A Variational Sum-Rule Approach to Elementary Excitations of a Trapped Bose-Einstein Condensate

We propose a new variational method which combines an excitation-energy sum rule and Fetter’s trial wave function to analytically find almost exact lowlying collective-mode frequencies of a trapped Bose-Einstein condensate. At zero temperature, our method gives excitation frequencies in excellent agreement with experimental results as well as numerical ones based on the Bogoliubov approximation. At finite temperature, it gives excitation frequencies in good agreement with numerical ones based on the Popov approximation. PACS numbers: 03.75.Fi, 05.30.jp, 67.40.Db, 67.55.Jd Typeset using REVTEX