1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equipartition's energy theorem

  1. Jun 26, 2013 #1

    I'm reading about the equipartition's energy theorem (classical statistics), and I was wondering about its validity when applied to different hamiltonians.

    The usual case, H=p ^2/2m, it yields 3/2KT in 3D, but what about more complicated H? Like H=|p|c, or a H with a complex V? would the theorem still be available for use?

  2. jcsd
  3. Jun 26, 2013 #2
    Equipartition of energy is only valid for a potential free system.

    Beyond that you may wanna look up the Virial Theorem
  4. Jun 26, 2013 #3
    It seems to work for harmonic potentials, if the temperature is high enough.
    See specific heats of solids (in harmonic approximation, high temperature limit).
    Or this:
  5. Jun 27, 2013 #4


    User Avatar
    Science Advisor
    Gold Member

    In 1-D is isn't too hard to derive the result for the cases H = |p|, or H = p^4. The derivation closely follows that of the quadratic case. In 3-D I suspect it is much more complicated, but I am often wrong!

  6. Jun 27, 2013 #5
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook