N electrons in a quantum dot: two-point Padé 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 . Two-point Padé approximants are obtained from the series expansions of the energy near the oscillator and Wigner limits. The approximants are expected to work with an error not greater than 2.5% over the entire interval .