Partition function for position-independent hamiltonian

  • Thread starter Einj
  • Start date
  • #1
470
58

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
 

Answers and Replies

  • #2
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.
 

Related Threads on Partition function for position-independent hamiltonian

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
504
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
9K
Replies
0
Views
906
  • Last Post
Replies
16
Views
9K
Replies
2
Views
852
Top