We just need the result that we obtained for a constant perturbation, Fermi’s Golden Rule, to compute the rate of transitions between the initial state (free particle of momentum \({\bf p}\)) to the f...We just need the result that we obtained for a constant perturbation, Fermi’s Golden Rule, to compute the rate of transitions between the initial state (free particle of momentum \({\bf p}\)) to the final state (free particle of momentum \({\bf p'}\)). \[V_{{\bf k'k}} \equiv \langle {\bf k}' |\hat{V} |{\bf k} \rangle = \int \int \int u^*_{{\bf k'}} ({\bf r}) V ({\bf r})u_{{\bf k}}({\bf r}) d\tau. \nonumber\]
