Uncertainty Principle of a nonrelatavistic particle

AI Thread Summary
The discussion revolves around demonstrating that the uncertainty in the velocity of a nonrelativistic particle exceeds 4% of its velocity when the uncertainty in its position is approximately twice its de-Broglie wavelength. Key equations include the uncertainty principle ΔpΔx > h/4π, momentum p = mv, and the position uncertainty Δx = 2nλ, where n is an integer. The participant seeks guidance on manipulating these equations to derive the desired inequality for velocity uncertainty. After some exploration of the equations and definitions, the participant confirms their understanding and expresses gratitude for the assistance received. The conversation highlights the application of quantum mechanics principles to solve a specific problem in particle physics.
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Homework Statement



If the uncertainty in the location of a nonrelativistic particle is about equal to twice its de-Broglie wavelength, show that the uncertainty in its velocity is greater than about 4% of its velocity.


Homework Equations



ΔpΔx>h/4Pi
p=mv
Δx=2nλ

The Attempt at a Solution



I've put the above equations together and manipulated them but I'm not really sure how to get to, Δv>0.04v using the above formulae. An indication of where to begin would be greatly appreciated.
 
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Identify said:
p=mv
You also have another equation for momentum from Quantum Mechanics.

Identify said:
Δx=2nλ
What is n?
 
n is an integer. n(lambda)=nh/p. So Lambda = h/p.
I have it now. Thankyou very much.
 
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