Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Zhejiang University(Science Edition)

Wigner function for the Klein-Gordon oscillator

Mohamed Abdulla, Sayipjamal Dulat A, Kang Li, Mamatabdulla Hekim

Published May 30, 2011• 0 citations
OpenAlex

Abstract

Wigner functions (WF) for the Klein-Gordon (KG) oscillators in usual and in non-commutative quantum mechanics was studied. First, the time independent Schrodinger equation on a commutative space was solved, then with the help of Bopp's shift method, the WF for the KG oscillators both on a non-commutative space (NCS) and a non commutative phase space (NCPS) was obtained.

Related papers

Wigner Functions for harmonic oscillator in noncommutative phase space

Jianhua Wang, Kang Li, Sayipjamal Dulat A

We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schrödinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the harmonic oscillator on NC space and NC phase space respectively.

arXiv:0908.1703•Aug 12, 2009•3 citations

Wigner function of charged harmonic oscillator in non-commutative phase spaces

Yan Jiang-feng

In this paper,Moyal-Weyl multiplcation sign and Bopp shift are introduced.By considering the relation of non-commutative in coordinate-coordinate and momentum-momentum,the Wigner function of charged harmonic oscillator in non-commutative phase spaces are discussed.By using algebraic relation of quantum mechanics in non-commutative phase space,it has been found that the Wigner function depends on the addition item of non-commutative parameters,compared with the commutative space.

Journal of Shaanxi University of Technology•Jan 1, 2010•0 citations

Wigner Functions for Klein-Gordon Oscillators in Non-commutative Space

Kang Li B, Jianhua Wang, Sayipjamal Dulat A +1 more

International Journal of Theoretical Physics•Nov 10, 2009•18 citations

Wigner Function of Two-Dimensional Charged Harmonic Oscillator in Non-Commutative Phase Space

Li Kang

The quantum harmonic oscillator is a basic model for many complex ones.After integration,the Wigner function of quantum harmonic oscillator can be expressed by a simple form,which can be used to solve many related problems.This paper has placed the harmonic oscillator in non-commutative phase space,and studied the Wigner function of two-dimensional charged harmonic oscillator in electric field.The results show that when the non-commutative parameter is zero,the Wigner function of two-dimensional charged harmonic oscillator is equivalent to its form in commutative space.

Journal of Hangzhou Teachers College•Jan 1, 2010•0 citations

q-Deformed Harmonic Oscillator in Phase Space

A. K. Aringazin, K. M. Aringazin, Sotirios Baskoutas +3 more

Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation and annihilation operators, both the usual and $q$-deformed, is investigated. We found that the Bopp-Kubo formulation is just non-commuting coordinates representation of the symbol calculus. The Wigner operator for the $q$-deformed harmonic oscillator is shown to be proportional to the 3-axis spherical angular momentum operator of the algebra $su_{q}(2)$. The relation of the Fock space for the harmonic oscillator and double Hilbert space of the Gelfand-Naimark-Segal construction is established. The quantum extension of the classical ergodiicity condition is proposed.

arXiv:hep-th/9811027•Nov 2, 1998•1 citation

Wigner functions and Moyal equation in noncommutative space

Wang Jian-hua

Firstly this paper makes a brief review of the Moyal equation and Wigner Functions in commutative space.Then,the Moyal equation which the Wigner Functions support is introduced in Non-communacative phase space.Finally,by redefining the raising and lowering operator,Wigner functions for the coherent state of two-dimensional Harmonic oscillators are obtained.

Journal of Zhejiang University(Science Edition)•Jan 1, 2011•0 citations
Wigner functions (WF) for the Klein-Gordon (KG) oscillators in usual and in non-commutative quantum mechanics was studied. First, the time independent Schrodinger equation on a commutative space was solved, then with the help of Bopp's shift method, the WF for the KG oscillators both on a non-commutative space (NCS) and a non commutative phase space (NCPS) was obtained.
The quantum harmonic oscillator is a basic model for many complex ones.After integration,the Wigner function of quantum harmonic oscillator can be expressed by a simple form,which can be used to solve many related problems.This paper has placed the harmonic oscillator in non-commutative phase space,and studied the Wigner function of two-dimensional charged harmonic oscillator in electric field.The results show that when the non-commutative parameter is zero,the Wigner function of two-dimensional charged harmonic oscillator is equivalent to its form in commutative space.
Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation and annihilation operators, both the usual and qqq-deformed, is investigated. We found that the Bopp-Kubo formulation is just non-commuting coordinates representation of the symbol calculus. The Wigner operator for the qqq-deformed harmonic oscillator is shown to be proportional to the 3-axis spherical angular momentum operator of the algebra suq(2)su_{q}(2)suq​(2). The relation of the Fock space for the harmonic oscillator and double Hilbert space of the Gelfand-Naimark-Segal construction is established. The quantum extension of the classical ergodiicity condition is proposed.