210 
THE QUANTUM 
[XV. 3 
XV. 3] 
) 
15 
direction of the field. Introducing an expression of this form 
for AH a and AH e , the equation becomes 
hAv = to -«0 X h e - JL . . . I 5 :6 
We notice that h, the quantum constant, occurs on both sides 
of the equation, and cancels out, leaving us with 
A / X* H 
A* = K - m e )— — . . . • 15 : 7 
m 0 A^Tto 
As Sommerfeld remarks—“ In our final formula the quantum 
theory has, in a certain sense, become latent, in that its char 
acteristic feature, the quantity h, has disappeared.” In this we 
see a reason for the possibility of accounting for the Zeeman 
effect on the classical theory. 
The change in frequency depends on the difference between 
the two quantum numbers m a and m e . In ordinary cases a 
“ selection principle ” is introduced limiting the change in the 
equatorial quantum number to the values ± 1 or o. In the 
first case, when the difference between these numbers is ±1, 
the frequencies of the resulting components are given by 
, e H 
V = Vo ± : , 
m 0 471c 
and each of these lines is circularly polarized in a plane perpen 
dicular to the field. When viewed longitudinally these lines 
appear circularly polarized, and when viewed transversely they 
appear plane polarized, perpendicular to the lines of the field. 
In the second case, when m a — m e = o, i.e. when the equatorial 
quantum number is unchanged, the line only appears when 
viewed transversely, for it is plane polarized with its electric 
vector parallel to the direction of the field. 
Thus the normal triplet can be accounted for by applying 
the quantum theory. 
3. Anomalous Zeeman Effects 
In actual observations normal Zeeman resolution is the ex 
ception rather than the rule. It is convenient to consider the 
change in a term due to an applied magnetic field. We may 
regard the change AH in the energy of a term as being equivalent 
to a certain change in frequency represented by /S.v where 
hj\v =AH 
= he H_ 
m 0 4 tic 
a * H 
m 0 4 nc 
— m/\v n !5 : 8 
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