Arbitrary-order Darboux transformations for Dunkl–Schrödinger equations with position-dependent mass

Abstract

We use a symmetrized Hamiltonian containing Dunkl operators to generate a Dunkl–Schrödinger equation with position-dependent mass. Our equation is shown to admit arbitrary-order Darboux transformations if the mass either has odd parity or is an inverse-square function. We construct the Darboux transformations and apply them to a Dunkl–Schrödinger system featuring a rational double well potential.