Equations of motion

  • Thread starter fengqiu
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  • #1
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Homework Statement


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)>


Homework Equations





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!
 

Answers and Replies

  • #2
Simon Bridge
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You know the definition of an expectation value for an operator don't you?
 
  • #3
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Yes but I'm not given x(t) so how would I find it's time derivative to average?

Cheeeers
 
  • #4
Simon Bridge
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x is an operator.
 
  • #5
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OHH I see what you mean, so operate on the free particle wave function THEN find derivative?

Cheers
 

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