{"title":"Inverse scattering for repulsive potential and strong singular interactions","authors":"Atsuhide Ishida","doi":"10.1063/5.0215713","DOIUrl":null,"url":null,"abstract":"In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator consisting of regular and singular parts. In this paper, the singular part is assumed to have much stronger singularities and the same uniqueness theorem is proved. By applying the time-dependent method invented by Enss and Weder [J. Math. Phys. 36(8), 3902–3921 (1995)], the high-velocity limit for a wider class of the scattering operator with stronger singularities also uniquely determines the interactions of a multi-dimensional system.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"11 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1063/5.0215713","RegionNum":3,"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
In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator consisting of regular and singular parts. In this paper, the singular part is assumed to have much stronger singularities and the same uniqueness theorem is proved. By applying the time-dependent method invented by Enss and Weder [J. Math. Phys. 36(8), 3902–3921 (1995)], the high-velocity limit for a wider class of the scattering operator with stronger singularities also uniquely determines the interactions of a multi-dimensional system.
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