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When can you apply Ehrenfest's theorem?

  1. Oct 3, 2014 #1
    I know when the initial state (##\Psi(x,0)##) is given, ##\frac{d<x>}{dt} \not=<p>##. I thought you can only apply Ehrenfest's theorem when ##\Psi## is a function of x and t, however it seems like you can also apply it to the time-independent part (##\psi(x)##) by itself as well. Can someone explain to me why Ehrenfest's theorem is valid for ##\psi(x)##?

    Last edited by a moderator: Oct 4, 2014
  2. jcsd
  3. Oct 3, 2014 #2


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    Staff: Mentor

    Tip: enclose your LaTeX code in $$, not $. Correction: for "inline" LaTeX (i.e. in the middle of ordinary text) use ##, not $$. Use $$ when you want the code to "stand alone" as a separate paragraph.

    You can edit your post if you don't wait too long, in which case you'll see "Edit" among the options at the bottom of the post. You apparently waited too long, so I fixed it for you.
    Last edited: Oct 4, 2014
  4. Oct 6, 2014 #3


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    Science Advisor

    Logan, why do you think that Ehrenfest theorem can be applied to a time-independent wave function?
  5. Oct 6, 2014 #4
    I think I see my confusion. It looks as if ET is being applied to ## \psi(x) ## but I think its just because the time dependent part disappears when you multiply it by its complex conjugate. Thanks!
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