Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry

Abstract

We consider $1+1$-dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Poschl-Teller potentials and obtain their solution in terms of exceptional orthogonal polynomials. Further, in the case of the trigonometric Scarf and the hyperbolic Poschl-Teller cases, new family of Dirac scalar potentials are generated using the idea of parametric symmetry and their solutions are obtained in terms of conventional as well as exceptional orthogonal polynomials.

24 pages, 10 figures, LaTex

References in corpus (6)

• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Exceptional orthogonal polynomials and the Darboux transformation
• Dirac Hamiltonian in a supersymmetric framework
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials
• DARBOUX partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials
• Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential