 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/ib/paper-4/6b/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

[A, B^{2}] = [A, B] B + B [A, B]

[L_{1}, L_{2}^{2}] [L_{1}, L_{3}^{2}] [L_{1}, L_{1}^{2}] = i ℏ (L_{3} L_{2} + L_{2} L_{3}), = - i ℏ (L_{2} L_{3} + L_{3} L_{2}), = 0.

The first two expressions cancel, even though the factors need not commute. Hence

[L_{1}, L^{2}] = 0.

The squared angular momentum operator commutes with each of its components by the same cyclic calculation.

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