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Partition function for position-independent hamiltonian

  1. Sep 17, 2013 #1
    Hi everyone. Suppose I have an Hamiltonian which doesn't depend on the position (think for example to the free-particle one [itex]H=p^2/2m[/itex]). I know that the classical partition function for the canonical ensemble is given by:
    $$
    Z(\beta)=\int{dpdq e^{-\beta H(p,q)}}.
    $$

    What does it happen to the integration over [itex]dq[/itex] if there is no q-dependence in the Hamiltonian? Is it just the volume of the system?

    Thank you
     
  2. jcsd
  3. Sep 18, 2013 #2
    yes,what you will get by this free particle hamiltonian is the single particle partition function for the classical ideal gas.You can evaluate things per unit volume.
     
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