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Does this question make sense in the quantum world?

Imagining a single photon (wave packet?) interacting with a single atom (its electrons etc) how do we currently describe/define the emitted photon in terms of its direction in relation to the incoming photon?

Now "scaling up" to a surface of atoms actually reflecting "light" according to the simple reflection rules like angle-in equals angle-out how do we manage to explain this effect in terms of the quantum world? How comes the probabilities work out for the out-going angle depending on the incoming-angle?

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Just remember that energy, momentum and angular momentum have to be conserved and you will get a spatial probability distribution. Of course, you have to take into account the recoil velocity of the atom as well. –  Antillar Maximus Mar 9 '12 at 0:47
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2 Answers

Not a full answer, but remember that any issue with path of particle must be done with a sum-over-paths (think it's called a Feynman integral) approach. I don't even think that $\angle i=\angle r$ is necessary for a single photon; it's only when we get multiple photons that interesting things happen.

You may want to see this

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There is a wise old saying by our friend Albert E, to the effect that every rascal claims knowledge of what a photon is, but is wrong. Hear me out because I have posted fundamental data on the nature of light since 2005.

New theory backed by experiment: The light is emitted in a pulse of energy hf, h=Planck's, f=frequency, and thereafter spreads classically. Contrary to 100 years of dualistic confusion, The absorption at the atom is continuous. At the atomic scale and in electrons kinetic energy and momentum can be absorbed over time. One needs to review the Compton effect, Compton Simon experiment, Bothe Geiger experiment, the photoelectric effect and several other experiments with my enhanced Loading theory to understand some simple properties of the charge wave. In other words, you were taught to think that my model was eliminated long ago. The history, theory, and unique beam split experiments that defy the photon model are all on my website. So to answer your question, there are no photons, but you can explain the fields in a straightforward way, or even use quantum mechanics, and you will end up with something close to what the loading theory predicts in most cases. But you will not understand it by QM because it calls for a collapse of the wave function over all space, an absurdity that we have all been confused into living with. Unquantized pulses of incoming energy can go into the calculation, but the outgoing pulse will be quantized in energy and sent in a direction. However, the hf wave will thereafter spread classically. By splitting the gamma-ray and getting two detections in coincidence at rates exceeding chance, I show that absorption is not quantized. It was a two-for-one effect so part of the energy had to be at the absorber ahead of time. If you do not use this model you are lost in duality and all its quantum weirdness. The world is not crazy after all.

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