Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 34D / c / Solution

The radial factoris sharply peaked, for large $n$, nearRequiring the orbit to lie inside a disk of radius $R$ permitsThus the total degeneracy at fixed $k_z$ is, up to the negligible boundary correction,Since the disk has area $\pi R^2$, the degeneracy of a Landau level per unit area isFor either sign of the charge-field product, replace $eB$ by $|eB|$.

Solved by gpt-5.6-sol high.