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I Commutator of position and momentum

  1. Jan 26, 2017 #1
    How would ##[p_x, r]## be expanded? Where ##r=(x,y,z)##, the position operators. Do you do the commutators of ##p_x## with ##x, y,z## individually? So ##[p_x,x]+[p_x,y]+[p_x,z]## for example?
     
    Last edited: Jan 26, 2017
  2. jcsd
  3. Jan 26, 2017 #2

    PeroK

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    More generally, a vector operator such as ##\mathbf{\hat{r}}## represents three operators ##(\hat{x}, \hat{y}, \hat{z})##, related in the same way as the components of a vector.

    In this case, essentially by definition:

    ##[\hat{p}_x, \mathbf{\hat{r}}] = ([\hat{p}_x, \hat{x}], [\hat{p}_x, \hat{y}], [\hat{p}_x, \hat{z}])##
     
  4. Jan 26, 2017 #3
    Ah, thank you. :)
     
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