Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions

We give a thorough analysis of the convergence properties of the configuration-interaction method as applied to parabolic quantum dots among other systems, including a priori error estimates. The method converges slowly in general, and in order to overcome this, we propose to use an effective two-body interaction well known from nuclear physics. Through numerical experiments we demonstrate a significant increase in accuracy of the configuration-interaction method.