利用特殊函数和类比法有序化排列正负指数幂算符  

Ordering positive and negative exponential power operators by virtue of special functions and analogy method

作　　者：王磊 李洪奇 徐兴磊 徐世民 王继锁[2] Wang Lei;Li Hong-Qi;Xu Xing-Lei;Xu Shi-Min;Wang Ji-Suo(College of Physics and Electronic Engineering,Heze University,Heze 274015,China;School of Physics and Physical Engineering,Qufu Normal University,Qufu 273165,China)

机构地区：[1]菏泽学院物理与电子工程学院,菏泽274015 [2]曲阜师范大学物理工程学院,曲阜273165

出　　处：《物理学报》2021年第4期80-90,共11页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11347026);山东省自然科学基金(批准号:ZR2020MA085,ZR2020MF113);菏泽学院科学研究基金(批准号:XY17KJ09,XY18PY13)资助的课题.

摘　　要：研究算符函数的有序化排列是一项重要的数理任务.本文利用特殊函数和正规乘积排序与反正规乘积排序间的互换法则法导出了幂算符(αα^+)^±n和(α^+α)^±n的正规与反正规乘积排序.进一步,利用类比法得到了算符(XP)^±n和(PX)^±n的坐标-动量排序与动量-坐标排序式.最后,对新得到的这些算符结果的应用进行一些讨论.Operator ordering is often fallen back on due to its convenience in quantum optics and quantum statistics,thus it is an important task to derive the various ordered forms of operators as directly as possible.In this paper we arrange quantum mechanical operators (αα^+)^±n and (α^+α)^±n in their normally and anti-normally ordered product forms by using special functions and general mutual transformation rules between normal and anti-normal orderings of operators.Furthermore,the Q-and P-ordered forms of power operators (XP)^±n and (PX)^±n are also obtained by the analogy method.Finally,some applications are discussed,such as the Glauber-Sudarshan-representation of chaotic light field and the generating functions of even and odd bivariate Hermite polynomials.

关 键 词：算符的有序排列 特殊函数 互换法则 类比法 

分 类 号：O413[理学—理论物理]