# Comment on 'Two-dimensional position-dependent massive particles in the presence of magnetic fields"

## TL;DR

This paper critiques and corrects the treatment of two-dimensional position-dependent mass particles in magnetic fields, specifically addressing inaccuracies in prior work and providing proper minimal coupling formulation.

## Contribution

It identifies and corrects errors in previous analyses of PDM particles in magnetic fields, offering a proper treatment of minimal coupling in this context.

## Key findings

- Corrected the treatment of minimal coupling for PDM in magnetic fields
- Highlighted inaccuracies in prior solutions and provided proper formulations
- Clarified the application of PDM von Roos Hamiltonian in magnetic environments

## Abstract

Using the well known position-dependent mass (PDM) von Roos Hamiltonian, Dutra and Oliveira (2009 J. Phys. A: Math. Theor. 42 025304) have studied the problem of two-dimensional PDM particles in the presence of magnetic fields. They have reported exact solutions for the wavefunctions and energies. In the first part of their study "PDM-Shr\"odinger equation in two-dimensional Cartesian coordinates", they have used the so called Zhu and Kroemer's ordering {\alpha}=-1/2={\gamma} and \b{eta}=0 <cite>5</cite>. While their treatment for this part is correct beyond doubt, their treatment of second part "PDM in a magnetic field" is improper . We address these improper treatments and report the correct presentation for minimal coupling under PDM settings.