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From angular momentum hamiltonian to angles(coordinates)

  1. Aug 3, 2012 #1
    I have a Hamiltonian, consisting only of angular momentum components Lx,Ly,Lz. I need to go from it to some coordinate representation. But I don't have derivatives Lx' etc. in H. So, when I'll go to coordinates and momenta I'll have Hamiltonian equations like p_i=0, which doesn't have sense.
    How I need to go from H to x,y,z or \phi,\theta,r.
    H=-K1Lx2+K2Lz2+HxLx+HyLy+HzLz

    Going from L to angles can make no problem according to https://www.physicsforums.com/showthread.php?t=161865 in example
    But back?
     
  2. jcsd
  3. Aug 3, 2012 #2
    Please, somebody! I need at least the guidance how to go in classical case from H=-K1Lx2+K2Lz2+HxLx+HyLy+HzLz to action-angle variables! I know how to do that in a variety examples having coordinates (i.e. harmonic oscillator or Kepler problem etc.) but I don't know what to do having angular momentum in the Hamiltonian! Rewriting via p\cros r doesn't help either!
     
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