Localization in disordered materials: Existence of mobility edges

Anderson's theory of localization in disordered systems is extended. It is shown that mobility edges exist, in agreement with the Mott-Cohen-Fritzsche- Ovshinsky model. As the randomness increases, the mobility edges move inwards into the band, and their coincidence is termed Anderson's transition. A criterion is developed restricting the energy regions where mobility edges can be found; explicit results are obtained for a Lorentzian distribution of single-site energies.