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Electrons do not follow fixed orbits around an atom's nucleus but exist within "clouds of probability" (orbitals), where there is a high chance of finding them. As one extends the search for electrons farther from the nucleus, the probability diminishes, though it never reaches zero. Consequently, there is a non-zero probability that an atom's electron could be located "on the other side of the Universe."

The question is: if an electron is everywhere in space and not confined in fixed orbits, how does it maintain an association with a specific nucleus and thus form an atom (or a molecule!), considering that there may be further atoms bonded with it and conversely more indistinguishable electrons? Is it a mere convention?

Michael Seifert
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Marco Fabbri
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So in Quantum mechanics an electron being in a bound state in an Atom does not just mean, that we don’t know exactly where it is and have a probability distribution describing at what point it actually might be. That would be the case, if we would know, that the wave function was a delta peak in position space and we just had incomplete information about, where exactly that delta peak is centered. In a bound state the electron is in fact delocalized around the center of your binding potential and exponentially decaying at large distances to the center. Collapsing to specific position is only happening, when measuring the position. Since the wave function of the electron in an atomic bound state is clearly centered around the nucleus, there is a definite association of that electron with the nucleus. Actually the fact, that this electron does occupy this specific bound state (including definite spin state), is the only way you can distinguish it from other electrons as they are indistinguishable otherwise.

Now, if you do some measurement, you might cause the electron wave function to collapse into small spacial area far away from the nucleus. If as mentioned in your question the system also does contain a lot of other stuff apart from the electron and the nucleus, which cause stronger interaction at the new position of the electron, the association with the previous nucleus would indeed be lost. In fact that is, how I imagine a tunneling transition to work. But it is key here that you changed the state of the electron by the measurement and only after the measurement the binding is lost.

For completeness I would like to mention that this whole picture of first looking at the electron nucleus interaction, then a measurement and then the interaction of the electron with new particles closer to its new positions is of course just a model. As for exact time development you would have to solve the entire many particle system without neglecting any pair interactions at any time. From my current understanding this whole hand wavy fuzz about “state → measurement → new state” probably is an artifact of the inability to solve a many particle system exactly, though I am somewhat unsure on this take. I mainly write this clarification to avoid getting asked what exactly I mean by measurement in this context.

Also if you are interested in a more statistical take on something somewhat related to your question you might be interested in reading this https://physics.stackexchange.com/a/774294/325089 .

Zaph
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