Energy Power Series Analysis of the Bound States of the One-dimensional Dirac Equation

Abstract In this work we consider the one-dimensional Dirac equation including an electrostatic potential with compact support, and focus on regime of bound states. We obtain exact expressions for both characteristic function eigenfunctions in L 2 (ℝ, ℂ ), given form power series energy parameter. This approach is meant arbitrary bounded potentials, so that a square special case theory here presented. derive efficient numerical method calculation approximate eigen-energies Finally, investigate physical sense are forbidden non-relativistic terms Klein tunneling.