  We use a nonlinear Schroedinger-Poisson equation to describe two interacting
electrons with opposite spins confined in a parabolic potential, a quantum dot.
We propose an effective form of the Poisson equation taking into account the
dimensional mismatch of the two-dimensional electronic system and the
three-dimensional electrostatics. The results agree with earlier numerical
calculations performed in a large basis of two-body states and provide a simple
model for continuous quantum-classical transition with increasing nonlinearity.
Specific intriguing properties due to eigenstate non-orthogonality are
emphasized.
