An application of the uncertainty principle

In summary, the conversation discusses the application of the uncertainty principle to an electron confined in a region of size L. It is determined that the uncertainty in position of the electron must satisfy Δx<L. Using the uncertainty principle, an approximate value for the uncertainty in momentum can be calculated. This leads to the calculation of an approximate value for the kinetic energy of the electron, as shown in the attached picture. The question is then raised about how the value of kinetic energy was determined given the uncertainty in momentum. It is explained that, since kinetic energy is always a positive quantity, its standard deviation cannot be larger than its average value. This leads to the suggestion that by mathematical calculation, it can be shown that the standard deviation of kinetic energy is equal
  • #1
Youyang Zhao
2
0
It is in the IB textbook. Said as an application of the uncertainty principle, consider an electron, which is known to be confined in a region of size L.
We know the uncertainty in position of the electron must satisfy Δx<L.
Therefore, according to the uncertainty principle, we can work out the approximate value of the uncertainty in momentum.
Then, as shown in the picture attached, an approximate value of the kinetic energy of the electron is worked out.
ImageUploadedByPhysics Forums1468640544.931531.jpg

I can not understand the process. How did they work out the value of kinetic energy (or value of the momentum) with the uncertainty of the momentum?
Asking questions for the first time. Thank you for your time and patience.
 
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  • #2
Well, a kinetic energy is always a positive quantity, so it would be kind of crazy if its standard deviation was larger than its average value.
 
  • #3
hilbert2 said:
Well, a kinetic energy is always a positive quantity, so it would be kind of crazy if its standard deviation was larger than its average value.

Does that mean by mathematical calculation, we can get the result that the standard deviation of the kinetic energy equals to Δp^2/2m, which is smaller than the average value of the kinetic energy?
 

Related to An application of the uncertainty principle

1. What is the uncertainty principle?

The uncertainty principle, also known as the Heisenberg uncertainty principle, is a fundamental principle in quantum mechanics that 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 apply in real-world situations?

The uncertainty principle applies in various situations, such as in the measurement of subatomic particles, the behavior of atoms and molecules, and the design of electronic devices.

3. What are the implications of the uncertainty principle?

The uncertainty principle has significant implications in the field of quantum mechanics, as it challenges our traditional understanding of determinism and causality. It also has practical applications in technology, such as in the development of quantum computing.

4. Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental principle in quantum mechanics and has been repeatedly confirmed through experiments. It is a crucial aspect of our understanding of the behavior of particles at the quantum level.

5. How does the uncertainty principle relate to other principles in physics?

The uncertainty principle is closely related to other principles in physics, such as the principle of complementarity and the wave-particle duality. These principles all contribute to our understanding of the behavior of particles at the subatomic level.

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