Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section F / 46 / a / ii / Solution

The probability current isFor the incident and transmitted travelling waves, $j_{\mathrm{in}}=\hslash k|A{|}^2/m$ and $j_{\mathrm{tr}}=\hslash k|F{|}^2/m$. Thus $P(E)=|F/A{|}^2$ here. If the asymptotic wave numbers differed, the ratio of outgoing to incoming velocities would also be required. Current conservation gives $P+|B/A{|}^2=1$ for a real nonabsorbing barrier.