 Solution

ID: past-exam-of-the-theoretical-physics-ii-course-of-the-university-of-cambridge/2014/paper-1/4/a/solution

With

β = (k_{B} T)^{- 1}

, the normalized canonical density operator is

ρ = \frac{e ^{- β H}}{Z}, Z = Tr e^{- β H} .

Its eigenvalues are the Boltzmann probabilities and its trace is one.

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