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Elementary Excitations in a BEC with Isotropic Harmonic Trap: Bogoliubov Equations versus Hydrodynamic Formalism

The elementary excitations for a BEC trapped by means of an isotropic harmonic oscillator are studied in the present work. The analysis of these perturbations is done in the context of the Bogoliubov equations and not resorting to the hydrodynamic version. The comparison between these two approaches will allow us to deduce a parameter explaining the role that the scattering length and the trap play in the way in which the frequency of these elementary excitations acquires information about the angular momentum of the corresponding solutions. It will be shown that outside the validity realm of the Thomas_fermi approximation the frequencies of the perturbations cannot inherit the information of the angular momentum codified in the functions escribing the elementary excitations.