Watermn's T Matrix and Quantum-Mechanical Transition Operator: Rigorous Derivation of Superposition T-Matrix Approach for Problem of Electromagnetic Scattering by System of Particles

In this paper we present rigorous and systematic derivation of the superposition T-matrix approach, which directly follows from the inhomogeneous wave equation. Starting from the complete integral solution of the inhomogeneous wave equation for a time harmonic field, we obtain first the equations for the Green's and transition operators. Then, expressing the free space dyadic Green's function in terms of spherical wave functions and separating variables, we find the equation for determining the matrix elements of transition loperator T for a system of particles using the matrix elements of T for isolated particles. We show that for divergence free electric field the matrix elements of T, expressed in spherical wave functions, directly connected to Waterman's T matrix.