非对易空间中的三维谐振子Wigner函数

概述了量子相空间分布函数引入的依据、非对易空间与非对易相空间的基本性质；讨论了非对易空间中量子相空间分布函数的具体表现形式；给出了在对易空间和非对易相空间中定态Schr-dinger方程和Wigner函数能量本征方程的表述式;并对照了它们在3种空间中的演变规律.最后，给出了在三维非对易空间和非对易相空间中谐振子模型Wigner函数的表达式.研究结果可以应用到更复杂的物理体系中. 

The Wigner function of the three dimensional harmonic oscillator in non commutative space

Firstly, the basic introduction to the distribution function in quantum phase space and the basic properties of non commutative space and non commutative phase space were briefly introduced. Then the specific forms of the quantum phase space distribution functions in non commutative space were also discussed; The specific forms of expression of the static Schrdinger equation and the energy eigenvalue equation of Wigner function were introduced in commutative space and non commutative phase space; The evolution rule of the forms in the three dimension spaces had been clearly proposed by comparison. Finally, the Wigner distribution functions of the harmonic oscillator in three dimensional non commutative space were given explicitly. The result of the study can be applied to more complex physical systems.