A RELATIVISTIC EQUATION FOR A SLOWLY VARYING POTENTIAL

A relativistic equation is derived for a slowly varying potential by s uitably approximating the one-dimensional Dirac equation. This equatio n is shown to be akin to the Schrodinger equation with an effective po tential and effective eigenvalues. An iterative procedure for solving this equation is indicated. As an application, the relativistic treatm ent of the Mathieu potential on the basis of this equation is consider ed and results are compared with those obtained by solving the exact o ne-dimensional Dirac equation. These results are likely to take adequa te account of the relativistic impacts on electrons near Fermi levels in metals.