Scattering of an electromagnetic wave on a free electron in the semiclassical approximation

A study was conducted to demonstrate scattering of an electromagnetic wave on a free electron in the semiclassical approximation. An electron was presented as a quantum particle to consider the light as an electromagnetic wave for conducting the investigations. The electromagnetic wave that was considered as the electron-density distribution was approximated with a certain function having the period Ae and decreasing as 1/r2 from the classical position at a point. Ae was considered as the quantum size of an electron nucleus surrounded with periodically arranged oscillators with quickly decreasing force. It was demonstrated that the mechanism that resulted in the dependence of the frequency and wavelength of the electron dipole radiation was the interference of waves emitted by different parts of the quantum electron.