 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-2/35c/b/solution

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

Use the ordered basis

(∣3/2 ⟩, ∣1/2 ⟩, ∣ - 1/2 ⟩, ∣ - 3/2 ⟩) .

The ladder coefficients are

3, 2, 3

, so

S_{+} = ℏ 0000300002000030, S_{-} = S_{+}^{†} .

Therefore

S_{x} = \frac{ℏ}{2} 0300302002030030

and

S_{y} = \frac{ℏ}{2} 0 i 3 00 - i 3 0 2 i 0 0 - 2 i 0 i 3 00 - i 3 0 .

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