Relativistic shape invariant potentials

TL;DR

This paper develops relativistic extensions of shape invariant potentials within the Dirac equation framework, deriving spectra and wavefunctions that generalize well-known nonrelativistic potentials like Rosen-Morse and Eckart.

Contribution

It introduces relativistic shape invariant potentials and provides exact solutions for their spectra and wavefunctions, extending classical potentials into the relativistic domain.

Findings

Derived relativistic spectra and wavefunctions for shape invariant potentials.

Reproduces classical potentials in the nonrelativistic limit.

Provides a framework for relativistic quantum potential models.

Abstract

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the relativistic spectra and spinor wavefunctions for all potentials in one of these classes. The nonrelativistic limit reproduces the usual Rosen-Morse I & II, Eckart, Poschl-Teller, and Scarf potentials.