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Statistical operator

  1. May 27, 2013 #1
    I have a question about statistical operator. In statistical physics you deal with temperature. So for example ##\hat{\rho}=\frac{1}{Z}e^{-\beta \hat{H}}## where ##\beta=\frac{1}{k_BT}##. In definition there is temperature. And also equivalent definition is
    ##\hat{\rho}=\sum_i w_i|\psi_i\rangle \langle \psi_i|## where in definition isn't temperature. I'm confused about this. Can you give me some explanation?
     
  2. jcsd
  3. May 27, 2013 #2
    Both your definitions are the same, the second is just the general expansion of a one-body operator. [itex]w_i[/itex] is the probability of being in state i, given by [itex]\langle\psi_i| \tfrac{1}{Z} e^{-\beta \hat{H}} |\psi_i\rangle[/itex]. It's the same as the first definition.
     
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