The Bose-Einstein statistics of particles, with special reference to the case of low temperatures

Abstract

In this paper, it has been shown that the usual demonstrations of the phenomenon of Bose-Einstein condensation are invalid. Exact formal solutions have been derived for the partition functions and the mean occupation numbers in classical and Bose statistics, and the theory of fluctuations in the case of Bose statistics has been given.In a second paper, convenient approximations will be derived for the mean occupation numbers in Bose statistics, and it will be shown that for temperatures well above the critical temperature of the supposed Bose-Einstein condensation the well-known resultfor the mean occupation numbers is valid, whilst for temperatures rather lower than this critical value it will be shown that particles will condense into the lowest available state. The critical temperatureT0is given bywhere the summation is over all energy levels except the lowest.