Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I know that for a particle under the potential


the equipartition theorem says that it contributes to the mean energy to $\frac{3k_BT}{2} $ (one half for each degree of freedom).

My question is: let's say we have a potential like this one, for instance 2 particles with an harmonic interaction potential, where $r_{eq}$ stands for the equilibrium point:


Note that in this case the coordinates $(x,y,z)$ are coupled in the potential.

How would one compute the contribution of such a potential to the mean energy? Is there any analogy to the equipartition theorem in a case like this?

share|cite|improve this question
Is r here a vector, or is it a constant distance? If it is a vector it's inconsistent, and if it's a constant you'll have a ring of minima rather than a point. – Nuclear_Wizard Apr 5 '14 at 12:22
It is a constant. – gunbl4d3 Apr 5 '14 at 12:33
To correct Nuclear_Wizard, you would have a spherical surface, since there are three dimensions. – fibonatic Apr 5 '14 at 20:30

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.