Recursive approaches determining the canonical ideal Bose gas partition function are reviewed that enable the Bose-Einstein condensate occupation probability to be calculated for a finite number of particles ensemble, where the thermodynamic limit approximation fails. In addition to the earlier known method recursive with respect to the number of particles, an iteration procedure with respect to the number of quantum states is proposed. The efficiency of both methods is demonstrated for an ideal Bose gas in a three-dimensional isotropic harmonic trap.

PACS: 05.30.Jp, 67.85.−d (all) DOI: 10.3367/UFNe.0180.201001e.0089 URL: https://ufn.ru/en/articles/2010/1/d/ 000278717900004 2-s2.0-77954799449 2010PhyU...53...83T Citation: Trifonov E D, Zagoulaev S N "On the Bose-Einstein condensate partition function for an ideal gas" Phys. Usp. 53 83–90 (2010) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Трифонов Е Д, Загуляев С Н «О функции распределения числа частиц в бозе-эйнштейновском конденсате идеального газа» УФН 180 89–96 (2010); DOI: 10.3367/UFNr.0180.201001e.0089