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Refraction: I want a qualitative Quantum Mechanical explanation of why do we see light rays -in the classical picture- bend when light goes from one medium to another. I read that it is due to conservation of energy and momentum, but haven't found an explanation about the reason of the change of angle.
Reflection: again a qualitative explanation of why the angle of incidence is equal to the angle of reflection.

EDIT 1: what I am looking for is really an explanation about what interactions are the photons going through(like absorption and emission by molecules for example) that when we take all the photon's interactions into account give us the macroscopic picture of how light reflects and refracts.

EDIT 2: I really want an answer containing the reason for why we get the angle of incidence is equal to the angle of reflection and why the angle if refraction is as it is.

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    $\begingroup$ There are no light rays in QM, so you can't really get an explanation for "that". What you can do is to couple a free em-wave state to a crystal lattice and recover that the direction of the wave vector of the quasi-particle state that exists inside the medium follows the known laws for refraction. Would that satisfy your request conceptually? I do believe that we had this question multiple times already, though... somebody will certainly dig up the links for you. $\endgroup$
    – CuriousOne
    Commented Nov 1, 2015 at 15:48
  • $\begingroup$ I have edited just when you posted the comment! Well, what I want really is what happens at a microscopic level that gives us the macroscopic picture of light that we have(the usual like angle of incidence is equal to angle of reflection and so on) $\endgroup$
    – TheQuantumMan
    Commented Nov 1, 2015 at 15:51
  • $\begingroup$ At the microscopic level the free em-state becomes a quasi-particle state. The results are, as far as I know, basically identical to semi-classical theory, unless we start looking at things like the interaction of a laser field with e.g. a bunch of ultracold atoms. $\endgroup$
    – CuriousOne
    Commented Nov 1, 2015 at 15:54
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/2041/2451 , physics.stackexchange.com/q/6428/2451 , physics.stackexchange.com/q/10301/2451 , physics.stackexchange.com/q/83105/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Nov 1, 2015 at 16:06
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    $\begingroup$ From this, you should really rephrase your question to account from 1: what you have learn since 2: what would help people understanding what you already know and what you seek at. $\endgroup$
    – Fabrice NEYRET
    Commented Nov 1, 2015 at 16:29

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How a classical electromagnetic wave emerges from innumerable photons can be seen in this blog entry. It is not simple, one needs quantum field theory to start with. One should get the interaction of a single photon with a crystal lattice , and one can get a quantum mechanical solution, which will give the probability of the photon to scatter or go through the crystal. Then one has to use the logic/math, outlined in the blog link above, to see how the classical beam with its diffraction would emerge

EDIT: what I am looking for is really an explanation about what interactions are the photons going through(like absorption and emission by molecules for example) that when we take all the photon's interactions into account give us the macroscopic picture of how light reflects and refracts.

Photons can interact with matter by

a) elastic scattering : only the angle changes and not the energy

b)inelastic scattering with the field of the matter they hit: in this case the frequency changes and thus the color.

c)absorption by atomic and molecular layers: in this case the photon disappears and no longer contributes to the light beam. The atom may de-excite and an equal frequency photon come out, but it will not longer be coherent with the light beam because the direction of emission will be different than the direction of the macroscopic beam.

So in reflection one can handwave of the individual photons scattering elastically and keeping the phases between them, and thus the images can be reflected.

In refraction though the quantum mechanical solutions have to come in so as to show that the scattered photons keep a coherence, and I cannot see how without solving for a specific lattice and summing up the individual photons one can handwave an index of refraction. See also the answer by Marek here. and this link here.

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