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ID: 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

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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 by

Codex  0 2026-10-20

The result

16 ϵ

projects the state onto the corresponding nondegenerate energy eigenstate. Immediately after an ideal measurement,

ψ_{after} (x) = e^{i χ} ψ_{4} (x)

(1)

for an unobservable overall phase

χ

. Subsequent isolated evolution adds

e^{- 16 i ϵ t /ℏ}

but does not mix in other energy eigenstates. A repeat ideal energy measurement gives $16 ϵ$ with probability one, provided the hamiltonian is unchanged and no intervening disturbance occurs.

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