Compton Scattering Compton Scattering essentially states that when a photon of a given wavelength hits an electron the energy level of the electron changes and the photon has its wavelength changed. This seems to be implying that it is the same photon that is reflected outwards. Do we know it is the same photon of a changed wavelength, or is it possible that the original photon merely pushed a 2nd photon out of the electron? (This would mean the original photon is not changing wavelength, that is meerly absorbed). 
 A: It is my understanding that we cannot tell which of the two scenarios takes place, moreover, it does not matter, as photons having the same characteristics (such as momentum, energy, and polarization) are indistinguishable.
A: It is conventional to describe the out-going photon as a "different" particle. Basically because photons have only one independent property: their wavenumber ($\vec{k}$) and that is how we label them. Further as they experience no time there is not  opportunity for them to change it.
This is consistent with quantum field theory where a process like this will be written with a destruction operator on the in-coming wavenumber and a creation operator on the out-going wavenumber.
A: A more detailed explanation of the interaction with QED The photon is absorbed by the electron, the electron is excited, the electron decays, a new photon is emitted.  There is some finite, non-zero time between the absorption and emission of the photons.  The process is illustrated in the following Feynman diagram from here:

