Three J values

[Johanna Waltenspiel]

We consider three orientations of L and S:
A: L and S parallel (0deg, cos(0)=1)
B: L and S orthogonoal (90deg, cos(90)=0)
C: L and S antiparallel (180deg, cos(180)=-1)

Consider that the Hamiltonian of the L-S coupling is proportional to the scalar product of L and S. The scalar product can be expressed as the product of their absolute values times the cosine of the angle between the two. This seems to suggest that:
J=0 is state A
J=1 is state B
J=2 is state C

[admin-hyperfinecourse]

Correct reasoning, but exactly the opposite conclusion than was expected. Please verify.

[Johanna Waltenspiel]

I think I probably confused myself by thinking about the Hamiltonian and low/high energies instead of just considering the values of L and S needed to get to the J-values associated with the energy levels.

When considering that J = L + S, J=0 would suggest antiparallel alignment for L and S to “cancel” each other.
With the same reasoning, J=2 needs a parallel alignment of S and L and the remaining J=1 corresponds to an orthogonal alignment.

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