Abstract: We study the ground and first excited states of the neutral and charged shallow donor system confined in a GaAs quantum well (QW) along one direction and by a parabolic potential in the plane perpendicular to the QW. The influence of an external perpendicular magnetic field and of the position of the donor on the energy of the states is studied. We investigate the dependence of the ground and excited states of the negatively charged donor on the confinement potential and external magnetic field. When the donor is displaced from the center of the QW the presence of the lateral confinement shifts the magnetic field induced angular momentum transitions and shifts the unbinding to higher magnetic field. (C) 2003 Published by Elsevier B.V.