- #1

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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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- Thread starter romeo6
- Start date

- #1

- 54

- 0

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?

- #2

Dr Transport

Science Advisor

Gold Member

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[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

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Daniel.

- #4

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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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