An exact band-structure method applied to the three-dimensional Mathieu problem

Abstract

A method assigned to solve exactly the Schrodinger equation with non-muffin-tin crystal potential is numerically tested. The approach is based on the Green function technique. It differs from the conventional multiple-scattering methods in that the wave field psi k is sought at some points within a cell rather than at the boundaries. The empty lattice and three-dimensional Mathieu problems are studied with the emphasis on convergence properties. Generally, the convergence is governed by three independent parameters, resulting as a consequence of the truncation of some infinite series, namely, the expansions of the Green function, potential and wavefunction psi k sought. It is numerically shown that, by increasing the three parameters mentioned, the calculated energy eigenvalues approach the exact ones.