 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/34e/b/i/solution

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

Translation preserves the alternating on-site term only when

(- 1)^{j + ℓ} = (- 1)^{j}

, so

[H_{t}, T_{ℓ}] = 0 ⟺ ℓ \in 2 Z .

The primitive lattice spacing is therefore

2 a

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