Abstract

The quantum dynamics of an electron in a uniform magnetic field is studied for two-dimensional geometries corresponding to integrable cases. The WKB approximations of the energies and the eigenfunctions of the semi-infinite plane and the disk are obtained. These analytical solutions are shown to be in excellent agreement with the numerical results obtained from the Schrodinger equations even for the lowest revels. It is shown for strong fields that the coalescence of the caustics with the boundary has to be taken into account in order to describe the gradual transition in the spectrum from Landau-like levels into edge levels.