 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-3/36a/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The Bose-Einstein distribution gives one occupation for the nondegenerate ground level and

M

identical contributions from the excited levels:

⟨ N_{0} ⟩ = \frac{1}{e ^{- β μ} - 1}, ⟨ N_{ϵ} ⟩ = \frac{M}{e ^{β (ϵ - μ)} - 1} .

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