The lattice basics: Wigner Seits cells. The lattice vectors etc

Reciprocal lattice. Wigner Seits cell - Brilloin zone in 1
dimension.

The big dots are reciprocal lattice points....

Illustrating that heat capacity of electrons will become important

for low temperatures. It is linear in T, lattice goes as T^{3}

Phase velocity - group velocity. How does the group velocity come
arround.