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Homework Help: Statistical physics. Density matrix

  1. May 5, 2016 #1
    1. The problem statement, all variables and given/known data
    A system is subject to Hamiltonian ##\hat{H}=-\gamma B_z \hat{S}_z##. Write down the density matrix.

    2. Relevant equations
    For canonical ensemble
    ##\hat{\rho}=\frac{1}{Tr(e^{-\beta \hat{H}})}e^{-\beta \hat{H}}##

    In general ##\rho=\sum_m |\psi_m\rangle \langle \psi_m|##

    3. The attempt at a solution
    How to know which definition of density matrix to use? Thanks.
  2. jcsd
  3. May 5, 2016 #2


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    Science Advisor
    Gold Member
    2017 Award

    The density matrix (statistical operator) is, of course, not determined by just giving the Hamiltonian but by the state of the system, because the statistical operator describes the state of the system. So there must be something missing from the problem statement or it is implied to consider a system in thermal equilibrium and to use the canonical ensemble. In the latter case it's not that difficult, if (again some information missing in the problem statement!) you know what spin your particle, i.e., ##s \in \{0,1/2,1,\ldots \}##.
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