Discovered by Swiss physicist Felix Bloch in 1929, its eigenstates are written ψ_nk(r) = e^(ik·r) u_nk(r), where u_nk shares the periodicity of the crystal lattice.
Because wavevectors differing by a reciprocal lattice vector K describe equivalent states, the crystal wavevector k can be restricted to the first Brillouin zone.
The second derivative of the band energy ε_n(k) with respect to k defines the effective mass tensor governing charge carrier acceleration in a band.