Independent electrons in a periodic potential: general aspects (7, 9, 14, 16 Nov. 2022)
Section outline
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Periodic potential: Bloch theorem, I and II proof (Ch. 8).
Consequences of the Block theorem: quasi-crystalline momentum; velocity; energy bands. (Ch. 8) [7 Nov.]
Fermi surfaces. Density of states (DoS): different approaches. Derivation of the DoS using the properties of the delta-function (see notes). Van Hove singularities in 1D, 2D, 3D (see other notes). (Ch. 8) [9 Nov.]
Brillouin zones, band folding and band indices, band plots in reduced zone / periodic / extended representation [14 Nov.] Fermi surfaces and their folding into the first Brillouin zone (end of Ch. 8 + Ch. 9].A nice applet for plotting the "empty lattice" bands: PHY.K02UF Molecular and Solid State Physicshttp://lampx.tugraz.at/~hadley/ss1/emfield/empty/empty.php