Nature of the band tails in one-dimensional disordered systems

A theoretical model for the density of states based on a tight-binding scheme for one-dimensional disordered systems is investigated within a self-consistent approach in terms of a probabilistic procedure. In particular an exact analytical expression is worked out for the density of states for the case of a Cauchy distribution for the site energies in the region of localized states. A particular attention is paid to the energies lying in the band tails. It is mainly shown that the band tails are sensitive to the typical nature of the disorder. (author). 35 refs, 1 fig