Bose-Einstein condensation in the harmonic oscillator potential

The Bose-Einstein condensation of a dilute gas of rubidium-87 atoms was achieved by cooling a small number of atoms in a magnetic trap. The effective potential of the trap is to lowest order harmonic and under these conditions we estimate the critical temperature and the heat capacity of an ideal gas of Bose particles. Previously this has been estimated within the semiclassical approximation. However, because of the small number of atoms, the resulting $T_c$ deviates slightly from our result obtained by exact numerical calculations. For the gap of the heat capacity at the transition point the deviation is $20\%$.