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(ik·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. Bloch’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, such as electrical and thermal conductivity, of certain metals and why the free-electron model is inadequate to give a quantitative description of the properties of most metals. Bloch’s theorem was formulated by the Swiss-born US physicist Felix Bloch (1905–83) in 1928. See also energy band.