Abstract
A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation forN
0 condensed bosons in an isotropic harmonic trap with oscillator lengthd
0 and interacting through a repulsive two-body scattering lengtha>0. The dimensionless parameterN
0
≡ N
0
a/d characterizes the effect of the interparticle interactions, with
1 for an ideal gas and
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 ofN
0
, along with illustrative numerical values. The straightforward generalization to an anisotropic harmonic trap is considered briefly.
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Fetter, A.L. Variational study of dilute Bose condensate in a harmonic trap. J Low Temp Phys 106, 643–652 (1997). https://doi.org/10.1007/BF02395929
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DOI: https://doi.org/10.1007/BF02395929