The relativistic Tamm model

Abstract

The exact solution of the one dimensional Dirac equation for an electron in a semi-infinite chain of Kronig-Penney type potentials (Tamm model) is presented. Expressions are derived for the bulk and surface states. It is shown that all the surface states obtained are simply relativistically corrected Tamm states. This is contrary to the prediction of Davison et al (1969-71) that a relativistic calculation yields a new type of states (called by them Dirac surface states) having no analogue in the nonrelativistic treatment of the problem. The discrepancy is explained.