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X,Y and Z operators of some algebra

  1. Jul 8, 2009 #1
    let be X,Y and Z operators of some algebra so

    [tex] [X_i , Y_j]= \epsilon _ijkX_k [/tex] where i,j and k range over X, Y and Z

    then i define the change of coordinates

    [tex] X= rcos(u) [/tex]

    [tex] Y= rsin(u) [/tex]

    [tex] Z=Z [/tex]

    again r, u and Z are new operators, the problem is , how can i find for example what is the value of [tex] [r, u] [/tex] or [tex] [r,z] [/tex] or [tex] [u,z] [/tex] ??
     
  2. jcsd
  3. Jul 8, 2009 #2

    HallsofIvy

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    Staff Emeritus
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    Re: Commutators

    If X, Y, and Z are in "some algebra", then what do "r cos(u)" and "r sin(u)" mean?
     
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