Bloch's Theorem

A quantum-mechanical statement that in a spatially periodic potential the eigenstates of a single electron can be written as a plane wave multiplied by a lattice-periodic function, ψ_k(r) = e^{i k·r} u_k(r), where u_k(r + R) = u_k(r) for every lattice vector R; this structure underlies band formation and the concept of crystal momentum.