Thomson scattering and energy shifts via theeq→·E→interaction

The problem of a nonrelativistic free charge interacting with radiation is considered from the theoretical viewpoint. In particular the scattering of light and the energy shifts associated with radiation are discussed using both quantum electrodynamics and the semiclassical theory. It is shown that the multipolar form of the Hamiltonian gives results identical to those of the conventional "$e\overrightarrow{\mathrm{p}}·\overrightarrow{\mathrm{A}}$" type of Hamiltonian. Comparisons are also made with calculations based on the space-translated Hamiltonian.