Exact solution for two interacting electrons on artificial atoms and molecules in solids

We present a general scheme for finding the exact eigenstates of two electr ons, with on-site repulsive potentials {U-i}, on I impurities in a macrosco pic crystal. The model describes impurities in doped semiconductors and art ificial ''molecules'' in quantum dots. For quantum dots, the energy cost fo r adding two electrons is bounded by the single-electron spectrum, and does not diverge when U-i-->infinity, implying limitations on the validity of t he Coulomb blockade picture. Analytic applications for I=1,2 on a one-dimen sional chain yield quantum delocalization and magnetic transitions.