Energy levels of ground state and low-lying excited states of hydrogenic impurities in InAs quantum rings are investigated with effective mass approximation and perturbation method.It shows that energy levels of electron do not change with electronic radial coordinate.They have characteristics of two-dimensional hydrogen atom energy levels in parabolic potential platform area.Energy levels of electron are sensitively dependent on radius of the quantum ring.There exist a minimum on account of parabolic confinement potential in area of parabolic potential with finite depth.Degenerate energy levels of the first excited state for hydrogenic impurities are not relieved.As n ≥ 2 degenerate energy levels are split and energy spacings increase with increase of the radius.

Ground-state energy of a planar quantum dot with two electrons is calculated with perturbation theory, numerically exact diagonalization and variational theory. Compared with earlier unrestricted Hartree-Fock studies, it is shown that a three-parameter variational wave function is an excellent representation of true ground state. It provides references for the understanding of planar quantum dots with more electrons.