Piecewise analytic approximation for Bose-Einstein condensates in isotropic harmonic traps

Abstract

Analytic simulacra of the wave functions in the regions around the origin and far from the origin were constructed to emulate the ground state and the single-vortex state of a Bose-Einstein condensate in an isotropic harmonic trap. It was found that the solution produced by this emulation for the ground state is an excellent approximation to the solution obtained numerically, for any value of N, large or small. Very simple analytic results for the wave function, the kinetic energy and the number of atoms were obtained. It was shown that the approximation can be very useful, because it provides a simple quantitative tool for the analysis of experimental data for trapped condensed gases, without relying on complex and extensive calculations.