## Quick Reference

A theorem relating to the quantum mechanics of crystals stating that the wave function ψ for an electron in a periodic potential has the form ψ(*r*) = exp(i*k***·***r*)U(*r*), where *k* is the wave vector, *r* is a position vector, and U(*r*) is a periodic function that satisfies U(*r*+*R*) = U(*r*), for all vectors *R* of the Bravais lattice of the crystal. Block's theorem is interpreted to mean that the wave function for an electron in a periodic potential is a plane wave modulated by a periodic function. This explains why a free-electron model has some success in describing the properties of certain metals although it is inadequate to give a quantitative description of the properties of most metals. Block's theorem was formulated by the German-born US physicist Felix Bloch (1905–83) in 1928. See also energy band.

ψ(*r*) = exp(i*k***·***r*)U(*r*)

U(*r*+*R*) = U(*r*)

*Subjects:*
Chemistry — Physics.