Relativistic generalization of the Saxon‐Hutner theorem

Abstract

Abstract It is shown how a delta potential can be replaced by appropriate boundary conditions for the wave function for the one‐dimensional Dirac equation. This technique is used to derive en explicit expression for the transfer matrix in the case of a linear chain of such potentials. Luttinger's proof of the Saxon‐Hutner theorem on band gaps is extended to the relativistic case by introducing necessary modifications.