高斯积分在量子表象理论中的应用

任刚，杜建明，张文海

REN Gang，DU Jian-ming，ZHANG Wen-hai

School of Electronic Engineering，Huainan Normal University，Huainan，Anhui 232038，China

Received:2018-08-04 Revised:2018-10-30 Online:2019-03-20 Published:2019-04-25

摘要： 首先证明了真空投影算符的正规乘积形式，然后结合有序算符内积分技术，把数学上的高斯积分推广到量子算符

的积分形式.通过表象的完备性与对称性，进一步给出了坐标表象、动量表象、中介表象和相干态表象的具体形式.

关键词: 高斯积分, 量子表象, 有序算符内积分技术

Abstract: At first，the normal product form of the vacuum projection operator is proved and then the Gaussian

integral in mathematics is extended to the integral form of the quantum operator. Using the completeness and symmetry

of quantum representation，the concrete forms of the coordinate representation，momentum representation，intermediate

representation and coherent state representation are given.

Key words: , Gaussian integral, quantum representation, technique of integration within an ordered product of operators

任刚, 杜建明, 张文海. 高斯积分在量子表象理论中的应用[J]. 大学物理, 2019, 38(3): 4-.

REN Gang, DU Jian-ming, ZHANG Wen-hai. Application of Gaussian integration in quantum representation theory[J]. College Physics, 2019, 38(3): 4-.

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