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I am a 12th grade student. I recently came across a statement that

An electron (like a photon) is neither a wave nor a particle. It is merely a solution to its wave function at that point.

Thus, solving the wavefunction of an electron in some atom (& limiting ourselves only to points of 90% probability), we get the electron's atomic orbital.
We cannot predict the exact location of an electron in an atom (at a given moment, or even at some moment in the future); we can only say with fair certainty that the electron would be (somewhere) in its orbital.

My questions are:

  1. Does the charge of the electron "travel" along with it, as the electron "moves" (unpredictably) in its orbital?
  2. Would this cause the electric field outside (or even inside) the atom at some point to fluctuate with time?
  3. Would the atomic orbital possess some (time averaged) "average charge density"? If so, can you provide me some hint on how to solve for it?

(Please let me know if my understanding of electrons in orbitals is completely wrong - I feel uncomfortable with it at times)

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  • $\begingroup$ "We cannot predict the exact location of an electron in an atom" - it's more subtle than that isn't it? That is, it's not that we cannot predict the exact location, it's that the electron (in a definite energy state) does not have an exact location, i.e., a definite energy state is not a state of definite position. $\endgroup$
    – Alfred Centauri
    Jun 5, 2022 at 12:49

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Welcome to SE.

Within quantum mechanics, it isn't a good idea to picture the electron and its wavefunction separately. The electron $is$ the wavefunction, so it doesn't "move inside" it. So it doesn't have a position that we just can't measure, it simply doesn't have a defined position.

Depending on the experimental setting, the electron can manifest more like a particle, or more like a wave. For example, inside the atom, the electron behaves mostly like a wave (no defined position, occupies a rather large volume). When it occupies an orbital, it's in a stationnary state: its wavefunction still changes over time, but its probability density doesn't (just like light's amplitude varies over time, but its intensity as perceived by your eye doesn't).

Because this density doesn't vary over time, the charge density associated with it doesn't either.

Of course, if some external influence forces the electron into a non-stationary state, this no longer holds.

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  • $\begingroup$ Not really. If it was spread, you would be able to devise a way to measure its density. But doing that boils down to measuring the position of the electron. And as soon as you do that, you force it into a particle-like behavior, and it'll manifest as a particle where you measured it. It's better to think of the charge as a property of the electron, not related to its spatial extension. In quantum field theory you can start asking deep questions about this, like how the electron interact with its own field, but not in "plain" quantum theory. $\endgroup$
    – Miyase
    Jun 5, 2022 at 16:02

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