Hi all,
This is an interesting puzzle and I think it is very wide spread
in physics. I relate this problem to my research, which is production
and suppression of the J/Psi. When it is produced, what happens is that
a c-cbar is formed but it does not know yet what state it is (J/Psi, Psi
prime, Chi's, ....). During the formation time, things can happen but
in the end, something comes out. OK, so what does that have to do with
the photon hitting the electron? Well, I believe that we can't mix E&M
and Quantum Mech. (sorry Mike, no semi-classical results) so this is
purley Quantum mechanical. The Photon hits the Electron and for the
short time that Ludwik desrcibes (due to Heisenberg Unicertainy - sort
of), we have a superposition of wavefunctions desciring all the possible
results (allowed because E conservation is not a worry in our dt).
These states include E level jumps (moving up the potential well), knock
on electrons, and Compton scattering. After sometime, the system comes
into reality (like particles coming on mass shell) and we get our one
result. However, I believe that most of the probablity lies in E level
jumping and that depends on various factors about the electron, photon,
and rest of the atom. I can research it more if you like.