Modified local density approximation for disordered potential arrays

The work described is relative to the problem of state densities in semi-conductors near a gap edge. The local density approximation (LDA) is explained and modifications to its original form described. In the linear chain, choice of the appropriate sub-chain length as the 'beat length', already shown to determine the range of a localized state, results in an unambiguous expression for the density of states N(E). An excellent fit is obtained to Monte Carlo results. The phenomenon of the 'locking' of psi to the well distribution is shown to exist in three dimensions, and the consequent applicability of the LDA to amorphous materials is argued for.