The Dirac-Oscillator Green's function

TL;DR

This paper derives the Green's function for the relativistic Dirac-Oscillator, enabling straightforward determination of bound state energies and providing a clear comparison with the nonrelativistic case.

Contribution

It presents a novel method to obtain the Dirac-Oscillator Green's function, linking relativistic and nonrelativistic problems transparently.

Findings

Explicit form of the Dirac-Oscillator Green's function

Simplified calculation of relativistic bound state energies

Clear mapping between relativistic and nonrelativistic problems

Abstract

We obtain the two-point Green's function for the relativistic Dirac-Oscillator 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 map of the latter into the former. The relativistic bound states energy spectrum is obtained by locating the energy poles of this Green's function in a simple and straightforward manner.