Quantitative results near the band edges of disordered systems

By combining the coherent-potential approximation, the potential-well analogy, and theories for the near tail in the density of states, we obtain, for the first time, explicitly quantitative results for the various quantities of interest near the band edges of disordered systems. These results exhibit a certain universality and can be expressed in terms of simple analytic functions, provided that disorder is not larger than about (1/5) of the bandwidth.