The calculation of stationary states is simplified considerably for periodic solids in which all of the potentials v i ( r i ) are the same, and the nuclear positions R i form a periodic array. Bloch's theorem holds for such a system, which means that the solutions of the Schrödinger equation may be written as a Bloch wave ψ ψ k ( r + R i ) = e i k ⋅ ⋅ R i ψ ψ k ( r ) .