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Tannor Quantum Mechanics derivative of variance of position

  1. Jan 16, 2016 #1
    0http://stackoverflow.com/questions/34833391/tannor-quantum-mechanics-derivative-of-variance-of-position# [Broken]


    In the Tannor textbook Introduction to Quantum Mechanics, there is a second derivative of chi on p37. It looks like this:

    χ"(t) = d/dt ( (1/m) * (<qp + pq> - 2<p><q> ) (Equation 1)

    Where χ is the variance of position, or χ= <q^2> - <q>^2 and q is position and p is momentum, and m is mass. Eventually this equation transforms into the following:

    χ"(t) = (2/(m2)) * ( <p2> - <p>2 - m*V"(<q>)*χ) (Equation 2)

    There is obviously Ehrenfest theorem used here. I found that the first term inside the bracket in Equation 1 goes to 0 using integrals. The second becomes the following:

    (2/m)*d/dt(<p><q>)

    = (2/(m2))(m*<q>V'(<q>) - m*(<q>*q-<q>2)V"(<q>) - <p>2)

    and now I'm stuck. What's the next step? How do I get <p2>?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jan 21, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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