非对易相空间中的狄拉克振子的能级和Wigner函数

非对易几何、弦论和圈量子引力理论的发展,使非对易空间受到越来越多的关注.非对易量子理论不同于平常的量子理论,它是弦尺度下的特殊的物理效应,处理非对易量子力学问题需要特殊方法.本文首先介绍了Moyal方程与Wigner函数,利用Moyal-Weyl乘法与Bopp变换将H(x,p)变换成^H(^x,^p),考虑坐标—坐标、动量—动量的非对易性,实现对非对易相空间中星乘本征方程的求解.并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狄拉克振子的Wigner函数和能级,研究结果发现非对易相空间中狄拉克振子的能级明显依赖于非对易参数.

Energy and Wigner functions of the Dirac oscillator in noncommutative phase space

With the development of noncommutative geometry,string theory and loop quantum gravity theory,the noncommutative space has been made more and more concerned.The noncommutative quantum theory is different from the ordinary quantum theory,which is a special physical effect under the string scale.Therefore,special methods are needed to deal with noncommutative quantum mechanics problems.In this paper,the Moyal equation and Wigner function first are introduced.Starting from Moyal-Weyl multiplication and Bopp transformation,H(x,p)is transformed into ^H(^x,^p)by considering the noncommutability of coordinate-coordinate,momentum-momentum to realize the star-multiplication eigenequation in the non-commutative phase space.The algebraic relationship of noncommutative phase space quantum mechanics is used to discuss the Wigner functions and energy levels of Dirac oscillator in noncommutative phase space.The results show that the energy level of the Dirac oscillator in the non-commutative phase space is obviously dependent on non-commutative parameters.