Abstract
The ground stateΨ of a simple-cubic crystal is assumed to be a product of single-particle functions and nearest-neighbor (NN) correlation functions. In this so called NNCA (NN-Correlation Approximation) the transfer-integral (TI) method allows an exact integration ofΨ2 over the coordinates in all cubic planes but one, leading to the probability-densityP for this plane. If only NN-correlations are retained inP (2nd NNCA) the TI-method leads to the probability-density for a row. Finally, after a 3rd NNCA, the 1- and 2-particle probability densities are obtained, which are used to calculate the expectation valueE = 〈Ψ|H|Ψ〉 of a Hamiltonian with arbitrary 2-body interaction.—For harmonic NN-interactions the 2nd and 3rd NNCA become exact, andE differs only by 1% from the exact result. The inclusion of small next-NN-interactions still improves this result, though the 2nd and 3rd NNCA are no longer exact.
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