The Relativistic Bound States of a Non Central Potential

TL;DR

This paper explores relativistic bound states of a particle in a ring-shaped potential using SUSYQM, deriving energy levels, wave functions, and thermodynamic properties, with numerical results illustrating the findings.

Contribution

It introduces a novel analysis of relativistic bound states in a non-central potential using SUSYQM, including derivation of energy eigenvalues and wave functions.

Findings

Derived relativistic energy eigenvalues and wave functions.

Analyzed non-relativistic limits of the system.

Numerical results demonstrating energy levels.

Abstract

We investigate the relativistic effects of a moving particle in the field of a pseudo-harmonic oscillatory ring-shaped potential under the spin and pseudo-spin symmetric Dirac wave equation. We obtain the bound state energy eigenvalue equation and the corresponding two-components spinor wave functions by using the formalism of Suppersymmetric Quantum Mechanics (SUSYQM). Furthermore, the non-relativistic limits are obtained by simply making a proper replacement of parameters. The thermodynamic properties are shortly studied. Our numerical results for the energy eigenvalues are presented too.