Equations of Motion Homework: Mass m in x Direction

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Homework Help Overview

The problem involves deriving equations of motion for a particle of mass m moving freely in the x direction, specifically focusing on operator expectations such as , , , and .

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the starting point for deriving the equations of motion, with one attempting to use the equation of motion involving the time derivative of and the Hamiltonian. Questions arise regarding how to find the average of the time derivative of the position operator.

Discussion Status

The discussion is ongoing, with participants exploring the definition of expectation values and the implications of treating x as an operator. Some guidance has been offered regarding the approach to take with the wave function and its derivatives.

Contextual Notes

There is a noted lack of information regarding the specific form of x(t) and its time derivative, which is central to the discussion.

fengqiu
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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 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!
 
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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
 
x is an operator.
 
OHH I see what you mean, so operate on the free particle wave function THEN find derivative?

Cheers
 

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