Non-monotonic random Schrodinger operators: The Anderson model

We prove exponential localization at all energies for one-dimensional conti nuous Anderson-type models with single site potentials of changing sign. A periodic background potential is allowed. The main problem arises from non- monotonicity; i.e., the operator does not depend monotonically in the form sense on the random parameters. We show that the method of "two-parameter s pectral averaging," recently devised by Buschmann and Stolz to prove locali zation for Poisson and random displacement models, can be modified to work for the type of Anderson model considered here. (C) 2000 Academic Press.