What happens at the QM level with a photon hitting a mirror?

The problem with any attempt to try and explain some macroscopic phenomenon in terms of the detailed interactions at the lowest level is that one encounters lots of complexity. If one looks at the interactions of photons with the electrons at the fundamental level, one finds that there are no vertices for elastic scattering; photons are always absorbed and re-emitted. Yet, it is true that a mirror must be doing some form of elastic scattering. How does that work?

Well, it is the result of an infinite number of such absorption and re-emission processes that happen in a quantum superposition. These different events interfere with each other in such a way that constructive interference builds up the picture of an elastic scattering process.

Here are the compton scattering lowest order diagrams

**There is nothing that forbids elastic scattering **, i.e. energies unchanged in the center of mass and only angles different.

Elastic scattering is logically necessary because if photons were absorbed and re-emitted, the phases between the photons from which the macroscopic classical electromagnetic light wave emerges would be lost, image coherence would be lost in mirrors. This is what happens with non-mirrors, mainly the scattered photons become point sources incoherently reflected and absorbed. Also, it is necessary for mirror reflection to keep the colors. Absorption and reemission would change the energy, if not elastic, and the frequency of the photons would change and thus the colors built up macroscopically.

To answer the title:

The mirror is macroscopic and its lattice has an effective electric field from the surface atoms. The photon hits the field by exchanging a virtual electron, where also the electron on the left is virtual to represent the field because it is tied up in a lattice. The photon scatters elastically in the center of mass, keeping the phases of the emergent beam and thus gives a faithful image back. The center of mass is almost identical to the laboratory center because the mirror is macroscopic and effectively it is the lattices mass that enters the kinematics (similar to a ball hitting a wall classically).

The question remaining is how the phases that define the classical beam as a superposition of photons are kept. My opinion is that one should go to the emergent E and B fields from the individual wave functions of the zillions of photons which also collectively interact with the lattice fields, making most probable scattering direction the classical ray direction of reflection, but I have no link or proof for this. Motl's link above justs deals with the emergence of the classical electromagnetic wave from the quantum mechanical fields and particles.

The type of surface decides whether coherent elastic scattering will dominate or diffuse scattering because of surface anomalies, or absorption and re-emission.

What is more interesting is when the lattice is transparent, where the photon has to interact with the whole lattice and keep color and phases. Here it is more evident that emissions and re-absorptions on individual charge centers cannot explain real transparent media that transfer colors and images. These enter in distortions and color changes.

There is this publication in Russian which calculates elastic scattering from bound electrons too.