Supersymmetric Solutions of D-Dimensional Dirac Equation for Woods-Saxon Potential in Minimal Length Formalism

TL;DR

This paper derives energy levels and wave functions for the D-dimensional Dirac equation with Woods-Saxon potential in a minimal length framework, using supersymmetric quantum mechanics and Pekeris approximation.

Contribution

It introduces a novel approach to solving the Dirac equation with Woods-Saxon potential in minimal length formalism using supersymmetric methods.

Findings

Energy eigenvalues depend on dimension and quantum numbers.

Bound-state energies vary with minimal length parameters.

Method effectively handles centrifugal terms in high dimensions.

Abstract

We obtain the energy eigenvalues and radial wave functions of the D-Dimensional Dirac equation in the case of spin symmetry for Woods-Saxon potential in minimal length formalism. The radial part of the D-Dimensional Dirac equation is solved by applied the supersymmetric quantum mechanics method using the Pekeris approximation to deal with the centrifugal term. The behavior of bound-state energy eigenvalues versus dimension and also quantum number is discussed for various minimal length parameters.