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Operators Commutation

  1. Nov 15, 2012 #1
    Can someone please explain to me how do we get the following:

    [P(x), L(y)]= i h(cut) P(z)

    P(x) is the momentum operator with respect to x
    and L(y) is the angular momentum operator with respect to y.

    I have also attached the solution. I am stuck at the underlined part. I do not know how to proceed from there.
     

    Attached Files:

  2. jcsd
  3. Nov 15, 2012 #2

    dextercioby

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    Px and Py commute, as per Born-Jordan commutation relations. Thus the term from with their commutator is 0 when you apply the general formula

    [A, BC] = [A,B]C+B[A,C] with [A,B] =0
     
    Last edited: Nov 15, 2012
  4. Nov 15, 2012 #3
    How did you obtain the general formula that you have stated in your reply?
     
  5. Nov 15, 2012 #4
    it should be as follows:
    [a,bc]=[a,b]c+b[a,c]
     
  6. Nov 16, 2012 #5
    [x,px]=ih/2∏ is the usual commutation rule,if that is what you are asking.
    EDIT:if you want to know how to get that underlined term then just write the commutator explicitly and see that pz commutes with px.
     
    Last edited: Nov 16, 2012
  7. Nov 16, 2012 #6
    You got it right in post #4. Just work it out staring from [itex][A, BC][/itex] and write out the commutator, then in the middle add zero in a fancy way.
     
  8. Nov 16, 2012 #7
    Yes, I got the answer. Thank you all for your help =)
     
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