Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

TL;DR

This paper solves the Dirac-Coulomb problem with a position-dependent mass using the asymptotic iteration method, deriving eigenfunctions in hypergeometric form to explore bound states.

Contribution

It introduces a novel approach to solving the Dirac equation with spatially varying mass using AIM, providing explicit eigenfunctions for bound states.

Findings

Eigenfunctions expressed in hypergeometric functions

Bound state energies calculated for position-dependent mass

Method demonstrates effectiveness for Coulomb potentials with variable mass

Abstract

The bound state solution of Coulomb Potentials in the Dirac equation is calculated for position dependent mass function M(r) within the framework of asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equation of AIM.