推导坐标、动量算符函数换序的新方法  

A new method for re-ordering of the coordinate and momentum operator functions

作　　者：杨阳[1] 范洪义[2] YANG Yang;FAN Hong-yi(Department of Physics and Optoelectronic Engineering,Weifang University,Weifang,Shandong 261061,China;Department of Material Science and Engineering,University of Science and Technology of China,Hefei,Anhui 230026,China)

机构地区：[1]潍坊学院物理与光电工程学院,山东潍坊261061 [2]中国科学技术大学材料科学与工程系,安徽合肥230026

出　　处：《大学物理》2018年第10期4-6,9,共4页College Physics

基　　金：国家自然科学基金(11775208)资助

摘　　要：由于坐标、动量算符的不对易性,坐标算符函数和动量算符函数的换序是量子力学中的一个基本问题.运用坐标表象的完备性及有序算符内积分方法可以容易导出坐标、动量算符函数的换序公式,尤其是坐标算符与动量算符幂次换序可以用一个双变量厄米多项式来表示.而且,用有序内积分方法可以导出坐标-动量中介表象的结构.Because the coordinate and the momentum operator do not communte,the re-ordering of the coordinate and the momentum operator functions is a fundamental problem in quantum mechanics.Using the completeness of coordinate and momentum representation and the integration within ordered product of operators,the re-ordering formulas of the coordinate operator and momentum operator function can be easily derived.In particular,a bivariate Hermite polynomial can be used to express the re-ordering of the power of coordinate and momentum exponential operator neatly.Furthermore,the structure of the coordinate-momentum intermediary representation can be derived by the integration within ordered product of operators.

关 键 词：表象 完备性 有序积分 厄米多项式 

分 类 号：O413.1[理学—理论物理]