Quantum systems with position-dependent effective mass and equispaced energy levels: New exact results and test of a perturbation scheme

Abstract

We use SUSY QM to obtain exact expressions for the potential and eigenfunctions of a quantum system with position dependent effective mass exhibiting equispaced energy levels similar to those seen in the harmonic oscillator spectra for the constant mass case. These expressions were only implicitly stated in previous works and for a specific mass function. We then obtained expressions of the potential and eigenfunctions for perturbed mass function, and show that it converges rapidly to exact results for the specific mass function provided before.