Help with canonical ensemble

  • Thread starter romeo6
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  • #1
romeo6
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Hi there,

I have a system with the following energy using the einstein model:

[tex]E_\nu=\sum_{i=1}^{2N} h\omega n_i+\sum_{j=1}^{N} h\omega n_j[/tex]
I need to set up a canonical ensemble for this.

How would I write the partition function please?
 

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  • #2
Dr Transport
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Isn't the partition function defined as

[tex] \int \frac{d^{3N}p d^{3N}q}{N! h^{3N}} e^{-\beta H(p,q)} [/tex]

for [tex] N [/tex] particles. You just need to substitute for the energy that you have and perform the integration (hint integrate over all the freuqncies [tex] \omega [/tex] and you should only have to do one and simplify).
 
  • #3
dextercioby
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First, it't [itex] \hbar [/itex] instead of "h" in E_{\nu}. Second, this looks like an application of quantum statistics, and so the classical partition function won't be of any use.

Daniel.
 
  • #4
romeo6
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Thanks, I think my problem is that I don't know how to set this up as thesummations have different upper values.

I want to write something like:

[tex]Q=\sum_{i=1}^{2N} e^{-\beta \hbar n_i}+\sum_{j=1}^N e^{-\beta \hbar n_j}[/tex]

where Q is the partition function.

Does this look anything like the partition function?
 

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