 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/35c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

\overline{n}_{r} = \frac{1}{e ^{β (E_{r} - μ)} - 1} .

Positivity requires

μ

not to exceed the ground-state energy, here zero. For a finite system above the condensation limit one has

μ < 0

; it approaches zero from below at Bose-Einstein condensation.

 New to topics? Read the docs here!