Density matrix in the canonical ensemble

  • #1
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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.
 

Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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