相空间中对应量子力学基本对易关系的积分变换及求Wigner函数的新途径

An integral-transformation corresponding to quantum mechanical fundamental commutative relation and its application in deriving Wigner function

本文指出相空间中存在有对应量子力学基本对易关系积分变换,其积分核是1/π::exp[±2i(q-Q)×(p-P)]::,其中::::表示Weyl排序,Q,P是坐标算符和动量算符,其功能是负责算符的三种常用排序(P-Q排序、Q-P排序和Weyl排序)规则之间的相互转化.此外,还导出了此积分核与Wigner算符之间的关系,以及Wigner函数在这类积分变换下的性质及用途.

In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1π ：：exp[±2i （q-Q） （p-P ）]：：, here ：：：：denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules（P-Q ordering, Q-P ordering and Weyl ordering）. We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained. In this paper, it can be found that there is a type of integra-transformation which corresponds to a quantum mechanical fundamental commutative relation, with its integral kernel being 1π ：：exp[±2i （q-Q） （p-P ）]：：, here ：：：：denotes Weyl ordering, and Q and P are the coordinate and the momentum operator, respectively. Such a transformation is responsible for the mutual-converting among three ordering rules（P-Q ordering, Q-P ordering and Weyl ordering）. We also deduce the relationship between this kernel and the Wigner operator, and in this way a new approach for deriving Wigner function in quantum states is obtained.