Harmonic oscillator partition function

[tonysilva]

Well what is the partition function of harmonic oscillator with this energy
E=hw(n+1/2) , n=1,3,5,...

Z=e^(-BE) right?

B=1/KT^2

How to expand this?

Thank you.

 

[kuruman]

Z=e^(-BE) right?

Wrong.

$Z={\sum}_{i}e^{-\beta E_i}$

 

[vela]

And $\beta = 1/kT$.