16 Early atomic physics
Fig. 1.6For the normal Zeeman effect a simple model of an atom (as in Fig. 1.5) explains the frequency of the light emitted
and its polarization (indicated by the arrows for the cases of transverse and longitudinal observation).
thex-axis only they-component is seen, and the radiation is linearly
polarized perpendicular to the magnetic field—see Fig. 1.6. These are
called theσ-components and, in contrast to theπ-component, they are
also seen in longitudinal observation—looking along thez-axis one sees
the electron’s circular motion and hence light that has circular polariza-
tion. Looking in the opposite direction to the magnetic field (from the
positivez-direction, orθ= 0 in polar coordinates) the circular motion(^37) This is left-circularly-polarized light in the anticlockwise direction is associated with the frequencyω 0 +ΩL. 37
(Corney 2000). In addition to showing that atoms contain electrons by measuring the
magnitude of the charge-to-mass ratioe/me, Zeeman also deduced the
sign of the charge by considering the polarization of the emitted light.
If the sign of the charge was not negative, as we assumed from the start,
light atω 0 +ΩLwould have the opposite handedness—from this Zeeman
could deduce the sign of the electron’s charge.
For situations that only involve orbital angular momentum (and no
spin) the predictions of this classical model correspond exactly to those
of quantum mechanics (including the correct polarizations), and the in-
tuition gained from this model gives useful guidance in more complicated
cases. Another reason for studying the classical treatment of the Zee-
man effect is that it furnishes an example of degenerate perturbation
theory in classical mechanics. We shall encounter degenerate perturba-
tion theory in quantum mechanics in several places in this book and an
understanding of the analogous procedure in classical mechanics is very
helpful.