LOW-ENERGY EXCITATIONS OF A BOSE-EINSTEIN CONDENSATE - A TIME-DEPENDENT VARIATIONAL ANALYSIS

We solve the time-dependent Gross-Pitaevskii equation by a variational ansatz to calculate the excitation spectrum of a Bose-Einstein conden sate in a trap. The trial wave function is a Gaussian which allows an essentially analytical treatment of the problem. Our results reproduce numerical calculations over the whole range from small to large parti cle numbers, and agree exactly with the Stringari results in the stron g interaction limit. Excellent agreement is obtained with the recent J ILA experiment and predictions for the negative scattering length case are also made.