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Gaussian wavefunction; expectation energy

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    3. The attempt at a solution

    The issue I'm having here is that the problem should be able to be done rather quickly. I can see how to solve for <H> using the operator, but there's a quick way that I'm not picking up on.

    I thought about solving <H> = <p^2> / 2m, but getting <p^2> is just as much of a pain.

    Any help ?
  2. jcsd
  3. Oct 18, 2011 #2


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    Science Advisor
    Homework Helper

    By definition,

    [tex]\langle H \rangle = \int \psi^* \hat H \psi \, dx[/tex]
    where, as you said
    [tex]\hat H = \frac{p^2}{2m}[/tex]

    and you should be able to do that using the second hint (remember that [itex]p \propto \partial/\partial x[/itex] in the position representation).
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