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In classical electromagnetism, reflection is explained using the Maxwell equations and boundary conditions. How is reflection explained in quantum optics? What happens to photons during reflection?

For context, I've got this question while reading YH Kim's "A Delayed Choice Quantum Eraser" (https://arxiv.org/pdf/quant-ph/9903047.pdf) and it says:

[...] photon 2 will follow the A path meeting BSA with 50% chance of being reflected or transmitted.

But what does it mean that a photon is reflected? does it gets absorbed and then reemitted? does the photon just changes it's momentum direction?

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    $\begingroup$ I am certain that thus is a duplicate. If you search on this site you should find a few threads discussing this. $\endgroup$ – my2cts Oct 25 '19 at 17:35
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You are correct, reflection at the QM level is not absorption and re-emission. Absorption and re-emission would change the energy level of the photons, their relative phase, relative angle (thus creating a diffuse reflection).

https://en.wikipedia.org/wiki/Diffuse_reflection

Mirror reflection is elastic scattering. That is the only way to keep the energy level, relative phase, relative angle of the photons, thus creating a mirror image (thus creating specular reflection).

https://en.wikipedia.org/wiki/Elastic_scattering

Specular reflection, also known as regular reflection, is the mirror-like reflection of waves, such as light, from a surface. In this process, each incident ray is reflected at the same angle to the surface normal as the incident ray, but on the opposing side of the surface normal in the plane formed by incident and reflected rays. The result is that an image reflected by the surface is reproduced in mirror-like (specular) fashion.

https://en.wikipedia.org/wiki/Specular_reflection

You are correct, during elastic scattering (reflection), the photon keeps its energy and phase, and changes angle (direction of momentum vector).

For reflection there should be elastic scattering in the center of mass so that the phases of the photons are kept and the image emerges intact on reflection. So it should be a QED feynman diagram of a photon scattering elastically off a field. The kinematics are similar to a ball bouncing off a wall, i.e. elastically scattering. The assumption is that the mass of the wall is practically infinite and the center of mass with respect to the ball+wall, where the elastic scattering happens is at the same (x,y,z) as the center of mass of the wall itself.

https://physics.stackexchange.com/a/248741/132371

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