How to Write a Canonical Ensemble for a System Using the Einstein Model

[romeo6]

Hi there,

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

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

How would I write the partition function please?

 

[Dr Transport]

Isn't the partition function defined as

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

for N particles. You just need to substitute for the energy that you have and perform the integration (hint integrate over all the freuqncies \omega and you should only have to do one and simplify).

 

[dextercioby]

First, it't \hbar 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.

 

[romeo6]

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:

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

where Q is the partition function.

Does this look anything like the partition function?