Abstract
A method is presented for the calculation of the one-electron Green function of the periodic lattice. The method depends on knowledge of the pseudopotential matrix element of the periodic lattice potential in the momentum representation and essentially inverts the matrix (E-H)-1. The matrix elements of G in the momentum representation are evaluated and graphs are presented for the case of germanium and silicon. They are found to have extrema at the symmetry points of the Brillouin zone. The matrix elements of G(r,r') are also evaluated numerically for the case of r=r=0 and enable the binding energy of a short range potential to be calculated. This can be regarded as an extension of Koster-Slater theory from a one band to a many band model.