{"title":"Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential","authors":"Keiichi Kato, Wataru Nakahashi, Yukihide Tadano","doi":"10.1063/5.0184443","DOIUrl":null,"url":null,"abstract":"We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sense that V(x) ≥ C|x|2+ɛ at infinity with constants C > 0 and ɛ > 0. More precisely, we show the fundamental solution E(t, x, y) does not belong to C1 as a function of (t, x, y), which partially solves Yajima’s conjecture.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"36 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-19","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/10.1063/5.0184443","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}
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Abstract
We study non-smoothness of the fundamental solution for the Schrödinger equation with a spherically symmetric and super-quadratic potential in the sense that V(x) ≥ C|x|2+ɛ at infinity with constants C > 0 and ɛ > 0. More precisely, we show the fundamental solution E(t, x, y) does not belong to C1 as a function of (t, x, y), which partially solves Yajima’s conjecture.
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