S. Scandolo, ICTP

Lesson 14 (Crystals: the quasi-free electron model)

This lecture takes up where the previous left off with the quasi-free electron model. The professor examines the validity of the assumptions behind the model: is the potential small compared to gaps between energy levels? Without screening, the Coulomb potential would be too strong for a perturbative treatment of the system. In order to explain properties of elements in the second column of the periodic table, we need to step out from one dimension. In three dimensions, the perturbed energy levels can overlap, thus the quasi-free electron model explains the metallic behaviour of these elements (e.g. Mg).

The rest of the lecture answers questions about perturbation theory with degenerate states. An illustrative example is given when calculating the new eigenstates on the boundary of the Brillouin zone for a potential with the wavelength of the crystal.

The homework is related: what happens if the wavelength of the potential is half the wavelength of the crystal?