Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions

TL;DR

This paper analyzes the convergence of the configuration-interaction method for quantum dots and introduces an effective interaction to improve accuracy, supported by numerical experiments.

Contribution

It proposes using an effective two-body interaction to enhance the convergence and accuracy of the configuration-interaction method for quantum systems.

Findings

Convergence of CI method is generally slow.

Effective interaction significantly improves accuracy.

Numerical results confirm enhanced performance.

Abstract

We give a thorough analysis of the convergence properties of the configuration-interaction method as applied to parabolic quantum dots among other systems, including \emph{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.