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Equipartition theorem

  1. Oct 26, 2009 #1
    I have one question. If I have Hamiltonian:

    [tex]H=\sum^{f_1}_{i=1}\alpha_iq_i^2+\sum^{f_2}_{i=1}\beta_ip_i^2[/tex]

    I can show that for the Hamiltonian of this type equipartition theorem is correct. Is there any Hamiltonian which is not a function od squares of coordinates and impulses are from which I can get this Hamiltonian some using canonical transformation. Example perhaps?
     
  2. jcsd
  3. Oct 26, 2009 #2
    What does it mean "equipartition theorem is correct" ?
    I think the hamiltonian is both integrable and separable, since it's not ergodic does the ensemble averages have sense?

    Ll.
     
  4. Oct 26, 2009 #3
    You can prove that every degree of fredom have the same energy - equipartition theorem only for the Hamiltonian

    [tex]
    H=\sum^{f_1}_{i=1}\alpha_iq_i^2+\sum^{f_2}_{i=1}\beta_ip_i^2
    [/tex]

    or maybe the Hamiltonian which canonical transformation is


    [tex]
    H=\sum^{f_1}_{i=1}\alpha_iq_i^2+\sum^{f_2}_{i=1}\beta_ip_i^2
    [/tex]

    I think that ''
    mysterious '' Hamiltonian have the same form as one as I wrote! So for example


    [tex]
    K=\sum^{F_1}_{i=1}\alpha_iQ_i^2+\sum^{F_2}_{i=1}\beta_iP_i^2
    [/tex]

    Am I right?
     
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