4. Independent electrons in a periodic potential: general aspects (22,24,29,31 Oct. 2025)
Schema della sezione
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Periodic potential: Bloch theorem, I and II [22 Oct.] proof (Ch. 8).
Consequences of the Block theorem: crystalline momentum; velocity; energy bands. (Ch. 8) [24 Oct.]
Fermi surfaces. Density of states (DoS): different approaches. Derivation of the DoS using the properties of the delta-function . Van Hove singularities. (Ch. 8) [24 Oct.]
Divergences in the DOS integrals - Van Hove singularities in 1D, 2D, 3D. Exercise n. 2 Ch. 8 of A&M [29 Oct]Brillouin zones, band folding and band indices [29 Oct]Band plots in reduced zone / periodic / extended representation Fermi surfaces and their folding into the first Brillouin zone (end of Ch. 8]. [31 Oct]"Empty lattice" band structure in 1D and FCC [31 Oct]
A nice applet for plotting the "empty lattice" bands: PHY.K02UF Molecular and Solid State Physicshttp://lampx.tugraz.at/~hadley/ss1/emfield/empty/empty.phpComments on selected slides on: band structures, Fermi surfaces, DOS [31 Oct]Calculation of k_F in the "empty lattice" model and comparison of the Fermi surface with the Brillouin zone [31 Oct]