A constant potential method for energy bands in solids

Abstract

The constant potential method assumes that the effective potential is spherically symmetrical within the inscribed spheres of the atomic polyhedra and constant in the space between them. The variation principle giving the energy levels of electrons in monoatomic lattices is expressed here as a surface integral over the boundary of the volume. Once certain "structure constants" appearing in this method have been calculated for a given type of lattice , they may be used with different potentials without much additional effort. This method has been tested with the empty lattice test for K=0 ( A1 type lattice ) and has further been applied to the monoatomic substance (A1). The results of some calculations have been reported in both cases.