Conditionally exactly solvable Dirac potential, including x 1/3 pseudoscalar interaction

Abstract

Abstract We study the solution of the 1D Dirac equation for a pseudoscalar potential, which includes an interaction term proportional to x 1 / 3 and a ~ 1 / x term with a fixed strength. This is a conditionally exactly solvable singular potential, symmetric with respect to the origin. A feature of the potential is that the effective potential for the Schrödinger equation, to which the Dirac equation can be reduced, splits into two known potentials: the first Stillinger potential and the second Exton potential for the positive and negative semiaxes, respectively. We present the solution and analyze the energy spectrum and wave functions of the bound states. Our results reveal notable differences between the Schrödinger and Dirac behaviors.