  The density of states of a Bose-condensed gas confined in a harmonic trap is
investigated. The predictions of Bogoliubov theory are compared with the ones
of Hartree-Fock theory and of the hydrodynamic model. We show that the
Hartree-Fock scheme provides an excellent description of the excitation
spectrum in a wide range of energy, revealing a major role played by
single-particle excitations in these confined systems. The crossover from the
hydrodynamic regime, holding at low energies, to the independent particle
regime is explicitly explored by studying the frequency of the surface mode as
a function of their angular momentum. The applicability of the semiclassical
approximation for the excited states is also discussed. We show that the
semiclassical approach provides simple and accurate formulae for the density of
states and the quantum depletion of the condensate.
