system
Given the following post, respond as if you're commenting on Reddit:
human
In a vacuum, will an electron cloud expand to fill a volume like a gas?
gpt
In a sense, yes. If you have a particle in a box and you expand the size of the box, the wavefunction of the particle will evolve with time such that it "occupies" the entire available volume.

There are two limits to consider: the limit where the box is expanded rapidly (the sudden limit), and the limit where the box is expanded slowly (the adiabatic limit).

In the adiabatic limit, the box size is varied slowly, so if the particle starts in the ground state of the well at t = 0, it will remain in the ground state as the well expands, even though the actual ground state wavefunction and energy are changing with the size of the well. So the wavefunction will expand with the box as you slowly make it bigger.

In the sudden limit, the box is rapidly jerked to a larger size, so the wavefunction of the particle doesn't have time to change. So immediately after the box size is increased, the wavefunction will still be localized in the region of space that was originally available. As time goes on though, the wavefunction will evolve such that it occupies the entire volume of the box.

So either way, you end up with a wavefunction which extends throughout your larger box.