Page 54 - Electrical Properties of Materials

Introduction 37

of Zeus’ head (and in full armour too!). Schrödinger’s equation is a product of
Schrödinger’s imagination; it cannot be derived from any set of physical as-
sumptions. Schrödinger’s equation is, of course, not unique in this respect. You
have met similar cases before.
In the sixth form you learned Newton’s equation. At the time you had just
gained your first glances into the hidden mysteries of physics. You would
not have dared to question your schoolmaster about the origin of Newton’s
equation. You were probably more reverent at the time, more willing to accept
the word of authorities, and besides, Newton’s equation looks so simple that
one’s credulity is not seriously tested. Force equals mass times acceleration;
anyone is prepared to believe that much. And it seems to work in practice.
At the university you are naturally more inquisitive than in your schooldays;
so you may have been a bit more reluctant to accept Maxwell’s equations when
you first met them. It must have been very disturbing to be asked to accept the
equation,
∂B
∇ × E E E =– , (3.1)
∂t
as the truth and nothing but the truth. But then you were shown that this
equation is really identical with the familiar induction law,
∂φ
V =– , (3.2)
∂t
and the latter merely expresses the result of a simple experiment. Similarly
∇ × H = J (3.3)

is only a rewriting of Ampère’s law. So all is well again or rather all would
be well if there was not another term on the right-hand side, the displacement
current ∂D/∂t. Now what is this term? Not many lecturers admit that it came
into existence as a pure artifice. Maxwell felt there should be one more term
there, and that was it. True, Maxwell himself made an attempt to justify the
introduction of displacement current by referring to the a.c. current in a ca-
pacitor, but very probably that was just a concession to the audience he had
to communicate with. He must have been more concerned with refuting the
theory of instantaneous action at a distance, and with deriving a velocity with
which disturbances can travel.
The extra term had no experimental basis, whatsoever. It was a brilliant
hypothesis which enabled Maxwell to predict the existence of electromagnetic
waves. When some years later Hertz managed to find these waves, the hypo-
∗
According to most historians’ defini-
thesis became a law. It was a momentous time in history, though most history tion, an event is important if it affects
books keep silent about the event. ∗ a large number of people to a consid-
I am telling you all this just to show that an equation which comes from erable extent for a long time. If his-
torians were faithful to this definition
nowhere in particular may represent physical reality. Of course, Schrödinger they should write a lot about Maxwell
had good reasons for setting up his equation. He had immediate success in and Hertz because by predicting and
several directions. Whilst Maxwell’s displacement current term explained no proving the existence of electromagnetic
waves, Maxwell and Hertz had more in-
experimental observation, Schrödinger’s equation could immediately account
fluence on the life of ordinary people
for the atomic spectrum of hydrogen, for the energy levels of the Planck os- nowadays than any nineteenth-century
cillator, for the non-radiation of electronic currents in atoms, and for the shift general, statesman, or philosopher.