We develop a method of finding analytical solutions of the Bogolyubov-de Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose-Einstein condensation.

Phys. Rev. A

Öhberg, P., Surkov, E. L., Tittonen, I., Stenholm, S., Wilkens, M., & Shlyapnikov, G. V. (1997). Low-energy elementary excitations of a trapped Bose-condensed gas. Phys. Rev. A, 56, 3346–3349.