角动量算符及其性质的研究

Research on Angular Momentum Operators and Their Properties

本文主要研究量子力学中角动量算符(包括轨道角动量算符、自旋角动量算符及总角动量算符)的定义及性质问题.通过将经典力学中的角动量与量子力学中的角动量算符进行比较,推导出量子力学中角动量算符的定义式,并根据以前学过的知识,进一步推导出其性质.通过研究会发现,轨道角动量算符、自旋角动量算符及总角动量算符有许多相似的性质,这样以后就可以将其中某一个算符已知的性质引用到其中另一个算符相似的性质,为研究量子力学中关于角动量算符的许多其他问题都提供了方便.

This paper mainly studied the definitions and properties of angular momentum operators(including orbital angular momentum operator,spin angular momentum operator and total angular momentum operator)in quantum mechanics.By comparing the angular momentum operators in classical mechanics with those in quantum mechanics,this paper deduced the definitions of angular momentum operators in quantum mechanics,and further deduced their properties according to the previous knowledge.Through research,it was found that orbital angular momentum operator,spin angular momentum operator and total angular momentum operator have many similar properties.Therefore,the known properties of one operator can be the reference for the similar properties of the other operator,which provides convenience for studying many other problems about angular momentum operators in quantum mechanics.