What is scattering by a potential and how does it affect a passing particle?

[Shaybay92]

"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?

 

[jtbell]

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.

 

[Shaybay92]

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)

 

[jtbell]

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.

 

[Shaybay92]

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.

 

[The_Duck]

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.