Solutions of one-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry

Abstract

We consider one-dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Pöschl-Teller potentials and obtain their solution in terms of exceptional orthogonal polynomials. Further, in the case of the trigonometric Scarf and the hyperbolic Pöschl-Teller cases, a new family of Dirac scalar potentials is generated using the idea of parametric symmetry and their solutions are obtained in terms of conventional as well as exceptional orthogonal polynomials. © 2023 World Scientific Publishing Company.