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Homework Help: Expectation values and operators.

  1. May 17, 2008 #1
    i'm just not sure on this little detail, and its keeping me from finishing this problem.

    take the arbitrary operator [tex]\tilde{p}^{n}\tilde{y}^{m}[/tex] where p is the momentum operator , and x is the x position operator

    the expectation value is then <[tex]\tilde{p}^{n}\tilde{y}^{m}[/tex] >

    is this the same as <[tex]\tilde{p}^{n}[/tex]> <[tex]\tilde{y}^{m}[/tex]>?

    if not, how would i go about calculating <[tex]\tilde{p}^{n}\tilde{y}^{m}[/tex] >?
     
    Last edited: May 17, 2008
  2. jcsd
  3. May 18, 2008 #2

    CompuChip

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    Homework Helper

    In general, they are not the same. The expectation value of an operator [itex]\hat A[/itex] is
    [tex]\int \Psi^*(x) \hat A(x) \Psi(x) \, \mathrm{d}x[/tex]
    where [itex]\Psi(x)[/itex] is your wavefunction (assuming you are talking QM here).
    In this case,
    [tex]\int \Psi^*(x) \hat p^n \hat y^m \Psi(x) \, \mathrm{d}x
    \neq
    \left( \int \Psi^*(x) \hat p^n \Psi(x) \, \mathrm{d}x \right)
    \left( \int \Psi^*(x) \hat y^m \Psi(x) \, \mathrm{d}x \right).
    [/tex]
    You could write out [itex]\hat p[/itex] in the position basis and work out what [itex]\hat p^n(y^m \Psi)[/itex] looks like.
     
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