 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-3/6c/solution

Codex  0 Created 2026-09-23 Updated 2026-10-03

Q ψ = x ψ, P ψ = - i ℏ \partial_{x} ψ .

Differentiating the expectation, substituting Schrödinger's equation, and integrating by parts gives Ehrenfest's relation

\frac{d}{d t} ⟨ P ⟩ = \frac{i}{ℏ} ⟨[H, P]⟩ = - k ⟨ Q ⟩ .

Thus the mean momentum changes according to the classical mean force $- k x$ .

 New to topics? Read the docs here!