The \(h\) is the proportionality constant which will be later known as Planck’s Constant. This relationship conflicted with classical electrodynamics in that the amplitude of the wave was responsible for the energy. He had also “quantized” light into photons. On top of this, he also considered photon-electron collisions (the photoelectric effect). Einstein predicted that it was not intensity of light which would scatter a free electron, but the energy of any given photon. In short, a large number of photons with insufficient energy will never scatter a free electron. However, a single photon with sufficient energy most certainly has a significantly higher probability of doing so. This also contradicts the classical interpretation of electromagnetism which predicts that intensity is responsible for scattering, not energy.
We now consider Compton Scattering \cite{Compton_1923}. We may demonstrate a relatively simple derivation of Compton’s formula in order to better conceptualize his experiment. Compton himself performed a very similar derivation using principles from two of Einstein’s 1905 papers. The aforementioned photoelectric effect paper as well as his paper on the theory of special relativity. \cite{Einstein_1905a}. Compton considered a classical collision which would occur between a photon and free electron.