Uncertainty Principle and angular position

In summary, the Uncertainty Principle states that it is impossible to simultaneously determine the exact position and momentum of a subatomic particle. This principle also applies to angular position and momentum, meaning that the more accurately one knows the angular position of a particle, the less certain they can be about its angular momentum, and vice versa. This concept has significant implications in the field of quantum mechanics and highlights the inherent uncertainty in the behavior of particles at a subatomic level.
  • #1
getcarter
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0
Verify that the uncertainty principle can be expressed in the form [PLAIN]http://www.colorado.edu/physics/phys2170/phys2170_spring96/hws/2170_hw73.gif,[/URL] where [PLAIN]http://www.colorado.edu/physics/phys2170/phys2170_spring96/hws/2170_hw74.gifis[/URL] the uncertainty in the angular momentum of a particle, and http://www.colorado.edu/physics/phys2170/phys2170_spring96/hws/2170_hw75.gif is the uncertainty in its angular position. (You may think of a particle, mass m, moving in a circle of fixed radius r, with speed v)

b) At what uncertainty in L will the angular position of a particle become completely indeterminate?
 
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  • #2
getcarter said:
Verify that the uncertainty principle can be expressed in the form [PLAIN]http://www.colorado.edu/physics/phys2170/phys2170_spring96/hws/2170_hw73.gif,[/URL] where [PLAIN]http://www.colorado.edu/physics/phys2170/phys2170_spring96/hws/2170_hw74.gifis[/URL] the uncertainty in the angular momentum of a particle, and http://www.colorado.edu/physics/phys2170/phys2170_spring96/hws/2170_hw75.gif is the uncertainty in its angular position. (You may think of a particle, mass m, moving in a circle of fixed radius r, with speed v)

b) At what uncertainty in L will the angular position of a particle become completely indeterminate?

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  • #3
is there a theta operator?
 

1. What is the Uncertainty Principle?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know both the position and momentum of a particle with complete certainty. This means that the more accurately we know the position of a particle, the less accurately we can know its momentum, and vice versa.

2. How does the Uncertainty Principle relate to angular position?

The Uncertainty Principle applies to all physical quantities, including angular position. This means that it is impossible to know both the angular position and angular momentum of a particle with complete certainty. As the angular position becomes more accurately known, the uncertainty in angular momentum increases, and vice versa.

3. What is the mathematical expression for the Uncertainty Principle?

The mathematical expression for the Uncertainty Principle is ΔxΔp ≥ h/4π, where Δx represents the uncertainty in position, Δp represents the uncertainty in momentum, and h is Planck's constant. This equation shows that the product of the uncertainties in position and momentum must be greater than or equal to a specific value.

4. How does the Uncertainty Principle affect our understanding of the world?

The Uncertainty Principle challenges our classical understanding of the world, where things are believed to have precise positions and velocities. It shows that at the quantum level, there is a fundamental limit to our ability to measure and predict the behavior of particles. This principle has greatly influenced our understanding of the subatomic world and has led to the development of new theories and technologies.

5. Can the Uncertainty Principle ever be violated?

No, the Uncertainty Principle is a fundamental principle of quantum mechanics and has been proven to hold true in all experiments. It is not a limitation of our measuring devices, but rather a fundamental property of the universe. However, there are ways to minimize the uncertainty in one quantity by sacrificing the uncertainty in another, but the principle itself cannot be violated.

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