Wave functions in disordered systems

Particular solutions of the stationary Schrödinger equation for ad-dimensional disordered tight binding model are found. The particular solution is defined by boundary conditions on one face of the system. The determination of the rate of growth of the mean square wave function leads to an exactly soluble eigenvalue problem ind – 1 dimensions. Ford 2 there are three types of particular wave functions in which the mean square amplitude (a) grows exponentially (b) decays exponentially (c) does not grow or decay but oscillates.Supported in part by the National Science Foundation under grant No. DMR 78-10276.