 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-4/33b/a/i/solution

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

J = J_{1} \otimes I_{2} + I_{1} \otimes J_{2} .

Suppressing the identity operators, its components and ladder operators are

J_{x} = J_{1 x} + J_{2 x}, J_{y} = J_{1 y} + J_{2 y}, J_{z} = J_{1 z} + J_{2 z},

J_{\pm} = J_{x} \pm i J_{y} = J_{1 \pm} + J_{2 \pm} .

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