Construction of angular-dependent potentials from trigonometric Pöschl-Teller systems within the Dunkl formalism

Axel Schulze-Halberg

doi:10.14311/AP.2023.63.0273

Authors

Axel Schulze-Halberg Indiana University Northwest, Department of Mathematics and Acturial Science and Department of Physics, 3400 Broadway, Gary IN 46408, United States of America

DOI:

https://doi.org/10.14311/AP.2023.63.0273

Keywords:

Dunkl operator, Schrodinger equation, trigonometric Poschl-Teller potential, angular equation, Darboux-Crum transformation

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.

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