 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2011/paper-2/section-b/b8/a/solution

Put

c = cos ω t

s = sin ω t

. The real part of the off-diagonal coherence vanishes:

⟨ S_{x} ⟩ = \frac{ℏ}{2} (c i s - i s c) = 0 .

This also follows from

[H, S_{x}] = 0

and its zero initial expectation. Individual measurements still give

\pm ℏ/2

, each with probability

1/2

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