Electrons at Absolute Zero -- do they still move?

[Vectronix]

TL;DR

do they still move?

Can we all agree that electrons still move at absolute zero?

 

[BvU]

Yes

 

[Nugatory]

Yes, but it is quite likely that “electrons move” doesn’t mean what you’re thinking.

 

[Vectronix]

You mean like it doesn't mean a point particle moving at high speeds around the nucleus?

 

[Nugatory]

You mean like it doesn't mean a point particle moving at high speeds around the nucleus?

That’s right, it certainly does not mean a point particle moving at high speeds around the nucleus. If that were in fact an accurate model atoms would be unstable; this was one of the original motivations for developing quantum mechanics as an alternative model.

The “absolute zero” part of your question is a bit of a red herring here - velocity isn’t a very useful concept when thinking about bound electrons under any conditions. We have a bunch of threads about how to think of bound electrons in quantum mechanics, chances are someone here will be able to point you to some.

Edit: the “Suggested for” list of threads below has some good ones.

 

[vanhees71]

TL;DR Summary: do they still move?

Can we all agree that electrons still move at absolute zero?

No, since at $T=0$ the electrons are in the ground state, which is an eigenstate of the Hamiltonian, and eigenstates of the Hamiltonian describe stationary states. So nothing moves.

 

[BvU]

I liked #2 better

 

[vanhees71]

Then, how can an energy eigenstate describe a moving particle? It's a stationary state!

 

[DrClaude]

Then, how can an energy eigenstate describe a moving particle? It's a stationary state!

But $\braket{p^2} \neq 0$. I guess it comes down to what "moving" means

 

[vanhees71]

These are quantum fluctuations, in this case "zero-point fluctuations", not motion.

 

[gentzen]

But $\braket{p^2} \neq 0$. I guess it comes down to what "moving" means

These are quantum fluctuations, in this case "zero-point fluctuations", not motion.

Moment without movement. Just like in Bohmian mechanics. Since nearly all physicists agree that this is a shortcoming of Bohmian mechanics, my guess would be that vanhees71 is wrong in this specific case. I just can't believe that Bohmian mechanics should be right in this respect. It will often be the ground state of an harmonic oscillator, and of course oscillate is what it will do.

 

[Nugatory]

OK this thread seems to have run way past OP's question.... Which was kinda sorta OK because it does demonstrate the extent to which the answer depends on how we define "moving" in the absence of the classical intuitive definition. But we're at the point of diminishing returns now, so I am closingthe thread.

As with all such thread closures, we can reopen it if there is more to say in response to the original question - just PM me or another mentor.