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Journal of Zhejiang University(Science Edition)

Wigner functions and Moyal equation in noncommutative space

Wang Jian-hua

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

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自旋1/2非对易朗道问题的Wigner函数(英文)

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Wigner函数在对量子体系状态的描述方面具有重要的意义。 讨论了自旋1/2非对易朗道问题的Wigner函数。首先回顾了对易空间中Wigner函数所服从的星本征方程, 然后给出了非对易相空间中自旋1/2朗道问题的Hamiltonian, 最后利用星本征方程(Moyal 方程)计算了非对易相空间中自旋1/2朗道问题具有矩阵表示形式的Wigner函数及其能级。 With great significance in describing the state of quantum system, the Wigner function of the spin half noncommutative Landau problem is studied in this paper. On the basis of the review of the Wigner function in the commutative space, which is subject to the *eigenvalue equation, Hamiltonian of the spin half Landau problem in the noncommutative phase space is given. Then, energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the noncommutative phase space are obtained by means of the *-eigenvalue equation (or Moyal equation).

原子核物理评论•Dec 20, 2011•0 citations
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.
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.
With great significance in describing the state of quantum system,the Wigner function of the spin half non-commutative Landau problem is studied in this paper.On the basis of the review of the Wigner function in the commutative space,which is subject to the *-eigenvalue equation,Hamiltonian of the spin half Landau problem in the non-commutative phase space is given.Then,energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the non-commutative phase space are obtained by means of the *-eigenvalue equation(or Moyal equation).
Wigner函数在对量子体系状态的描述方面具有重要的意义。 讨论了自旋1/2非对易朗道问题的Wigner函数。首先回顾了对易空间中Wigner函数所服从的星本征方程, 然后给出了非对易相空间中自旋1/2朗道问题的Hamiltonian, 最后利用星本征方程(Moyal 方程)计算了非对易相空间中自旋1/2朗道问题具有矩阵表示形式的Wigner函数及其能级。 With great significance in describing the state of quantum system, the Wigner function of the spin half noncommutative Landau problem is studied in this paper. On the basis of the review of the Wigner function in the commutative space, which is subject to the *eigenvalue equation, Hamiltonian of the spin half Landau problem in the noncommutative phase space is given. Then, energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the noncommutative phase space are obtained by means of the *-eigenvalue equation (or Moyal equation).