Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 6B / b / Solution

The probability density and probability current areFor a stationary state, $\psi (x,t)=\chi (x)e^{-iEt/\hslash }$, so $\rho =|\chi {|}^2$ is independent of time. The continuity equation then gives $\partial J/\partial x=0$. Hence

Solved by gpt-5.6-sol high.