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Expectation value of the square of the observable

  1. Feb 12, 2007 #1
    1. The problem statement, all variables and given/known data
    I know how to compute the expectation value of an observable. But how does one compute the expectation value of an observable's square?

    2. Relevant equations
    [tex]\langle Q \rangle = \int_{-\infty}^{\infty} \Psi^* \hat{Q} \Psi \; dx[/tex]
    [tex]\langle Q^2 \rangle = \int_{-\infty}^{\infty} \Psi^* (\hat{Q} \Psi)^2 \; dx \; ???[/tex]
     
    Last edited: Feb 12, 2007
  2. jcsd
  3. Feb 12, 2007 #2

    dextercioby

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    No, the square is defined by double application of the operator

    [tex] A^2 \psi =A\left(A \psi \right) \ , \forall \psi\in D(A) \ \mbox{and} \ {} A\psi \in D(A)[/tex]
     
  4. Feb 12, 2007 #3
    I tried double application after I posted and got more elegant answers. Thanks dextercioby.
     
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