 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2010/paper-2/section-a/2/solution

c_{n}, c_{n^{'}}

and a time-independent observable

A

⟨ A ⟩ (t) = ∣ c_{n} ∣^{2} A_{nn} + ∣ c_{n^{'}} ∣^{2} A_{n^{'} n^{'}} + 2 Re [c_{n}^{*} c_{n^{'}} A_{n n^{'}} e^{- i (n^{'} - n) ω t}] .

The interference term therefore has

T = \frac{2 π}{∣ n - n ^{'} ∣ ω} (n \neq = n^{'}) .

This is the period of two-state quantum interference. If the off-diagonal matrix element or either amplitude vanishes, the expectation value is constant, so this is not its unique fundamental period. Equal energies likewise give no beat.

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