Rigorous derivation of superposition T-matrix approach from solution of inhomogeneous wave equation

The problem of electromagnetic scattering by a system of particles is considered. Starting from the integral solution of the inhomogeneous wave equation, the equations for Green's and transition operators are derived. By expressing the free space dyadic Green's function in terms of vector spherical wave functions, the relations between the matrix elements of the dyadic transition operator and T matrix are established. On the basis of these relations the equations which allow determining the T matrices for a system of particles using T matrices for isolated particles are derived.