具有超二次方和球对称势的薛定谔方程基本解的非平稳性

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-07-19 DOI:10.1063/5.0184443

Keiichi Kato, Wataru Nakahashi, Yukihide Tadano

{"title":"具有超二次方和球对称势的薛定谔方程基本解的非平稳性","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 &gt; 0 and ɛ &gt; 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":"{\"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 &gt; 0 and ɛ &gt; 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}","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}

引用次数: 0

摘要

我们研究了具有球对称超二次势的薛定谔方程基本解的非光滑性，即在无穷远处 V(x) ≥ C|x|2+ɛ 且常数 C > 0 和 ɛ > 0。更确切地说，我们证明了基本解 E(t, x, y) 作为 (t, x, y) 的函数不属于 C1，从而部分解决了矢岛猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Non-smoothness of the fundamental solutions for Schrödinger equations with super-quadratic and spherically symmetric potential

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.