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 (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 $\lambda \to 0$ 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.

LaTeX, 19 pages, 09 figures, 03 tables