Bloch waves and scattering by impurities

The reciprocal lattice representation of the Green function method used by Ziman in 1965 for calculating band structures is derived. It is shown that the coefficients ν g introduced by Ziman are the Fourier coefficients of the wave function outside the potential wells of a `muffin tin' lattice. The relationship between the method and the augmented plane wave approach is discussed. An exact formulation of the problem of Bloch wave scattering from an impurity potential is given. Simple approximations are suggested for tightly bound electrons for nearly free electrons and for d-band electrons.