 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/15b/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The phase has unit modulus and

X = x + g t^{2} /2

, hence

⟨ X ⟩_{Θ} = ⟨ x ⟩_{ψ} + \frac{1}{2} g t^{2} .

⟨ X ⟩ = a + v t

. Therefore

⟨ x ⟩_{ψ} = a + v t - \frac{1}{2} g t^{2} .

The wavepacket centre obeys the classical constant-acceleration trajectory, an instance of the correspondence principle.

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