Ground state properties of a one-dimensional condensate of hard core   bosons in a harmonic trap
  The exact N-particle ground state wave function for a one-dimensional condensate of hard core bosons in a harmonic trap is employed to obtain accurate numerical results for the one-particle density matrix, occupation number distribution of the natural orbitals, and momentum distribution. Our results show that the occupation of the lowest orbital varies as N^{0.59}, in contrast to N^{0.5} for a spatially uniform system, and N for a true BEC. 
M. D. Girardeau, E. M. Wright, and J. M. Triscari