Scattering by a potential

In summary, when a particle travels past a potential well, there is a probability that it will be reflected or transmitted. In the one-dimensional case, this means the particle may be redirected in the opposite direction or continue in its original direction, while in the two- or three-dimensional case, it may emerge in a different direction than it entered. This phenomenon can be explained by the interaction between the particle and the potential, which can be represented as an electric field or potential in classical and quantum mechanics.
  • #1
Shaybay92
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"Scattering" by a potential

When we have an unbound particle traveling past a potential well, what does it mean when it is said that the potential well will "scatter" the particle?
 
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  • #2


In the one-dimensional case, it means that there is some probability that the particle will be reflected instead of transmitted.

In the two- or three-dimensional case, it means that there is some probability that the particle will emerge in a different direction than it entered.
 
  • #3


What do you mean when you say transmitted/reflected? If we are talking about a beam of electrons moving towards an attractive square potential (-ve well), what is meant by whether it is transmitted or not..? (In 1D)
 
  • #4


Suppose the particle is coming in from the -x direction, that is, it is traveling in the +x direction. Then:

Transmitted = after interacting with the barrier, it is traveling in the +x direction.

Reflected = after interacting with the barrier, it is traveling in the -x direction.
 
  • #5


Ok, but how physically does this make sense? How does the fact it goes past a potential change its path? I suppose I still don't fully understand what potential wells represent physically.
 
  • #6


In classical mechanics a proton, say, produces an electric field, and a passing electron can be deflected ("scattered") by this electric field. You can also write the problem in terms of the electron moving in an electric potential set up by the proton. This is how you have to do the problem in quantum mechanics.
 

1. What is scattering by a potential?

Scattering by a potential is a phenomenon in which a particle or wave is deflected or redirected by an external force or field, known as a potential. This can occur in various systems, such as in quantum mechanics, electromagnetism, and acoustics.

2. How does scattering by a potential affect particles or waves?

The effect of scattering by a potential on particles or waves depends on the strength and nature of the potential. In some cases, particles or waves may be completely absorbed or transmitted through the potential, while in other cases, they may be deflected or scattered in different directions.

3. What is the difference between elastic and inelastic scattering by a potential?

Elastic scattering by a potential refers to the case where the total energy of the particle or wave is conserved after interacting with the potential, while inelastic scattering involves a change in the total energy due to the interaction with the potential.

4. How is scattering by a potential related to the concept of cross-section?

The cross-section is a measure of the likelihood of a particle or wave being scattered by a potential. It is directly proportional to the area of the target that the particle or wave interacts with and provides information about the scattering properties of the potential.

5. What are some real-world applications of scattering by a potential?

Scattering by a potential has many applications in different fields of science and technology. Some examples include the study of atomic and nuclear interactions, the development of medical imaging techniques, and the design of materials with specific optical or acoustic properties.

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