Partition function for position-independent hamiltonian

  • Thread starter Einj
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  • #1
Einj
470
58
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
 

Answers and Replies

  • #2
andrien
1,024
32
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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