Brillouin zones
Assuming idealized free electron behaviour in a three-dimensional simple cubic
lattice, calculate the ratio of the energy of an electron at the corner of the first
Brillouin zone to the energy of an electron at the midpoint of a face of the first Brillouin zone.
If a metal has a cubic lattice with parameter of 0.3 nm and its Fermi surface just
touches the Brillouin zone boundary, determine the Fermi energy, the number of
conduction electron states NQ(£) per unit volume, and the density of states D(E)
per unit volume at the Fermi level.