Energy spectrum of a confined two-dimensional particle in an external magnetic field

The energy spectrum of a particle confined within a circle in the presence of an external magnetic field perpendicular to the plane of confinement is studied both exactly and approximately by the quasiclassical formalism (Wen tzel-Kramers-Brillouin). For pure spatial confinement (without magnetic fie ld) the energy spectrum for states other than the ground state is twofold d egenerate, while in the case of pure magnetic confinement the spectrum show s the infinite-fold degeneration, typical of Landau states. For both types of confinement, the latter infinite-fold degeneration is lifted due to spat ial confinement. Interestingly enough, for a given ratio between spatial an d magnetic confining lengths, the magnetic flux is quantized. The condition s for the quantization of the flux are established; the nature and peculiar ity of the energy spectrum are also discussed. (C) 2000 American Associatio n of Physics Teachers.