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.

• Received 28 March 1956

DOI:https://doi.org/10.1103/PhysRev.103.1159