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Homework Help: Partition function

  1. Apr 11, 2008 #1
    1. The problem statement, all variables and given/known data
    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?


    2. Relevant equations



    3. 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?
     
  2. jcsd
  3. Apr 11, 2008 #2
    Even without quantum considerations, you end up with over counting if the particles are identical. See Gibb's Paradox.
     
  4. Apr 11, 2008 #3
    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?
     
  5. Apr 12, 2008 #4
    It is not true for the quantum case. The quantum case is easier handled via grand-partition function.
     
  6. Apr 12, 2008 #5
    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?
     
  7. Apr 13, 2008 #6
    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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