On the calculation of the energy of a Bloch wave in a metal
Abstract
General formulae for the calculation of the energy E( k) of a Bloch wave with reduced wave vector k are obtained by the application of the dynamical theory of lattice interferences to electron waves. This method requires the computation of the zeros of an infinite determinant which in fair approximation might be replaced by a determinant with a few rows and columns only. Its elements are the sum of two functions, a function of E and k, resulting from interference of multipole waves of free electrons (and therefore independent of the lattice potential), and a function of E only, resulting from scattering of free electron waves by the field around one atom. Of the latter terms only those in the principal diagonal are of importance.
 Publication:

Physica
 Pub Date:
 August 1947
 DOI:
 10.1016/00318914(47)90013X
 Bibcode:
 1947Phy....13..392K