What is the purpose of using a potential well to model a particle's confinement?

[Jacky]

What does a particle in a potential well means?
What is the physical interpretation of it?
Could anyone anser this topic

 

[amirghaderi]

particle in potential well is like an electron in electric field of proton in hydrogen atom . in hydrogen the well is sphrical

 

[Domenicaccio]

In very general terms, you use the potential well to model a situation under which the particle is forbidden to leave a certain region of space, for whatever reason.

For example, for the electron of a hydrogen atom the model is quite good, because the energy required to strip the electron away is high. The model sets the potential energy barrier to infinite as if you were assuming that the energy required is so high that in your case you can be pretty sure it will never be reached.

A similar situation could be a conduction electron in a block of metal, and the box is the entire block. If for your purposes you can assume that nothing will give it the opportunity to leave the block, then you can use the potential well as a model. Of course, it's a very rough model, it doesn't mean it will be precise enough for all purposes... in fact in the metal case it might give you too much an approximated wavefunction, and you may want to instead include the effect of all the lattice to get a wavefunction and therefore a probability density more representative of the real thing.

But it's an important model nonetheless because the rough result (the shapes of the eigenfunctions) is still "visible" in more precise models.