# Equations of motion

## 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)>

## 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

Simon Bridge
Science Advisor
Homework Helper
You know the definition of an expectation value for an operator don't you?

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

Cheeeers

Simon Bridge
Science Advisor
Homework Helper
x is an operator.

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

Cheers