XII. A variation principle for electronic wave functions in crystals

A variation principle giving the energy levels of electrons in polyatomic lattices is presented. When used in conjunction with the cellular method it includes the matching of the wave functions across cell boundaries without the need of making ad hoc assumptions. Values of ∇ k E(k) can be obtained from quantities used to determine E(k) without carrying out any numerical differentiation. The results of some calculations on the valency bands of lead sulphide are reported.