system
Given the following post, respond as if you're commenting on Reddit:
human
Do electrons actually move around the nucleus?

What does it mean for an electron to have a "probability cloud"? I understand that's the probability of finding it at every point in space, but does he move? just appears ad disappears? Is it just a mathematical cloud of probabilities that collapses when measured? Or does the electron just moves around the nucleus in some way that we don't understand yet?
gpt
Strictly speaking, no. While it does have momentum and kinetic energy, there's no notion of movement in quantum mechanics. Once you measure the electron position somewhere, the state has collapsed (under whatever your interpretation of what that "really" means) into that eigenstate and won't change (in the idealized case) - this gets a bit muddied by the fact that the position basis is not discrete but that can be solved by having a better definition of what measuring position means.

You can have something that looks like movement if you have a reasonably well localized wave packet with a non-zero group velocity, where the center of the packet will move, but that's not a situation that applies to a bound state of electron around a nucleus.