The methods of previous papers by the authors are applied to a simplified impurity calculation. This is the case of a localized perturbation in a simple cubic lattice. We consider the effect of the perturbation on a single band which is describable in terms of a Wannier function which only has nearest neighbor interactions. The results of this calculation are compared with some approximate treatments of impurity calculations.
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Koster et al. (1954) studied this question.
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