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## Homework Statement

We have a quantum rotor in two dimensions with a Hamiltonian given by [tex]\hat{H}=-\dfrac{\hbar^2}{2I}\dfrac{d^2}{d\theta^2} [/tex]. Write an expression for the density matrix [tex]\rho_ {\theta' \theta}=\langle \theta' | \hat{\rho} | \theta \rangle[/tex]

## Homework Equations

[tex]\hat{H}=-\dfrac{\hbar^2}{2I}\dfrac{d^2}{d\theta^2} [/tex]

[tex]\rho_ {\theta' \theta}=\langle \theta' | \hat{\rho} | \theta \rangle[/tex]

## The Attempt at a Solution

In the canonical ensemble, I know that [tex] \hat{\rho} [/tex] is given by:

[tex] \hat{\rho} =\dfrac{1}{Z} e^{-\beta \hat{H}}[/tex] where Z is the partition function. But this is about as far as I can get. Any assistance towards a solution would be greatly appreciated.