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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 Bose-Einstein condensate.
Girardeau et al. (Mon,) studied this question.