{"title":"Construction of angular-dependent potentials from trigonometric Pöschl-Teller systems within the Dunkl formalism","authors":"Axel Schulze-Halberg","doi":"10.14311/ap.2023.63.0273","DOIUrl":null,"url":null,"abstract":"We generate solvable cases of the two angular equations resulting from variable separation in the three-dimensional Dunkl-Schrödinger equation expressed in spherical coordinates. It is shown that the Dunkl formalism interrelates these angular equations with trigonometric Pöschl-Teller systems. Based on this interrelation, we use point transformations and Darboux-Crum transformations to construct new solvable cases of the angular equations. Instead of the stationary energy, we use the constants due to the separation of variables as transformation parameters for our Darboux-Crum transformations.","PeriodicalId":45804,"journal":{"name":"Acta Polytechnica","volume":"89 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Polytechnica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14311/ap.2023.63.0273","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We generate solvable cases of the two angular equations resulting from variable separation in the three-dimensional Dunkl-Schrödinger equation expressed in spherical coordinates. It is shown that the Dunkl formalism interrelates these angular equations with trigonometric Pöschl-Teller systems. Based on this interrelation, we use point transformations and Darboux-Crum transformations to construct new solvable cases of the angular equations. Instead of the stationary energy, we use the constants due to the separation of variables as transformation parameters for our Darboux-Crum transformations.
期刊介绍：
Acta Polytechnica is a scientific journal published by CTU in Prague. The main title, Acta Polytechnica, is accompanied by the subtitle Journal of Advanced Engineering, which defines the scope of the journal more precisely - Acta Polytechnica covers a wide spectrum of engineering topics, physics and mathematics. Our aim is to be a high-quality multi-disciplinary journal publishing the results of basic research and also applied research. We place emphasis on the quality of all published papers. The journal should also serve as a bridge between basic research in natural sciences and applied research in all technical disciplines. The innovative research results published by young researchers or by postdoctoral fellows, and also the high-quality papers by researchers from the international scientific community, reflect the good position of CTU in the World University Rankings. We hope that you will find our journal interesting, and that it will serve as a valuable source of scientific information.
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