N electrons in a quantum dot: Two-point Pade approximants

Abstract

We present analytic estimates for the energy levels of N electrons (N = 2 - 5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter β=(effective Rydberg/effective dot energy)^{1/6}. Two-point Pade approximants are obtained from the series expansions of the energy near the oscillator ($β\to 0$) and Wigner ($β\to\infty$) limits. The approximants are expected to work with an error not greater than 2.5% in the entire interval $0\leβ< \infty$.

27 pages. LaTeX. 6 figures not included