Solution of the relativistic Dirac-Morse problem

TL;DR

This paper derives a relativistic version of the Morse potential within the Dirac equation framework, providing new solutions for bound states and wavefunctions in a spherically symmetric electromagnetic field.

Contribution

It introduces a relativistic Dirac-Morse potential by adding an exponential term, extending the Dirac equation solutions beyond Coulomb and oscillator cases.

Findings

Derived relativistic bound state spectrum

Obtained explicit spinor wavefunctions

Reproduces Morse potential in nonrelativistic limit

Abstract

Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version of the S-wave Morse potential. This is accomplished by adding a simple exponential potential term to the Dirac operator, which in the nonrelativistic limit reproduces the usual Morse potential. The relativistic bound states spectrum and spinor wavefunctions are obtained.