中文摘要：

量子谐振子是许多复杂模型的基础，它的Wigner函数积分后能写成简单的形式，可用来讨论许多实际问题．文章主要把谐振子模型放在了非对易相空间，在有外加电场的情况下，研究二维带电谐振子在电场中的Wigner函数．从结果可以看出，当非对易参数取0时，二维带电谐振子的Wigner函数与对易空间具有相同形式．

英文摘要：

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.