Emerging 2D isospectral configurations for position-dependent mass quantum systems

TL;DR

This paper introduces a new class of exactly solvable two-dimensional quantum systems with position-dependent masses that are isospectral to constant mass systems, including magnetic field interactions, and explores their coherent states.

Contribution

It constructs a general framework for isospectral PDM quantum systems, including magnetic interactions, and develops SU(2) coherent states for these systems.

Findings

Successfully constructed isospectral PDM systems with magnetic fields

Developed SU(2) coherent states for these systems

Analyzed effects of non-homogeneous magnetic fields

Abstract

In this work we construct a general class of exactly solvable non-relativistic bi-dimensional quantum systems with position-dependent masses (PDM). These systems are isospectral to a given system with constant mass. The case of a charged particle with a PDM interacting with an external magnetic field is included in the present investigation. We apply the approach in order to construct the SU(2) coherent states in some examples which are isospectral to the two-dimensional anisotropic harmonic oscillator, and discuss the impact of the introduction of special non-homogeneous external magnetic fields.