Imagine an EM wave impinging on a metal. Fresnel's formulas tell us that no wave can propagate through the metal, or that the transmitted field is an evascent wave with some penetration depth dependent on the refraction index of the metal.
If we now would like to zoom into the microscopic physics of the reflection, we would have to take into account the crystalline structure of the metal, which imposes a certain electronic band-structure, which in turn determine the way the electrons respond to the external EM perturbation. We should calculate the reflected field from the back action of the electron motion on the incident field.
Do you know of a semiclassical way of solving this problem? Is it feasable to compute numerically a set of coupled Maxwell-Schroedinger equations?