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I What can this observable represent?

  1. Jan 7, 2017 #1
    ## \hat{A}=
    \begin{pmatrix}
    1 &- 1 \\
    -1&1
    \end{pmatrix}
    ##
    this is written in a basis ##\left ( |1>,|2> \right )##
    So, i know this is an Hermitian operator, so it can represent an observable.
    Can this operator represent an electric dipole moment? A momentum? A component of the orbital angular momentum?

    1- for the momentum, i assume, since we can write ##\hat{p} ## as creation and annihilation operators, this would have no diagonal terms in this basis. What about the others, any suggestions?

    Thank you!
     
    Last edited: Jan 7, 2017
  2. jcsd
  3. Jan 7, 2017 #2

    Mentz114

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    Gold Member

    It is ##\mathbf{1} - \sigma_x## where ##\sigma_x## is a Pauli spin matrix but I can't think what observable it could be.
     
  4. Jan 8, 2017 #3

    Zafa Pi

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    Gold Member

    It is singular and has one eigenvector [1,-1]. So it yields the probability a planer polarized photon will emerge from a polarized lens whose axis is at -45 degrees from the horizontal.
    Here is a ? just in case I'm wrong.
     
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