非对易相空间中带电谐振子的能级分裂

非对易空间效应是出现在弦的尺度下的一种物理效应，由于这种效应的出现，引起了量子力学中的物理量的一系列变化．本文介绍了非对易相空间量子力学的代数关系．并且把Moyal—Weyl乘法在非对易相空间中通过一个广义Bopp’s变换转变成普通的乘法．文章的工作重点是把单粒子量子力学的产生和消灭算符推广到非对易空间中服从玻色爱因斯坦统计的态矢量空间的玻色子系统，在非微扰的情况下，重新定义产生和消灭算符．在所考虑的相空间变量的对易关系中包含了坐标坐标和动量-动量两个方面的非对易性；讨论了非对易相空间中服从玻色爱因斯坦统计的粒子的连续性备件；在所给出的相空间变量的对易关系中包含了空间空间和动量动量两个方面的非对易性．利用这些对易关系，进一步讨论了二维带电线性谐振子在外电场中的Hamiltonian算符的形式：最后给出了非对易相空间中带电线性谐振子在外电场中的能级分裂情况．

Energy splitting of the charged isotropic harmonic oscillator in noncommutative phase space

In the string scale,the effect of noncommutativity of space may appear.In this paper,the non-commutative(NC) phase space was introduced.It was found that the Moyal-Weyl product in NC phase space can be transformed to ordinary product by using a generalized Bopp's shift.After the discussion of the constrain condition for Bose-Einstein statistics in NC Phase space,the Hamiltonian operator of the two dimensional charged harmonic oscillator in external electric field was discussed.Finally,the energy splitting for charged harmonic oscillator in external field was given in detail.