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## Homework Statement

Imagine a system with N distinguishable particles. Each particle may be in two states of energy: -ε and +ε.

Find the the partition function of the system

## Homework Equations

## The Attempt at a Solution

I know that I have to find the partition function for a single function, Z, and my final result will be Z

^{N}. Now, I'll say that:

(Where it says ε it's meant to be ε(r) )

Z = Ʃ

_{r}exp(-β(ε - ε) ) = Ʃ

_{r}exp(-βε) * exp(βε) =

= Ʃ

_{r}exp(-βε) * Ʃ

_{r}exp(βε)

I'm sure this is incorrect. It doesn't make sense in my head.. E(r) is the energy associated with each microstate, therefore saying that E(r) = ε(r) - ε(r) can't make any sense! I know that the result is:

Z = ( exp(βε) + exp(-βε) )

^{N}

I have no idea how to get there tho. How did it became a sum? How do I get rid of the summatories?

Any help will be appreciated!

Thanks.