Impurity Bands and Perturbation Theory

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Abstract
Perturbation theory can be applied to calculate the density of states of an electron moving in a random potential produced by impurity centers, but for small concentrations the usual approximations are unreliable and do not predict correctly the shape of the impurity band. A new chain of approximations is obtained by expressing the Green's function of the electron in terms of a "self-propagator." It is shown that this method leads to more realistic results.