The Relativistic Dirac-Morse Green's function

TL;DR

This paper derives the Green's function for the relativistic Dirac-Morse problem using a new approach, enabling straightforward extraction of bound state energies and facilitating comparison with the nonrelativistic case.

Contribution

It introduces a novel method for solving the Dirac equation with Morse potential, providing explicit Green's function and energy spectrum analysis.

Findings

Green's function for the relativistic Dirac-Morse problem is explicitly obtained.

Bound state energies are efficiently determined from the Green's function poles.

The approach allows clear comparison between relativistic and nonrelativistic solutions.

Abstract

Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain the two-point Green's function of the relativistic Dirac-Morse problem. This is accomplished by setting up the relativistic problem in such a way that makes comparison with the nonrelativistic problem highly transparent and results in a mapping of the latter into the former. The relativistic bound states energy spectrum is easily obtained by locating the energy poles of the Green's function components in a simple and straightforward manner.