That Heisenberg Uncertainity Principle

In summary, the Heisenberg Uncertainty Principle states that if a particle is confined within a length x, then its momentum will be uncertain by h/2x PI. It is a statistical statement about the outcomes of a large number of measurements and not a statement about the uncertainty of individual measurements. The more general version of the principle involves the product of expectation values of two observables and their commutators. The equations mentioned in the conversation are just different forms of the principle and describe the relationship between position and momentum measurements.
  • #1
PeterPeter
23
0
Does the Heisenberg Uncertainity Principle mean:
1) If a particle is confined within a length x then it must jiggle around with a momentum given by p ~ h/2x PI

OR

2) If we measure the position of a particle to an accuracy of x then its momentum will be uncertain by ~ h/2x PI
 
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  • #2
It means neither.

It says if you have a large number of similarly prepared systems, measure the position on half of them, and momentum on the other half, then the variance of those results will be as per the uncertainly relations.

It is not a statement about uncertainly of measurement - you can measure momentum or position as accurately as you like - its a statistical statement about the outcomes of a large number of measurements.

Thanks
Bill
 
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Likes vanhees71
  • #3
The more general version of the uncertainty principle, derived by the cauchy schwarz inequality states thet the product of the expectation values of two observables is greater than or equivaleent to half the expectation value of the commutators of the observables. The Heisenberg uncertainty principle just uses the fact that the commutator of X the position and P the momentum is -ih(bar) and substitiues that in the equation. The equations you wrote are just reformations of the principle
 

What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa.

Who discovered the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle was discovered by the German physicist Werner Heisenberg in 1927.

What is the significance of the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle has significant implications for our understanding of the behavior of particles at the atomic and subatomic level. It also plays a crucial role in the development of quantum mechanics and our understanding of the fundamental laws of nature.

Can the Heisenberg Uncertainty Principle be violated?

No, the Heisenberg Uncertainty Principle is a fundamental law of nature and cannot be violated. It is a consequence of the wave-particle duality of particles at the quantum level.

How is the Heisenberg Uncertainty Principle applied in real-world situations?

The Heisenberg Uncertainty Principle is commonly used in various fields, such as quantum computing, nuclear physics, and chemistry, to understand and predict the behavior of particles at the atomic and subatomic level. It also has practical applications in technologies such as MRI machines and electron microscopes.

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