Zeeman effect - spin orbit coupling

[Chemist20]

As far as I know: the possible orientations that the total angular momentum can take (given my Mj) are degenerate. if we apply a magnetic field, degeneracy will be lost and different states arise. this is the zeeman effect

but when looking up on google for zeeman effect, a webpage used as an example the splitting of the ml values por p orbitals. hence it said that in a magnetic field, the three different orientations of the orbital angular momentum would not be degenerate and hence px py pz would have different energies.

What I don't get is why are they talking about orbital angular momentum without including the spin angular momentum and hence talking about L instead of J ?

 

[jtbell]

Many books and courses introduce the Zeeman effect using only orbital angular momentum because it's easier. It also follows the historical development because physicists started to study the Zeeman effect before they knew anything about spin.

Of course, if you don't include spin, you can't explain many actual examples of Zeeman splitting. People talked about the "normal Zeeman effect" (which did fit the orbital-only calculations) and the "anomalous Zeeman effect" (which didn't).

Then Uhlenbeck and Goudsmit "invented" spin, and it turned out to be what was needed to explain the "anomalous Zeeman effect."

 

[Chemist20]

Many books and courses introduce the Zeeman effect using only orbital angular momentum because it's easier. It also follows the historical development because physicists started to study the Zeeman effect before they knew anything about spin.

Of course, if you don't include spin, you can't explain many actual examples of Zeeman splitting. People talked about the "normal Zeeman effect" (which did fit the orbital-only calculations) and the "anomalous Zeeman effect" (which didn't).

Then Uhlenbeck and Goudsmit "invented" spin, and it turned out to be what was needed to explain the "anomalous Zeeman effect."

great thanks!

so... when technically the 2p level splits into 3 different ones due to the interaction of the orbital angular momentum with the magnetic field, are these three different levels called "states"? because this is the term they use when they talking about splitting of the J levels.

 

[DrDu]

You also have to take in mind what you actually observe in experiment. In an optical transition, e.g. in hydrogen atom from 1s to 2p there is a selection rule Delta S=0. So you will not observe the splitting of the spin but only the splitting of the orbital momentum. Only in heavier elements where spin orbit interaction is important, you will see the splitting due to spin.

 

[jtbell]

when technically the 2p level splits into 3 different ones due to the interaction of the orbital angular momentum with the magnetic field, are these three different levels called "states"? because this is the term they use when they talking about splitting of the J levels.

I would say that 2p consists of three different states to begin with, with different values of m (-1, 0, +1), and with different wave functions that contain different spherical harmonics. With no external magnetic field, these states are degenerate, that is, they have the same energy. An external magnetic field gives them different energies and removes the degeneracy.