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Homework Help: Condition for expectation value of an operator to depend on time

  1. Feb 2, 2014 #1
    1. The problem statement, all variables and given/known data

    A particle is in a 1D harmonic oscillator potential. Under what conditions will the
    expectation value of an operator Q (no explicit time dependence) depend on time if
    (i) the particle is initially in a momentum eigenstate?
    (ii) the particle is initially in an energy eigenstate?

    2. Relevant equations

    The first two parts of this question required me to show that

    [itex]\frac{d}{dt}[/itex]<Q> = [itex]\frac{i}{hbar}[/itex] <[H,Q]> + <[itex]\frac{d}{dt}[/itex]Q>

    Q is any hermitian operator. I did this fine and then derived the virial theorem from this, which is where the rate of change of the expectation for Q is zero. I'm assuming I'm supposed to use this equation to find the conditions, but to be perfectly honest I have no idea how to approach this at all.

    I know that if the operator commutes with the Hamiltonian H then it will have no dependence on time, but how can I use this to answer the question?
    Last edited: Feb 2, 2014
  2. jcsd
  3. Feb 2, 2014 #2
    Please delete this post.
    Last edited: Feb 2, 2014
  4. Feb 3, 2014 #3
    Thanks for the help david, what a complete waste of both of our time. Maybe it's far too obvious for you? I have no idea whats wrong with my post, so it'd be great if you could enlighten me.
  5. Feb 3, 2014 #4


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    I think David meant he wanted his post deleted, not your thread.
  6. Feb 3, 2014 #5
    Oh sorry, apologies if that's the case.
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