Say a photon hits a free electron at rest. I understand that there is a formula for the Compton scattering when the photon is scattered with an angle $\theta$, but I don't understand what determines that angle $\theta$. If one photon hits such an electron, won't it be scattered through a unique angle? It seems it is not so, since there is the angle $\theta$ as a parameter.
[Physics] Compton scattering angle
photonsquantum mechanicsscattering
Best Answer
As all scattering process in quantum mechanics, finding the scattered particle at a particular direction is random, because the scattered wavefunction is not a plane wave.
The usual derivation of Compton scattering overlooks the wave nature of electron and light, and hence gives you false perception that the scattered electrons and photons have a definite four-momentum in any individual event. In fact, they are in superposition of momentum eigenstates after scattering.