Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 13B / iii / Solution

Using the quadratic form of the Hamiltonian,
$E_{av}=({\hslash }^2/2m)\int |\psi \prime {|}^{2}dx=2{\pi }^2{\hslash }^2/(m{a}^2)$.

Solved by gpt-5.6-sol high.