Minimum uncertainty of the momentum of a small particle

[AndrejN96]

Homework Statement

Find the minimum uncertainty of the momentum of a small particle with mass m=1g, which is confined within a region of width a=1cm.

Homework Equations

Delta(p)*Delta(x)>=hbar/2

The Attempt at a Solution

Delta(p)*Delta(x)=hbar/2
Delta(p)*10^(-2)=hbar/2
Delta(p)=10^2*hbar/2

This looks pretty straightforward to me, but the given mass in this problem is what confuses me.

 

[rude man]

I think you have it right & putting in the mass is a red herring. Maybe they meant to ask for the minimum uncertainty in the velocity.

 

[insightful]

You might want to scan this:

http://en.wikipedia.org/wiki/Particle_in_a_box

Pull quote:

"The uncertainties in position and momentum (

and

) are defined as being equal to the square root of their respective variances, so that:

This product increases with increasing n, having a minimum value for n=1. The value of this product for n=1 is about equal to 0.568

..."