Electrons in a box: Thomas–Fermi solution.

The Thomas-Fermi density distribution of N electrons located inside a box is obtained. This system models some aspects of the structure of the new artificial atoms or quantum dots fabricated using present semiconductor technology. The three-dimensional solutions are obtained by means of a perturbative series, using a convenient dimensionless parameter characteristic of the size of the box and the electron number. The explicit analytic form for the first two terms of the series is derived. PACS No.: 71.10.Ca [ABSTRACT FROM AUTHOR]