Random Schrödinger operators with a background potential

Abstract: We consider one-dimensional random Schr\"odinger operators with a background potential, arising in the inverse problem of scattering. We study the influence of the background potential on the essential spectrum of the random Schr\"odinger operator and obtain Anderson Localization for a larger class of one-dimensional Schr\"odinger operators. Further, we prove the existence of the integrated density of states and give a formula for it.