Abstract
Scattering of light and electron beam by Hydrogen atom should be described by the coupled Maxwell–Schrödinger equations. However, the coupled equations are nonlinear, and so the calculations can be done only by perturbation procedure neglecting the self action; i.e., in the Born approximation. This approximation leads to some inconsistency breaking the charge conservation law, which should be fixed in a true nonlinear approach.
The corresponding scattering cross sections are similar to the classical ones given by the Thomson and Rutherford formulas respectively.
The calculation of the scattering of light relies on the limiting amplitude principle and the limiting absorption principle, which allow to explain the Einstein’s rules for the photoelectric effect.
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Komech, A. (2013). Scattering of Light and Particles. In: Quantum Mechanics: Genesis and Achievements. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5542-0_8
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