1996/07/24 by Alexander L. Fetter · 2 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Strong Light-Matter Interactions #cond-mat
paper · pdf · doi:10.1007/bf02395929
14 pages, RevTeX, submitted to Journal of Low Temperature Physics
arxiv created 1996/07/24 · openalex publication_date 1997/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation for N0 condensed bosons in an isotropic harmonic trap with oscillator length d0 and interacting through a repulsive two-body scattering length a>0. The dimensionless parameter \cal N0 ≡ N0a/d0 characterizes the effect of the interparticle interactions, with \cal N0 ≪ 1 for an ideal gas and \cal N0 ≫ 1 for a strongly interacting system (the Thomas-Fermi limit). The trial function interpolates smoothly between these two limits, and the three separate contributions (kinetic energy, trap potential energy, and two-body interaction energy) to the variational condensate energy and the condensate chemical potential are determined parametrically for any value of \cal N0, along with illustrative numerical values. The straightforward generalization to an anisotropic harmonic trap is considered briefly.