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Expectation value calculation

  1. Apr 17, 2012 #1
    How can we compute the expectation value, <[itex]\widehat{x}[/itex][itex]\widehat{p}[/itex]> where ψ(x) is a normalized wavefunction? (The result is i[itex]\hbar[/itex]/2)
     
  2. jcsd
  3. Apr 18, 2012 #2

    tom.stoer

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    Science Advisor

    If you want to do the calculation in x-space you have to use the momentum operator represented by [itex]-i\hbar\partial_x[/itex]; then you get the integral

    [tex]\langle\psi|\hat{x}\hat{p}|\psi\rangle = \int_\mathbb{R}dx\,\psi^\ast(x)\,x\,(-i\hbar)\,\partial_x\,\psi(x)[/tex]

    Note that your result [itex]i\hbar/2[/itex] cannot be correct in general.
     
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