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

Abstract

We extend our recent works [Int. J. Mod. Phys. A 38, 2350069 (2023)] and obtain one-parameter [Formula: see text] family of rationally extended Dirac–Lorentz scalar potentials with their explicit solutions in terms of [Formula: see text] exceptional orthogonal polynomials. We further show that as the parameter [Formula: see text] or [Formula: see text], 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.