Exactly solvable model of electronic states in a three-dimensional disordered Hamiltonian: non-existence of localized states

An exactly solvable model of a disordered Hamiltonian, valid in three dimensions, is presented. The ensemble-averaged Green function, and hence the density of eigenstates, for the model are found exactly. It is shown that the states in the tail of the distribution are not localized as has been suggested by several authors.