Analytical results for the interaction energy of a trapped, weakly interacting Bose-Einstein condensate

We examine the problem of a repulsive, weakly interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per particle is between zero and one and find that the interaction energy decreases linearly as a Function of the angular momentum in agreement with previous numerical and limiting analytical studies.