Generalized Darboux algorithms for Dunkl–Schrödinger equations with position-dependent mass at fixed energy

Abstract

We apply generalized Darboux transformations to Schrödinger equations at fixed energy that contain Dunkl derivatives, and are equipped with a position-dependent mass. Our Darboux transformations, originating from coupled Korteweg–De Vries systems, consist of two algorithms that generate new solutions, potentials and position-dependent mass functions for the Dunkl–Schrödinger system.