Excitons in a parabolic quantum dot in magnetic fields

The properties of an exciton in a parabolic quantum dot in an external magnetic field are studied theoretically using an effective-mass Hamiltonian. The results for the energy and the optical absorption of the ground state and the low-lying excited states are presented. The Hamiltonian is written in terms of the center of mass and relative coordinates, and it is shown that, due to the coupling between the center of mass and relative motion, optical-absorption energies reveal an interesting anticrossing behavior. It is also shown that the ground-state properties are approximately determined by that part of the total Hamiltonian that depends only on the relative coordinates.