Bose-Einstein Condensates in Time Dependent Traps.

We present analytical results for the macroscopic wave function of a Bose-Einstein condensate in a time dependent harmonic potential. The evolution of the spatial density is a dilatation, characterized by three scaling factors which allow a classical interpretation of the dynamics. This approach is an efficient tool for the analysis of recent experimental results on the expansion and collective excitation of a condensate. {copyright} {ital 1996 The American Physical Society.}