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Equations of motion

  1. Apr 30, 2014 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m moves freely in space in the x direction.
    (a) Derive equations of motion for the following operator expectations:

    <x(t)>, <p(t)> , <X^2(t)>,<P^2(t)>


    2. Relevant equations



    3. The attempt at a solution

    baah I dont even know....
    I guess we'll start from the equation of motion d<x(t)>/dt = 1/ih <[X(t),H]> + <dx(t)/dt>
    but how do I find the average of dx(t)/dt?

    thanks!
     
  2. jcsd
  3. Apr 30, 2014 #2

    Simon Bridge

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    You know the definition of an expectation value for an operator don't you?
     
  4. May 1, 2014 #3
    Yes but I'm not given x(t) so how would I find it's time derivative to average?

    Cheeeers
     
  5. May 1, 2014 #4

    Simon Bridge

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    x is an operator.
     
  6. May 1, 2014 #5
    OHH I see what you mean, so operate on the free particle wave function THEN find derivative?

    Cheers
     
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