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Commutatos and angular momentum

  1. Feb 4, 2015 #1
    1. The problem statement, all variables and given/known data
    Let e and f be unit vectors. Le = eL is the definition of the component of angular momentum in direction e. Calculate the commutator [Le,Lf ] in terms of e, f and L

    2. Relevant equations
    [A,B]=(AB-BA)

    3. The attempt at a solution

    we know that L=r x p, in classical mechanics, and in quantum physics we have the operators for angular momentum in cartesian coordinates for example, but in my problem I have just two direction, e and f, and I am obtaining as answering 0. How can I do this exercise ? thanks
    upload_2015-2-4_23-34-19.png
     
  2. jcsd
  3. Feb 4, 2015 #2

    TSny

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    Welcome to PF!

    Since you know the commutation relations for the Cartesian components of L, it might be a good idea to write out e##\cdot##L and f##\cdot##L in terms of the Cartesian components of L.
     
  4. Feb 5, 2015 #3
    Are the unit vectors ##\hat{e}## and ##\hat{f}## some arbitrary unit vectors in Cartesian space? In that case, it might be easy to start with something simple such as ##\hat{e} = \hat{x}## and ##\hat{f} = \hat{y}## and then moving into a more general case.
     
  5. Feb 5, 2015 #4
    but, and about the z component for example, if I do this in two coordenates, the answer will be zero, maybe is zero the solution, I do not know
     
  6. Feb 5, 2015 #5

    BvU

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    Why zero ? Follow Sigurdsson's sound advice and post your workings, please.
     
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