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Partition function

  • Thread starter Pacopag
  • Start date
  • #1
197
4

Homework Statement


If we have a system of N independent particles and the partition function for one particle is Z_1, then is the partition function for the N particle system Z=(Z_1)^N?


Homework Equations





The Attempt at a Solution


I'm pretty sure that this is true for a classical system, but I'm not sure if it's true for a quantum system. Does the Pauli exclusion principle spoil this somehow?
 

Answers and Replies

  • #2
980
2
Even without quantum considerations, you end up with over counting if the particles are identical. See Gibb's Paradox.
 
  • #3
197
4
Right. Sorry, I meant to write
[tex]Z={1\over {N!}}(Z_1)^N[/tex]
Does that take care of over counting?
What about the quantum case?
 
  • #4
980
2
It is not true for the quantum case. The quantum case is easier handled via grand-partition function.
 
  • #5
197
4
So in the quantum case, if we want to use the canonical ensemble, we have to calculate the whole partition function all in one shot?
 
  • #6
980
2
Yep. But like I said, usually, you calculate the grand-partition function (which factorises neatly into a function of single particle states).
 

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