Abstract
A simple cubic hydrogenic lattice in the extreme tight binding approximation with only one energy band is set up as a model for an insulator. A two particle Green's function equation for one full and one empty state is derived with a mutual interaction potential. The model is a generalization of one by Hubbard applying only one particle Green's functions to electrons in narrow energy bands. The model is also a generalization of one by Slater and Koster which applies to electron-impurity interactions. It is shown that the energy of a pair of full and empty states depends on the orientation and magnitude of the relative crystal momentum of the pair. Kohn's criterion for the insulating state is satisfied by all bound pairs. A qualitative discussion of this lattice as a superposition of pairs is also given on the basis of the quasi-chemical equilibrium theory.
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