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Angular momentum and Hamiltonian commutator

  1. Jan 11, 2010 #1

    Is it generally the case that [J, H] = dJ/dt?

    I saw this appear in a problem involving a spin 1/2 system interacting with a magnetic field.

    If so, why?This seems like a very basic relation but I'm having a bit of brain freeze and can't see the answer right now.
  2. jcsd
  3. Jan 11, 2010 #2


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    You can just work out the commutator yourself by decomposing J and H into component operators. It won't work if J is spin, but you can try it for L.
  4. Jan 11, 2010 #3
    This is just the equation of motion of an operator in the Heisenberg picture, isn't it?
  5. Jan 11, 2010 #4
    Okay, so in the Heisenberg scheme I can say that for any operator O, [O, H] = dO/dt?

    Is this a postulate or derived from something else?
  6. Jan 11, 2010 #5
    It's a dynamical equation which is equivalent to the Schrödinger equation. In the Schrödinger picture the states change with time, in the Heisenberg picture the operators change with time.

  7. Jan 11, 2010 #6
    Thanks for the link. I think my confusion arose because I'm used to thinking of the Hamiltonian in terms of the Schrodinger picture and have not gotten used to the Heisenberg formulation.
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