# Solutions of the three-dimensional radial Dirac equation from the Schr\"odinger equation with one-dimensional Morse potential

## TL;DR

This paper derives exact solutions for the 3D radial Dirac equation by mapping it onto the Schrödinger equation with Morse potential, unifying various known results including the Dirac oscillator.

## Contribution

It introduces a unified method to solve the radial Dirac equation using the nonrelativistic Morse potential solutions, providing new analytical bound-state solutions.

## Key findings

- Eigenfunctions in terms of generalized Laguerre polynomials
- Eigenenergies from polynomial equations
- Recovery of known results like the Dirac oscillator

## Abstract

New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of equations that can be transformed into polynomial equations. Several analytical results found in the literature, including the Dirac oscillator, are obtained as particular cases of this unified approach.