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In this paper the quantum hydrodynamic equation describing the collective,low energy excitations of a dilute atomic Bose gas in a given trappingpotential is investigated with the JWKB semiclassical method. In the case ofspherically symmetric harmonic confining potential a good agreement is shownbetween the semiclassical and the exact energy eigenvalues as well as wavefunctions. It is also demonstrated that for larger quantum numbers thecalculation of the semiclassical wave function is numerically more stable thanthe exact polynomial with large alternating coefficients.Comment: 12 pages, 7 figure

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Semiclassical solution of the quantum hydrodynamic equation for trapped Bose-Einstein condensed gas in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>l</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mn /></mml:math>case

Semiclassical solution of the quantum hydrodynamic equation for trapped Bose-Einstein condensed gas in thel=0case