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Approximate solutions for k=0 of the Hartree-Fock-Slater equations for a perfect silicon crystal have been obtained by the orthogonalized plane-wave method. Estimates of the energy eigenvalues of the valence and conduction states for k=0 are given. A simple method for obtaining a first approximation to the crystal potential and its Fourier coefficients was used. Approximate analytic wave functions and corresponding energy eigenvalues for the 1s, 2s, and 2p states in the isolated silicon atom were determined by a variational technique.
Truman O. Woodruff (Sat,) studied this question.