Solving Statistical Mechanics PS6: Consider N Oscillators

[bon]

Homework Statement

Trying to solve 2(a) on this problem set:

http://docs.google.com/viewer?a=v&q...3AiZT6&sig=AHIEtbSSU6Yh_bICouU_44M_Vg-XlMBYTQ

Homework Equations

The Attempt at a Solution

The thing is..I\'m not sure how to calculate the partition function.

For a single SHO the energy levels are given by (n+1/2)hbar w so we sum over n = 0 to infinty and get the partition fn from which we can derive all thermodynamic quantities..what do we sum over here? how to do we get the partition fn?
Thanks!

 

[nickjer]

You do the exact same thing you do for a single harmonic oscillator, but now there are N oscillators. Knowing that E = E1+E2+...+EN and e^{A+B}=e^A e^B, you can solve this problem very similarly to a single oscillator. I suggest first writing out the partition function, and you will get more help with the math.