 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-2/15a/v/solution

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

With

L = x p_{y} - y p_{x}

, the canonical commutators give

[L, x] = i ℏ y, [L, y] = - i ℏ x, [L, p_{x}] = i ℏ p_{y}, [L, p_{y}] = - i ℏ p_{x} .

[L, x^{2} + y^{2}] = 0, [L, p_{x}^{2} + p_{y}^{2}] = 0.

Therefore rotational symmetry of the isotropic oscillator gives

[L, H] = 0 .

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