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States counting of many particales under a constraint

  1. Oct 27, 2009 #1
    Let’s say i have n identical classical non interacting particles and N sites where i can put them in. BUT the total energy is given.
    The number of possible states is (N)^n/n!/(n/2)!
    Where N^n is the total possibilities to arrange the particles.
    We divide it by n! since they are identical.
    and the reason we divide by (n/2)! has some thing to do with the fact that the energy is given but I don’t know how.

    i whould be very thankful to any one who can say why (n/2)!

    thanks shai
     
  2. jcsd
  3. Oct 27, 2009 #2
    What determines the energy for a given distribution? This is kinda the input you need for the question you're asking...
     
  4. Oct 27, 2009 #3
    Maxwell - Boltzman as usual. I though about it but i fail to see how it leads to the n/2!
     
  5. Oct 27, 2009 #4
    No, no, that's a distribution function for finite temperature. You're working in a microcanonical ensemble, so you don't have temperature (the energy is fixed).

    What I'm asking is: what's the energy for a given configuration of the particles among the lattice sites. Do all configurations give the same energy or not? It's the only possible source of where the (n/2)! is coming from as far as I can tell.
     
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