Understanding quantum models In quantum mechanics we have different models like the infinite and finite square well, potential barrier, etc. What I don't understand is how these are applicable to real life situations. For example, in a one dimensional potential well we have two points where the potential goes to infinity. Now, if we were to apply this in real life situations then what would these "potentials" be? Can we take the example of two parallel plates with large voltage and a single particle between them? If yes, then in what other ways can this model be used? Also, does the potential used in the model refer only to the electrostatic potential or can it mean something else in other situations.
Edit: I am not looking for only the one dimensional potential well and took the example here just to explain my doubts. I just want to know how real life situations can be solved with quantum modelling. Also, what does negative energy in a quantum system mean?
 A: These models may seems really strange when you learn QM for the first time since they don't have much sense in real problems. 
In QM books, these examples are mainly used to demostrate the process of applying Schrodinger's equation to some problems. And we alwasy start with the easiest one, which is one-dimensional infinite potential, then one-dimensional finite potential, then tree-dimensional.
The first very exact real problem in the book will be the hydrogen atom, which will be far more complex to solve than the above problems. Everything suddenly make sense to the real world when this come out.
The above simple models has some application to real problems, too, like any problem in which the particle is restricted to a finite region, but in most case the result is very rough since too much approximations are made.
A: Here is a real-wordish application of the one-dimensional well. Consider the problem of non-interacting particles in a three-dimensional box. The three spatial directions decouple in this situation so that one may consider three one-dimensional problems instead. A real box will have some permeability, but let's assume it to be negligable. This can be modelled by letting the potential rise infinitely steep. 
A: The energies of sigma bonding and antibonding orbitals of diatomic molecules can be estimated by the eigenvalues of an electron of a one-dimensional box with a length three times as large as the nuclear separation. 
This works nicely especially for the unbound resonances. I can look up the reference if you want it.
