The time independent Schrödinger equation for two electrons confined in an external potential is solved using semi-analytical methods. Approximation methods for more than two electrons are developed using the Hartree-Fock and Green Function methods of many-body theory. It is also demonstrated that, for a parabolic external potential, the determination of the strength of the external confinement is greatly improved by characterizing the strength of the confining potential separate from the effective mass.