In a crystal lattice, the wavefunctions ψ ψ k ( r ) and ψ ψ k ′ ( r ) are simply Bloch waves. When it is possible, analytic expression of the Matrix elements are commonly found by Fourier expanding the Hamiltonian H', as in the case of Impurity scattering or acoustic phonon scattering. In the important case of a transition from an energy state E to an energy state E' due to a phonon of wave vector q and frequency ω ω q , the energy and momentum change is: