 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-1/13b/ii/solution

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

The walls give

ω = nπ / (2 a)

; normalisation gives

A = 1/ a

, and

E_{n} = ℏ^{2} π^{2} n^{2} / (8 m a^{2})

. Product-to-sum integration over

(- a, a)

gives

⟨ ψ_{n}, ψ_{m} ⟩ = δ_{nm}

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