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 > T_c) this function has the usual form ω₀(n₀) =(1 — e^μ)e^μn_o, where μ is the chemical potential in the temperature units. For T < T_c, 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.