Excitons in quantum dots with parabolic confinement

We study excitons in quantum dots with parabolic confining potentials, by solving the electron-hole effective-mass Hamiltonian. We obtain an exact solution for excitons in quantum dots. The exact solution can be obtained in this case because the parabolic form of the confining potential allows the separation of the center-of-mass coordinate and the relative coordinate. The center-of-mass motion of the exciton is a harmonic oscillator. Various approximation methods can now be tested against this exact solution. We compare our exact results with results produced by the configuration-interaction method.