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Density matrix in the canonical ensemble

  1. Nov 14, 2014 #1
    1. The problem statement, all variables and given/known data

    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]

    2. Relevant 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]

    3. 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.
     
  2. jcsd
  3. Nov 20, 2014 #2
    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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