Transmission probability (tunneling) question

In summary, the transmission probability for electrons with energy greater than the barrier potential Vo is given by T = [ 1 + (Vo²*sin²(βa))/(4E*(E - Vo)) ]^(-1), where a is the width of the barrier. To find the maximum reflection, the width of the barrier needs to be calculated. It is important to note that maximum reflection does not necessarily mean 100% reflection. The reflection coefficient is not always expected to be 1 and finding the maximum does not necessarily involve taking the derivative. The formula for β may also be relevant, but numerical answers are not the focus at this time. Any guidance would be appreciated.
  • #1
mclame22
13
0
A beam of 11 eV electrons is directed towards a barrier of potential Vo = 3.8 eV. Compute the width of the barrier for which the reflection is maximized (Note: this is NOT asking for when reflection is 100%).

Transmission probability for E > Vo:
T = [ 1 + (Vo²*sin²(βa))/(4E*(E - Vo)) ]^(-1)

where a is the width of the barrier.

I need a bit of help starting this question. I do not understand why maximum reflection is not 100% reflection, or T = 0. Finding when something is a maximum makes me think "derivative = 0," but other than that I'm really unsure about where to go. And there is a formula for β but I am not very concerned with numerical answers right now. Any advice is appreciated.
 
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  • #2
Why would you expect the reflection coefficient to be 1?
 

1. What is transmission probability (tunneling)?

Transmission probability, also known as tunneling, is a quantum mechanical phenomenon where particles are able to pass through a potential barrier that would normally be impossible to cross based on classical physics principles. This occurs due to the wave-like nature of particles at a subatomic level.

2. How is tunneling related to quantum mechanics?

Tunneling is a fundamental concept in quantum mechanics and is a result of the particle-wave duality of matter. In classical mechanics, particles would not have enough energy to pass through a potential barrier, but in quantum mechanics, particles can behave as waves and have a probability of passing through the barrier.

3. What factors affect the transmission probability of particles?

The transmission probability of particles is affected by the energy of the particles, the height and width of the potential barrier, and the mass of the particles. Higher energy particles have a higher probability of tunneling, while taller and wider barriers decrease the probability. Heavier particles also have a lower probability of tunneling.

4. How is tunneling used in technology?

Tunneling is used in a variety of technologies, including scanning tunneling microscopes, which use the tunneling of electrons to create images of surfaces at the atomic level. It is also utilized in quantum tunneling devices, such as tunnel diodes, which are used in electronic circuits for their unique properties.

5. Are there any real-world applications of tunneling?

Yes, tunneling has many real-world applications, including in nuclear fusion reactions, where particles must tunnel through the Coulomb barrier to fuse together. It is also used in the development of tunneling transistors, which could potentially lead to more efficient and powerful electronic devices. Additionally, tunneling is a crucial concept in understanding the behavior of semiconductors, which are used in many modern technologies.

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