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

Orthonormal energy eigenstates contribute incoherently to the expectation of energy:Therefore $⟨E⟩\simeq 13.2018ϵ$ for the normalized literal decimals. Ignoring the small rounding-induced norm error gives $13.2104ϵ$, conventionally reported at this precision as about $13.2ϵ$. The mean need not equal an individual energy eigenvalue.