Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2019 / Paper 2 / Section A(ii) / 15 / iv / c / Solution

The measured energy selects $n=3$. Immediately after an ideal projective measurement, the normalized state is ${\psi }_3(x)$ up to an overall phase, with no surviving $n=1,2,4$ components. At later times before any further disturbance it is $e^{-i9c(t-t_0)/\hslash }{\psi }_3(x)$, where $t_0$ is the measurement time. A repeated energy measurement returns $9c$ with probability one.