 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/33b/a/i/solution

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

Since

O

commutes with every angular momentum operator, it commutes with

J^{2}

. Taking a matrix element of

[O, J^{2}] = 0

gives

(j^{'} (j^{'} + 1) - j (j + 1)) ⟨ j, m ∣ O ∣ j^{'}, m^{'} ⟩ = 0.

The allowed nonnegative values of

j

make

j (j + 1)

injective, so the matrix element vanishes unless

j = j^{'}

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