{"title":"No eigenvectors embedded in the singular continuous spectrum of Schrödinger operators","authors":"Kota Ujino","doi":"10.1007/s13324-024-00948-5","DOIUrl":null,"url":null,"abstract":"<div><p>In general a Schrödinger operator with a sparse potential has singular continuous spectrum, and some open interval is purely singular continuous spectrum. We give a sufficient condition so that the endpoint of the open interval is not an eigenvalue. An example of a Schrödinger operator with a negative sparse potential on the half-line which has no nonnegative embedded eigenvalue for any boundary conditions is given.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00948-5","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In general a Schrödinger operator with a sparse potential has singular continuous spectrum, and some open interval is purely singular continuous spectrum. We give a sufficient condition so that the endpoint of the open interval is not an eigenvalue. An example of a Schrödinger operator with a negative sparse potential on the half-line which has no nonnegative embedded eigenvalue for any boundary conditions is given.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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