Electronic Energy Bands in Crystals

In a previous paper, a variational principle was derived for the energy levels of a crystal. The variational principle was stated in terms of the Wannier functions of the crystal instead of the more usual Bloch waves. In this paper, the variational principle has been applied to two problems, to the one-dimensional cosine potential, and to the energy levels of the valence band of lithium. The method of forming the trial function is discussed. It was found more convenient to use the Wannier function in momentum space rather than in configuration space. In the lithium case, our results are compared with those obtained by the Wigner-Seitz spherical approximation.