Supersymmetric analysis for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions

TL;DR

This paper applies supersymmetric quantum mechanics to analyze the Dirac equation with specific symmetric potentials, deriving explicit solutions for Coulomb and Kratzer potentials in multiple dimensions.

Contribution

It introduces explicit shift operators for the Dirac Hamiltonian under spin and pseudo-spin symmetry regimes, enabling exact solutions for certain potentials.

Findings

Derived explicit shift operators for the Dirac Hamiltonian.

Obtained exact solutions for Coulomb and Kratzer potentials.

Extended analysis to d-dimensional Dirac equations.

Abstract

A supersymmetric analysis is presented for the d-dimensional Dirac equation with central potentials under spin-symmetric (S(r) = V(r)) and pseudo-spin-symmetric (S(r) = - V(r)) regimes. We construct the explicit shift operators that are required to factorize the Dirac Hamiltonian with the Kratzer potential. Exact solutions are provided for both the Coulomb and Kratzer potentials.