On uncertainty relations in noncommutative phase space

AbstractThe uncertainty relations are discussed on a noncommutative plane when noncommutativity of momentum spaces is considered. It is possible to construct normalizable states by simultaneously saturating two coordinate-momentum uncertainty relations. However, under the natural condition θη ≪ 4ħ2 one can not construct a normalizable state by simultaneously saturating any other pairs out of four basic nontrivial uncertainty relations.

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ON DEFORMED BOSON ALGEBRA AND VACUUM PROJECTION OPERATOR ON NONCOMMUTATIVE PLANE

International Journal of Modern Physics A ◽

10.1142/s0217751x13500206 ◽

2013 ◽

Vol 28 (07) ◽

pp. 1350020

Author(s):

GAO-FU LIU ◽

HONG-LING LIU ◽

GUANG-JIE GUO

Keyword(s):

Phase Space ◽

Projection Operator ◽

Coherent States ◽

Completeness Relation ◽

Noncommutative Phase Space ◽

Normal Ordering ◽

Expansion Form ◽

Noncommutative Plane

In the noncommutative phase space, a new mapping is proposed to express the noncommutative coordinate and momentum operators in terms of the ordinary coordinate and momentum operators under the case of large noncommutativity parameters (μν>1). Using this mapping matrix, the deformed boson operators can be expressed in terms of the ordinary boson operators. Thus, the normal ordering expansion form of vacuum projection operator is obtained. As an application, the completeness relation of the two-mode deformed coherent states is verified by using the vacuum projection operator.

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COMMUTATOR ANOMALY IN NONCOMMUTATIVE QUANTUM MECHANICS

Modern Physics Letters A ◽

10.1142/s0217732306020585 ◽

2006 ◽

Vol 21 (39) ◽

pp. 2971-2976 ◽

Cited By ~ 7

Author(s):

SAYIPJAMAL DULAT ◽

KANG LI

Keyword(s):

Quantum Mechanics ◽

Phase Space ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Uncertainty Relation ◽

Uncertainty Relations ◽

Noncommutative Phase Space ◽

Noncommutative Quantum Mechanics ◽

Physical Observable ◽

Noncommutative Quantum

In this paper, the Schrödinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space–space and space–momentum as well as momentum–momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.

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Length in a Noncommutative Phase Space

Ukrainian Journal of Physics ◽

10.15407/ujpe63.2.102 ◽

2018 ◽

Vol 63 (2) ◽

pp. 102 ◽

Cited By ~ 1

Author(s):

Kh. P. Gnatenko ◽

V. M. Tkachuk

Keyword(s):

Phase Space ◽

Lower Bound ◽

Eigenvalue Problem ◽

Minimal Length ◽

Uncertainty Relations ◽

Noncommutative Phase Space

We study restrictions on the length in a noncommutative phase space caused by noncommutativity. The uncertainty relations for coordinates and momenta are considered, and the lower bound of the length is found. We also consider the eigenvalue problem for the squared length operator and find the expression for the minimal length in the noncommutative phase space.

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Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

Advances in High Energy Physics ◽

10.1155/2017/1723567 ◽

2017 ◽

Vol 2017 ◽

pp. 1-6

Author(s):

H. Panahi ◽

A. Savadi

Keyword(s):

Exact Solution ◽

Phase Space ◽

Algebraic Approach ◽

Wave Functions ◽

Dirac Oscillator ◽

Noncommutative Phase Space ◽

Energy Eigenvalues ◽

Good Agreement

We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that the results are in good agreement with those obtained previously via a different method.

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Composite system in rotationally invariant noncommutative phase space

International Journal of Modern Physics A ◽

10.1142/s0217751x18500379 ◽

2018 ◽

Vol 33 (07) ◽

pp. 1850037 ◽

Cited By ~ 10

Author(s):

Kh. P. Gnatenko ◽

V. M. Tkachuk

Keyword(s):

Phase Space ◽

Composite System ◽

Particle System ◽

Rotational Symmetry ◽

Center Of Mass ◽

Noncommutative Space ◽

Effective Parameters ◽

Noncommutative Phase Space ◽

Noncommutative Algebra ◽

Rotationally Invariant

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

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