	reference	NOUN
ejpam-5828	375	2	[	[	X
ejpam-5828	375	3	1	1	NUM
ejpam-5828	375	4	]	]	PUNCT
ejpam-5828	375	5	m.	m.	NOUN
ejpam-5828	375	6	razavy	razavy	NOUN
ejpam-5828	375	7	.	.	PUNCT
ejpam-5828	376	1	classical	classical	ADJ
ejpam-5828	376	2	and	and	CCONJ
ejpam-5828	376	3	quantum	quantum	ADJ
ejpam-5828	376	4	dissipative	dissipative	NOUN
ejpam-5828	376	5	systems	system	NOUN
ejpam-5828	376	6	.	.	PUNCT
ejpam-5828	377	1	2017	2017	NUM
ejpam-5828	377	2	.	.	PUNCT
ejpam-5828	378	1	[	[	X
ejpam-5828	378	2	2	2	X
ejpam-5828	378	3	]	]	X
ejpam-5828	378	4	y.	y.	PROPN
ejpam-5828	378	5	fujiwara	fujiwara	PROPN
ejpam-5828	378	6	s.	s.	PROPN
ejpam-5828	378	7	deguchi	deguchi	PROPN
ejpam-5828	378	8	.	.	PUNCT
ejpam-5828	378	9	”	"	PUNCT
ejpam-5828	378	10	quantization	quantization	NOUN
ejpam-5828	378	11	of	of	ADP
ejpam-5828	378	12	the	the	DET
ejpam-5828	378	13	damped	damp	VERB
ejpam-5828	378	14	harmonic	harmonic	NOUN
ejpam-5828	378	15	oscillator	oscillator	NOUN
ejpam-5828	378	16	based	base	VERB
ejpam-5828	378	17	on	on	ADP
ejpam-5828	378	18	a	a	DET
ejpam-5828	378	19	modified	modify	VERB
ejpam-5828	378	20	bateman	bateman	NOUN
ejpam-5828	378	21	lagrangian	lagrangian	PROPN
ejpam-5828	378	22	.	.	PUNCT
ejpam-5828	379	1	physical	physical	PROPN
ejpam-5828	379	2	review	review	PROPN
ejpam-5828	379	3	a	a	PRON
ejpam-5828	379	4	,	,	PUNCT
ejpam-5828	379	5	101(2):022105	101(2):022105	PROPN
ejpam-5828	379	6	,	,	PUNCT
ejpam-5828	379	7	2020	2020	NUM
ejpam-5828	379	8	.	.	PUNCT
ejpam-5828	380	1	[	[	X
ejpam-5828	380	2	3	3	X
ejpam-5828	380	3	]	]	X
ejpam-5828	380	4	b.	b.	PROPN
ejpam-5828	380	5	m.	m.	PROPN
ejpam-5828	380	6	al	al	PROPN
ejpam-5828	380	7	-	-	PUNCT
ejpam-5828	380	8	khamiseh	khamiseh	PROPN
ejpam-5828	380	9	m.	m.	PROPN
ejpam-5828	380	10	a.	a.	NOUN
ejpam-5828	380	11	yousif	yousif	PROPN
ejpam-5828	381	1	p.	p.	PROPN
ejpam-5828	381	2	o.	o.	PROPN
ejpam-5828	382	1	mohammed	mohammed	PROPN
ejpam-5828	382	2	y.	y.	PROPN
ejpam-5828	382	3	s.	s.	PROPN
ejpam-5828	382	4	hamed	hamed	PROPN
ejpam-5828	382	5	y.	y.	PROPN
ejpam-5828	382	6	m.	m.	PROPN
ejpam-5828	382	7	alawaideh	alawaideh	PROPN
ejpam-5828	382	8	,	,	PUNCT
ejpam-5828	382	9	a.	a.	NOUN
ejpam-5828	382	10	a.	a.	NOUN
ejpam-5828	382	11	lupas	lupas	PROPN
ejpam-5828	382	12	.	.	PUNCT
ejpam-5828	383	1	hamiltonian	hamiltonian	ADJ
ejpam-5828	383	2	formulation	formulation	NOUN
ejpam-5828	383	3	for	for	ADP
ejpam-5828	383	4	continuous	continuous	ADJ
ejpam-5828	383	5	systems	system	NOUN
ejpam-5828	383	6	with	with	ADP
ejpam-5828	383	7	second	second	ADJ
ejpam-5828	383	8	-	-	PUNCT
ejpam-5828	383	9	order	order	NOUN
ejpam-5828	383	10	derivatives	derivative	NOUN
ejpam-5828	383	11	:	:	PUNCT
ejpam-5828	383	12	a	a	DET
ejpam-5828	383	13	study	study	NOUN
ejpam-5828	383	14	of	of	ADP
ejpam-5828	383	15	podolsky	podolsky	ADJ
ejpam-5828	383	16	generalized	generalized	ADJ
ejpam-5828	383	17	electrodynamics	electrodynamic	NOUN
ejpam-5828	383	18	.	.	PUNCT
ejpam-5828	384	1	axioms	axiom	NOUN
ejpam-5828	384	2	,	,	PUNCT
ejpam-5828	384	3	13(10):665	13(10):665	NUM
ejpam-5828	384	4	,	,	PUNCT
ejpam-5828	384	5	2024	2024	NUM
ejpam-5828	384	6	.	.	PUNCT
ejpam-5828	385	1	[	[	X
ejpam-5828	385	2	4	4	X
ejpam-5828	385	3	]	]	X
ejpam-5828	385	4	h.	h.	PROPN
ejpam-5828	385	5	dekker	dekker	PROPN
ejpam-5828	385	6	.	.	PUNCT
ejpam-5828	386	1	”	"	PUNCT
ejpam-5828	386	2	quantization	quantization	NOUN
ejpam-5828	386	3	of	of	ADP
ejpam-5828	386	4	the	the	DET
ejpam-5828	386	5	linearly	linearly	ADV
ejpam-5828	386	6	damped	damp	VERB
ejpam-5828	386	7	harmonic	harmonic	ADJ
ejpam-5828	386	8	oscillator	oscillator	NOUN
ejpam-5828	386	9	.	.	PUNCT
ejpam-5828	387	1	physical	physical	PROPN
ejpam-5828	387	2	review	review	NOUN
ejpam-5828	387	3	a	a	DET
ejpam-5828	387	4	,	,	PUNCT
ejpam-5828	387	5	16(5):2126	16(5):2126	NUM
ejpam-5828	387	6	,	,	PUNCT
ejpam-5828	387	7	1977	1977	NUM
ejpam-5828	387	8	.	.	PUNCT
ejpam-5828	388	1	[	[	X
ejpam-5828	388	2	5	5	X
ejpam-5828	388	3	]	]	PUNCT
ejpam-5828	388	4	v.	v.	ADP
ejpam-5828	388	5	tarasov	tarasov	NOUN
ejpam-5828	388	6	.	.	PUNCT
ejpam-5828	389	1	quantum	quantum	ADJ
ejpam-5828	389	2	mechanics	mechanic	NOUN
ejpam-5828	389	3	of	of	ADP
ejpam-5828	389	4	non	non	ADJ
ejpam-5828	389	5	-	-	ADJ
ejpam-5828	389	6	hamiltonian	hamiltonian	ADJ
ejpam-5828	389	7	and	and	CCONJ
ejpam-5828	389	8	dissipative	dissipative	ADJ
ejpam-5828	389	9	systems	system	NOUN
ejpam-5828	389	10	.	.	PUNCT
ejpam-5828	390	1	elsevier	elsevier	NOUN
ejpam-5828	390	2	,	,	PUNCT
ejpam-5828	390	3	2008	2008	NUM
ejpam-5828	390	4	.	.	PUNCT
ejpam-5828	391	1	[	[	X
ejpam-5828	391	2	6	6	NUM
ejpam-5828	391	3	]	]	PUNCT
ejpam-5828	391	4	h.	h.	PROPN
ejpam-5828	391	5	majima	majima	PROPN
ejpam-5828	391	6	and	and	CCONJ
ejpam-5828	391	7	a.	a.	PROPN
ejpam-5828	391	8	suzuki	suzuki	PROPN
ejpam-5828	391	9	.	.	PUNCT
ejpam-5828	391	10	quantization	quantization	NOUN
ejpam-5828	391	11	and	and	CCONJ
ejpam-5828	391	12	instability	instability	NOUN
ejpam-5828	391	13	of	of	ADP
ejpam-5828	391	14	the	the	DET
ejpam-5828	391	15	damped	damp	VERB
ejpam-5828	391	16	harmonic	harmonic	ADJ
ejpam-5828	391	17	oscillator	oscillator	NOUN
ejpam-5828	391	18	subject	subject	NOUN
ejpam-5828	391	19	to	to	ADP
ejpam-5828	391	20	a	a	DET
ejpam-5828	391	21	time	time	NOUN
ejpam-5828	391	22	-	-	PUNCT
ejpam-5828	391	23	dependent	dependent	ADJ
ejpam-5828	391	24	force	force	NOUN
ejpam-5828	391	25	.	.	PUNCT
ejpam-5828	392	1	annals	annal	NOUN
ejpam-5828	392	2	of	of	ADP
ejpam-5828	392	3	physics	physics	NOUN
ejpam-5828	392	4	,	,	PUNCT
ejpam-5828	392	5	326(12):3000	326(12):3000	NUM
ejpam-5828	392	6	–	–	PUNCT
ejpam-5828	392	7	3012	3012	NUM
ejpam-5828	392	8	,	,	PUNCT
ejpam-5828	392	9	2011	2011	NUM
ejpam-5828	392	10	.	.	PUNCT
ejpam-5828	393	1	[	[	X
ejpam-5828	393	2	7	7	X
ejpam-5828	393	3	]	]	X
ejpam-5828	393	4	s.	s.	PROPN
ejpam-5828	393	5	deguchi	deguchi	PROPN
ejpam-5828	393	6	,	,	PUNCT
ejpam-5828	393	7	y.	y.	PROPN
ejpam-5828	393	8	fujiwara	fujiwara	PROPN
ejpam-5828	393	9	,	,	PUNCT
ejpam-5828	393	10	and	and	CCONJ
ejpam-5828	393	11	k.	k.	PROPN
ejpam-5828	393	12	nakano	nakano	PROPN
ejpam-5828	393	13	.	.	PUNCT
ejpam-5828	394	1	two	two	NUM
ejpam-5828	394	2	quantization	quantization	NOUN
ejpam-5828	394	3	approaches	approach	VERB
ejpam-5828	394	4	to	to	ADP
ejpam-5828	394	5	the	the	DET
ejpam-5828	394	6	bateman	bateman	PROPN
ejpam-5828	394	7	oscillator	oscillator	PROPN
ejpam-5828	394	8	model	model	PROPN
ejpam-5828	394	9	.	.	PUNCT
ejpam-5828	395	1	annals	annal	NOUN
ejpam-5828	395	2	of	of	ADP
ejpam-5828	395	3	physics	physics	NOUN
ejpam-5828	395	4	,	,	PUNCT
ejpam-5828	395	5	403:34–46	403:34–46	NUM
ejpam-5828	395	6	,	,	PUNCT
ejpam-5828	395	7	2019	2019	NUM
ejpam-5828	395	8	.	.	PUNCT
ejpam-5828	396	1	[	[	X
ejpam-5828	396	2	8	8	NUM
ejpam-5828	396	3	]	]	PUNCT
ejpam-5828	396	4	a.	a.	NOUN
ejpam-5828	396	5	suzuki	suzuki	PROPN
ejpam-5828	396	6	and	and	CCONJ
ejpam-5828	396	7	h.	h.	PROPN
ejpam-5828	396	8	majima	majima	PROPN
ejpam-5828	396	9	.	.	PUNCT
ejpam-5828	397	1	on	on	ADP
ejpam-5828	397	2	the	the	DET
ejpam-5828	397	3	quantum	quantum	ADJ
ejpam-5828	397	4	mechanical	mechanical	ADJ
ejpam-5828	397	5	treatment	treatment	NOUN
ejpam-5828	397	6	of	of	ADP
ejpam-5828	397	7	the	the	DET
ejpam-5828	397	8	bateman	bateman	NOUN
ejpam-5828	397	9	-	-	PUNCT
ejpam-5828	397	10	morse	morse	PROPN
ejpam-5828	397	11	feshbach	feshbach	NOUN
ejpam-5828	397	12	damped	damp	VERB
ejpam-5828	397	13	oscillator	oscillator	NOUN
ejpam-5828	397	14	with	with	ADP
ejpam-5828	397	15	variable	variable	ADJ
ejpam-5828	397	16	mass	mass	PROPN
ejpam-5828	397	17	.	.	PUNCT
ejpam-5828	397	18	journal	journal	PROPN
ejpam-5828	397	19	of	of	ADP
ejpam-5828	397	20	modern	modern	ADJ
ejpam-5828	397	21	physics	physic	NOUN
ejpam-5828	397	22	,	,	PUNCT
ejpam-5828	397	23	7(16):2329–2340	7(16):2329–2340	NUM
ejpam-5828	397	24	,	,	PUNCT
ejpam-5828	397	25	2016	2016	NUM
ejpam-5828	397	26	.	.	PUNCT
ejpam-5828	398	1	[	[	X
ejpam-5828	398	2	9	9	NUM
ejpam-5828	398	3	]	]	X
ejpam-5828	398	4	h.	h.	PROPN
ejpam-5828	398	5	r.	r.	PROPN
ejpam-5828	398	6	lewis	lewis	PROPN
ejpam-5828	398	7	and	and	CCONJ
ejpam-5828	398	8	w.	w.	PROPN
ejpam-5828	398	9	b.	b.	PROPN
ejpam-5828	398	10	riesenfeld	riesenfeld	PROPN
ejpam-5828	398	11	.	.	PUNCT
ejpam-5828	399	1	an	an	DET
ejpam-5828	399	2	exact	exact	ADJ
ejpam-5828	399	3	quantum	quantum	NOUN
ejpam-5828	399	4	theory	theory	NOUN
ejpam-5828	399	5	of	of	ADP
ejpam-5828	399	6	the	the	DET
ejpam-5828	399	7	timeb	timeb	NOUN
ejpam-5828	399	8	.	.	PUNCT
ejpam-5828	400	1	m.	m.	NOUN
ejpam-5828	400	2	al	al	PROPN
ejpam-5828	400	3	-	-	PUNCT
ejpam-5828	400	4	khamiseh	khamiseh	PROPN
ejpam-5828	400	5	et	et	PROPN
ejpam-5828	400	6	al	al	PROPN
ejpam-5828	400	7	.	.	PUNCT
ejpam-5828	400	8	/	/	SYM
ejpam-5828	400	9	eur	eur	PROPN
ejpam-5828	400	10	.	.	PUNCT
ejpam-5828	401	1	j.	j.	PROPN
ejpam-5828	401	2	pure	pure	PROPN
ejpam-5828	401	3	appl	appl	PROPN
ejpam-5828	401	4	.	.	PROPN
ejpam-5828	401	5	math	math	PROPN
ejpam-5828	401	6	,	,	PUNCT
ejpam-5828	401	7	18	18	NUM
ejpam-5828	401	8	(	(	PUNCT
ejpam-5828	401	9	2	2	NUM
ejpam-5828	401	10	)	)	PUNCT
ejpam-5828	401	11	(	(	PUNCT
ejpam-5828	401	12	2025	2025	NUM
ejpam-5828	401	13	)	)	PUNCT
ejpam-5828	401	14	,	,	PUNCT
ejpam-5828	401	15	5828	5828	NUM
ejpam-5828	401	16	21	21	NUM
ejpam-5828	401	17	of	of	ADP
ejpam-5828	401	18	25	25	NUM
ejpam-5828	401	19	dependent	dependent	ADJ
ejpam-5828	401	20	harmonic	harmonic	ADJ
ejpam-5828	401	21	oscillator	oscillator	NOUN
ejpam-5828	401	22	and	and	CCONJ
ejpam-5828	401	23	of	of	ADP
ejpam-5828	401	24	a	a	DET
ejpam-5828	401	25	charged	charge	VERB
ejpam-5828	401	26	particle	particle	NOUN
ejpam-5828	401	27	in	in	ADP
ejpam-5828	401	28	a	a	DET
ejpam-5828	401	29	time	time	NOUN
ejpam-5828	401	30	dependent	dependent	ADJ
ejpam-5828	401	31	electromagnetic	electromagnetic	ADJ
ejpam-5828	401	32	field	field	NOUN
ejpam-5828	401	33	.	.	PUNCT
ejpam-5828	402	1	journal	journal	PROPN
ejpam-5828	402	2	of	of	ADP
ejpam-5828	402	3	mathematical	mathematical	ADJ
ejpam-5828	402	4	physics	physics	NOUN
ejpam-5828	402	5	,	,	PUNCT
ejpam-5828	402	6	10(8):1458–1473	10(8):1458–1473	NUM
ejpam-5828	402	7	,	,	PUNCT
ejpam-5828	402	8	1969	1969	NUM
ejpam-5828	402	9	.	.	PUNCT
ejpam-5828	403	1	[	[	X
ejpam-5828	403	2	10	10	NUM
ejpam-5828	403	3	]	]	X
ejpam-5828	403	4	r.	r.	PROPN
ejpam-5828	403	5	jan	jan	PROPN
ejpam-5828	403	6	,	,	PUNCT
ejpam-5828	403	7	m.	m.	NOUN
ejpam-5828	403	8	alsulami	alsulami	NOUN
ejpam-5828	403	9	,	,	PUNCT
ejpam-5828	403	10	and	and	CCONJ
ejpam-5828	403	11	n.	n.	PROPN
ejpam-5828	403	12	n.	n.	PROPN
ejpam-5828	403	13	a.	a.	PROPN
ejpam-5828	403	14	razak	razak	PROPN
ejpam-5828	403	15	.	.	PUNCT
ejpam-5828	404	1	modeling	model	VERB
ejpam-5828	404	2	the	the	DET
ejpam-5828	404	3	response	response	NOUN
ejpam-5828	404	4	of	of	ADP
ejpam-5828	404	5	the	the	DET
ejpam-5828	404	6	immune	immune	ADJ
ejpam-5828	404	7	system	system	NOUN
ejpam-5828	404	8	to	to	ADP
ejpam-5828	404	9	hiv	hiv	PROPN
ejpam-5828	404	10	-	-	PUNCT
ejpam-5828	404	11	tumor	tumor	NOUN
ejpam-5828	404	12	interaction	interaction	NOUN
ejpam-5828	404	13	via	via	ADP
ejpam-5828	404	14	a	a	DET
ejpam-5828	404	15	fractional	fractional	ADJ
ejpam-5828	404	16	framework	framework	NOUN
ejpam-5828	404	17	.	.	PUNCT
ejpam-5828	405	1	european	european	ADJ
ejpam-5828	405	2	journal	journal	PROPN
ejpam-5828	405	3	of	of	ADP
ejpam-5828	405	4	pure	pure	ADJ
ejpam-5828	405	5	and	and	CCONJ
ejpam-5828	405	6	applied	applied	ADJ
ejpam-5828	405	7	mathematics	mathematic	NOUN
ejpam-5828	405	8	,	,	PUNCT
ejpam-5828	405	9	18(1):5670–5670	18(1):5670–5670	NUM
ejpam-5828	405	10	,	,	PUNCT
ejpam-5828	405	11	2025	2025	NUM
ejpam-5828	405	12	.	.	PUNCT
ejpam-5828	406	1	[	[	X
ejpam-5828	406	2	11	11	NUM
ejpam-5828	406	3	]	]	X
ejpam-5828	406	4	krumreich	krumreich	PROPN
ejpam-5828	406	5	c.	c.	PROPN
ejpam-5828	406	6	e.	e.	PROPN
ejpam-5828	406	7	lazo	lazo	PROPN
ejpam-5828	406	8	,	,	PUNCT
ejpam-5828	406	9	m.	m.	NOUN
ejpam-5828	406	10	j.	j.	PROPN
ejpam-5828	406	11	the	the	DET
ejpam-5828	406	12	action	action	NOUN
ejpam-5828	406	13	principle	principle	NOUN
ejpam-5828	406	14	for	for	ADP
ejpam-5828	406	15	dissipative	dissipative	ADJ
ejpam-5828	406	16	systems	system	NOUN
ejpam-5828	406	17	.	.	PUNCT
ejpam-5828	407	1	journal	journal	PROPN
ejpam-5828	407	2	of	of	ADP
ejpam-5828	407	3	mathematical	mathematical	ADJ
ejpam-5828	407	4	physics	physics	NOUN
ejpam-5828	407	5	,	,	PUNCT
ejpam-5828	407	6	55(12	55(12	NUM
ejpam-5828	407	7	)	)	PUNCT
ejpam-5828	407	8	,	,	PUNCT
ejpam-5828	407	9	2014	2014	NUM
ejpam-5828	407	10	.	.	PUNCT
ejpam-5828	408	1	[	[	X
ejpam-5828	408	2	12	12	NUM
ejpam-5828	408	3	]	]	X
ejpam-5828	408	4	y.	y.	PROPN
ejpam-5828	408	5	m.	m.	PROPN
ejpam-5828	408	6	alawaideh	alawaideh	PROPN
ejpam-5828	408	7	,	,	PUNCT
ejpam-5828	408	8	b.	b.	PROPN
ejpam-5828	408	9	m.	m.	PROPN
ejpam-5828	408	10	al	al	PROPN
ejpam-5828	408	11	-	-	PUNCT
ejpam-5828	408	12	khamiseh	khamiseh	PROPN
ejpam-5828	408	13	,	,	PUNCT
ejpam-5828	408	14	m.	m.	NOUN
ejpam-5828	408	15	kanan	kanan	PROPN
ejpam-5828	408	16	,	,	PUNCT
ejpam-5828	408	17	and	and	CCONJ
ejpam-5828	408	18	f.	f.	PROPN
ejpam-5828	408	19	tesgera	tesgera	PROPN
ejpam-5828	408	20	.	.	PUNCT
ejpam-5828	408	21	”	"	PUNCT
ejpam-5828	408	22	fractional	fractional	ADJ
ejpam-5828	408	23	quantization	quantization	NOUN
ejpam-5828	408	24	of	of	ADP
ejpam-5828	408	25	podolsky	podolsky	ADJ
ejpam-5828	408	26	electrodynamics	electrodynamic	NOUN
ejpam-5828	408	27	using	use	VERB
ejpam-5828	408	28	fractional	fractional	PROPN
ejpam-5828	408	29	hamilton	hamilton	PROPN
ejpam-5828	408	30	-	-	PUNCT
ejpam-5828	408	31	jacobi	jacobi	PROPN
ejpam-5828	408	32	formulation	formulation	PROPN
ejpam-5828	408	33	.	.	PUNCT
ejpam-5828	409	1	progress	progress	NOUN
ejpam-5828	409	2	in	in	ADP
ejpam-5828	409	3	fractional	fractional	ADJ
ejpam-5828	409	4	differentiation	differentiation	NOUN
ejpam-5828	409	5	and	and	CCONJ
ejpam-5828	409	6	applications	application	NOUN
ejpam-5828	409	7	,	,	PUNCT
ejpam-5828	409	8	page	page	NOUN
ejpam-5828	409	9	doi	doi	NOUN
ejpam-5828	409	10	:	:	PUNCT
ejpam-5828	409	11	10.18576	10.18576	NUM
ejpam-5828	409	12	/	/	SYM
ejpam-5828	409	13	pfda/090202	pfda/090202	PROPN
ejpam-5828	409	14	.	.	PUNCT
ejpam-5828	409	15	,	,	PUNCT
ejpam-5828	409	16	2023	2023	NUM
ejpam-5828	409	17	.	.	PUNCT
ejpam-5828	410	1	[	[	X
ejpam-5828	410	2	13	13	NUM
ejpam-5828	410	3	]	]	PUNCT
ejpam-5828	410	4	z.	z.	PROPN
ejpam-5828	410	5	m.	m.	PROPN
ejpam-5828	410	6	li	li	PROPN
ejpam-5828	410	7	and	and	CCONJ
ejpam-5828	410	8	j.	j.	PROPN
ejpam-5828	410	9	h.	h.	PROPN
ejpam-5828	410	10	park	park	PROPN
ejpam-5828	410	11	.	.	PUNCT
ejpam-5828	411	1	dissipative	dissipative	ADJ
ejpam-5828	411	2	fuzzy	fuzzy	ADJ
ejpam-5828	411	3	tracking	tracking	NOUN
ejpam-5828	411	4	control	control	NOUN
ejpam-5828	411	5	for	for	ADP
ejpam-5828	411	6	nonlinear	nonlinear	ADJ
ejpam-5828	411	7	networked	networked	ADJ
ejpam-5828	411	8	systems	system	NOUN
ejpam-5828	411	9	with	with	ADP
ejpam-5828	411	10	quantization	quantization	NOUN
ejpam-5828	411	11	.	.	PUNCT
ejpam-5828	412	1	ieee	ieee	NOUN
ejpam-5828	412	2	transactions	transaction	NOUN
ejpam-5828	412	3	on	on	ADP
ejpam-5828	412	4	systems	system	NOUN
ejpam-5828	412	5	,	,	PUNCT
ejpam-5828	412	6	man	man	NOUN
ejpam-5828	412	7	,	,	PUNCT
ejpam-5828	412	8	and	and	CCONJ
ejpam-5828	412	9	cybernetics	cybernetic	NOUN
ejpam-5828	412	10	:	:	PUNCT
ejpam-5828	412	11	systems	system	NOUN
ejpam-5828	412	12	,	,	PUNCT
ejpam-5828	412	13	50(12):5130–5141	50(12):5130–5141	NUM
ejpam-5828	412	14	,	,	PUNCT
ejpam-5828	412	15	2018	2018	NUM
ejpam-5828	412	16	.	.	PUNCT
ejpam-5828	413	1	[	[	X
ejpam-5828	413	2	14	14	NUM
ejpam-5828	413	3	]	]	PUNCT
ejpam-5828	413	4	m.	m.	NOUN
ejpam-5828	413	5	mollai	mollai	PROPN
ejpam-5828	413	6	and	and	CCONJ
ejpam-5828	413	7	s.	s.	PROPN
ejpam-5828	413	8	m.	m.	PROPN
ejpam-5828	413	9	saberi	saberi	PROPN
ejpam-5828	413	10	fathi	fathi	PROPN
ejpam-5828	413	11	.	.	PUNCT
ejpam-5828	414	1	an	an	DET
ejpam-5828	414	2	application	application	NOUN
ejpam-5828	414	3	of	of	ADP
ejpam-5828	414	4	the	the	DET
ejpam-5828	414	5	madelung	madelung	PROPN
ejpam-5828	414	6	formalism	formalism	NOUN
ejpam-5828	414	7	for	for	ADP
ejpam-5828	414	8	dissipating	dissipate	VERB
ejpam-5828	414	9	and	and	CCONJ
ejpam-5828	414	10	decaying	decay	VERB
ejpam-5828	414	11	systems	system	NOUN
ejpam-5828	414	12	.	.	PUNCT
ejpam-5828	415	1	symmetry	symmetry	NOUN
ejpam-5828	415	2	,	,	PUNCT
ejpam-5828	415	3	,	,	PUNCT
ejpam-5828	415	4	13(50):812	13(50):812	NUM
ejpam-5828	415	5	,	,	PUNCT
ejpam-5828	415	6	2021	2021	NUM
ejpam-5828	415	7	.	.	PUNCT
ejpam-5828	416	1	[	[	X
ejpam-5828	416	2	15	15	NUM
ejpam-5828	416	3	]	]	PUNCT
ejpam-5828	416	4	a.	a.	PROPN
ejpam-5828	416	5	k.	k.	PROPN
ejpam-5828	416	6	kapoor	kapoor	PROPN
ejpam-5828	416	7	,	,	PUNCT
ejpam-5828	416	8	p.	p.	PROPN
ejpam-5828	416	9	k.	k.	PROPN
ejpam-5828	417	1	panigrahi	panigrahi	PROPN
ejpam-5828	417	2	,	,	PUNCT
ejpam-5828	417	3	and	and	CCONJ
ejpam-5828	417	4	s.	s.	PROPN
ejpam-5828	417	5	s.	s.	PROPN
ejpam-5828	417	6	ranjani	ranjani	PROPN
ejpam-5828	417	7	.	.	PUNCT
ejpam-5828	418	1	quantum	quantum	PROPN
ejpam-5828	418	2	hamilton	hamilton	PROPN
ejpam-5828	418	3	-	-	PUNCT
ejpam-5828	418	4	jacobi	jacobi	PROPN
ejpam-5828	418	5	formalism	formalism	NOUN
ejpam-5828	418	6	,	,	PUNCT
ejpam-5828	418	7	”	"	PUNCT
ejpam-5828	418	8	in	in	ADP
ejpam-5828	418	9	quantum	quantum	PROPN
ejpam-5828	418	10	hamilton	hamilton	PROPN
ejpam-5828	418	11	-	-	PUNCT
ejpam-5828	418	12	jacobi	jacobi	PROPN
ejpam-5828	418	13	formalism	formalism	NOUN
ejpam-5828	418	14	.	.	PUNCT
ejpam-5828	419	1	2022	2022	NUM
ejpam-5828	419	2	.	.	PUNCT
ejpam-5828	420	1	[	[	X
ejpam-5828	420	2	16	16	NUM
ejpam-5828	420	3	]	]	X
ejpam-5828	420	4	d.	d.	PROPN
ejpam-5828	420	5	schuch	schuch	PROPN
ejpam-5828	420	6	,	,	PUNCT
ejpam-5828	420	7	o.	o.	PROPN
ejpam-5828	420	8	castaños	castaños	PROPN
ejpam-5828	420	9	,	,	PUNCT
ejpam-5828	420	10	and	and	CCONJ
ejpam-5828	420	11	o.	o.	PROPN
ejpam-5828	420	12	rosas	rosas	PROPN
ejpam-5828	420	13	-	-	PUNCT
ejpam-5828	420	14	ortiz	ortiz	PROPN
ejpam-5828	420	15	.	.	PUNCT
ejpam-5828	421	1	generalized	generalized	ADJ
ejpam-5828	421	2	creation	creation	NOUN
ejpam-5828	421	3	and	and	CCONJ
ejpam-5828	421	4	annihilation	annihilation	NOUN
ejpam-5828	421	5	operators	operator	NOUN
ejpam-5828	421	6	via	via	ADP
ejpam-5828	421	7	complex	complex	ADJ
ejpam-5828	421	8	nonlinear	nonlinear	ADJ
ejpam-5828	421	9	riccati	riccati	PROPN
ejpam-5828	421	10	equations	equation	NOUN
ejpam-5828	421	11	.	.	PUNCT
ejpam-5828	422	1	2013	2013	NUM
ejpam-5828	422	2	.	.	PUNCT
ejpam-5828	423	1	[	[	X
ejpam-5828	423	2	17	17	NUM
ejpam-5828	423	3	]	]	PUNCT
ejpam-5828	423	4	j.	j.	PROPN
ejpam-5828	423	5	awrejcewicz	awrejcewicz	PROPN
ejpam-5828	423	6	t.	t.	PROPN
ejpam-5828	423	7	abdeljawadm	abdeljawadm	PROPN
ejpam-5828	423	8	.	.	PUNCT
ejpam-5828	424	1	b.	b.	PROPN
ejpam-5828	425	1	riaz	riaz	PROPN
ejpam-5828	425	2	a.	a.	PROPN
ejpam-5828	425	3	a.	a.	PROPN
ejpam-5828	425	4	zafar	zafar	PROPN
ejpam-5828	425	5	,	,	PUNCT
ejpam-5828	425	6	g.	g.	PROPN
ejpam-5828	425	7	kudra	kudra	PROPN
ejpam-5828	425	8	.	.	PUNCT
ejpam-5828	426	1	a	a	DET
ejpam-5828	426	2	comparative	comparative	ADJ
ejpam-5828	426	3	study	study	NOUN
ejpam-5828	426	4	of	of	ADP
ejpam-5828	426	5	the	the	DET
ejpam-5828	426	6	fractional	fractional	ADJ
ejpam-5828	426	7	oscillators	oscillator	NOUN
ejpam-5828	426	8	.	.	PUNCT
ejpam-5828	427	1	alexandria	alexandria	PROPN
ejpam-5828	427	2	engineering	engineering	PROPN
ejpam-5828	427	3	journal	journal	PROPN
ejpam-5828	427	4	,	,	PUNCT
ejpam-5828	427	5	59(4):2649–2676	59(4):2649–2676	NUM
ejpam-5828	427	6	,	,	PUNCT
ejpam-5828	427	7	2020	2020	NUM
ejpam-5828	427	8	.	.	PUNCT
ejpam-5828	428	1	[	[	X
ejpam-5828	428	2	18	18	NUM
ejpam-5828	428	3	]	]	PUNCT
ejpam-5828	428	4	m.	m.	NOUN
ejpam-5828	428	5	serhan	serhan	PROPN
ejpam-5828	428	6	,	,	PUNCT
ejpam-5828	428	7	m.	m.	NOUN
ejpam-5828	428	8	abusini	abusini	PROPN
ejpam-5828	428	9	,	,	PUNCT
ejpam-5828	428	10	a.	a.	PROPN
ejpam-5828	428	11	al	al	PROPN
ejpam-5828	428	12	-	-	PUNCT
ejpam-5828	428	13	jamel	jamel	PROPN
ejpam-5828	428	14	,	,	PUNCT
ejpam-5828	428	15	h.	h.	PROPN
ejpam-5828	428	16	el	el	PROPN
ejpam-5828	428	17	-	-	PROPN
ejpam-5828	428	18	nasser	nasser	PROPN
ejpam-5828	428	19	,	,	PUNCT
ejpam-5828	428	20	and	and	CCONJ
ejpam-5828	428	21	e.	e.	PROPN
ejpam-5828	428	22	m.	m.	PROPN
ejpam-5828	428	23	rabe	rabe	NOUN
ejpam-5828	428	24	.	.	PUNCT
ejpam-5828	429	1	quantization	quantization	NOUN
ejpam-5828	429	2	of	of	ADP
ejpam-5828	429	3	the	the	DET
ejpam-5828	429	4	damped	damped	ADJ
ejpam-5828	429	5	harmonic	harmonic	PROPN
ejpam-5828	429	6	oscillator	oscillator	NOUN
ejpam-5828	429	7	.	.	PUNCT
ejpam-5828	430	1	journal	journal	PROPN
ejpam-5828	430	2	of	of	ADP
ejpam-5828	430	3	mathematical	mathematical	ADJ
ejpam-5828	430	4	physics	physics	NOUN
ejpam-5828	430	5	,	,	PUNCT
ejpam-5828	430	6	59(8	59(8	NUM
ejpam-5828	430	7	)	)	PUNCT
ejpam-5828	430	8	,	,	PUNCT
ejpam-5828	430	9	2018	2018	NUM
ejpam-5828	430	10	.	.	PUNCT
ejpam-5828	431	1	[	[	X
ejpam-5828	431	2	19	19	NUM
ejpam-5828	431	3	]	]	PUNCT
ejpam-5828	431	4	s.	s.	PROPN
ejpam-5828	431	5	k.	k.	PROPN
ejpam-5828	431	6	bose	bose	PROPN
ejpam-5828	431	7	and	and	CCONJ
ejpam-5828	431	8	u.	u.	PROPN
ejpam-5828	431	9	b.	b.	PROPN
ejpam-5828	431	10	dubey	dubey	PROPN
ejpam-5828	431	11	.	.	PUNCT
ejpam-5828	432	1	application	application	NOUN
ejpam-5828	432	2	of	of	ADP
ejpam-5828	432	3	coherent	coherent	ADJ
ejpam-5828	432	4	states	state	NOUN
ejpam-5828	432	5	to	to	PART
ejpam-5828	432	6	anharmonic	anharmonic	VERB
ejpam-5828	432	7	,	,	PUNCT
ejpam-5828	432	8	timedependent	timedependent	NOUN
ejpam-5828	432	9	and	and	CCONJ
ejpam-5828	432	10	damped	damped	NOUN
ejpam-5828	432	11	oscillator	oscillator	NOUN
ejpam-5828	432	12	systems	system	NOUN
ejpam-5828	432	13	.	.	PUNCT
ejpam-5828	433	1	fortschritte	fortschritte	PROPN
ejpam-5828	433	2	der	der	PROPN
ejpam-5828	433	3	physik	physik	PROPN
ejpam-5828	433	4	/	/	SYM
ejpam-5828	433	5	progress	progress	NOUN
ejpam-5828	433	6	of	of	ADP
ejpam-5828	433	7	physics	physics	NOUN
ejpam-5828	433	8	,	,	PUNCT
ejpam-5828	433	9	35(10):675–705	35(10):675–705	NUM
ejpam-5828	433	10	,	,	PUNCT
ejpam-5828	433	11	1987	1987	NUM
ejpam-5828	433	12	.	.	PUNCT
ejpam-5828	434	1	[	[	X
ejpam-5828	434	2	20	20	NUM
ejpam-5828	434	3	]	]	PUNCT
ejpam-5828	434	4	a.	a.	PROPN
ejpam-5828	434	5	haque	haque	PROPN
ejpam-5828	434	6	r.	r.	PROPN
ejpam-5828	434	7	mahapatra	mahapatra	PROPN
ejpam-5828	434	8	.	.	PUNCT
ejpam-5828	435	1	quantisation	quantisation	NOUN
ejpam-5828	435	2	of	of	ADP
ejpam-5828	435	3	the	the	DET
ejpam-5828	435	4	damped	damp	VERB
ejpam-5828	435	5	free	free	ADJ
ejpam-5828	435	6	particle	particle	NOUN
ejpam-5828	435	7	.	.	PUNCT
ejpam-5828	436	1	pramana	pramana	PROPN
ejpam-5828	436	2	,	,	PUNCT
ejpam-5828	436	3	,	,	PUNCT
ejpam-5828	436	4	97(4):166	97(4):166	NOUN
ejpam-5828	436	5	,	,	PUNCT
ejpam-5828	436	6	2023	2023	NUM
ejpam-5828	436	7	.	.	PUNCT
ejpam-5828	437	1	[	[	X
ejpam-5828	437	2	21	21	NUM
ejpam-5828	437	3	]	]	PUNCT
ejpam-5828	437	4	á.	á.	VERB
ejpam-5828	437	5	gómez	gómez	NOUN
ejpam-5828	437	6	-	-	PUNCT
ejpam-5828	437	7	león	león	PROPN
ejpam-5828	437	8	,	,	PUNCT
ejpam-5828	437	9	t.	t.	PROPN
ejpam-5828	437	10	ramos	ramos	PROPN
ejpam-5828	437	11	,	,	PUNCT
ejpam-5828	437	12	d.	d.	PROPN
ejpam-5828	437	13	porras	porras	PROPN
ejpam-5828	437	14	,	,	PUNCT
ejpam-5828	437	15	and	and	CCONJ
ejpam-5828	437	16	a.	a.	NOUN
ejpam-5828	437	17	gonzález	gonzález	PROPN
ejpam-5828	437	18	-	-	PUNCT
ejpam-5828	437	19	tudela	tudela	NOUN
ejpam-5828	437	20	.	.	PUNCT
ejpam-5828	437	21	decimation	decimation	NOUN
ejpam-5828	437	22	technique	technique	NOUN
ejpam-5828	437	23	for	for	ADP
ejpam-5828	437	24	open	open	ADJ
ejpam-5828	437	25	quantum	quantum	NOUN
ejpam-5828	437	26	systems	system	NOUN
ejpam-5828	437	27	:	:	PUNCT
ejpam-5828	437	28	a	a	DET
ejpam-5828	437	29	case	case	NOUN
ejpam-5828	437	30	study	study	NOUN
ejpam-5828	437	31	with	with	ADP
ejpam-5828	437	32	driven	drive	VERB
ejpam-5828	437	33	-	-	PUNCT
ejpam-5828	437	34	dissipative	dissipative	ADJ
ejpam-5828	437	35	bosonic	bosonic	NOUN
ejpam-5828	437	36	chains	chain	NOUN
ejpam-5828	437	37	.	.	PUNCT
ejpam-5828	438	1	physical	physical	ADJ
ejpam-5828	438	2	review	review	PROPN
ejpam-5828	438	3	a	a	DET
ejpam-5828	438	4	,	,	PUNCT
ejpam-5828	438	5	105(5):052223	105(5):052223	PROPN
ejpam-5828	438	6	,	,	PUNCT
ejpam-5828	438	7	2022	2022	NUM
ejpam-5828	438	8	.	.	PUNCT
ejpam-5828	439	1	[	[	X
ejpam-5828	439	2	22	22	NUM
ejpam-5828	439	3	]	]	PUNCT
ejpam-5828	439	4	r.	r.	PROPN
ejpam-5828	439	5	p.	p.	PROPN
ejpam-5828	439	6	feynman	feynman	PROPN
ejpam-5828	439	7	and	and	CCONJ
ejpam-5828	439	8	f.	f.	PROPN
ejpam-5828	439	9	l.	l.	PROPN
ejpam-5828	439	10	vernon	vernon	PROPN
ejpam-5828	439	11	.	.	PUNCT
ejpam-5828	440	1	the	the	DET
ejpam-5828	440	2	theory	theory	NOUN
ejpam-5828	440	3	of	of	ADP
ejpam-5828	440	4	a	a	DET
ejpam-5828	440	5	general	general	ADJ
ejpam-5828	440	6	quantum	quantum	NOUN
ejpam-5828	440	7	system	system	NOUN
ejpam-5828	440	8	interacting	interact	VERB
ejpam-5828	440	9	with	with	ADP
ejpam-5828	440	10	a	a	DET
ejpam-5828	440	11	linear	linear	ADJ
ejpam-5828	440	12	dissipative	dissipative	ADJ
ejpam-5828	440	13	system	system	NOUN
ejpam-5828	440	14	.	.	PUNCT
ejpam-5828	441	1	annals	annal	NOUN
ejpam-5828	441	2	of	of	ADP
ejpam-5828	441	3	physics	physics	NOUN
ejpam-5828	441	4	,	,	PUNCT
ejpam-5828	441	5	281(1	281(1	NUM
ejpam-5828	441	6	-	-	SYM
ejpam-5828	441	7	2):547	2):547	NUM
ejpam-5828	441	8	–	–	PUNCT
ejpam-5828	441	9	607	607	NUM
ejpam-5828	441	10	,	,	PUNCT
ejpam-5828	441	11	2000	2000	NUM
ejpam-5828	441	12	.	.	PUNCT
ejpam-5828	442	1	[	[	X
ejpam-5828	442	2	23	23	NUM
ejpam-5828	442	3	]	]	X
ejpam-5828	442	4	e.	e.	PROPN
ejpam-5828	442	5	m.	m.	PROPN
ejpam-5828	442	6	rabei	rabei	PROPN
ejpam-5828	442	7	and	and	CCONJ
ejpam-5828	442	8	a.	a.	PROPN
ejpam-5828	442	9	al	al	PROPN
ejpam-5828	442	10	-	-	PUNCT
ejpam-5828	442	11	jamel	jamel	PROPN
ejpam-5828	442	12	.	.	PUNCT
ejpam-5828	443	1	quantisation	quantisation	NOUN
ejpam-5828	443	2	of	of	ADP
ejpam-5828	443	3	particle	particle	NOUN
ejpam-5828	443	4	motion	motion	NOUN
ejpam-5828	443	5	in	in	ADP
ejpam-5828	443	6	dissipative	dissipative	ADJ
ejpam-5828	443	7	harmonic	harmonic	ADJ
ejpam-5828	443	8	environment	environment	NOUN
ejpam-5828	443	9	.	.	PUNCT
ejpam-5828	444	1	pramana	pramana	PROPN
ejpam-5828	444	2	,	,	PUNCT
ejpam-5828	444	3	94(1):1	94(1):1	PROPN
ejpam-5828	444	4	,	,	PUNCT
ejpam-5828	444	5	2020	2020	NUM
ejpam-5828	444	6	.	.	PUNCT
ejpam-5828	445	1	[	[	X
ejpam-5828	445	2	24	24	NUM
ejpam-5828	445	3	]	]	X
ejpam-5828	445	4	y.	y.	PROPN
ejpam-5828	445	5	w.	w.	PROPN
ejpam-5828	445	6	huang	huang	PROPN
ejpam-5828	445	7	,	,	PUNCT
ejpam-5828	445	8	p.	p.	PROPN
ejpam-5828	445	9	y.	y.	PROPN
ejpam-5828	445	10	yang	yang	PROPN
ejpam-5828	445	11	,	,	PUNCT
ejpam-5828	445	12	and	and	CCONJ
ejpam-5828	445	13	w.	w.	PROPN
ejpam-5828	445	14	m.	m.	PROPN
ejpam-5828	445	15	zhang	zhang	PROPN
ejpam-5828	445	16	.	.	PUNCT
ejpam-5828	445	17	quantum	quantum	PROPN
ejpam-5828	445	18	theory	theory	NOUN
ejpam-5828	445	19	of	of	ADP
ejpam-5828	445	20	dissipative	dissipative	ADJ
ejpam-5828	445	21	topological	topological	ADJ
ejpam-5828	445	22	systems	system	NOUN
ejpam-5828	445	23	.	.	PUNCT
ejpam-5828	446	1	physical	physical	ADJ
ejpam-5828	446	2	review	review	PROPN
ejpam-5828	446	3	b	b	PROPN
ejpam-5828	446	4	,	,	PUNCT
ejpam-5828	446	5	102(16):165116	102(16):165116	PROPN
ejpam-5828	446	6	,	,	PUNCT
ejpam-5828	446	7	2020	2020	NUM
ejpam-5828	446	8	.	.	PUNCT
ejpam-5828	447	1	b.	b.	PROPN
ejpam-5828	447	2	m.	m.	PROPN
ejpam-5828	447	3	al	al	PROPN
ejpam-5828	447	4	-	-	PUNCT
ejpam-5828	447	5	khamiseh	khamiseh	PROPN
ejpam-5828	447	6	et	et	PROPN
ejpam-5828	447	7	al	al	PROPN
ejpam-5828	447	8	.	.	PUNCT
ejpam-5828	447	9	/	/	SYM
ejpam-5828	447	10	eur	eur	PROPN
ejpam-5828	447	11	.	.	PUNCT
ejpam-5828	448	1	j.	j.	PROPN
ejpam-5828	448	2	pure	pure	PROPN
ejpam-5828	448	3	appl	appl	PROPN
ejpam-5828	448	4	.	.	PROPN
ejpam-5828	448	5	math	math	PROPN
ejpam-5828	448	6	,	,	PUNCT
ejpam-5828	448	7	18	18	NUM
ejpam-5828	448	8	(	(	PUNCT
ejpam-5828	448	9	2	2	NUM
ejpam-5828	448	10	)	)	PUNCT
ejpam-5828	448	11	(	(	PUNCT
ejpam-5828	448	12	2025	2025	NUM
ejpam-5828	448	13	)	)	PUNCT
ejpam-5828	448	14	,	,	PUNCT
ejpam-5828	448	15	5828	5828	NUM
ejpam-5828	448	16	22	22	NUM
ejpam-5828	448	17	of	of	ADP
ejpam-5828	448	18	25	25	NUM
ejpam-5828	448	19	appendix	appendix	NOUN
ejpam-5828	448	20	a	a	DET
ejpam-5828	448	21	:	:	PUNCT
ejpam-5828	448	22	detailed	detailed	ADJ
ejpam-5828	448	23	derivations	derivation	NOUN
ejpam-5828	448	24	and	and	CCONJ
ejpam-5828	448	25	solution	solution	NOUN
ejpam-5828	448	26	steps	step	NOUN
ejpam-5828	448	27	in	in	ADP
ejpam-5828	448	28	this	this	DET
ejpam-5828	448	29	appendix	appendix	NOUN
ejpam-5828	448	30	,	,	PUNCT
ejpam-5828	448	31	we	we	PRON
ejpam-5828	448	32	present	present	VERB
ejpam-5828	448	33	an	an	DET
ejpam-5828	448	34	analysis	analysis	NOUN
ejpam-5828	448	35	of	of	ADP
ejpam-5828	448	36	the	the	DET
ejpam-5828	448	37	hamilton	hamilton	PROPN
ejpam-5828	448	38	-	-	PUNCT
ejpam-5828	448	39	jacobi	jacobi	PROPN
ejpam-5828	448	40	equation	equation	NOUN
ejpam-5828	448	41	for	for	ADP
ejpam-5828	448	42	the	the	DET
ejpam-5828	448	43	motion	motion	NOUN
ejpam-5828	448	44	of	of	ADP
ejpam-5828	448	45	a	a	DET
ejpam-5828	448	46	two	two	NUM
ejpam-5828	448	47	-	-	PUNCT
ejpam-5828	448	48	dimensional	dimensional	ADJ
ejpam-5828	448	49	harmonic	harmonic	ADJ
ejpam-5828	448	50	oscillator	oscillator	NOUN
ejpam-5828	448	51	using	use	VERB
ejpam-5828	448	52	staeckel	staeckel	NOUN
ejpam-5828	448	53	boundary	boundary	ADJ
ejpam-5828	448	54	conditions	condition	NOUN
ejpam-5828	448	55	for	for	ADP
ejpam-5828	448	56	separation	separation	NOUN
ejpam-5828	448	57	of	of	ADP
ejpam-5828	448	58	variables	variable	NOUN
ejpam-5828	448	59	.	.	PUNCT
ejpam-5828	449	1	the	the	DET
ejpam-5828	449	2	hamiltonian	hamiltonian	ADJ
ejpam-5828	449	3	equation	equation	NOUN
ejpam-5828	449	4	for	for	ADP
ejpam-5828	449	5	the	the	DET
ejpam-5828	449	6	dissipative	dissipative	ADJ
ejpam-5828	449	7	system	system	NOUN
ejpam-5828	449	8	is	be	AUX
ejpam-5828	449	9	derived	derive	VERB
ejpam-5828	449	10	and	and	CCONJ
ejpam-5828	449	11	analyzed	analyze	VERB
ejpam-5828	449	12	using	use	VERB
ejpam-5828	449	13	the	the	DET
ejpam-5828	449	14	hamilton	hamilton	PROPN
ejpam-5828	449	15	-	-	PUNCT
ejpam-5828	449	16	jacobi	jacobi	PROPN
ejpam-5828	449	17	function	function	PROPN
ejpam-5828	449	18	w	w	PROPN
ejpam-5828	449	19	(	(	PUNCT
ejpam-5828	449	20	q	q	NOUN
ejpam-5828	449	21	)	)	PUNCT
ejpam-5828	449	22	to	to	PART
ejpam-5828	449	23	separate	separate	VERB
ejpam-5828	449	24	the	the	DET
ejpam-5828	449	25	variables	variable	NOUN
ejpam-5828	449	26	in	in	ADP
ejpam-5828	449	27	the	the	DET
ejpam-5828	449	28	x	x	NOUN
ejpam-5828	449	29	and	and	CCONJ
ejpam-5828	449	30	y	y	PROPN
ejpam-5828	449	31	directions	direction	NOUN
ejpam-5828	449	32	.	.	PUNCT
ejpam-5828	450	1	after	after	ADP
ejpam-5828	450	2	applying	apply	VERB
ejpam-5828	450	3	staeckel	staeckel	NOUN
ejpam-5828	450	4	conditions	condition	NOUN
ejpam-5828	450	5	,	,	PUNCT
ejpam-5828	450	6	precise	precise	ADJ
ejpam-5828	450	7	mathematical	mathematical	ADJ
ejpam-5828	450	8	solutions	solution	NOUN
ejpam-5828	450	9	are	be	AUX
ejpam-5828	450	10	obtained	obtain	VERB
ejpam-5828	450	11	,	,	PUNCT
ejpam-5828	450	12	enabling	enable	VERB
ejpam-5828	450	13	a	a	DET
ejpam-5828	450	14	deeper	deep	ADJ
ejpam-5828	450	15	understanding	understanding	NOUN
ejpam-5828	450	16	of	of	ADP
ejpam-5828	450	17	the	the	DET
ejpam-5828	450	18	system	system	NOUN
ejpam-5828	450	19	’s	’s	PART
ejpam-5828	450	20	behavior	behavior	NOUN
ejpam-5828	450	21	and	and	CCONJ
ejpam-5828	450	22	the	the	DET
ejpam-5828	450	23	calculation	calculation	NOUN
ejpam-5828	450	24	of	of	ADP
ejpam-5828	450	25	energy	energy	NOUN
ejpam-5828	450	26	levels	level	NOUN
ejpam-5828	450	27	and	and	CCONJ
ejpam-5828	450	28	quantum	quantum	NOUN
ejpam-5828	450	29	states	state	NOUN
ejpam-5828	450	30	using	use	VERB
ejpam-5828	450	31	creation	creation	NOUN
ejpam-5828	450	32	and	and	CCONJ
ejpam-5828	450	33	annihilation	annihilation	NOUN
ejpam-5828	450	34	operators	operator	NOUN
ejpam-5828	450	35	.	.	PUNCT
ejpam-5828	451	1	1	1	NUM
ejpam-5828	451	2	2	2	NUM
ejpam-5828	451	3	m	m	VERB
ejpam-5828	451	4	(	(	PUNCT
ejpam-5828	451	5	(	(	PUNCT
ejpam-5828	451	6	∂wx	∂wx	PROPN
ejpam-5828	451	7	∂x	∂x	PROPN
ejpam-5828	451	8	)	)	PUNCT
ejpam-5828	451	9	2	2	NUM
ejpam-5828	452	1	+	+	SYM
ejpam-5828	452	2	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	452	3	2	2	NUM
ejpam-5828	452	4	+	+	CCONJ
ejpam-5828	452	5	(	(	PUNCT
ejpam-5828	452	6	∂wy	∂wy	PROPN
ejpam-5828	452	7	∂y	∂y	NUM
ejpam-5828	452	8	)	)	PUNCT
ejpam-5828	452	9	2	2	NUM
ejpam-5828	453	1	+	+	NUM
ejpam-5828	453	2	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	453	3	2	2	NUM
ejpam-5828	453	4	)	)	PUNCT
ejpam-5828	454	1	=	=	SYM
ejpam-5828	454	2	α	α	PROPN
ejpam-5828	454	3	(	(	PUNCT
ejpam-5828	454	4	a.1	a.1	NOUN
ejpam-5828	454	5	)	)	PUNCT
ejpam-5828	454	6	by	by	ADP
ejpam-5828	454	7	employing	employ	VERB
ejpam-5828	454	8	variable	variable	ADJ
ejpam-5828	454	9	separation	separation	NOUN
ejpam-5828	454	10	in	in	ADP
ejpam-5828	454	11	equation	equation	NOUN
ejpam-5828	454	12	(	(	PUNCT
ejpam-5828	454	13	a.1	a.1	NOUN
ejpam-5828	454	14	)	)	PUNCT
ejpam-5828	454	15	above	above	ADV
ejpam-5828	454	16	in	in	ADP
ejpam-5828	454	17	terms	term	NOUN
ejpam-5828	454	18	of	of	ADP
ejpam-5828	454	19	and	and	CCONJ
ejpam-5828	454	20	wy	wy	PROPN
ejpam-5828	454	21	,	,	PUNCT
ejpam-5828	454	22	resulting	result	VERB
ejpam-5828	454	23	in	in	ADP
ejpam-5828	454	24	:	:	PUNCT
ejpam-5828	454	25	1	1	NUM
ejpam-5828	454	26	2	2	NUM
ejpam-5828	454	27	m	m	VERB
ejpam-5828	454	28	(	(	PUNCT
ejpam-5828	454	29	(	(	PUNCT
ejpam-5828	454	30	∂wy	∂wy	PROPN
ejpam-5828	454	31	∂y	∂y	X
ejpam-5828	454	32	)	)	PUNCT
ejpam-5828	454	33	2	2	NUM
ejpam-5828	455	1	+	+	NUM
ejpam-5828	455	2	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	455	3	2	2	NUM
ejpam-5828	455	4	)	)	PUNCT
ejpam-5828	455	5	−	−	NOUN
ejpam-5828	456	1	1	1	NUM
ejpam-5828	456	2	2	2	NUM
ejpam-5828	456	3	m	m	NUM
ejpam-5828	456	4	2λ2y2	2λ2y2	NUM
ejpam-5828	456	5	=	=	SYM
ejpam-5828	456	6	αy	αy	ADJ
ejpam-5828	456	7	(	(	PUNCT
ejpam-5828	456	8	a.2	a.2	SYM
ejpam-5828	456	9	)	)	PUNCT
ejpam-5828	456	10	1	1	NUM
ejpam-5828	456	11	2	2	NUM
ejpam-5828	456	12	m	m	VERB
ejpam-5828	456	13	(	(	PUNCT
ejpam-5828	456	14	(	(	PUNCT
ejpam-5828	456	15	∂wx	∂wx	PROPN
ejpam-5828	456	16	∂x	∂x	PROPN
ejpam-5828	456	17	)	)	PUNCT
ejpam-5828	456	18	2	2	NUM
ejpam-5828	457	1	+	+	SYM
ejpam-5828	457	2	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	457	3	2	2	NUM
ejpam-5828	457	4	)	)	PUNCT
ejpam-5828	457	5	−	−	NOUN
ejpam-5828	457	6	1	1	NUM
ejpam-5828	457	7	2	2	NUM
ejpam-5828	457	8	m2λ2x2	m2λ2x2	NOUN
ejpam-5828	457	9	+	+	CCONJ
ejpam-5828	457	10	αy	αy	NOUN
ejpam-5828	457	11	=	=	PUNCT
ejpam-5828	457	12	αx	αx	PROPN
ejpam-5828	457	13	(	(	PUNCT
ejpam-5828	457	14	a.3	a.3	NOUN
ejpam-5828	457	15	)	)	PUNCT
ejpam-5828	457	16	after	after	ADP
ejpam-5828	457	17	integration	integration	NOUN
ejpam-5828	457	18	,	,	PUNCT
ejpam-5828	457	19	we	we	PRON
ejpam-5828	457	20	may	may	AUX
ejpam-5828	457	21	express	express	VERB
ejpam-5828	457	22	equations	equation	NOUN
ejpam-5828	457	23	(	(	PUNCT
ejpam-5828	457	24	a.2	a.2	SYM
ejpam-5828	457	25	)	)	PUNCT
ejpam-5828	457	26	and	and	CCONJ
ejpam-5828	457	27	(	(	PUNCT
ejpam-5828	457	28	a.3	a.3	X
ejpam-5828	457	29	)	)	PUNCT
ejpam-5828	457	30	as	as	SCONJ
ejpam-5828	457	31	follows	follow	VERB
ejpam-5828	457	32	:	:	PUNCT
ejpam-5828	457	33	wy′	wy′	PROPN
ejpam-5828	457	34	=	=	SYM
ejpam-5828	457	35	∫	∫	PROPN
ejpam-5828	458	1	y	y	PROPN
ejpam-5828	459	1	′	′	NOUN
ejpam-5828	459	2	0	0	NUM
ejpam-5828	460	1	√	√	INTJ
ejpam-5828	461	1	(	(	PUNCT
ejpam-5828	461	2	2mαy	2mαy	PROPN
ejpam-5828	461	3	−	−	NOUN
ejpam-5828	461	4	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	461	5	2	2	NUM
ejpam-5828	462	1	+	+	CCONJ
ejpam-5828	462	2	1	1	NUM
ejpam-5828	462	3	2	2	NUM
ejpam-5828	462	4	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	462	5	2)dy	2)dy	NUM
ejpam-5828	462	6	(	(	PUNCT
ejpam-5828	462	7	a.4	a.4	NOUN
ejpam-5828	462	8	)	)	PUNCT
ejpam-5828	462	9	wx′	wx′	NOUN
ejpam-5828	463	1	=	=	SYM
ejpam-5828	463	2	∫	∫	PROPN
ejpam-5828	463	3	x	x	PUNCT
ejpam-5828	464	1	′	′	NOUN
ejpam-5828	464	2	0	0	NUM
ejpam-5828	464	3	√	√	NUM
ejpam-5828	464	4	(	(	PUNCT
ejpam-5828	464	5	2mα−	2mα−	NUM
ejpam-5828	464	6	2mαy	2mαy	NUM
ejpam-5828	464	7	−	−	PROPN
ejpam-5828	464	8	4π2m2v2xy	4π2m2v2xy	NOUN
ejpam-5828	464	9	2	2	NUM
ejpam-5828	464	10	+	+	CCONJ
ejpam-5828	464	11	1	1	NUM
ejpam-5828	464	12	2	2	NUM
ejpam-5828	464	13	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	464	14	2)dx	2)dx	NOUN
ejpam-5828	464	15	(	(	PUNCT
ejpam-5828	464	16	a.5	a.5	NOUN
ejpam-5828	464	17	)	)	PUNCT
ejpam-5828	464	18	substituting	substitute	VERB
ejpam-5828	464	19	equations	equation	NOUN
ejpam-5828	464	20	.	.	PUNCT
ejpam-5828	465	1	(	(	PUNCT
ejpam-5828	465	2	a.4	a.4	X
ejpam-5828	465	3	)	)	PUNCT
ejpam-5828	465	4	and	and	CCONJ
ejpam-5828	465	5	(	(	PUNCT
ejpam-5828	465	6	a.5	a.5	NOUN
ejpam-5828	465	7	)	)	PUNCT
ejpam-5828	465	8	into	into	ADP
ejpam-5828	465	9	the	the	DET
ejpam-5828	465	10	equation	equation	NOUN
ejpam-5828	465	11	wy′	wy′	ADV
ejpam-5828	466	1	+	+	CCONJ
ejpam-5828	466	2	wx′	wx′	X
ejpam-5828	466	3	=	=	SYM
ejpam-5828	466	4	w	w	PROPN
ejpam-5828	466	5	,	,	PUNCT
ejpam-5828	466	6	we	we	PRON
ejpam-5828	466	7	obtain	obtain	VERB
ejpam-5828	466	8	:	:	PUNCT
ejpam-5828	467	1	w	w	PROPN
ejpam-5828	467	2	=	=	PUNCT
ejpam-5828	467	3	∫	∫	PROPN
ejpam-5828	467	4	y	y	PROPN
ejpam-5828	467	5	′	′	NOUN
ejpam-5828	467	6	0	0	NUM
ejpam-5828	468	1	√	√	INTJ
ejpam-5828	469	1	(	(	PUNCT
ejpam-5828	469	2	2mαy	2mαy	PROPN
ejpam-5828	469	3	−	−	NOUN
ejpam-5828	469	4	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	469	5	2	2	NUM
ejpam-5828	470	1	+	+	CCONJ
ejpam-5828	470	2	1	1	NUM
ejpam-5828	470	3	2	2	NUM
ejpam-5828	470	4	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	470	5	2)dy+	2)dy+	NUM
ejpam-5828	470	6	∫	∫	NOUN
ejpam-5828	470	7	x	x	SYM
ejpam-5828	471	1	′	′	NUM
ejpam-5828	471	2	0	0	NUM
ejpam-5828	471	3	√	√	NUM
ejpam-5828	471	4	(	(	PUNCT
ejpam-5828	471	5	2mα−	2mα−	NUM
ejpam-5828	471	6	2mαy	2mαy	NUM
ejpam-5828	471	7	−	−	PROPN
ejpam-5828	471	8	4π2m2v2xy	4π2m2v2xy	NOUN
ejpam-5828	471	9	2	2	NUM
ejpam-5828	471	10	+	+	CCONJ
ejpam-5828	471	11	1	1	NUM
ejpam-5828	471	12	2	2	NUM
ejpam-5828	471	13	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	471	14	2)dx	2)dx	NOUN
ejpam-5828	471	15	with	with	ADP
ejpam-5828	471	16	these	these	DET
ejpam-5828	471	17	result	result	NOUN
ejpam-5828	471	18	,	,	PUNCT
ejpam-5828	471	19	the	the	DET
ejpam-5828	471	20	hamilton	hamilton	PROPN
ejpam-5828	471	21	-	-	PUNCT
ejpam-5828	471	22	jacobi	jacobi	PROPN
ejpam-5828	471	23	function	function	PROPN
ejpam-5828	471	24	s(q	s(q	PROPN
ejpam-5828	471	25	,	,	PUNCT
ejpam-5828	471	26	α	α	NOUN
ejpam-5828	471	27	,	,	PUNCT
ejpam-5828	471	28	t	t	PROPN
ejpam-5828	471	29	)	)	PUNCT
ejpam-5828	471	30	=	=	NOUN
ejpam-5828	471	31	w	w	X
ejpam-5828	471	32	(	(	PUNCT
ejpam-5828	471	33	q	q	NOUN
ejpam-5828	471	34	,	,	PUNCT
ejpam-5828	471	35	α)−	α)−	NOUN
ejpam-5828	471	36	αt	αt	NOUN
ejpam-5828	471	37	becomes	become	VERB
ejpam-5828	471	38	:	:	PUNCT
ejpam-5828	471	39	s(q	s(q	NOUN
ejpam-5828	471	40	,	,	PUNCT
ejpam-5828	471	41	α	α	NOUN
ejpam-5828	471	42	,	,	PUNCT
ejpam-5828	471	43	t	t	PROPN
ejpam-5828	471	44	)	)	PUNCT
ejpam-5828	471	45	=	=	SYM
ejpam-5828	472	1	∫	∫	PROPN
ejpam-5828	473	1	y	y	PROPN
ejpam-5828	474	1	′	′	NOUN
ejpam-5828	474	2	0	0	NUM
ejpam-5828	475	1	√	√	INTJ
ejpam-5828	476	1	(	(	PUNCT
ejpam-5828	476	2	2mαy	2mαy	PROPN
ejpam-5828	476	3	−	−	NOUN
ejpam-5828	476	4	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	476	5	2	2	NUM
ejpam-5828	477	1	+	+	CCONJ
ejpam-5828	477	2	1	1	NUM
ejpam-5828	477	3	2	2	NUM
ejpam-5828	477	4	m2λ2yy	m2λ2yy	NOUN
ejpam-5828	477	5	2)dy+	2)dy+	NUM
ejpam-5828	477	6	∫	∫	NOUN
ejpam-5828	477	7	x	x	SYM
ejpam-5828	478	1	′	′	NUM
ejpam-5828	478	2	0	0	NUM
ejpam-5828	478	3	√	√	NUM
ejpam-5828	478	4	(	(	PUNCT
ejpam-5828	478	5	2mα−	2mα−	NUM
ejpam-5828	478	6	2mαy	2mαy	NUM
ejpam-5828	478	7	−	−	PROPN
ejpam-5828	478	8	4π2m2v2xy	4π2m2v2xy	NOUN
ejpam-5828	478	9	2	2	NUM
ejpam-5828	478	10	+	+	CCONJ
ejpam-5828	478	11	1	1	NUM
ejpam-5828	478	12	2	2	NUM
ejpam-5828	478	13	m2λ2xx	m2λ2xx	NOUN
ejpam-5828	478	14	2)dx−	2)dx−	NUM
ejpam-5828	478	15	αt	αt	NOUN
ejpam-5828	478	16	taking	take	VERB
ejpam-5828	478	17	the	the	DET
ejpam-5828	478	18	derivative	derivative	NOUN
ejpam-5828	478	19	with	with	ADP
ejpam-5828	478	20	respect	respect	NOUN
ejpam-5828	478	21	to	to	ADP
ejpam-5828	478	22	αi	αi	NOUN
ejpam-5828	478	23	for	for	ADP
ejpam-5828	478	24	equation	equation	NOUN
ejpam-5828	478	25	(	(	PUNCT
ejpam-5828	478	26	a.6	a.6	PROPN
ejpam-5828	478	27	)	)	PUNCT
ejpam-5828	478	28	,	,	PUNCT
ejpam-5828	478	29	one	one	PRON
ejpam-5828	478	30	gets	get	VERB
ejpam-5828	478	31	:	:	PUNCT
ejpam-5828	478	32	by′	by′	NOUN
ejpam-5828	478	33	=	=	SYM
ejpam-5828	478	34	∂s	∂s	PROPN
ejpam-5828	478	35	∂αy′	∂αy′	PROPN
ejpam-5828	478	36	=	=	PUNCT
ejpam-5828	479	1	∫	∫	PROPN
ejpam-5828	479	2	y	y	PROPN
ejpam-5828	480	1	′	′	NUM
ejpam-5828	480	2	0	0	NUM
ejpam-5828	481	1	m	m	VERB
ejpam-5828	481	2	2mαy	2mαy	NUM
ejpam-5828	481	3	−	−	NOUN
ejpam-5828	481	4	4π2m2v2yy	4π2m2v2yy	NOUN
ejpam-5828	481	5	2	2	NUM
ejpam-5828	482	1	+	+	CCONJ
ejpam-5828	482	2	1	1	NUM
ejpam-5828	482	3	2	2	NUM
ejpam-5828	482	4	m	m	NUM
ejpam-5828	482	5	2λ2yy	2λ2yy	NUM
ejpam-5828	482	6	2	2	NUM
ejpam-5828	482	7	)	)	PUNCT
ejpam-5828	482	8	dy−	dy−	PROPN
ejpam-5828	482	9	b.	b.	PROPN
ejpam-5828	482	10	m.	m.	PROPN
ejpam-5828	483	1	al	al	PROPN
ejpam-5828	483	2	-	-	PUNCT
ejpam-5828	483	3	khamiseh	khamiseh	PROPN
ejpam-5828	483	4	et	et	PROPN
ejpam-5828	483	5	al	al	PROPN
ejpam-5828	483	6	.	.	PUNCT
ejpam-5828	483	7	/	/	SYM
ejpam-5828	483	8	eur	eur	PROPN
ejpam-5828	483	9	.	.	PUNCT
ejpam-5828	484	1	j.	j.	PROPN
ejpam-5828	484	2	pure	pure	PROPN
ejpam-5828	484	3	appl	appl	PROPN
ejpam-5828	484	4	.	.	PROPN
ejpam-5828	484	5	math	math	PROPN
ejpam-5828	484	6	,	,	PUNCT
ejpam-5828	484	7	18	18	NUM
ejpam-5828	484	8	(	(	PUNCT
ejpam-5828	484	9	2	2	NUM
ejpam-5828	484	10	)	)	PUNCT
ejpam-5828	484	11	(	(	PUNCT
ejpam-5828	484	12	2025	2025	NUM
ejpam-5828	484	13	)	)	PUNCT
ejpam-5828	484	14	,	,	PUNCT
ejpam-5828	484	15	5828	5828	NUM
ejpam-5828	484	16	23	23	NUM
ejpam-5828	484	17	of	of	ADP
ejpam-5828	484	18	25	25	NUM
ejpam-5828	484	19	sin−1	sin−1	PROPN
ejpam-5828	484	20	(	(	PUNCT
ejpam-5828	484	21	√	√	PROPN
ejpam-5828	484	22	(	(	PUNCT
ejpam-5828	484	23	2mπ2v2	2mπ2v2	NUM
ejpam-5828	484	24	y	y	PROPN
ejpam-5828	484	25	′−	′−	PROPN
ejpam-5828	484	26	1	1	NUM
ejpam-5828	484	27	4	4	NUM
ejpam-5828	484	28	mλ2	mλ2	NOUN
ejpam-5828	484	29	y	y	NOUN
ejpam-5828	485	1	′	′	NUM
ejpam-5828	485	2	α	α	NOUN
ejpam-5828	485	3	y	y	NOUN
ejpam-5828	485	4	′	′	NUM
ejpam-5828	485	5	)	)	PUNCT
ejpam-5828	486	1	y	y	PROPN
ejpam-5828	486	2	′	′	NUM
ejpam-5828	486	3	)	)	PUNCT
ejpam-5828	487	1	√	√	NUM
ejpam-5828	488	1	4π2v2	4π2v2	NUM
ejpam-5828	488	2	y′	y′	NOUN
ejpam-5828	489	1	−	−	PROPN
ejpam-5828	489	2	sin−1	sin−1	PROPN
ejpam-5828	489	3	(	(	PUNCT
ejpam-5828	489	4	√	√	PROPN
ejpam-5828	489	5	(	(	PUNCT
ejpam-5828	489	6	2mπ2v2	2mπ2v2	NUM
ejpam-5828	489	7	x	x	SYM
ejpam-5828	489	8	′−	′−	NOUN
ejpam-5828	489	9	1	1	NUM
ejpam-5828	489	10	4	4	NUM
ejpam-5828	489	11	mλ2	mλ2	NOUN
ejpam-5828	489	12	x	x	NOUN
ejpam-5828	489	13	′	′	NUM
ejpam-5828	489	14	α−α	α−α	NUM
ejpam-5828	489	15	y	y	NOUN
ejpam-5828	489	16	′	′	NUM
ejpam-5828	489	17	)	)	PUNCT
ejpam-5828	490	1	x	x	SYM
ejpam-5828	490	2	′	′	NUM
ejpam-5828	490	3	)	)	PUNCT
ejpam-5828	491	1	√	√	PROPN
ejpam-5828	492	1	4π2v2	4π2v2	NUM
ejpam-5828	492	2	x′	x′	PROPN
ejpam-5828	492	3	(	(	PUNCT
ejpam-5828	492	4	a.7	a.7	NOUN
ejpam-5828	492	5	)	)	PUNCT
ejpam-5828	492	6	βx′	βx′	PUNCT
ejpam-5828	493	1	+	+	NUM
ejpam-5828	493	2	t	t	X
ejpam-5828	493	3	=	=	SYM
ejpam-5828	493	4	∫	∫	PROPN
ejpam-5828	493	5	x	x	PUNCT
ejpam-5828	494	1	′	′	NUM
ejpam-5828	494	2	0	0	NUM
ejpam-5828	495	1	m	m	VERB
ejpam-5828	495	2	2mα−	2mα−	NUM
ejpam-5828	496	1	2mαy	2mαy	NUM
ejpam-5828	496	2	−	−	NOUN
ejpam-5828	496	3	4π2m2v2xx	4π2m2v2xx	NOUN
ejpam-5828	496	4	2	2	NUM
ejpam-5828	496	5	+	+	CCONJ
ejpam-5828	496	6	1	1	NUM
ejpam-5828	496	7	2	2	NUM
ejpam-5828	496	8	m	m	NUM
ejpam-5828	496	9	2λ2xx	2λ2xx	NUM
ejpam-5828	496	10	2	2	NUM
ejpam-5828	496	11	)	)	PUNCT
ejpam-5828	496	12	dx	dx	PROPN
ejpam-5828	497	1	=	=	SYM
ejpam-5828	497	2	sin−1	sin−1	PROPN
ejpam-5828	497	3	(	(	PUNCT
ejpam-5828	497	4	√	√	PROPN
ejpam-5828	497	5	(	(	PUNCT
ejpam-5828	497	6	2mπ2v2	2mπ2v2	NUM
ejpam-5828	497	7	x	x	SYM
ejpam-5828	497	8	′−	′−	NOUN
ejpam-5828	497	9	1	1	NUM
ejpam-5828	497	10	4	4	NUM
ejpam-5828	497	11	mλ2	mλ2	NOUN
ejpam-5828	497	12	x	x	NOUN
ejpam-5828	497	13	′	′	NUM
ejpam-5828	497	14	α−α	α−α	NUM
ejpam-5828	497	15	y	y	NOUN
ejpam-5828	497	16	′	′	NUM
ejpam-5828	497	17	)	)	PUNCT
ejpam-5828	497	18	x	x	SYM
ejpam-5828	497	19	′	′	NUM
ejpam-5828	497	20	)	)	PUNCT
ejpam-5828	498	1	√	√	PROPN
ejpam-5828	499	1	4π2v2	4π2v2	NUM
ejpam-5828	499	2	x′	x′	PROPN
ejpam-5828	499	3	(	(	PUNCT
ejpam-5828	499	4	a.8	a.8	NOUN
ejpam-5828	499	5	)	)	PUNCT
ejpam-5828	499	6	equation	equation	NOUN
ejpam-5828	499	7	(	(	PUNCT
ejpam-5828	499	8	a.8	a.8	NOUN
ejpam-5828	499	9	)	)	PUNCT
ejpam-5828	499	10	allows	allow	VERB
ejpam-5828	499	11	us	we	PRON
ejpam-5828	499	12	to	to	PART
ejpam-5828	499	13	formulate	formulate	VERB
ejpam-5828	499	14	the	the	DET
ejpam-5828	499	15	result	result	NOUN
ejpam-5828	499	16	as	as	ADP
ejpam-5828	499	17	βx′	βx′	NOUN
ejpam-5828	499	18	+	+	NUM
ejpam-5828	499	19	t	t	NOUN
ejpam-5828	499	20	=	=	SYM
ejpam-5828	499	21	sin−1	sin−1	PROPN
ejpam-5828	499	22	(	(	PUNCT
ejpam-5828	499	23	√	√	PROPN
ejpam-5828	499	24	(	(	PUNCT
ejpam-5828	499	25	2mπ2v2	2mπ2v2	NUM
ejpam-5828	499	26	x	x	SYM
ejpam-5828	499	27	′−	′−	NOUN
ejpam-5828	499	28	1	1	NUM
ejpam-5828	499	29	4	4	NUM
ejpam-5828	499	30	mλ2	mλ2	NOUN
ejpam-5828	499	31	x	x	NOUN
ejpam-5828	499	32	′	′	NUM
ejpam-5828	499	33	α−α	α−α	NUM
ejpam-5828	499	34	y	y	NOUN
ejpam-5828	499	35	′	′	NUM
ejpam-5828	499	36	)	)	PUNCT
ejpam-5828	500	1	x	x	SYM
ejpam-5828	500	2	′	′	NUM
ejpam-5828	500	3	)	)	PUNCT
ejpam-5828	501	1	√	√	PROPN
ejpam-5828	502	1	4π2v2	4π2v2	NUM
ejpam-5828	502	2	x′	x′	PROPN
ejpam-5828	503	1	after	after	ADP
ejpam-5828	503	2	some	some	DET
ejpam-5828	503	3	algebraic	algebraic	ADJ
ejpam-5828	503	4	work	work	NOUN
ejpam-5828	503	5	,	,	PUNCT
ejpam-5828	503	6	we	we	PRON
ejpam-5828	503	7	obtain	obtain	VERB
ejpam-5828	503	8	:	:	PUNCT
ejpam-5828	503	9	x	x	X
ejpam-5828	503	10	′	′	X
ejpam-5828	503	11	=	=	PUNCT
ejpam-5828	504	1	√√√√	√√√√	NOUN
ejpam-5828	504	2	(	(	PUNCT
ejpam-5828	504	3	α−	α−	ADP
ejpam-5828	504	4	αy	αy	ADP
ejpam-5828	504	5	2mπ2v2	2mπ2v2	NUM
ejpam-5828	504	6	x′	x′	PUNCT
ejpam-5828	504	7	−	−	NUM
ejpam-5828	504	8	1	1	NUM
ejpam-5828	504	9	4mλ	4mλ	NOUN
ejpam-5828	504	10	2	2	NUM
ejpam-5828	504	11	x′	x′	NUM
ejpam-5828	504	12	)	)	PUNCT
ejpam-5828	504	13	sin	sin	NOUN
ejpam-5828	505	1	[	[	X
ejpam-5828	505	2	√	√	NOUN
ejpam-5828	505	3	4π2v2	4π2v2	NUM
ejpam-5828	505	4	x′	x′	PROPN
ejpam-5828	506	1	(	(	PUNCT
ejpam-5828	506	2	βx′	βx′	PROPN
ejpam-5828	506	3	+	+	NUM
ejpam-5828	506	4	t	t	NOUN
ejpam-5828	506	5	)	)	PUNCT
ejpam-5828	506	6	]	]	PUNCT
ejpam-5828	506	7	(	(	PUNCT
ejpam-5828	506	8	a.9	a.9	X
ejpam-5828	506	9	)	)	PUNCT
ejpam-5828	506	10	the	the	DET
ejpam-5828	506	11	above	above	ADJ
ejpam-5828	506	12	equation	equation	NOUN
ejpam-5828	506	13	is	be	AUX
ejpam-5828	506	14	exactly	exactly	ADV
ejpam-5828	506	15	the	the	DET
ejpam-5828	506	16	same	same	ADJ
ejpam-5828	506	17	as	as	ADP
ejpam-5828	506	18	the	the	DET
ejpam-5828	506	19	equation	equation	NOUN
ejpam-5828	506	20	that	that	PRON
ejpam-5828	506	21	has	have	AUX
ejpam-5828	506	22	been	be	AUX
ejpam-5828	506	23	derived	derive	VERB
ejpam-5828	506	24	by	by	ADP
ejpam-5828	506	25	(	(	PUNCT
ejpam-5828	506	26	equation	equation	NOUN
ejpam-5828	506	27	(	(	PUNCT
ejpam-5828	506	28	15.a	15.a	NUM
ejpam-5828	506	29	)	)	PUNCT
ejpam-5828	506	30	)	)	PUNCT
ejpam-5828	506	31	in	in	ADP
ejpam-5828	506	32	the	the	DET
ejpam-5828	506	33	same	same	ADJ
ejpam-5828	506	34	classical	classical	ADJ
ejpam-5828	506	35	solution	solution	NOUN
ejpam-5828	506	36	.	.	PUNCT
ejpam-5828	507	1	the	the	DET
ejpam-5828	507	2	formulation	formulation	NOUN
ejpam-5828	507	3	enabled	enable	VERB
ejpam-5828	507	4	a	a	DET
ejpam-5828	507	5	mathematically	mathematically	ADV
ejpam-5828	507	6	rigorous	rigorous	ADJ
ejpam-5828	507	7	description	description	NOUN
ejpam-5828	507	8	of	of	ADP
ejpam-5828	507	9	the	the	DET
ejpam-5828	507	10	system	system	NOUN
ejpam-5828	507	11	dynamics	dynamic	NOUN
ejpam-5828	507	12	,	,	PUNCT
ejpam-5828	507	13	accurately	accurately	ADV
ejpam-5828	507	14	deriving	derive	VERB
ejpam-5828	507	15	energy	energy	NOUN
ejpam-5828	507	16	levels	level	NOUN
ejpam-5828	507	17	and	and	CCONJ
ejpam-5828	507	18	quantum	quantum	NOUN
ejpam-5828	507	19	states	state	NOUN
ejpam-5828	507	20	through	through	ADP
ejpam-5828	507	21	creation	creation	NOUN
ejpam-5828	507	22	and	and	CCONJ
ejpam-5828	507	23	annihilation	annihilation	NOUN
ejpam-5828	507	24	operators	operator	NOUN
ejpam-5828	507	25	,	,	PUNCT
ejpam-5828	507	26	highlighting	highlight	VERB
ejpam-5828	507	27	the	the	DET
ejpam-5828	507	28	strength	strength	NOUN
ejpam-5828	507	29	of	of	ADP
ejpam-5828	507	30	this	this	DET
ejpam-5828	507	31	method	method	NOUN
ejpam-5828	507	32	.	.	PUNCT
ejpam-5828	508	1	the	the	DET
ejpam-5828	508	2	creation	creation	NOUN
ejpam-5828	508	3	and	and	CCONJ
ejpam-5828	508	4	annihilation	annihilation	NOUN
ejpam-5828	508	5	operators	operator	NOUN
ejpam-5828	508	6	provide	provide	VERB
ejpam-5828	508	7	a	a	DET
ejpam-5828	508	8	powerful	powerful	ADJ
ejpam-5828	508	9	framework	framework	NOUN
ejpam-5828	508	10	for	for	ADP
ejpam-5828	508	11	quantizing	quantize	VERB
ejpam-5828	508	12	the	the	DET
ejpam-5828	508	13	dissipative	dissipative	ADJ
ejpam-5828	508	14	two	two	NUM
ejpam-5828	508	15	-	-	PUNCT
ejpam-5828	508	16	dimensional	dimensional	ADJ
ejpam-5828	508	17	anisotropic	anisotropic	NOUN
ejpam-5828	508	18	harmonic	harmonic	ADJ
ejpam-5828	508	19	oscillator	oscillator	NOUN
ejpam-5828	508	20	.	.	PUNCT
ejpam-5828	509	1	by	by	ADP
ejpam-5828	509	2	expressing	express	VERB
ejpam-5828	509	3	position	position	NOUN
ejpam-5828	509	4	and	and	CCONJ
ejpam-5828	509	5	momentum	momentum	NOUN
ejpam-5828	509	6	in	in	ADP
ejpam-5828	509	7	terms	term	NOUN
ejpam-5828	509	8	of	of	ADP
ejpam-5828	509	9	these	these	DET
ejpam-5828	509	10	operators	operator	NOUN
ejpam-5828	509	11	,	,	PUNCT
ejpam-5828	509	12	the	the	DET
ejpam-5828	509	13	hamiltonian	hamiltonian	NOUN
ejpam-5828	509	14	is	be	AUX
ejpam-5828	509	15	simplified	simplify	VERB
ejpam-5828	509	16	,	,	PUNCT
ejpam-5828	509	17	enabling	enable	VERB
ejpam-5828	509	18	the	the	DET
ejpam-5828	509	19	systematic	systematic	ADJ
ejpam-5828	509	20	derivation	derivation	NOUN
ejpam-5828	509	21	of	of	ADP
ejpam-5828	509	22	energy	energy	NOUN
ejpam-5828	509	23	eigenvalues	eigenvalue	NOUN
ejpam-5828	509	24	and	and	CCONJ
ejpam-5828	509	25	eigenfunctions	eigenfunction	NOUN
ejpam-5828	509	26	.	.	PUNCT
ejpam-5828	510	1	the	the	DET
ejpam-5828	510	2	energy	energy	NOUN
ejpam-5828	510	3	levels	level	NOUN
ejpam-5828	510	4	are	be	AUX
ejpam-5828	510	5	expressed	express	VERB
ejpam-5828	510	6	in	in	ADP
ejpam-5828	510	7	terms	term	NOUN
ejpam-5828	510	8	of	of	ADP
ejpam-5828	510	9	quantum	quantum	ADJ
ejpam-5828	510	10	numbers	number	NOUN
ejpam-5828	510	11	nx	nx	X
ejpam-5828	510	12	and	and	CCONJ
ejpam-5828	510	13	ny	ny	PROPN
ejpam-5828	510	14	,	,	PUNCT
ejpam-5828	510	15	while	while	SCONJ
ejpam-5828	510	16	the	the	DET
ejpam-5828	510	17	wavefunctions	wavefunction	NOUN
ejpam-5828	510	18	are	be	AUX
ejpam-5828	510	19	constructed	construct	VERB
ejpam-5828	510	20	using	use	VERB
ejpam-5828	510	21	hermite	hermite	ADJ
ejpam-5828	510	22	polynomials	polynomial	NOUN
ejpam-5828	510	23	.	.	PUNCT
ejpam-5828	511	1	this	this	DET
ejpam-5828	511	2	approach	approach	NOUN
ejpam-5828	511	3	ensures	ensure	VERB
ejpam-5828	511	4	consistency	consistency	NOUN
ejpam-5828	511	5	with	with	ADP
ejpam-5828	511	6	classical	classical	ADJ
ejpam-5828	511	7	mechanics	mechanic	NOUN
ejpam-5828	511	8	and	and	CCONJ
ejpam-5828	511	9	other	other	ADJ
ejpam-5828	511	10	quantization	quantization	NOUN
ejpam-5828	511	11	methods	method	NOUN
ejpam-5828	511	12	,	,	PUNCT
ejpam-5828	511	13	such	such	ADJ
ejpam-5828	511	14	as	as	ADP
ejpam-5828	511	15	the	the	DET
ejpam-5828	511	16	wkb	wkb	NOUN
ejpam-5828	511	17	approximation	approximation	NOUN
ejpam-5828	511	18	and	and	CCONJ
ejpam-5828	511	19	canonical	canonical	ADJ
ejpam-5828	511	20	quantization	quantization	NOUN
ejpam-5828	511	21	,	,	PUNCT
ejpam-5828	511	22	demonstrating	demonstrate	VERB
ejpam-5828	511	23	the	the	DET
ejpam-5828	511	24	robustness	robustness	NOUN
ejpam-5828	511	25	and	and	CCONJ
ejpam-5828	511	26	versatility	versatility	NOUN
ejpam-5828	511	27	of	of	ADP
ejpam-5828	511	28	the	the	DET
ejpam-5828	511	29	operator	operator	NOUN
ejpam-5828	511	30	formalism	formalism	NOUN
ejpam-5828	511	31	in	in	ADP
ejpam-5828	511	32	analyzing	analyze	VERB
ejpam-5828	511	33	dissipative	dissipative	ADJ
ejpam-5828	511	34	quantum	quantum	NOUN
ejpam-5828	511	35	systems	system	NOUN
ejpam-5828	511	36	.	.	PUNCT
ejpam-5828	512	1	b.	b.	PROPN
ejpam-5828	512	2	m.	m.	PROPN
ejpam-5828	512	3	al	al	PROPN
ejpam-5828	512	4	-	-	PUNCT
ejpam-5828	512	5	khamiseh	khamiseh	PROPN
ejpam-5828	512	6	et	et	PROPN
ejpam-5828	512	7	al	al	PROPN
ejpam-5828	512	8	.	.	PUNCT
ejpam-5828	512	9	/	/	SYM
ejpam-5828	512	10	eur	eur	PROPN
ejpam-5828	512	11	.	.	PUNCT
ejpam-5828	513	1	j.	j.	PROPN
ejpam-5828	513	2	pure	pure	PROPN
ejpam-5828	513	3	appl	appl	PROPN
ejpam-5828	513	4	.	.	PROPN
ejpam-5828	513	5	math	math	PROPN
ejpam-5828	513	6	,	,	PUNCT
ejpam-5828	513	7	18	18	NUM
ejpam-5828	513	8	(	(	PUNCT
ejpam-5828	513	9	2	2	NUM
ejpam-5828	513	10	)	)	PUNCT
ejpam-5828	513	11	(	(	PUNCT
ejpam-5828	513	12	2025	2025	NUM
ejpam-5828	513	13	)	)	PUNCT
ejpam-5828	513	14	,	,	PUNCT
ejpam-5828	513	15	5828	5828	NUM
ejpam-5828	513	16	24	24	NUM
ejpam-5828	513	17	of	of	ADP
ejpam-5828	513	18	25	25	NUM
ejpam-5828	513	19	appendix	appendix	NOUN
ejpam-5828	513	20	b	b	NOUN
ejpam-5828	513	21	:	:	PUNCT
ejpam-5828	513	22	additional	additional	ADJ
ejpam-5828	513	23	derivations	derivation	NOUN
ejpam-5828	513	24	and	and	CCONJ
ejpam-5828	513	25	quantization	quantization	NOUN
ejpam-5828	513	26	in	in	ADP
ejpam-5828	513	27	this	this	DET
ejpam-5828	513	28	appendix	appendix	NOUN
ejpam-5828	513	29	,	,	PUNCT
ejpam-5828	513	30	we	we	PRON
ejpam-5828	513	31	provide	provide	VERB
ejpam-5828	513	32	further	further	ADJ
ejpam-5828	513	33	derivations	derivation	NOUN
ejpam-5828	513	34	concerning	concern	VERB
ejpam-5828	513	35	the	the	DET
ejpam-5828	513	36	quantum	quantum	ADJ
ejpam-5828	513	37	treatment	treatment	NOUN
ejpam-5828	513	38	of	of	ADP
ejpam-5828	513	39	the	the	DET
ejpam-5828	513	40	dissipative	dissipative	ADJ
ejpam-5828	513	41	twodimensional	twodimensional	ADJ
ejpam-5828	513	42	anisotropic	anisotropic	NOUN
ejpam-5828	513	43	harmonic	harmonic	ADJ
ejpam-5828	513	44	oscillator	oscillator	NOUN
ejpam-5828	513	45	.	.	PUNCT
ejpam-5828	514	1	we	we	PRON
ejpam-5828	514	2	discuss	discuss	VERB
ejpam-5828	514	3	the	the	DET
ejpam-5828	514	4	application	application	NOUN
ejpam-5828	514	5	of	of	ADP
ejpam-5828	514	6	heisenberg	heisenberg	PROPN
ejpam-5828	514	7	’s	’s	PART
ejpam-5828	514	8	equations	equation	NOUN
ejpam-5828	514	9	and	and	CCONJ
ejpam-5828	514	10	the	the	DET
ejpam-5828	514	11	standard	standard	ADJ
ejpam-5828	514	12	rules	rule	NOUN
ejpam-5828	514	13	of	of	ADP
ejpam-5828	514	14	quantization	quantization	NOUN
ejpam-5828	514	15	to	to	PART
ejpam-5828	514	16	derive	derive	VERB
ejpam-5828	514	17	the	the	DET
ejpam-5828	514	18	equations	equation	NOUN
ejpam-5828	514	19	of	of	ADP
ejpam-5828	514	20	motion	motion	NOUN
ejpam-5828	514	21	for	for	ADP
ejpam-5828	514	22	the	the	DET
ejpam-5828	514	23	system	system	NOUN
ejpam-5828	514	24	in	in	ADP
ejpam-5828	514	25	its	its	PRON
ejpam-5828	514	26	quantum	quantum	ADJ
ejpam-5828	514	27	form	form	NOUN
ejpam-5828	514	28	.	.	PUNCT
ejpam-5828	515	1	additionally	additionally	ADV
ejpam-5828	515	2	,	,	PUNCT
ejpam-5828	515	3	a	a	DET
ejpam-5828	515	4	thorough	thorough	ADJ
ejpam-5828	515	5	analysis	analysis	NOUN
ejpam-5828	515	6	of	of	ADP
ejpam-5828	515	7	the	the	DET
ejpam-5828	515	8	creation	creation	NOUN
ejpam-5828	515	9	and	and	CCONJ
ejpam-5828	515	10	annihilation	annihilation	NOUN
ejpam-5828	515	11	operators	operator	NOUN
ejpam-5828	515	12	is	be	AUX
ejpam-5828	515	13	presented	present	VERB
ejpam-5828	515	14	,	,	PUNCT
ejpam-5828	515	15	which	which	PRON
ejpam-5828	515	16	are	be	AUX
ejpam-5828	515	17	instrumental	instrumental	ADJ
ejpam-5828	515	18	in	in	ADP
ejpam-5828	515	19	deriving	derive	VERB
ejpam-5828	515	20	the	the	DET
ejpam-5828	515	21	energy	energy	NOUN
ejpam-5828	515	22	eigenvalues	eigenvalue	NOUN
ejpam-5828	515	23	and	and	CCONJ
ejpam-5828	515	24	wave	wave	NOUN
ejpam-5828	515	25	functions	function	NOUN
ejpam-5828	515	26	.	.	PUNCT
ejpam-5828	516	1	the	the	DET
ejpam-5828	516	2	goal	goal	NOUN
ejpam-5828	516	3	of	of	ADP
ejpam-5828	516	4	this	this	DET
ejpam-5828	516	5	section	section	NOUN
ejpam-5828	516	6	is	be	AUX
ejpam-5828	516	7	to	to	PART
ejpam-5828	516	8	offer	offer	VERB
ejpam-5828	516	9	deeper	deep	ADJ
ejpam-5828	516	10	insights	insight	NOUN
ejpam-5828	516	11	into	into	ADP
ejpam-5828	516	12	the	the	DET
ejpam-5828	516	13	quantum	quantum	ADJ
ejpam-5828	516	14	methodology	methodology	NOUN
ejpam-5828	516	15	employed	employ	VERB
ejpam-5828	516	16	and	and	CCONJ
ejpam-5828	516	17	to	to	PART
ejpam-5828	516	18	illustrate	illustrate	VERB
ejpam-5828	516	19	the	the	DET
ejpam-5828	516	20	consistent	consistent	ADJ
ejpam-5828	516	21	derivation	derivation	NOUN
ejpam-5828	516	22	of	of	ADP
ejpam-5828	516	23	both	both	CCONJ
ejpam-5828	516	24	classical	classical	ADJ
ejpam-5828	516	25	and	and	CCONJ
ejpam-5828	516	26	quantum	quantum	ADJ
ejpam-5828	516	27	results	result	NOUN
ejpam-5828	516	28	.	.	PUNCT
ejpam-5828	517	1	the	the	DET
ejpam-5828	517	2	commutation	commutation	NOUN
ejpam-5828	517	3	relations	relation	NOUN
ejpam-5828	517	4	are	be	AUX
ejpam-5828	517	5	as	as	SCONJ
ejpam-5828	517	6	follows	follow	VERB
ejpam-5828	517	7	:	:	PUNCT
ejpam-5828	517	8	ẍ	ẍ	X
ejpam-5828	518	1	=	=	SYM
ejpam-5828	519	1	ṗx	ṗx	PROPN
ejpam-5828	519	2	m	m	VERB
ejpam-5828	519	3	therefore	therefore	ADV
ejpam-5828	519	4	ẍ+	ẍ+	INTJ
ejpam-5828	519	5	(	(	PUNCT
ejpam-5828	519	6	42x	42x	X
ejpam-5828	519	7	−	−	ADP
ejpam-5828	520	1	1	1	NUM
ejpam-5828	520	2	4	4	NUM
ejpam-5828	520	3	λ2x)x	λ2x)x	NOUN
ejpam-5828	520	4	=	=	SYM
ejpam-5828	520	5	0	0	NUM
ejpam-5828	520	6	(	(	PUNCT
ejpam-5828	520	7	b.1	b.1	NOUN
ejpam-5828	520	8	)	)	PUNCT
ejpam-5828	520	9	ÿ	ÿ	NOUN
ejpam-5828	520	10	=	=	SYM
ejpam-5828	520	11	ṗy	ṗy	PROPN
ejpam-5828	520	12	m	m	VERB
ejpam-5828	520	13	which	which	PRON
ejpam-5828	520	14	means	mean	VERB
ejpam-5828	520	15	that	that	SCONJ
ejpam-5828	520	16	ÿ	ÿ	PROPN
ejpam-5828	520	17	+	+	CCONJ
ejpam-5828	520	18	(	(	PUNCT
ejpam-5828	520	19	42y	42y	NOUN
ejpam-5828	520	20	−	−	NOUN
ejpam-5828	520	21	1	1	NUM
ejpam-5828	520	22	4	4	NUM
ejpam-5828	520	23	λ2y)y	λ2y)y	NOUN
ejpam-5828	520	24	=	=	SYM
ejpam-5828	520	25	0	0	PUNCT
ejpam-5828	520	26	(	(	PUNCT
ejpam-5828	520	27	b.2	b.2	VERB
ejpam-5828	520	28	)	)	PUNCT
ejpam-5828	520	29	given	give	VERB
ejpam-5828	520	30	the	the	DET
ejpam-5828	520	31	complete	complete	ADJ
ejpam-5828	520	32	alignment	alignment	NOUN
ejpam-5828	520	33	with	with	ADP
ejpam-5828	520	34	equations	equation	NOUN
ejpam-5828	520	35	(	(	PUNCT
ejpam-5828	520	36	2	2	NUM
ejpam-5828	520	37	)	)	PUNCT
ejpam-5828	520	38	and	and	CCONJ
ejpam-5828	520	39	(	(	PUNCT
ejpam-5828	520	40	3	3	NUM
ejpam-5828	520	41	)	)	PUNCT
ejpam-5828	520	42	,	,	PUNCT
ejpam-5828	520	43	it	it	PRON
ejpam-5828	520	44	follows	follow	VERB
ejpam-5828	520	45	that	that	SCONJ
ejpam-5828	520	46	{	{	PUNCT
ejpam-5828	520	47	x	x	NOUN
ejpam-5828	520	48	,	,	PUNCT
ejpam-5828	520	49	px	px	PROPN
ejpam-5828	520	50	}	}	PUNCT
ejpam-5828	520	51	=	=	SYM
ejpam-5828	520	52	{	{	PUNCT
ejpam-5828	520	53	y	y	PROPN
ejpam-5828	520	54	,	,	PUNCT
ejpam-5828	520	55	py	py	X
ejpam-5828	520	56	}	}	PUNCT
ejpam-5828	520	57	=	=	SYM
ejpam-5828	520	58	1	1	NUM
ejpam-5828	520	59	implies	imply	VERB
ejpam-5828	520	60	[	[	X
ejpam-5828	520	61	x	x	X
ejpam-5828	520	62	,	,	PUNCT
ejpam-5828	520	63	px	px	X
ejpam-5828	520	64	]	]	PUNCT
ejpam-5828	520	65	=	=	PUNCT
ejpam-5828	521	1	[	[	X
ejpam-5828	521	2	y	y	PROPN
ejpam-5828	521	3	,	,	PUNCT
ejpam-5828	521	4	py	py	X
ejpam-5828	521	5	]	]	X
ejpam-5828	521	6	=	=	PUNCT
ejpam-5828	521	7	ih	ih	INTJ
ejpam-5828	521	8	we	we	PRON
ejpam-5828	521	9	can	can	AUX
ejpam-5828	521	10	now	now	ADV
ejpam-5828	521	11	proceed	proceed	VERB
ejpam-5828	521	12	to	to	PART
ejpam-5828	521	13	introduce	introduce	VERB
ejpam-5828	521	14	the	the	DET
ejpam-5828	521	15	pairs	pair	NOUN
ejpam-5828	521	16	associated	associate	VERB
ejpam-5828	521	17	with	with	ADP
ejpam-5828	521	18	creation	creation	NOUN
ejpam-5828	521	19	and	and	CCONJ
ejpam-5828	521	20	annihilation	annihilation	NOUN
ejpam-5828	521	21	[	[	X
ejpam-5828	521	22	23	23	NUM
ejpam-5828	521	23	]	]	PUNCT
ejpam-5828	521	24	.	.	PUNCT
ejpam-5828	521	25	a+	a+	PUNCT
ejpam-5828	522	1	=	=	PUNCT
ejpam-5828	522	2	2∑	2∑	NUM
ejpam-5828	522	3	i=1	i=1	SYM
ejpam-5828	522	4	√	√	VERB
ejpam-5828	522	5	mwi	mwi	PROPN
ejpam-5828	522	6	2h	2h	NUM
ejpam-5828	522	7	(	(	PUNCT
ejpam-5828	522	8	xj	xj	PROPN
ejpam-5828	522	9	−	−	PROPN
ejpam-5828	523	1	i	i	PRON
ejpam-5828	523	2	pj	pj	PROPN
ejpam-5828	523	3	mwj	mwj	PROPN
ejpam-5828	523	4	a+	a+	PUNCT
ejpam-5828	523	5	=	=	PUNCT
ejpam-5828	523	6	2∑	2∑	NUM
ejpam-5828	523	7	i=1	i=1	SYM
ejpam-5828	523	8	√	√	VERB
ejpam-5828	523	9	mwi	mwi	PROPN
ejpam-5828	523	10	2h	2h	NUM
ejpam-5828	523	11	(	(	PUNCT
ejpam-5828	523	12	xj	xj	PROPN
ejpam-5828	523	13	+	+	CCONJ
ejpam-5828	523	14	i	i	PRON
ejpam-5828	523	15	pj	pj	PROPN
ejpam-5828	523	16	mwj	mwj	PROPN
ejpam-5828	523	17	(	(	PUNCT
ejpam-5828	523	18	b.3	b.3	PROPN
ejpam-5828	523	19	)	)	PUNCT
ejpam-5828	523	20	then	then	ADV
ejpam-5828	523	21	,	,	PUNCT
ejpam-5828	523	22	solving	solve	VERB
ejpam-5828	523	23	for	for	ADP
ejpam-5828	523	24	xj	xj	PROPN
ejpam-5828	523	25	and	and	CCONJ
ejpam-5828	523	26	pj	pj	PROPN
ejpam-5828	523	27	,	,	PUNCT
ejpam-5828	523	28	we	we	PRON
ejpam-5828	523	29	have	have	VERB
ejpam-5828	523	30	:	:	PUNCT
ejpam-5828	523	31	xj	xj	PROPN
ejpam-5828	523	32	=	=	PROPN
ejpam-5828	524	1	2∑	2∑	NUM
ejpam-5828	524	2	i=1	i=1	NUM
ejpam-5828	524	3	√	√	PROPN
ejpam-5828	524	4	h	h	NOUN
ejpam-5828	524	5	mwj	mwj	NOUN
ejpam-5828	524	6	(	(	PUNCT
ejpam-5828	524	7	ai	ai	VERB
ejpam-5828	524	8	+	+	NOUN
ejpam-5828	524	9	a+j	a+j	NUM
ejpam-5828	524	10	)	)	PUNCT
ejpam-5828	525	1	pj	pj	PROPN
ejpam-5828	526	1	=	=	PUNCT
ejpam-5828	527	1	−i	−i	ADJ
ejpam-5828	527	2	2∑	2∑	NUM
ejpam-5828	527	3	i=1	i=1	X
ejpam-5828	527	4	(	(	PUNCT
ejpam-5828	527	5	ai	ai	VERB
ejpam-5828	527	6	−	−	PROPN
ejpam-5828	527	7	a+j	a+j	NUM
ejpam-5828	527	8	)	)	PUNCT
ejpam-5828	527	9	a	a	DET
ejpam-5828	527	10	(	(	PUNCT
ejpam-5828	527	11	b.4	b.4	NOUN
ejpam-5828	527	12	)	)	PUNCT
ejpam-5828	527	13	it	it	PRON
ejpam-5828	527	14	is	be	AUX
ejpam-5828	527	15	easy	easy	ADJ
ejpam-5828	527	16	to	to	PART
ejpam-5828	527	17	verify	verify	VERB
ejpam-5828	527	18	that	that	SCONJ
ejpam-5828	528	1	[	[	X
ejpam-5828	528	2	xj	xj	PROPN
ejpam-5828	528	3	,	,	PUNCT
ejpam-5828	528	4	pj	pj	PROPN
ejpam-5828	528	5	]	]	PUNCT
ejpam-5828	528	6	=	=	SYM
ejpam-5828	528	7	ik	ik	PROPN
ejpam-5828	528	8	implies	imply	VERB
ejpam-5828	528	9	[	[	X
ejpam-5828	528	10	a	a	X
ejpam-5828	528	11	,	,	PUNCT
ejpam-5828	528	12	a+	a+	ADP
ejpam-5828	528	13	]	]	X
ejpam-5828	528	14	=	=	SYM
ejpam-5828	528	15	1	1	X
ejpam-5828	528	16	.	.	PUNCT
ejpam-5828	529	1	once	once	SCONJ
ejpam-5828	529	2	we	we	PRON
ejpam-5828	529	3	compute	compute	VERB
ejpam-5828	530	1	h	h	NOUN
ejpam-5828	530	2	=	=	NOUN
ejpam-5828	530	3	pxẋ+	pxẋ+	NUM
ejpam-5828	531	1	pyẏ	pyẏ	PROPN
ejpam-5828	531	2	−	−	PROPN
ejpam-5828	531	3	l	l	NOUN
ejpam-5828	531	4	,	,	PUNCT
ejpam-5828	531	5	we	we	PRON
ejpam-5828	531	6	obtain	obtain	VERB
ejpam-5828	531	7	:	:	PUNCT
ejpam-5828	532	1	h	h	NOUN
ejpam-5828	532	2	=	=	PUNCT
ejpam-5828	533	1	2∑	2∑	NUM
ejpam-5828	533	2	i=1	i=1	X
ejpam-5828	533	3	hwj(a	hwj(a	X
ejpam-5828	534	1	+	+	CCONJ
ejpam-5828	534	2	j	j	PROPN
ejpam-5828	534	3	aj	aj	PROPN
ejpam-5828	534	4	+	+	PROPN
ejpam-5828	534	5	1	1	NUM
ejpam-5828	534	6	2	2	NUM
ejpam-5828	534	7	)	)	PUNCT
ejpam-5828	534	8	(	(	PUNCT
ejpam-5828	534	9	b.5	b.5	NOUN
ejpam-5828	534	10	)	)	PUNCT
ejpam-5828	534	11	the	the	DET
ejpam-5828	534	12	energy	energy	NOUN
ejpam-5828	534	13	eigenvalues	eigenvalue	NOUN
ejpam-5828	534	14	are	be	AUX
ejpam-5828	534	15	given	give	VERB
ejpam-5828	534	16	by	by	ADP
ejpam-5828	534	17	:	:	PUNCT
ejpam-5828	534	18	e	e	NOUN
ejpam-5828	534	19	=	=	SYM
ejpam-5828	534	20	en	en	X
ejpam-5828	534	21	=	=	SYM
ejpam-5828	534	22	hwj(2πnxvx	hwj(2πnxvx	PROPN
ejpam-5828	534	23	+	+	CCONJ
ejpam-5828	534	24	2yvy	2yvy	NUM
ejpam-5828	534	25	+	+	CCONJ
ejpam-5828	534	26	1	1	NUM
ejpam-5828	534	27	2	2	NUM
ejpam-5828	534	28	2π(vx	2π(vx	NUM
ejpam-5828	534	29	+	+	CCONJ
ejpam-5828	534	30	vy	vy	NOUN
ejpam-5828	534	31	)	)	PUNCT
ejpam-5828	534	32	(	(	PUNCT
ejpam-5828	534	33	b.6	b.6	ADP
ejpam-5828	534	34	)	)	PUNCT
ejpam-5828	534	35	where	where	SCONJ
ejpam-5828	534	36	nx	nx	PROPN
ejpam-5828	534	37	=	=	SYM
ejpam-5828	534	38	1	1	NUM
ejpam-5828	534	39	,	,	PUNCT
ejpam-5828	534	40	2	2	NUM
ejpam-5828	534	41	,	,	PUNCT
ejpam-5828	534	42	·	·	PUNCT
ejpam-5828	534	43	·	·	PUNCT
ejpam-5828	534	44	·	·	PUNCT
ejpam-5828	534	45	and	and	CCONJ
ejpam-5828	534	46	ny	ny	X
ejpam-5828	534	47	=	=	SYM
ejpam-5828	534	48	1	1	NUM
ejpam-5828	534	49	,	,	PUNCT
ejpam-5828	534	50	2	2	NUM
ejpam-5828	534	51	,	,	PUNCT
ejpam-5828	534	52	·	·	PUNCT
ejpam-5828	534	53	·	·	PUNCT
ejpam-5828	534	54	·	·	PUNCT
ejpam-5828	534	55	the	the	DET
ejpam-5828	534	56	ground	ground	NOUN
ejpam-5828	534	57	-	-	PUNCT
ejpam-5828	534	58	state	state	NOUN
ejpam-5828	534	59	wave	wave	NOUN
ejpam-5828	534	60	function	function	NOUN
ejpam-5828	534	61	ψ0(x	ψ0(x	SYM
ejpam-5828	534	62	,	,	PUNCT
ejpam-5828	534	63	y	y	NOUN
ejpam-5828	534	64	)	)	PUNCT
ejpam-5828	534	65	)	)	PUNCT
ejpam-5828	534	66	obeys	obey	VERB
ejpam-5828	534	67	a	a	PRON
ejpam-5828	534	68	ψ0(x	ψ0(x	NOUN
ejpam-5828	534	69	,	,	PUNCT
ejpam-5828	534	70	y	y	NOUN
ejpam-5828	534	71	)	)	PUNCT
ejpam-5828	534	72	)	)	PUNCT
ejpam-5828	535	1	=	=	PUNCT
ejpam-5828	535	2	0	0	NUM
ejpam-5828	536	1	where	where	SCONJ
ejpam-5828	536	2	ψ0(x	ψ0(x	ADP
ejpam-5828	536	3	,	,	PUNCT
ejpam-5828	536	4	y	y	NOUN
ejpam-5828	536	5	)	)	PUNCT
ejpam-5828	536	6	)	)	PUNCT
ejpam-5828	537	1	=	=	PUNCT
ejpam-5828	537	2	ϕ0(x)υ0(x	ϕ0(x)υ0(x	NOUN
ejpam-5828	537	3	)	)	PUNCT
ejpam-5828	537	4	(	(	PUNCT
ejpam-5828	537	5	b.7	b.7	NOUN
ejpam-5828	537	6	)	)	PUNCT
ejpam-5828	537	7	b.	b.	PROPN
ejpam-5828	537	8	m.	m.	PROPN
ejpam-5828	538	1	al	al	PROPN
ejpam-5828	538	2	-	-	PUNCT
ejpam-5828	538	3	khamiseh	khamiseh	PROPN
ejpam-5828	538	4	et	et	PROPN
ejpam-5828	538	5	al	al	PROPN
ejpam-5828	538	6	.	.	PUNCT
ejpam-5828	538	7	/	/	SYM
ejpam-5828	538	8	eur	eur	PROPN
ejpam-5828	538	9	.	.	PUNCT
ejpam-5828	539	1	j.	j.	PROPN
ejpam-5828	539	2	pure	pure	PROPN
ejpam-5828	539	3	appl	appl	PROPN
ejpam-5828	539	4	.	.	PROPN
ejpam-5828	539	5	math	math	PROPN
ejpam-5828	539	6	,	,	PUNCT
ejpam-5828	539	7	18	18	NUM
ejpam-5828	539	8	(	(	PUNCT
ejpam-5828	539	9	2	2	NUM
ejpam-5828	539	10	)	)	PUNCT
ejpam-5828	539	11	(	(	PUNCT
ejpam-5828	539	12	2025	2025	NUM
ejpam-5828	539	13	)	)	PUNCT
ejpam-5828	539	14	,	,	PUNCT
ejpam-5828	539	15	5828	5828	NUM
ejpam-5828	539	16	25	25	NUM
ejpam-5828	539	17	of	of	ADP
ejpam-5828	539	18	25	25	NUM
ejpam-5828	539	19	the	the	DET
ejpam-5828	539	20	ground	ground	NOUN
ejpam-5828	539	21	-	-	PUNCT
ejpam-5828	539	22	state	state	NOUN
ejpam-5828	539	23	wave	wave	NOUN
ejpam-5828	539	24	function	function	NOUN
ejpam-5828	539	25	ψ0(x	ψ0(x	SYM
ejpam-5828	539	26	,	,	PUNCT
ejpam-5828	539	27	y	y	NOUN
ejpam-5828	539	28	)	)	PUNCT
ejpam-5828	539	29	)	)	PUNCT
ejpam-5828	539	30	,	,	PUNCT
ejpam-5828	539	31	expressed	express	VERB
ejpam-5828	539	32	as	as	ADP
ejpam-5828	539	33	the	the	DET
ejpam-5828	539	34	product	product	NOUN
ejpam-5828	539	35	of	of	ADP
ejpam-5828	539	36	functions	function	NOUN
ejpam-5828	539	37	ϕ0(x)υ0(x	ϕ0(x)υ0(x	PROPN
ejpam-5828	539	38	)	)	PUNCT
ejpam-5828	539	39	,	,	PUNCT
ejpam-5828	539	40	satisfies	satisfy	VERB
ejpam-5828	539	41	the	the	DET
ejpam-5828	539	42	condition	condition	NOUN
ejpam-5828	539	43	ψ0(x	ψ0(x	SYM
ejpam-5828	539	44	,	,	PUNCT
ejpam-5828	539	45	y	y	NOUN
ejpam-5828	539	46	)	)	PUNCT
ejpam-5828	539	47	)	)	PUNCT
ejpam-5828	540	1	=	=	SYM
ejpam-5828	540	2	0	0	NUM
ejpam-5828	540	3	,	,	PUNCT
ejpam-5828	540	4	resulting	result	VERB
ejpam-5828	540	5	in	in	ADP
ejpam-5828	540	6	:	:	PUNCT
ejpam-5828	540	7	ϕ0(x	ϕ0(x	X
ejpam-5828	540	8	)	)	PUNCT
ejpam-5828	540	9	=	=	SYM
ejpam-5828	541	1	(	(	PUNCT
ejpam-5828	541	2	mwx	mwx	NOUN
ejpam-5828	541	3	πk	πk	PROPN
ejpam-5828	541	4	)	)	PUNCT
ejpam-5828	541	5	1	1	NUM
ejpam-5828	541	6	4	4	NUM
ejpam-5828	541	7	e	e	X
ejpam-5828	541	8	−mwxx2	−mwxx2	X
ejpam-5828	541	9	2h	2h	NUM
ejpam-5828	541	10	(	(	PUNCT
ejpam-5828	541	11	b.8	b.8	NOUN
ejpam-5828	541	12	)	)	PUNCT
ejpam-5828	541	13	υ0(x	υ0(x	NOUN
ejpam-5828	541	14	)	)	PUNCT
ejpam-5828	541	15	=	=	SYM
ejpam-5828	541	16	(	(	PUNCT
ejpam-5828	541	17	mwx	mwx	NOUN
ejpam-5828	541	18	πk	πk	PROPN
ejpam-5828	541	19	)	)	PUNCT
ejpam-5828	541	20	1	1	NUM
ejpam-5828	541	21	4	4	NUM
ejpam-5828	541	22	e	e	NOUN
ejpam-5828	541	23	−mwyy2	−mwyy2	ADP
ejpam-5828	541	24	2h	2h	NUM
ejpam-5828	541	25	(	(	PUNCT
ejpam-5828	541	26	b.9	b.9	NOUN
ejpam-5828	541	27	)	)	PUNCT
ejpam-5828	541	28	when	when	SCONJ
ejpam-5828	541	29	we	we	PRON
ejpam-5828	541	30	replace	replace	VERB
ejpam-5828	541	31	equation	equation	NOUN
ejpam-5828	541	32	(	(	PUNCT
ejpam-5828	541	33	b.7	b.7	NOUN
ejpam-5828	541	34	)	)	PUNCT
ejpam-5828	541	35	and	and	CCONJ
ejpam-5828	541	36	(	(	PUNCT
ejpam-5828	541	37	b.8	b.8	X
ejpam-5828	541	38	)	)	PUNCT
ejpam-5828	541	39	with	with	ADP
ejpam-5828	541	40	equation	equation	NOUN
ejpam-5828	541	41	(	(	PUNCT
ejpam-5828	541	42	b.6	b.6	ADP
ejpam-5828	541	43	)	)	PUNCT
ejpam-5828	541	44	,	,	PUNCT
ejpam-5828	541	45	we	we	PRON
ejpam-5828	541	46	get	get	VERB
ejpam-5828	541	47	:	:	PUNCT
ejpam-5828	541	48	ψ0(x	ψ0(x	NUM
ejpam-5828	541	49	,	,	PUNCT
ejpam-5828	541	50	y	y	NOUN
ejpam-5828	541	51	)	)	PUNCT
ejpam-5828	541	52	)	)	PUNCT
ejpam-5828	542	1	=	=	PRON
ejpam-5828	542	2	(	(	PUNCT
ejpam-5828	542	3	m	m	NOUN
ejpam-5828	542	4	πh	πh	NOUN
ejpam-5828	542	5	)	)	PUNCT
ejpam-5828	542	6	1	1	NUM
ejpam-5828	542	7	2	2	NUM
ejpam-5828	542	8	(	(	PUNCT
ejpam-5828	542	9	wx	wx	PROPN
ejpam-5828	542	10	)	)	PUNCT
ejpam-5828	542	11	1	1	NUM
ejpam-5828	542	12	4	4	NUM
ejpam-5828	542	13	(	(	PUNCT
ejpam-5828	542	14	wy	wy	PROPN
ejpam-5828	542	15	)	)	PUNCT
ejpam-5828	542	16	1	1	NUM
ejpam-5828	542	17	4	4	NUM
ejpam-5828	542	18	e	e	X
ejpam-5828	542	19	−m(wyy2+wxx2	−m(wyy2+wxx2	X
ejpam-5828	542	20	)	)	PUNCT
ejpam-5828	542	21	2h	2h	NUM
ejpam-5828	542	22	(	(	PUNCT
ejpam-5828	542	23	b.10	b.10	NOUN
ejpam-5828	542	24	)	)	PUNCT
ejpam-5828	542	25	hermite	hermite	ADJ
ejpam-5828	542	26	polynomials	polynomial	NOUN
ejpam-5828	542	27	allow	allow	VERB
ejpam-5828	542	28	us	we	PRON
ejpam-5828	542	29	to	to	PART
ejpam-5828	542	30	express	express	VERB
ejpam-5828	542	31	the	the	DET
ejpam-5828	542	32	eigenfunctions	eigenfunction	NOUN
ejpam-5828	542	33	for	for	ADP
ejpam-5828	542	34	every	every	DET
ejpam-5828	542	35	given	give	VERB
ejpam-5828	542	36	state	state	NOUN
ejpam-5828	542	37	n	n	PROPN
ejpam-5828	542	38	as	as	SCONJ
ejpam-5828	542	39	follows	follow	VERB
ejpam-5828	542	40	:	:	PUNCT
ejpam-5828	542	41	hnm(x	hnm(x	PROPN
ejpam-5828	542	42	,	,	PUNCT
ejpam-5828	542	43	y	y	NOUN
ejpam-5828	542	44	)	)	PUNCT
ejpam-5828	542	45	=	=	SYM
ejpam-5828	542	46	bnm(−1)n+mex	bnm(−1)n+mex	PUNCT
ejpam-5828	542	47	2+y2	2+y2	NOUN
ejpam-5828	542	48	∂	∂	NOUN
ejpam-5828	542	49	m+n	m+n	NUM
ejpam-5828	542	50	n∂m	n∂m	VERB
ejpam-5828	542	51	e−x	e−x	PROPN
ejpam-5828	542	52	2−y2	2−y2	NUM
ejpam-5828	542	53	(	(	PUNCT
ejpam-5828	542	54	b.11	b.11	NOUN
ejpam-5828	542	55	)	)	PUNCT
ejpam-5828	542	56	ψnm(x	ψnm(x	PROPN
ejpam-5828	542	57	,	,	PUNCT
ejpam-5828	542	58	y	y	NOUN
ejpam-5828	542	59	)	)	PUNCT
ejpam-5828	542	60	)	)	PUNCT
ejpam-5828	543	1	=	=	PRON
ejpam-5828	543	2	(	(	PUNCT
ejpam-5828	543	3	m	m	NOUN
ejpam-5828	543	4	πh	πh	NOUN
ejpam-5828	543	5	)	)	PUNCT
ejpam-5828	543	6	1	1	NUM
ejpam-5828	543	7	2	2	NUM
ejpam-5828	543	8	(	(	PUNCT
ejpam-5828	543	9	wx	wx	PROPN
ejpam-5828	543	10	)	)	PUNCT
ejpam-5828	543	11	1	1	NUM
ejpam-5828	543	12	4	4	NUM
ejpam-5828	543	13	(	(	PUNCT
ejpam-5828	543	14	wy	wy	PROPN
ejpam-5828	543	15	)	)	PUNCT
ejpam-5828	543	16	1	1	NUM
ejpam-5828	543	17	4	4	NUM
ejpam-5828	543	18	e	e	X
ejpam-5828	543	19	−m(wyy2+wxx2	−m(wyy2+wxx2	X
ejpam-5828	543	20	)	)	PUNCT
ejpam-5828	543	21	2h	2h	NUM
ejpam-5828	543	22	hnm	hnm	X
ejpam-5828	543	23	(	(	PUNCT
ejpam-5828	543	24	nwx	nwx	PROPN
ejpam-5828	543	25	h	h	PROPN
ejpam-5828	543	26	x	x	NOUN
ejpam-5828	543	27	,	,	PUNCT
ejpam-5828	543	28	mwy	mwy	PROPN
ejpam-5828	543	29	h	h	PROPN
ejpam-5828	543	30	y	y	PROPN
ejpam-5828	543	31	)	)	PUNCT
ejpam-5828	543	32	(	(	PUNCT
ejpam-5828	543	33	b.12	b.12	NOUN
ejpam-5828	543	34	)	)	PUNCT
ejpam-5828	543	35	these	these	DET
ejpam-5828	543	36	expressions	expression	NOUN
ejpam-5828	543	37	,	,	PUNCT
ejpam-5828	543	38	particularly	particularly	ADV
ejpam-5828	543	39	(	(	PUNCT
ejpam-5828	543	40	)	)	PUNCT
ejpam-5828	543	41	,	,	PUNCT
ejpam-5828	543	42	validate	validate	VERB
ejpam-5828	543	43	the	the	DET
ejpam-5828	543	44	findings	finding	NOUN
ejpam-5828	543	45	presented	present	VERB
ejpam-5828	543	46	in	in	ADP
ejpam-5828	543	47	equation	equation	NOUN
ejpam-5828	543	48	22	22	NUM
ejpam-5828	543	49	,	,	PUNCT
ejpam-5828	543	50	indicating	indicate	VERB
ejpam-5828	543	51	their	their	PRON
ejpam-5828	543	52	consistency	consistency	NOUN
ejpam-5828	543	53	and	and	CCONJ
ejpam-5828	543	54	concordance	concordance	NOUN
ejpam-5828	543	55	with	with	ADP
ejpam-5828	543	56	the	the	DET
ejpam-5828	543	57	obtained	obtain	VERB
ejpam-5828	543	58	results	result	NOUN