Rationally extended potentials and Xm-Jacobi–type solutions of the two-dimensional massless Dirac equation

We present closed-form solutions of the two-dimensional massless Dirac equation for hyperbolic potentials that are rationally extended in terms of Xm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ X_{m}$\end{document}-Jacobi polynomials. Our method of construction is based on rational extensions of nonrelativistic Scarf and Pöschl-Teller models that include PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {PT}$\end{document}-symmetric and energy-dependent cases.