Wave propagation through an assembly of spheres: II. The density of single-particle eigenstates

Abstract

Edwards' formalism for the density of single-particle eigenstates in a system of random scattering centres is not valid if the true potential is replaced by an energy-dependent pseudo-potential. When the system is such that the scattering potentials do not overlap, the density of states may be expressed in a form which involves the scattering phase shifts and the positions of the scatterers rather than the potential. The resulting formalism for the density of states of such a system is a generalization of the Green function method for determining band structure, and reduces to it for a regular lattice.