By taking the hydrodynamic limit we derive, at T=0, an explicit solution of
the linearized time dependent Gross-Pitaevskii equation for the order parameter
of a Bose gas confined in a harmonic trap and interacting with repulsive
forces. The dispersion law ω=ω0(2n2+2nℓ+3n+ℓ)1/2 for the
elementary excitations is obtained, to be compared with the prediction
ω=ω0(2n+ℓ) of the noninteracting harmonic oscillator model.
Here n is the number of radial nodes and ℓ is the orbital angular
momentum. The effects of the kinetic energy pressure, neglected in the
hydrodynamic approximation, are estimated using a sum rule approach. Results
are also presented for deformed traps and attractive forces.Comment: uuencoded file including 12 pages REVTEX and 1 figur