 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/34a/d/solution

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

Since

[X, H] = i P

and

⟨ P ⟩ = 2 ω ℑ α

, the bound is

Δ X Δ H \geq ω /2 ∣ℑ α ∣

. The left side is

ω /2 ∣ α ∣

, so equality holds exactly when

ℜ α = 0

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