QUANTUM CORRECTIONS TO THE GROUND-STATE OF A TRAPPED BOSE-EINSTEIN CONDENSATE

In the mean-field approximation, the number density rho(r) for the gro und state of a Bose-Einstein condensate trapped by an external potenti al V(r) satisfies a classical field equation called the Gross-Pitaevsk ii equation. We show that quantum corrections to rho are dominated by quantum fluctuations with wavelengths of order 1/root(rho a), where a is the S-wave scattering length. By expanding the equations for the Ha rtree-Fock approximation to second order in the gradient expansion, we derive local correction terms to the Gross-Pitaevskii equation for rh o that take into account the dominant effects of quantum fluctuations. We also show that the gradient expansions for the density and for the condensate break down at fourth order and at second order, respective ly.