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We investigate the low energy excitations of a dilute atomic Bose gas confined in a harmonic trap of frequency ₀ and interacting with repulsive forces. The dispersion law 0ex{0ex}=0ex{0ex}₀ (2n^2+2n+3n+) ^1/2 for the elementary excitations is obtained for large numbers of atoms in the trap, to be compared with the prediction 0ex{0ex}=0ex{0ex}₀ (2n+) of the noninteracting harmonic oscillator model. Here n is the number of radial nodes and 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.
S. Stringari (Mon,) studied this question.
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