The canonical commutation relation also implies that the position and momentum operators are Fourier conjugates of each other. Consequently, functions originally defined in terms of their position dependence can be converted to functions of momentum using the Fourier transform. In solid-state physics, the Schrödinger equation is often written for functions of momentum, as Bloch's theorem ensures the periodic crystal lattice potential couples \tilde{\Psi}(p) with \tilde{\Psi}(p+K) for only discrete reciprocal lattice vectors K . This makes it convenient to solve the momentum-space Schrödinger equation at each point in the Brillouin zone independently of the other points in the Brillouin zone.
