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Homework Help: Does this operator commute with the Hamiltonian operator?

  1. Dec 3, 2017 #1
    1. The problem statement, all variables and given/known data
    Show that the mean value of a time-independent operator over an
    energy eigenstate is constant in time.

    2. Relevant equations
    Ehrenfest theorem

    3. The attempt at a solution
    I get most of it, I'm just wondering how to say/show that this operator will commute with the Hamiltonian operator.
    Is it correct to say that because they both act on energy eigenstates, they must commute?
    If so, is there a way to show this?
  2. jcsd
  3. Dec 3, 2017 #2


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    Science Advisor
    Homework Helper

    What is the form of the time-dependent energy eigenfunction? Say at ##t=0## this eigenfunction is ##|n\rangle## having energy ##E_n##, how does it look like at a later time ##t##?
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