Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / Section A / A5 / Solution

The infinite square well levels for width $L$ are $E_n=n^2{h}^2/(8m_e{L}^2)$. Starting in the ground state, the smallest excitation is $1\to 2$, and its electric-dipole matrix element is nonzero. It therefore sets the longest absorption wavelength:The corresponding energy separation is about $12.4\mathrm{eV}$. Elastic scattering of light is a different process from the stipulated absorption into an excited well state.