Equations of Motion Homework: Mass m in x Direction

In summary, the conversation discusses how to derive equations of motion for operator expectations such as position, momentum, and their squares for a free particle in the x direction. The equation of motion for <x(t)> is given, but the average of <dx(t)/dt> is unknown. The conversation suggests finding the time derivative of x(t) by operating on the free particle wave function.
  • #1
fengqiu
19
1

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

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

Cheers
 

1. What is the equation for calculating mass in the x direction?

The equation for calculating mass in the x direction is m = Fx / ax, where m is the mass, Fx is the force in the x direction, and ax is the acceleration in the x direction.

2. How do I determine the force in the x direction?

The force in the x direction can be determined by using the equation Fx = m * ax, where Fx is the force in the x direction, m is the mass, and ax is the acceleration in the x direction.

3. Can I use this equation for any object in motion?

Yes, this equation can be used for any object in motion as long as the mass and acceleration are known. It is particularly useful for solving problems involving constant acceleration in the x direction.

4. What are the units for mass in the x direction?

The units for mass in the x direction are typically kilograms (kg), as mass is a measure of an object's inertia and is not affected by the direction of motion.

5. How does this equation relate to Newton's Second Law of Motion?

This equation, m = Fx / ax, is an application of Newton's Second Law of Motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this equation, Fx represents the net force in the x direction and ax represents the acceleration in the x direction.

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