COLLECTIVE EXCITATIONS OF WEAKLY COUPLED BOSE CONDENSATES CONFINED INHARMONIC TRAPS

We use ordinary first-order perturbation theory in the mean-field inte raction to derive analytic expressions for the frequencies of the exci tation modes of a dilute Bose-Einstein condensate under confinement. T he confining trap is modelled by a harmonic potential having either sp herical or cylindrical symmetry. The expressions obtained are valid fo r all quantum numbers of the appropriate symmetry and for attractive a s well as repulsive effective interactions. Comparison with available numerical calculations is made.