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
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 ZN. Now, I'll say that:
(Where it says ε it's meant to be ε(r) )
Z = Ʃr exp(-β(ε - ε) ) = Ʃr exp(-βε) * exp(βε) =
= Ʃr exp(-βε) * Ʃr 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!