id	sid	tid	token	lemma	pos
ap-1799	1	1	acta	acta	PROPN
ap-1799	1	2	polytechnica	polytechnica	PROPN
ap-1799	1	3	acta	acta	PROPN
ap-1799	1	4	polytechnica	polytechnica	PROPN
ap-1799	1	5	53(3):268–270	53(3):268–270	PROPN
ap-1799	1	6	,	,	PUNCT
ap-1799	1	7	2013	2013	NUM
ap-1799	1	8	©	©	PROPN
ap-1799	1	9	czech	czech	PROPN
ap-1799	1	10	technical	technical	PROPN
ap-1799	1	11	university	university	PROPN
ap-1799	1	12	in	in	ADP
ap-1799	1	13	prague	prague	PROPN
ap-1799	1	14	,	,	PUNCT
ap-1799	1	15	2013	2013	NUM
ap-1799	1	16	available	available	ADJ
ap-1799	1	17	online	online	ADV
ap-1799	1	18	at	at	ADP
ap-1799	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1799	1	20	the	the	DET
ap-1799	1	21	two	two	NUM
ap-1799	1	22	-	-	PUNCT
ap-1799	1	23	dimensional	dimensional	ADJ
ap-1799	1	24	harmonic	harmonic	ADJ
ap-1799	1	25	oscillator	oscillator	NOUN
ap-1799	1	26	on	on	ADP
ap-1799	1	27	a	a	DET
ap-1799	1	28	noncommutative	noncommutative	ADJ
ap-1799	1	29	space	space	NOUN
ap-1799	1	30	with	with	ADP
ap-1799	1	31	minimal	minimal	ADJ
ap-1799	1	32	uncertainties	uncertainty	NOUN
ap-1799	1	33	sanjib	sanjib	ADJ
ap-1799	1	34	dey∗	dey∗	NOUN
ap-1799	1	35	,	,	PUNCT
ap-1799	1	36	andreas	andreas	PROPN
ap-1799	1	37	fring	fring	PROPN
ap-1799	1	38	department	department	PROPN
ap-1799	1	39	of	of	ADP
ap-1799	1	40	mathematical	mathematical	ADJ
ap-1799	1	41	science	science	NOUN
ap-1799	1	42	,	,	PUNCT
ap-1799	1	43	city	city	PROPN
ap-1799	1	44	university	university	PROPN
ap-1799	1	45	london	london	PROPN
ap-1799	1	46	,	,	PUNCT
ap-1799	1	47	northampton	northampton	PROPN
ap-1799	1	48	square	square	PROPN
ap-1799	1	49	,	,	PUNCT
ap-1799	1	50	london	london	PROPN
ap-1799	1	51	ec1v	ec1v	PROPN
ap-1799	1	52	0hb	0hb	NOUN
ap-1799	1	53	,	,	PUNCT
ap-1799	1	54	uk	uk	PROPN
ap-1799	1	55	∗	∗	NOUN
ap-1799	1	56	corresponding	correspond	VERB
ap-1799	1	57	author	author	NOUN
ap-1799	1	58	:	:	PUNCT
ap-1799	1	59	sanjib.dey.1@city.ac.uk	sanjib.dey.1@city.ac.uk	VERB
ap-1799	1	60	abstract	abstract	ADJ
ap-1799	1	61	.	.	PUNCT
ap-1799	2	1	the	the	DET
ap-1799	2	2	two	two	NUM
ap-1799	2	3	dimensional	dimensional	ADJ
ap-1799	2	4	set	set	NOUN
ap-1799	2	5	of	of	ADP
ap-1799	2	6	canonical	canonical	ADJ
ap-1799	2	7	relations	relation	NOUN
ap-1799	2	8	giving	give	VERB
ap-1799	2	9	rise	rise	NOUN
ap-1799	2	10	to	to	ADP
ap-1799	2	11	minimal	minimal	ADJ
ap-1799	2	12	uncertainties	uncertainty	NOUN
ap-1799	2	13	previously	previously	ADV
ap-1799	2	14	constructed	construct	VERB
ap-1799	2	15	from	from	ADP
ap-1799	2	16	a	a	DET
ap-1799	2	17	q	q	ADV
ap-1799	2	18	-	-	PUNCT
ap-1799	2	19	deformed	deform	VERB
ap-1799	2	20	oscillator	oscillator	NOUN
ap-1799	2	21	algebra	algebra	NOUN
ap-1799	2	22	is	be	AUX
ap-1799	2	23	further	far	ADV
ap-1799	2	24	investigated	investigate	VERB
ap-1799	2	25	.	.	PUNCT
ap-1799	3	1	we	we	PRON
ap-1799	3	2	provide	provide	VERB
ap-1799	3	3	a	a	DET
ap-1799	3	4	representation	representation	NOUN
ap-1799	3	5	for	for	ADP
ap-1799	3	6	this	this	DET
ap-1799	3	7	algebra	algebra	NOUN
ap-1799	3	8	in	in	ADP
ap-1799	3	9	terms	term	NOUN
ap-1799	3	10	of	of	ADP
ap-1799	3	11	a	a	DET
ap-1799	3	12	flat	flat	ADJ
ap-1799	3	13	noncommutative	noncommutative	ADJ
ap-1799	3	14	space	space	NOUN
ap-1799	3	15	and	and	CCONJ
ap-1799	3	16	employ	employ	VERB
ap-1799	3	17	it	it	PRON
ap-1799	3	18	to	to	PART
ap-1799	3	19	study	study	VERB
ap-1799	3	20	the	the	DET
ap-1799	3	21	eigenvalue	eigenvalue	PROPN
ap-1799	3	22	spectrum	spectrum	NOUN
ap-1799	3	23	for	for	ADP
ap-1799	3	24	the	the	DET
ap-1799	3	25	harmonic	harmonic	ADJ
ap-1799	3	26	oscillator	oscillator	NOUN
ap-1799	3	27	on	on	ADP
ap-1799	3	28	this	this	DET
ap-1799	3	29	space	space	NOUN
ap-1799	3	30	.	.	PUNCT
ap-1799	4	1	the	the	DET
ap-1799	4	2	perturbative	perturbative	ADJ
ap-1799	4	3	expression	expression	NOUN
ap-1799	4	4	for	for	ADP
ap-1799	4	5	the	the	DET
ap-1799	4	6	eigenenergy	eigenenergy	NOUN
ap-1799	4	7	indicates	indicate	VERB
ap-1799	4	8	that	that	SCONJ
ap-1799	4	9	the	the	DET
ap-1799	4	10	model	model	NOUN
ap-1799	4	11	might	might	AUX
ap-1799	4	12	possess	possess	VERB
ap-1799	4	13	an	an	DET
ap-1799	4	14	exceptional	exceptional	ADJ
ap-1799	4	15	point	point	NOUN
ap-1799	4	16	at	at	ADP
ap-1799	4	17	which	which	PRON
ap-1799	4	18	the	the	DET
ap-1799	4	19	spectrum	spectrum	NOUN
ap-1799	4	20	becomes	become	VERB
ap-1799	4	21	complex	complex	ADJ
ap-1799	4	22	and	and	CCONJ
ap-1799	4	23	its	its	PRON
ap-1799	4	24	pt	pt	NOUN
ap-1799	4	25	-	-	PUNCT
ap-1799	4	26	symmetry	symmetry	NOUN
ap-1799	4	27	is	be	AUX
ap-1799	4	28	spontaneously	spontaneously	ADV
ap-1799	4	29	broken	break	VERB
ap-1799	4	30	.	.	PUNCT
ap-1799	5	1	keywords	keyword	NOUN
ap-1799	5	2	:	:	PUNCT
ap-1799	5	3	noncommutative	noncommutative	ADJ
ap-1799	5	4	space	space	NOUN
ap-1799	5	5	,	,	PUNCT
ap-1799	5	6	non	non	ADJ
ap-1799	5	7	-	-	ADJ
ap-1799	5	8	hermitian	hermitian	ADJ
ap-1799	5	9	operators	operator	NOUN
ap-1799	5	10	,	,	PUNCT
ap-1799	5	11	2d	2d	NOUN
ap-1799	5	12	-	-	PUNCT
ap-1799	5	13	systems	system	NOUN
ap-1799	5	14	.	.	PUNCT
ap-1799	6	1	in	in	ADP
ap-1799	6	2	[	[	X
ap-1799	6	3	1	1	X
ap-1799	6	4	]	]	PUNCT
ap-1799	6	5	we	we	PRON
ap-1799	6	6	demonstrated	demonstrate	VERB
ap-1799	6	7	how	how	SCONJ
ap-1799	6	8	canonical	canonical	ADJ
ap-1799	6	9	relations	relation	NOUN
ap-1799	6	10	implying	imply	VERB
ap-1799	6	11	minimal	minimal	ADJ
ap-1799	6	12	uncertainties	uncertainty	NOUN
ap-1799	6	13	can	can	AUX
ap-1799	6	14	be	be	AUX
ap-1799	6	15	derived	derive	VERB
ap-1799	6	16	from	from	ADP
ap-1799	6	17	a	a	DET
ap-1799	6	18	q	q	ADV
ap-1799	6	19	-	-	PUNCT
ap-1799	6	20	deformed	deform	VERB
ap-1799	6	21	oscillator	oscillator	NOUN
ap-1799	6	22	algebra	algebra	NOUN
ap-1799	6	23	for	for	ADP
ap-1799	6	24	the	the	DET
ap-1799	6	25	creation	creation	NOUN
ap-1799	6	26	and	and	CCONJ
ap-1799	6	27	annihilation	annihilation	NOUN
ap-1799	6	28	operators	operator	NOUN
ap-1799	6	29	a†i	a†i	PROPN
ap-1799	6	30	,	,	PUNCT
ap-1799	6	31	ai	ai	VERB
ap-1799	7	1	aia	aia	PROPN
ap-1799	7	2	†	†	X
ap-1799	7	3	j	j	PROPN
ap-1799	7	4	−	−	PROPN
ap-1799	7	5	q	q	PROPN
ap-1799	7	6	2δija†jai	2δija†jai	NUM
ap-1799	7	7	=	=	SYM
ap-1799	7	8	δij	δij	NOUN
ap-1799	7	9	,	,	PUNCT
ap-1799	8	1	[	[	X
ap-1799	8	2	a†i	a†i	X
ap-1799	8	3	,	,	PUNCT
ap-1799	8	4	a	a	DET
ap-1799	8	5	†	†	X
ap-1799	8	6	j	j	PROPN
ap-1799	8	7	]	]	X
ap-1799	8	8	=	=	PUNCT
ap-1799	8	9	0	0	NUM
ap-1799	8	10	,	,	PUNCT
ap-1799	8	11	[	[	X
ap-1799	8	12	ai	ai	VERB
ap-1799	8	13	,	,	PUNCT
ap-1799	8	14	aj	aj	PROPN
ap-1799	8	15	]	]	PUNCT
ap-1799	9	1	=	=	SYM
ap-1799	9	2	0	0	NUM
ap-1799	9	3	,	,	PUNCT
ap-1799	9	4			PROPN
ap-1799	9	5	for	for	ADP
ap-1799	9	6	i	i	PROPN
ap-1799	9	7	,	,	PUNCT
ap-1799	9	8	j	j	PROPN
ap-1799	9	9	=	=	SYM
ap-1799	9	10	1	1	NUM
ap-1799	9	11	,	,	PUNCT
ap-1799	9	12	2	2	NUM
ap-1799	9	13	,	,	PUNCT
ap-1799	9	14	3	3	NUM
ap-1799	9	15	;	;	PUNCT
ap-1799	9	16	q	q	NOUN
ap-1799	9	17	∈	∈	PROPN
ap-1799	9	18	r	r	NOUN
ap-1799	9	19	,	,	PUNCT
ap-1799	9	20	(	(	PUNCT
ap-1799	9	21	1	1	X
ap-1799	9	22	)	)	PUNCT
ap-1799	9	23	as	as	SCONJ
ap-1799	9	24	investigated	investigate	VERB
ap-1799	9	25	for	for	ADP
ap-1799	9	26	instance	instance	NOUN
ap-1799	9	27	in	in	ADP
ap-1799	9	28	[	[	X
ap-1799	9	29	2–6	2–6	NOUN
ap-1799	9	30	]	]	X
ap-1799	9	31	.	.	PUNCT
ap-1799	10	1	starting	start	VERB
ap-1799	10	2	from	from	ADP
ap-1799	10	3	the	the	DET
ap-1799	10	4	general	general	ADJ
ap-1799	10	5	ansatz	ansatz	NOUN
ap-1799	10	6	x	x	X
ap-1799	10	7	=	=	SYM
ap-1799	10	8	κ̂1(a†1	κ̂1(a†1	PROPN
ap-1799	10	9	+	+	NOUN
ap-1799	10	10	a1	a1	NOUN
ap-1799	10	11	)	)	PUNCT
ap-1799	11	1	+	+	CCONJ
ap-1799	11	2	κ̂2(a†2	κ̂2(a†2	PROPN
ap-1799	11	3	+	+	SYM
ap-1799	11	4	a2	a2	PROPN
ap-1799	11	5	)	)	PUNCT
ap-1799	12	1	+	+	CCONJ
ap-1799	12	2	κ̂3(a†3	κ̂3(a†3	PROPN
ap-1799	12	3	+	+	NOUN
ap-1799	12	4	a3	a3	NOUN
ap-1799	12	5	)	)	PUNCT
ap-1799	12	6	,	,	PUNCT
ap-1799	12	7	(	(	PUNCT
ap-1799	12	8	2a	2a	NUM
ap-1799	12	9	)	)	PUNCT
ap-1799	13	1	y	y	PROPN
ap-1799	13	2	=	=	PRON
ap-1799	13	3	iκ̂4(a†1	iκ̂4(a†1	X
ap-1799	13	4	−a1	−a1	PROPN
ap-1799	13	5	)	)	PUNCT
ap-1799	14	1	+	+	CCONJ
ap-1799	14	2	iκ̂5(a†2	iκ̂5(a†2	X
ap-1799	14	3	−a2	−a2	NOUN
ap-1799	14	4	)	)	PUNCT
ap-1799	15	1	+	+	CCONJ
ap-1799	15	2	iκ̂6(a†3	iκ̂6(a†3	PROPN
ap-1799	15	3	−a3	−a3	PROPN
ap-1799	15	4	)	)	PUNCT
ap-1799	15	5	,	,	PUNCT
ap-1799	15	6	(	(	PUNCT
ap-1799	15	7	2b	2b	NUM
ap-1799	15	8	)	)	PUNCT
ap-1799	15	9	z	z	NOUN
ap-1799	16	1	=	=	SYM
ap-1799	16	2	κ̂7(a†1	κ̂7(a†1	PROPN
ap-1799	16	3	+	+	NOUN
ap-1799	16	4	a1	a1	NOUN
ap-1799	16	5	)	)	PUNCT
ap-1799	16	6	+	+	NUM
ap-1799	16	7	κ̂8(a†2	κ̂8(a†2	NUM
ap-1799	16	8	+	+	NOUN
ap-1799	16	9	a2	a2	PROPN
ap-1799	16	10	)	)	PUNCT
ap-1799	17	1	+	+	CCONJ
ap-1799	17	2	κ̂9(a†3	κ̂9(a†3	PROPN
ap-1799	17	3	+	+	PROPN
ap-1799	17	4	a3	a3	NOUN
ap-1799	17	5	)	)	PUNCT
ap-1799	17	6	,	,	PUNCT
ap-1799	17	7	(	(	PUNCT
ap-1799	17	8	2c	2c	NOUN
ap-1799	17	9	)	)	PUNCT
ap-1799	17	10	px	px	PROPN
ap-1799	17	11	=	=	PUNCT
ap-1799	17	12	iκ̌10(a†1	iκ̌10(a†1	PROPN
ap-1799	17	13	−a1	−a1	PROPN
ap-1799	17	14	)	)	PUNCT
ap-1799	17	15	+	+	NUM
ap-1799	17	16	iκ̌11(a†2	iκ̌11(a†2	ADJ
ap-1799	17	17	−a2	−a2	NOUN
ap-1799	17	18	)	)	PUNCT
ap-1799	18	1	+	+	CCONJ
ap-1799	18	2	iκ̌12(a†3	iκ̌12(a†3	PROPN
ap-1799	18	3	−a3	−a3	PROPN
ap-1799	18	4	)	)	PUNCT
ap-1799	18	5	,	,	PUNCT
ap-1799	18	6	(	(	PUNCT
ap-1799	18	7	2d	2d	NOUN
ap-1799	18	8	)	)	PUNCT
ap-1799	18	9	py	py	NOUN
ap-1799	18	10	=	=	SYM
ap-1799	18	11	κ̌13(a†1	κ̌13(a†1	PROPN
ap-1799	18	12	+	+	NOUN
ap-1799	18	13	a1	a1	NOUN
ap-1799	18	14	)	)	PUNCT
ap-1799	18	15	+	+	CCONJ
ap-1799	18	16	κ̌14(a†2	κ̌14(a†2	VERB
ap-1799	18	17	+	+	NOUN
ap-1799	18	18	a2	a2	NOUN
ap-1799	18	19	)	)	PUNCT
ap-1799	19	1	+	+	NUM
ap-1799	19	2	κ̌15(a†3	κ̌15(a†3	NOUN
ap-1799	19	3	+	+	NOUN
ap-1799	19	4	a3	a3	NOUN
ap-1799	19	5	)	)	PUNCT
ap-1799	19	6	,	,	PUNCT
ap-1799	19	7	(	(	PUNCT
ap-1799	19	8	2e	2e	NOUN
ap-1799	19	9	)	)	PUNCT
ap-1799	19	10	pz	pz	NOUN
ap-1799	19	11	=	=	NOUN
ap-1799	19	12	iκ̌16(a†1	iκ̌16(a†1	NOUN
ap-1799	19	13	−a1	−a1	PROPN
ap-1799	19	14	)	)	PUNCT
ap-1799	19	15	+	+	NUM
ap-1799	19	16	iκ̌17(a†2	iκ̌17(a†2	PROPN
ap-1799	19	17	−a2	−a2	PROPN
ap-1799	19	18	)	)	PUNCT
ap-1799	20	1	+	+	CCONJ
ap-1799	20	2	iκ̌18(a†3	iκ̌18(a†3	PROPN
ap-1799	20	3	−a3	−a3	PROPN
ap-1799	20	4	)	)	PUNCT
ap-1799	20	5	,	,	PUNCT
ap-1799	20	6	(	(	PUNCT
ap-1799	20	7	2f	2f	NOUN
ap-1799	20	8	)	)	PUNCT
ap-1799	20	9	with	with	ADP
ap-1799	20	10	κ̂i	κ̂i	X
ap-1799	20	11	=	=	PUNCT
ap-1799	20	12	κi	κi	NOUN
ap-1799	20	13	√	√	ADP
ap-1799	20	14	~/(mω	~/(mω	NUM
ap-1799	20	15	)	)	PUNCT
ap-1799	20	16	for	for	ADP
ap-1799	20	17	i	i	PROPN
ap-1799	20	18	=	=	NOUN
ap-1799	20	19	1	1	NUM
ap-1799	20	20	,	,	PUNCT
ap-1799	20	21	.	.	PUNCT
ap-1799	20	22	.	.	PUNCT
ap-1799	21	1	.	.	PUNCT
ap-1799	22	1	,	,	PUNCT
ap-1799	22	2	9	9	NUM
ap-1799	22	3	and	and	CCONJ
ap-1799	22	4	κ̌i	κ̌i	PROPN
ap-1799	22	5	=	=	PUNCT
ap-1799	22	6	κi	κi	NOUN
ap-1799	22	7	√	√	PROPN
ap-1799	22	8	mω~	mω~	PROPN
ap-1799	22	9	for	for	ADP
ap-1799	22	10	i	i	PRON
ap-1799	22	11	=	=	PROPN
ap-1799	22	12	10	10	NUM
ap-1799	22	13	,	,	PUNCT
ap-1799	22	14	.	.	PUNCT
ap-1799	22	15	.	.	PUNCT
ap-1799	23	1	.	.	PUNCT
ap-1799	24	1	,	,	PUNCT
ap-1799	24	2	18	18	NUM
ap-1799	24	3	we	we	PRON
ap-1799	24	4	constructed	construct	VERB
ap-1799	24	5	some	some	DET
ap-1799	24	6	particular	particular	ADJ
ap-1799	24	7	solutions	solution	NOUN
ap-1799	24	8	and	and	CCONJ
ap-1799	24	9	investigated	investigate	VERB
ap-1799	24	10	the	the	DET
ap-1799	24	11	harmonic	harmonic	ADJ
ap-1799	24	12	oscillator	oscillator	NOUN
ap-1799	24	13	on	on	ADP
ap-1799	24	14	these	these	DET
ap-1799	24	15	spaces	space	NOUN
ap-1799	24	16	.	.	PUNCT
ap-1799	25	1	here	here	ADV
ap-1799	25	2	we	we	PRON
ap-1799	25	3	provide	provide	VERB
ap-1799	25	4	an	an	DET
ap-1799	25	5	additional	additional	ADJ
ap-1799	25	6	two	two	NUM
ap-1799	25	7	dimensional	dimensional	ADJ
ap-1799	25	8	solution	solution	NOUN
ap-1799	25	9	previously	previously	ADV
ap-1799	25	10	reported	report	VERB
ap-1799	25	11	in	in	ADP
ap-1799	25	12	[	[	X
ap-1799	25	13	6	6	NUM
ap-1799	25	14	]	]	PUNCT
ap-1799	25	15	.	.	PUNCT
ap-1799	26	1	setting	set	VERB
ap-1799	26	2	κ3	κ3	PROPN
ap-1799	26	3	=	=	PUNCT
ap-1799	26	4	κ6	κ6	PROPN
ap-1799	26	5	=	=	SYM
ap-1799	26	6	κ7	κ7	NOUN
ap-1799	26	7	=	=	NOUN
ap-1799	26	8	κ12	κ12	NOUN
ap-1799	26	9	=	=	SYM
ap-1799	26	10	κ15	κ15	NOUN
ap-1799	26	11	=	=	SYM
ap-1799	26	12	κ16	κ16	NOUN
ap-1799	26	13	=	=	SYM
ap-1799	26	14	κ17	κ17	NOUN
ap-1799	26	15	=	=	PROPN
ap-1799	26	16	κ18	κ18	NOUN
ap-1799	26	17	=	=	NOUN
ap-1799	26	18	0	0	NUM
ap-1799	26	19	in	in	ADP
ap-1799	26	20	equations	equation	NOUN
ap-1799	26	21	(	(	PUNCT
ap-1799	26	22	2a)–(2f	2a)–(2f	NUM
ap-1799	26	23	)	)	PUNCT
ap-1799	26	24	,	,	PUNCT
ap-1799	26	25	employing	employ	VERB
ap-1799	26	26	the	the	DET
ap-1799	26	27	constraints	constraint	NOUN
ap-1799	26	28	reported	report	VERB
ap-1799	26	29	in	in	ADP
ap-1799	26	30	[	[	X
ap-1799	26	31	6	6	NUM
ap-1799	26	32	]	]	PUNCT
ap-1799	26	33	together	together	ADV
ap-1799	26	34	with	with	ADP
ap-1799	26	35	the	the	DET
ap-1799	26	36	subsequent	subsequent	ADJ
ap-1799	26	37	nontrivial	nontrivial	NOUN
ap-1799	26	38	limit	limit	NOUN
ap-1799	26	39	q	q	X
ap-1799	26	40	→	→	SYM
ap-1799	26	41	1	1	NUM
ap-1799	26	42	,	,	PUNCT
ap-1799	26	43	the	the	DET
ap-1799	26	44	deformed	deform	VERB
ap-1799	26	45	oscillator	oscillator	NOUN
ap-1799	26	46	algebra	algebra	NOUN
ap-1799	26	47	[	[	X
ap-1799	26	48	x	x	X
ap-1799	26	49	,	,	PUNCT
ap-1799	26	50	y	y	PROPN
ap-1799	26	51	]	]	PUNCT
ap-1799	27	1	=	=	PUNCT
ap-1799	27	2	iθ	iθ	NOUN
ap-1799	27	3	(	(	PUNCT
ap-1799	27	4	1	1	NUM
ap-1799	27	5	+	+	CCONJ
ap-1799	27	6	τ̂y	τ̂y	X
ap-1799	27	7	2	2	NUM
ap-1799	27	8	)	)	PUNCT
ap-1799	27	9	,	,	PUNCT
ap-1799	27	10	[	[	X
ap-1799	27	11	px	px	X
ap-1799	27	12	,	,	PUNCT
ap-1799	27	13	py	py	X
ap-1799	27	14	]	]	X
ap-1799	27	15	=	=	PUNCT
ap-1799	27	16	iτ̂	iτ̂	PROPN
ap-1799	27	17	~2	~2	NOUN
ap-1799	27	18	θ	θ	X
ap-1799	27	19	y	y	PROPN
ap-1799	27	20	2	2	NUM
ap-1799	27	21	,	,	PUNCT
ap-1799	27	22	[	[	X
ap-1799	27	23	x	x	X
ap-1799	27	24	,	,	PUNCT
ap-1799	27	25	px	px	X
ap-1799	27	26	]	]	X
ap-1799	27	27	=	=	PUNCT
ap-1799	27	28	i~	i~	PROPN
ap-1799	27	29	(	(	PUNCT
ap-1799	27	30	1	1	NUM
ap-1799	27	31	+	+	CCONJ
ap-1799	27	32	τ̂y	τ̂y	X
ap-1799	27	33	2	2	NUM
ap-1799	27	34	)	)	PUNCT
ap-1799	27	35	,	,	PUNCT
ap-1799	28	1	[	[	X
ap-1799	28	2	y	y	NOUN
ap-1799	28	3	,	,	PUNCT
ap-1799	28	4	py	py	X
ap-1799	28	5	]	]	X
ap-1799	28	6	=	=	PUNCT
ap-1799	28	7	i~	i~	PROPN
ap-1799	28	8	(	(	PUNCT
ap-1799	28	9	1	1	NUM
ap-1799	28	10	+	+	CCONJ
ap-1799	28	11	τ̂y	τ̂y	X
ap-1799	28	12	2	2	NUM
ap-1799	28	13	)	)	PUNCT
ap-1799	28	14	,	,	PUNCT
ap-1799	29	1	[	[	X
ap-1799	29	2	x	x	X
ap-1799	29	3	,	,	PUNCT
ap-1799	29	4	py	py	X
ap-1799	29	5	]	]	X
ap-1799	29	6	=	=	SYM
ap-1799	29	7	0	0	NUM
ap-1799	29	8	,	,	PUNCT
ap-1799	29	9	[	[	X
ap-1799	29	10	y	y	X
ap-1799	29	11	,	,	PUNCT
ap-1799	29	12	px	px	X
ap-1799	29	13	]	]	X
ap-1799	29	14	=	=	SYM
ap-1799	29	15	0	0	NUM
ap-1799	29	16	,	,	PUNCT
ap-1799	29	17	(	(	PUNCT
ap-1799	29	18	3	3	X
ap-1799	29	19	)	)	PUNCT
ap-1799	29	20	was	be	AUX
ap-1799	29	21	obtained	obtain	VERB
ap-1799	29	22	,	,	PUNCT
ap-1799	29	23	with	with	ADP
ap-1799	29	24	τ̂	τ̂	PUNCT
ap-1799	29	25	=	=	SYM
ap-1799	29	26	τmω/~	τmω/~	NOUN
ap-1799	29	27	having	have	VERB
ap-1799	29	28	the	the	DET
ap-1799	29	29	dimension	dimension	NOUN
ap-1799	29	30	of	of	ADP
ap-1799	29	31	an	an	DET
ap-1799	29	32	inverse	inverse	NOUN
ap-1799	29	33	squared	square	VERB
ap-1799	29	34	length	length	NOUN
ap-1799	29	35	.	.	PUNCT
ap-1799	30	1	by	by	ADP
ap-1799	30	2	the	the	DET
ap-1799	30	3	same	same	ADJ
ap-1799	30	4	reasoning	reasoning	NOUN
ap-1799	30	5	as	as	SCONJ
ap-1799	30	6	provided	provide	VERB
ap-1799	30	7	in	in	ADP
ap-1799	30	8	[	[	X
ap-1799	30	9	1	1	NUM
ap-1799	30	10	,	,	PUNCT
ap-1799	30	11	5–9	5–9	NOUN
ap-1799	30	12	]	]	X
ap-1799	30	13	,	,	PUNCT
ap-1799	30	14	we	we	PRON
ap-1799	30	15	find	find	VERB
ap-1799	30	16	the	the	DET
ap-1799	30	17	minimal	minimal	ADJ
ap-1799	30	18	uncertainties	uncertainty	NOUN
ap-1799	30	19	∆xmin	∆xmin	NOUN
ap-1799	30	20	=	=	SYM
ap-1799	30	21	|θ|	|θ|	NOUN
ap-1799	30	22	√	√	PROPN
ap-1799	30	23	τ̂	τ̂	PUNCT
ap-1799	31	1	+	+	SYM
ap-1799	31	2	τ̂2〈y	τ̂2〈y	PUNCT
ap-1799	31	3	〉	〉	NOUN
ap-1799	31	4	2ρ	2ρ	NOUN
ap-1799	31	5	,	,	PUNCT
ap-1799	31	6	∆ymin	∆ymin	NOUN
ap-1799	31	7	=	=	SYM
ap-1799	31	8	0	0	NUM
ap-1799	31	9	,	,	PUNCT
ap-1799	31	10	∆(px)min	∆(px)min	PUNCT
ap-1799	32	1	=	=	SYM
ap-1799	32	2	0	0	PROPN
ap-1799	32	3	,	,	PUNCT
ap-1799	32	4	∆(py)min	∆(py)min	NOUN
ap-1799	32	5	=	=	PUNCT
ap-1799	32	6	~	~	PUNCT
ap-1799	32	7	√	√	NUM
ap-1799	32	8	τ̂	τ̂	PUNCT
ap-1799	33	1	+	+	SYM
ap-1799	33	2	τ̂2〈y	τ̂2〈y	PUNCT
ap-1799	33	3	〉	〉	NOUN
ap-1799	33	4	2ρ	2ρ	NOUN
ap-1799	33	5	,	,	PUNCT
ap-1799	33	6	(	(	PUNCT
ap-1799	33	7	4	4	X
ap-1799	33	8	)	)	PUNCT
ap-1799	33	9	where	where	SCONJ
ap-1799	33	10	〈	〈	PROPN
ap-1799	33	11	.〉ρ	.〉ρ	PROPN
ap-1799	33	12	denotes	denote	VERB
ap-1799	33	13	the	the	DET
ap-1799	33	14	inner	inner	ADJ
ap-1799	33	15	product	product	NOUN
ap-1799	33	16	on	on	ADP
ap-1799	33	17	a	a	DET
ap-1799	33	18	hilbert	hilbert	NOUN
ap-1799	33	19	space	space	NOUN
ap-1799	33	20	with	with	ADP
ap-1799	33	21	metric	metric	ADJ
ap-1799	33	22	ρ	ρ	PROPN
ap-1799	33	23	in	in	ADP
ap-1799	33	24	which	which	PRON
ap-1799	33	25	the	the	DET
ap-1799	33	26	operators	operator	NOUN
ap-1799	33	27	x	x	SYM
ap-1799	33	28	,	,	PUNCT
ap-1799	33	29	y	y	PROPN
ap-1799	33	30	,	,	PUNCT
ap-1799	33	31	px	px	PROPN
ap-1799	33	32	and	and	CCONJ
ap-1799	33	33	py	py	PROPN
ap-1799	33	34	are	be	AUX
ap-1799	33	35	hermitian	hermitian	ADJ
ap-1799	33	36	.	.	PUNCT
ap-1799	34	1	so	so	ADV
ap-1799	34	2	far	far	ADV
ap-1799	34	3	no	no	DET
ap-1799	34	4	representation	representation	NOUN
ap-1799	34	5	for	for	ADP
ap-1799	34	6	the	the	DET
ap-1799	34	7	two	two	NUM
ap-1799	34	8	dimensional	dimensional	ADJ
ap-1799	34	9	algebra	algebra	NOUN
ap-1799	34	10	(	(	PUNCT
ap-1799	34	11	3	3	NUM
ap-1799	34	12	)	)	PUNCT
ap-1799	34	13	has	have	AUX
ap-1799	34	14	been	be	AUX
ap-1799	34	15	provided	provide	VERB
ap-1799	34	16	.	.	PUNCT
ap-1799	35	1	here	here	ADV
ap-1799	35	2	we	we	PRON
ap-1799	35	3	find	find	VERB
ap-1799	35	4	that	that	SCONJ
ap-1799	35	5	it	it	PRON
ap-1799	35	6	can	can	AUX
ap-1799	35	7	be	be	AUX
ap-1799	35	8	represented	represent	VERB
ap-1799	35	9	by	by	ADP
ap-1799	35	10	x	x	X
ap-1799	35	11	=	=	SYM
ap-1799	35	12	x0	x0	PROPN
ap-1799	35	13	+	+	CCONJ
ap-1799	35	14	τ̂	τ̂	PUNCT
ap-1799	35	15	y2	y2	PROPN
ap-1799	35	16	0x0	0x0	NUM
ap-1799	35	17	,	,	PUNCT
ap-1799	35	18	y	y	PROPN
ap-1799	35	19	=	=	SYM
ap-1799	35	20	y0	y0	PROPN
ap-1799	35	21	,	,	PUNCT
ap-1799	35	22	px	px	NOUN
ap-1799	35	23	=	=	PUNCT
ap-1799	35	24	px0	px0	PROPN
ap-1799	35	25	,	,	PUNCT
ap-1799	35	26	py	py	INTJ
ap-1799	35	27	=	=	NOUN
ap-1799	35	28	py0	py0	PROPN
ap-1799	35	29	−	−	PROPN
ap-1799	35	30	τ̂	τ̂	PUNCT
ap-1799	35	31	~	~	PUNCT
ap-1799	35	32	θ	θ	X
ap-1799	35	33	y2	y2	PROPN
ap-1799	35	34	0x0	0x0	NOUN
ap-1799	35	35	,	,	PUNCT
ap-1799	35	36	(	(	PUNCT
ap-1799	35	37	5	5	NUM
ap-1799	35	38	)	)	PUNCT
ap-1799	35	39	where	where	SCONJ
ap-1799	35	40	x0	x0	PROPN
ap-1799	35	41	,	,	PUNCT
ap-1799	35	42	y0	y0	PROPN
ap-1799	35	43	,	,	PUNCT
ap-1799	35	44	px0	px0	NOUN
ap-1799	35	45	,	,	PUNCT
ap-1799	35	46	py0	py0	PRON
ap-1799	35	47	satisfy	satisfy	VERB
ap-1799	35	48	the	the	DET
ap-1799	35	49	common	common	ADJ
ap-1799	35	50	commutation	commutation	NOUN
ap-1799	35	51	relations	relation	NOUN
ap-1799	35	52	for	for	ADP
ap-1799	35	53	the	the	DET
ap-1799	35	54	flat	flat	ADJ
ap-1799	35	55	noncommutative	noncommutative	ADJ
ap-1799	35	56	space	space	NOUN
ap-1799	36	1	[	[	X
ap-1799	36	2	x0	x0	PROPN
ap-1799	36	3	,	,	PUNCT
ap-1799	36	4	y0	y0	PROPN
ap-1799	36	5	]	]	X
ap-1799	36	6	=	=	PUNCT
ap-1799	36	7	iθ	iθ	NOUN
ap-1799	36	8	,	,	PUNCT
ap-1799	36	9	[	[	X
ap-1799	36	10	x0	x0	PROPN
ap-1799	36	11	,	,	PUNCT
ap-1799	36	12	px0	px0	X
ap-1799	36	13	]	]	PUNCT
ap-1799	36	14	=	=	PUNCT
ap-1799	36	15	i~	i~	ADJ
ap-1799	36	16	,	,	PUNCT
ap-1799	36	17	[	[	X
ap-1799	36	18	x0	x0	PROPN
ap-1799	36	19	,	,	PUNCT
ap-1799	36	20	py0	py0	X
ap-1799	36	21	]	]	PUNCT
ap-1799	36	22	=	=	PUNCT
ap-1799	36	23	0	0	NUM
ap-1799	36	24	,	,	PUNCT
ap-1799	36	25	[	[	X
ap-1799	36	26	px0	px0	NOUN
ap-1799	36	27	,	,	PUNCT
ap-1799	36	28	py0	py0	X
ap-1799	36	29	]	]	PUNCT
ap-1799	36	30	=	=	PUNCT
ap-1799	36	31	0	0	NUM
ap-1799	36	32	,	,	PUNCT
ap-1799	36	33	[	[	X
ap-1799	36	34	y0	y0	NOUN
ap-1799	36	35	,	,	PUNCT
ap-1799	36	36	py0	py0	X
ap-1799	36	37	]	]	PUNCT
ap-1799	36	38	=	=	PUNCT
ap-1799	37	1	i~	i~	ADJ
ap-1799	37	2	,	,	PUNCT
ap-1799	37	3	[	[	X
ap-1799	37	4	y0	y0	NOUN
ap-1799	37	5	,	,	PUNCT
ap-1799	37	6	px0	px0	NOUN
ap-1799	37	7	]	]	PUNCT
ap-1799	38	1	=	=	PUNCT
ap-1799	38	2	0	0	NUM
ap-1799	38	3	,	,	PUNCT
ap-1799	38	4	for	for	ADP
ap-1799	38	5	θ	θ	PROPN
ap-1799	38	6	∈	∈	PROPN
ap-1799	38	7	r.	r.	PROPN
ap-1799	38	8	(	(	PUNCT
ap-1799	38	9	6	6	NUM
ap-1799	38	10	)	)	PUNCT
ap-1799	38	11	clearly	clearly	ADV
ap-1799	38	12	there	there	PRON
ap-1799	38	13	exist	exist	VERB
ap-1799	38	14	many	many	ADJ
ap-1799	38	15	more	more	ADJ
ap-1799	38	16	solutions	solution	NOUN
ap-1799	38	17	that	that	SCONJ
ap-1799	38	18	one	one	PRON
ap-1799	38	19	may	may	AUX
ap-1799	38	20	construct	construct	VERB
ap-1799	38	21	in	in	ADP
ap-1799	38	22	this	this	DET
ap-1799	38	23	systematic	systematic	ADJ
ap-1799	38	24	manner	manner	NOUN
ap-1799	38	25	from	from	ADP
ap-1799	38	26	the	the	DET
ap-1799	38	27	268	268	NUM
ap-1799	38	28	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	ADJ
ap-1799	38	29	vol	vol	NOUN
ap-1799	38	30	.	.	PUNCT
ap-1799	39	1	53	53	NUM
ap-1799	39	2	no	no	NOUN
ap-1799	39	3	.	.	PUNCT
ap-1799	40	1	3/2013	3/2013	PROPN
ap-1799	40	2	two	two	NUM
ap-1799	40	3	-	-	PUNCT
ap-1799	40	4	dimensional	dimensional	ADJ
ap-1799	40	5	harmonic	harmonic	ADJ
ap-1799	40	6	oscillator	oscillator	NOUN
ap-1799	40	7	on	on	ADP
ap-1799	40	8	a	a	DET
ap-1799	40	9	noncommutative	noncommutative	ADJ
ap-1799	40	10	space	space	NOUN
ap-1799	40	11	ansatz	ansatz	ADJ
ap-1799	40	12	(	(	PUNCT
ap-1799	40	13	2a)–(2f	2a)–(2f	NUM
ap-1799	40	14	)	)	PUNCT
ap-1799	40	15	,	,	PUNCT
ap-1799	40	16	which	which	PRON
ap-1799	40	17	will	will	AUX
ap-1799	40	18	not	not	PART
ap-1799	40	19	be	be	AUX
ap-1799	40	20	our	our	PRON
ap-1799	40	21	concern	concern	NOUN
ap-1799	40	22	here	here	ADV
ap-1799	40	23	.	.	PUNCT
ap-1799	41	1	instead	instead	ADV
ap-1799	41	2	we	we	PRON
ap-1799	41	3	will	will	AUX
ap-1799	41	4	study	study	VERB
ap-1799	41	5	a	a	DET
ap-1799	41	6	concrete	concrete	ADJ
ap-1799	41	7	model	model	NOUN
ap-1799	41	8	,	,	PUNCT
ap-1799	41	9	i.e.	i.e.	X
ap-1799	41	10	the	the	DET
ap-1799	41	11	twodimensional	twodimensional	ADJ
ap-1799	41	12	harmonic	harmonic	ADJ
ap-1799	41	13	oscillator	oscillator	NOUN
ap-1799	41	14	on	on	ADP
ap-1799	41	15	the	the	DET
ap-1799	41	16	noncommutative	noncommutative	ADJ
ap-1799	41	17	space	space	NOUN
ap-1799	41	18	described	describe	VERB
ap-1799	41	19	by	by	ADP
ap-1799	41	20	algebra	algebra	PROPN
ap-1799	41	21	(	(	PUNCT
ap-1799	41	22	3	3	NUM
ap-1799	41	23	)	)	PUNCT
ap-1799	41	24	.	.	PUNCT
ap-1799	42	1	using	use	VERB
ap-1799	42	2	representation	representation	NOUN
ap-1799	42	3	(	(	PUNCT
ap-1799	42	4	5	5	NUM
ap-1799	42	5	)	)	PUNCT
ap-1799	42	6	,	,	PUNCT
ap-1799	42	7	the	the	DET
ap-1799	42	8	corresponding	corresponding	ADJ
ap-1799	42	9	hamiltonian	hamiltonian	ADJ
ap-1799	42	10	reads	read	VERB
ap-1799	42	11	h2d	h2d	ADJ
ap-1799	42	12	ncho	ncho	NOUN
ap-1799	42	13	=	=	NOUN
ap-1799	42	14	1	1	NUM
ap-1799	42	15	2	2	NUM
ap-1799	42	16	m	m	VERB
ap-1799	42	17	(	(	PUNCT
ap-1799	42	18	p	p	NOUN
ap-1799	42	19	2	2	NUM
ap-1799	42	20	x	x	SYM
ap-1799	43	1	+	+	X
ap-1799	43	2	p	p	X
ap-1799	43	3	2	2	NUM
ap-1799	43	4	y	y	NOUN
ap-1799	43	5	)	)	PUNCT
ap-1799	44	1	+	+	CCONJ
ap-1799	44	2	mω2	mω2	NOUN
ap-1799	44	3	2	2	NUM
ap-1799	44	4	(	(	PUNCT
ap-1799	44	5	x2	x2	PROPN
ap-1799	45	1	+	+	CCONJ
ap-1799	45	2	y	y	PROPN
ap-1799	45	3	2	2	NUM
ap-1799	45	4	)	)	PUNCT
ap-1799	45	5	=	=	PUNCT
ap-1799	46	1	h2d	h2d	PUNCT
ap-1799	46	2	fncho	fncho	ADJ
ap-1799	46	3	+	+	CCONJ
ap-1799	46	4	τ̂	τ̂	X
ap-1799	46	5	2	2	NUM
ap-1799	46	6	[	[	PUNCT
ap-1799	46	7	mω2{y2	mω2{y2	NOUN
ap-1799	46	8	0x0	0x0	NOUN
ap-1799	46	9	,	,	PUNCT
ap-1799	46	10	x0	x0	PROPN
ap-1799	46	11	}	}	PUNCT
ap-1799	46	12	−	−	PROPN
ap-1799	46	13	~	~	PUNCT
ap-1799	46	14	mθ	mθ	X
ap-1799	46	15	{	{	PUNCT
ap-1799	46	16	y2	y2	PROPN
ap-1799	46	17	0x0	0x0	NOUN
ap-1799	46	18	,	,	PUNCT
ap-1799	46	19	py0	py0	ADJ
ap-1799	46	20	}	}	PUNCT
ap-1799	46	21	]	]	PUNCT
ap-1799	47	1	+	+	CCONJ
ap-1799	47	2	τ̂2	τ̂2	SYM
ap-1799	47	3	2	2	NUM
ap-1799	47	4	[	[	PUNCT
ap-1799	47	5	mω2	mω2	NOUN
ap-1799	47	6	+	+	CCONJ
ap-1799	47	7	~2	~2	NOUN
ap-1799	47	8	mθ2	mθ2	NOUN
ap-1799	47	9	]	]	PUNCT
ap-1799	48	1	y2	y2	INTJ
ap-1799	48	2	0x0y	0x0y	NOUN
ap-1799	48	3	2	2	NUM
ap-1799	48	4	0x0	0x0	NOUN
ap-1799	48	5	,	,	PUNCT
ap-1799	48	6	(	(	PUNCT
ap-1799	48	7	7	7	X
ap-1799	48	8	)	)	PUNCT
ap-1799	48	9	where	where	SCONJ
ap-1799	48	10	we	we	PRON
ap-1799	48	11	used	use	VERB
ap-1799	48	12	the	the	DET
ap-1799	48	13	standard	standard	ADJ
ap-1799	48	14	notation	notation	NOUN
ap-1799	48	15	for	for	ADP
ap-1799	48	16	the	the	DET
ap-1799	48	17	anticommutator	anticommutator	NOUN
ap-1799	48	18	{	{	PUNCT
ap-1799	48	19	a	a	DET
ap-1799	48	20	,	,	PUNCT
ap-1799	48	21	b	b	NOUN
ap-1799	48	22	}	}	PUNCT
ap-1799	48	23	:	:	PUNCT
ap-1799	48	24	=	=	SYM
ap-1799	48	25	ab	ab	PROPN
ap-1799	49	1	+	+	CCONJ
ap-1799	50	1	ba	ba	PROPN
ap-1799	50	2	.	.	PUNCT
ap-1799	51	1	evidently	evidently	ADV
ap-1799	51	2	this	this	DET
ap-1799	51	3	hamiltonian	hamiltonian	NOUN
ap-1799	51	4	is	be	AUX
ap-1799	51	5	non	non	ADJ
ap-1799	51	6	-	-	ADJ
ap-1799	51	7	hermitian	hermitian	ADJ
ap-1799	51	8	with	with	ADP
ap-1799	51	9	regard	regard	NOUN
ap-1799	51	10	to	to	ADP
ap-1799	51	11	the	the	DET
ap-1799	51	12	standard	standard	ADJ
ap-1799	51	13	inner	inner	ADJ
ap-1799	51	14	product	product	NOUN
ap-1799	51	15	,	,	PUNCT
ap-1799	51	16	but	but	CCONJ
ap-1799	51	17	respects	respect	VERB
ap-1799	51	18	an	an	DET
ap-1799	51	19	antilinear	antilinear	ADJ
ap-1799	51	20	symmetry	symmetry	NOUN
ap-1799	51	21	pt	pt	X
ap-1799	51	22	±	±	NUM
ap-1799	51	23	:	:	PUNCT
ap-1799	51	24	x0	x0	PROPN
ap-1799	51	25	→	→	PUNCT
ap-1799	51	26	±x0	±x0	NOUN
ap-1799	51	27	,	,	PUNCT
ap-1799	51	28	y0	y0	PROPN
ap-1799	51	29	→	→	SYM
ap-1799	51	30	∓y0	∓y0	ADJ
ap-1799	51	31	,	,	PUNCT
ap-1799	51	32	px0	px0	NOUN
ap-1799	51	33	→	→	SYM
ap-1799	51	34	∓px0	∓px0	PROPN
ap-1799	51	35	,	,	PUNCT
ap-1799	51	36	py0	py0	X
ap-1799	51	37	→	→	SYM
ap-1799	51	38	±py0	±py0	NUM
ap-1799	51	39	,	,	PUNCT
ap-1799	51	40	i→	i→	VERB
ap-1799	51	41	−i	−i	PROPN
ap-1799	51	42	.	.	PUNCT
ap-1799	52	1	this	this	PRON
ap-1799	52	2	suggests	suggest	VERB
ap-1799	52	3	that	that	SCONJ
ap-1799	52	4	its	its	PRON
ap-1799	52	5	eigenvalue	eigenvalue	PROPN
ap-1799	52	6	spectrum	spectrum	NOUN
ap-1799	52	7	might	might	AUX
ap-1799	52	8	be	be	AUX
ap-1799	52	9	real	real	ADJ
ap-1799	52	10	,	,	PUNCT
ap-1799	52	11	or	or	CCONJ
ap-1799	52	12	at	at	ADP
ap-1799	52	13	least	least	ADJ
ap-1799	52	14	real	real	ADJ
ap-1799	52	15	in	in	ADP
ap-1799	52	16	parts	part	NOUN
ap-1799	52	17	[	[	X
ap-1799	52	18	10–12	10–12	NUM
ap-1799	52	19	]	]	PUNCT
ap-1799	52	20	.	.	PUNCT
ap-1799	53	1	let	let	VERB
ap-1799	53	2	us	we	PRON
ap-1799	53	3	now	now	ADV
ap-1799	53	4	investigate	investigate	VERB
ap-1799	53	5	the	the	DET
ap-1799	53	6	spectrum	spectrum	NOUN
ap-1799	53	7	perturbatively	perturbatively	ADV
ap-1799	53	8	around	around	ADP
ap-1799	53	9	the	the	DET
ap-1799	53	10	solution	solution	NOUN
ap-1799	53	11	of	of	ADP
ap-1799	53	12	the	the	DET
ap-1799	53	13	standard	standard	ADJ
ap-1799	53	14	harmonic	harmonic	ADJ
ap-1799	53	15	oscillator	oscillator	NOUN
ap-1799	53	16	.	.	PUNCT
ap-1799	54	1	in	in	ADP
ap-1799	54	2	order	order	NOUN
ap-1799	54	3	to	to	PART
ap-1799	54	4	perform	perform	VERB
ap-1799	54	5	such	such	DET
ap-1799	54	6	a	a	DET
ap-1799	54	7	computation	computation	NOUN
ap-1799	54	8	we	we	PRON
ap-1799	54	9	need	need	VERB
ap-1799	54	10	to	to	PART
ap-1799	54	11	convert	convert	VERB
ap-1799	54	12	flat	flat	ADJ
ap-1799	54	13	noncommutative	noncommutative	ADJ
ap-1799	54	14	space	space	NOUN
ap-1799	54	15	into	into	ADP
ap-1799	54	16	the	the	DET
ap-1799	54	17	standard	standard	ADJ
ap-1799	54	18	canonical	canonical	ADJ
ap-1799	54	19	variable	variable	ADJ
ap-1799	54	20	xs	xs	PROPN
ap-1799	54	21	,	,	PUNCT
ap-1799	54	22	ys	ys	NOUN
ap-1799	54	23	,	,	PUNCT
ap-1799	54	24	pxs	pxs	NOUN
ap-1799	54	25	and	and	CCONJ
ap-1799	54	26	pys	pys	PROPN
ap-1799	54	27	.	.	PUNCT
ap-1799	55	1	this	this	PRON
ap-1799	55	2	is	be	AUX
ap-1799	55	3	achieved	achieve	VERB
ap-1799	55	4	by	by	ADP
ap-1799	55	5	means	mean	NOUN
ap-1799	55	6	of	of	ADP
ap-1799	55	7	a	a	DET
ap-1799	55	8	so	so	ADV
ap-1799	55	9	-	-	PUNCT
ap-1799	55	10	called	call	VERB
ap-1799	55	11	bopp	bopp	NOUN
ap-1799	55	12	-	-	PUNCT
ap-1799	55	13	shift	shift	NOUN
ap-1799	55	14	x0	x0	PROPN
ap-1799	55	15	→	→	SYM
ap-1799	55	16	xs	xs	PROPN
ap-1799	55	17	−	−	PROPN
ap-1799	55	18	θ	θ	PROPN
ap-1799	55	19	~pys	~pys	NOUN
ap-1799	55	20	,	,	PUNCT
ap-1799	55	21	y0	y0	PROPN
ap-1799	55	22	→	→	SYM
ap-1799	55	23	ys	ys	ADJ
ap-1799	55	24	,	,	PUNCT
ap-1799	55	25	px0	px0	X
ap-1799	55	26	→	→	SYM
ap-1799	55	27	pxs	pxs	NOUN
ap-1799	55	28	and	and	CCONJ
ap-1799	55	29	py0	py0	PROPN
ap-1799	55	30	→	→	SYM
ap-1799	55	31	pys	pys	PROPN
ap-1799	55	32	.	.	PUNCT
ap-1799	56	1	the	the	DET
ap-1799	56	2	hamiltonian	hamiltonian	NOUN
ap-1799	56	3	in	in	ADP
ap-1799	56	4	(	(	PUNCT
ap-1799	56	5	7	7	NUM
ap-1799	56	6	)	)	PUNCT
ap-1799	56	7	then	then	ADV
ap-1799	56	8	acquires	acquire	VERB
ap-1799	56	9	the	the	DET
ap-1799	56	10	form	form	NOUN
ap-1799	56	11	h2d	h2d	ADJ
ap-1799	56	12	ncho	ncho	NOUN
ap-1799	56	13	=	=	PUNCT
ap-1799	56	14	h2d	h2d	PUNCT
ap-1799	56	15	ho	ho	ADJ
ap-1799	56	16	+	+	CCONJ
ap-1799	56	17	mθ2ω2	mθ2ω2	PROPN
ap-1799	56	18	2~2	2~2	NUM
ap-1799	56	19	p2	p2	PROPN
ap-1799	56	20	ys	ys	NOUN
ap-1799	56	21	−	−	PROPN
ap-1799	56	22	mθω2	mθω2	PROPN
ap-1799	56	23	2~	2~	PROPN
ap-1799	56	24	{	{	PUNCT
ap-1799	56	25	xs	xs	PROPN
ap-1799	56	26	,	,	PUNCT
ap-1799	56	27	pys	pys	PROPN
ap-1799	56	28	}	}	PUNCT
ap-1799	56	29	+	+	CCONJ
ap-1799	56	30	τ̂	τ̂	SYM
ap-1799	56	31	2	2	NUM
ap-1799	56	32	[	[	PUNCT
ap-1799	56	33	mω2{y2	mω2{y2	NOUN
ap-1799	56	34	sxs	sxs	PROPN
ap-1799	56	35	,	,	PUNCT
ap-1799	56	36	xs	xs	PROPN
ap-1799	56	37	}	}	PUNCT
ap-1799	56	38	−	−	PROPN
ap-1799	56	39	~	~	PUNCT
ap-1799	56	40	mθ	mθ	X
ap-1799	56	41	{	{	PUNCT
ap-1799	56	42	y2	y2	PROPN
ap-1799	56	43	sxs	sxs	PROPN
ap-1799	56	44	,	,	PUNCT
ap-1799	56	45	pys	pys	PROPN
ap-1799	56	46	}	}	PUNCT
ap-1799	56	47	]	]	PUNCT
ap-1799	57	1	+	+	CCONJ
ap-1799	57	2	τ̂	τ̂	SYM
ap-1799	57	3	2	2	NUM
ap-1799	57	4	[	[	X
ap-1799	57	5	(	(	PUNCT
ap-1799	57	6	1	1	NUM
ap-1799	57	7	m	m	NOUN
ap-1799	57	8	+	+	X
ap-1799	57	9	mθ2ω2	mθ2ω2	PROPN
ap-1799	57	10	~2	~2	NOUN
ap-1799	57	11	)	)	PUNCT
ap-1799	57	12	{	{	PUNCT
ap-1799	57	13	y2	y2	PROPN
ap-1799	57	14	spys	spys	PROPN
ap-1799	57	15	,	,	PUNCT
ap-1799	57	16	pys	pys	PROPN
ap-1799	57	17	}	}	PUNCT
ap-1799	57	18	−	−	PROPN
ap-1799	57	19	mθω2	mθω2	PROPN
ap-1799	57	20	~	~	PUNCT
ap-1799	57	21	(	(	PUNCT
ap-1799	57	22	{	{	PUNCT
ap-1799	57	23	y2	y2	INTJ
ap-1799	57	24	spys	spys	PROPN
ap-1799	57	25	,	,	PUNCT
ap-1799	57	26	xs}+	xs}+	PROPN
ap-1799	57	27	{	{	PUNCT
ap-1799	57	28	y2	y2	PROPN
ap-1799	57	29	sxs	sxs	PROPN
ap-1799	57	30	,	,	PUNCT
ap-1799	57	31	pys	pys	PROPN
ap-1799	57	32	}	}	PUNCT
ap-1799	57	33	)	)	PUNCT
ap-1799	57	34	]	]	PUNCT
ap-1799	58	1	−	−	PROPN
ap-1799	58	2	τ̂2	τ̂2	NOUN
ap-1799	58	3	2	2	NUM
ap-1799	58	4	[	[	PUNCT
ap-1799	58	5	mθω2	mθω2	NOUN
ap-1799	58	6	~	~	PUNCT
ap-1799	58	7	+	+	CCONJ
ap-1799	58	8	~	~	PUNCT
ap-1799	58	9	mθ	mθ	NOUN
ap-1799	58	10	]	]	X
ap-1799	58	11	(	(	PUNCT
ap-1799	58	12	y2	y2	INTJ
ap-1799	58	13	spys	spys	PROPN
ap-1799	58	14	y2	y2	PROPN
ap-1799	58	15	sxs	sxs	PROPN
ap-1799	58	16	+	+	CCONJ
ap-1799	58	17	y2	y2	ADV
ap-1799	58	18	sxsy	sxsy	VERB
ap-1799	58	19	2	2	NUM
ap-1799	58	20	spys	spys	NOUN
ap-1799	58	21	)	)	PUNCT
ap-1799	59	1	+	+	CCONJ
ap-1799	59	2	τ̂2	τ̂2	SYM
ap-1799	59	3	2	2	NUM
ap-1799	59	4	[	[	PUNCT
ap-1799	59	5	1	1	NUM
ap-1799	59	6	m	m	NOUN
ap-1799	59	7	+	+	X
ap-1799	59	8	mθ2ω2	mθ2ω2	PROPN
ap-1799	59	9	~2	~2	NOUN
ap-1799	59	10	]	]	PUNCT
ap-1799	59	11	y2	y2	PROPN
ap-1799	59	12	spys	spys	PROPN
ap-1799	59	13	y2	y2	PROPN
ap-1799	59	14	spys	spys	PROPN
ap-1799	59	15	+	+	CCONJ
ap-1799	59	16	τ̂2	τ̂2	SYM
ap-1799	59	17	2	2	NUM
ap-1799	59	18	[	[	PUNCT
ap-1799	59	19	mω2	mω2	NOUN
ap-1799	59	20	+	+	CCONJ
ap-1799	59	21	~2	~2	NOUN
ap-1799	59	22	mθ2	mθ2	NOUN
ap-1799	59	23	]	]	PUNCT
ap-1799	60	1	y2	y2	PROPN
ap-1799	60	2	sxsy	sxsy	VERB
ap-1799	60	3	2	2	NUM
ap-1799	60	4	sxs	sx	NOUN
ap-1799	60	5	=	=	PUNCT
ap-1799	60	6	h2d	h2d	PUNCT
ap-1799	60	7	ho	ho	PROPN
ap-1799	60	8	(	(	PUNCT
ap-1799	60	9	xs	xs	PROPN
ap-1799	60	10	,	,	PUNCT
ap-1799	60	11	ys	ys	PROPN
ap-1799	60	12	,	,	PUNCT
ap-1799	60	13	pxs	pxs	PROPN
ap-1799	60	14	,	,	PUNCT
ap-1799	60	15	pys	pys	PROPN
ap-1799	60	16	)	)	PUNCT
ap-1799	61	1	+	+	ADP
ap-1799	61	2	h2d	h2d	ADJ
ap-1799	61	3	nc	nc	PROPN
ap-1799	61	4	(	(	PUNCT
ap-1799	61	5	xs	xs	PROPN
ap-1799	61	6	,	,	PUNCT
ap-1799	61	7	ys	ys	PROPN
ap-1799	61	8	,	,	PUNCT
ap-1799	61	9	pxs	pxs	PROPN
ap-1799	61	10	,	,	PUNCT
ap-1799	61	11	pys	pys	PROPN
ap-1799	61	12	)	)	PUNCT
ap-1799	61	13	.	.	PUNCT
ap-1799	62	1	(	(	PUNCT
ap-1799	62	2	8)	8)	NUM
ap-1799	62	3	in	in	ADP
ap-1799	62	4	this	this	DET
ap-1799	62	5	formulation	formulation	NOUN
ap-1799	62	6	we	we	PRON
ap-1799	62	7	may	may	AUX
ap-1799	62	8	now	now	ADV
ap-1799	62	9	proceed	proceed	VERB
ap-1799	62	10	to	to	PART
ap-1799	62	11	expand	expand	VERB
ap-1799	62	12	perturbatively	perturbatively	ADV
ap-1799	62	13	around	around	ADP
ap-1799	62	14	the	the	DET
ap-1799	62	15	standard	standard	ADJ
ap-1799	62	16	two	two	NUM
ap-1799	62	17	dimensional	dimensional	ADJ
ap-1799	62	18	fock	fock	ADJ
ap-1799	62	19	space	space	NOUN
ap-1799	62	20	harmonic	harmonic	ADJ
ap-1799	62	21	oscillator	oscillator	NOUN
ap-1799	62	22	solution	solution	NOUN
ap-1799	62	23	with	with	ADP
ap-1799	62	24	normalized	normalize	VERB
ap-1799	62	25	eigenstates	eigenstate	NOUN
ap-1799	62	26	|n1n2	|n1n2	NOUN
ap-1799	62	27	〉	〉	NOUN
ap-1799	62	28	=	=	SYM
ap-1799	62	29	(	(	PUNCT
ap-1799	62	30	a†1)n1(a†2)n2	a†1)n1(a†2)n2	ADJ
ap-1799	62	31	√	√	PROPN
ap-1799	62	32	n1!n2	n1!n2	NOUN
ap-1799	62	33	!	!	PUNCT
ap-1799	63	1	|00	|00	NOUN
ap-1799	63	2	〉	〉	NOUN
ap-1799	63	3	,	,	PUNCT
ap-1799	63	4	a†i	a†i	PROPN
ap-1799	63	5	|n1n2	|n1n2	NOUN
ap-1799	63	6	〉	〉	PROPN
ap-1799	63	7	=	=	SYM
ap-1799	63	8	√	√	PROPN
ap-1799	63	9	ni	ni	NOUN
ap-1799	64	1	+	+	PROPN
ap-1799	64	2	1	1	NUM
ap-1799	64	3	∣∣(n1	∣∣(n1	PUNCT
ap-1799	64	4	+	+	CCONJ
ap-1799	64	5	δi1)(n2	δi1)(n2	PRON
ap-1799	64	6	+	+	CCONJ
ap-1799	64	7	δi2	δi2	X
ap-1799	64	8	)	)	PUNCT
ap-1799	64	9	〉	〉	NOUN
ap-1799	64	10	,	,	PUNCT
ap-1799	64	11	ai|00	ai|00	ADV
ap-1799	64	12	〉	〉	NOUN
ap-1799	64	13	=	=	SYM
ap-1799	64	14	0	0	NUM
ap-1799	64	15	,	,	PUNCT
ap-1799	64	16	ai|n1n2	ai|n1n2	ADJ
ap-1799	64	17	〉	〉	NOUN
ap-1799	64	18	=	=	SYM
ap-1799	65	1	√	√	PROPN
ap-1799	65	2	ni	ni	PROPN
ap-1799	65	3	∣∣(n1	∣∣(n1	PROPN
ap-1799	65	4	−	−	PROPN
ap-1799	65	5	δi1)(n2	δi1)(n2	PRON
ap-1799	65	6	−	−	PRON
ap-1799	65	7	δi2	δi2	NOUN
ap-1799	65	8	)	)	PUNCT
ap-1799	65	9	〉	〉	NOUN
ap-1799	65	10	,	,	PUNCT
ap-1799	65	11	(	(	PUNCT
ap-1799	65	12	9	9	NUM
ap-1799	65	13	)	)	PUNCT
ap-1799	65	14	for	for	ADP
ap-1799	65	15	i	i	PRON
ap-1799	65	16	=	=	SYM
ap-1799	65	17	1	1	NUM
ap-1799	65	18	,	,	PUNCT
ap-1799	65	19	2	2	NUM
ap-1799	65	20	,	,	PUNCT
ap-1799	65	21	such	such	ADJ
ap-1799	65	22	thath2d	thath2d	PROPN
ap-1799	65	23	ho	ho	INTJ
ap-1799	65	24	|nl	|nl	SYM
ap-1799	65	25	〉	〉	NUM
ap-1799	65	26	=	=	SYM
ap-1799	65	27	e	e	X
ap-1799	65	28	(	(	PUNCT
ap-1799	65	29	0	0	NUM
ap-1799	65	30	)	)	PUNCT
ap-1799	65	31	nl	nl	PROPN
ap-1799	65	32	|nl	|nl	PROPN
ap-1799	65	33	〉	〉	PROPN
ap-1799	65	34	.	.	PUNCT
ap-1799	66	1	the	the	DET
ap-1799	66	2	energy	energy	NOUN
ap-1799	66	3	eigenvalues	eigenvalue	VERB
ap-1799	66	4	for	for	ADP
ap-1799	66	5	the	the	DET
ap-1799	66	6	hamiltonian	hamiltonian	ADJ
ap-1799	66	7	h2d	h2d	PROPN
ap-1799	66	8	ncho	ncho	PROPN
ap-1799	66	9	then	then	ADV
ap-1799	66	10	result	result	VERB
ap-1799	66	11	to	to	ADP
ap-1799	66	12	e	e	PROPN
ap-1799	66	13	(	(	PUNCT
ap-1799	66	14	p	p	NOUN
ap-1799	66	15	)	)	PUNCT
ap-1799	66	16	nl	nl	NOUN
ap-1799	66	17	=	=	SYM
ap-1799	66	18	e	e	X
ap-1799	66	19	(	(	PUNCT
ap-1799	66	20	0	0	NUM
ap-1799	66	21	)	)	PUNCT
ap-1799	66	22	nl	nl	NOUN
ap-1799	66	23	+	+	CCONJ
ap-1799	66	24	e	e	X
ap-1799	66	25	(	(	PUNCT
ap-1799	66	26	1	1	X
ap-1799	66	27	)	)	PUNCT
ap-1799	66	28	nl	nl	NOUN
ap-1799	66	29	+	+	CCONJ
ap-1799	66	30	e	e	X
ap-1799	66	31	(	(	PUNCT
ap-1799	66	32	2	2	NUM
ap-1799	66	33	)	)	PUNCT
ap-1799	66	34	nl	nl	NOUN
ap-1799	66	35	+	+	NOUN
ap-1799	66	36	o(τ2	o(τ2	X
ap-1799	66	37	)	)	PUNCT
ap-1799	66	38	=	=	SYM
ap-1799	66	39	e	e	X
ap-1799	66	40	(	(	PUNCT
ap-1799	66	41	0	0	NUM
ap-1799	66	42	)	)	PUNCT
ap-1799	66	43	nl	nl	NOUN
ap-1799	67	1	+	+	CCONJ
ap-1799	68	1	〈	〈	PROPN
ap-1799	68	2	nl|h2d	nl|h2d	NOUN
ap-1799	68	3	nc	nc	PROPN
ap-1799	68	4	|nl	|nl	PROPN
ap-1799	68	5	〉	〉	PROPN
ap-1799	68	6	+	+	NUM
ap-1799	68	7	∑	∑	PROPN
ap-1799	68	8	p	p	X
ap-1799	68	9	,	,	PUNCT
ap-1799	68	10	q	q	NOUN
ap-1799	68	11	6	6	NUM
ap-1799	68	12	=	=	NOUN
ap-1799	68	13	n+l	n+l	NOUN
ap-1799	68	14	=	=	NOUN
ap-1799	68	15	p+q	p+q	NOUN
ap-1799	68	16	〈	〈	X
ap-1799	68	17	nl|h2d	nl|h2d	NOUN
ap-1799	68	18	nc	nc	PROPN
ap-1799	68	19	|pq〉〈pq|h2d	|pq〉〈pq|h2d	PROPN
ap-1799	68	20	nc	nc	PROPN
ap-1799	68	21	|nl	|nl	PROPN
ap-1799	68	22	〉	〉	PROPN
ap-1799	68	23	e	e	X
ap-1799	68	24	(	(	PUNCT
ap-1799	68	25	0	0	NUM
ap-1799	68	26	)	)	PUNCT
ap-1799	68	27	nl	nl	NOUN
ap-1799	68	28	−	−	PROPN
ap-1799	68	29	e	e	X
ap-1799	68	30	(	(	PUNCT
ap-1799	68	31	0	0	NUM
ap-1799	68	32	)	)	PUNCT
ap-1799	68	33	pq	pq	NOUN
ap-1799	69	1	+	+	NOUN
ap-1799	69	2	o(τ2	o(τ2	NUM
ap-1799	69	3	)	)	PUNCT
ap-1799	70	1	=	=	SYM
ap-1799	70	2	ω~(n+	ω~(n+	NOUN
ap-1799	71	1	l	l	NOUN
ap-1799	71	2	+	+	CCONJ
ap-1799	71	3	1	1	X
ap-1799	71	4	)	)	PUNCT
ap-1799	71	5	+	+	CCONJ
ap-1799	71	6	1	1	NUM
ap-1799	71	7	16	16	NUM
ap-1799	71	8	~	~	SYM
ap-1799	71	9	ωω	ωω	PRON
ap-1799	71	10	[	[	PUNCT
ap-1799	71	11	2n−	2n−	PROPN
ap-1799	71	12	(	(	PUNCT
ap-1799	71	13	2l	2l	NOUN
ap-1799	71	14	+	+	SYM
ap-1799	71	15	1)ω	1)ω	NUM
ap-1799	71	16	+	+	NOUN
ap-1799	71	17	10l	10l	NOUN
ap-1799	71	18	+	+	CCONJ
ap-1799	71	19	6	6	NUM
ap-1799	71	20	]	]	PUNCT
ap-1799	71	21	+	+	CCONJ
ap-1799	71	22	1	1	NUM
ap-1799	71	23	8	8	NUM
ap-1799	71	24	~	~	NOUN
ap-1799	71	25	τω	τω	PRON
ap-1799	71	26	[	[	PUNCT
ap-1799	71	27	ω	ω	X
ap-1799	71	28	(	(	PUNCT
ap-1799	71	29	8nl	8nl	NOUN
ap-1799	71	30	+	+	CCONJ
ap-1799	71	31	4n+	4n+	NUM
ap-1799	71	32	6l2	6l2	NUM
ap-1799	71	33	+	+	NUM
ap-1799	71	34	10l	10l	NOUN
ap-1799	71	35	+	+	CCONJ
ap-1799	71	36	5	5	NUM
ap-1799	71	37	)	)	PUNCT
ap-1799	72	1	+	+	CCONJ
ap-1799	73	1	10nl	10nl	ADJ
ap-1799	73	2	+	+	CCONJ
ap-1799	73	3	5n+	5n+	NUM
ap-1799	73	4	5l2	5l2	NUM
ap-1799	73	5	+	+	CCONJ
ap-1799	73	6	10l	10l	NOUN
ap-1799	73	7	+	+	CCONJ
ap-1799	73	8	5	5	NUM
ap-1799	73	9	]	]	PUNCT
ap-1799	74	1	+	+	ADJ
ap-1799	74	2	o(τ2	o(τ2	NUM
ap-1799	74	3	)	)	PUNCT
ap-1799	75	1	,	,	PUNCT
ap-1799	75	2	(	(	PUNCT
ap-1799	75	3	10	10	NUM
ap-1799	75	4	)	)	PUNCT
ap-1799	75	5	where	where	SCONJ
ap-1799	75	6	ω	ω	NOUN
ap-1799	75	7	=	=	SYM
ap-1799	75	8	m2θ2ω2/~2	m2θ2ω2/~2	PROPN
ap-1799	75	9	.	.	PUNCT
ap-1799	76	1	we	we	PRON
ap-1799	76	2	note	note	VERB
ap-1799	76	3	the	the	DET
ap-1799	76	4	minus	minus	ADJ
ap-1799	76	5	sign	sign	NOUN
ap-1799	76	6	in	in	ADP
ap-1799	76	7	one	one	NUM
ap-1799	76	8	of	of	ADP
ap-1799	76	9	the	the	DET
ap-1799	76	10	terms	term	NOUN
ap-1799	76	11	,	,	PUNCT
ap-1799	76	12	which	which	PRON
ap-1799	76	13	might	might	AUX
ap-1799	76	14	be	be	AUX
ap-1799	76	15	an	an	DET
ap-1799	76	16	indication	indication	NOUN
ap-1799	76	17	for	for	ADP
ap-1799	76	18	the	the	DET
ap-1799	76	19	existence	existence	NOUN
ap-1799	76	20	of	of	ADP
ap-1799	76	21	an	an	DET
ap-1799	76	22	exceptional	exceptional	ADJ
ap-1799	76	23	point	point	NOUN
ap-1799	76	24	[	[	X
ap-1799	76	25	13	13	NUM
ap-1799	76	26	,	,	PUNCT
ap-1799	76	27	14	14	NUM
ap-1799	76	28	]	]	PUNCT
ap-1799	76	29	in	in	ADP
ap-1799	76	30	the	the	DET
ap-1799	76	31	spectrum	spectrum	NOUN
ap-1799	76	32	.	.	PUNCT
ap-1799	77	1	naturally	naturally	ADV
ap-1799	77	2	it	it	PRON
ap-1799	77	3	would	would	AUX
ap-1799	77	4	be	be	AUX
ap-1799	77	5	very	very	ADV
ap-1799	77	6	interesting	interesting	ADJ
ap-1799	77	7	to	to	PART
ap-1799	77	8	obtain	obtain	VERB
ap-1799	77	9	a	a	DET
ap-1799	77	10	more	more	ADV
ap-1799	77	11	precise	precise	ADJ
ap-1799	77	12	expression	expression	NOUN
ap-1799	77	13	for	for	ADP
ap-1799	77	14	the	the	DET
ap-1799	77	15	eigenenergies	eigenenergie	NOUN
ap-1799	77	16	,	,	PUNCT
ap-1799	77	17	but	but	CCONJ
ap-1799	77	18	nonetheless	nonetheless	ADV
ap-1799	77	19	as	as	SCONJ
ap-1799	77	20	has	have	AUX
ap-1799	77	21	turned	turn	VERB
ap-1799	77	22	out	out	ADP
ap-1799	77	23	to	to	PART
ap-1799	77	24	be	be	AUX
ap-1799	77	25	very	very	ADV
ap-1799	77	26	useful	useful	ADJ
ap-1799	77	27	in	in	ADP
ap-1799	77	28	the	the	DET
ap-1799	77	29	one	one	NUM
ap-1799	77	30	dimensional	dimensional	ADJ
ap-1799	77	31	setting	setting	NOUN
ap-1799	77	32	[	[	X
ap-1799	77	33	15	15	NUM
ap-1799	77	34	]	]	X
ap-1799	77	35	the	the	DET
ap-1799	77	36	first	first	ADJ
ap-1799	77	37	order	order	NOUN
ap-1799	77	38	approximations	approximation	NOUN
ap-1799	77	39	is	be	AUX
ap-1799	77	40	very	very	ADV
ap-1799	77	41	useful	useful	ADJ
ap-1799	77	42	for	for	ADP
ap-1799	77	43	the	the	DET
ap-1799	77	44	computation	computation	NOUN
ap-1799	77	45	of	of	ADP
ap-1799	77	46	coherent	coherent	ADJ
ap-1799	77	47	states	state	NOUN
ap-1799	78	1	[	[	X
ap-1799	78	2	16	16	NUM
ap-1799	78	3	]	]	PUNCT
ap-1799	78	4	.	.	PUNCT
ap-1799	79	1	acknowledgements	acknowledgement	NOUN
ap-1799	79	2	s.d	s.d	PROPN
ap-1799	79	3	.	.	PROPN
ap-1799	79	4	is	be	AUX
ap-1799	79	5	supported	support	VERB
ap-1799	79	6	by	by	ADP
ap-1799	79	7	a	a	DET
ap-1799	79	8	city	city	NOUN
ap-1799	79	9	university	university	NOUN
ap-1799	79	10	research	research	NOUN
ap-1799	79	11	fellowship	fellowship	NOUN
ap-1799	79	12	.	.	PUNCT
ap-1799	80	1	references	reference	NOUN
ap-1799	80	2	[	[	X
ap-1799	80	3	1	1	NUM
ap-1799	80	4	]	]	PUNCT
ap-1799	80	5	s.	s.	PROPN
ap-1799	80	6	dey	dey	PROPN
ap-1799	80	7	,	,	PUNCT
ap-1799	80	8	a.	a.	NOUN
ap-1799	80	9	fring	fring	NOUN
ap-1799	80	10	,	,	PUNCT
ap-1799	80	11	and	and	CCONJ
ap-1799	80	12	l.	l.	PROPN
ap-1799	80	13	gouba	gouba	PROPN
ap-1799	80	14	,	,	PUNCT
ap-1799	80	15	pt	pt	ADJ
ap-1799	80	16	-	-	ADJ
ap-1799	80	17	symmetric	symmetric	ADJ
ap-1799	80	18	noncommutative	noncommutative	ADJ
ap-1799	80	19	spaces	space	NOUN
ap-1799	80	20	with	with	ADP
ap-1799	80	21	minimal	minimal	ADJ
ap-1799	80	22	volume	volume	NOUN
ap-1799	80	23	uncertainty	uncertainty	NOUN
ap-1799	80	24	relations	relation	NOUN
ap-1799	80	25	,	,	PUNCT
ap-1799	80	26	j.	j.	PROPN
ap-1799	80	27	phys	phys	PROPN
ap-1799	80	28	.	.	PUNCT
ap-1799	81	1	a	a	DET
ap-1799	81	2	:	:	PUNCT
ap-1799	81	3	math	math	NOUN
ap-1799	81	4	.	.	PUNCT
ap-1799	82	1	theor	theor	PROPN
ap-1799	82	2	.	.	PUNCT
ap-1799	83	1	45	45	NUM
ap-1799	83	2	(	(	PUNCT
ap-1799	83	3	2012	2012	NUM
ap-1799	83	4	)	)	PUNCT
ap-1799	83	5	385302	385302	NUM
ap-1799	84	1	[	[	X
ap-1799	84	2	2	2	NUM
ap-1799	84	3	]	]	PUNCT
ap-1799	84	4	l.	l.	PROPN
ap-1799	84	5	c.	c.	PROPN
ap-1799	84	6	biedenham	biedenham	PROPN
ap-1799	84	7	,	,	PUNCT
ap-1799	84	8	the	the	DET
ap-1799	84	9	quantum	quantum	PROPN
ap-1799	84	10	group	group	NOUN
ap-1799	84	11	group	group	NOUN
ap-1799	84	12	su(2)q	su(2)q	PROPN
ap-1799	84	13	and	and	CCONJ
ap-1799	84	14	a	a	DET
ap-1799	84	15	q	q	NOUN
ap-1799	84	16	-	-	PUNCT
ap-1799	84	17	analogue	analogue	NOUN
ap-1799	84	18	of	of	ADP
ap-1799	84	19	the	the	DET
ap-1799	84	20	boson	boson	NOUN
ap-1799	84	21	operators	operator	NOUN
ap-1799	84	22	,	,	PUNCT
ap-1799	84	23	j.	j.	PROPN
ap-1799	84	24	phys	phys	PROPN
ap-1799	84	25	.	.	PUNCT
ap-1799	85	1	a22	a22	PROPN
ap-1799	85	2	,	,	PUNCT
ap-1799	85	3	l873	l873	PROPN
ap-1799	85	4	–	–	PUNCT
ap-1799	85	5	l878	l878	PROPN
ap-1799	85	6	(	(	PUNCT
ap-1799	85	7	1989	1989	NUM
ap-1799	85	8	)	)	PUNCT
ap-1799	85	9	.	.	PUNCT
ap-1799	86	1	[	[	X
ap-1799	86	2	3	3	NUM
ap-1799	86	3	]	]	PUNCT
ap-1799	86	4	a.	a.	NOUN
ap-1799	86	5	j.	j.	PROPN
ap-1799	86	6	macfarlane	macfarlane	PROPN
ap-1799	86	7	,	,	PUNCT
ap-1799	86	8	on	on	ADP
ap-1799	86	9	q	q	NOUN
ap-1799	86	10	-	-	PUNCT
ap-1799	86	11	analogues	analogue	NOUN
ap-1799	86	12	of	of	ADP
ap-1799	86	13	the	the	DET
ap-1799	86	14	quantum	quantum	ADJ
ap-1799	86	15	harmonic	harmonic	NOUN
ap-1799	86	16	oscillator	oscillator	NOUN
ap-1799	86	17	and	and	CCONJ
ap-1799	86	18	the	the	DET
ap-1799	86	19	quantum	quantum	NOUN
ap-1799	86	20	group	group	NOUN
ap-1799	86	21	su(2)q	su(2)q	PROPN
ap-1799	86	22	,	,	PUNCT
ap-1799	86	23	j.	j.	PROPN
ap-1799	86	24	phys	phys	PROPN
ap-1799	86	25	.	.	PUNCT
ap-1799	87	1	a22	a22	PROPN
ap-1799	87	2	,	,	PUNCT
ap-1799	87	3	4581–4588	4581–4588	NUM
ap-1799	87	4	(	(	PUNCT
ap-1799	87	5	1989	1989	NUM
ap-1799	87	6	)	)	PUNCT
ap-1799	87	7	.	.	PUNCT
ap-1799	88	1	[	[	X
ap-1799	88	2	4	4	NUM
ap-1799	88	3	]	]	PUNCT
ap-1799	88	4	c.-p	c.-p	PROPN
ap-1799	88	5	.	.	PUNCT
ap-1799	89	1	su	su	PROPN
ap-1799	89	2	and	and	CCONJ
ap-1799	89	3	h.-c	h.-c	PROPN
ap-1799	89	4	.	.	PUNCT
ap-1799	90	1	fu	fu	PROPN
ap-1799	90	2	,	,	PUNCT
ap-1799	90	3	the	the	DET
ap-1799	90	4	q	q	ADV
ap-1799	90	5	-	-	PUNCT
ap-1799	90	6	deformed	deform	VERB
ap-1799	90	7	boson	boson	NOUN
ap-1799	90	8	realisation	realisation	NOUN
ap-1799	90	9	of	of	ADP
ap-1799	90	10	the	the	DET
ap-1799	90	11	quantum	quantum	NOUN
ap-1799	90	12	group	group	NOUN
ap-1799	90	13	su(n)q	su(n)q	X
ap-1799	90	14	and	and	CCONJ
ap-1799	90	15	its	its	PRON
ap-1799	90	16	representations	representation	NOUN
ap-1799	90	17	,	,	PUNCT
ap-1799	90	18	j.	j.	PROPN
ap-1799	90	19	phys	phys	PROPN
ap-1799	90	20	.	.	PUNCT
ap-1799	91	1	a22	a22	PROPN
ap-1799	91	2	,	,	PUNCT
ap-1799	91	3	l983	l983	PROPN
ap-1799	91	4	–	–	PUNCT
ap-1799	91	5	l986	l986	PROPN
ap-1799	91	6	(	(	PUNCT
ap-1799	91	7	1989	1989	NUM
ap-1799	91	8	)	)	PUNCT
ap-1799	91	9	.	.	PUNCT
ap-1799	92	1	[	[	X
ap-1799	92	2	5	5	X
ap-1799	92	3	]	]	PUNCT
ap-1799	92	4	b.	b.	PROPN
ap-1799	92	5	bagchi	bagchi	PROPN
ap-1799	92	6	and	and	CCONJ
ap-1799	92	7	a.	a.	NOUN
ap-1799	92	8	fring	fring	PROPN
ap-1799	92	9	,	,	PUNCT
ap-1799	92	10	minimal	minimal	ADJ
ap-1799	92	11	length	length	NOUN
ap-1799	92	12	in	in	ADP
ap-1799	92	13	quantum	quantum	ADJ
ap-1799	92	14	mechanics	mechanic	NOUN
ap-1799	92	15	and	and	CCONJ
ap-1799	92	16	non	non	ADJ
ap-1799	92	17	-	-	ADJ
ap-1799	92	18	hermitian	hermitian	ADJ
ap-1799	92	19	hamiltonian	hamiltonian	ADJ
ap-1799	92	20	systems	system	NOUN
ap-1799	92	21	,	,	PUNCT
ap-1799	92	22	phys	phy	NOUN
ap-1799	92	23	.	.	PUNCT
ap-1799	93	1	lett	lett	PROPN
ap-1799	93	2	.	.	PUNCT
ap-1799	94	1	a373	a373	NUM
ap-1799	94	2	,	,	PUNCT
ap-1799	94	3	4307–4310	4307–4310	NUM
ap-1799	94	4	(	(	PUNCT
ap-1799	94	5	2009	2009	NUM
ap-1799	94	6	)	)	PUNCT
ap-1799	94	7	.	.	PUNCT
ap-1799	95	1	[	[	X
ap-1799	95	2	6	6	NUM
ap-1799	95	3	]	]	PUNCT
ap-1799	95	4	a.	a.	NOUN
ap-1799	95	5	fring	fring	PROPN
ap-1799	95	6	,	,	PUNCT
ap-1799	95	7	l.	l.	PROPN
ap-1799	95	8	gouba	gouba	PROPN
ap-1799	95	9	,	,	PUNCT
ap-1799	95	10	and	and	CCONJ
ap-1799	95	11	b.	b.	PROPN
ap-1799	95	12	bagchi	bagchi	PROPN
ap-1799	95	13	,	,	PUNCT
ap-1799	95	14	minimal	minimal	ADJ
ap-1799	95	15	areas	area	NOUN
ap-1799	95	16	from	from	ADP
ap-1799	95	17	q	q	ADJ
ap-1799	95	18	-	-	PUNCT
ap-1799	95	19	deformed	deform	VERB
ap-1799	95	20	oscillator	oscillator	NOUN
ap-1799	95	21	algebras	algebra	NOUN
ap-1799	95	22	,	,	PUNCT
ap-1799	95	23	j.	j.	PROPN
ap-1799	95	24	phys	phys	PROPN
ap-1799	95	25	.	.	PUNCT
ap-1799	96	1	a43	a43	PROPN
ap-1799	96	2	,	,	PUNCT
ap-1799	96	3	425202	425202	NUM
ap-1799	96	4	(	(	PUNCT
ap-1799	96	5	2010	2010	NUM
ap-1799	96	6	)	)	PUNCT
ap-1799	96	7	.	.	PUNCT
ap-1799	97	1	[	[	X
ap-1799	97	2	7	7	X
ap-1799	97	3	]	]	PUNCT
ap-1799	97	4	a.	a.	NOUN
ap-1799	97	5	kempf	kempf	PROPN
ap-1799	97	6	,	,	PUNCT
ap-1799	97	7	uncertainty	uncertainty	NOUN
ap-1799	97	8	relation	relation	NOUN
ap-1799	97	9	in	in	ADP
ap-1799	97	10	quantum	quantum	ADJ
ap-1799	97	11	mechanics	mechanic	NOUN
ap-1799	97	12	with	with	ADP
ap-1799	97	13	quantum	quantum	NOUN
ap-1799	97	14	group	group	NOUN
ap-1799	97	15	symmetry	symmetry	NOUN
ap-1799	97	16	,	,	PUNCT
ap-1799	97	17	j.	j.	PROPN
ap-1799	97	18	math	math	PROPN
ap-1799	97	19	.	.	PUNCT
ap-1799	98	1	phys	phy	NOUN
ap-1799	98	2	.	.	PUNCT
ap-1799	99	1	35	35	NUM
ap-1799	99	2	,	,	PUNCT
ap-1799	99	3	4483–4496	4483–4496	NUM
ap-1799	99	4	(	(	PUNCT
ap-1799	99	5	1994	1994	NUM
ap-1799	99	6	)	)	PUNCT
ap-1799	99	7	.	.	PUNCT
ap-1799	100	1	[	[	X
ap-1799	100	2	8	8	NUM
ap-1799	100	3	]	]	X
ap-1799	100	4	a.	a.	NOUN
ap-1799	100	5	kempf	kempf	PROPN
ap-1799	100	6	,	,	PUNCT
ap-1799	100	7	g.	g.	PROPN
ap-1799	100	8	mangano	mangano	PROPN
ap-1799	100	9	,	,	PUNCT
ap-1799	100	10	and	and	CCONJ
ap-1799	100	11	r.	r.	PROPN
ap-1799	100	12	b.	b.	PROPN
ap-1799	100	13	mann	mann	PROPN
ap-1799	100	14	,	,	PUNCT
ap-1799	100	15	hilbert	hilbert	NOUN
ap-1799	100	16	space	space	NOUN
ap-1799	100	17	representation	representation	NOUN
ap-1799	100	18	of	of	ADP
ap-1799	100	19	the	the	DET
ap-1799	100	20	minimal	minimal	ADJ
ap-1799	100	21	length	length	NOUN
ap-1799	100	22	uncertainty	uncertainty	NOUN
ap-1799	100	23	relation	relation	NOUN
ap-1799	100	24	,	,	PUNCT
ap-1799	100	25	phys	phy	NOUN
ap-1799	100	26	.	.	PUNCT
ap-1799	101	1	rev	rev	PROPN
ap-1799	101	2	.	.	PROPN
ap-1799	101	3	d52	d52	PROPN
ap-1799	101	4	,	,	PUNCT
ap-1799	101	5	1108–1118	1108–1118	NUM
ap-1799	101	6	(	(	PUNCT
ap-1799	101	7	1995	1995	NUM
ap-1799	101	8	)	)	PUNCT
ap-1799	101	9	.	.	PUNCT
ap-1799	102	1	[	[	X
ap-1799	102	2	9	9	NUM
ap-1799	102	3	]	]	PUNCT
ap-1799	102	4	a.	a.	NOUN
ap-1799	102	5	fring	fring	PROPN
ap-1799	102	6	,	,	PUNCT
ap-1799	102	7	l.	l.	PROPN
ap-1799	102	8	gouba	gouba	PROPN
ap-1799	102	9	,	,	PUNCT
ap-1799	102	10	and	and	CCONJ
ap-1799	102	11	f.	f.	PROPN
ap-1799	102	12	g.	g.	PROPN
ap-1799	102	13	scholtz	scholtz	PROPN
ap-1799	102	14	,	,	PUNCT
ap-1799	102	15	strings	string	NOUN
ap-1799	102	16	from	from	ADP
ap-1799	102	17	dynamical	dynamical	ADJ
ap-1799	102	18	noncommutative	noncommutative	ADJ
ap-1799	102	19	space	space	NOUN
ap-1799	102	20	-	-	PUNCT
ap-1799	102	21	time	time	NOUN
ap-1799	102	22	,	,	PUNCT
ap-1799	102	23	j.	j.	PROPN
ap-1799	102	24	phys	phys	PROPN
ap-1799	102	25	.	.	PUNCT
ap-1799	103	1	a43	a43	PROPN
ap-1799	103	2	,	,	PUNCT
ap-1799	103	3	345401(10	345401(10	NUM
ap-1799	103	4	)	)	PUNCT
ap-1799	103	5	(	(	PUNCT
ap-1799	103	6	2010	2010	NUM
ap-1799	103	7	)	)	PUNCT
ap-1799	103	8	.	.	PUNCT
ap-1799	104	1	[	[	X
ap-1799	104	2	10	10	NUM
ap-1799	104	3	]	]	X
ap-1799	104	4	c.	c.	PROPN
ap-1799	104	5	m.	m.	PROPN
ap-1799	104	6	bender	bender	PROPN
ap-1799	104	7	and	and	CCONJ
ap-1799	104	8	s.	s.	PROPN
ap-1799	104	9	boettcher	boettcher	PROPN
ap-1799	104	10	,	,	PUNCT
ap-1799	104	11	real	real	ADJ
ap-1799	104	12	spectra	spectra	NOUN
ap-1799	104	13	in	in	ADP
ap-1799	104	14	non	non	ADJ
ap-1799	104	15	-	-	ADJ
ap-1799	104	16	hermitian	hermitian	ADJ
ap-1799	104	17	hamiltonians	hamiltonian	NOUN
ap-1799	104	18	having	have	VERB
ap-1799	104	19	pt	pt	PROPN
ap-1799	104	20	symmetry	symmetry	NOUN
ap-1799	104	21	,	,	PUNCT
ap-1799	104	22	phys	phy	NOUN
ap-1799	104	23	.	.	PUNCT
ap-1799	105	1	rev	rev	PROPN
ap-1799	105	2	.	.	PROPN
ap-1799	105	3	lett	lett	PROPN
ap-1799	105	4	.	.	PROPN
ap-1799	106	1	80	80	NUM
ap-1799	106	2	,	,	PUNCT
ap-1799	106	3	5243–5246	5243–5246	NUM
ap-1799	106	4	(	(	PUNCT
ap-1799	106	5	1998	1998	NUM
ap-1799	106	6	)	)	PUNCT
ap-1799	106	7	.	.	PUNCT
ap-1799	107	1	269	269	NUM
ap-1799	107	2	s.	s.	PROPN
ap-1799	107	3	dey	dey	PROPN
ap-1799	107	4	,	,	PUNCT
ap-1799	107	5	a.	a.	NOUN
ap-1799	107	6	fring	fring	NOUN
ap-1799	107	7	acta	acta	PROPN
ap-1799	107	8	polytechnica	polytechnica	PROPN
ap-1799	108	1	[	[	X
ap-1799	108	2	11	11	NUM
ap-1799	108	3	]	]	PUNCT
ap-1799	108	4	a.	a.	NOUN
ap-1799	108	5	mostafazadeh	mostafazadeh	PROPN
ap-1799	108	6	,	,	PUNCT
ap-1799	108	7	pseudo	pseudo	NOUN
ap-1799	108	8	-	-	NOUN
ap-1799	108	9	hermiticity	hermiticity	NOUN
ap-1799	108	10	versus	versus	ADP
ap-1799	108	11	pt	pt	PROPN
ap-1799	108	12	symmetry	symmetry	NOUN
ap-1799	108	13	:	:	PUNCT
ap-1799	108	14	the	the	DET
ap-1799	108	15	necessary	necessary	ADJ
ap-1799	108	16	condition	condition	NOUN
ap-1799	108	17	for	for	ADP
ap-1799	108	18	the	the	DET
ap-1799	108	19	reality	reality	NOUN
ap-1799	108	20	of	of	ADP
ap-1799	108	21	the	the	DET
ap-1799	108	22	spectrum	spectrum	NOUN
ap-1799	108	23	of	of	ADP
ap-1799	108	24	a	a	DET
ap-1799	108	25	non	non	ADJ
ap-1799	108	26	-	-	ADJ
ap-1799	108	27	hermitian	hermitian	ADJ
ap-1799	108	28	hamiltonian	hamiltonian	NOUN
ap-1799	108	29	,	,	PUNCT
ap-1799	108	30	j.	j.	PROPN
ap-1799	108	31	maths	maths	PROPN
ap-1799	108	32	.	.	PUNCT
ap-1799	109	1	phys	phy	NOUN
ap-1799	109	2	.	.	PUNCT
ap-1799	110	1	43	43	NUM
ap-1799	110	2	,	,	PUNCT
ap-1799	110	3	202–212	202–212	NUM
ap-1799	110	4	(	(	PUNCT
ap-1799	110	5	2002	2002	NUM
ap-1799	110	6	)	)	PUNCT
ap-1799	110	7	.	.	PUNCT
ap-1799	111	1	[	[	X
ap-1799	111	2	12	12	NUM
ap-1799	111	3	]	]	X
ap-1799	111	4	c.	c.	PROPN
ap-1799	111	5	m.	m.	PROPN
ap-1799	111	6	bender	bender	PROPN
ap-1799	111	7	,	,	PUNCT
ap-1799	111	8	making	make	VERB
ap-1799	111	9	sense	sense	NOUN
ap-1799	111	10	of	of	ADP
ap-1799	111	11	non	non	ADJ
ap-1799	111	12	-	-	ADJ
ap-1799	111	13	hermitian	hermitian	ADJ
ap-1799	111	14	hamiltonians	hamiltonian	NOUN
ap-1799	111	15	,	,	PUNCT
ap-1799	111	16	rept	rept	NOUN
ap-1799	111	17	.	.	PUNCT
ap-1799	111	18	prog	prog	NOUN
ap-1799	111	19	.	.	PUNCT
ap-1799	112	1	phys	phy	NOUN
ap-1799	112	2	.	.	PUNCT
ap-1799	113	1	70	70	NUM
ap-1799	113	2	,	,	PUNCT
ap-1799	113	3	947–1018	947–1018	NUM
ap-1799	113	4	(	(	PUNCT
ap-1799	113	5	2007	2007	NUM
ap-1799	113	6	)	)	PUNCT
ap-1799	113	7	.	.	PUNCT
ap-1799	114	1	[	[	X
ap-1799	114	2	13	13	NUM
ap-1799	114	3	]	]	X
ap-1799	114	4	c.	c.	PROPN
ap-1799	114	5	m.	m.	PROPN
ap-1799	114	6	bender	bender	PROPN
ap-1799	114	7	and	and	CCONJ
ap-1799	114	8	t.	t.	PROPN
ap-1799	114	9	t.	t.	PROPN
ap-1799	114	10	wu	wu	PROPN
ap-1799	114	11	,	,	PUNCT
ap-1799	114	12	anharmonic	anharmonic	ADJ
ap-1799	114	13	oscillator	oscillator	NOUN
ap-1799	114	14	,	,	PUNCT
ap-1799	114	15	phys	phy	NOUN
ap-1799	114	16	.	.	PUNCT
ap-1799	115	1	rev	rev	PROPN
ap-1799	115	2	.	.	PROPN
ap-1799	115	3	184	184	NUM
ap-1799	115	4	,	,	PUNCT
ap-1799	115	5	1231–1260	1231–1260	NUM
ap-1799	115	6	(	(	PUNCT
ap-1799	115	7	1969	1969	NUM
ap-1799	115	8	)	)	PUNCT
ap-1799	115	9	.	.	PUNCT
ap-1799	116	1	[	[	X
ap-1799	116	2	14	14	NUM
ap-1799	116	3	]	]	PUNCT
ap-1799	116	4	t.	t.	PROPN
ap-1799	116	5	kato	kato	PROPN
ap-1799	116	6	,	,	PUNCT
ap-1799	116	7	perturbation	perturbation	NOUN
ap-1799	116	8	theory	theory	NOUN
ap-1799	116	9	for	for	ADP
ap-1799	116	10	linear	linear	PROPN
ap-1799	116	11	operators	operator	NOUN
ap-1799	116	12	,	,	PUNCT
ap-1799	116	13	(	(	PUNCT
ap-1799	116	14	springer	springer	NOUN
ap-1799	116	15	,	,	PUNCT
ap-1799	116	16	berlin	berlin	PROPN
ap-1799	116	17	)	)	PUNCT
ap-1799	116	18	(	(	PUNCT
ap-1799	116	19	1966	1966	NUM
ap-1799	116	20	)	)	PUNCT
ap-1799	116	21	.	.	PUNCT
ap-1799	117	1	[	[	X
ap-1799	117	2	15	15	NUM
ap-1799	117	3	]	]	X
ap-1799	117	4	s.	s.	PROPN
ap-1799	117	5	dey	dey	PROPN
ap-1799	117	6	,	,	PUNCT
ap-1799	117	7	a.	a.	NOUN
ap-1799	117	8	fring	fring	PROPN
ap-1799	117	9	,	,	PUNCT
ap-1799	117	10	l.	l.	PROPN
ap-1799	117	11	gouba	gouba	PROPN
ap-1799	117	12	,	,	PUNCT
ap-1799	117	13	and	and	CCONJ
ap-1799	117	14	p.	p.	PROPN
ap-1799	117	15	g.	g.	PROPN
ap-1799	117	16	castro	castro	PROPN
ap-1799	117	17	,	,	PUNCT
ap-1799	117	18	timedependent	timedependent	NOUN
ap-1799	117	19	q	q	ADJ
ap-1799	117	20	-	-	PUNCT
ap-1799	117	21	deformed	deform	VERB
ap-1799	117	22	coherent	coherent	ADJ
ap-1799	117	23	states	state	NOUN
ap-1799	117	24	for	for	ADP
ap-1799	117	25	generalised	generalised	ADJ
ap-1799	117	26	uncertainty	uncertainty	NOUN
ap-1799	117	27	relations	relation	NOUN
ap-1799	117	28	,	,	PUNCT
ap-1799	117	29	phys	phy	NOUN
ap-1799	117	30	.	.	PUNCT
ap-1799	117	31	rev	rev	PROPN
ap-1799	117	32	.	.	PUNCT
ap-1799	118	1	d	d	X
ap-1799	118	2	87	87	NUM
ap-1799	118	3	,	,	PUNCT
ap-1799	118	4	084033	084033	NUM
ap-1799	118	5	(	(	PUNCT
ap-1799	118	6	2013	2013	NUM
ap-1799	118	7	)	)	PUNCT
ap-1799	118	8	.	.	PUNCT
ap-1799	119	1	[	[	X
ap-1799	119	2	16	16	NUM
ap-1799	119	3	]	]	X
ap-1799	119	4	s.	s.	PROPN
ap-1799	119	5	dey	dey	PROPN
ap-1799	119	6	and	and	CCONJ
ap-1799	119	7	a.	a.	NOUN
ap-1799	119	8	fring	fring	PROPN
ap-1799	119	9	,	,	PUNCT
ap-1799	119	10	squeezed	squeeze	VERB
ap-1799	119	11	coherent	coherent	ADJ
ap-1799	119	12	states	state	NOUN
ap-1799	119	13	for	for	ADP
ap-1799	119	14	noncommutative	noncommutative	ADJ
ap-1799	119	15	spaces	space	NOUN
ap-1799	119	16	with	with	ADP
ap-1799	119	17	minimal	minimal	ADJ
ap-1799	119	18	length	length	NOUN
ap-1799	119	19	uncertainity	uncertainity	NOUN
ap-1799	119	20	relations	relation	NOUN
ap-1799	119	21	,	,	PUNCT
ap-1799	119	22	phys	phy	NOUN
ap-1799	119	23	.	.	PUNCT
ap-1799	120	1	rev	rev	PROPN
ap-1799	120	2	d	d	PROPN
ap-1799	120	3	86	86	NUM
ap-1799	120	4	,	,	PUNCT
ap-1799	120	5	064038	064038	NUM
ap-1799	120	6	(	(	PUNCT
ap-1799	120	7	2012	2012	NUM
ap-1799	120	8	)	)	PUNCT
ap-1799	120	9	.	.	PUNCT
ap-1799	121	1	270	270	NUM
ap-1799	121	2	acta	acta	PROPN
ap-1799	121	3	polytechnica	polytechnica	PROPN
ap-1799	121	4	53(3):268–270	53(3):268–270	PROPN
ap-1799	121	5	,	,	PUNCT
ap-1799	121	6	2013	2013	NUM
ap-1799	121	7	acknowledgements	acknowledgement	NOUN
ap-1799	121	8	references	reference	NOUN