Dirac Equation in the Presence of Hartmann and Ring-Shaped Oscillator Potentials

TL;DR

This paper derives exact relativistic solutions of the Dirac equation for Hartmann and Ring-Shaped oscillator potentials, comparing them with non-relativistic models to analyze energy spectra and parameter restrictions.

Contribution

It provides new exact solutions for the Dirac equation with specific potentials, linking relativistic and non-relativistic quantum models.

Findings

Exact solutions for Dirac equation with specified potentials

Comparison of relativistic and non-relativistic parameter restrictions

Insights into energy spectrum limitations in relativistic quantum systems

Abstract

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation obtained by Dirac equation with the non-relativistic solvable models is the most efficient methods. By this technique, the exact relativistic solutions of Dirac equation for Hartmann and Ring-Shaped oscillator potentials are accessible, when the scalar potential equals to the vector potential. Using solvable non-relativistic quantum mechanics systems as a basic model and considering the physical conditions provide the changes in the restrictions of relativistic parameters based on the non-relativistic definitions of parameters.