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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


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    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
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