  The quantum dynamics of an electron in a uniform magnetic field is studied
for geometries corresponding to integrable cases. We obtain the uniform
asymptotic approximation of the WKB energies and wavefunctions for the
semi-infinite plane and the disc. These analytical solutions are shown to be in
excellent agreement with the numerical results obtained from the Schrodinger
equations even for the lowest energy states. The classically exact notions of
bulk and edge states are followed to their semi-classical limit, when the
uniform approximation provides the connection between bulk and edge.
