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Commutators of Angular momentum operator

  1. May 9, 2012 #1
    The letters next to p and L should be subscripts.
    [Lz, px] = [xpy − ypx, px] = [xpy, px] − [ypx, px] = py[x, px] −0 = i(hbar)py

    1.In this calculation, why is [x, px] not 0 even they commute?

    2.Why is py put on the left instead of the right in the second last step? i thought it should be put on the right bec it's on the right of x in the third step, and we have to keep the orders for operators.

    3.With L=rxp, why are we multiplying i(hbar) instead of multiplying by i/ (hbar), coz at the beginning, we change all the d/dx or d/dy or d/dz to px, py, pz, why aren't we multiplying i/(hbar) to compensate what we change for convenient calculation?
  2. jcsd
  3. May 9, 2012 #2


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    Gold Member

    Why do you think [itex][x,p_x]=0[/itex]? That should be one of the first things you learned about QM.

    Your [itex]p_y[/itex] should be to the right, yes, but inevitably it doesn't matter considering [itex][x,p_x][/itex] is equal to a constant.

    As for why you multiply by [itex]i\hbar[/itex], what do you mean "at the beginning"?
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