Many interesting information about the properties of electrons
in a crystal is encoded in the so-called band structure, which,
for the semiconducting material gallium arsenide (GaAs), looks
like this: Source: Michael Rohlfing, Peter Krüger, and Johannes
Pollmann: Quasiparticle band-structure calculations for C, Si,
Ge, GaAs, and SiC using Gaussian-orbital basis sets, Phys. Rev.
B48 (1993) 17791-17805 (doi: 10.1103/PhysRevB.48.17791), Fig. 3.
The band structure plot shows the energy of electrons in the
crystal as a function of momentum. Energy, along the vertical
axis, is measured in units of electron Volt (eV), while
momentum, on the horizontal axis, is given along specific
directions in the crystal, which are denoted by the symbols Γ,
Δ, X, Λ, and L. For free electrons under conditions as typically
encountered in solid-state physics, the relation between Energy
E and momentum p is simply given by the classical, Newtonian
formula E = p²/2m, where m is the mass of the electron. In a
plot, energy as a function