One continuous parameter family of Dirac Lorentz scalar potentials associated with exceptional orthogonal polynomials

TL;DR

This paper introduces a one-parameter family of extended Dirac scalar potentials linked to exceptional orthogonal polynomials, revealing connections to known potentials as the parameter varies.

Contribution

It constructs a new one-parameter family of rationally extended Dirac scalar potentials using exceptional orthogonal polynomials, expanding the class of solvable models.

Findings

Derived explicit solutions in terms of $X_{m}$ exceptional orthogonal polynomials.

Showed the potential reduces to known types (Pursey and Abraham-Moses) at specific parameter values.

Identified the number of bound states decreases with potential extensions.

Abstract

We extend our recent works [ Int. J. Mod. Phys. A 38 (2023) 2350069-1] and obtain one parameter $(\lambda)$ family of rationally extended Dirac Lorentz scalar potentials with their explicit solutions in terms of $X_{m}$ exceptional orthogonal polynomials. We further show that as the parameter $\lambda \rightarrow 0$ or $-1$, we get the corresponding rationally extended Pursey and the rationally extended Abraham-Moses type of scalar potentials respectively, which have one bound state less than the starting scalar potentials.