 Solution

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

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

i ℏ \partial_{t} ψ = H ψ

. Differentiate

⟨ A ⟩ = ⟨ ψ ∣ A ∣ ψ ⟩

, use the equation and its adjoint, and include explicit time dependence of the operator. This gives Ehrenfest theorem

i ℏ \frac{d}{d t} ⟨ A ⟩ = ⟨[A, H]⟩ + i ℏ ⟨ \frac{\partial A}{\partial t} ⟩ .

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