A transfer-matrix method for the determination of one-dimensional band structures

Abstract

We show that the discretized forms of the Schrodinger and the Dirac equations for an arbitrary potential in one dimension are equivalent to the Poincare map of the corresponding wave equation for an array of delta-function potentials. Therefore, the dynamics of particles in general periodic potentials may be studied by means of an equivalent generalized Kronig-Penney model, in which there exist several delta-function potentials in each unit cell. Taking into account the techniques of dynamical systems, the transfer matrix method is then used in a simple form to compute the energy band edges and the dispersion law inside the allowed bands.