 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/34c/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

∣ n_{1} n_{2} ⟩

n_{a} \in {0, 1}

, are exact eigenvectors, with

H_{tot} ∣ n_{1} n_{2} ⟩ = (E_{1} n_{1} + E_{2} n_{2}) ∣ n_{1} n_{2} ⟩ .

Thus the energies attached to

∣00 ⟩, ∣01 ⟩, ∣10 ⟩, ∣11 ⟩

are respectively

0, E_{2}, E_{1}, E_{1} + E_{2} .

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