Magnetic alignment in a strong B-field

[Sojourner01]

Homework Statement

The question is on the behavior of the magnetic and spin axes in a strong B-field (the Paschen-Back Effect, I believe it's called. Anyway...). I've got almost everything nailed down, except for one thing. In the example I've looked up http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/paschen.html#c1", there doesn't seem to be a state for ml=1, ms=-1/2 and similarly, ml=-1 and ms=1/2.

Why can't the orbital and spin angular momenta have opposite orientations when they're decoupled by the strong field?

 

[Jhero]

I would like to address this question by first clarifying the terminology used. The Paschen-Back effect refers to the splitting of atomic energy levels in an atom when subjected to a strong magnetic field. This effect is observed when the spin and orbital angular momenta of the electrons in the atom interact with the external magnetic field.

Now, to address the question at hand, it is important to understand that the orbital and spin angular momenta are inherently coupled in an atom. This means that they cannot have opposite orientations, as they are both influenced by the same external magnetic field. In other words, the magnetic field affects both the orbital and spin angular momenta in the same direction.

In the example provided, the states of ml=1, ms=-1/2 and ml=-1, ms=1/2 are not allowed because they violate the Pauli exclusion principle. This principle states that no two electrons in an atom can have the same set of quantum numbers, including the spin quantum number (ms). Therefore, in the presence of a strong magnetic field, the possible states for an electron with ml=1 are ms=1/2 and ms=-1/2, but not both.

Furthermore, the orbital and spin angular momenta cannot be decoupled in the presence of a strong magnetic field. While the magnetic field can affect the orientations of these momenta, they are still connected and cannot have opposite orientations.

In summary, the reason why the states of ml=1, ms=-1/2 and ml=-1, ms=1/2 are not allowed in the example provided is due to the Pauli exclusion principle and the inherent coupling of the orbital and spin angular momenta in an atom. I hope this clarifies your understanding of the Paschen-Back effect and the behavior of the magnetic and spin axes in a strong magnetic field.