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.