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 $(\lambda )$ 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 $\lambda \to 0$ 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.