Semiclassical Solution of the Quantum Hydrodynamic Equation for Trapped   Bose-condensed Gas in the l=0 Case
  In this paper the quantum hydrodynamic equation describing the collective, low energy excitations of a dilute atomic Bose gas in a given trapping potential is investigated with the JWKB semiclassical method. In the case of spherically symmetric harmonic confining potential a good agreement is shown between the semiclassical and the exact energy eigenvalues as well as wave functions. It is also demonstrated that for larger quantum numbers the calculation of the semiclassical wave function is numerically more stable than the exact polynomial with large alternating coefficients. 
Tamas Tasnadi