利用特殊函数和类比法有序化排列正负指数幂算符

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.

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

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.