Bose Condensate in External Potential : A Thomas - Fermi Approach

The Thomas-Fermi method [1] [2] was designed for the calculation of the electron density in a heavy atom, by treating the electrons as locally free. Lieb and Simon [3] showed that the treatment is exact in the limit when the atomic number goes to infinity. Application to a confined Bose condensate was pioneered by Goldman, Silvera, and Legget [4], and by Oliva [5], and recently reconsidered by Chou, Yang, and Yu [6]. I shall describe some work on this subject, done in collaboration with E. Timmermans and P. Tommasini [7]. First, let us review the original method of Thomas and Fermi. Suppose V (r) = −eΦ(r) denotes the effective potential energy of an electron in an atom, at a distance r from the nucleus. (See Fig.1).