The Cloud of Bose-Einstein Condensate in a harmonic trap

In this paper, we calculate the volume of a Bose-Einstein condensate (BEC) cloud confined within a harmonic trap induced by a magneto-optical trap. Three primary factors influencing the volume of the BEC cloud are examined: thermal motion, interatomic interactions, and the uncertainty in momentum and position. These considerations enable the definition of certain thermodynamic variables, leading to the establishment of the thermodynamic equations of state.