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Abstract A general expression is written down for the density of states of non-interacting electrons in a disordered system. The expression is obtained on the basis of two simplifying assumptions; the geometric approximation, which is connected with the disorder, and an approximation concerning the potential which is commonly used in band structure calculations. In the case of a perfect lattice the result of Kohn & Rostoker (1954) for the band structure of the lattice is derived, and details of the density of states are available from the formula thus obtained. It is shown how the change in the energy of the electrons due to the presence of a phonon can be obtained.
J L Beeby (Tue,) studied this question.