{"title":"New Wine in Old Bottle: An Improved Perspective on the Greene-Aldrich Approximation for the Generalized Pöschl-Teller Potential","authors":"P. Rajesh Kumar","doi":"10.1007/s11182-024-03234-w","DOIUrl":null,"url":null,"abstract":"<p>The generalized Pöschl–Teller potential is well-known and is widely applied in molecular physics, chemistry, and nonlinear physics. In the past, when the vintage Greene–Aldrich approximation scheme for the centrifugal potential of the generalized Pöschl–Teller potential was examined, the consensus was that it would break down or become unreliable for large values of the potential parameter α. However, this study challenges that perspective by reviewing the problem in a new light and proposing a new and improved Greene–Aldrich approximation that mitigates the breakdown effect. Additionally, it is demonstrated that the energy eigenvalues produced for short and long-range potentials are in considerably closer agreement with those obtained using the numerical integration method than with the results of earlier research.</p>","PeriodicalId":770,"journal":{"name":"Russian Physics Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Physics Journal","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11182-024-03234-w","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The generalized Pöschl–Teller potential is well-known and is widely applied in molecular physics, chemistry, and nonlinear physics. In the past, when the vintage Greene–Aldrich approximation scheme for the centrifugal potential of the generalized Pöschl–Teller potential was examined, the consensus was that it would break down or become unreliable for large values of the potential parameter α. However, this study challenges that perspective by reviewing the problem in a new light and proposing a new and improved Greene–Aldrich approximation that mitigates the breakdown effect. Additionally, it is demonstrated that the energy eigenvalues produced for short and long-range potentials are in considerably closer agreement with those obtained using the numerical integration method than with the results of earlier research.
期刊介绍:
Russian Physics Journal covers the broad spectrum of specialized research in applied physics, with emphasis on work with practical applications in solid-state physics, optics, and magnetism. Particularly interesting results are reported in connection with: electroluminescence and crystal phospors; semiconductors; phase transformations in solids; superconductivity; properties of thin films; and magnetomechanical phenomena.