Spin of an Electron: Meaning & Quantum Number

[Aniket1]

What does the spin of an electron mean?
Is it the z component of the spin angular momentum or the spin quantum number?

 

[Simon Bridge]

It means that it has a particular behavior when it goes through an asymmetric magnetic field... "as if" it had a magnetic dipole. The "z-component" is the amount of the dipole along the z-axis (determined by the apparatus).

 

[Aniket1]

What I wanted to ask is, whenever we refer to the word spin for an electron, which of the following does it mean:
Spin angular momentum
z component of spin angular momentum
Spin quantum number

 

[Simon Bridge]

Any or all of the above - depending on context.

 

[jtbell]

When we say the electron is "spin 1/2" we refer to the quantum number $s$ for the magnitude of the intrinsic angular momentum.

When we say an electron is "spin up" or "spin down" we refer (indirectly) to the quantum number $m_s$ for the z-component of the intrinsic angular momentum (+1/2 or -1/2).

 

[Cody Richeson]

This is something that confuses me. Are we saying that the electron is literally spinning on its axis, like a spinning top, or the Earth, or is it incorrect for me to think of the electron from a spherical perspective?

 

[Simon Bridge]

This is something that confuses me. Are we saying that the electron is literally spinning on its axis,

No.

... is it incorrect for me to think of the electron from a spherical perspective?

Yes. - at least, it would be inaccurate and possibly misleading to think of an electron as a spinning sphere.

QM has a lot of terms for things that don't make a lot of literal sense. In this case, the word is used because the property being described has similar math to that resulting from rotating charge distributions. But that's just the math. There is no (other) indication that electrons have an uneven charge distribution. Think of it as a nick-name.

 

[ImaLooser]

What does the spin of an electron mean?
Is it the z component of the spin angular momentum or the spin quantum number?

It has very little to do with spin as we know it. It is just a name, so things will be easier if you forget about spin and think of it as something entirely new called quantum spin.

Even Richard Feynman was unable to explain it simply, so I'm not going to try. I'd recommend looking at the Stern-Gerlach experiment, then maybe at the polarization of light.

 

[FeynmanIsCool]

This is something that confuses me. Are we saying that the electron is literally spinning on its axis, like a spinning top, or the Earth, or is it incorrect for me to think of the electron from a spherical perspective?

Spin has no macroscopic analog, but I like to picture it as more of a "quality" of the particle, and how it reacts with polarization. Up and Down spins effects can be seen by passing electrons through a B field (where up and down spins will be attracted to different poles) because the distribution of charge on a particle is separate from its mass (what Simon Bridge said).