Quantum Tunneling from Bent Circular Wire

In summary, the problem involves an electron entering a straight pipe with a circular cross section and then being bent at a larger radius before being aligned back again. The goal is to find the probability of the electron jumping out using the tunneling probability in the WKB approximation. However, due to the lack of information and assumptions needed, it is difficult to solve the problem. This problem is part of a series of odd questions on a physics forum.
  • #1
Ichigo449
49
1

Homework Statement


The electron enters a straight pipe of circular cross section (radius r). The tube is bent at a radius R≫r by the angle α and then is aligned back again. Find the probability that the electron will jump out

Homework Equations


Tunneling probability in WKB approximation.

The Attempt at a Solution


Unsure of what the potential should be and the effect that the bend has.
 
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  • #2
If that is the full problem statement, it looks odd. You'll have to add many assumptions to get a result.
 
  • #3
  • #4
I guess that is a very short version - it gives an idea of the problem, but it doesn't have the actual numbers necessary to solve it. Same with the other two problems.
 

1. What is quantum tunneling from bent circular wire?

Quantum tunneling from bent circular wire refers to the phenomenon in which a particle is able to pass through a potential barrier, such as a curved wire, even though it does not have enough energy to overcome the barrier according to classical physics. This occurs due to the probabilistic nature of quantum mechanics, where particles are described as waves that can exist in multiple states simultaneously.

2. How does quantum tunneling from bent circular wire occur?

Quantum tunneling from bent circular wire occurs when a particle approaches the potential barrier and is described by a wave function that extends beyond the barrier. This allows for a small probability that the particle will "tunnel" through the barrier and emerge on the other side. The probability of tunneling is dependent on various factors, such as the strength of the barrier and the energy of the particle.

3. What are the applications of quantum tunneling from bent circular wire?

Quantum tunneling from bent circular wire has various applications in technology and scientific research. It is used in scanning tunneling microscopy, where it allows for the measurement of surface features on an atomic scale. It is also utilized in quantum computing, where tunneling allows for the manipulation and transfer of information between quantum bits (qubits).

4. Are there any limitations to quantum tunneling from bent circular wire?

Yes, there are limitations to quantum tunneling from bent circular wire. The probability of tunneling decreases as the barrier becomes thicker or higher. Additionally, the process of tunneling is highly sensitive to external factors, such as temperature and noise, which can disrupt the delicate quantum states involved in the tunneling process.

5. How does quantum tunneling from bent circular wire relate to other quantum phenomena?

Quantum tunneling from bent circular wire is just one example of the many counterintuitive phenomena that occur at the quantum level. It is closely related to other quantum effects such as wave-particle duality, superposition, and entanglement. Understanding these phenomena is crucial for developing new technologies and advancing our understanding of the fundamental laws of nature.

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