Solution (source code)

= Solution

The measured <energy> selects $n=3$. Immediately after an ideal <projective measurement>, the normalized state is \b[$\psi_3(x)$ up to an overall phase], with no surviving $n=1,2,4$ components. At later times before any further disturbance it is $e^{-i9c(t-t_0)/\hbar}\psi_3(x)$, where $t_0$ is the measurement time. A repeated <energy measurement> returns \b[$9c$ with <probability> one].