{"title":"Periodic potentials and PT symmetry","authors":"A. Khare, U. Sukhatme","doi":"10.1088/0305-4470/39/32/S14","DOIUrl":null,"url":null,"abstract":"We enlarge the limited class of analytically solvable one-dimensional periodic potentials with a finite number of band gaps by considering the complex, PT-symmetric generalized associated Lamé (GAL) potential with four parameters and applying supersymmetry. We obtain three duality relations which relate the band-edge eigenstates of the twenty four GAL potentials obtained by permutation of the four parameters.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/32/S14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
We enlarge the limited class of analytically solvable one-dimensional periodic potentials with a finite number of band gaps by considering the complex, PT-symmetric generalized associated Lamé (GAL) potential with four parameters and applying supersymmetry. We obtain three duality relations which relate the band-edge eigenstates of the twenty four GAL potentials obtained by permutation of the four parameters.