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

Abstract

We construct arbitrary-order Darboux transformations for Schrödinger 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 Schrödinger case. We apply our method to generate several solvable Dunkl-Schrödinger equations.

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

“…An example for such a case is given by the two-dimensional massless Dirac equation at zero energy, where the transformation parameter for the Darboux-Crum transformations is given by the wave number [24]. In another application to the one-dimensional Dunkl-Schrödinger equation, the transformation parameter consists of a constant involving the Dunkl constants [25]. As a result, transformed potentials in the latter reference are dependent on the stationary energy.…”