{"title":"ON BOUNDARY CONDITIONS AND THE RIGGED HILBERT SPACE FORMALISM OF QUANTUM MECHANICS","authors":"Nadia Boudi, Zakariae Ennadifi","doi":"10.1016/S0034-4877(23)00025-3","DOIUrl":null,"url":null,"abstract":"<div><p><span>We discuss canonical rigged Hilbert space constructions. We focus on cyclic self-adjoint operators and use the one-dimensional free </span>Hamiltonian<span><span> on the half-line as a model. We propose a nonstandard construction that can be generalized to many quantum systems. Our construction is motivated by the Stone–von Neumann </span>uniqueness theorem.</span></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"91 2","pages":"Pages 199-217"},"PeriodicalIF":1.0000,"publicationDate":"2023-04-01","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/S0034487723000253","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}
引用次数: 0
Abstract
We discuss canonical rigged Hilbert space constructions. We focus on cyclic self-adjoint operators and use the one-dimensional free Hamiltonian on the half-line as a model. We propose a nonstandard construction that can be generalized to many quantum systems. Our construction is motivated by the Stone–von Neumann uniqueness theorem.
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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