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Operator commutator (Heisenberg picture)

  1. Oct 27, 2009 #1
    1. The problem statement, all variables and given/known data
    It's a part of a bigger problem, but what I need help with is finding the commutator between x(t) and x(t) at a different time. So basically I need [x(t1),x(t2)]


    2. Relevant equations
    [tex]A(t)=e^{iHt/\hbar}Ae^{-iHt/\hbar}[/tex]



    3. The attempt at a solution
    The farthest I can get is writing out the commutator using the above equation:
    [x(t1),x(t2)] =
    [tex]e^{iHt1/\hbar}xe^{-iHt1/\hbar}e^{iHt2/\hbar}xe^{-iHt2/\hbar}-e^{iHt2/\hbar}xe^{-iHt2/\hbar}e^{iHt1/\hbar}xe^{-iHt1/\hbar}[/tex]

    But that's just a big mess, and I don't know how to move forward from there. Can anyone help me out?
     
  2. jcsd
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