Semiclassical Solution of the Quantum Hydrodynamic Equation for Trapped Bose-condensed Gas in the l=0 Case
arXiv:cond-mat/0011076 · doi:10.1103/PhysRevA.63.023614
Abstract
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.
12 pages, 7 figures
References in corpus (7)
- Theory of Bose-Einstein condensation in trapped gases
- Low-energy elementary excitations of a trapped Bose-condensed gas
- Hydrodynamic excitations of Bose condensates in anisotropic traps
- Collective excitations in Bose-Einstein condensates in triaxially anisotropic parabolic traps
- Classical quasi-particle dynamics in trapped Bose condensates
- Semiclassical wave functions and energy levels of Bose-condensed gases in spherically symmetric traps
- Quasi-particle excitations and dynamical structure function of trapped Bose-condensates in the WKB approximation