On the electron energy spectrum in a desordered chain of deltafunction potentials

The aim of the present paper is to establish the general properties of the energy spectrum of the electron in a disordered chain of deltafunction potentials. The case of a one-dimensional chain of N deltapotential sites differing in intensity and arbitrarily distributed on the real axis is discussed. Everywhere, except on the support of the delta-functions the potential energy is zero. The general solution of the corresponding Schrodinger equation for a particle with mass m, located in the described potential field, is written down. In the case E>0, E being the electron energy, the energy levels are obtained. The density of states rho(E) is calculated. rho(E) has a singularity √[E-Esub(2p)]. In the case of a disordered lattice it is supposed (the problem being one-dimensional) that the singularity in rho(E) is of the same type. (S.P.)