# Quick partition function question. (Stat. Mech.)

1. Apr 23, 2009

### camzie69

Physical interpretation of the partition function. Consider a single-particle quantum system whose states are labeled with an index i = 1, 2, 3, ... with corresponding energies E1, E2, E3, ... . Set the zero of energy at the ground state energy so that E1 = 0. Argue that, if the absolute temperature T is such that kT = En, where n is some integer, then n is the approximate value of the partition function (15.4). Therefore, the partition function is equal to the number of states which are likely to be occupied.

15.4 $$\sum$$ e^-Ej/kT

3. The attempt at a solution

I tried expanding terms and plugging in for kT=En yielding this but not sure where or if to proceed from here...its not correct right now...

e^-E1/En + e^-E2/En ... + e^-En/En

This gives me 1 for the first term which is a promising first step because if all the exponentials equal one I have the correct solution 1+1+1+...=n but I'm not sure if this is the case of much less how to prove this is the case.

Should this be posted in the mathematics section?

Last edited: Apr 23, 2009