text: The above problem raises the question for α > 1: if a Bose gas with a fixed number of particles is lowered down below the critical temperature, what happens?
  The problem here is that the Thomas–Fermi approximation has set the degeneracy of the ground state to zero, which is wrong. There is no ground state to accept the condensate and so particles simply disappear from the continuum of states. It turns out, however, that the macroscopic equation gives an accurate estimate of the number of particles in the excited states, and it is not a bad approximation to simply "tack on" a ground state term to accept the particles that fall out of the continuum:
  where N is the number of particles in the ground state condensate.
  Thus in the macroscopic limit, when T , the value of z is pinned to 1 and N takes up the remainder of particles. For T > T there is the normal behaviour, with N = 0. This approach gives the fraction of condensed particles in the macroscopic limit: