Some details of the density of states of a disordered alloy

The density of states of an electron in a tight-binding model of a disordered one-dimensional alloy has been computed with high precision using a development of an exact method due to Schmidt (1957). The 'special energies' at which the density of states vanishes are in accordance with the analytical theory. In the vicinity of a region of infinite density of special energies the envelope of the density of states is found to vary exponentially.