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

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

1996-11-19

arxiv.org/abs/cond-mat/9611141v1

J. Phys.: Cond. Matter 9 (1997) 4643 - 4657

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

27 pages. LaTeX. 6 figures not included

Scientific paper

10.1088/0953-8984/9/22/017

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 \beta=(effective Rydberg/effective dot energy)^{1/6}. Two-point Pade approximants are obtained from the series expansions of the energy near the oscillator ($\beta\to 0$) and Wigner ($\beta\to\infty$) limits. The approximants are expected to work with an error not greater than 2.5% in the entire interval $0\le\beta < \infty$.

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