Bloch's Theorem
A fundamental theorem of solid-state physics stating that wave functions for electrons in a periodic crystal potential equal plane waves modulated by a lattice-periodic function.
Governing formula
ψ_k(r) = e^(i k · r) u_k(r), u_k(r + R) = u_k(r)
SI unit
Quantum Wave Function State
In depth
Formulated by Felix Bloch. Shows that electrons move through ideal periodic crystal lattices as modulated plane waves (Bloch waves) without scattering, explaining why ideal crystals conduct electricity with high mobility.
Examples in the real world
Deriving electronic energy band structures and band gaps in crystalline solids.