Symmetrized combinations of plane waves and matrix elements of the hamiltonian for cubic lattices

Abstract

General expressions are given for the “generators“ of all the symmetrized combinations of plane waves (SCPW) which transform according to the irreducible representations of the group of the wave vector k at the various symmetry points and along the symmetry axes of the Brillouin zones of the simple cubic, body-centered cubic, face-centered cubic, and zincblende lattices. These general expressions for the “generators” of the SCPW were constructed using normalized projection operators. A method is presented for simplifying the calculation of matrix elements of the Hamiltonian between symmetrized wave functions. These matrix elements are reduced to the form of matrix elements between an unsymmetrized function and a symmetrized function using normalized projection operators.