ABSTRACT
At low temperatures, the number of particles in the ground state, with ε = 0, becomes large, and care must be exercised in the evaluation of the integral. e density of states given by Equation 4.14 has the form ρ(ε) ∝ ε1/2, which gives ρ(ε) = 0 for ε = 0. e ground state is therefore excluded in the integral. For fermions, this introduces a negligible error because the exclusion principle prevents multiple occupancy of a particular state but for bosons this is not the case. At very low temperatures, the number of bosons in the ground state may be expected to become macroscopically large.
