Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2018 / Paper 2 / Section A(ii) / 14 / ii / d / Solution

The result $16ϵ$ projects the state onto the corresponding nondegenerate energy eigenstate. Immediately after an ideal measurement,for an unobservable overall phase $\chi$. Subsequent isolated evolution adds $e^{-16iϵt/\hslash }$ but does not mix in other energy eigenstates. A repeat ideal energy measurement gives $16ϵ$ with probability one, provided the hamiltonian is unchanged and no intervening disturbance occurs.