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## Main Question or Discussion Point

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

$$

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