Spin and orbital magnetic moments?

[pivoxa15]

The books said that total magnetic moment of an electron is spin + orbital magnetic moment.

But is the orbital magnetic moment realistic quantum mechanically? I thought electrons doesn't have a trajectory. The Stern Garlach experiment showed that silver atoms only split into two paths after being in a magnetic field. But if orbital magnetic moment was also present then shouldn't there be less distinction in that the paths may have been more spread out or random.

 

[jtbell]

The net orbital angular momentum of the 47 electrons in a silver atom is zero, and their spins "pair up" so the total angular momentum (orbital + spin) comes only from the spin of the outermost electron.

 

[Meir Achuz]

The books said that total magnetic moment of an electron is spin + orbital magnetic moment.

But is the orbital magnetic moment realistic quantum mechanically? I thought electrons doesn't have a trajectory. The Stern Garlach experiment showed that silver atoms only split into two paths after being in a magnetic field. But if orbital magnetic moment was also present then shouldn't there be less distinction in that the paths may have been more spread out or random.

Orbital angular momentum is also quantized. If an atom has both S and L, then J=L+S. (QM addition. This is called "L-S coupling".)
J is quantized and would determine the SG splitting.

 

[pivoxa15]

The angular momentum of an electron is also quantised and a real phenomena in that it can be measured (although only one component at a time). Classically moving charges generate a magnetic field so that is why we associate an orbital magnetic moment to an electron in an atom. But the angular momentum is quantised and that is why the magnetic moment is also quantised.

 

[dextercioby]

The books said that total magnetic moment of an electron is spin + orbital magnetic moment.

But is the orbital magnetic moment realistic quantum mechanically? I thought electrons doesn't have a trajectory. The Stern Garlach experiment showed that silver atoms only split into two paths after being in a magnetic field. But if orbital magnetic moment was also present then shouldn't there be less distinction in that the paths may have been more spread out or random.

Well, since it's given by

$$\hat{\mu}_{orb} \sim \hat{\vec{L}}\cdot \vec{B}$$,

i'd say it's pretty realistic...

Daniel.

P.S. For $l\neq 0$ stationary states of the H-atom it gives a contribution to the shifting of the normal energy levels.