Uncertainty Principle: L & Angular Position

In summary, the uncertainty principle states that the uncertainty in the angular momentum of a particle (represented by ∆L) multiplied by the uncertainty in its angular position (represented by ∆θ) must be greater than or equal to a constant value. This can be expressed as ∆L ∆θ ≥ ħ/2, where ħ is the reduced Planck's constant. When the uncertainty in L reaches a certain value, the angular position of the particle becomes completely indeterminate. To prove this relation, one must show that ∆L ∆θ ≥ ħ/2 is always true for all possible values of ∆L and ∆θ.
  • #1
getcarter
36
0
Verify that the uncertainty principle can be expressed in the form
2170_hw73.gif
, where
2170_hw74.gif
is the uncertainty in the angular momentum of a particle, and
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
What have you tried? You need to show some sort of attempt to get assistance here as per forum policy.
 
  • #3
Once you have answered part (b), you will see that the relation that you're supposed to prove in part (a) cannot be quite correct!
 

Related to Uncertainty Principle: L & Angular Position

1. What is the Uncertainty Principle?

The Uncertainty Principle, also known as the Heisenberg Uncertainty Principle, states that it is impossible to know both the exact position and momentum of a particle at the same time.

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

The Uncertainty Principle also applies to angular position, meaning that it is impossible to know both the exact angular position and angular momentum of a particle simultaneously.

3. Why is the Uncertainty Principle important in quantum mechanics?

The Uncertainty Principle is important in quantum mechanics because it sets a fundamental limit on our ability to accurately measure and predict the behavior of particles at the subatomic level. It also helps to explain certain phenomenon, such as the wave-particle duality of particles.

4. Can the Uncertainty Principle be overcome?

No, the Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be overcome. However, it does not limit our ability to make accurate predictions and measurements at a macroscopic level.

5. How does the Uncertainty Principle impact our understanding of the physical world?

The Uncertainty Principle challenges our traditional understanding of cause and effect, as it shows that the act of measuring a particle can alter its behavior. It also highlights the limitations of our ability to fully understand and control the behavior of particles at the quantum level.

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