Electron wave function collapse

[phil ess]

As far as I understand it, an electron exists as a probability cloud around an atom, representing all the possible places it could be. Then when we make an observation the wave function collapses to one point where we see the electron. So what happens if we keep looking at it? Does the elctron jump around randomly between different positions? I don't imagine it would just stay in the same place, but what does it do?

Sorry if I have worded the question poorly, thanks!

 

[f95toli]

The wiki page on the quantum zeno effect (which is what you are referring to) is pretty good

http://en.wikipedia.org/wiki/Zeno_effect

 

[Naty1]

I can understand the description for a theoretically isolated atom in a vacuum...but not for one in the real world...

Wikipedia says

The quantum Zeno effect is the suppression of unitary time evolution caused by quantum decoherence in quantum systems provided by a variety of sources: measurement, interactions with the environment

I just got done reading elsewhere that decoherence and entropy go hand in hand, inexorably, as nature constantly disperses information and samples just about everything via decohence with the environment...information is dispersed, entropy increases, in fact it can't be stopped in any pratical way.

So I would have thought that for certain a typical electron in an atom would be undergoing near constant decoherence from interactions/samplings with the environment... nature "measures" everything all the time what with photons, gravitons, cosmic rays, vibrations, TV signals,etc bombarding everything...so how do we suppose an electron in the real world would not be closely coupled to it? How can it stay in an uncertain "cloud".

For example, a conductor of electricity with impressed voltage has no problem picking the loosly bound electrons for transport to a neighbor...it's not like a tightly bound one pops up and moves along...the loosely bound outer shell electrons sure know who they are!

 

[f95toli]

So I would have thought that for certain a typical electron in an atom would be undergoing near constant decoherence from interactions/samplings with the environment...

Correct. Although, it is the state of the electron that is being "measured"; not the electron itself (an electron bound to an ion is not free so you can't think of it as an independent particle in this context).
Anyway, the fact that the states interacts with the environment (even if it is only the vacuum) is the reason why real energy levels in atoms have a non-zero width (which in turn is why you can see lines in spectroscopy); the width of the level in frequency is simply given by 1/lifetime.
However, the coherence times for most states in atoms are pretty long so in most calculations we can model the levels as being discrete.

 

[lightarrow]

Anyway, the fact that the states interacts with the environment (even if it is only the vacuum) is the reason why real energy levels in atoms have a non-zero width (which in turn is why you can see lines in spectroscopy); the width of the level in frequency is simply given by 1/lifetime.

This is interesting but I'm not sure to have understood it well. Do you mean that the line's width of an atom's spectrum is in some way related with the void's energy?