量子力学纯态表象与混合态表象间的积分变换

Integration Transformation between Pure State Representation and Mixed State Representation in Quantum Mechanics

在量子力学中,表象变换通常指的是两个纯态表象之间的变换,如由坐标表象变换到动量表象.本文在纯态表象(坐标表象和动量表象)和混合态表象(Weyl-Wigner表象)之间建立一种新的积分变换.基于此,提出了一种获得系统密度算符Wigner函数的新方法,并直接导出了菲涅尔算符的Weyl经典对应和分数阶压缩算符的正规乘积表示.

Representation transformation in quantum mechanics usually refers to the transform between two pure state representations,for example,from coordinate representation to momentum representation.In this paper we nd the new integration transformation between the pure state representations(coordinate representation and momentum representation)and the mixed state representation(the Weyl-Wigner representation).Using this transformation,we find a new approach for obtaining Wigner function of operators,which helps us to find the Weyl classical correspondence of Fresnel operator and the normal ordering product of a fractional squeezing operator.