Uncertainty Principle of a nonrelatavistic particle

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SUMMARY

The discussion focuses on the uncertainty principle for a nonrelativistic particle, specifically addressing the relationship between position uncertainty and velocity uncertainty. It establishes that if the uncertainty in location (Δx) is approximately twice the de-Broglie wavelength (2nλ), then the uncertainty in velocity (Δv) must exceed 4% of the particle's velocity (v). Key equations referenced include ΔpΔx > h/4π and p = mv, with the manipulation of these equations leading to the conclusion regarding Δv.

PREREQUISITES
  • Understanding of the de-Broglie wavelength
  • Familiarity with the uncertainty principle in quantum mechanics
  • Basic knowledge of momentum (p = mv)
  • Concept of integer multiples in quantum mechanics (n)
NEXT STEPS
  • Study the implications of the uncertainty principle in quantum mechanics
  • Learn about the de-Broglie wavelength and its applications
  • Explore the relationship between momentum and velocity in quantum systems
  • Investigate the role of integer n in quantum mechanics and its significance
USEFUL FOR

Students and educators in physics, particularly those focusing on quantum mechanics and the principles governing particle behavior at nonrelativistic speeds.

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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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