Heisenberg's Uncertainty Principle

  • Thread starter BOAS
  • Start date
  • #1
555
19
Hello,

i'm solving some quite simple problems using the uncertainty principle, but I don't have access to the solutions and I really don't have a feel for what a 'sensible' answer is... When finding the minimum uncertainty in velocity, I end up with things greater than the speed of light, so I want to check i'm not making an error somewhere.

Homework Statement



Suppose that an electron is trapped in a small region and the uncertainty in it's position is [itex]10^{-15}[/itex]m. What is the minimum uncertainty in the particles momentum? What uncertainty in the electrons velocity does this correspond to?

Homework Equations





The Attempt at a Solution



[itex](\Delta y)(\Delta p_{y}) \geq \frac{h}{4 \pi}[/itex]

Since we're dealing the minimum uncertainty, we can equate the two.

[itex](\Delta p_{y}) = \frac{h}{4 \pi (\Delta y)}[/itex] = 5.27 x 10-20 kgms-1

[itex]p = mv[/itex]

[itex]\Delta p_{y} = m (\Delta v_{y})[/itex]

[itex]\Delta v_{y} = \frac{\Delta p_{y}}{m}[/itex] = 5.79 x 1010 ms-1

This answer just seems absurd, maybe it's a consequence of the accuracy we know the electrons position to, but like I said I have no way of checking what a sensible answer is.

So, have I gone wrong somewhere?

Thanks for any help you can give.
 

Answers and Replies

  • #2
1,948
201
Your mistake is to use the formula p = mv which is the non-relativistic formula. Try using p = γmv, where γ = (1 - v2/c2)-1/2.
 
  • #3
555
19
Your mistake is to use the formula p = mv which is the non-relativistic formula. Try using p = γmv, where γ = (1 - v2/c2)-1/2.

Aha! Thanks, I was looking at an old example from my notes but evidently it was intended to show why the heisenberg uncertainty principle is negligible at the macroscopic level of a ping pong ball.
 

Related Threads on Heisenberg's Uncertainty Principle

  • Last Post
Replies
3
Views
1K
Replies
1
Views
210
Replies
3
Views
6K
Replies
2
Views
1K
Replies
14
Views
6K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
6
Views
2K
Replies
5
Views
4K
Replies
2
Views
5K
Replies
57
Views
3K
Top