 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-3/6b/b/solution

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

ρ = ∣ ψ ∣^{2}, J = \frac{ℏ}{2 mi} (ψ^{*} \frac{\partial ψ}{\partial x} - ψ \frac{\partial ψ ^{*}}{\partial x}) .

ψ (x, t) = χ (x) e^{- i Et /ℏ}

, so

ρ = ∣ χ ∣^{2}

is independent of time. The continuity equation then gives

\partial J / \partial x = 0

. Hence

J is independent of x .

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