Electron Fundamentals

I'm very interested in the topic of contact and the uncertainty principle. I understand that no atom's actually touch each other but are considered in contact when the small repulsive force of the negatively charged electrons get closer to one another. I researched a little online and found out that theoretically freezing an electron will not stop its movement. So what if you put an electron in a spherical magnet? Would that stop it from moving? The second part would be where you have the same spherical magnetic enclosure but with 2 trapped electrons inside. If you increased the magnetic strength of the sphere to infinity would the 2 electron's ever touch? I realize you can't realistically do these experiments but would these work theoretically?
- Aaron Rasmussen (age 21)
Marshfield

Your question is very valuable because it shows what problems come up when you try to describe the small-scale world as if it were made out of small parts like the ones we are familiar with on a big scale. It isn't.

We have some old discussions of these issues:

Atoms do "actually touch each other" in the following sense. The electrons (and other parts) are not little dots, but spread out waves. The wave functions of their electrons overlap in some spatial region. 

By "freezing an electron" I think you mean putting it in the lowest energy state available to it in an atom. The wave in such a state doesn't move around, at least not relative to the atom's nucleus. However, just as the wave sits spread out over different positions, it also has a distribution of different velocities. It's tricky to see how that can be combined with it not going anwhere, but maybe it helps to think of a standing clasical wave.

You want to know what would happen if the electron were trapped by something other than an atomic nucleus, maybe by a magnetic field. It turns out that there is no magnetic field pattern that can trap an electron, as shown long ago by Earnshaw. Still, your basic question about other trapping can be answered. There's nothing special about atoms. Any confined electron state always has s pread of velocities in it. The minimum spread is described by the Heisenberg uncertainty relation.

Maybe the best example of two electrons "touching" is a helium atom. The two electrons have waves distributed in just the same way around the nucleus.

Mike W.

(published on 06/09/2015)