轨道角动量算符与矢量算符及标量算符对易关系的严格证明

秦绪明, 康东彪, 郝红军, 赵冬秋, 张希威

doi:10.16854/j.cnki.1000-0712.220022

大学物理 >

2022 , Vol. 41 >Issue 12: 12

DOI: https://doi.org/10.16854/j.cnki.1000-0712.220022

教学讨论

轨道角动量算符与矢量算符及标量算符对易关系的严格证明

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1. 安阳师范学院物理与电气工程学院，河南安阳455000;2. 浙江广厦建设职业技术大学智能制造学院，浙江金华322100

秦绪明（1981—），男，吉林辉南人，安阳师范学院物理与电气工程学院讲师，博士，主要从事物理教学和材料计算研究工作.

收稿日期: 2022-01-19

修回日期: 2022-04-14

网络出版日期: 2023-02-16

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Strict proof of the commutation relations between orbital angular momentum operator and vector operator as well as scalar operator

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1. School of Physics and Electrical Engineering, Anyang Normal University, Anyang, Henan 455000, China;
2. School of Intelligent Manufacturing, Zhejiang Guangsha Vocational and Technical University of construction, Jinhua, Zhejiang 322100, China

Received date: 2022-01-19

Revised date: 2022-04-14

Online published: 2023-02-16

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摘要

本文利用矢量算符和标量算符在空间发生旋转时的变换特性，证明了轨道角动量算符与矢量算符及标量算符的对易关系，并构造了几个具体的标量算符和矢量算符，对此对易关系进行验证. 最后还讨论了矢量算符和标量算符的定义.

关键词： 角动量算符; 矢量算符; 标量算符; 对易关系

本文引用格式

秦绪明, 康东彪, 郝红军, 赵冬秋, 张希威 . 轨道角动量算符与矢量算符及标量算符对易关系的严格证明[J]. 大学物理, 2022 , 41(12) : 12 . DOI: 10.16854/j.cnki.1000-0712.220022

Abstract

Using the transformation characteristics of vector operator and scalar operator when space is rotated, this paper strictly proves the commutation relations between orbital angular momentum operator and vector operator as well as scalar operator, and constructs several specific scalar operators and vector operators to verify the commutation relations. Finally, the definitions of vector operator and scalar operator are discussed.

Key words： angular momentum operator; vector operator; scalar operator; commutation relations

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