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By exact numerical solutions of the Gross-Pitaevskii (GP) equation in 3D, weassess the validity of 1D and 2D approximations in the study of Bose-Einsteincondensates confined in harmonic trap potentials. Typically, theseapproximations are performed when one or more of the harmonic frequencies aremuch greater than the remaining ones, using arguments based on the adiabaticevolution of the initial approximated state. Deviations from the 3D solutionare evaluated as a function of both the effective interaction strength and theratio between the trap frequencies that define the reduced dimension where thecondensate is confined. The observables analyzed are both stationary anddynamical character, namely, the chemical potential, the wave functionprofiles, and the time evolution of the approximated 1D and 2D stationarystates, considered as initial states in the 3D GP equation. Our study, besidessetting quantitative limits on approximations previously developed, should beuseful in actual experimental studies where quasi-1D and quasi-2D conditionsare assumed. From a qualitative perspective, 1D and 2D approximations certainlybecome valid when the anisotropy is large, but in addition, the interactionstrength needs to be above a certain threshold.

Validity of Gross-Pitaevskii solutions of harmonically confined BEC gases in reduced dimensions