Statistical Mechanics of a Trapped Bose-Einstein Condensate

Bose-Einstein condensation (BEC) in a gas has now been achieved. Alkali atoms ($^{87}Rb$, $^{23}Na$ and $^{7}Li$) have been cooled to the point of condensation (temperature of 100 nK) using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. This important experimental result has also renewed the interest on theoretical studies of BEC. In this contribution we discuss the statistical mechanics of the trapped BEC at zero temperature. In particular, we study the stability of the condensate by using a variational method with local and non-local interaction between the particles.