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Operator r is a diagonal matrix in position representation

  1. Jan 27, 2016 #1
    What does it mean by "In the position representation -- in which r is diagonal" in the paragraph below? How can we show that?

    Screen Shot 2016-01-28 at 4.23.08 am.png

    Does it mean equation (3) in http://scienceworld.wolfram.com/physics/PositionOperator.html? (where I believe the matrix is in the ##|E_n>## basis)
     
  2. jcsd
  3. Jan 27, 2016 #2

    blue_leaf77

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    The matrix element of position operator ##\hat{\mathbf{r}}## in position representation reads as
    $$
    \langle \mathbf{r'} | \hat{\mathbf{r}} | \mathbf{r''} \rangle= \mathbf{r'} \delta(\mathbf{r'}-\mathbf{r''})
    $$
    which vanishes for off-diagonal elements.
     
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