BASIS FUNCTIONS FOR ARBITRARY CELLS IN MULTIPLE-SCATTERING THEORY

We present a formal and numerical study of the solutions of the Schrodinger equation associated with spatially bounded, but otherwise arbitrarily shaped potentials. We show that the scattering matrix (t-matrix), is sufficient to represent the solution everywhere outside the cell, not just outside a sphere bounding the cell. We also show that the basis function in the interior of the cell is independent of the potential surrounding the cell. We illustrate our formal results with the results of numerical calculations and discuss the implications of these results to multiple-scattering theory and to the calculation of the electronic structure of solids.