DARBOUX partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials

TL;DR

This paper presents a method to construct Darboux pairs of pseudoscalar and scalar Dirac potentials linked with exceptional orthogonal polynomials, including applications to extended radial oscillator models.

Contribution

It introduces a novel approach for generating Darboux partner potentials in Dirac equations using exceptional orthogonal polynomials, expanding the toolkit for quantum potential design.

Findings

Constructed Darboux partner potentials for Dirac equations.

Analyzed properties and regularity conditions of the transformed potentials.

Applied the method to the rationally extended radial oscillator model.

Abstract

We introduce a method for constructing Darboux (or supersymmetric) pairs of pseudoscalar and scalar Dirac potentials that are associated with exceptional orthogonal polynomials. Properties of the transformed potentials and regularity conditions are discussed. As an application, we consider a pseudoscalar Dirac potential related to the Schroeodinger model for the rationally extended radial oscillator. The pseudoscalar partner potentials are constructed under first- and second-order Darboux transformations.