 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/33b/b/i/solution

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

The unperturbed ground state is

∣0, 0 ⟩

ℏ ω

. Since

H_{int} ∣0, 0 ⟩ = \frac{λ ℏ}{2 ω} ∣1, 1 ⟩,

∣Ω ⟩ = ∣0, 0 ⟩ - \frac{λ}{4 ω ^{2}} ∣1, 1 ⟩ + O (λ^{2}), E_{Ω} = ℏ ω + O (λ^{2}) .

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