Abstract
We emulate the ground state and the single-vortex state of a Bose-Einstein condensate in an isotropic harmonic trap by constructing analytic simulacra of the wave functions in the regions around the origin and far from the origin. These simulacra are generalizations of asymptotic solutions of the nonlinear Schrodinger equation and they are matched by requiring continuity not only of the wave function and of its slope, but of its curvature as well. The resulting piecewise analytic simulacra coincide almost perfectly with the numerically obtained solutions. Analytic expressions are obtained for the kinetic energy and the number of atoms, and they too are in very good agreement with the corresponding numerical results.
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