教学研究

量子力学角动量算符的压缩态表象

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  • 1. 武夷学院机电工程学院,福建武夷山354300;2. 中国科学技术大学材料科学与工程系,安徽合肥230026
展德会(1979—),男,山东泰安人,武夷学院机电工程学院副教授,博士,主要从事大学物理教学和量子光学、量子信息研究工作.
展德会,E-mail: dhzhan@mail.ustc.edu.cn

收稿日期: 2023-06-24

  修回日期: 2023-12-27

  网络出版日期: 2024-11-12

基金资助

武夷学院引进人才科研启动经费项目(YJ201808)资助

Squeezed state representation of angular momentum operators in quantum mechanics

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  • 1. College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300,china;
    2. Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Received date: 2023-06-24

  Revised date: 2023-12-27

  Online published: 2024-11-12

摘要

我们注意到角动量上升、下降算符在绕第三轴的转动变换下呈现压缩变换的特性,故而对照双模压缩变换的特性寻求角动量算符的新的玻色算符实现. 通过建立量子力学两体纠缠态表象后,我们发现了一类新的玻色实现,从而可以用压缩的观点来表述量子转动.我们还研究了在这种表示下角动量上升、下降算符对纠缠态表象作用的结果和应用.这说明在量子力学课堂教育中,引入纠缠态表象是必要的.按照本文的思路,还可以构建多粒子纠缠态表象并发现角动量的多模玻色实现.

本文引用格式

展德会, 范洪义 . 量子力学角动量算符的压缩态表象[J]. 大学物理, 2024 , 43(9) : 9 . DOI: 10.16854/j.cnki.1000-0712.230237

Abstract

We notice that the angular momentum raising and lowering operators exhibit squeezing transformation property under rotating around the third axis, so we compare this with two-mode squeezing operator to find new Bose realization of angular momentum operators. By observing the quantum mechanical bipartite entangled state representation,we find the new Bose realization of angular momentum operators, which enables us to view quantum rotation as squeezing. We also study the new raising and lowering operators’ character in the entangled state representation. This shows that the entangled state representation is of necessity to teaching quantum mechanics. We expect that new multi-partite entangled state representation can be constructed and multi-mode Bose realization of angular momentum operator can be found.


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