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Expectation of an Hermitian operator is real.

  1. Oct 30, 2007 #1
    1. The problem statement, all variables and given/known data

    WTS [itex] \langle \hat{A} \rangle = \langle \hat{A} \rangle^\ast [/itex]

    3. The attempt at a solution

    [itex]\langle \hat{A} \rangle^\ast = \left(\int \phi_l^\ast \hat{A} \phi_m dx\right)^\ast=\left(\int (\hat{A}\phi_l)^\ast \phi_m dx\right)^\ast= \int \phi_m^\ast \hat{A}\phi_l dx[/itex]. So far, I haven't seen why this equals [itex]\int \phi_l^\ast \hat{A} \phi_m dx[/itex].

  2. jcsd
  3. Oct 30, 2007 #2


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    Homework Helper

    use same fields to show
    eg. [tex](\Psi, A\Psi) = (\Psi, A\Psi)^*[/tex]
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