130_notes.dvi

add B-field

n=2

S1/2

P3/2 P1/2

S P1/2

1/2

P3/2

add relativity

add Darwin

• spin-orbit

The factor

(

1 ± 2 ℓ^1 +1

)

is known as theLandegFactorbecause the state splits as if it had this

gyromagnetic ratio. We know that it is in fact a combination of the orbital and spin g factors in a
state of definitej.

In the strong field limit we could use states of definitemℓandmsand calculate the effects of the
fine structure,H 1 +H 2 , as a correction. We will not calculate this here. If the field is very strong,
we can neglect the fine structure entirely. Then the calculation is easy.

E=E^0 n+

eB ̄h

2 mc

(mℓ+ 2ms)

In this limit, the field has partially removed the degeneracy inmℓandms, but notℓ. For example,
the energies of all thesen= 3 states are the same.

ℓ= 2 mℓ= 0 ms=^12

ℓ= 1 mℓ= 0 ms=^12

ℓ= 2 mℓ= 2 ms=−^12