LOCALIZATION FOR RANDOM SCHRODINGER-OPERATORS WITH POISSON POTENTIAL

Localization at all energies is proved for the one-dimensional random Schrodinger operator with Poisson potential Sigma(j) f (x - X(j)(omega)). The single site potential f is assumed to be non-negative and compactly supported. The result holds for arbitrary density of the Poisson process. Eigenfunctions decay exponentially at the rate of the Lyapunov exponent. Crucial to the proof is a new result on spectral averaging.