{"title":"对称双阱势Hill方程的本征函数","authors":"A. Kabataş","doi":"10.31801/cfsuasmas.974409","DOIUrl":null,"url":null,"abstract":"Throughout this paper the asymptotic approximations for eigen- functions of eigenvalue problems associated with Hill’s equation satisfying periodic and semi-periodic boundary conditions are derived when the potential is symmetric double well. These approximations are used to determine the Green’s functions of the related problems. Then, the obtained results are adapted to the Whittaker-Hill equation which has the symmetric double well potential and is widely investigated in the literature.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On eigenfunctions of Hill's equation with symmetric double well potential\",\"authors\":\"A. Kabataş\",\"doi\":\"10.31801/cfsuasmas.974409\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Throughout this paper the asymptotic approximations for eigen- functions of eigenvalue problems associated with Hill’s equation satisfying periodic and semi-periodic boundary conditions are derived when the potential is symmetric double well. These approximations are used to determine the Green’s functions of the related problems. Then, the obtained results are adapted to the Whittaker-Hill equation which has the symmetric double well potential and is widely investigated in the literature.\",\"PeriodicalId\":44692,\"journal\":{\"name\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31801/cfsuasmas.974409\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.974409","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On eigenfunctions of Hill's equation with symmetric double well potential
Throughout this paper the asymptotic approximations for eigen- functions of eigenvalue problems associated with Hill’s equation satisfying periodic and semi-periodic boundary conditions are derived when the potential is symmetric double well. These approximations are used to determine the Green’s functions of the related problems. Then, the obtained results are adapted to the Whittaker-Hill equation which has the symmetric double well potential and is widely investigated in the literature.