Harmonic oscillator partition function

Thread starter tonysilva
Start date Sep 9, 2011
Tags

Function Harmonic Harmonic oscillator Oscillator Partition Partition function

Sep 9, 2011

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.

Physics news on Phys.org

Sep 10, 2011

kuruman

Science Advisor

Homework Helper

Education Advisor

Insights Author

Gold Member

tonysilva said:

Z=e^(-BE) right?

Wrong.

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

Sep 10, 2011

vela

Staff Emeritus

Science Advisor

Homework Helper

And \beta = 1/kT.

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...

View full post »

Thread 'How do I solve the 3D magnetic field of a Halbach Rotor?'

Boundary conditions: The derived Dirichlet and Neumann boundary conditions In terms of the magnetic scalar potential:

View full post »

Thread 'Help to convert units of a simple formula'

The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?

View full post »