Abstract

In the presence of interactions, when the scattering length a is much less than the mean interparticle spacing, the nonlinear Gross-Pitaevskii equation (GPE), which employs mean-field theory, can describe the zero-temperature properties of a non-uniform Bose-Einstein condensate [1]. In some restricted situations, exact analytical solutions have already been found, but in general, solutions to the Gross-Pitaevskii equation need numerical methods [2]. Here, we numericaly solve the time- independent Gross-Pitaevskii equation for a U-shaped permanent magnetic microtrap [3], created by permanent magnetic slabs, and obtain the wave function as well as density for the rubidium atoms. We also compare these solutions with the Tomas-Fermi wave function and density.