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Ehrenfest's theorem

  1. Apr 20, 2007 #1
    1. The problem statement, all variables and given/known data
    Griffith's problem 1.12
    Calculate [itex] d\left<p\right>/dt. [/itex]

    Answer [tex] \frac{d\left<p\right>}{dt} = \left<\frac{dV}{dx}\right> [/tex]

    2. The attempt at a solution

    so we know that

    [tex] \left<p\right> = -i\hbar \int \left(\Psi^* \frac{d\Psi}{dx}\right) dx [/tex]

    so then

    [tex] \frac{d\left<p\right>}{dt} = -i\hbar \int \left( \frac{\partial\Psi^*}{\partial t} \frac{\partial\Psi}{\partial x} + \Psi^* \frac{\partial^2 \Psi}{\partial t \partial x} \right) dx [/tex]

    im not quite sure if one can simplify this further ... i mean we cant integrate wrt x because all the terms in the integrand have x dependance... don't they?? Should i intergate by parts to proceed??

    I think a couple of extra terms would be required, no?

    Thanks for the help!!
     
  2. jcsd
  3. Apr 20, 2007 #2
    Now there is this famous equation for [tex]\frac{\partial \Psi}{\partial t}[/tex], what's it called again... :rofl:
     
  4. Apr 20, 2007 #3
    shhhhhhhhh you

    i got the required answer anyway

    thansk for your help :tongue2:
     
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