Unified derivation of the translational addition theorems for the spherical scalar and vector wave functions

Abstract

The translational addition theorems for the spherical scalar and vector wave functions are derived in a novel, unified way based on the simple and well-known concepts of the radiation and incoming wave patterns.This approach makes the derivation simpler and more transparent compared to the previous approaches.As a result, we also obtain alternative and partly simpler expressions for the translation coefficients in the vector case.