Darboux transformations for Dunkl-Schroedinger equations with energy dependent potential and position dependent mass

TL;DR

This paper develops a method to generate solvable Dunkl-Schroedinger equations with energy-dependent potentials and position-dependent mass using Darboux transformations, linking them to standard Schroedinger equations.

Contribution

It introduces a systematic construction of Darboux transformations for complex Dunkl-Schroedinger equations, expanding solvable models in quantum mechanics.

Findings

Constructed arbitrary-order Darboux transformations for Dunkl-Schroedinger equations.

Linked complex equations to standard Schroedinger equations via point transformations.

Generated several new solvable Dunkl-Schroedinger models.

Abstract

We construct arbitrary-order Darboux transformations for Schroedinger equations with energy-dependent potential and position-dependent mass within the Dunkl formalism. Our construction is based on a point transformation that interrelates our equations with the standard Schroedinger case. We apply our method to generate several solvable Dunkl-Schroedinger equations.