Eigenvalues and eigenvectors of the translation matrices of spherical waves of multiple-scattering theory

Abstract

The exponential nature of the translation matrixG of spherical free waves has been set forth in a previous paper. The explicit expression of the exponential form of the translation matrix is given here, once the eigenvectors and the eigenvalues ofG have been found. In addition, the eigenproblem relative to the matrix which transforms outgoing waves scattered by a centre in a set of spherical free waves centred at a different point is solved.