Classical Theory explanation of Compton Effect We all have studied in introduction to quantum mechanics about Compton Effect. In all the books I have read, it says that classical theory can't explain the shift in wavelength because the incident EM wave will oscillate the electron at the frequency of light, and the oscillating electron will emit radiation of the same frequency. This is all well and good, but while reading Quantum Physics[Berkeley Series],the author mentioned something among the lines that ( not exact sentence) , the em waves oscillate electrons and that in turn produces the light of same frequency, also some loosely bound electrons are ejected from the atom which  radiate the light of the slightly different frequency. 
Is this explanation correct, if so what was the problem in mathematically describing this theory? Also , if this is the case, how is the ejected electron different from the ones in photoelectric effect. 
 A: Compton scattering, unlike the photoelectric effect, can occur for a free electron. For a free electron, the classical theory can't explain the shift in wavelength. A theory of Compton scattering has to explain all observations, not just some of them, so it needs to explain the case where the electron is free.
Of course there is no such thing as a perfectly free electron, since there is no such thing as an exactly vanishing electric field. However, the electrons in ordinary matter are an excellent approximation to free electrons, because the atomic binding energies, on the order of eV, are negligible compared to the MeV energies of the photons.
There is also a problem with classical explanations of the photoelectric effect and Compton scattering, because they can't explain the entanglement between electrons in different atoms. Without this entanglement, each atom's probability of being ionized is independent, and then conservation of energy and momentum hold only at the statistical level. This lack of correlation was a prediction of the BKS theory, which was disproved by the Nobel prize-winning 1925 Bothe-Geiger experiment.
