Magnetic field dependence of the exciton energy in a quantum disk

The groundstate energy and binding energy of an exciton, confined in a^M quantum disk, are calculated as a function of an external magnetic field. The confinement potential is a hard wall of finite height. The diamagnetic shift is investigated for magnetic fields up to 40$T$. Our results are applied to $In_{y}Al_{1-y}As/Al_{x}Ga_{1-x}As$ self-assembled quantum dots and very good agreement with experiments is obtained. Furthermore, we investigated the influence of the dot size on the diamagnetic shift by changing the disk radius. The exciton excited states are found as a function of the magnetic field. The relative angular momentum is not a quantum number and changes with the magnetic field strength.