Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 35C / b / Solution

The Bose-Einstein distribution isPositivity requires $\mu$ not to exceed the ground-state energy, here zero. For a finite system above the condensation limit one has $\mu <0$; it approaches zero from below at Bose-Einstein condensation.

Solved by gpt-5.6-sol high.