# The relativistic Aharonov-Bohm-Coulomb system with position-dependent mass

## TL;DR

This paper investigates the relativistic Aharonov-Bohm-Coulomb system with a position-dependent mass, deriving eigenfunctions and energy spectra, and analyzing the effects of system parameters on energy levels.

## Contribution

It provides explicit solutions for the eigenfunctions and energy spectrum of a relativistic Dirac particle with PDM in the ABC system, including the effects of key parameters.

## Key findings

- Eigenfunctions are expressed in terms of generalized Laguerre polynomials.
- Energy spectrum depends on parameters Z, Φ_AB, and κ.
- Discrete energy spectrum exists even without ABC system parameters.

## Abstract

In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the left-handed and right-handed projection operators. Next, we explicitly obtain the eigenfunctions and the energy spectrum of the particle. We verify that these eigenfunctions are written in terms of the generalized Laguerre polynomials and the energy spectrum depends on the parameters Z, $\Phi_{AB}$ and $\kappa$. We notice that the parameter $\kappa$ has the function of increasing the values of the energy levels of the system. In addition, the usual ABC system is recovered when one considers the limit of constant mass ($\kappa\to{0}$). Moreover, also we note that even in the absence of ABC system ($Z=\Phi_{AB}=0$), the particle with PDM still has a discrete energy spectrum.