Finite size effects on the collective oscillations of a trapped Bose gas

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Sum rules are used to calculate the corrections to the hydrodynamic collective frequencies of a harmonically trapped Bose gas at T=0, due to finite size effects. We show that, with logarithmic accuracy, the relative corrections behave like (aho/R)⁴(R/aho), where R is the Thomas-Fermi radius of the condensate and aho is the oscillator length. Results are given for both spherical and axi-symmetric trapping.