Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry

TL;DR

This paper solves the 1+1-dimensional Dirac equation with extended scalar potentials linked to exceptional orthogonal polynomials, introducing new potentials via parametric symmetry and providing explicit solutions.

Contribution

It presents solutions to the Dirac equation with rationally extended potentials and introduces new scalar potentials using parametric symmetry, expanding the class of solvable models.

Findings

Explicit solutions for Dirac equation with extended potentials

Introduction of new scalar potentials via parametric symmetry

Solutions expressed in terms of exceptional orthogonal polynomials

Abstract

We consider $1+1$-dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Poschl-Teller potentials and obtain their solution in terms of exceptional orthogonal polynomials. Further, in the case of the trigonometric Scarf and the hyperbolic Poschl-Teller cases, new family of Dirac scalar potentials are generated using the idea of parametric symmetry and their solutions are obtained in terms of conventional as well as exceptional orthogonal polynomials.