Magnetism 1

( )
0 so Z Z
B µ
H = H + H + J + S H L+ 2 S = J + S since J = L+ S
→ the problem is that s mixes states with different .
ml, ms
l, s⋅ l = i l × s)
, only the Z-components are conserved.
[ ] (
⇒ the spin-orbit interaction lifts the degeneracy between different levels with
s and l (without a magnetic field), it leads to a different kind of splitting than the
Zeeman-splitting → levels with the same j-value are degenerate for some
s , l .
E( J) −E( J − 1) λ
= ( J( J + 1) ) −
2
= λ ⋅J
L( L+ 1) − S( S+ 1) 1
−
2
J −1 J − L L+ 1 − S S+
1
for same
s , l , J = l±½
( ) ( ( ) ( ) ( ) )
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