{"title":"New operator realization of angular momentum for description of electron's motion in uniform magnetic field","authors":"Cheng Da , Hony-Yi Fan","doi":"10.1016/S0034-4877(24)00058-2","DOIUrl":null,"url":null,"abstract":"<div><div>By introducing appropriate electron's coordinate eigenstate and momentum eigenstate we propose new realization of angular momentum operators for describing electron's motion in uniform magnetic field. The coordinate eigenstates make up a representation and embody quantum entanglement between magnetic field and electron. The eigenstate of angular momentum's lowering-ascending operator <strong><em>L</em><sub>±</sub></strong> are derived, the way we tackle this problem is to make an analogue between the transform\n<span><math><mrow><msup><mi>e</mi><mrow><mn>2</mn><mi>f</mi><msub><mi>L</mi><mi>z</mi></msub></mrow></msup><msub><mi>L</mi><mo>±</mo></msub><msup><mi>e</mi><mrow><mo>-</mo><mn>2</mn><mi>f</mi><msub><mi>L</mi><mi>z</mi></msub></mrow></msup></mrow></math></span> to the squeezing mechanism. All these discussions reveal that the quantum theory for charged particles' motion in magnetic field needs to be developed.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 1","pages":"Pages 105-115"},"PeriodicalIF":1.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000582","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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Abstract
By introducing appropriate electron's coordinate eigenstate and momentum eigenstate we propose new realization of angular momentum operators for describing electron's motion in uniform magnetic field. The coordinate eigenstates make up a representation and embody quantum entanglement between magnetic field and electron. The eigenstate of angular momentum's lowering-ascending operator L± are derived, the way we tackle this problem is to make an analogue between the transform
to the squeezing mechanism. All these discussions reveal that the quantum theory for charged particles' motion in magnetic field needs to be developed.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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