Uncertainty Principle of a nonrelatavistic particle

In summary, using the equations ΔpΔx>h/4Pi, p=mv, and Δx=2nλ, it can be shown that the uncertainty in the velocity of a nonrelativistic particle is greater than about 4% of its velocity when the uncertainty in its location is about equal to twice its de-Broglie wavelength. This is due to the relationship between momentum and position in Quantum Mechanics, where n is an integer and λ is the de-Broglie wavelength.
  • #1
Identify
12
0

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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  • #2
Identify said:
p=mv
You also have another equation for momentum from Quantum Mechanics.

Identify said:
Δx=2nλ
What is n?
 
  • #3
n is an integer. n(lambda)=nh/p. So Lambda = h/p.
I have it now. Thankyou very much.
 

FAQ: Uncertainty Principle of a nonrelatavistic particle

What is the Uncertainty Principle of a nonrelatavistic particle?

The Uncertainty Principle of a nonrelatavistic particle, also known as the Heisenberg Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle with absolute certainty. This means that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

Why is the Uncertainty Principle important?

The Uncertainty Principle is important because it sets a limit on the precision with which we can measure certain properties of a particle. It also has significant implications for our understanding of the behavior of particles at the quantum level and has been a key factor in the development of quantum mechanics.

How does the Uncertainty Principle relate to classical mechanics?

The Uncertainty Principle is a fundamental principle of quantum mechanics and does not have a direct counterpart in classical mechanics. In classical mechanics, it is possible to know the exact position and momentum of a particle at any given time. However, at the quantum level, the behavior of particles is inherently probabilistic, and the Uncertainty Principle reflects this fundamental difference.

Can the Uncertainty Principle be violated?

No, the Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be violated. It is a consequence of the wave-particle duality of particles, which means that particles can exhibit both wave-like and particle-like behavior. Any attempt to measure the position or momentum of a particle with absolute precision will result in a loss of information about the other property.

Does the Uncertainty Principle apply to all particles?

Yes, the Uncertainty Principle applies to all particles, including nonrelativistic particles such as electrons, protons, and neutrons. It also applies to relativistic particles, such as photons and subatomic particles. The Uncertainty Principle is a fundamental principle of quantum mechanics and applies to all particles at the quantum level.

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