角动量平方算符的矢量分析计算  

CALCULATING THE SQUARE OPERATOR OF ANGULAR MOMENTUM BY VECTOR ANALYSIS

作　　者：周运清 黄文涛 周恺元 

机构地区：[1]浙江海洋大学物理系,浙江省海洋大数据挖掘与应用重点实验室,浙江舟山316022

出　　处：《物理与工程》2016年第6期48-50,共3页Physics and Engineering

基　　金：浙江海洋学院科研启动项目(21065013413);中青年资助项目(11062101712);校级重大项目(X12ZD10);浙江省自然基金项目(Y6110250,LY14A040001);国家自然基金(11304281,31201001)资助

摘　　要：量子物理是从经典物理中发展而来的,在其教学中有意识地挖掘现有教材以便与经典进行对比,指出两者的差异,并说明在什么条件下量子描述退化为经典描述,具有十分重要的教学价值,而角动量的平方算符的推导刚好提供了这样的契机.本文利用矢量算符分析的方法来推导出在球坐标系下角动量平方算符的表达式,同时与经典的角动量平方进行了比较,得到量子角动量平方算符比其经典对应量多出含普朗克常数的项,在经典极限下,前者退化为后者.作为拓展,最后用Bohm规则计算了角动量平方算符.Quantum physics has been developed from classical physics.In the teaching process,we should be aware of digging into the existing teaching materials in order to compare with the classics,point out their difference and show under what conditions quantum description degenerates into classic description,which has very important teaching value.The derivation of the square of the angular momentum of provides the opportunity for this purpose.In this paper,the expression of the square operator of angular momentum in spherical coordinate is derived by the method of vector analysis,and then compares with the square of classical angular momentum.We obtain that in comparison with its classical counterpart,the square operator of quantum angular momentum has an extra term of Planck＇s constant＇s order,and in the classical limit,the quantum result is reduced to its classical counterpart.Finally,as an extension,the Bohm＇s rule is used to calculate the square operator of the angular momentum.

关 键 词：经典物理 量子物理 角动量平方算符 球坐标系 Bohm规则 

分 类 号：O413.1[理学—理论物理]