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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