 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-2/32c/b/solution

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

Suppose a normalizable solution satisfies

L ψ = - κ^{2} ψ

\overline{ψ}

, integration over

R

- κ^{2} \int_{R} ∣ ψ ∣^{2} d x = \int_{R} \overline{ψ} L ψ d x = \int_{R} p^{2} ∣ ψ^{'} ∣^{2} d x \geq 0.

The boundary term vanishes for a normalizable eigenfunction. The left side is negative unless

ψ = 0

, so no nontrivial normalizable solution exists.

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