Critical temperature and condensed fraction of Bose-Einstein condensation in an external potential

Based on Bose-Einstein condensation at minimized momentum state, we get the expressions for the critical temperature and condensed fraction of Bose-Einstein condensation (BEC) in an external potential in the three-dimensional (3D) case. For the 1D and 2D cases, we present not only the critical temperature and corresponding particles but also the condition of BEC occurrence.