Relativistic treatment of localized states. A review

Abstract

Based on the solution of the Dirac equation for the appropriately modified Kronig–Penney potential, an overall picture is given of the relativistic theory of localized surface and impurity states. Emphasis is placed on the important aspects of the theory, such as the discussion of the accurate and approximate continuity conditions and their use in deriving the localized state energy and existence expressions. The article concludes with a comparative study of the classification of the localized states into their relativistic and Dirac species.