Equations of Motion Homework: Mass m in x Direction

[fengqiu]

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 don't 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!

 

[Simon Bridge]

You know the definition of an expectation value for an operator don't you?

 

[fengqiu]

Yes but I'm not given x(t) so how would I find it's time derivative to average?

Cheeeers

 

[Simon Bridge]

x is an operator.

 

[fengqiu]

OHH I see what you mean, so operate on the free particle wave function THEN find derivative?

Cheers