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Baker-Campbell Formula

  1. Aug 4, 2016 #1
    1. The problem statement, all variables and given/known data
    Hi, I am really struggling with this Campbell-Hausdorff formula. The question requires me to use it to prove

    ei/h omega.L (x , p) e-i/h omega.L = R(omega).(x, p) where L is the momentum operator, x and p are the position and momentum operator respectively and R(omega) is the rotation in SO(3) R(omega) = eomegaa (it)a
    2. Relevant equations


    3. The attempt at a solution
    So I have only managed to expand the LHS using the Campbell formula and now I am failing to evaluate the commutators. Thank you very much for the help.
     
  2. jcsd
  3. Aug 4, 2016 #2

    samalkhaiat

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    Science Advisor

    Use [itex](it_{i})_{jk} = \epsilon_{ijk}[/itex], to write [itex](i\omega \cdot t)_{jk} = \omega_{i}\epsilon_{ijk}[/itex]. You also need to use [itex][L_{i} , X_{j}] = i \epsilon_{ijk} X_{k}[/itex], and similar one for [itex]P_{j}[/itex].
     
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