Bloch's Theorem

Condensed Matter · 1928

Equation: ψ_k(r) = e^(i·k·r)·u_k(r)
Field: Condensed Matter
Named After: Felix Bloch
Year: 1928

Symbols

ψ_k electron wavefunction in a crystal · k crystal momentum · u_k a function with the lattice's own periodicity · the plane wave e^(i·k·r) rides the lattice unimpeded

Significance

The Schrödinger equation solved in the periodic potential of a crystal: electrons travel as waves shaped by the lattice, scattering only off imperfections — why copper conducts at all. The allowed and forbidden energies this form produces are the band structure, the blueprint of every material's electronic personality.