Relativistic Killingbeck Energy States Under an External Magnetic Fields

TL;DR

This paper investigates the relativistic Dirac equation with Killingbeck potential under magnetic and Aharonov-Bohm flux fields, deriving bound state spectra and wave functions considering spin symmetries.

Contribution

It provides a novel analytical solution to the Dirac equation with Killingbeck potential in external magnetic fields using the biconfluent Heun method, including spin and pseudo-spin symmetry analysis.

Findings

Spectra are similar under spin and pseudo-spin symmetries with slight energy differences.

Bound state energies and wave functions are explicitly obtained.

Results can be reduced to non-relativistic forms.

Abstract

We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries, are very similar with a slight difference in energy spacing between different states.