id	sid	tid	token	lemma	pos
american_scientific_journal-3700	1	1	10	10	NUM
american_scientific_journal-3700	1	2	american	american	ADJ
american_scientific_journal-3700	1	3	scientific	scientific	ADJ
american_scientific_journal-3700	1	4	research	research	NOUN
american_scientific_journal-3700	1	5	journal	journal	NOUN
american_scientific_journal-3700	1	6	for	for	ADP
american_scientific_journal-3700	1	7	engineering	engineering	NOUN
american_scientific_journal-3700	1	8	,	,	PUNCT
american_scientific_journal-3700	1	9	technology	technology	NOUN
american_scientific_journal-3700	1	10	,	,	PUNCT
american_scientific_journal-3700	1	11	and	and	CCONJ
american_scientific_journal-3700	1	12	sciences	science	NOUN
american_scientific_journal-3700	1	13	(	(	PUNCT
american_scientific_journal-3700	1	14	asrjets	asrjet	NOUN
american_scientific_journal-3700	1	15	)	)	PUNCT
american_scientific_journal-3700	1	16	issn	issn	PROPN
american_scientific_journal-3700	1	17	(	(	PUNCT
american_scientific_journal-3700	1	18	print	print	NOUN
american_scientific_journal-3700	1	19	)	)	PUNCT
american_scientific_journal-3700	1	20	2313	2313	NUM
american_scientific_journal-3700	1	21	-	-	SYM
american_scientific_journal-3700	1	22	4410	4410	NUM
american_scientific_journal-3700	1	23	,	,	PUNCT
american_scientific_journal-3700	1	24	issn	issn	PROPN
american_scientific_journal-3700	1	25	(	(	PUNCT
american_scientific_journal-3700	1	26	online	online	ADJ
american_scientific_journal-3700	1	27	)	)	PUNCT
american_scientific_journal-3700	1	28	2313	2313	NUM
american_scientific_journal-3700	1	29	-	-	SYM
american_scientific_journal-3700	1	30	4402	4402	NUM
american_scientific_journal-3700	1	31	©	©	PROPN
american_scientific_journal-3700	1	32	global	global	ADJ
american_scientific_journal-3700	1	33	society	society	NOUN
american_scientific_journal-3700	1	34	of	of	ADP
american_scientific_journal-3700	1	35	scientific	scientific	ADJ
american_scientific_journal-3700	1	36	research	research	NOUN
american_scientific_journal-3700	1	37	and	and	CCONJ
american_scientific_journal-3700	1	38	researchers	researcher	NOUN
american_scientific_journal-3700	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-3700	1	40	potential	potential	ADJ
american_scientific_journal-3700	1	41	dependent	dependent	ADJ
american_scientific_journal-3700	1	42	frictional	frictional	ADJ
american_scientific_journal-3700	1	43	schrodinger	schrodinger	NOUN
american_scientific_journal-3700	1	44	equation	equation	NOUN
american_scientific_journal-3700	1	45	ebtisam	ebtisam	PROPN
american_scientific_journal-3700	1	46	a.	a.	PROPN
american_scientific_journal-3700	1	47	mohameda	mohameda	PROPN
american_scientific_journal-3700	1	48	*	*	PROPN
american_scientific_journal-3700	1	49	,	,	PUNCT
american_scientific_journal-3700	1	50	mubarak	mubarak	PROPN
american_scientific_journal-3700	1	51	dirarb	dirarb	PROPN
american_scientific_journal-3700	1	52	,	,	PUNCT
american_scientific_journal-3700	1	53	ibrahim	ibrahim	PROPN
american_scientific_journal-3700	1	54	a.	a.	PROPN
american_scientific_journal-3700	1	55	i.	i.	PROPN
american_scientific_journal-3700	1	56	hammadc	hammadc	PROPN
american_scientific_journal-3700	1	57	,	,	PUNCT
american_scientific_journal-3700	1	58	a.	a.	NOUN
american_scientific_journal-3700	1	59	elfakid	elfakid	PROPN
american_scientific_journal-3700	1	60	,	,	PUNCT
american_scientific_journal-3700	1	61	ibrahim	ibrahim	PROPN
american_scientific_journal-3700	1	62	alfakie	alfakie	PROPN
american_scientific_journal-3700	1	63	ajazan	ajazan	PROPN
american_scientific_journal-3700	1	64	university	university	PROPN
american_scientific_journal-3700	1	65	,	,	PUNCT
american_scientific_journal-3700	1	66	department	department	NOUN
american_scientific_journal-3700	1	67	of	of	ADP
american_scientific_journal-3700	1	68	physics	physics	PROPN
american_scientific_journal-3700	1	69	,	,	PUNCT
american_scientific_journal-3700	1	70	jazan	jazan	NOUN
american_scientific_journal-3700	1	71	,	,	PUNCT
american_scientific_journal-3700	1	72	saudi	saudi	PROPN
american_scientific_journal-3700	1	73	arabia	arabia	PROPN
american_scientific_journal-3700	1	74	akordofan	akordofan	PROPN
american_scientific_journal-3700	1	75	university	university	PROPN
american_scientific_journal-3700	1	76	,	,	PUNCT
american_scientific_journal-3700	1	77	department	department	NOUN
american_scientific_journal-3700	1	78	of	of	ADP
american_scientific_journal-3700	1	79	physics	physics	PROPN
american_scientific_journal-3700	1	80	,	,	PUNCT
american_scientific_journal-3700	1	81	el	el	PROPN
american_scientific_journal-3700	1	82	-	-	PUNCT
american_scientific_journal-3700	1	83	obeid	obeid	PROPN
american_scientific_journal-3700	1	84	,	,	PUNCT
american_scientific_journal-3700	1	85	sudan	sudan	PROPN
american_scientific_journal-3700	1	86	b	b	PROPN
american_scientific_journal-3700	1	87	,	,	PUNCT
american_scientific_journal-3700	1	88	d	d	PROPN
american_scientific_journal-3700	1	89	,	,	PUNCT
american_scientific_journal-3700	1	90	esudan	esudan	PROPN
american_scientific_journal-3700	1	91	university	university	PROPN
american_scientific_journal-3700	1	92	of	of	ADP
american_scientific_journal-3700	1	93	science	science	NOUN
american_scientific_journal-3700	1	94	and	and	CCONJ
american_scientific_journal-3700	1	95	technology	technology	NOUN
american_scientific_journal-3700	1	96	,	,	PUNCT
american_scientific_journal-3700	1	97	department	department	NOUN
american_scientific_journal-3700	1	98	of	of	ADP
american_scientific_journal-3700	1	99	physics	physics	PROPN
american_scientific_journal-3700	1	100	,	,	PUNCT
american_scientific_journal-3700	1	101	khartoum	khartoum	PROPN
american_scientific_journal-3700	1	102	,	,	PUNCT
american_scientific_journal-3700	1	103	sudan	sudan	PROPN
american_scientific_journal-3700	1	104	calzaiem	calzaiem	PROPN
american_scientific_journal-3700	1	105	alazhari	alazhari	PROPN
american_scientific_journal-3700	1	106	university	university	PROPN
american_scientific_journal-3700	1	107	,	,	PUNCT
american_scientific_journal-3700	1	108	department	department	NOUN
american_scientific_journal-3700	1	109	of	of	ADP
american_scientific_journal-3700	1	110	physics	physics	PROPN
american_scientific_journal-3700	1	111	,	,	PUNCT
american_scientific_journal-3700	1	112	omdurman	omdurman	PROPN
american_scientific_journal-3700	1	113	,	,	PUNCT
american_scientific_journal-3700	1	114	sudan	sudan	PROPN
american_scientific_journal-3700	1	115	aemail	aemail	NOUN
american_scientific_journal-3700	1	116	:	:	PUNCT
american_scientific_journal-3700	1	117	ebtisam99@yahoo.com	ebtisam99@yahoo.com	X
american_scientific_journal-3700	1	118	bemail	bemail	NOUN
american_scientific_journal-3700	1	119	:	:	PUNCT
american_scientific_journal-3700	1	120	mubarakdirar@gmail.com	mubarakdirar@gmail.com	X
american_scientific_journal-3700	1	121	cemail	cemail	NOUN
american_scientific_journal-3700	1	122	:	:	PUNCT
american_scientific_journal-3700	1	123	kshiky1986@gmail.com	kshiky1986@gmail.com	X
american_scientific_journal-3700	2	1	abstract	abstract	ADJ
american_scientific_journal-3700	2	2	by	by	ADP
american_scientific_journal-3700	2	3	treating	treat	VERB
american_scientific_journal-3700	2	4	particles	particle	NOUN
american_scientific_journal-3700	2	5	as	as	SCONJ
american_scientific_journal-3700	2	6	harmonic	harmonic	ADJ
american_scientific_journal-3700	2	7	oscillator	oscillator	NOUN
american_scientific_journal-3700	2	8	is	be	AUX
american_scientific_journal-3700	2	9	obtained	obtain	VERB
american_scientific_journal-3700	2	10	the	the	DET
american_scientific_journal-3700	2	11	friction	friction	NOUN
american_scientific_journal-3700	2	12	energy	energy	NOUN
american_scientific_journal-3700	2	13	related	relate	VERB
american_scientific_journal-3700	2	14	to	to	ADP
american_scientific_journal-3700	2	15	the	the	DET
american_scientific_journal-3700	2	16	momentum	momentum	NOUN
american_scientific_journal-3700	2	17	.	.	PUNCT
american_scientific_journal-3700	3	1	the	the	DET
american_scientific_journal-3700	3	2	energy	energy	NOUN
american_scientific_journal-3700	3	3	and	and	CCONJ
american_scientific_journal-3700	3	4	the	the	DET
american_scientific_journal-3700	3	5	corresponding	corresponding	ADJ
american_scientific_journal-3700	3	6	newtonian	newtonian	ADJ
american_scientific_journal-3700	3	7	operator	operator	NOUN
american_scientific_journal-3700	3	8	is	be	AUX
american_scientific_journal-3700	3	9	found	find	VERB
american_scientific_journal-3700	3	10	.	.	PUNCT
american_scientific_journal-3700	4	1	this	this	DET
american_scientific_journal-3700	4	2	result	result	NOUN
american_scientific_journal-3700	4	3	in	in	ADP
american_scientific_journal-3700	4	4	a	a	DET
american_scientific_journal-3700	4	5	new	new	ADJ
american_scientific_journal-3700	4	6	schrodinger	schrodinger	NOUN
american_scientific_journal-3700	4	7	equation	equation	NOUN
american_scientific_journal-3700	4	8	accounting	account	VERB
american_scientific_journal-3700	4	9	for	for	ADP
american_scientific_journal-3700	4	10	the	the	DET
american_scientific_journal-3700	4	11	effect	effect	NOUN
american_scientific_journal-3700	4	12	of	of	ADP
american_scientific_journal-3700	4	13	friction	friction	NOUN
american_scientific_journal-3700	4	14	.	.	PUNCT
american_scientific_journal-3700	5	1	this	this	DET
american_scientific_journal-3700	5	2	new	new	ADJ
american_scientific_journal-3700	5	3	equation	equation	NOUN
american_scientific_journal-3700	5	4	shows	show	VERB
american_scientific_journal-3700	5	5	that	that	SCONJ
american_scientific_journal-3700	5	6	the	the	DET
american_scientific_journal-3700	5	7	energy	energy	NOUN
american_scientific_journal-3700	5	8	and	and	CCONJ
american_scientific_journal-3700	5	9	mass	mass	NOUN
american_scientific_journal-3700	5	10	are	be	AUX
american_scientific_journal-3700	5	11	quantized	quantize	VERB
american_scientific_journal-3700	5	12	,	,	PUNCT
american_scientific_journal-3700	5	13	if	if	SCONJ
american_scientific_journal-3700	5	14	one	one	NUM
american_scientific_journal-3700	5	15	treats	treat	VERB
american_scientific_journal-3700	5	16	particles	particle	NOUN
american_scientific_journal-3700	5	17	as	as	ADP
american_scientific_journal-3700	5	18	strings	string	NOUN
american_scientific_journal-3700	5	19	.	.	PUNCT
american_scientific_journal-3700	6	1	the	the	DET
american_scientific_journal-3700	6	2	radioactive	radioactive	ADJ
american_scientific_journal-3700	6	3	decay	decay	NOUN
american_scientific_journal-3700	6	4	law	law	NOUN
american_scientific_journal-3700	6	5	and	and	CCONJ
american_scientific_journal-3700	6	6	collision	collision	NOUN
american_scientific_journal-3700	6	7	probability	probability	NOUN
american_scientific_journal-3700	6	8	is	be	AUX
american_scientific_journal-3700	6	9	also	also	ADV
american_scientific_journal-3700	6	10	derived	derive	VERB
american_scientific_journal-3700	6	11	.	.	PUNCT
american_scientific_journal-3700	7	1	key	key	ADJ
american_scientific_journal-3700	7	2	words	word	NOUN
american_scientific_journal-3700	7	3	:	:	PUNCT
american_scientific_journal-3700	7	4	friction	friction	NOUN
american_scientific_journal-3700	7	5	;	;	PUNCT
american_scientific_journal-3700	7	6	string	string	NOUN
american_scientific_journal-3700	7	7	;	;	PUNCT
american_scientific_journal-3700	7	8	harmonic	harmonic	ADJ
american_scientific_journal-3700	7	9	oscillator	oscillator	NOUN
american_scientific_journal-3700	7	10	;	;	PUNCT
american_scientific_journal-3700	7	11	radioactive	radioactive	ADJ
american_scientific_journal-3700	7	12	decay	decay	NOUN
american_scientific_journal-3700	7	13	law	law	NOUN
american_scientific_journal-3700	7	14	;	;	PUNCT
american_scientific_journal-3700	7	15	collision	collision	NOUN
american_scientific_journal-3700	7	16	probability	probability	NOUN
american_scientific_journal-3700	7	17	.	.	PUNCT
american_scientific_journal-3700	8	1	1	1	X
american_scientific_journal-3700	8	2	.	.	X
american_scientific_journal-3700	8	3	introduction	introduction	NOUN
american_scientific_journal-3700	8	4	quantum	quantum	NOUN
american_scientific_journal-3700	8	5	mechanics	mechanic	NOUN
american_scientific_journal-3700	8	6	include	include	VERB
american_scientific_journal-3700	8	7	two	two	NUM
american_scientific_journal-3700	8	8	independent	independent	ADJ
american_scientific_journal-3700	8	9	formulations	formulation	NOUN
american_scientific_journal-3700	8	10	.	.	PUNCT
american_scientific_journal-3700	9	1	the	the	DET
american_scientific_journal-3700	9	2	first	first	ADJ
american_scientific_journal-3700	9	3	formulation	formulation	NOUN
american_scientific_journal-3700	9	4	,	,	PUNCT
american_scientific_journal-3700	9	5	called	call	VERB
american_scientific_journal-3700	9	6	matrix	matrix	NOUN
american_scientific_journal-3700	9	7	mechanics	mechanic	NOUN
american_scientific_journal-3700	9	8	,	,	PUNCT
american_scientific_journal-3700	9	9	was	be	AUX
american_scientific_journal-3700	9	10	developed	develop	VERB
american_scientific_journal-3700	9	11	by	by	ADP
american_scientific_journal-3700	9	12	heisenberg	heisenberg	PROPN
american_scientific_journal-3700	9	13	(	(	PUNCT
american_scientific_journal-3700	9	14	1925	1925	NUM
american_scientific_journal-3700	9	15	)	)	PUNCT
american_scientific_journal-3700	9	16	to	to	PART
american_scientific_journal-3700	9	17	describe	describe	VERB
american_scientific_journal-3700	9	18	atomic	atomic	ADJ
american_scientific_journal-3700	9	19	structure	structure	NOUN
american_scientific_journal-3700	9	20	starting	start	VERB
american_scientific_journal-3700	9	21	from	from	ADP
american_scientific_journal-3700	9	22	the	the	DET
american_scientific_journal-3700	9	23	observed	observe	VERB
american_scientific_journal-3700	9	24	spectral	spectral	ADJ
american_scientific_journal-3700	9	25	lines	line	NOUN
american_scientific_journal-3700	9	26	of	of	ADP
american_scientific_journal-3700	9	27	atoms	atom	NOUN
american_scientific_journal-3700	9	28	.	.	PUNCT
american_scientific_journal-3700	10	1	heisenberg	heisenberg	PROPN
american_scientific_journal-3700	10	2	founded	found	VERB
american_scientific_journal-3700	10	3	his	his	PRON
american_scientific_journal-3700	10	4	theory	theory	NOUN
american_scientific_journal-3700	10	5	on	on	ADP
american_scientific_journal-3700	10	6	the	the	DET
american_scientific_journal-3700	10	7	notion	notion	NOUN
american_scientific_journal-3700	10	8	that	that	SCONJ
american_scientific_journal-3700	10	9	the	the	DET
american_scientific_journal-3700	10	10	only	only	ADJ
american_scientific_journal-3700	10	11	allowed	allow	VERB
american_scientific_journal-3700	10	12	values	value	NOUN
american_scientific_journal-3700	10	13	of	of	ADP
american_scientific_journal-3700	10	14	photon	photon	NOUN
american_scientific_journal-3700	10	15	are	be	AUX
american_scientific_journal-3700	10	16	due	due	ADJ
american_scientific_journal-3700	10	17	to	to	ADP
american_scientific_journal-3700	10	18	the	the	DET
american_scientific_journal-3700	10	19	transition	transition	NOUN
american_scientific_journal-3700	10	20	of	of	ADP
american_scientific_journal-3700	10	21	electrons	electron	NOUN
american_scientific_journal-3700	10	22	between	between	ADP
american_scientific_journal-3700	10	23	energy	energy	NOUN
american_scientific_journal-3700	10	24	levels	level	NOUN
american_scientific_journal-3700	10	25	of	of	ADP
american_scientific_journal-3700	10	26	atoms	atom	NOUN
american_scientific_journal-3700	10	27	as	as	ADP
american_scientific_journal-3700	10	28	discrete	discrete	ADJ
american_scientific_journal-3700	10	29	quanta	quanta	PROPN
american_scientific_journal-3700	10	30	.	.	PUNCT
american_scientific_journal-3700	11	1	expressing	express	VERB
american_scientific_journal-3700	11	2	dynamical	dynamical	ADJ
american_scientific_journal-3700	11	3	quantities	quantity	NOUN
american_scientific_journal-3700	11	4	such	such	ADJ
american_scientific_journal-3700	11	5	as	as	ADP
american_scientific_journal-3700	11	6	energy	energy	NOUN
american_scientific_journal-3700	11	7	,	,	PUNCT
american_scientific_journal-3700	11	8	position	position	NOUN
american_scientific_journal-3700	11	9	,	,	PUNCT
american_scientific_journal-3700	11	10	momentum	momentum	NOUN
american_scientific_journal-3700	11	11	and	and	CCONJ
american_scientific_journal-3700	11	12	angular	angular	ADJ
american_scientific_journal-3700	11	13	momentum	momentum	NOUN
american_scientific_journal-3700	11	14	in	in	ADP
american_scientific_journal-3700	11	15	terms	term	NOUN
american_scientific_journal-3700	11	16	of	of	ADP
american_scientific_journal-3700	11	17	matrices	matrix	NOUN
american_scientific_journal-3700	11	18	,	,	PUNCT
american_scientific_journal-3700	11	19	he	he	PRON
american_scientific_journal-3700	11	20	obtained	obtain	VERB
american_scientific_journal-3700	11	21	an	an	DET
american_scientific_journal-3700	11	22	eigenvalue	eigenvalue	NOUN
american_scientific_journal-3700	11	23	that	that	PRON
american_scientific_journal-3700	11	24	describes	describe	VERB
american_scientific_journal-3700	11	25	the	the	DET
american_scientific_journal-3700	11	26	dynamics	dynamic	NOUN
american_scientific_journal-3700	11	27	of	of	ADP
american_scientific_journal-3700	11	28	microscopic	microscopic	ADJ
american_scientific_journal-3700	11	29	systems	system	NOUN
american_scientific_journal-3700	11	30	;	;	PUNCT
american_scientific_journal-3700	11	31	the	the	DET
american_scientific_journal-3700	11	32	diagonalization	diagonalization	NOUN
american_scientific_journal-3700	11	33	of	of	ADP
american_scientific_journal-3700	11	34	the	the	DET
american_scientific_journal-3700	11	35	hamiltonian	hamiltonian	ADJ
american_scientific_journal-3700	11	36	matrix	matrix	NOUN
american_scientific_journal-3700	11	37	yields	yield	VERB
american_scientific_journal-3700	11	38	the	the	DET
american_scientific_journal-3700	11	39	energy	energy	NOUN
american_scientific_journal-3700	11	40	spectrum	spectrum	NOUN
american_scientific_journal-3700	11	41	and	and	CCONJ
american_scientific_journal-3700	11	42	the	the	DET
american_scientific_journal-3700	11	43	state	state	NOUN
american_scientific_journal-3700	11	44	vectors	vector	NOUN
american_scientific_journal-3700	11	45	of	of	ADP
american_scientific_journal-3700	11	46	the	the	DET
american_scientific_journal-3700	11	47	system	system	NOUN
american_scientific_journal-3700	11	48	.	.	PUNCT
american_scientific_journal-3700	12	1	matrix	matrix	NOUN
american_scientific_journal-3700	12	2	mechanics	mechanic	NOUN
american_scientific_journal-3700	12	3	was	be	AUX
american_scientific_journal-3700	12	4	very	very	ADV
american_scientific_journal-3700	12	5	successful	successful	ADJ
american_scientific_journal-3700	12	6	in	in	ADP
american_scientific_journal-3700	12	7	accounting	account	VERB
american_scientific_journal-3700	12	8	for	for	ADP
american_scientific_journal-3700	12	9	the	the	DET
american_scientific_journal-3700	12	10	discrete	discrete	ADJ
american_scientific_journal-3700	12	11	quanta	quanta	NOUN
american_scientific_journal-3700	12	12	of	of	ADP
american_scientific_journal-3700	12	13	light	light	NOUN
american_scientific_journal-3700	12	14	emitted	emit	VERB
american_scientific_journal-3700	12	15	and	and	CCONJ
american_scientific_journal-3700	12	16	absorbed	absorb	VERB
american_scientific_journal-3700	12	17	by	by	ADP
american_scientific_journal-3700	12	18	atoms.the	atoms.the	DET
american_scientific_journal-3700	12	19	second	second	ADJ
american_scientific_journal-3700	12	20	formulation	formulation	NOUN
american_scientific_journal-3700	12	21	,	,	PUNCT
american_scientific_journal-3700	12	22	called	call	VERB
american_scientific_journal-3700	12	23	wave	wave	NOUN
american_scientific_journal-3700	12	24	mechanics	mechanic	NOUN
american_scientific_journal-3700	12	25	,	,	PUNCT
american_scientific_journal-3700	12	26	was	be	AUX
american_scientific_journal-3700	12	27	due	due	ADJ
american_scientific_journal-3700	12	28	to	to	ADP
american_scientific_journal-3700	12	29	schrödinger	schrödinger	ADJ
american_scientific_journal-3700	12	30	(	(	PUNCT
american_scientific_journal-3700	12	31	1926	1926	NUM
american_scientific_journal-3700	12	32	)	)	PUNCT
american_scientific_journal-3700	12	33	.	.	PUNCT
american_scientific_journal-3700	13	1	it	it	PRON
american_scientific_journal-3700	13	2	is	be	AUX
american_scientific_journal-3700	13	3	a	a	DET
american_scientific_journal-3700	13	4	generalization	generalization	NOUN
american_scientific_journal-3700	13	5	of	of	ADP
american_scientific_journal-3700	13	6	the	the	DET
american_scientific_journal-3700	13	7	de	de	PROPN
american_scientific_journal-3700	13	8	broglie	broglie	PROPN
american_scientific_journal-3700	13	9	’s	’s	PART
american_scientific_journal-3700	13	10	postulate	postulate	NOUN
american_scientific_journal-3700	13	11	.	.	PUNCT
american_scientific_journal-3700	14	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-3700	15	1	*	*	PUNCT
american_scientific_journal-3700	15	2	corresponding	correspond	VERB
american_scientific_journal-3700	15	3	author	author	NOUN
american_scientific_journal-3700	15	4	.	.	PUNCT
american_scientific_journal-3700	16	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-3700	16	2	american	american	PROPN
american_scientific_journal-3700	16	3	scientific	scientific	PROPN
american_scientific_journal-3700	16	4	research	research	NOUN
american_scientific_journal-3700	16	5	journal	journal	NOUN
american_scientific_journal-3700	16	6	for	for	ADP
american_scientific_journal-3700	16	7	engineering	engineering	NOUN
american_scientific_journal-3700	16	8	,	,	PUNCT
american_scientific_journal-3700	16	9	technology	technology	NOUN
american_scientific_journal-3700	16	10	,	,	PUNCT
american_scientific_journal-3700	16	11	and	and	CCONJ
american_scientific_journal-3700	16	12	sciences	science	NOUN
american_scientific_journal-3700	16	13	(	(	PUNCT
american_scientific_journal-3700	16	14	asrjets	asrjet	NOUN
american_scientific_journal-3700	16	15	)	)	PUNCT
american_scientific_journal-3700	16	16	(	(	PUNCT
american_scientific_journal-3700	16	17	2018	2018	NUM
american_scientific_journal-3700	16	18	)	)	PUNCT
american_scientific_journal-3700	16	19	volume	volume	NOUN
american_scientific_journal-3700	16	20	39	39	NUM
american_scientific_journal-3700	16	21	,	,	PUNCT
american_scientific_journal-3700	16	22	no	no	DET
american_scientific_journal-3700	16	23	1	1	NUM
american_scientific_journal-3700	16	24	,	,	PUNCT
american_scientific_journal-3700	16	25	pp	pp	ADV
american_scientific_journal-3700	16	26	10	10	NUM
american_scientific_journal-3700	16	27	-	-	SYM
american_scientific_journal-3700	16	28	18	18	NUM
american_scientific_journal-3700	16	29	11	11	NUM
american_scientific_journal-3700	16	30	de	de	X
american_scientific_journal-3700	16	31	broglie	broglie	PROPN
american_scientific_journal-3700	16	32	assumes	assume	VERB
american_scientific_journal-3700	16	33	that	that	SCONJ
american_scientific_journal-3700	16	34	particles	particle	NOUN
american_scientific_journal-3700	16	35	like	like	ADP
american_scientific_journal-3700	16	36	electrons	electron	NOUN
american_scientific_journal-3700	16	37	behave	behave	VERB
american_scientific_journal-3700	16	38	as	as	ADP
american_scientific_journal-3700	16	39	waves	wave	NOUN
american_scientific_journal-3700	16	40	.	.	PUNCT
american_scientific_journal-3700	17	1	this	this	DET
american_scientific_journal-3700	17	2	method	method	NOUN
american_scientific_journal-3700	17	3	,	,	PUNCT
american_scientific_journal-3700	17	4	describes	describe	VERB
american_scientific_journal-3700	17	5	the	the	DET
american_scientific_journal-3700	17	6	dynamics	dynamic	NOUN
american_scientific_journal-3700	17	7	of	of	ADP
american_scientific_journal-3700	17	8	microscopic	microscopic	ADJ
american_scientific_journal-3700	17	9	matter	matter	NOUN
american_scientific_journal-3700	17	10	by	by	ADP
american_scientific_journal-3700	17	11	means	mean	NOUN
american_scientific_journal-3700	17	12	of	of	ADP
american_scientific_journal-3700	17	13	a	a	DET
american_scientific_journal-3700	17	14	wave	wave	NOUN
american_scientific_journal-3700	17	15	equation	equation	NOUN
american_scientific_journal-3700	17	16	,	,	PUNCT
american_scientific_journal-3700	17	17	called	call	VERB
american_scientific_journal-3700	17	18	the	the	DET
american_scientific_journal-3700	17	19	schrodinger	schrodinger	PROPN
american_scientific_journal-3700	17	20	equation	equation	NOUN
american_scientific_journal-3700	17	21	.	.	PUNCT
american_scientific_journal-3700	18	1	schrodinger	schrodinger	PROPN
american_scientific_journal-3700	18	2	equation	equation	NOUN
american_scientific_journal-3700	18	3	describes	describe	VERB
american_scientific_journal-3700	18	4	successfully	successfully	ADV
american_scientific_journal-3700	18	5	the	the	DET
american_scientific_journal-3700	18	6	behavior	behavior	NOUN
american_scientific_journal-3700	18	7	of	of	ADP
american_scientific_journal-3700	18	8	atoms	atom	NOUN
american_scientific_journal-3700	18	9	.	.	PUNCT
american_scientific_journal-3700	19	1	despite	despite	SCONJ
american_scientific_journal-3700	19	2	the	the	DET
american_scientific_journal-3700	19	3	remarkable	remarkable	ADJ
american_scientific_journal-3700	19	4	successes	success	NOUN
american_scientific_journal-3700	19	5	of	of	ADP
american_scientific_journal-3700	19	6	quantum	quantum	ADJ
american_scientific_journal-3700	19	7	equations	equation	NOUN
american_scientific_journal-3700	19	8	,	,	PUNCT
american_scientific_journal-3700	19	9	but	but	CCONJ
american_scientific_journal-3700	19	10	they	they	PRON
american_scientific_journal-3700	19	11	suffer	suffer	VERB
american_scientific_journal-3700	19	12	from	from	ADP
american_scientific_journal-3700	19	13	noticeable	noticeable	ADJ
american_scientific_journal-3700	19	14	setbacks	setback	NOUN
american_scientific_journal-3700	19	15	.	.	PUNCT
american_scientific_journal-3700	20	1	for	for	ADP
american_scientific_journal-3700	20	2	example	example	NOUN
american_scientific_journal-3700	20	3	,	,	PUNCT
american_scientific_journal-3700	20	4	the	the	DET
american_scientific_journal-3700	20	5	quantum	quantum	ADJ
american_scientific_journal-3700	20	6	equation	equation	NOUN
american_scientific_journal-3700	20	7	can	can	AUX
american_scientific_journal-3700	20	8	not	not	PART
american_scientific_journal-3700	20	9	differentiate	differentiate	VERB
american_scientific_journal-3700	20	10	between	between	ADP
american_scientific_journal-3700	20	11	the	the	DET
american_scientific_journal-3700	20	12	behavior	behavior	NOUN
american_scientific_journal-3700	20	13	of	of	ADP
american_scientific_journal-3700	20	14	two	two	NUM
american_scientific_journal-3700	20	15	particles	particle	NOUN
american_scientific_journal-3700	20	16	subjected	subject	VERB
american_scientific_journal-3700	20	17	to	to	ADP
american_scientific_journal-3700	20	18	the	the	DET
american_scientific_journal-3700	20	19	same	same	ADJ
american_scientific_journal-3700	20	20	potential	potential	NOUN
american_scientific_journal-3700	20	21	,	,	PUNCT
american_scientific_journal-3700	20	22	but	but	CCONJ
american_scientific_journal-3700	20	23	one	one	NUM
american_scientific_journal-3700	20	24	moves	move	NOUN
american_scientific_journal-3700	20	25	in	in	ADP
american_scientific_journal-3700	20	26	free	free	ADJ
american_scientific_journal-3700	20	27	space	space	NOUN
american_scientific_journal-3700	20	28	and	and	CCONJ
american_scientific_journal-3700	20	29	the	the	DET
american_scientific_journal-3700	20	30	other	other	ADJ
american_scientific_journal-3700	20	31	moves	move	NOUN
american_scientific_journal-3700	20	32	inside	inside	ADP
american_scientific_journal-3700	20	33	matter	matter	NOUN
american_scientific_journal-3700	20	34	.	.	PUNCT
american_scientific_journal-3700	21	1	this	this	PRON
american_scientific_journal-3700	21	2	is	be	AUX
american_scientific_journal-3700	21	3	in	in	ADP
american_scientific_journal-3700	21	4	direct	direct	ADJ
american_scientific_journal-3700	21	5	conflict	conflict	NOUN
american_scientific_journal-3700	21	6	whit	whit	NOUN
american_scientific_journal-3700	21	7	experimental	experimental	ADJ
american_scientific_journal-3700	21	8	observations	observation	NOUN
american_scientific_journal-3700	21	9	[	[	X
american_scientific_journal-3700	21	10	1].this	1].this	NUM
american_scientific_journal-3700	21	11	is	be	AUX
american_scientific_journal-3700	21	12	since	since	SCONJ
american_scientific_journal-3700	21	13	the	the	DET
american_scientific_journal-3700	21	14	particle	particle	NOUN
american_scientific_journal-3700	21	15	move	move	NOUN
american_scientific_journal-3700	21	16	in	in	ADP
american_scientific_journal-3700	21	17	a	a	DET
american_scientific_journal-3700	21	18	media	media	NOUN
american_scientific_journal-3700	21	19	is	be	AUX
american_scientific_journal-3700	21	20	affected	affect	VERB
american_scientific_journal-3700	21	21	by	by	ADP
american_scientific_journal-3700	21	22	fraction	fraction	NOUN
american_scientific_journal-3700	21	23	.	.	PUNCT
american_scientific_journal-3700	22	1	friction	friction	NOUN
american_scientific_journal-3700	22	2	is	be	AUX
american_scientific_journal-3700	22	3	the	the	DET
american_scientific_journal-3700	22	4	force	force	NOUN
american_scientific_journal-3700	22	5	resisting	resist	VERB
american_scientific_journal-3700	22	6	the	the	DET
american_scientific_journal-3700	22	7	relative	relative	ADJ
american_scientific_journal-3700	22	8	motion	motion	NOUN
american_scientific_journal-3700	22	9	of	of	ADP
american_scientific_journal-3700	22	10	solid	solid	ADJ
american_scientific_journal-3700	22	11	surfaces	surface	NOUN
american_scientific_journal-3700	22	12	,	,	PUNCT
american_scientific_journal-3700	22	13	fluid	fluid	ADJ
american_scientific_journal-3700	22	14	layers	layer	NOUN
american_scientific_journal-3700	22	15	,	,	PUNCT
american_scientific_journal-3700	22	16	as	as	ADP
american_scientific_journal-3700	22	17	an	an	DET
american_scientific_journal-3700	22	18	example	example	NOUN
american_scientific_journal-3700	22	19	of	of	ADP
american_scientific_journal-3700	22	20	friction	friction	NOUN
american_scientific_journal-3700	22	21	;	;	PUNCT
american_scientific_journal-3700	22	22	we	we	PRON
american_scientific_journal-3700	22	23	can	can	AUX
american_scientific_journal-3700	22	24	consider	consider	VERB
american_scientific_journal-3700	22	25	a	a	DET
american_scientific_journal-3700	22	26	body	body	NOUN
american_scientific_journal-3700	22	27	moving	move	VERB
american_scientific_journal-3700	22	28	rapidly	rapidly	ADV
american_scientific_journal-3700	22	29	against	against	ADP
american_scientific_journal-3700	22	30	a	a	DET
american_scientific_journal-3700	22	31	stationary	stationary	ADJ
american_scientific_journal-3700	22	32	background	background	NOUN
american_scientific_journal-3700	22	33	.	.	PUNCT
american_scientific_journal-3700	23	1	its	its	PRON
american_scientific_journal-3700	23	2	kinetic	kinetic	ADJ
american_scientific_journal-3700	23	3	energy	energy	NOUN
american_scientific_journal-3700	23	4	is	be	AUX
american_scientific_journal-3700	23	5	dissipated	dissipate	VERB
american_scientific_journal-3700	23	6	,	,	PUNCT
american_scientific_journal-3700	23	7	generating	generate	VERB
american_scientific_journal-3700	23	8	heat	heat	NOUN
american_scientific_journal-3700	23	9	and	and	CCONJ
american_scientific_journal-3700	23	10	entropy	entropy	NOUN
american_scientific_journal-3700	23	11	in	in	ADP
american_scientific_journal-3700	23	12	the	the	DET
american_scientific_journal-3700	23	13	environment	environment	NOUN
american_scientific_journal-3700	23	14	,	,	PUNCT
american_scientific_journal-3700	23	15	the	the	DET
american_scientific_journal-3700	23	16	amount	amount	NOUN
american_scientific_journal-3700	23	17	of	of	ADP
american_scientific_journal-3700	23	18	dissipation	dissipation	NOUN
american_scientific_journal-3700	23	19	is	be	AUX
american_scientific_journal-3700	23	20	proportional	proportional	ADJ
american_scientific_journal-3700	23	21	to	to	ADP
american_scientific_journal-3700	23	22	the	the	DET
american_scientific_journal-3700	23	23	velocity	velocity	NOUN
american_scientific_journal-3700	23	24	[	[	X
american_scientific_journal-3700	23	25	2	2	NUM
american_scientific_journal-3700	23	26	]	]	PUNCT
american_scientific_journal-3700	23	27	.	.	PUNCT
american_scientific_journal-3700	24	1	the	the	DET
american_scientific_journal-3700	24	2	fraction	fraction	NOUN
american_scientific_journal-3700	24	3	is	be	AUX
american_scientific_journal-3700	24	4	observed	observe	VERB
american_scientific_journal-3700	24	5	in	in	ADP
american_scientific_journal-3700	24	6	micro	micro	ADJ
american_scientific_journal-3700	24	7	-	-	ADJ
american_scientific_journal-3700	24	8	mechanical	mechanical	ADJ
american_scientific_journal-3700	24	9	systems	system	NOUN
american_scientific_journal-3700	24	10	at	at	ADP
american_scientific_journal-3700	24	11	low	low	ADJ
american_scientific_journal-3700	24	12	temperatures	temperature	NOUN
american_scientific_journal-3700	24	13	,	,	PUNCT
american_scientific_journal-3700	24	14	in	in	ADP
american_scientific_journal-3700	24	15	superfluid	superfluid	NOUN
american_scientific_journal-3700	24	16	theory	theory	NOUN
american_scientific_journal-3700	24	17	,	,	PUNCT
american_scientific_journal-3700	24	18	and	and	CCONJ
american_scientific_journal-3700	24	19	even	even	ADV
american_scientific_journal-3700	24	20	in	in	ADP
american_scientific_journal-3700	24	21	quantum	quantum	ADJ
american_scientific_journal-3700	24	22	cosmology	cosmology	NOUN
american_scientific_journal-3700	25	1	[	[	X
american_scientific_journal-3700	25	2	3	3	NUM
american_scientific_journal-3700	25	3	]	]	PUNCT
american_scientific_journal-3700	25	4	.	.	PUNCT
american_scientific_journal-3700	26	1	in	in	ADP
american_scientific_journal-3700	26	2	particular	particular	ADJ
american_scientific_journal-3700	26	3	,	,	PUNCT
american_scientific_journal-3700	26	4	friction	friction	NOUN
american_scientific_journal-3700	26	5	is	be	AUX
american_scientific_journal-3700	26	6	the	the	DET
american_scientific_journal-3700	26	7	term	term	NOUN
american_scientific_journal-3700	26	8	widely	widely	ADV
american_scientific_journal-3700	26	9	used	use	VERB
american_scientific_journal-3700	26	10	in	in	ADP
american_scientific_journal-3700	26	11	descriptions	description	NOUN
american_scientific_journal-3700	26	12	of	of	ADP
american_scientific_journal-3700	26	13	ion	ion	NOUN
american_scientific_journal-3700	26	14	collisions	collision	NOUN
american_scientific_journal-3700	26	15	.	.	PUNCT
american_scientific_journal-3700	27	1	frictional	frictional	ADJ
american_scientific_journal-3700	27	2	forces	force	NOUN
american_scientific_journal-3700	27	3	depend	depend	VERB
american_scientific_journal-3700	27	4	in	in	ADP
american_scientific_journal-3700	27	5	this	this	DET
american_scientific_journal-3700	27	6	case	case	NOUN
american_scientific_journal-3700	27	7	on	on	ADP
american_scientific_journal-3700	27	8	position	position	NOUN
american_scientific_journal-3700	27	9	and	and	CCONJ
american_scientific_journal-3700	27	10	their	their	PRON
american_scientific_journal-3700	27	11	range	range	NOUN
american_scientific_journal-3700	27	12	is	be	AUX
american_scientific_journal-3700	27	13	comparable	comparable	ADJ
american_scientific_journal-3700	27	14	with	with	ADP
american_scientific_journal-3700	27	15	the	the	DET
american_scientific_journal-3700	27	16	nuclear	nuclear	ADJ
american_scientific_journal-3700	27	17	radius	radius	NOUN
american_scientific_journal-3700	27	18	[	[	X
american_scientific_journal-3700	27	19	4	4	NUM
american_scientific_journal-3700	27	20	]	]	PUNCT
american_scientific_journal-3700	27	21	.	.	PUNCT
american_scientific_journal-3700	28	1	thus	thus	ADV
american_scientific_journal-3700	28	2	,	,	PUNCT
american_scientific_journal-3700	28	3	this	this	DET
american_scientific_journal-3700	28	4	work	work	NOUN
american_scientific_journal-3700	28	5	is	be	AUX
american_scientific_journal-3700	28	6	concerned	concern	VERB
american_scientific_journal-3700	28	7	with	with	ADP
american_scientific_journal-3700	28	8	deriving	derive	VERB
american_scientific_journal-3700	28	9	schrodinger	schrodinger	ADJ
american_scientific_journal-3700	28	10	equation	equation	NOUN
american_scientific_journal-3700	28	11	for	for	ADP
american_scientific_journal-3700	28	12	quantum	quantum	NOUN
american_scientific_journal-3700	28	13	system	system	NOUN
american_scientific_journal-3700	28	14	suffering	suffer	VERB
american_scientific_journal-3700	28	15	from	from	ADP
american_scientific_journal-3700	28	16	fraction	fraction	NOUN
american_scientific_journal-3700	28	17	.	.	PUNCT
american_scientific_journal-3700	29	1	this	this	PRON
american_scientific_journal-3700	29	2	is	be	AUX
american_scientific_journal-3700	29	3	done	do	VERB
american_scientific_journal-3700	29	4	in	in	ADP
american_scientific_journal-3700	29	5	section	section	NOUN
american_scientific_journal-3700	29	6	2	2	NUM
american_scientific_journal-3700	29	7	.	.	PUNCT
american_scientific_journal-3700	29	8	applications	application	NOUN
american_scientific_journal-3700	29	9	for	for	ADP
american_scientific_journal-3700	29	10	harmonic	harmonic	ADJ
american_scientific_journal-3700	29	11	oscillator	oscillator	NOUN
american_scientific_journal-3700	29	12	and	and	CCONJ
american_scientific_journal-3700	29	13	radioactive	radioactive	ADJ
american_scientific_journal-3700	29	14	decay	decay	NOUN
american_scientific_journal-3700	29	15	low	low	ADJ
american_scientific_journal-3700	29	16	are	be	AUX
american_scientific_journal-3700	29	17	in	in	ADP
american_scientific_journal-3700	29	18	sections	section	NOUN
american_scientific_journal-3700	29	19	(	(	PUNCT
american_scientific_journal-3700	29	20	3	3	NUM
american_scientific_journal-3700	29	21	)	)	PUNCT
american_scientific_journal-3700	29	22	and	and	CCONJ
american_scientific_journal-3700	29	23	(	(	PUNCT
american_scientific_journal-3700	29	24	4	4	X
american_scientific_journal-3700	29	25	)	)	PUNCT
american_scientific_journal-3700	29	26	respectively	respectively	ADV
american_scientific_journal-3700	29	27	[	[	X
american_scientific_journal-3700	29	28	5	5	NUM
american_scientific_journal-3700	29	29	,	,	PUNCT
american_scientific_journal-3700	29	30	6	6	NUM
american_scientific_journal-3700	29	31	,	,	PUNCT
american_scientific_journal-3700	29	32	7	7	NUM
american_scientific_journal-3700	29	33	]	]	PUNCT
american_scientific_journal-3700	29	34	.	.	PUNCT
american_scientific_journal-3700	30	1	2	2	X
american_scientific_journal-3700	30	2	.	.	X
american_scientific_journal-3700	30	3	schrodinger	schrodinger	ADJ
american_scientific_journal-3700	30	4	equation	equation	NOUN
american_scientific_journal-3700	30	5	for	for	ADP
american_scientific_journal-3700	30	6	frictional	frictional	ADJ
american_scientific_journal-3700	30	7	medium	medium	NOUN
american_scientific_journal-3700	30	8	according	accord	VERB
american_scientific_journal-3700	30	9	to	to	ADP
american_scientific_journal-3700	30	10	plank	plank	NOUN
american_scientific_journal-3700	30	11	and	and	CCONJ
american_scientific_journal-3700	30	12	de	de	X
american_scientific_journal-3700	30	13	broglie	broglie	PROPN
american_scientific_journal-3700	30	14	hypothesis	hypothesis	NOUN
american_scientific_journal-3700	30	15	the	the	DET
american_scientific_journal-3700	30	16	quantum	quantum	PROPN
american_scientific_journal-3700	30	17	quanta	quanta	PROPN
american_scientific_journal-3700	30	18	are	be	AUX
american_scientific_journal-3700	30	19	treated	treat	VERB
american_scientific_journal-3700	30	20	as	as	ADP
american_scientific_journal-3700	30	21	wave	wave	NOUN
american_scientific_journal-3700	30	22	packets	packet	NOUN
american_scientific_journal-3700	30	23	.	.	PUNCT
american_scientific_journal-3700	31	1	pure	pure	ADJ
american_scientific_journal-3700	31	2	waves	wave	NOUN
american_scientific_journal-3700	31	3	is	be	AUX
american_scientific_journal-3700	31	4	a	a	DET
american_scientific_journal-3700	31	5	wave	wave	NOUN
american_scientific_journal-3700	31	6	packet	packet	NOUN
american_scientific_journal-3700	31	7	consisting	consist	VERB
american_scientific_journal-3700	31	8	of	of	ADP
american_scientific_journal-3700	31	9	single	single	ADJ
american_scientific_journal-3700	31	10	wave	wave	NOUN
american_scientific_journal-3700	31	11	having	have	VERB
american_scientific_journal-3700	31	12	specific	specific	ADJ
american_scientific_journal-3700	31	13	wave	wave	NOUN
american_scientific_journal-3700	31	14	length	length	NOUN
american_scientific_journal-3700	31	15	.while	.while	ADP
american_scientific_journal-3700	31	16	a	a	DET
american_scientific_journal-3700	31	17	localized	localized	ADJ
american_scientific_journal-3700	31	18	particle	particle	NOUN
american_scientific_journal-3700	31	19	is	be	AUX
american_scientific_journal-3700	31	20	a	a	DET
american_scientific_journal-3700	31	21	wave	wave	NOUN
american_scientific_journal-3700	31	22	packet	packet	NOUN
american_scientific_journal-3700	31	23	having	have	VERB
american_scientific_journal-3700	31	24	a	a	DET
american_scientific_journal-3700	31	25	very	very	ADV
american_scientific_journal-3700	31	26	large	large	ADJ
american_scientific_journal-3700	31	27	of	of	ADP
american_scientific_journal-3700	31	28	interfering	interfere	VERB
american_scientific_journal-3700	31	29	waves	wave	NOUN
american_scientific_journal-3700	31	30	having	have	VERB
american_scientific_journal-3700	31	31	different	different	ADJ
american_scientific_journal-3700	31	32	wave	wave	NOUN
american_scientific_journal-3700	31	33	lengths	length	NOUN
american_scientific_journal-3700	31	34	.	.	PUNCT
american_scientific_journal-3700	32	1	this	this	PRON
american_scientific_journal-3700	32	2	means	mean	VERB
american_scientific_journal-3700	32	3	that	that	SCONJ
american_scientific_journal-3700	32	4	any	any	DET
american_scientific_journal-3700	32	5	quantum	quantum	ADJ
american_scientific_journal-3700	32	6	system	system	NOUN
american_scientific_journal-3700	32	7	is	be	AUX
american_scientific_journal-3700	32	8	a	a	DET
american_scientific_journal-3700	32	9	single	single	ADJ
american_scientific_journal-3700	32	10	or	or	CCONJ
american_scientific_journal-3700	32	11	aggregate	aggregate	NOUN
american_scientific_journal-3700	32	12	of	of	ADP
american_scientific_journal-3700	32	13	oscillators	oscillator	NOUN
american_scientific_journal-3700	32	14	.	.	PUNCT
american_scientific_journal-3700	33	1	moreover	moreover	ADV
american_scientific_journal-3700	33	2	,	,	PUNCT
american_scientific_journal-3700	33	3	according	accord	VERB
american_scientific_journal-3700	33	4	to	to	ADP
american_scientific_journal-3700	33	5	string	string	NOUN
american_scientific_journal-3700	33	6	theory	theory	NOUN
american_scientific_journal-3700	33	7	matter	matter	NOUN
american_scientific_journal-3700	33	8	building	building	NOUN
american_scientific_journal-3700	33	9	blocks	block	NOUN
american_scientific_journal-3700	33	10	are	be	AUX
american_scientific_journal-3700	33	11	treated	treat	VERB
american_scientific_journal-3700	33	12	as	as	ADP
american_scientific_journal-3700	33	13	vibrating	vibrate	VERB
american_scientific_journal-3700	33	14	string	string	NOUN
american_scientific_journal-3700	33	15	.	.	PUNCT
american_scientific_journal-3700	34	1	motivated	motivate	VERB
american_scientific_journal-3700	34	2	by	by	ADP
american_scientific_journal-3700	34	3	all	all	DET
american_scientific_journal-3700	34	4	there	there	NOUN
american_scientific_journal-3700	34	5	hypothesis	hypothesis	NOUN
american_scientific_journal-3700	34	6	,	,	PUNCT
american_scientific_journal-3700	34	7	the	the	DET
american_scientific_journal-3700	34	8	energy	energy	NOUN
american_scientific_journal-3700	34	9	dissipated	dissipate	VERB
american_scientific_journal-3700	34	10	by	by	ADP
american_scientific_journal-3700	34	11	fraction	fraction	NOUN
american_scientific_journal-3700	34	12	can	can	AUX
american_scientific_journal-3700	34	13	be	be	AUX
american_scientific_journal-3700	34	14	derived	derive	VERB
american_scientific_journal-3700	34	15	consider	consider	VERB
american_scientific_journal-3700	34	16	now	now	ADV
american_scientific_journal-3700	34	17	a	a	DET
american_scientific_journal-3700	34	18	fractional	fractional	ADJ
american_scientific_journal-3700	34	19	force	force	NOUN
american_scientific_journal-3700	34	20	ff	ff	NOUN
american_scientific_journal-3700	34	21	in	in	ADP
american_scientific_journal-3700	34	22	terms	term	NOUN
american_scientific_journal-3700	34	23	of	of	ADP
american_scientific_journal-3700	34	24	mass	mass	NOUN
american_scientific_journal-3700	34	25	m	m	PROPN
american_scientific_journal-3700	34	26	,	,	PUNCT
american_scientific_journal-3700	34	27	relaxation	relaxation	NOUN
american_scientific_journal-3700	34	28	time	time	NOUN
american_scientific_journal-3700	34	29	𝜏𝜏	𝜏𝜏	NOUN
american_scientific_journal-3700	34	30	and	and	CCONJ
american_scientific_journal-3700	34	31	velocity	velocity	VERB
american_scientific_journal-3700	34	32	υ	υ	PRON
american_scientific_journal-3700	34	33	to	to	PART
american_scientific_journal-3700	34	34	be	be	AUX
american_scientific_journal-3700	34	35	ef	ef	X
american_scientific_journal-3700	34	36	=	=	PUNCT
american_scientific_journal-3700	35	1	mv	mv	X
american_scientific_journal-3700	35	2	𝜏𝜏	𝜏𝜏	INTJ
american_scientific_journal-3700	35	3	(	(	PUNCT
american_scientific_journal-3700	35	4	1	1	X
american_scientific_journal-3700	35	5	)	)	PUNCT
american_scientific_journal-3700	35	6	considering	consider	VERB
american_scientific_journal-3700	35	7	matter	matter	NOUN
american_scientific_journal-3700	35	8	building	building	NOUN
american_scientific_journal-3700	35	9	blocks	block	NOUN
american_scientific_journal-3700	35	10	as	as	ADP
american_scientific_journal-3700	35	11	oscillators	oscillator	NOUN
american_scientific_journal-3700	35	12	υ	υ	NOUN
american_scientific_journal-3700	35	13	=	=	SYM
american_scientific_journal-3700	35	14	υ	υ	PROPN
american_scientific_journal-3700	35	15	°	°	PROPN
american_scientific_journal-3700	35	16	eiwt	eiwt	NOUN
american_scientific_journal-3700	35	17	(	(	PUNCT
american_scientific_journal-3700	35	18	2	2	NUM
american_scientific_journal-3700	35	19	)	)	PUNCT
american_scientific_journal-3700	35	20	thus	thus	ADV
american_scientific_journal-3700	35	21	,	,	PUNCT
american_scientific_journal-3700	35	22	the	the	DET
american_scientific_journal-3700	35	23	displacement	displacement	NOUN
american_scientific_journal-3700	35	24	is	be	AUX
american_scientific_journal-3700	35	25	given	give	VERB
american_scientific_journal-3700	35	26	by	by	ADP
american_scientific_journal-3700	35	27	:	:	PUNCT
american_scientific_journal-3700	35	28	𝑥𝑥	𝑥𝑥	ADP
american_scientific_journal-3700	35	29	=	=	PUNCT
american_scientific_journal-3700	35	30	�	�	X
american_scientific_journal-3700	35	31	𝑣𝑣𝑣𝑣𝑣𝑣	𝑣𝑣𝑣𝑣𝑣𝑣	NOUN
american_scientific_journal-3700	35	32	=	=	SYM
american_scientific_journal-3700	35	33	𝜐𝜐𝜊𝜊	𝜐𝜐𝜊𝜊	PROPN
american_scientific_journal-3700	35	34	�	�	PROPN
american_scientific_journal-3700	35	35	𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖𝑣𝑣𝑣𝑣	𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖𝑣𝑣𝑣𝑣	ADJ
american_scientific_journal-3700	35	36	=	=	SYM
american_scientific_journal-3700	35	37	𝜐𝜐𝜊𝜊	𝜐𝜐𝜊𝜊	NOUN
american_scientific_journal-3700	35	38	𝑖𝑖𝑖𝑖	𝑖𝑖𝑖𝑖	ADJ
american_scientific_journal-3700	35	39	𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖	𝑒𝑒𝑖𝑖𝑖𝑖𝑖𝑖	NOUN
american_scientific_journal-3700	36	1	=	=	SYM
american_scientific_journal-3700	36	2	𝑣𝑣	𝑣𝑣	PROPN
american_scientific_journal-3700	36	3	𝑖𝑖𝑖𝑖	𝑖𝑖𝑖𝑖	ADV
american_scientific_journal-3700	36	4	(	(	PUNCT
american_scientific_journal-3700	36	5	3	3	X
american_scientific_journal-3700	36	6	)	)	PUNCT
american_scientific_journal-3700	36	7	the	the	DET
american_scientific_journal-3700	36	8	total	total	ADJ
american_scientific_journal-3700	36	9	dissipative	dissipative	ADJ
american_scientific_journal-3700	36	10	energy	energy	NOUN
american_scientific_journal-3700	36	11	𝐸𝐸𝑓𝑓	𝐸𝐸𝑓𝑓	PROPN
american_scientific_journal-3700	36	12	is	be	AUX
american_scientific_journal-3700	36	13	given	give	VERB
american_scientific_journal-3700	36	14	by	by	ADP
american_scientific_journal-3700	36	15	:	:	PUNCT
american_scientific_journal-3700	36	16	ef	ef	PROPN
american_scientific_journal-3700	36	17	=	=	PUNCT
american_scientific_journal-3700	36	18	�	�	PROPN
american_scientific_journal-3700	36	19	𝐹𝐹𝑓𝑓	𝐹𝐹𝑓𝑓	PROPN
american_scientific_journal-3700	36	20	.𝑣𝑣𝑥𝑥	.𝑣𝑣𝑥𝑥	NOUN
american_scientific_journal-3700	36	21	=	=	PROPN
american_scientific_journal-3700	36	22	m	m	PROPN
american_scientific_journal-3700	36	23	iw𝜏𝜏	iw𝜏𝜏	PROPN
american_scientific_journal-3700	36	24	�	�	PROPN
american_scientific_journal-3700	36	25	𝜐𝜐𝑣𝑣𝜐𝜐	𝜐𝜐𝑣𝑣𝜐𝜐	NOUN
american_scientific_journal-3700	36	26	=	=	PUNCT
american_scientific_journal-3700	36	27	𝑚𝑚𝑣𝑣2	𝑚𝑚𝑣𝑣2	NOUN
american_scientific_journal-3700	37	1	2𝑖𝑖𝑖𝑖𝜏𝜏	2𝑖𝑖𝑖𝑖𝜏𝜏	NUM
american_scientific_journal-3700	37	2	=	=	SYM
american_scientific_journal-3700	37	3	𝑖𝑖𝑚𝑚𝑣𝑣2	𝑖𝑖𝑚𝑚𝑣𝑣2	NOUN
american_scientific_journal-3700	37	4	2𝑖𝑖2𝜏𝜏𝑖𝑖	2𝑖𝑖2𝜏𝜏𝑖𝑖	NUM
american_scientific_journal-3700	37	5	=	=	SYM
american_scientific_journal-3700	37	6	−𝑖𝑖𝑚𝑚𝑣𝑣2	−𝑖𝑖𝑚𝑚𝑣𝑣2	PROPN
american_scientific_journal-3700	37	7	2𝑖𝑖𝜏𝜏	2𝑖𝑖𝜏𝜏	NUM
american_scientific_journal-3700	37	8	=	=	SYM
american_scientific_journal-3700	37	9	−	−	PROPN
american_scientific_journal-3700	37	10	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-3700	37	11	𝑖𝑖𝜏𝜏	𝑖𝑖𝜏𝜏	X
american_scientific_journal-3700	37	12	�	�	PROPN
american_scientific_journal-3700	37	13	1	1	NUM
american_scientific_journal-3700	37	14	2	2	NUM
american_scientific_journal-3700	37	15	𝑚𝑚𝑣𝑣2	𝑚𝑚𝑣𝑣2	NOUN
american_scientific_journal-3700	37	16	�	�	X
american_scientific_journal-3700	37	17	=	=	SYM
american_scientific_journal-3700	37	18	−𝑖𝑖	−𝑖𝑖	PROPN
american_scientific_journal-3700	37	19	𝑖𝑖𝜏𝜏	𝑖𝑖𝜏𝜏	X
american_scientific_journal-3700	37	20	�	�	PROPN
american_scientific_journal-3700	37	21	𝑃𝑃2	𝑃𝑃2	PROPN
american_scientific_journal-3700	37	22	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	37	23	�	�	PROPN
american_scientific_journal-3700	37	24	(	(	PUNCT
american_scientific_journal-3700	37	25	4	4	NUM
american_scientific_journal-3700	37	26	)	)	PUNCT
american_scientific_journal-3700	37	27	american	american	ADJ
american_scientific_journal-3700	37	28	scientific	scientific	ADJ
american_scientific_journal-3700	37	29	research	research	NOUN
american_scientific_journal-3700	37	30	journal	journal	NOUN
american_scientific_journal-3700	37	31	for	for	ADP
american_scientific_journal-3700	37	32	engineering	engineering	NOUN
american_scientific_journal-3700	37	33	,	,	PUNCT
american_scientific_journal-3700	37	34	technology	technology	NOUN
american_scientific_journal-3700	37	35	,	,	PUNCT
american_scientific_journal-3700	37	36	and	and	CCONJ
american_scientific_journal-3700	37	37	sciences	science	NOUN
american_scientific_journal-3700	37	38	(	(	PUNCT
american_scientific_journal-3700	37	39	asrjets	asrjet	NOUN
american_scientific_journal-3700	37	40	)	)	PUNCT
american_scientific_journal-3700	37	41	(	(	PUNCT
american_scientific_journal-3700	37	42	2018	2018	NUM
american_scientific_journal-3700	37	43	)	)	PUNCT
american_scientific_journal-3700	37	44	volume	volume	NOUN
american_scientific_journal-3700	37	45	39	39	NUM
american_scientific_journal-3700	37	46	,	,	PUNCT
american_scientific_journal-3700	37	47	no	no	DET
american_scientific_journal-3700	37	48	1	1	NUM
american_scientific_journal-3700	37	49	,	,	PUNCT
american_scientific_journal-3700	37	50	pp	pp	ADV
american_scientific_journal-3700	37	51	10	10	NUM
american_scientific_journal-3700	37	52	-	-	SYM
american_scientific_journal-3700	37	53	18	18	NUM
american_scientific_journal-3700	37	54	12	12	NUM
american_scientific_journal-3700	37	55	but	but	CCONJ
american_scientific_journal-3700	37	56	according	accord	VERB
american_scientific_journal-3700	37	57	to	to	ADP
american_scientific_journal-3700	37	58	newtonian	newtonian	ADJ
american_scientific_journal-3700	37	59	mechanics	mechanic	NOUN
american_scientific_journal-3700	37	60	the	the	DET
american_scientific_journal-3700	37	61	total	total	ADJ
american_scientific_journal-3700	37	62	energy	energy	NOUN
american_scientific_journal-3700	37	63	can	can	AUX
american_scientific_journal-3700	37	64	be	be	AUX
american_scientific_journal-3700	37	65	expressed	express	VERB
american_scientific_journal-3700	37	66	in	in	ADP
american_scientific_journal-3700	37	67	terms	term	NOUN
american_scientific_journal-3700	37	68	of	of	ADP
american_scientific_journal-3700	37	69	the	the	DET
american_scientific_journal-3700	37	70	kinetic	kinetic	ADJ
american_scientific_journal-3700	37	71	and	and	CCONJ
american_scientific_journal-3700	37	72	potential	potential	ADJ
american_scientific_journal-3700	37	73	energy	energy	NOUN
american_scientific_journal-3700	37	74	v	v	NOUN
american_scientific_journal-3700	37	75	in	in	ADP
american_scientific_journal-3700	37	76	the	the	DET
american_scientific_journal-3700	37	77	form	form	NOUN
american_scientific_journal-3700	37	78	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	37	79	=	=	SYM
american_scientific_journal-3700	37	80	𝐾𝐾	𝐾𝐾	PROPN
american_scientific_journal-3700	37	81	+	+	CCONJ
american_scientific_journal-3700	37	82	𝑉𝑉	𝑉𝑉	NOUN
american_scientific_journal-3700	37	83	=	=	SYM
american_scientific_journal-3700	37	84	𝑃𝑃	𝑃𝑃	NOUN
american_scientific_journal-3700	37	85	2	2	NUM
american_scientific_journal-3700	37	86	2𝑀𝑀	2𝑀𝑀	NUM
american_scientific_journal-3700	37	87	+	+	CCONJ
american_scientific_journal-3700	37	88	𝑉𝑉	𝑉𝑉	NOUN
american_scientific_journal-3700	37	89	(	(	PUNCT
american_scientific_journal-3700	37	90	5	5	NUM
american_scientific_journal-3700	37	91	)	)	PUNCT
american_scientific_journal-3700	37	92	thus	thus	ADV
american_scientific_journal-3700	37	93	according	accord	VERB
american_scientific_journal-3700	37	94	to	to	ADP
american_scientific_journal-3700	37	95	eq	eq	PROPN
american_scientific_journal-3700	37	96	.	.	PUNCT
american_scientific_journal-3700	38	1	(	(	PUNCT
american_scientific_journal-3700	38	2	5	5	NUM
american_scientific_journal-3700	38	3	)	)	PUNCT
american_scientific_journal-3700	38	4	and	and	CCONJ
american_scientific_journal-3700	38	5	eq	eq	NOUN
american_scientific_journal-3700	38	6	.	.	PUNCT
american_scientific_journal-3700	39	1	(	(	PUNCT
american_scientific_journal-3700	39	2	4	4	X
american_scientific_journal-3700	39	3	)	)	PUNCT
american_scientific_journal-3700	39	4	𝐸𝐸𝑓𝑓	𝐸𝐸𝑓𝑓	PROPN
american_scientific_journal-3700	39	5	is	be	AUX
american_scientific_journal-3700	39	6	given	give	VERB
american_scientific_journal-3700	39	7	by	by	ADP
american_scientific_journal-3700	39	8	𝐸𝐸𝑓𝑓	𝐸𝐸𝑓𝑓	PROPN
american_scientific_journal-3700	39	9	=	=	SYM
american_scientific_journal-3700	39	10	−𝑖𝑖	−𝑖𝑖	NOUN
american_scientific_journal-3700	39	11	𝑖𝑖𝜏𝜏	𝑖𝑖𝜏𝜏	X
american_scientific_journal-3700	39	12	(	(	PUNCT
american_scientific_journal-3700	39	13	e	e	NOUN
american_scientific_journal-3700	39	14	−	−	PROPN
american_scientific_journal-3700	39	15	v	v	NOUN
american_scientific_journal-3700	39	16	)	)	PUNCT
american_scientific_journal-3700	39	17	(	(	PUNCT
american_scientific_journal-3700	39	18	6	6	NUM
american_scientific_journal-3700	39	19	)	)	PUNCT
american_scientific_journal-3700	39	20	but	but	CCONJ
american_scientific_journal-3700	39	21	using	use	VERB
american_scientific_journal-3700	39	22	plank	plank	NOUN
american_scientific_journal-3700	39	23	hypothesis	hypothesis	NOUN
american_scientific_journal-3700	39	24	the	the	DET
american_scientific_journal-3700	39	25	energy	energy	NOUN
american_scientific_journal-3700	39	26	e	e	NOUN
american_scientific_journal-3700	39	27	is	be	AUX
american_scientific_journal-3700	39	28	given	give	VERB
american_scientific_journal-3700	39	29	by	by	ADP
american_scientific_journal-3700	39	30	:	:	PUNCT
american_scientific_journal-3700	39	31	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	39	32	=	=	SYM
american_scientific_journal-3700	39	33	ℏ𝜔𝜔	ℏ𝜔𝜔	NOUN
american_scientific_journal-3700	39	34	(	(	PUNCT
american_scientific_journal-3700	39	35	7	7	NUM
american_scientific_journal-3700	39	36	)	)	PUNCT
american_scientific_journal-3700	39	37	in	in	ADP
american_scientific_journal-3700	39	38	view	view	NOUN
american_scientific_journal-3700	39	39	of	of	ADP
american_scientific_journal-3700	39	40	eqs	eqs	PROPN
american_scientific_journal-3700	39	41	.	.	PUNCT
american_scientific_journal-3700	40	1	(	(	PUNCT
american_scientific_journal-3700	40	2	6	6	NUM
american_scientific_journal-3700	40	3	)	)	PUNCT
american_scientific_journal-3700	40	4	and	and	CCONJ
american_scientific_journal-3700	40	5	(	(	PUNCT
american_scientific_journal-3700	40	6	7	7	X
american_scientific_journal-3700	40	7	)	)	PUNCT
american_scientific_journal-3700	40	8	the	the	DET
american_scientific_journal-3700	40	9	frictional	frictional	ADJ
american_scientific_journal-3700	40	10	energy	energy	NOUN
american_scientific_journal-3700	40	11	is	be	AUX
american_scientific_journal-3700	40	12	given	give	VERB
american_scientific_journal-3700	40	13	by	by	ADP
american_scientific_journal-3700	40	14	ef	ef	X
american_scientific_journal-3700	40	15	=	=	PUNCT
american_scientific_journal-3700	40	16	−𝑖𝑖ℏ	−𝑖𝑖ℏ	NOUN
american_scientific_journal-3700	40	17	ℏ𝑖𝑖𝜏𝜏	ℏ𝑖𝑖𝜏𝜏	NOUN
american_scientific_journal-3700	40	18	(	(	PUNCT
american_scientific_journal-3700	40	19	e	e	NOUN
american_scientific_journal-3700	40	20	−	−	PROPN
american_scientific_journal-3700	40	21	v	v	NOUN
american_scientific_journal-3700	40	22	)	)	PUNCT
american_scientific_journal-3700	40	23	=	=	SYM
american_scientific_journal-3700	40	24	𝑖𝑖ℏ	𝑖𝑖ℏ	X
american_scientific_journal-3700	40	25	𝜏𝜏𝐸𝐸	𝜏𝜏𝐸𝐸	PROPN
american_scientific_journal-3700	40	26	(	(	PUNCT
american_scientific_journal-3700	40	27	v	v	ADP
american_scientific_journal-3700	40	28	−	−	PROPN
american_scientific_journal-3700	40	29	e	e	NOUN
american_scientific_journal-3700	40	30	)	)	PUNCT
american_scientific_journal-3700	40	31	ef	ef	NOUN
american_scientific_journal-3700	40	32	=	=	PUNCT
american_scientific_journal-3700	40	33	𝑖𝑖ℏ	𝑖𝑖ℏ	PROPN
american_scientific_journal-3700	40	34	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	40	35	�	�	PROPN
american_scientific_journal-3700	40	36	v	v	PROPN
american_scientific_journal-3700	40	37	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	40	38	−	−	PROPN
american_scientific_journal-3700	40	39	1	1	NUM
american_scientific_journal-3700	40	40	�	�	PROPN
american_scientific_journal-3700	40	41	(	(	PUNCT
american_scientific_journal-3700	40	42	8)	8)	NUM
american_scientific_journal-3700	40	43	thus	thus	ADV
american_scientific_journal-3700	40	44	the	the	DET
american_scientific_journal-3700	40	45	hamiltonian	hamiltonian	ADJ
american_scientific_journal-3700	40	46	classical	classical	ADJ
american_scientific_journal-3700	40	47	relation	relation	NOUN
american_scientific_journal-3700	40	48	for	for	ADP
american_scientific_journal-3700	40	49	a	a	DET
american_scientific_journal-3700	40	50	particle	particle	NOUN
american_scientific_journal-3700	40	51	in	in	ADP
american_scientific_journal-3700	40	52	a	a	DET
american_scientific_journal-3700	40	53	fractional	fractional	ADJ
american_scientific_journal-3700	40	54	medium	medium	NOUN
american_scientific_journal-3700	40	55	is	be	AUX
american_scientific_journal-3700	40	56	given	give	VERB
american_scientific_journal-3700	40	57	by	by	ADP
american_scientific_journal-3700	41	1	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	41	2	=	=	SYM
american_scientific_journal-3700	41	3	𝐻𝐻	𝐻𝐻	PROPN
american_scientific_journal-3700	41	4	=	=	SYM
american_scientific_journal-3700	41	5	𝑃𝑃2	𝑃𝑃2	NOUN
american_scientific_journal-3700	41	6	2𝑚𝑚	2𝑚𝑚	NOUN
american_scientific_journal-3700	42	1	+	+	CCONJ
american_scientific_journal-3700	42	2	𝑉𝑉	𝑉𝑉	NOUN
american_scientific_journal-3700	42	3	+	+	CCONJ
american_scientific_journal-3700	42	4	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	42	5	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	42	6	�	�	PROPN
american_scientific_journal-3700	42	7	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	42	8	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	42	9	−	−	PROPN
american_scientific_journal-3700	42	10	1	1	NUM
american_scientific_journal-3700	42	11	�	�	NOUN
american_scientific_journal-3700	42	12	=	=	PUNCT
american_scientific_journal-3700	42	13	𝑃𝑃2	𝑃𝑃2	PROPN
american_scientific_journal-3700	42	14	2𝑚𝑚	2𝑚𝑚	NOUN
american_scientific_journal-3700	43	1	+	+	CCONJ
american_scientific_journal-3700	43	2	𝑉𝑉	𝑉𝑉	NOUN
american_scientific_journal-3700	43	3	+	+	CCONJ
american_scientific_journal-3700	43	4	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	43	5	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	43	6	�	�	PROPN
american_scientific_journal-3700	43	7	𝑉𝑉−𝐸𝐸	𝑉𝑉−𝐸𝐸	ADJ
american_scientific_journal-3700	43	8	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	43	9	�	�	PROPN
american_scientific_journal-3700	43	10	(	(	PUNCT
american_scientific_journal-3700	43	11	9	9	NUM
american_scientific_journal-3700	43	12	)	)	PUNCT
american_scientific_journal-3700	43	13	therefore	therefore	ADV
american_scientific_journal-3700	43	14	𝐸𝐸2	𝐸𝐸2	PROPN
american_scientific_journal-3700	43	15	=	=	PUNCT
american_scientific_journal-3700	43	16	�	�	PROPN
american_scientific_journal-3700	43	17	𝑃𝑃	𝑃𝑃	ADJ
american_scientific_journal-3700	43	18	2	2	NUM
american_scientific_journal-3700	43	19	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	43	20	+	+	CCONJ
american_scientific_journal-3700	43	21	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	43	22	�	�	PROPN
american_scientific_journal-3700	43	23	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	43	24	+	+	CCONJ
american_scientific_journal-3700	43	25	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	43	26	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	43	27	(	(	PUNCT
american_scientific_journal-3700	43	28	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	43	29	−	−	PROPN
american_scientific_journal-3700	43	30	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	43	31	)	)	PUNCT
american_scientific_journal-3700	43	32	(	(	PUNCT
american_scientific_journal-3700	43	33	10	10	NUM
american_scientific_journal-3700	43	34	)	)	PUNCT
american_scientific_journal-3700	43	35	to	to	PART
american_scientific_journal-3700	43	36	find	find	VERB
american_scientific_journal-3700	43	37	the	the	DET
american_scientific_journal-3700	43	38	schrodinger	schrodinger	ADJ
american_scientific_journal-3700	43	39	equation	equation	NOUN
american_scientific_journal-3700	43	40	corresponding	correspond	VERB
american_scientific_journal-3700	43	41	to	to	ADP
american_scientific_journal-3700	43	42	this	this	DET
american_scientific_journal-3700	43	43	relation	relation	NOUN
american_scientific_journal-3700	43	44	multiplies	multiply	VERB
american_scientific_journal-3700	43	45	both	both	DET
american_scientific_journal-3700	43	46	sides	side	NOUN
american_scientific_journal-3700	43	47	of	of	ADP
american_scientific_journal-3700	43	48	eq	eq	PROPN
american_scientific_journal-3700	43	49	.	.	PUNCT
american_scientific_journal-3700	44	1	(	(	PUNCT
american_scientific_journal-3700	44	2	10	10	NUM
american_scientific_journal-3700	44	3	)	)	PUNCT
american_scientific_journal-3700	44	4	by	by	ADP
american_scientific_journal-3700	44	5	ψ	ψ	X
american_scientific_journal-3700	44	6	to	to	PART
american_scientific_journal-3700	44	7	get	get	VERB
american_scientific_journal-3700	44	8	:	:	PUNCT
american_scientific_journal-3700	44	9	𝐸𝐸2ψ	𝐸𝐸2ψ	PART
american_scientific_journal-3700	44	10	=	=	PUNCT
american_scientific_journal-3700	44	11	�	�	PROPN
american_scientific_journal-3700	44	12	𝑃𝑃	𝑃𝑃	ADJ
american_scientific_journal-3700	44	13	2	2	NUM
american_scientific_journal-3700	44	14	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	44	15	+	+	CCONJ
american_scientific_journal-3700	44	16	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	44	17	�	�	NOUN
american_scientific_journal-3700	44	18	𝐸𝐸ψ	𝐸𝐸ψ	NOUN
american_scientific_journal-3700	44	19	+	+	CCONJ
american_scientific_journal-3700	44	20	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	44	21	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	44	22	(	(	PUNCT
american_scientific_journal-3700	44	23	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	44	24	−	−	PROPN
american_scientific_journal-3700	44	25	𝐸𝐸)ψ	𝐸𝐸)ψ	ADJ
american_scientific_journal-3700	44	26	(	(	PUNCT
american_scientific_journal-3700	44	27	11	11	NUM
american_scientific_journal-3700	44	28	)	)	PUNCT
american_scientific_journal-3700	44	29	considering	consider	VERB
american_scientific_journal-3700	44	30	the	the	DET
american_scientific_journal-3700	44	31	wave	wave	NOUN
american_scientific_journal-3700	44	32	function	function	NOUN
american_scientific_journal-3700	44	33	ψ	ψ	X
american_scientific_journal-3700	44	34	=	=	X
american_scientific_journal-3700	44	35	𝐴𝐴𝑒𝑒	𝐴𝐴𝑒𝑒	NOUN
american_scientific_journal-3700	44	36	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-3700	44	37	ℏ	ℏ	PROPN
american_scientific_journal-3700	44	38	.(𝑝𝑝𝑝𝑝−𝐸𝐸𝑖𝑖	.(𝑝𝑝𝑝𝑝−𝐸𝐸𝑖𝑖	PUNCT
american_scientific_journal-3700	44	39	)	)	PUNCT
american_scientific_journal-3700	44	40	(	(	PUNCT
american_scientific_journal-3700	44	41	12	12	NUM
american_scientific_journal-3700	44	42	)	)	PUNCT
american_scientific_journal-3700	44	43	hence	hence	ADV
american_scientific_journal-3700	44	44	𝜕𝜕ψ	𝜕𝜕ψ	PROPN
american_scientific_journal-3700	44	45	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	NOUN
american_scientific_journal-3700	45	1	=	=	SYM
american_scientific_journal-3700	46	1	−	−	PROPN
american_scientific_journal-3700	46	2	𝑖𝑖	𝑖𝑖	NOUN
american_scientific_journal-3700	47	1	ℏ	ℏ	PROPN
american_scientific_journal-3700	47	2	eψ	eψ	PROPN
american_scientific_journal-3700	47	3	american	american	PROPN
american_scientific_journal-3700	47	4	scientific	scientific	PROPN
american_scientific_journal-3700	47	5	research	research	PROPN
american_scientific_journal-3700	47	6	journal	journal	NOUN
american_scientific_journal-3700	47	7	for	for	ADP
american_scientific_journal-3700	47	8	engineering	engineering	NOUN
american_scientific_journal-3700	47	9	,	,	PUNCT
american_scientific_journal-3700	47	10	technology	technology	NOUN
american_scientific_journal-3700	47	11	,	,	PUNCT
american_scientific_journal-3700	47	12	and	and	CCONJ
american_scientific_journal-3700	47	13	sciences	science	NOUN
american_scientific_journal-3700	47	14	(	(	PUNCT
american_scientific_journal-3700	47	15	asrjets	asrjet	NOUN
american_scientific_journal-3700	47	16	)	)	PUNCT
american_scientific_journal-3700	47	17	(	(	PUNCT
american_scientific_journal-3700	47	18	2018	2018	NUM
american_scientific_journal-3700	47	19	)	)	PUNCT
american_scientific_journal-3700	47	20	volume	volume	NOUN
american_scientific_journal-3700	47	21	39	39	NUM
american_scientific_journal-3700	47	22	,	,	PUNCT
american_scientific_journal-3700	47	23	no	no	DET
american_scientific_journal-3700	47	24	1	1	NUM
american_scientific_journal-3700	47	25	,	,	PUNCT
american_scientific_journal-3700	47	26	pp	pp	ADV
american_scientific_journal-3700	47	27	10	10	NUM
american_scientific_journal-3700	47	28	-	-	SYM
american_scientific_journal-3700	47	29	18	18	NUM
american_scientific_journal-3700	47	30	13	13	NUM
american_scientific_journal-3700	47	31	𝐸𝐸ψ	𝐸𝐸ψ	NOUN
american_scientific_journal-3700	47	32	=	=	SYM
american_scientific_journal-3700	48	1	𝑖𝑖ℏ	𝑖𝑖ℏ	PROPN
american_scientific_journal-3700	48	2	𝜕𝜕ψ	𝜕𝜕ψ	PROPN
american_scientific_journal-3700	48	3	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	NUM
american_scientific_journal-3700	48	4	𝜕𝜕2ψ	𝜕𝜕2ψ	PROPN
american_scientific_journal-3700	48	5	𝜕𝜕𝑖𝑖2	𝜕𝜕𝑖𝑖2	NOUN
american_scientific_journal-3700	48	6	=	=	SYM
american_scientific_journal-3700	48	7	−	−	NOUN
american_scientific_journal-3700	48	8	𝑖𝑖2	𝑖𝑖2	NOUN
american_scientific_journal-3700	49	1	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	49	2	𝐸𝐸2ψ	𝐸𝐸2ψ	X
american_scientific_journal-3700	49	3	(	(	PUNCT
american_scientific_journal-3700	49	4	13	13	NUM
american_scientific_journal-3700	49	5	)	)	PUNCT
american_scientific_journal-3700	49	6	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	49	7	𝜕𝜕	𝜕𝜕	ADJ
american_scientific_journal-3700	49	8	2ψ	2ψ	NUM
american_scientific_journal-3700	49	9	𝜕𝜕𝑖𝑖2	𝜕𝜕𝑖𝑖2	NOUN
american_scientific_journal-3700	49	10	=	=	SYM
american_scientific_journal-3700	49	11	𝐸𝐸2ψ	𝐸𝐸2ψ	X
american_scientific_journal-3700	49	12	(	(	PUNCT
american_scientific_journal-3700	49	13	14	14	NUM
american_scientific_journal-3700	49	14	)	)	PUNCT
american_scientific_journal-3700	49	15	similarly	similarly	ADV
american_scientific_journal-3700	49	16	differentiating	differentiate	VERB
american_scientific_journal-3700	49	17	the	the	DET
american_scientific_journal-3700	49	18	wave	wave	NOUN
american_scientific_journal-3700	49	19	function	function	NOUN
american_scientific_journal-3700	49	20	respect	respect	NOUN
american_scientific_journal-3700	49	21	to	to	ADP
american_scientific_journal-3700	49	22	x	x	SYM
american_scientific_journal-3700	49	23	yields	yield	NOUN
american_scientific_journal-3700	49	24	𝜕𝜕ψ	𝜕𝜕ψ	PROPN
american_scientific_journal-3700	49	25	𝜕𝜕𝑥𝑥	𝜕𝜕𝑥𝑥	PUNCT
american_scientific_journal-3700	50	1	=	=	PUNCT
american_scientific_journal-3700	50	2	𝑖𝑖	𝑖𝑖	PUNCT
american_scientific_journal-3700	50	3	ℏ	ℏ	X
american_scientific_journal-3700	50	4	pψ	pψ	INTJ
american_scientific_journal-3700	50	5	𝑖𝑖ℏ	𝑖𝑖ℏ	NOUN
american_scientific_journal-3700	50	6	𝜕𝜕ψ	𝜕𝜕ψ	NOUN
american_scientific_journal-3700	50	7	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	PUNCT
american_scientific_journal-3700	51	1	=	=	PUNCT
american_scientific_journal-3700	51	2	pψ	pψ	PROPN
american_scientific_journal-3700	51	3	𝜕𝜕2ψ	𝜕𝜕2ψ	PROPN
american_scientific_journal-3700	51	4	𝜕𝜕𝑥𝑥2	𝜕𝜕𝑥𝑥2	ADP
american_scientific_journal-3700	51	5	=	=	PUNCT
american_scientific_journal-3700	51	6	𝑖𝑖2	𝑖𝑖2	NOUN
american_scientific_journal-3700	51	7	ℏ2	ℏ2	AUX
american_scientific_journal-3700	51	8	𝑃𝑃2ψ	𝑃𝑃2ψ	PROPN
american_scientific_journal-3700	51	9	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	51	10	𝜕𝜕	𝜕𝜕	VERB
american_scientific_journal-3700	51	11	2ψ	2ψ	NOUN
american_scientific_journal-3700	51	12	𝜕𝜕𝑝𝑝2	𝜕𝜕𝑝𝑝2	ADV
american_scientific_journal-3700	51	13	=	=	PUNCT
american_scientific_journal-3700	51	14	−ℏ2∇2ψ	−ℏ2∇2ψ	PRON
american_scientific_journal-3700	51	15	=	=	SYM
american_scientific_journal-3700	51	16	𝑃𝑃2ψ	𝑃𝑃2ψ	X
american_scientific_journal-3700	51	17	(	(	PUNCT
american_scientific_journal-3700	51	18	15	15	NUM
american_scientific_journal-3700	51	19	)	)	PUNCT
american_scientific_journal-3700	51	20	thus	thus	ADV
american_scientific_journal-3700	51	21	inserting	insert	VERB
american_scientific_journal-3700	51	22	eqs	eqs	PROPN
american_scientific_journal-3700	51	23	.	.	PUNCT
american_scientific_journal-3700	52	1	(	(	PUNCT
american_scientific_journal-3700	52	2	13	13	NUM
american_scientific_journal-3700	52	3	)	)	PUNCT
american_scientific_journal-3700	52	4	,	,	PUNCT
american_scientific_journal-3700	52	5	(	(	PUNCT
american_scientific_journal-3700	52	6	14	14	NUM
american_scientific_journal-3700	52	7	)	)	PUNCT
american_scientific_journal-3700	52	8	and	and	CCONJ
american_scientific_journal-3700	52	9	(	(	PUNCT
american_scientific_journal-3700	52	10	15	15	NUM
american_scientific_journal-3700	52	11	)	)	PUNCT
american_scientific_journal-3700	52	12	into	into	ADP
american_scientific_journal-3700	52	13	eq	eq	NOUN
american_scientific_journal-3700	52	14	.	.	PUNCT
american_scientific_journal-3700	53	1	(	(	PUNCT
american_scientific_journal-3700	53	2	11	11	NUM
american_scientific_journal-3700	53	3	)	)	PUNCT
american_scientific_journal-3700	53	4	yields	yield	VERB
american_scientific_journal-3700	53	5	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	53	6	𝜕𝜕2ψ	𝜕𝜕2ψ	PROPN
american_scientific_journal-3700	53	7	𝜕𝜕𝑥𝑥2	𝜕𝜕𝑥𝑥2	ADP
american_scientific_journal-3700	53	8	=	=	SYM
american_scientific_journal-3700	53	9	�	�	PROPN
american_scientific_journal-3700	53	10	−	−	NOUN
american_scientific_journal-3700	53	11	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	53	12	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	53	13	∇2	∇2	PROPN
american_scientific_journal-3700	53	14	+	+	CCONJ
american_scientific_journal-3700	53	15	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	53	16	�	�	PROPN
american_scientific_journal-3700	53	17	𝑖𝑖ℏ	𝑖𝑖ℏ	NOUN
american_scientific_journal-3700	53	18	𝜕𝜕ψ	𝜕𝜕ψ	PROPN
american_scientific_journal-3700	53	19	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	PROPN
american_scientific_journal-3700	54	1	+	+	CCONJ
american_scientific_journal-3700	54	2	𝑖𝑖ℏ	𝑖𝑖ℏ	PRON
american_scientific_journal-3700	54	3	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	54	4	�	�	PROPN
american_scientific_journal-3700	54	5	−𝑖𝑖ℏ	−𝑖𝑖ℏ	NOUN
american_scientific_journal-3700	54	6	𝜕𝜕ψ	𝜕𝜕ψ	NOUN
american_scientific_journal-3700	54	7	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	NOUN
american_scientific_journal-3700	55	1	+	+	NUM
american_scientific_journal-3700	55	2	𝑉𝑉ψ	𝑉𝑉ψ	PROPN
american_scientific_journal-3700	55	3	�	�	PROPN
american_scientific_journal-3700	55	4	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	55	5	𝜕𝜕	𝜕𝜕	PROPN
american_scientific_journal-3700	55	6	2ψ	2ψ	NOUN
american_scientific_journal-3700	55	7	𝜕𝜕𝑝𝑝2	𝜕𝜕𝑝𝑝2	ADV
american_scientific_journal-3700	55	8	=	=	SYM
american_scientific_journal-3700	55	9	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	55	10	�	�	SYM
american_scientific_journal-3700	55	11	−	−	NOUN
american_scientific_journal-3700	55	12	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	55	13	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	55	14	∇2	∇2	PROPN
american_scientific_journal-3700	55	15	+	+	CCONJ
american_scientific_journal-3700	55	16	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	55	17	�	�	PROPN
american_scientific_journal-3700	55	18	𝜕𝜕ψ	𝜕𝜕ψ	PROPN
american_scientific_journal-3700	55	19	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PART
american_scientific_journal-3700	56	1	+	+	NUM
american_scientific_journal-3700	56	2	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	56	3	𝜏𝜏	𝜏𝜏	VERB
american_scientific_journal-3700	56	4	𝜕𝜕ψ	𝜕𝜕ψ	PROPN
american_scientific_journal-3700	56	5	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PUNCT
american_scientific_journal-3700	57	1	+	+	CCONJ
american_scientific_journal-3700	57	2	𝑖𝑖ℏ	𝑖𝑖ℏ	PRON
american_scientific_journal-3700	57	3	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	57	4	𝑉𝑉ψ	𝑉𝑉ψ	PROPN
american_scientific_journal-3700	57	5	(	(	PUNCT
american_scientific_journal-3700	57	6	16	16	NUM
american_scientific_journal-3700	57	7	)	)	PUNCT
american_scientific_journal-3700	57	8	3	3	NUM
american_scientific_journal-3700	57	9	.	.	X
american_scientific_journal-3700	57	10	harmonic	harmonic	ADJ
american_scientific_journal-3700	57	11	oscillator	oscillator	NOUN
american_scientific_journal-3700	57	12	solution	solution	NOUN
american_scientific_journal-3700	57	13	to	to	PART
american_scientific_journal-3700	57	14	see	see	VERB
american_scientific_journal-3700	57	15	how	how	SCONJ
american_scientific_journal-3700	57	16	fraction	fraction	NOUN
american_scientific_journal-3700	57	17	force	force	NOUN
american_scientific_journal-3700	57	18	consider	consider	VERB
american_scientific_journal-3700	57	19	the	the	DET
american_scientific_journal-3700	57	20	solution	solution	NOUN
american_scientific_journal-3700	57	21	of	of	ADP
american_scientific_journal-3700	57	22	eq	eq	PROPN
american_scientific_journal-3700	57	23	.	.	PUNCT
american_scientific_journal-3700	58	1	(	(	PUNCT
american_scientific_journal-3700	58	2	12	12	NUM
american_scientific_journal-3700	58	3	)	)	PUNCT
american_scientific_journal-3700	58	4	in	in	ADP
american_scientific_journal-3700	58	5	the	the	DET
american_scientific_journal-3700	58	6	form	form	NOUN
american_scientific_journal-3700	58	7	ψ	ψ	X
american_scientific_journal-3700	58	8	=	=	SYM
american_scientific_journal-3700	58	9	𝑒𝑒−𝑖𝑖	𝑒𝑒−𝑖𝑖	X
american_scientific_journal-3700	58	10	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	58	11	ℏ𝑖𝑖𝑢𝑢(𝑣𝑣	ℏ𝑖𝑖𝑢𝑢(𝑣𝑣	NOUN
american_scientific_journal-3700	58	12	)	)	PUNCT
american_scientific_journal-3700	58	13	=	=	SYM
american_scientific_journal-3700	58	14	𝑓𝑓(𝑣𝑣)𝑢𝑢(𝑣𝑣	𝑓𝑓(𝑣𝑣)𝑢𝑢(𝑣𝑣	X
american_scientific_journal-3700	58	15	)	)	PUNCT
american_scientific_journal-3700	58	16	=	=	SYM
american_scientific_journal-3700	58	17	𝑓𝑓𝑢𝑢	𝑓𝑓𝑢𝑢	NOUN
american_scientific_journal-3700	58	18	𝜕𝜕ψ	𝜕𝜕ψ	PROPN
american_scientific_journal-3700	58	19	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	PUNCT
american_scientific_journal-3700	58	20	=	=	SYM
american_scientific_journal-3700	58	21	−𝑖𝑖	−𝑖𝑖	PROPN
american_scientific_journal-3700	58	22	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	58	23	ℏ	ℏ	PROPN
american_scientific_journal-3700	58	24	𝑓𝑓𝑢𝑢	𝑓𝑓𝑢𝑢	NOUN
american_scientific_journal-3700	58	25	𝜕𝜕2ψ	𝜕𝜕2ψ	PROPN
american_scientific_journal-3700	58	26	𝜕𝜕𝑝𝑝2	𝜕𝜕𝑝𝑝2	ADV
american_scientific_journal-3700	58	27	=	=	SYM
american_scientific_journal-3700	58	28	𝑖𝑖2𝐸𝐸2	𝑖𝑖2𝐸𝐸2	NUM
american_scientific_journal-3700	59	1	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	59	2	𝑓𝑓𝑢𝑢	𝑓𝑓𝑢𝑢	VERB
american_scientific_journal-3700	59	3	=	=	PUNCT
american_scientific_journal-3700	60	1	−𝐸𝐸2	−𝐸𝐸2	NOUN
american_scientific_journal-3700	60	2	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	60	3	𝑓𝑓𝑢𝑢	𝑓𝑓𝑢𝑢	VERB
american_scientific_journal-3700	60	4	(	(	PUNCT
american_scientific_journal-3700	60	5	17	17	NUM
american_scientific_journal-3700	60	6	)	)	PUNCT
american_scientific_journal-3700	60	7	a	a	DET
american_scientific_journal-3700	60	8	direct	direct	ADJ
american_scientific_journal-3700	60	9	substitution	substitution	NOUN
american_scientific_journal-3700	60	10	in	in	ADP
american_scientific_journal-3700	60	11	eq	eq	ADP
american_scientific_journal-3700	60	12	.	.	PUNCT
american_scientific_journal-3700	61	1	(	(	PUNCT
american_scientific_journal-3700	61	2	16	16	NUM
american_scientific_journal-3700	61	3	)	)	PUNCT
american_scientific_journal-3700	61	4	gives	give	VERB
american_scientific_journal-3700	61	5	𝐸𝐸2𝑓𝑓𝑢𝑢	𝐸𝐸2𝑓𝑓𝑢𝑢	NOUN
american_scientific_journal-3700	61	6	=	=	PUNCT
american_scientific_journal-3700	61	7	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	61	8	�	�	PROPN
american_scientific_journal-3700	61	9	−	−	NOUN
american_scientific_journal-3700	61	10	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	61	11	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	61	12	∇2𝑢𝑢	∇2𝑢𝑢	PROPN
american_scientific_journal-3700	61	13	+	+	CCONJ
american_scientific_journal-3700	61	14	𝑉𝑉𝑢𝑢	𝑉𝑉𝑢𝑢	PROPN
american_scientific_journal-3700	61	15	�	�	PROPN
american_scientific_journal-3700	61	16	𝑓𝑓	𝑓𝑓	ADP
american_scientific_journal-3700	61	17	�	�	PROPN
american_scientific_journal-3700	61	18	−𝑖𝑖𝐸𝐸	−𝑖𝑖𝐸𝐸	NUM
american_scientific_journal-3700	61	19	ℏ	ℏ	PROPN
american_scientific_journal-3700	61	20	�	�	PROPN
american_scientific_journal-3700	61	21	−	−	PROPN
american_scientific_journal-3700	61	22	𝑖𝑖	𝑖𝑖	NOUN
american_scientific_journal-3700	61	23	𝐸𝐸ℏ	𝐸𝐸ℏ	NOUN
american_scientific_journal-3700	61	24	2	2	NUM
american_scientific_journal-3700	61	25	ℏ𝜏𝜏	ℏ𝜏𝜏	NOUN
american_scientific_journal-3700	61	26	𝑓𝑓𝑢𝑢	𝑓𝑓𝑢𝑢	NOUN
american_scientific_journal-3700	61	27	+	+	CCONJ
american_scientific_journal-3700	61	28	𝑖𝑖	𝑖𝑖	PUNCT
american_scientific_journal-3700	61	29	ℏ	ℏ	PRON
american_scientific_journal-3700	61	30	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	61	31	𝑉𝑉𝑓𝑓𝑢𝑢	𝑉𝑉𝑓𝑓𝑢𝑢	PROPN
american_scientific_journal-3700	61	32	(	(	PUNCT
american_scientific_journal-3700	61	33	18	18	NUM
american_scientific_journal-3700	61	34	)	)	PUNCT
american_scientific_journal-3700	61	35	dividing	divide	VERB
american_scientific_journal-3700	61	36	both	both	DET
american_scientific_journal-3700	61	37	sides	side	NOUN
american_scientific_journal-3700	61	38	of	of	ADP
american_scientific_journal-3700	61	39	eq	eq	PROPN
american_scientific_journal-3700	61	40	.	.	PUNCT
american_scientific_journal-3700	62	1	(	(	PUNCT
american_scientific_journal-3700	62	2	18	18	NUM
american_scientific_journal-3700	62	3	)	)	PUNCT
american_scientific_journal-3700	62	4	by	by	ADP
american_scientific_journal-3700	62	5	f	f	PROPN
american_scientific_journal-3700	62	6	yields	yield	NOUN
american_scientific_journal-3700	62	7	american	american	PROPN
american_scientific_journal-3700	62	8	scientific	scientific	PROPN
american_scientific_journal-3700	62	9	research	research	PROPN
american_scientific_journal-3700	62	10	journal	journal	NOUN
american_scientific_journal-3700	62	11	for	for	ADP
american_scientific_journal-3700	62	12	engineering	engineering	NOUN
american_scientific_journal-3700	62	13	,	,	PUNCT
american_scientific_journal-3700	62	14	technology	technology	NOUN
american_scientific_journal-3700	62	15	,	,	PUNCT
american_scientific_journal-3700	62	16	and	and	CCONJ
american_scientific_journal-3700	62	17	sciences	science	NOUN
american_scientific_journal-3700	62	18	(	(	PUNCT
american_scientific_journal-3700	62	19	asrjets	asrjet	NOUN
american_scientific_journal-3700	62	20	)	)	PUNCT
american_scientific_journal-3700	62	21	(	(	PUNCT
american_scientific_journal-3700	62	22	2018	2018	NUM
american_scientific_journal-3700	62	23	)	)	PUNCT
american_scientific_journal-3700	62	24	volume	volume	NOUN
american_scientific_journal-3700	62	25	39	39	NUM
american_scientific_journal-3700	62	26	,	,	PUNCT
american_scientific_journal-3700	62	27	no	no	DET
american_scientific_journal-3700	62	28	1	1	NUM
american_scientific_journal-3700	62	29	,	,	PUNCT
american_scientific_journal-3700	62	30	pp	pp	ADV
american_scientific_journal-3700	62	31	10	10	NUM
american_scientific_journal-3700	62	32	-	-	SYM
american_scientific_journal-3700	62	33	18	18	NUM
american_scientific_journal-3700	62	34	14	14	NUM
american_scientific_journal-3700	62	35	𝐸𝐸2𝑢𝑢	𝐸𝐸2𝑢𝑢	NOUN
american_scientific_journal-3700	62	36	=	=	PUNCT
american_scientific_journal-3700	63	1	+	+	ADJ
american_scientific_journal-3700	63	2	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	63	3	�	�	NOUN
american_scientific_journal-3700	63	4	−	−	NOUN
american_scientific_journal-3700	63	5	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	63	6	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	63	7	∇2𝑢𝑢	∇2𝑢𝑢	PROPN
american_scientific_journal-3700	63	8	+	+	CCONJ
american_scientific_journal-3700	63	9	𝑉𝑉𝑢𝑢	𝑉𝑉𝑢𝑢	PROPN
american_scientific_journal-3700	63	10	�	�	PROPN
american_scientific_journal-3700	63	11	−	−	PROPN
american_scientific_journal-3700	63	12	𝑖𝑖	𝑖𝑖	NOUN
american_scientific_journal-3700	63	13	𝐸𝐸ℏ	𝐸𝐸ℏ	NOUN
american_scientific_journal-3700	63	14	𝜏𝜏	𝜏𝜏	VERB
american_scientific_journal-3700	63	15	𝑢𝑢	𝑢𝑢	ADP
american_scientific_journal-3700	63	16	+	+	CCONJ
american_scientific_journal-3700	63	17	𝑖𝑖	𝑖𝑖	NUM
american_scientific_journal-3700	63	18	ℏ	ℏ	NOUN
american_scientific_journal-3700	63	19	𝜏𝜏	𝜏𝜏	ADP
american_scientific_journal-3700	63	20	𝑉𝑉𝑢𝑢	𝑉𝑉𝑢𝑢	PROPN
american_scientific_journal-3700	63	21	(	(	PUNCT
american_scientific_journal-3700	63	22	19	19	NUM
american_scientific_journal-3700	63	23	)	)	PUNCT
american_scientific_journal-3700	63	24	dividing	divide	VERB
american_scientific_journal-3700	63	25	both	both	DET
american_scientific_journal-3700	63	26	sides	side	NOUN
american_scientific_journal-3700	63	27	of	of	ADP
american_scientific_journal-3700	63	28	eq	eq	PROPN
american_scientific_journal-3700	63	29	.	.	PUNCT
american_scientific_journal-3700	64	1	(	(	PUNCT
american_scientific_journal-3700	64	2	19	19	NUM
american_scientific_journal-3700	64	3	)	)	PUNCT
american_scientific_journal-3700	64	4	by	by	ADP
american_scientific_journal-3700	64	5	+	+	PROPN
american_scientific_journal-3700	64	6	e	e	NOUN
american_scientific_journal-3700	64	7	yields	yield	NOUN
american_scientific_journal-3700	64	8	�	�	PROPN
american_scientific_journal-3700	64	9	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	64	10	+	+	CCONJ
american_scientific_journal-3700	64	11	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	64	12	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	64	13	�	�	PROPN
american_scientific_journal-3700	64	14	𝑢𝑢	𝑢𝑢	NOUN
american_scientific_journal-3700	64	15	=	=	SYM
american_scientific_journal-3700	64	16	−	−	PROPN
american_scientific_journal-3700	65	1	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	65	2	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	65	3	∇2𝑢𝑢	∇2𝑢𝑢	PROPN
american_scientific_journal-3700	65	4	+	+	CCONJ
american_scientific_journal-3700	65	5	𝑉𝑉	𝑉𝑉	PROPN
american_scientific_journal-3700	65	6	�	�	NOUN
american_scientific_journal-3700	65	7	1	1	NUM
american_scientific_journal-3700	65	8	+	+	NUM
american_scientific_journal-3700	65	9	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	65	10	𝜏𝜏𝐸𝐸	𝜏𝜏𝐸𝐸	PROPN
american_scientific_journal-3700	65	11	�	�	PROPN
american_scientific_journal-3700	65	12	𝑢𝑢	𝑢𝑢	PRON
american_scientific_journal-3700	65	13	−	−	PROPN
american_scientific_journal-3700	65	14	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	65	15	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	65	16	∇2𝑢𝑢	∇2𝑢𝑢	PROPN
american_scientific_journal-3700	65	17	+	+	CCONJ
american_scientific_journal-3700	65	18	𝑐𝑐1𝑉𝑉𝑢𝑢	𝑐𝑐1𝑉𝑉𝑢𝑢	NOUN
american_scientific_journal-3700	65	19	=	=	PUNCT
american_scientific_journal-3700	65	20	𝐸𝐸1𝑢𝑢	𝐸𝐸1𝑢𝑢	NOUN
american_scientific_journal-3700	65	21	(	(	PUNCT
american_scientific_journal-3700	65	22	20	20	NUM
american_scientific_journal-3700	65	23	)	)	PUNCT
american_scientific_journal-3700	65	24	where	where	SCONJ
american_scientific_journal-3700	65	25	𝑐𝑐1	𝑐𝑐1	PROPN
american_scientific_journal-3700	65	26	=	=	NOUN
american_scientific_journal-3700	65	27	1	1	NUM
american_scientific_journal-3700	65	28	+	+	NUM
american_scientific_journal-3700	65	29	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	65	30	𝜏𝜏𝐸𝐸	𝜏𝜏𝐸𝐸	ADJ
american_scientific_journal-3700	65	31	𝐸𝐸1	𝐸𝐸1	PROPN
american_scientific_journal-3700	65	32	=	=	SYM
american_scientific_journal-3700	65	33	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	66	1	+	+	CCONJ
american_scientific_journal-3700	66	2	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	66	3	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	66	4	(	(	PUNCT
american_scientific_journal-3700	66	5	21	21	NUM
american_scientific_journal-3700	66	6	)	)	PUNCT
american_scientific_journal-3700	66	7	for	for	ADP
american_scientific_journal-3700	66	8	harmonic	harmonic	ADJ
american_scientific_journal-3700	66	9	oscillator	oscillator	NOUN
american_scientific_journal-3700	66	10	one	one	NUM
american_scientific_journal-3700	66	11	finds	find	VERB
american_scientific_journal-3700	66	12	𝑉𝑉	𝑉𝑉	NOUN
american_scientific_journal-3700	66	13	=	=	SYM
american_scientific_journal-3700	66	14	1	1	NUM
american_scientific_journal-3700	66	15	2	2	NUM
american_scientific_journal-3700	66	16	𝑘𝑘𝑥𝑥2	𝑘𝑘𝑥𝑥2	NOUN
american_scientific_journal-3700	66	17	(	(	PUNCT
american_scientific_journal-3700	66	18	22	22	NUM
american_scientific_journal-3700	66	19	)	)	PUNCT
american_scientific_journal-3700	66	20	thus	thus	ADV
american_scientific_journal-3700	66	21	substituting	substitute	VERB
american_scientific_journal-3700	66	22	this	this	DET
american_scientific_journal-3700	66	23	expression	expression	NOUN
american_scientific_journal-3700	66	24	in	in	ADP
american_scientific_journal-3700	66	25	eq	eq	ADP
american_scientific_journal-3700	66	26	.	.	PUNCT
american_scientific_journal-3700	67	1	(	(	PUNCT
american_scientific_journal-3700	67	2	20	20	NUM
american_scientific_journal-3700	67	3	)	)	PUNCT
american_scientific_journal-3700	67	4	gives	give	VERB
american_scientific_journal-3700	67	5	−	−	PROPN
american_scientific_journal-3700	67	6	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	67	7	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	67	8	∇2u	∇2u	PROPN
american_scientific_journal-3700	68	1	+	+	CCONJ
american_scientific_journal-3700	68	2	𝑐𝑐1	𝑐𝑐1	NOUN
american_scientific_journal-3700	68	3	1	1	NUM
american_scientific_journal-3700	68	4	2	2	NUM
american_scientific_journal-3700	68	5	k𝑥𝑥2	k𝑥𝑥2	NOUN
american_scientific_journal-3700	68	6	=	=	SYM
american_scientific_journal-3700	68	7	𝐸𝐸1u	𝐸𝐸1u	X
american_scientific_journal-3700	68	8	(	(	PUNCT
american_scientific_journal-3700	68	9	23	23	NUM
american_scientific_journal-3700	68	10	)	)	PUNCT
american_scientific_journal-3700	68	11	let	let	VERB
american_scientific_journal-3700	68	12	now	now	ADV
american_scientific_journal-3700	68	13	𝑘𝑘𝜊𝜊	𝑘𝑘𝜊𝜊	ADV
american_scientific_journal-3700	69	1	=	=	PRON
american_scientific_journal-3700	69	2	𝑐𝑐1𝑘𝑘	𝑐𝑐1𝑘𝑘	PROPN
american_scientific_journal-3700	69	3	(	(	PUNCT
american_scientific_journal-3700	69	4	24	24	NUM
american_scientific_journal-3700	69	5	)	)	PUNCT
american_scientific_journal-3700	69	6	therefore	therefore	ADV
american_scientific_journal-3700	69	7	equation	equation	NOUN
american_scientific_journal-3700	69	8	(	(	PUNCT
american_scientific_journal-3700	69	9	23	23	NUM
american_scientific_journal-3700	69	10	)	)	PUNCT
american_scientific_journal-3700	69	11	became	become	VERB
american_scientific_journal-3700	69	12	−	−	PROPN
american_scientific_journal-3700	69	13	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	69	14	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	70	1	∇2u	∇2u	PROPN
american_scientific_journal-3700	71	1	+	+	CCONJ
american_scientific_journal-3700	71	2	1	1	NUM
american_scientific_journal-3700	71	3	2	2	NUM
american_scientific_journal-3700	71	4	𝑘𝑘𝜊𝜊𝑥𝑥2	𝑘𝑘𝜊𝜊𝑥𝑥2	NOUN
american_scientific_journal-3700	71	5	=	=	SYM
american_scientific_journal-3700	71	6	𝐸𝐸1u	𝐸𝐸1u	X
american_scientific_journal-3700	71	7	(	(	PUNCT
american_scientific_journal-3700	71	8	25	25	NUM
american_scientific_journal-3700	71	9	)	)	PUNCT
american_scientific_journal-3700	71	10	thus	thus	ADV
american_scientific_journal-3700	71	11	substituting	substitute	VERB
american_scientific_journal-3700	71	12	eq	eq	ADP
american_scientific_journal-3700	71	13	.	.	PUNCT
american_scientific_journal-3700	71	14	(	(	PUNCT
american_scientific_journal-3700	71	15	21	21	NUM
american_scientific_journal-3700	71	16	)	)	PUNCT
american_scientific_journal-3700	71	17	into	into	ADP
american_scientific_journal-3700	71	18	eq	eq	NOUN
american_scientific_journal-3700	71	19	.	.	PUNCT
american_scientific_journal-3700	72	1	(	(	PUNCT
american_scientific_journal-3700	72	2	25	25	NUM
american_scientific_journal-3700	72	3	)	)	PUNCT
american_scientific_journal-3700	72	4	gives	give	VERB
american_scientific_journal-3700	72	5	𝐸𝐸1	𝐸𝐸1	PROPN
american_scientific_journal-3700	72	6	=	=	SYM
american_scientific_journal-3700	72	7	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	73	1	+	+	CCONJ
american_scientific_journal-3700	73	2	𝑖𝑖ℏ	𝑖𝑖ℏ	PRON
american_scientific_journal-3700	73	3	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	73	4	=	=	PUNCT
american_scientific_journal-3700	73	5	�	�	PROPN
american_scientific_journal-3700	73	6	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-3700	73	7	+	+	NOUN
american_scientific_journal-3700	73	8	1	1	NUM
american_scientific_journal-3700	73	9	2	2	NUM
american_scientific_journal-3700	73	10	�	�	NOUN
american_scientific_journal-3700	73	11	ℏ𝜔𝜔	ℏ𝜔𝜔	NOUN
american_scientific_journal-3700	73	12	(	(	PUNCT
american_scientific_journal-3700	73	13	26	26	NUM
american_scientific_journal-3700	73	14	)	)	PUNCT
american_scientific_journal-3700	73	15	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	73	16	=	=	SYM
american_scientific_journal-3700	73	17	�	�	PROPN
american_scientific_journal-3700	73	18	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-3700	73	19	+	+	NOUN
american_scientific_journal-3700	73	20	1	1	NUM
american_scientific_journal-3700	73	21	2	2	NUM
american_scientific_journal-3700	73	22	�	�	NOUN
american_scientific_journal-3700	73	23	ℏ𝜔𝜔	ℏ𝜔𝜔	NOUN
american_scientific_journal-3700	73	24	−	−	PROPN
american_scientific_journal-3700	73	25	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	73	26	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	73	27	(	(	PUNCT
american_scientific_journal-3700	73	28	27	27	NUM
american_scientific_journal-3700	73	29	)	)	PUNCT
american_scientific_journal-3700	73	30	the	the	DET
american_scientific_journal-3700	73	31	frequency	frequency	NOUN
american_scientific_journal-3700	73	32	is	be	AUX
american_scientific_journal-3700	73	33	given	give	VERB
american_scientific_journal-3700	73	34	according	accord	VERB
american_scientific_journal-3700	73	35	to	to	ADP
american_scientific_journal-3700	73	36	eq	eq	PROPN
american_scientific_journal-3700	73	37	.	.	PUNCT
american_scientific_journal-3700	74	1	(	(	PUNCT
american_scientific_journal-3700	74	2	24	24	NUM
american_scientific_journal-3700	74	3	)	)	PUNCT
american_scientific_journal-3700	74	4	and	and	CCONJ
american_scientific_journal-3700	74	5	eq	eq	NOUN
american_scientific_journal-3700	74	6	.	.	PUNCT
american_scientific_journal-3700	75	1	(	(	PUNCT
american_scientific_journal-3700	75	2	21	21	NUM
american_scientific_journal-3700	75	3	)	)	PUNCT
american_scientific_journal-3700	75	4	to	to	PART
american_scientific_journal-3700	75	5	be	be	AUX
american_scientific_journal-3700	75	6	𝑘𝑘𝜊𝜊	𝑘𝑘𝜊𝜊	ADJ
american_scientific_journal-3700	75	7	=	=	SYM
american_scientific_journal-3700	75	8	𝑚𝑚𝜔𝜔2	𝑚𝑚𝜔𝜔2	ADJ
american_scientific_journal-3700	75	9	american	american	ADJ
american_scientific_journal-3700	75	10	scientific	scientific	ADJ
american_scientific_journal-3700	75	11	research	research	NOUN
american_scientific_journal-3700	75	12	journal	journal	NOUN
american_scientific_journal-3700	75	13	for	for	ADP
american_scientific_journal-3700	75	14	engineering	engineering	NOUN
american_scientific_journal-3700	75	15	,	,	PUNCT
american_scientific_journal-3700	75	16	technology	technology	NOUN
american_scientific_journal-3700	75	17	,	,	PUNCT
american_scientific_journal-3700	75	18	and	and	CCONJ
american_scientific_journal-3700	75	19	sciences	science	NOUN
american_scientific_journal-3700	75	20	(	(	PUNCT
american_scientific_journal-3700	75	21	asrjets	asrjet	NOUN
american_scientific_journal-3700	75	22	)	)	PUNCT
american_scientific_journal-3700	75	23	(	(	PUNCT
american_scientific_journal-3700	75	24	2018	2018	NUM
american_scientific_journal-3700	75	25	)	)	PUNCT
american_scientific_journal-3700	75	26	volume	volume	NOUN
american_scientific_journal-3700	75	27	39	39	NUM
american_scientific_journal-3700	75	28	,	,	PUNCT
american_scientific_journal-3700	75	29	no	no	DET
american_scientific_journal-3700	75	30	1	1	NUM
american_scientific_journal-3700	75	31	,	,	PUNCT
american_scientific_journal-3700	75	32	pp	pp	ADV
american_scientific_journal-3700	75	33	10	10	NUM
american_scientific_journal-3700	75	34	-	-	SYM
american_scientific_journal-3700	75	35	18	18	NUM
american_scientific_journal-3700	75	36	15	15	NUM
american_scientific_journal-3700	75	37	𝑐𝑐1𝑘𝑘	𝑐𝑐1𝑘𝑘	NOUN
american_scientific_journal-3700	75	38	=	=	SYM
american_scientific_journal-3700	75	39	�	�	PROPN
american_scientific_journal-3700	75	40	1	1	NUM
american_scientific_journal-3700	75	41	+	+	CCONJ
american_scientific_journal-3700	75	42	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	75	43	𝜏𝜏𝐸𝐸	𝜏𝜏𝐸𝐸	VERB
american_scientific_journal-3700	75	44	�	�	PROPN
american_scientific_journal-3700	75	45	𝑘𝑘	𝑘𝑘	NOUN
american_scientific_journal-3700	75	46	=	=	SYM
american_scientific_journal-3700	75	47	𝑚𝑚𝜔𝜔2	𝑚𝑚𝜔𝜔2	NOUN
american_scientific_journal-3700	75	48	�	�	PROPN
american_scientific_journal-3700	75	49	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	75	50	+	+	CCONJ
american_scientific_journal-3700	75	51	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	75	52	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	75	53	�	�	PROPN
american_scientific_journal-3700	75	54	𝑘𝑘	𝑘𝑘	NOUN
american_scientific_journal-3700	75	55	=	=	SYM
american_scientific_journal-3700	75	56	𝑚𝑚𝜔𝜔2𝐸𝐸	𝑚𝑚𝜔𝜔2𝐸𝐸	PROPN
american_scientific_journal-3700	75	57	(	(	PUNCT
american_scientific_journal-3700	75	58	28	28	NUM
american_scientific_journal-3700	75	59	)	)	PUNCT
american_scientific_journal-3700	75	60	thus	thus	ADV
american_scientific_journal-3700	75	61	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	75	62	=	=	SYM
american_scientific_journal-3700	75	63	�	�	PROPN
american_scientific_journal-3700	75	64	𝑚𝑚𝜔𝜔2	𝑚𝑚𝜔𝜔2	NOUN
american_scientific_journal-3700	75	65	𝑘𝑘	𝑘𝑘	NOUN
american_scientific_journal-3700	75	66	−	−	PROPN
american_scientific_journal-3700	75	67	1	1	NUM
american_scientific_journal-3700	75	68	�	�	PROPN
american_scientific_journal-3700	75	69	−1	−1	NOUN
american_scientific_journal-3700	75	70	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	75	71	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	75	72	(	(	PUNCT
american_scientific_journal-3700	75	73	29	29	NUM
american_scientific_journal-3700	75	74	)	)	PUNCT
american_scientific_journal-3700	75	75	from	from	ADP
american_scientific_journal-3700	75	76	(	(	PUNCT
american_scientific_journal-3700	75	77	3	3	NUM
american_scientific_journal-3700	75	78	-	-	SYM
american_scientific_journal-3700	75	79	12	12	NUM
american_scientific_journal-3700	75	80	)	)	PUNCT
american_scientific_journal-3700	75	81	and	and	CCONJ
american_scientific_journal-3700	75	82	(	(	PUNCT
american_scientific_journal-3700	75	83	3.13	3.13	NUM
american_scientific_journal-3700	75	84	)	)	PUNCT
american_scientific_journal-3700	75	85	0	0	NUM
american_scientific_journal-3700	76	1	=	=	SYM
american_scientific_journal-3700	76	2	−	−	PROPN
american_scientific_journal-3700	76	3	𝑚𝑚𝜔𝜔2	𝑚𝑚𝜔𝜔2	NOUN
american_scientific_journal-3700	76	4	𝑘𝑘	𝑘𝑘	PROPN
american_scientific_journal-3700	76	5	+	+	CCONJ
american_scientific_journal-3700	76	6	�	�	NOUN
american_scientific_journal-3700	76	7	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-3700	76	8	+	+	NOUN
american_scientific_journal-3700	76	9	1	1	NUM
american_scientific_journal-3700	76	10	2	2	NUM
american_scientific_journal-3700	76	11	�	�	NOUN
american_scientific_journal-3700	76	12	ℏ𝜔𝜔	ℏ𝜔𝜔	NOUN
american_scientific_journal-3700	76	13	𝑚𝑚	𝑚𝑚	ADP
american_scientific_journal-3700	76	14	=	=	PUNCT
american_scientific_journal-3700	76	15	�	�	PROPN
american_scientific_journal-3700	76	16	1	1	NUM
american_scientific_journal-3700	76	17	+	+	CCONJ
american_scientific_journal-3700	76	18	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-3700	76	19	𝜏𝜏(𝑛𝑛+12	𝜏𝜏(𝑛𝑛+12	PROPN
american_scientific_journal-3700	76	20	)	)	PUNCT
american_scientific_journal-3700	76	21	�	�	PROPN
american_scientific_journal-3700	76	22	𝑘𝑘	𝑘𝑘	ADP
american_scientific_journal-3700	76	23	𝜔𝜔2	𝜔𝜔2	PROPN
american_scientific_journal-3700	76	24	(	(	PUNCT
american_scientific_journal-3700	76	25	30	30	NUM
american_scientific_journal-3700	76	26	)	)	PUNCT
american_scientific_journal-3700	76	27	thus	thus	ADV
american_scientific_journal-3700	76	28	,	,	PUNCT
american_scientific_journal-3700	76	29	from	from	ADP
american_scientific_journal-3700	76	30	eq	eq	ADP
american_scientific_journal-3700	76	31	.	.	PUNCT
american_scientific_journal-3700	77	1	(	(	PUNCT
american_scientific_journal-3700	77	2	30	30	NUM
american_scientific_journal-3700	77	3	)	)	PUNCT
american_scientific_journal-3700	77	4	one	one	NUM
american_scientific_journal-3700	77	5	finds	find	VERB
american_scientific_journal-3700	77	6	the	the	DET
american_scientific_journal-3700	77	7	mass	mass	NOUN
american_scientific_journal-3700	77	8	is	be	AUX
american_scientific_journal-3700	77	9	quantized	quantize	VERB
american_scientific_journal-3700	77	10	4	4	NUM
american_scientific_journal-3700	77	11	.	.	PUNCT
american_scientific_journal-3700	77	12	radioactive	radioactive	ADJ
american_scientific_journal-3700	77	13	decay	decay	NOUN
american_scientific_journal-3700	77	14	low	low	ADJ
american_scientific_journal-3700	77	15	and	and	CCONJ
american_scientific_journal-3700	77	16	collision	collision	NOUN
american_scientific_journal-3700	77	17	probability	probability	NOUN
american_scientific_journal-3700	77	18	consider	consider	VERB
american_scientific_journal-3700	77	19	now	now	ADV
american_scientific_journal-3700	77	20	eq	eq	ADJ
american_scientific_journal-3700	77	21	.	.	PUNCT
american_scientific_journal-3700	78	1	(	(	PUNCT
american_scientific_journal-3700	78	2	16	16	NUM
american_scientific_journal-3700	78	3	)	)	PUNCT
american_scientific_journal-3700	78	4	for	for	ADP
american_scientific_journal-3700	78	5	constant	constant	ADJ
american_scientific_journal-3700	78	6	potential	potential	NOUN
american_scientific_journal-3700	78	7	𝑉𝑉𝜊𝜊	𝑉𝑉𝜊𝜊	PROPN
american_scientific_journal-3700	78	8	using	use	VERB
american_scientific_journal-3700	78	9	the	the	DET
american_scientific_journal-3700	78	10	separation	separation	NOUN
american_scientific_journal-3700	78	11	of	of	ADP
american_scientific_journal-3700	78	12	variables	variable	NOUN
american_scientific_journal-3700	78	13	let	let	VERB
american_scientific_journal-3700	78	14	the	the	DET
american_scientific_journal-3700	78	15	wave	wave	NOUN
american_scientific_journal-3700	78	16	function	function	NOUN
american_scientific_journal-3700	78	17	ψ	ψ	PART
american_scientific_journal-3700	78	18	be	be	AUX
american_scientific_journal-3700	78	19	in	in	ADP
american_scientific_journal-3700	78	20	the	the	DET
american_scientific_journal-3700	78	21	form	form	NOUN
american_scientific_journal-3700	78	22	ψ(𝑟𝑟	ψ(𝑟𝑟	NOUN
american_scientific_journal-3700	78	23	,	,	PUNCT
american_scientific_journal-3700	78	24	𝑣𝑣	𝑣𝑣	NOUN
american_scientific_journal-3700	78	25	)	)	PUNCT
american_scientific_journal-3700	78	26	=	=	PUNCT
american_scientific_journal-3700	78	27	𝑓𝑓(𝑣𝑣)𝑢𝑢(𝑟𝑟	𝑓𝑓(𝑣𝑣)𝑢𝑢(𝑟𝑟	X
american_scientific_journal-3700	78	28	)	)	PUNCT
american_scientific_journal-3700	78	29	=	=	VERB
american_scientific_journal-3700	79	1	𝑓𝑓𝑢𝑢	𝑓𝑓𝑢𝑢	NOUN
american_scientific_journal-3700	79	2	(	(	PUNCT
american_scientific_journal-3700	79	3	31	31	NUM
american_scientific_journal-3700	79	4	)	)	PUNCT
american_scientific_journal-3700	79	5	a	a	DET
american_scientific_journal-3700	79	6	direct	direct	ADJ
american_scientific_journal-3700	79	7	substitution	substitution	NOUN
american_scientific_journal-3700	79	8	of	of	ADP
american_scientific_journal-3700	79	9	equation	equation	NOUN
american_scientific_journal-3700	79	10	(	(	PUNCT
american_scientific_journal-3700	79	11	31	31	NUM
american_scientific_journal-3700	79	12	)	)	PUNCT
american_scientific_journal-3700	79	13	in	in	ADP
american_scientific_journal-3700	79	14	equation	equation	NOUN
american_scientific_journal-3700	79	15	(	(	PUNCT
american_scientific_journal-3700	79	16	16	16	NUM
american_scientific_journal-3700	79	17	)	)	PUNCT
american_scientific_journal-3700	79	18	gives	give	VERB
american_scientific_journal-3700	79	19	−ℏ2𝑢𝑢	−ℏ2𝑢𝑢	NUM
american_scientific_journal-3700	79	20	𝜕𝜕2𝑓𝑓	𝜕𝜕2𝑓𝑓	PROPN
american_scientific_journal-3700	79	21	𝜕𝜕𝑣𝑣2	𝜕𝜕𝑣𝑣2	ADJ
american_scientific_journal-3700	79	22	=	=	SYM
american_scientific_journal-3700	79	23	�	�	PROPN
american_scientific_journal-3700	79	24	−	−	NOUN
american_scientific_journal-3700	79	25	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	79	26	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	79	27	∇2	∇2	PROPN
american_scientific_journal-3700	79	28	+	+	CCONJ
american_scientific_journal-3700	79	29	𝑉𝑉𝜊𝜊	𝑉𝑉𝜊𝜊	PROPN
american_scientific_journal-3700	79	30	�	�	PROPN
american_scientific_journal-3700	79	31	𝑢𝑢	𝑢𝑢	ADP
american_scientific_journal-3700	79	32	�	�	PROPN
american_scientific_journal-3700	80	1	𝑖𝑖ℏ	𝑖𝑖ℏ	PROPN
american_scientific_journal-3700	80	2	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	PUNCT
american_scientific_journal-3700	80	3	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	PRON
american_scientific_journal-3700	80	4	�	�	PROPN
american_scientific_journal-3700	80	5	+	+	CCONJ
american_scientific_journal-3700	80	6	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	80	7	𝜏𝜏	𝜏𝜏	ADP
american_scientific_journal-3700	80	8	𝑉𝑉𝜊𝜊𝑢𝑢𝑓𝑓	𝑉𝑉𝜊𝜊𝑢𝑢𝑓𝑓	PROPN
american_scientific_journal-3700	80	9	+	+	CCONJ
american_scientific_journal-3700	80	10	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	80	11	𝜏𝜏	𝜏𝜏	VERB
american_scientific_journal-3700	80	12	𝑢𝑢	𝑢𝑢	PROPN
american_scientific_journal-3700	80	13	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	PUNCT
american_scientific_journal-3700	80	14	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	NOUN
american_scientific_journal-3700	80	15	thus	thus	ADV
american_scientific_journal-3700	80	16	�	�	X
american_scientific_journal-3700	80	17	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	80	18	𝜕𝜕	𝜕𝜕	PROPN
american_scientific_journal-3700	80	19	2𝑓𝑓	2𝑓𝑓	ADJ
american_scientific_journal-3700	80	20	𝜕𝜕𝑖𝑖2	𝜕𝜕𝑖𝑖2	NOUN
american_scientific_journal-3700	80	21	−	−	ADP
american_scientific_journal-3700	80	22	𝑖𝑖ℏ	𝑖𝑖ℏ	NOUN
american_scientific_journal-3700	80	23	𝜏𝜏	𝜏𝜏	ADP
american_scientific_journal-3700	80	24	𝑉𝑉𝜊𝜊𝑓𝑓	𝑉𝑉𝜊𝜊𝑓𝑓	PROPN
american_scientific_journal-3700	80	25	−	−	PROPN
american_scientific_journal-3700	80	26	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	80	27	𝜏𝜏	𝜏𝜏	ADP
american_scientific_journal-3700	80	28	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	PUNCT
american_scientific_journal-3700	80	29	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PRON
american_scientific_journal-3700	80	30	�	�	PROPN
american_scientific_journal-3700	80	31	𝑢𝑢	𝑢𝑢	NOUN
american_scientific_journal-3700	80	32	=	=	SYM
american_scientific_journal-3700	80	33	�	�	PROPN
american_scientific_journal-3700	80	34	−	−	NOUN
american_scientific_journal-3700	80	35	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	80	36	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	80	37	∇2	∇2	PROPN
american_scientific_journal-3700	80	38	+	+	CCONJ
american_scientific_journal-3700	80	39	𝑉𝑉𝜊𝜊	𝑉𝑉𝜊𝜊	PROPN
american_scientific_journal-3700	80	40	�	�	PROPN
american_scientific_journal-3700	80	41	𝑢𝑢	𝑢𝑢	NOUN
american_scientific_journal-3700	80	42	�	�	PROPN
american_scientific_journal-3700	80	43	𝑖𝑖ℏ	𝑖𝑖ℏ	PROPN
american_scientific_journal-3700	80	44	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	PUNCT
american_scientific_journal-3700	80	45	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PRON
american_scientific_journal-3700	80	46	�	�	PROPN
american_scientific_journal-3700	80	47	(	(	PUNCT
american_scientific_journal-3700	80	48	32	32	NUM
american_scientific_journal-3700	80	49	)	)	PUNCT
american_scientific_journal-3700	80	50	divide	divide	VERB
american_scientific_journal-3700	80	51	both	both	DET
american_scientific_journal-3700	80	52	sides	side	NOUN
american_scientific_journal-3700	80	53	of	of	ADP
american_scientific_journal-3700	80	54	eq	eq	PROPN
american_scientific_journal-3700	80	55	.	.	PUNCT
american_scientific_journal-3700	81	1	(	(	PUNCT
american_scientific_journal-3700	81	2	32	32	NUM
american_scientific_journal-3700	81	3	)	)	PUNCT
american_scientific_journal-3700	81	4	by	by	ADP
american_scientific_journal-3700	81	5	fu	fu	NOUN
american_scientific_journal-3700	81	6	to	to	PART
american_scientific_journal-3700	81	7	get	get	VERB
american_scientific_journal-3700	81	8	�	�	PROPN
american_scientific_journal-3700	81	9	𝑖𝑖ℏ	𝑖𝑖ℏ	PROPN
american_scientific_journal-3700	81	10	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	PUNCT
american_scientific_journal-3700	81	11	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PRON
american_scientific_journal-3700	81	12	�	�	PROPN
american_scientific_journal-3700	81	13	−1	−1	NOUN
american_scientific_journal-3700	81	14	�	�	PROPN
american_scientific_journal-3700	81	15	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	81	16	𝜕𝜕	𝜕𝜕	PROPN
american_scientific_journal-3700	81	17	2𝑓𝑓	2𝑓𝑓	ADJ
american_scientific_journal-3700	81	18	𝜕𝜕𝑖𝑖2	𝜕𝜕𝑖𝑖2	NOUN
american_scientific_journal-3700	82	1	−	−	PUNCT
american_scientific_journal-3700	82	2	𝑖𝑖𝑉𝑉𝜊𝜊ℏ	𝑖𝑖𝑉𝑉𝜊𝜊ℏ	PUNCT
american_scientific_journal-3700	82	3	𝜏𝜏	𝜏𝜏	VERB
american_scientific_journal-3700	82	4	𝑓𝑓	𝑓𝑓	ADP
american_scientific_journal-3700	82	5	−	−	PROPN
american_scientific_journal-3700	82	6	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	82	7	𝜏𝜏	𝜏𝜏	ADP
american_scientific_journal-3700	82	8	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	PUNCT
american_scientific_journal-3700	82	9	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PRON
american_scientific_journal-3700	82	10	�	�	PROPN
american_scientific_journal-3700	82	11	=	=	SYM
american_scientific_journal-3700	82	12	1	1	NUM
american_scientific_journal-3700	82	13	𝑢𝑢	𝑢𝑢	NUM
american_scientific_journal-3700	82	14	�	�	NOUN
american_scientific_journal-3700	82	15	−	−	NOUN
american_scientific_journal-3700	82	16	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	82	17	2𝑚𝑚	2𝑚𝑚	ADJ
american_scientific_journal-3700	82	18	∇2	∇2	PROPN
american_scientific_journal-3700	82	19	+	+	CCONJ
american_scientific_journal-3700	82	20	𝑉𝑉𝜊𝜊	𝑉𝑉𝜊𝜊	PROPN
american_scientific_journal-3700	82	21	�	�	NOUN
american_scientific_journal-3700	82	22	𝑢𝑢	𝑢𝑢	NOUN
american_scientific_journal-3700	82	23	=	=	SYM
american_scientific_journal-3700	82	24	𝐸𝐸𝜊𝜊	𝐸𝐸𝜊𝜊	PROPN
american_scientific_journal-3700	82	25	(	(	PUNCT
american_scientific_journal-3700	82	26	33	33	NUM
american_scientific_journal-3700	82	27	)	)	PUNCT
american_scientific_journal-3700	82	28	taking	take	VERB
american_scientific_journal-3700	82	29	the	the	DET
american_scientific_journal-3700	82	30	time	time	NOUN
american_scientific_journal-3700	82	31	part	part	NOUN
american_scientific_journal-3700	82	32	of	of	ADP
american_scientific_journal-3700	82	33	eq	eq	PROPN
american_scientific_journal-3700	82	34	.	.	PUNCT
american_scientific_journal-3700	83	1	(	(	PUNCT
american_scientific_journal-3700	83	2	33	33	NUM
american_scientific_journal-3700	83	3	)	)	PUNCT
american_scientific_journal-3700	83	4	only	only	ADV
american_scientific_journal-3700	83	5	gives	give	VERB
american_scientific_journal-3700	83	6	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	83	7	𝜕𝜕	𝜕𝜕	PROPN
american_scientific_journal-3700	83	8	2𝑓𝑓	2𝑓𝑓	ADJ
american_scientific_journal-3700	83	9	𝜕𝜕𝑖𝑖2	𝜕𝜕𝑖𝑖2	NOUN
american_scientific_journal-3700	84	1	−	−	PUNCT
american_scientific_journal-3700	84	2	𝑖𝑖𝑉𝑉𝜊𝜊ℏ	𝑖𝑖𝑉𝑉𝜊𝜊ℏ	PUNCT
american_scientific_journal-3700	84	3	𝜏𝜏	𝜏𝜏	VERB
american_scientific_journal-3700	84	4	𝑓𝑓	𝑓𝑓	ADP
american_scientific_journal-3700	84	5	−	−	PROPN
american_scientific_journal-3700	84	6	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	84	7	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	84	8	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	PUNCT
american_scientific_journal-3700	84	9	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PRON
american_scientific_journal-3700	84	10	=	=	PUNCT
american_scientific_journal-3700	85	1	𝑖𝑖ℏ𝐸𝐸𝜊𝜊	𝑖𝑖ℏ𝐸𝐸𝜊𝜊	PROPN
american_scientific_journal-3700	85	2	𝜕𝜕𝑓𝑓	𝜕𝜕𝑓𝑓	INTJ
american_scientific_journal-3700	85	3	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	INTJ
american_scientific_journal-3700	85	4	(	(	PUNCT
american_scientific_journal-3700	85	5	34	34	NUM
american_scientific_journal-3700	85	6	)	)	PUNCT
american_scientific_journal-3700	85	7	american	american	ADJ
american_scientific_journal-3700	85	8	scientific	scientific	ADJ
american_scientific_journal-3700	85	9	research	research	NOUN
american_scientific_journal-3700	85	10	journal	journal	NOUN
american_scientific_journal-3700	85	11	for	for	ADP
american_scientific_journal-3700	85	12	engineering	engineering	NOUN
american_scientific_journal-3700	85	13	,	,	PUNCT
american_scientific_journal-3700	85	14	technology	technology	NOUN
american_scientific_journal-3700	85	15	,	,	PUNCT
american_scientific_journal-3700	85	16	and	and	CCONJ
american_scientific_journal-3700	85	17	sciences	science	NOUN
american_scientific_journal-3700	85	18	(	(	PUNCT
american_scientific_journal-3700	85	19	asrjets	asrjet	NOUN
american_scientific_journal-3700	85	20	)	)	PUNCT
american_scientific_journal-3700	85	21	(	(	PUNCT
american_scientific_journal-3700	85	22	2018	2018	NUM
american_scientific_journal-3700	85	23	)	)	PUNCT
american_scientific_journal-3700	85	24	volume	volume	NOUN
american_scientific_journal-3700	85	25	39	39	NUM
american_scientific_journal-3700	85	26	,	,	PUNCT
american_scientific_journal-3700	85	27	no	no	DET
american_scientific_journal-3700	85	28	1	1	NUM
american_scientific_journal-3700	85	29	,	,	PUNCT
american_scientific_journal-3700	85	30	pp	pp	ADV
american_scientific_journal-3700	85	31	10	10	NUM
american_scientific_journal-3700	85	32	-	-	SYM
american_scientific_journal-3700	85	33	18	18	NUM
american_scientific_journal-3700	85	34	16	16	NUM
american_scientific_journal-3700	85	35	consider	consider	VERB
american_scientific_journal-3700	85	36	the	the	DET
american_scientific_journal-3700	85	37	case	case	NOUN
american_scientific_journal-3700	85	38	when	when	SCONJ
american_scientific_journal-3700	85	39	the	the	DET
american_scientific_journal-3700	85	40	potential	potential	NOUN
american_scientific_journal-3700	85	41	vanishes	vanish	VERB
american_scientific_journal-3700	85	42	𝑉𝑉𝜊𝜊	𝑉𝑉𝜊𝜊	PROPN
american_scientific_journal-3700	85	43	=	=	SYM
american_scientific_journal-3700	85	44	0	0	PUNCT
american_scientific_journal-3700	85	45	(	(	PUNCT
american_scientific_journal-3700	85	46	35	35	NUM
american_scientific_journal-3700	85	47	)	)	PUNCT
american_scientific_journal-3700	85	48	hence	hence	ADV
american_scientific_journal-3700	85	49	−ℏ2	−ℏ2	PROPN
american_scientific_journal-3700	85	50	𝜕𝜕	𝜕𝜕	PROPN
american_scientific_journal-3700	85	51	2𝑓𝑓	2𝑓𝑓	ADJ
american_scientific_journal-3700	85	52	𝜕𝜕𝑖𝑖2	𝜕𝜕𝑖𝑖2	NOUN
american_scientific_journal-3700	85	53	−	−	PROPN
american_scientific_journal-3700	85	54	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	85	55	𝑖𝑖	𝑖𝑖	ADP
american_scientific_journal-3700	85	56	𝜕𝜕f	𝜕𝜕f	NOUN
american_scientific_journal-3700	85	57	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	NOUN
american_scientific_journal-3700	85	58	=	=	SYM
american_scientific_journal-3700	85	59	iℏ𝐸𝐸𝜊𝜊	iℏ𝐸𝐸𝜊𝜊	PROPN
american_scientific_journal-3700	85	60	𝜕𝜕f	𝜕𝜕f	NOUN
american_scientific_journal-3700	85	61	𝜕𝜕𝑖𝑖	𝜕𝜕𝑖𝑖	PRON
american_scientific_journal-3700	85	62	(	(	PUNCT
american_scientific_journal-3700	85	63	36	36	NUM
american_scientific_journal-3700	85	64	)	)	PUNCT
american_scientific_journal-3700	85	65	consider	consider	VERB
american_scientific_journal-3700	85	66	now	now	ADV
american_scientific_journal-3700	85	67	a	a	DET
american_scientific_journal-3700	85	68	solution	solution	NOUN
american_scientific_journal-3700	85	69	f	f	X
american_scientific_journal-3700	85	70	=	=	SYM
american_scientific_journal-3700	85	71	ae−	ae−	PROPN
american_scientific_journal-3700	85	72	i	i	PRON
american_scientific_journal-3700	85	73	ℏet	ℏet	VERB
american_scientific_journal-3700	85	74	𝜕𝜕f	𝜕𝜕f	PROPN
american_scientific_journal-3700	85	75	𝜕𝜕𝑣𝑣	𝜕𝜕𝑣𝑣	NOUN
american_scientific_journal-3700	85	76	=	=	SYM
american_scientific_journal-3700	85	77	−𝑖𝑖	−𝑖𝑖	PROPN
american_scientific_journal-3700	85	78	ℏ	ℏ	PROPN
american_scientific_journal-3700	85	79	𝐸𝐸𝑓𝑓	𝐸𝐸𝑓𝑓	PROPN
american_scientific_journal-3700	85	80	𝜕𝜕2𝑓𝑓	𝜕𝜕2𝑓𝑓	PROPN
american_scientific_journal-3700	85	81	𝜕𝜕𝑖𝑖2	𝜕𝜕𝑖𝑖2	NOUN
american_scientific_journal-3700	85	82	=	=	PUNCT
american_scientific_journal-3700	86	1	+	+	NUM
american_scientific_journal-3700	86	2	𝑖𝑖2	𝑖𝑖2	ADJ
american_scientific_journal-3700	86	3	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	86	4	𝐸𝐸2𝑓𝑓	𝐸𝐸2𝑓𝑓	PROPN
american_scientific_journal-3700	87	1	=	=	PUNCT
american_scientific_journal-3700	87	2	−𝐸𝐸2	−𝐸𝐸2	NOUN
american_scientific_journal-3700	87	3	ℏ2	ℏ2	NOUN
american_scientific_journal-3700	87	4	𝑓𝑓	𝑓𝑓	VERB
american_scientific_journal-3700	87	5	(	(	PUNCT
american_scientific_journal-3700	87	6	37	37	NUM
american_scientific_journal-3700	87	7	)	)	PUNCT
american_scientific_journal-3700	87	8	inserting	insert	VERB
american_scientific_journal-3700	87	9	eq	eq	ADP
american_scientific_journal-3700	87	10	.	.	PUNCT
american_scientific_journal-3700	88	1	(	(	PUNCT
american_scientific_journal-3700	88	2	37	37	NUM
american_scientific_journal-3700	88	3	)	)	PUNCT
american_scientific_journal-3700	88	4	in	in	ADP
american_scientific_journal-3700	88	5	eq	eq	ADP
american_scientific_journal-3700	88	6	.	.	PUNCT
american_scientific_journal-3700	89	1	(	(	PUNCT
american_scientific_journal-3700	89	2	36	36	NUM
american_scientific_journal-3700	89	3	)	)	PUNCT
american_scientific_journal-3700	89	4	yields	yield	NOUN
american_scientific_journal-3700	89	5	𝐸𝐸2𝑓𝑓	𝐸𝐸2𝑓𝑓	PROPN
american_scientific_journal-3700	90	1	+	+	CCONJ
american_scientific_journal-3700	90	2	iℏ	iℏ	ADP
american_scientific_journal-3700	90	3	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	90	4	𝐸𝐸𝑓𝑓	𝐸𝐸𝑓𝑓	PROPN
american_scientific_journal-3700	90	5	=	=	SYM
american_scientific_journal-3700	90	6	𝑖𝑖ℏ𝐸𝐸𝜊𝜊	𝑖𝑖ℏ𝐸𝐸𝜊𝜊	PROPN
american_scientific_journal-3700	90	7	�	�	PROPN
american_scientific_journal-3700	90	8	−	−	PROPN
american_scientific_journal-3700	90	9	𝑖𝑖	𝑖𝑖	ADP
american_scientific_journal-3700	90	10	ℏ	ℏ	PROPN
american_scientific_journal-3700	90	11	𝐸𝐸𝑓𝑓	𝐸𝐸𝑓𝑓	PROPN
american_scientific_journal-3700	90	12	�	�	PROPN
american_scientific_journal-3700	90	13	(	(	PUNCT
american_scientific_journal-3700	90	14	38	38	NUM
american_scientific_journal-3700	90	15	)	)	PUNCT
american_scientific_journal-3700	90	16	dividing	divide	VERB
american_scientific_journal-3700	90	17	both	both	DET
american_scientific_journal-3700	90	18	sides	side	NOUN
american_scientific_journal-3700	90	19	of	of	ADP
american_scientific_journal-3700	90	20	eq	eq	PROPN
american_scientific_journal-3700	90	21	.	.	PUNCT
american_scientific_journal-3700	91	1	(	(	PUNCT
american_scientific_journal-3700	91	2	38	38	NUM
american_scientific_journal-3700	91	3	)	)	PUNCT
american_scientific_journal-3700	91	4	by	by	ADP
american_scientific_journal-3700	91	5	f	f	PROPN
american_scientific_journal-3700	91	6	gives	give	VERB
american_scientific_journal-3700	91	7	𝐸𝐸2	𝐸𝐸2	PROPN
american_scientific_journal-3700	91	8	+	+	CCONJ
american_scientific_journal-3700	91	9	𝑖𝑖ℏ	𝑖𝑖ℏ	NUM
american_scientific_journal-3700	91	10	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	91	11	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	92	1	=	=	SYM
american_scientific_journal-3700	92	2	𝐸𝐸𝜊𝜊𝐸𝐸	𝐸𝐸𝜊𝜊𝐸𝐸	NOUN
american_scientific_journal-3700	92	3	(	(	PUNCT
american_scientific_journal-3700	92	4	39	39	NUM
american_scientific_journal-3700	92	5	)	)	PUNCT
american_scientific_journal-3700	92	6	rearranging	rearrange	VERB
american_scientific_journal-3700	92	7	both	both	DET
american_scientific_journal-3700	92	8	sides	side	NOUN
american_scientific_journal-3700	92	9	of	of	ADP
american_scientific_journal-3700	92	10	eq	eq	PROPN
american_scientific_journal-3700	92	11	.	.	PUNCT
american_scientific_journal-3700	93	1	(	(	PUNCT
american_scientific_journal-3700	93	2	39	39	NUM
american_scientific_journal-3700	93	3	)	)	PUNCT
american_scientific_journal-3700	93	4	gives	give	VERB
american_scientific_journal-3700	93	5	𝐸𝐸2	𝐸𝐸2	PROPN
american_scientific_journal-3700	93	6	=	=	PUNCT
american_scientific_journal-3700	93	7	�	�	PROPN
american_scientific_journal-3700	93	8	𝐸𝐸𝜊𝜊	𝐸𝐸𝜊𝜊	PROPN
american_scientific_journal-3700	93	9	−	−	PROPN
american_scientific_journal-3700	93	10	𝑖𝑖ℏ	𝑖𝑖ℏ	PROPN
american_scientific_journal-3700	93	11	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	93	12	�	�	PROPN
american_scientific_journal-3700	93	13	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	93	14	(	(	PUNCT
american_scientific_journal-3700	93	15	40	40	NUM
american_scientific_journal-3700	93	16	)	)	PUNCT
american_scientific_journal-3700	93	17	dividing	divide	VERB
american_scientific_journal-3700	93	18	both	both	DET
american_scientific_journal-3700	93	19	sides	side	NOUN
american_scientific_journal-3700	93	20	of	of	ADP
american_scientific_journal-3700	93	21	eq	eq	PROPN
american_scientific_journal-3700	93	22	.	.	PUNCT
american_scientific_journal-3700	94	1	(	(	PUNCT
american_scientific_journal-3700	94	2	4	4	NUM
american_scientific_journal-3700	94	3	)	)	PUNCT
american_scientific_journal-3700	94	4	by	by	ADP
american_scientific_journal-3700	94	5	e	e	NOUN
american_scientific_journal-3700	94	6	gives	give	VERB
american_scientific_journal-3700	94	7	𝐸𝐸	𝐸𝐸	PROPN
american_scientific_journal-3700	94	8	=	=	SYM
american_scientific_journal-3700	94	9	�	�	PROPN
american_scientific_journal-3700	94	10	𝐸𝐸𝜊𝜊	𝐸𝐸𝜊𝜊	PROPN
american_scientific_journal-3700	94	11	−	−	PROPN
american_scientific_journal-3700	94	12	𝑖𝑖ℏ	𝑖𝑖ℏ	PROPN
american_scientific_journal-3700	94	13	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	94	14	�	�	PROPN
american_scientific_journal-3700	94	15	(	(	PUNCT
american_scientific_journal-3700	94	16	41	41	NUM
american_scientific_journal-3700	94	17	)	)	PUNCT
american_scientific_journal-3700	94	18	inserting	insert	VERB
american_scientific_journal-3700	94	19	eq	eq	X
american_scientific_journal-3700	94	20	.	.	PUNCT
american_scientific_journal-3700	95	1	(	(	PUNCT
american_scientific_journal-3700	95	2	41	41	NUM
american_scientific_journal-3700	95	3	)	)	PUNCT
american_scientific_journal-3700	95	4	in	in	ADP
american_scientific_journal-3700	95	5	eq	eq	ADP
american_scientific_journal-3700	95	6	.	.	PUNCT
american_scientific_journal-3700	96	1	(	(	PUNCT
american_scientific_journal-3700	96	2	47	47	NUM
american_scientific_journal-3700	96	3	)	)	PUNCT
american_scientific_journal-3700	96	4	gives	give	VERB
american_scientific_journal-3700	96	5	𝑓𝑓	𝑓𝑓	ADP
american_scientific_journal-3700	96	6	=	=	PUNCT
american_scientific_journal-3700	96	7	𝐴𝐴𝑒𝑒	𝐴𝐴𝑒𝑒	ADJ
american_scientific_journal-3700	96	8	−𝑖𝑖	−𝑖𝑖	NOUN
american_scientific_journal-3700	96	9	ℏ	ℏ	PROPN
american_scientific_journal-3700	96	10	�	�	PROPN
american_scientific_journal-3700	96	11	𝐸𝐸𝜊𝜊−	𝐸𝐸𝜊𝜊−	NOUN
american_scientific_journal-3700	96	12	𝑖𝑖ℏ	𝑖𝑖ℏ	X
american_scientific_journal-3700	96	13	𝜏𝜏	𝜏𝜏	PROPN
american_scientific_journal-3700	96	14	�	�	PROPN
american_scientific_journal-3700	96	15	𝑖𝑖	𝑖𝑖	NOUN
american_scientific_journal-3700	96	16	=	=	PUNCT
american_scientific_journal-3700	96	17	𝐴𝐴𝑒𝑒	𝐴𝐴𝑒𝑒	PROPN
american_scientific_journal-3700	96	18	.−	.−	PUNCT
american_scientific_journal-3700	97	1	𝑡𝑡	𝑡𝑡	PROPN
american_scientific_journal-3700	97	2	𝜏𝜏𝑒𝑒−	𝜏𝜏𝑒𝑒−	NOUN
american_scientific_journal-3700	97	3	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-3700	97	4	ℏ𝐸𝐸𝜊𝜊𝑖𝑖	ℏ𝐸𝐸𝜊𝜊𝑖𝑖	NOUN
american_scientific_journal-3700	97	5	hence	hence	ADV
american_scientific_journal-3700	97	6	𝑓𝑓	𝑓𝑓	ADJ
american_scientific_journal-3700	97	7	=	=	PUNCT
american_scientific_journal-3700	97	8	𝐴𝐴𝑒𝑒	𝐴𝐴𝑒𝑒	NOUN
american_scientific_journal-3700	97	9	−𝑡𝑡	−𝑡𝑡	NOUN
american_scientific_journal-3700	97	10	𝜏𝜏	𝜏𝜏	ADJ
american_scientific_journal-3700	97	11	𝑒𝑒−	𝑒𝑒−	PUNCT
american_scientific_journal-3700	97	12	𝑖𝑖	𝑖𝑖	X
american_scientific_journal-3700	97	13	ℏ𝐸𝐸𝜊𝜊𝑖𝑖	ℏ𝐸𝐸𝜊𝜊𝑖𝑖	X
american_scientific_journal-3700	97	14	(	(	PUNCT
american_scientific_journal-3700	97	15	42	42	NUM
american_scientific_journal-3700	97	16	)	)	PUNCT
american_scientific_journal-3700	97	17	american	american	ADJ
american_scientific_journal-3700	97	18	scientific	scientific	ADJ
american_scientific_journal-3700	97	19	research	research	NOUN
american_scientific_journal-3700	97	20	journal	journal	NOUN
american_scientific_journal-3700	97	21	for	for	ADP
american_scientific_journal-3700	97	22	engineering	engineering	NOUN
american_scientific_journal-3700	97	23	,	,	PUNCT
american_scientific_journal-3700	97	24	technology	technology	NOUN
american_scientific_journal-3700	97	25	,	,	PUNCT
american_scientific_journal-3700	97	26	and	and	CCONJ
american_scientific_journal-3700	97	27	sciences	science	NOUN
american_scientific_journal-3700	97	28	(	(	PUNCT
american_scientific_journal-3700	97	29	asrjets	asrjet	NOUN
american_scientific_journal-3700	97	30	)	)	PUNCT
american_scientific_journal-3700	97	31	(	(	PUNCT
american_scientific_journal-3700	97	32	2018	2018	NUM
american_scientific_journal-3700	97	33	)	)	PUNCT
american_scientific_journal-3700	97	34	volume	volume	NOUN
american_scientific_journal-3700	97	35	39	39	NUM
american_scientific_journal-3700	97	36	,	,	PUNCT
american_scientific_journal-3700	97	37	no	no	DET
american_scientific_journal-3700	97	38	1	1	NUM
american_scientific_journal-3700	97	39	,	,	PUNCT
american_scientific_journal-3700	97	40	pp	pp	ADV
american_scientific_journal-3700	97	41	10	10	NUM
american_scientific_journal-3700	97	42	-	-	SYM
american_scientific_journal-3700	97	43	18	18	NUM
american_scientific_journal-3700	97	44	17	17	NUM
american_scientific_journal-3700	97	45	since	since	SCONJ
american_scientific_journal-3700	97	46	the	the	DET
american_scientific_journal-3700	97	47	probability	probability	NOUN
american_scientific_journal-3700	97	48	and	and	CCONJ
american_scientific_journal-3700	97	49	number	number	NOUN
american_scientific_journal-3700	97	50	of	of	ADP
american_scientific_journal-3700	97	51	particles	particle	NOUN
american_scientific_journal-3700	97	52	are	be	AUX
american_scientific_journal-3700	97	53	given	give	VERB
american_scientific_journal-3700	97	54	by	by	ADP
american_scientific_journal-3700	97	55	𝑛𝑛	𝑛𝑛	NOUN
american_scientific_journal-3700	97	56	=	=	PUNCT
american_scientific_journal-3700	97	57	|𝑓𝑓|2	|𝑓𝑓|2	PUNCT
american_scientific_journal-3700	98	1	=	=	SYM
american_scientific_journal-3700	98	2	𝑓𝑓𝑓𝑓\	𝑓𝑓𝑓𝑓\	PROPN
american_scientific_journal-3700	98	3	=	=	SYM
american_scientific_journal-3700	98	4	𝐴𝐴2𝑒𝑒	𝐴𝐴2𝑒𝑒	PROPN
american_scientific_journal-3700	98	5	−2𝑡𝑡	−2𝑡𝑡	X
american_scientific_journal-3700	98	6	𝜏𝜏	𝜏𝜏	PROPN
american_scientific_journal-3700	98	7	(	(	PUNCT
american_scientific_journal-3700	98	8	43	43	NUM
american_scientific_journal-3700	98	9	)	)	PUNCT
american_scientific_journal-3700	98	10	eq	eq	NOUN
american_scientific_journal-3700	98	11	.	.	PUNCT
american_scientific_journal-3700	99	1	(	(	PUNCT
american_scientific_journal-3700	99	2	43	43	NUM
american_scientific_journal-3700	99	3	)	)	PUNCT
american_scientific_journal-3700	99	4	is	be	AUX
american_scientific_journal-3700	99	5	the	the	DET
american_scientific_journal-3700	99	6	ordinary	ordinary	ADJ
american_scientific_journal-3700	99	7	radioactive	radioactive	ADJ
american_scientific_journal-3700	99	8	decay	decay	NOUN
american_scientific_journal-3700	99	9	low	low	ADJ
american_scientific_journal-3700	99	10	with	with	ADP
american_scientific_journal-3700	99	11	𝜆𝜆	𝜆𝜆	NOUN
american_scientific_journal-3700	99	12	=	=	SYM
american_scientific_journal-3700	99	13	2	2	NUM
american_scientific_journal-3700	99	14	𝜏𝜏	𝜏𝜏	NOUN
american_scientific_journal-3700	99	15	,	,	PUNCT
american_scientific_journal-3700	99	16	𝑛𝑛𝜊𝜊	𝑛𝑛𝜊𝜊	NOUN
american_scientific_journal-3700	99	17	=	=	SYM
american_scientific_journal-3700	99	18	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-3700	99	19	(	(	PUNCT
american_scientific_journal-3700	99	20	44	44	NUM
american_scientific_journal-3700	99	21	)	)	PUNCT
american_scientific_journal-3700	99	22	i.e.	i.e.	X
american_scientific_journal-3700	99	23	𝑛𝑛	𝑛𝑛	X
american_scientific_journal-3700	99	24	=	=	SYM
american_scientific_journal-3700	99	25	𝑛𝑛𝜊𝜊𝑒𝑒−𝜆𝜆𝑖𝑖	𝑛𝑛𝜊𝜊𝑒𝑒−𝜆𝜆𝑖𝑖	X
american_scientific_journal-3700	99	26	(	(	PUNCT
american_scientific_journal-3700	99	27	45	45	NUM
american_scientific_journal-3700	99	28	)	)	PUNCT
american_scientific_journal-3700	99	29	this	this	DET
american_scientific_journal-3700	99	30	expression	expression	NOUN
american_scientific_journal-3700	99	31	also	also	ADV
american_scientific_journal-3700	99	32	gives	give	VERB
american_scientific_journal-3700	99	33	collision	collision	NOUN
american_scientific_journal-3700	99	34	probability	probability	NOUN
american_scientific_journal-3700	99	35	p	p	NOUN
american_scientific_journal-3700	99	36	with	with	ADP
american_scientific_journal-3700	99	37	𝑝𝑝	𝑝𝑝	NOUN
american_scientific_journal-3700	99	38	=	=	PUNCT
american_scientific_journal-3700	99	39	𝑛𝑛	𝑛𝑛	AUX
american_scientific_journal-3700	99	40	𝑝𝑝𝜊𝜊	𝑝𝑝𝜊𝜊	VERB
american_scientific_journal-3700	99	41	=	=	PUNCT
american_scientific_journal-3700	99	42	𝐴𝐴2	𝐴𝐴2	PROPN
american_scientific_journal-3700	99	43	𝜏𝜏𝜊𝜊	𝜏𝜏𝜊𝜊	NOUN
american_scientific_journal-3700	99	44	=	=	X
american_scientific_journal-3700	99	45	𝜏𝜏	𝜏𝜏	ADP
american_scientific_journal-3700	99	46	2⁄	2⁄	NUM
american_scientific_journal-3700	99	47	(	(	PUNCT
american_scientific_journal-3700	99	48	46	46	NUM
american_scientific_journal-3700	99	49	)	)	PUNCT
american_scientific_journal-3700	99	50	to	to	PART
american_scientific_journal-3700	99	51	get	get	VERB
american_scientific_journal-3700	99	52	𝑝𝑝	𝑝𝑝	NOUN
american_scientific_journal-3700	99	53	=	=	PUNCT
american_scientific_journal-3700	99	54	𝑝𝑝𝜊𝜊	𝑝𝑝𝜊𝜊	VERB
american_scientific_journal-3700	99	55	𝑒𝑒	𝑒𝑒	ADP
american_scientific_journal-3700	99	56	−𝑡𝑡	−𝑡𝑡	PROPN
american_scientific_journal-3700	99	57	𝜏𝜏𝜊𝜊	𝜏𝜏𝜊𝜊	X
american_scientific_journal-3700	99	58	(	(	PUNCT
american_scientific_journal-3700	99	59	47	47	NUM
american_scientific_journal-3700	99	60	)	)	PUNCT
american_scientific_journal-3700	99	61	eq	eq	NOUN
american_scientific_journal-3700	99	62	.	.	PUNCT
american_scientific_journal-3700	100	1	(	(	PUNCT
american_scientific_journal-3700	100	2	47	47	NUM
american_scientific_journal-3700	100	3	)	)	PUNCT
american_scientific_journal-3700	100	4	is	be	AUX
american_scientific_journal-3700	100	5	the	the	DET
american_scientific_journal-3700	100	6	ordinary	ordinary	ADJ
american_scientific_journal-3700	100	7	collision	collision	NOUN
american_scientific_journal-3700	100	8	probability	probability	NOUN
american_scientific_journal-3700	100	9	relation	relation	NOUN
american_scientific_journal-3700	100	10	.	.	PUNCT
american_scientific_journal-3700	101	1	5	5	X
american_scientific_journal-3700	101	2	.	.	X
american_scientific_journal-3700	101	3	discussion	discussion	NOUN
american_scientific_journal-3700	101	4	new	new	ADJ
american_scientific_journal-3700	101	5	schrodinger	schrodinger	PROPN
american_scientific_journal-3700	101	6	equation	equation	NOUN
american_scientific_journal-3700	101	7	for	for	ADP
american_scientific_journal-3700	101	8	frictional	frictional	ADJ
american_scientific_journal-3700	101	9	medium	medium	NOUN
american_scientific_journal-3700	101	10	was	be	AUX
american_scientific_journal-3700	101	11	derived	derive	VERB
american_scientific_journal-3700	101	12	by	by	ADP
american_scientific_journal-3700	101	13	using	use	VERB
american_scientific_journal-3700	101	14	de	de	PROPN
american_scientific_journal-3700	101	15	broglie	broglie	PROPN
american_scientific_journal-3700	101	16	hypothesis	hypothesis	NOUN
american_scientific_journal-3700	101	17	about	about	ADP
american_scientific_journal-3700	101	18	the	the	DET
american_scientific_journal-3700	101	19	wave	wave	NOUN
american_scientific_journal-3700	101	20	nature	nature	NOUN
american_scientific_journal-3700	101	21	of	of	ADP
american_scientific_journal-3700	101	22	atomic	atomic	ADJ
american_scientific_journal-3700	101	23	particles	particle	NOUN
american_scientific_journal-3700	101	24	,	,	PUNCT
american_scientific_journal-3700	101	25	besides	besides	SCONJ
american_scientific_journal-3700	101	26	assuming	assume	VERB
american_scientific_journal-3700	101	27	that	that	SCONJ
american_scientific_journal-3700	101	28	particles	particle	NOUN
american_scientific_journal-3700	101	29	are	be	AUX
american_scientific_journal-3700	101	30	vibrating	vibrate	VERB
american_scientific_journal-3700	101	31	strings	string	NOUN
american_scientific_journal-3700	101	32	.	.	PUNCT
american_scientific_journal-3700	102	1	the	the	DET
american_scientific_journal-3700	102	2	two	two	NUM
american_scientific_journal-3700	102	3	hypotheses	hypothesis	NOUN
american_scientific_journal-3700	102	4	require	require	VERB
american_scientific_journal-3700	102	5	that	that	SCONJ
american_scientific_journal-3700	102	6	for	for	ADP
american_scientific_journal-3700	102	7	frictional	frictional	ADJ
american_scientific_journal-3700	102	8	medium	medium	NOUN
american_scientific_journal-3700	102	9	the	the	DET
american_scientific_journal-3700	102	10	classical	classical	ADJ
american_scientific_journal-3700	102	11	energy	energy	NOUN
american_scientific_journal-3700	102	12	is	be	AUX
american_scientific_journal-3700	102	13	that	that	PRON
american_scientific_journal-3700	102	14	of	of	ADP
american_scientific_journal-3700	102	15	a	a	DET
american_scientific_journal-3700	102	16	harmonic	harmonic	ADJ
american_scientific_journal-3700	102	17	oscillator	oscillator	NOUN
american_scientific_journal-3700	103	1	[	[	X
american_scientific_journal-3700	103	2	see	see	VERB
american_scientific_journal-3700	103	3	eqs	eqs	X
american_scientific_journal-3700	103	4	.	.	PUNCT
american_scientific_journal-3700	104	1	(	(	PUNCT
american_scientific_journal-3700	104	2	2	2	NUM
american_scientific_journal-3700	104	3	)	)	PUNCT
american_scientific_journal-3700	104	4	,	,	PUNCT
american_scientific_journal-3700	104	5	(	(	PUNCT
american_scientific_journal-3700	104	6	3	3	NUM
american_scientific_journal-3700	104	7	)	)	PUNCT
american_scientific_journal-3700	104	8	,	,	PUNCT
american_scientific_journal-3700	104	9	(	(	PUNCT
american_scientific_journal-3700	104	10	4	4	NUM
american_scientific_journal-3700	104	11	)	)	PUNCT
american_scientific_journal-3700	104	12	and	and	CCONJ
american_scientific_journal-3700	104	13	(	(	PUNCT
american_scientific_journal-3700	104	14	5	5	NUM
american_scientific_journal-3700	104	15	)	)	PUNCT
american_scientific_journal-3700	104	16	]	]	PUNCT
american_scientific_journal-3700	104	17	using	use	VERB
american_scientific_journal-3700	104	18	canonical	canonical	ADJ
american_scientific_journal-3700	104	19	quantization	quantization	NOUN
american_scientific_journal-3700	104	20	method	method	NOUN
american_scientific_journal-3700	104	21	by	by	ADP
american_scientific_journal-3700	104	22	replacing	replace	VERB
american_scientific_journal-3700	104	23	the	the	DET
american_scientific_journal-3700	104	24	momentum	momentum	NOUN
american_scientific_journal-3700	104	25	and	and	CCONJ
american_scientific_journal-3700	104	26	energy	energy	NOUN
american_scientific_journal-3700	104	27	with	with	ADP
american_scientific_journal-3700	104	28	their	their	PRON
american_scientific_journal-3700	104	29	corresponding	correspond	VERB
american_scientific_journal-3700	104	30	operators	operator	NOUN
american_scientific_journal-3700	104	31	,	,	PUNCT
american_scientific_journal-3700	104	32	[	[	X
american_scientific_journal-3700	104	33	see	see	VERB
american_scientific_journal-3700	104	34	eqs	eqs	X
american_scientific_journal-3700	104	35	.	.	PUNCT
american_scientific_journal-3700	105	1	(	(	PUNCT
american_scientific_journal-3700	105	2	12	12	NUM
american_scientific_journal-3700	105	3	)	)	PUNCT
american_scientific_journal-3700	105	4	,	,	PUNCT
american_scientific_journal-3700	105	5	(	(	PUNCT
american_scientific_journal-3700	105	6	13	13	NUM
american_scientific_journal-3700	105	7	)	)	PUNCT
american_scientific_journal-3700	105	8	and	and	CCONJ
american_scientific_journal-3700	105	9	(	(	PUNCT
american_scientific_journal-3700	105	10	14	14	NUM
american_scientific_journal-3700	105	11	)	)	PUNCT
american_scientific_journal-3700	105	12	]	]	PUNCT
american_scientific_journal-3700	105	13	,	,	PUNCT
american_scientific_journal-3700	105	14	a	a	DET
american_scientific_journal-3700	105	15	new	new	ADJ
american_scientific_journal-3700	105	16	frictional	frictional	ADJ
american_scientific_journal-3700	105	17	schrodinger	schrodinger	NOUN
american_scientific_journal-3700	105	18	equation	equation	NOUN
american_scientific_journal-3700	105	19	was	be	AUX
american_scientific_journal-3700	105	20	derived	derive	VERB
american_scientific_journal-3700	105	21	[	[	PUNCT
american_scientific_journal-3700	105	22	see	see	NOUN
american_scientific_journal-3700	105	23	eq	eq	ADP
american_scientific_journal-3700	105	24	.	.	PUNCT
american_scientific_journal-3700	106	1	(	(	PUNCT
american_scientific_journal-3700	106	2	15	15	NUM
american_scientific_journal-3700	106	3	)	)	PUNCT
american_scientific_journal-3700	106	4	]	]	PUNCT
american_scientific_journal-3700	106	5	.	.	PUNCT
american_scientific_journal-3700	107	1	it	it	PRON
american_scientific_journal-3700	107	2	is	be	AUX
american_scientific_journal-3700	107	3	very	very	ADV
american_scientific_journal-3700	107	4	interesting	interesting	ADJ
american_scientific_journal-3700	107	5	to	to	PART
american_scientific_journal-3700	107	6	note	note	VERB
american_scientific_journal-3700	107	7	that	that	SCONJ
american_scientific_journal-3700	107	8	using	use	VERB
american_scientific_journal-3700	107	9	separation	separation	NOUN
american_scientific_journal-3700	107	10	of	of	ADP
american_scientific_journal-3700	107	11	variables	variable	NOUN
american_scientific_journal-3700	107	12	the	the	DET
american_scientific_journal-3700	107	13	time	time	NOUN
american_scientific_journal-3700	107	14	dependent	dependent	ADJ
american_scientific_journal-3700	107	15	part	part	NOUN
american_scientific_journal-3700	107	16	was	be	AUX
american_scientific_journal-3700	107	17	used	use	VERB
american_scientific_journal-3700	107	18	to	to	PART
american_scientific_journal-3700	107	19	derive	derive	VERB
american_scientific_journal-3700	107	20	radioactive	radioactive	ADJ
american_scientific_journal-3700	107	21	decay	decay	NOUN
american_scientific_journal-3700	107	22	law	law	NOUN
american_scientific_journal-3700	107	23	as	as	SCONJ
american_scientific_journal-3700	107	24	shown	show	VERB
american_scientific_journal-3700	107	25	by	by	ADP
american_scientific_journal-3700	107	26	eq	eq	PROPN
american_scientific_journal-3700	107	27	.	.	PUNCT
american_scientific_journal-3700	108	1	(	(	PUNCT
american_scientific_journal-3700	108	2	43	43	NUM
american_scientific_journal-3700	108	3	)	)	PUNCT
american_scientific_journal-3700	108	4	and	and	CCONJ
american_scientific_journal-3700	108	5	the	the	DET
american_scientific_journal-3700	108	6	collision	collision	NOUN
american_scientific_journal-3700	108	7	probability	probability	NOUN
american_scientific_journal-3700	108	8	as	as	SCONJ
american_scientific_journal-3700	108	9	shown	show	VERB
american_scientific_journal-3700	108	10	by	by	ADP
american_scientific_journal-3700	108	11	eq	eq	PROPN
american_scientific_journal-3700	108	12	.	.	PUNCT
american_scientific_journal-3700	109	1	(	(	PUNCT
american_scientific_journal-3700	109	2	47	47	NUM
american_scientific_journal-3700	109	3	)	)	PUNCT
american_scientific_journal-3700	109	4	.	.	PUNCT
american_scientific_journal-3700	110	1	solving	solve	VERB
american_scientific_journal-3700	110	2	for	for	ADP
american_scientific_journal-3700	110	3	harmonic	harmonic	ADJ
american_scientific_journal-3700	110	4	oscillator	oscillator	NOUN
american_scientific_journal-3700	110	5	the	the	DET
american_scientific_journal-3700	110	6	expression	expression	NOUN
american_scientific_journal-3700	110	7	for	for	ADP
american_scientific_journal-3700	110	8	energy	energy	NOUN
american_scientific_journal-3700	110	9	is	be	AUX
american_scientific_journal-3700	110	10	quantized	quantize	VERB
american_scientific_journal-3700	110	11	with	with	ADP
american_scientific_journal-3700	110	12	additional	additional	ADJ
american_scientific_journal-3700	110	13	frictional	frictional	ADJ
american_scientific_journal-3700	110	14	term	term	NOUN
american_scientific_journal-3700	110	15	[	[	X
american_scientific_journal-3700	110	16	see	see	VERB
american_scientific_journal-3700	110	17	eq	eq	ADP
american_scientific_journal-3700	110	18	.	.	PUNCT
american_scientific_journal-3700	111	1	(	(	PUNCT
american_scientific_journal-3700	111	2	27	27	NUM
american_scientific_journal-3700	111	3	)	)	PUNCT
american_scientific_journal-3700	111	4	]	]	PUNCT
american_scientific_journal-3700	111	5	.	.	PUNCT
american_scientific_journal-3700	112	1	the	the	DET
american_scientific_journal-3700	112	2	solution	solution	NOUN
american_scientific_journal-3700	112	3	of	of	ADP
american_scientific_journal-3700	112	4	eq	eq	PROPN
american_scientific_journal-3700	112	5	.	.	PUNCT
american_scientific_journal-3700	113	1	(	(	PUNCT
american_scientific_journal-3700	113	2	27	27	NUM
american_scientific_journal-3700	113	3	)	)	PUNCT
american_scientific_journal-3700	113	4	shows	show	VERB
american_scientific_journal-3700	113	5	that	that	SCONJ
american_scientific_journal-3700	113	6	the	the	DET
american_scientific_journal-3700	113	7	mass	mass	NOUN
american_scientific_journal-3700	113	8	is	be	AUX
american_scientific_journal-3700	113	9	quantized	quantize	VERB
american_scientific_journal-3700	113	10	.	.	PUNCT
american_scientific_journal-3700	114	1	american	american	ADJ
american_scientific_journal-3700	114	2	scientific	scientific	ADJ
american_scientific_journal-3700	114	3	research	research	PROPN
american_scientific_journal-3700	114	4	journal	journal	NOUN
american_scientific_journal-3700	114	5	for	for	ADP
american_scientific_journal-3700	114	6	engineering	engineering	NOUN
american_scientific_journal-3700	114	7	,	,	PUNCT
american_scientific_journal-3700	114	8	technology	technology	NOUN
american_scientific_journal-3700	114	9	,	,	PUNCT
american_scientific_journal-3700	114	10	and	and	CCONJ
american_scientific_journal-3700	114	11	sciences	science	NOUN
american_scientific_journal-3700	114	12	(	(	PUNCT
american_scientific_journal-3700	114	13	asrjets	asrjet	NOUN
american_scientific_journal-3700	114	14	)	)	PUNCT
american_scientific_journal-3700	114	15	(	(	PUNCT
american_scientific_journal-3700	114	16	2018	2018	NUM
american_scientific_journal-3700	114	17	)	)	PUNCT
american_scientific_journal-3700	114	18	volume	volume	NOUN
american_scientific_journal-3700	114	19	39	39	NUM
american_scientific_journal-3700	114	20	,	,	PUNCT
american_scientific_journal-3700	114	21	no	no	DET
american_scientific_journal-3700	114	22	1	1	NUM
american_scientific_journal-3700	114	23	,	,	PUNCT
american_scientific_journal-3700	114	24	pp	pp	ADV
american_scientific_journal-3700	114	25	10	10	NUM
american_scientific_journal-3700	114	26	-	-	SYM
american_scientific_journal-3700	114	27	18	18	NUM
american_scientific_journal-3700	114	28	18	18	NUM
american_scientific_journal-3700	114	29	6	6	NUM
american_scientific_journal-3700	114	30	.	.	PUNCT
american_scientific_journal-3700	114	31	conclusion	conclusion	NOUN
american_scientific_journal-3700	114	32	the	the	DET
american_scientific_journal-3700	114	33	schrodinger	schrodinger	ADJ
american_scientific_journal-3700	114	34	equation	equation	NOUN
american_scientific_journal-3700	114	35	for	for	ADP
american_scientific_journal-3700	114	36	frictional	frictional	ADJ
american_scientific_journal-3700	114	37	medium	medium	NOUN
american_scientific_journal-3700	114	38	shows	show	NOUN
american_scientific_journal-3700	114	39	that	that	SCONJ
american_scientific_journal-3700	114	40	the	the	DET
american_scientific_journal-3700	114	41	energy	energy	NOUN
american_scientific_journal-3700	114	42	and	and	CCONJ
american_scientific_journal-3700	114	43	mass	mass	NOUN
american_scientific_journal-3700	114	44	are	be	AUX
american_scientific_journal-3700	114	45	quantized	quantize	VERB
american_scientific_journal-3700	114	46	.	.	PUNCT
american_scientific_journal-3700	115	1	it	it	PRON
american_scientific_journal-3700	115	2	is	be	AUX
american_scientific_journal-3700	115	3	also	also	ADV
american_scientific_journal-3700	115	4	used	use	VERB
american_scientific_journal-3700	115	5	to	to	PART
american_scientific_journal-3700	115	6	derive	derive	VERB
american_scientific_journal-3700	115	7	radioactive	radioactive	ADJ
american_scientific_journal-3700	115	8	decay	decay	NOUN
american_scientific_journal-3700	115	9	low	low	ADJ
american_scientific_journal-3700	115	10	and	and	CCONJ
american_scientific_journal-3700	115	11	collision	collision	NOUN
american_scientific_journal-3700	115	12	probability	probability	NOUN
american_scientific_journal-3700	115	13	.	.	PUNCT
american_scientific_journal-3700	116	1	references	reference	NOUN
american_scientific_journal-3700	116	2	[	[	X
american_scientific_journal-3700	116	3	1	1	NUM
american_scientific_journal-3700	116	4	]	]	PUNCT
american_scientific_journal-3700	116	5	.	.	PUNCT
american_scientific_journal-3700	117	1	david	david	PROPN
american_scientific_journal-3700	117	2	s.	s.	PROPN
american_scientific_journal-3700	117	3	saxson	saxson	PROPN
american_scientific_journal-3700	117	4	,	,	PUNCT
american_scientific_journal-3700	117	5	elementary	elementary	ADJ
american_scientific_journal-3700	117	6	quantum	quantum	NOUN
american_scientific_journal-3700	117	7	mechanics	mechanic	NOUN
american_scientific_journal-3700	117	8	,	,	PUNCT
american_scientific_journal-3700	117	9	dovered	dovere	VERB
american_scientific_journal-3700	117	10	.	.	PUNCT
american_scientific_journal-3700	118	1	p.cm	p.cm	ADJ
american_scientific_journal-3700	118	2	,	,	PUNCT
american_scientific_journal-3700	118	3	isbn-10	isbn-10	NOUN
american_scientific_journal-3700	118	4	:	:	PUNCT
american_scientific_journal-3700	118	5	048648596x	048648596x	NUM
american_scientific_journal-3700	118	6	,	,	PUNCT
american_scientific_journal-3700	118	7	(	(	PUNCT
american_scientific_journal-3700	118	8	2012	2012	NUM
american_scientific_journal-3700	118	9	)	)	PUNCT
american_scientific_journal-3700	118	10	.	.	PUNCT
american_scientific_journal-3700	119	1	[	[	X
american_scientific_journal-3700	119	2	2	2	NUM
american_scientific_journal-3700	119	3	]	]	PUNCT
american_scientific_journal-3700	119	4	.	.	PUNCT
american_scientific_journal-3700	120	1	richard	richard	PROPN
american_scientific_journal-3700	120	2	p.	p.	PROPN
american_scientific_journal-3700	120	3	feynman	feynman	PROPN
american_scientific_journal-3700	120	4	and	and	CCONJ
american_scientific_journal-3700	120	5	a.	a.	PROPN
american_scientific_journal-3700	120	6	r.	r.	PROPN
american_scientific_journal-3700	120	7	hibbs	hibbs	PROPN
american_scientific_journal-3700	120	8	,	,	PUNCT
american_scientific_journal-3700	120	9	quantum	quantum	ADJ
american_scientific_journal-3700	120	10	mechanics	mechanic	NOUN
american_scientific_journal-3700	120	11	and	and	CCONJ
american_scientific_journal-3700	120	12	path	path	NOUN
american_scientific_journal-3700	120	13	integrals	integral	NOUN
american_scientific_journal-3700	120	14	,	,	PUNCT
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american_scientific_journal-3700	120	16	–	–	PUNCT
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american_scientific_journal-3700	120	18	,	,	PUNCT
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american_scientific_journal-3700	120	20	:	:	PUNCT
american_scientific_journal-3700	120	21	0070206503	0070206503	NUM
american_scientific_journal-3700	120	22	,	,	PUNCT
american_scientific_journal-3700	120	23	(	(	PUNCT
american_scientific_journal-3700	120	24	1965	1965	NUM
american_scientific_journal-3700	120	25	)	)	PUNCT
american_scientific_journal-3700	120	26	.	.	PUNCT
american_scientific_journal-3700	121	1	[	[	X
american_scientific_journal-3700	121	2	3	3	NUM
american_scientific_journal-3700	121	3	]	]	PUNCT
american_scientific_journal-3700	121	4	.	.	PUNCT
american_scientific_journal-3700	122	1	b.	b.	PROPN
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american_scientific_journal-3700	122	3	,	,	PUNCT
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american_scientific_journal-3700	122	12	,	,	PUNCT
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american_scientific_journal-3700	122	16	,	,	PUNCT
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american_scientific_journal-3700	122	21	,	,	PUNCT
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american_scientific_journal-3700	122	23	-	-	PUNCT
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american_scientific_journal-3700	122	25	-	-	PUNCT
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american_scientific_journal-3700	122	27	-	-	PUNCT
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american_scientific_journal-3700	122	29	-	-	PUNCT
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american_scientific_journal-3700	122	31	,	,	PUNCT
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american_scientific_journal-3700	122	34	)	)	PUNCT
american_scientific_journal-3700	122	35	.	.	PUNCT
american_scientific_journal-3700	123	1	[	[	X
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american_scientific_journal-3700	123	4	.	.	PUNCT
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american_scientific_journal-3700	123	6	,	,	PUNCT
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american_scientific_journal-3700	123	9	,	,	PUNCT
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american_scientific_journal-3700	125	2	.	.	PUNCT
american_scientific_journal-3700	126	1	29	29	NUM
american_scientific_journal-3700	126	2	.	.	X
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american_scientific_journal-3700	127	1	[	[	X
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american_scientific_journal-3700	127	7	:	:	PUNCT
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american_scientific_journal-3700	127	9	-	-	SYM
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american_scientific_journal-3700	127	11	,	,	PUNCT
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american_scientific_journal-3700	129	20	-	-	SYM
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american_scientific_journal-3700	129	22	,	,	PUNCT
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american_scientific_journal-3700	130	24	,	,	PUNCT
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american_scientific_journal-3700	130	28	-	-	SYM
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american_scientific_journal-3700	130	30	-	-	PUNCT
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american_scientific_journal-3700	130	32	-	-	PUNCT
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american_scientific_journal-3700	130	34	-	-	SYM
american_scientific_journal-3700	130	35	6	6	NUM
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american_scientific_journal-3700	131	4	.	.	PUNCT
american_scientific_journal-3700	132	1	g.	g.	PROPN
american_scientific_journal-3700	132	2	aruldhas	aruldhas	PROPN
american_scientific_journal-3700	132	3	,	,	PUNCT
american_scientific_journal-3700	132	4	quantum	quantum	NOUN
american_scientific_journal-3700	132	5	mechanics	mechanic	NOUN
american_scientific_journal-3700	132	6	,	,	PUNCT
american_scientific_journal-3700	132	7	2nd	2nd	ADJ
american_scientific_journal-3700	132	8	ed	ed	NOUN
american_scientific_journal-3700	132	9	,	,	PUNCT
american_scientific_journal-3700	132	10	phi	phi	NOUN
american_scientific_journal-3700	132	11	leaming	leame	VERB
american_scientific_journal-3700	132	12	private	private	ADJ
american_scientific_journal-3700	132	13	limited	limited	ADJ
american_scientific_journal-3700	132	14	.	.	PUNCT
american_scientific_journal-3700	133	1	new	new	ADJ
american_scientific_journal-3700	133	2	delhi	delhi	PROPN
american_scientific_journal-3700	133	3	,	,	PUNCT
american_scientific_journal-3700	133	4	isbn	isbn	ADJ
american_scientific_journal-3700	133	5	10	10	NUM
american_scientific_journal-3700	133	6	:	:	SYM
american_scientific_journal-3700	133	7	8120336356	8120336356	NUM
american_scientific_journal-3700	133	8	,	,	PUNCT
american_scientific_journal-3700	133	9	(	(	PUNCT
american_scientific_journal-3700	133	10	2009	2009	NUM
american_scientific_journal-3700	133	11	)	)	PUNCT
american_scientific_journal-3700	133	12	.	.	PUNCT