 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/36e/b/solution

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

Write the normalized trial state as

1 - ϵ^{2} ∣0 ⟩ + ϵ ∣ η ⟩

with

η ⊥ 0

. The cross term vanishes because

H ∣0 ⟩ = E_{0} ∣0 ⟩

, so the energy error is

ϵ^{2} (⟨ η ∣ H ∣ η ⟩ - E_{0}) = O (ϵ^{2})

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