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

2000/11/05 by Tamás Tasnádi, Tamas Tasnadi
Physics and Astronomy · #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Eigenvalues and eigenvectors #Harmonic oscillator #Mathematical physics #Physics #Quantum #Quantum mechanics #Quantum, superfluid, helium dynamics #Semiclassical physics #Strong Light-Matter Interactions #Trapping #Wave function #cond-mat.soft #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreva.63.023614

12 pages, 7 figures

arxiv created 2000/11/05 · openalex publication_date 2001/01/18 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper the quantum hydrodynamic equation describing the collective, low-energy excitations of a dilute atomic Bose-Einstein 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.

Citations

• Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions
• Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor
• Semiclassical approximations in wave mechanics
• Structure of a quantized vortex in boson systems
• Low-energy elementary excitations of a trapped Bose-condensed gas
• On Certain Approximate Solutions of Lineae Differential Equations of the Second Order *
• Bose-Einstein Condensation in a Gas of Sodium Atoms