Other Solution Methods

Abstract

In Chaps. 3 and 4 we became familiar with two different ways of approximating the Green functions related to the scattering problems by finite series expansions in terms of appropriate eigensolutions of the Helmholtz and vector-wave equation. Both of the described ways produce the same expressions. The thus approximated Green functions result in corresponding series expansions of the scattered field with expansion coefficients calculated via the T-matrix from the known expansion coefficients of the primary incident field at the scatterer surface. Demonstrating that the T-matrix is a decisive element of the relevant Green function and that some important properties of the T-matrix like symmetry and unitarity are related to corresponding properties of the Green function can be considered to be the most important results of these two chapters. But there still exist other solution methods for the scattering problem of our interest which have been derived historically from other principles and assumptions used in the foregoing two chapters.