Visualisation in Quantum mechanics

[CAF123]

A particle in the ground state of a potential well can only gain energy by making a transition to one of the higher allowed energy levels.
Let's consider this well to be a 1 dimensional infinite potential well with the electron bouncing between the walls of the well with certain discrete energies.
Two questions:

Is the energy level diagram just a pictorial representation of the varying quantised energies that the electron can possibly have?

If we were to view this electron, if it jumped to another energy level, how would this manifest itself into something we could observe, ie if it moved to some higher level, would we simply observe the electron moving faster between the walls of the well?

Many thanks.

 

[mfb]

Is the energy level diagram just a pictorial representation of the varying quantised energies that the electron can possibly have?

It is a representation of the energy eigenstates. The electron can be in a superposition of them, with arbitrary expectation values for the energy (but at least the ground state energy).

If we were to view this electron, if it jumped to another energy level, how would this manifest itself into something we could observe

It could absorb or emit a photon, for example.

would we simply observe the electron moving faster between the walls of the well?

If you can observe an actual "movement" of the electron (for example by measuring the charge distribution somehow), you disturb it in a significant way and change its states every time you measure it.

The energy eigenstates do not represent an electron bouncing back and forth.

 

[CAF123]

When you say it could absorb or emit a photon, does this also apply to the infinite potential well? (I know it can be applied to an atomic potential such as the energy levels in an atom)
So if an infinite potential well, if the electron absorbed a photon, it would have greater energy?

Also, for an electron in an atom, when it receives a photon, it jumps to a higher energy level. This corresponds to the electron moving to another shell in the atomic structure?
What happens in an infinite potential well? The energy level diagram is still present, but this time there is no shells or anything to properly 'visualise' what is going on?

Many thanks.

 

[mfb]

So if an infinite potential well, if the electron absorbed a photon, it would have greater energy?

This is true for all potential well shapes, yes.

Also, for an electron in an atom, when it receives a photon, it jumps to a higher energy level. This corresponds to the electron moving to another shell in the atomic structure?

It can go to a different state in the same "shell", too.

What happens in an infinite potential well? The energy level diagram is still present, but this time there is no shells or anything to properly 'visualise' what is going on?

Well, you could call every energy state a "shell".

 

[CAF123]

Thanks, but what is this 'shell' in the infinite potential well?

 

[tom.stoer]

In atomic physics "shell" is nothing else but a name for "a set of electron states in an atom" with the same principal quantum number n. The n'th shell contains N=2n² states, where N can be calculated from the allowed values for the quantum numbers l=0,1,...,n-1; m=-l,-l+1,...,l-1,l and s = +1/2, -1/2.

In a one-dim. problem the quantum numbers l and m do not exist b/c they label the representations of the 3-dim. rotation group SO(3). So in one dim. a "shell" would be a set of states for same n and different s, so the n'th "shell" would always contain two states s = +1/2, -1/2. Neglecting spin the n'th shell is identical with the n'th state; I don't think that it makes much sense to use "shell" here.

http://en.wikipedia.org/wiki/Electron_configuration#Shells_and_subshells