 In particular, given an energy state , the number of non-interacting bosons in thermal equilibrium at temperature is given by the Bose occupation number

where the constant is determined by an equation describing the conservation of the number of particles

with being the density of states of the system.This last equation may lack a solution at low enough temperatures when for .In this case a critical temperature is found such that for the system is in a Bose-Einstein condensed phase and a finite fraction of the bosons are in the ground state.