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The distribution function and fluctuations of the number of particles in an ideal Bose gas confined by a trap

The distribution function ω0(n0) of the number n0 of particles in the condensate of an ideal Bose gas confined by a trap is found. It is shown that at the temperature above the critical one (T > Tc) this function has the usual form ω0(n0) =(1 — eμ)eμno, where μ is the chemical potential in the temperature units. For T < Tc, this distribution changes almost in a jump to a Gaussian distribution, which depends on the trap potential only parametrically. The centre of this function shifts to larger values of n0 with decreasing temperature and its width tends to zero, which corresponds to the suppression of fluctuations.