Collective excitations of a trapped bose-condensed gas

We investigate the low energy excitations of a dilute atomic Bose gas confined in a harmonic trap of frequency omega(0) and interacting with repulsive forces. The dispersion law omega = omega(0)(2n(3) + 2nl + 3n + l)(1/2) for the elementary excitations is obtained for large numbers of atoms in the trap, to be compared with the prediction omega = omega(0)(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 are estimated using a sum rule approach. Results are also presented for deformed traps and attractive forces.