非对易相空间中带电谐振子的Wigner函数

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

从Moyal—Weyl乘法与Bopp变换出发，考虑了坐标-坐标、动量-动量的非对易性；利用非对易相空间量子力学的代数关系，讨论了非对易相空间中带电谐振子的Wigner函数，在所给出的非对易相空间带电谐振子的Wigner函数中出现了依赖于非对易参数的附加项。

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.