Heisenberg Uncertainty Principle - h/(4.Phi) versus h/(2.Phi)

In summary, the Heisenberg Uncertainty Principle has two different forms that are often quoted, h/(4.Pi) and h/(2.Pi). The latter is considered to be more correct and can be derived from the general uncertainty principle. The reason for this discrepancy and its origin in history is explained in detail on the Wikipedia page for the uncertainty principle. When solving problems involving the HUP, it is important to use the correct form, h/(2.Pi). Any other constant is incorrect.
  • #1
jvicens
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Heisenberg Uncertainty Principle - h/(4.Pi) versus h/(2.Pi)

What's the reason behind the factor 2 in the way some books/papers present Heisenberg Uncertainty Principle?
h/(4.Pi) versus h/(2.Pi)
When in history did this discrepancy arise and who was responsible for that?
Ultimately, which figure should we use when we are solving HUP problems?
 
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  • #2
I think you mean [itex]h/4\pi[/itex] and [itex]h/2\pi[/itex]. I would refer you to http://en.wikipedia.org/wiki/Uncertainty_principle which provides an excellent description of the general uncertainty principle and also explains why the two reults are often quoted. The more correct one is [itex]h/4\pi[/itex].
 
  • #3
The correct one is with [tex] \frac{\hbar}{2} [/tex] as it can be shown starting with the general uncertainty relations.

Any other constant is incorrect.

Daniel.
 

Related to Heisenberg Uncertainty Principle - h/(4.Phi) versus h/(2.Phi)

1. What is the Heisenberg Uncertainty Principle?

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 subatomic particle. This is due to the wave-particle duality of particles, which means that they exhibit both particle-like and wave-like behaviors.

2. What is the significance of h/(4.Phi) versus h/(2.Phi) in the Heisenberg Uncertainty Principle?

The values of h/(4.Phi) and h/(2.Phi) are related to the Planck constant, h, and the mathematical constant, Phi. These values represent the minimum uncertainty in the position and momentum of a particle, respectively. The difference between the two values reflects the inherent uncertainty in measuring both position and momentum simultaneously.

3. How does the Heisenberg Uncertainty Principle impact our understanding of the world?

The Heisenberg Uncertainty Principle challenges our classical understanding of the world and highlights the limitations of our ability to measure and predict the behavior of subatomic particles. It also has practical implications in fields such as quantum computing and cryptography.

4. Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental principle in quantum mechanics and has been extensively tested and proven. It is a fundamental aspect of the nature of particles and cannot be violated.

5. How does the Heisenberg Uncertainty Principle relate to the observer effect?

The Heisenberg Uncertainty Principle is often mistakenly conflated with the observer effect, which refers to the impact of an observer on the observed phenomenon. While the uncertainty principle describes the inherent limitations of measuring a particle's position and momentum, the observer effect refers to the potential disturbance caused by the act of measuring. They are two separate concepts, but they are related in that both highlight the limitations of our ability to observe and understand the quantum world.

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