Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schroedinger Hamiltonians

TL;DR

This paper constructs exactly solvable quantum potentials with position-dependent mass, whose bound states are described by exceptional orthogonal polynomials, extending classical solutions and maintaining shape invariance.

Contribution

It introduces new exactly solvable potentials in position-dependent mass systems using exceptional orthogonal polynomials, demonstrating their shape invariance and isospectrality.

Findings

Bound states expressed via Laguerre- or Jacobi-type exceptional polynomials

Potentials are shape invariant and isospectral to classical polynomial-based potentials

Extension of solvable models in quantum mechanics with position-dependent mass

Abstract

Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials. These potentials are shown to be shape invariant and isospectral to the potentials whose bound state solutions involve classical Laguerre or Jacobi polynomials.