Theory of an impurity state in a crystal

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Abstract
A review is given of the theory of the effects of single-, or low-concentration impurities on the properties of otherwise perfect crystals. The subjects considered include electron density, anomalies in the temperature dependence of the spontaneous magnetization of a ferromagnetic insulator and the spectrum of lattice vibrations. All the problems are considered from a single mathematical point of view in which the approximation of localized perturbations and Green function techniques are used. The conditions for the occurrence of localized and virtual states are discussed. The review concludes with a formulation of the general methods of the theory.