When at some quantum state, it is said about an electron that its momentum is zero, does it mean it has no mass? Or no scalar speed?
How can an electron have zero momentum? Does it "condensates" like butter spread all over its orbital? Or does it still undulate in its orbital but somehow loses whatever it is that gives it mass?
I cannot understand this concept.
This answer is in the language of quantum mechanics. I took a crack at explaining that language without explicit math the other day, but I just going to put the bare QM here. I recognize that it will probably be quite unsatisfying for many readers, but the simple fact is that QM follows it's own rules and there is not a one-to-one analogy with the rules of the world that we think we interact with on a daily basis.
It really means that the state of the system is an eigenstate of the total angular momentum operator that corresponds to a measurement of 0.
The system is not in an eigenstate of position; nor of linear momentum; nor of linear velocity. Which means it is an error to speak (or think) of the electron as having a value for any of these things. You can measure them, of course, but in doing so you (1) get a result that is drawn from a distribution rather than always the same and (2) change the state of the system by measuring it.
So, no it doesn't mean that the electron is stopped (possessed of velocity or momentum of zero), though a measurement of the velocity or momentum might turn up zero in some cases.
There are two kinds of momentum for the electron, intrinsic spin momentum, which it always has, and angular momentum, which what you are taking about. An electron does and always will have, mass, spin angular momentum, and electric charge.
If you think of the electron as something like a marble, you will get the wrong picture of both its spin angular momentum and its orbital angular momentum.
Don't think of the electron going around the nucleus, like a planet going around the Sun. At the quantum level, its all about forgetting classical concepts and filling your brain insead with mathematical ones, because common sense no longer applies.
The only thing that is of any importance is the electron's wavefunction. The electron has orbital angular momentum if the wavefunction, which describes it's position, allows for it. That is the basis for whether or not, the electron has orbital angular momentum. Some electrons do, some don't. In the hydrogen atom , the ground state electron has no orbital momentum. If you try to think classically, this makes no sense. If you read the Wikipedia article linked below, it might.
The orbital angular momentum has no relation to mass, that's because the electron has mass and it's embedded in us to think, if it has mass and spins around, it's got angular momentum. No, not in the quantum world.
The orbital angular momentum itself has strong fluctuations and it is zero only on average. If you find it impossible to stop think of it in terms of planets, then think that the electron is orbiting around the nucleus, but this orbiting does not have a prefered trajectory, i.e. it goes in all directions around the nucleus.
I was going to include a picture of orbitals of electrons, but that would just bring the classical picture into your mind again.
In his answer, dmckee says:
It really means that the state of the system is an eigenstate of the total angular momentum operator that corresponds to a measurement of 0.
This is an example of dropping the classical world picture, and instead applying mathematical language to describe the quantum world.
Have a read of this Angular Momentum Wikipedia., but please DON'T take the illustrations literally.
