Quantum harmonic oscillator system

[rayveldkamp]

Hi,
I am wondering how i would go about calculating the canonical partition function for a system of N quantum harmonic oscillators. The idea of the question is that we are treating photons as oscillators with a discrete energy spectrum. I'm confused as whether to use Maxwell-Boltmann treatment, or Bose-Einstein treatment to determine the partition function, both methods don't seem to be working, so any help would be appreciated.
Thanks

Ray

 

[marlon]

Hi,
I am wondering how i would go about calculating the canonical partition function for a system of N quantum harmonic oscillators. The idea of the question is that we are treating photons as oscillators with a discrete energy spectrum. I'm confused as whether to use Maxwell-Boltmann treatment, or Bose-Einstein treatment to determine the partition function, both methods don't seem to be working, so any help would be appreciated.
Thanks

Ray

the link between QFT and the statistical physics is the execution of a Wick rotation by replacing time t by imaginary time it. this allows for analytical continuiation of the gaussian integrals. But i do not think you know all of this.

Besides, have you realized that photons are spin 1 particles, thus bosons...

marlon

 

[rayveldkamp]

Yes that sounds great, but i have not yet studied any QFT, just QM and statistical mechanics. Anyway my attempt is to use the Grand Canonical Partition function, but since in this question the particle number is fixed, i set the chemical potential equal to zero.
However the question wants to approximate the discrete sum by an integral, in which case i have to include an extra factor of 1/(4pi hbar)^N, this is where i am stuck, i figure i have to integrate over the phase space but am not sure how to express the partition function in terms of position and momentum

Ray