{"title":"具有非光滑周期势的schrÖdinger方程的微扰理论公式","authors":"Yulia Karpeshina","doi":"10.1070/SM1992V071N01ABEH002127","DOIUrl":null,"url":null,"abstract":"Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schr?dinger operator in . An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"PERTURBATION THEORY FORMULAS FOR THE SCHRÖDINGER EQUATION WITH A NONSMOOTH PERIODIC POTENTIAL\",\"authors\":\"Yulia Karpeshina\",\"doi\":\"10.1070/SM1992V071N01ABEH002127\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schr?dinger operator in . An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V071N01ABEH002127\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V071N01ABEH002127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
PERTURBATION THEORY FORMULAS FOR THE SCHRÖDINGER EQUATION WITH A NONSMOOTH PERIODIC POTENTIAL
Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schr?dinger operator in . An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.
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