Employing asymptotic formulas from the partition theory of numbers, we derive the microcanonical probability distribution of the ground state occupation number for a one-dimensional ideal Bose gas confined at low temperatures by a harmonic potential. We compare the grand canonical analysis to the microcanonical one, and show how the fluctuation catastrophe characteristic for the grand canonical ensemble is avoided by the proper microcanonical approach. © 1996 The American Physical Society.

• Received 8 February 1996

DOI:https://doi.org/10.1103/PhysRevE.54.3495