Semiclassical corrections to the oscillation frequencies of a trapped Bose-Einstein condensate

The oscillation frequencies of collective excitations of a trapped Bose-Ein stein condensate, when calculated in the mean-field approximation and in th e Thomas-Fermi limit, are independent of the scattering length a. We calcul ate the leading corrections to the frequencies from quantum fluctuations ar ound the mean field. The semiclassical correction is proportional to N(1/5) a(6/5). where N is the number of atoms in the condensate. The correction is positive semidefinite and is zero for surface modes whose eigenfunctions h ave a vanishing Laplacian. The shift in the frequency of the lowest quadrup ole mode for an axially symmetric trap is large enough that it should be me asurable in future experiments.