[saspinski (OP)]

One of the methods to know the crystalline structure of materials is the X-ray diffration. The periodic array of atoms make possible that the scatering of an incoming electromagnetic wave be in phase for some angles of the directions source-sample and sample-detector.

My doubt is how to describe what happens when the incoming wave reaches one atom. In some texts, the eletrons vibrate according to the wave frequency, and being an accelerated charge, send a new (scattered) wave, in phase with the original and in the same frequency.

But the quantum description of the event is the absortion of a photon by the atom and further release of another one.

According to the first (classical) description, a spherical wave spreads from the moving electron. Because the inter-atomic distances are much smaller than the distance  sample-detector, the later records basically plane waves with the same direction. 

But according to the QM explanation, the photon released by the atom, after returning from the excited state, has some direction, and only by coincidence is the direction sample-detector.

Or I can say that the wave function of this photon is a spherical one, a superposition of infinite plane wave vectors in all directions? And when a photon is detected, its wave function collapses to that direction sample-detector.

[Hoffmanz]

I want to know the source of the information and to publish this information, can I ask more?