Page 53 - Electrical Properties of Materials

The electron

3 That’s how it is, says Pooh.

A.A. Milne Now we are six

3.1 Introduction

We have seen that some experimental results can be explained if we regard the
electron as a particle, whereas the explanation of some other experiments is
possible only if we look upon our electron as a wave. Now which is it? Is it a
particle or is it a wave? It is neither, it is an electron.
An electron is an electron; this seems a somewhat tautological definition.
What does it mean? I want to say by this that we don’t have to regard the elec-
tron as something else, something we are already familiar with. It helps, of
course, to know that the electron sometimes behaves as a particle because we
have some intuitive idea of what particles are supposed to do. It is helpful to
know that the electron may behave as a wave because we know a lot about
waves. But we do not have to look at the electron as something else. It is suf-
ficient to say that an electron is an electron as long as we have some means of
predicting its properties.
How can we predict what an electron will do? Well, how can we predict any
physical phenomenon? We need some mathematical relationship between the
variables. Prediction and mathematics are intimately connected in science—or
are they? Can we make predictions without any mathematics at all? We can.
Seeing, for example, dark heavy clouds gathering in the sky we may say that
‘it is going to rain’ and on a large number of occasions we will be right. But this
is not really a very profound and accurate prediction. We are unable to specify
how dark the clouds should be for a certain amount of rain, and we would find
it hard to guess the temporal variation of the positions of the clouds. So, as you
know very well, meteorology is not yet an exact science.
In physics fairly good predictions are needed because otherwise it is difficult
to get further money for research. In engineering the importance of predictions
can hardly be overestimated. If the designer of a bridge or of a telephone ex-
change makes some wrong predictions, this mistake may bring upon him the
full legal apparatus of the state or the frequent curses of the subscribers. Thus,
for engineers, prediction is not a trifling matter.
Now what about the electron? Can we predict its properties? Yes, we can
because we have an equation which describes the behaviour of the electron
in mathematical terms. It is called Schrödinger’s (Nobel Prize, 1933) equa-
tion. Now I suppose you would like to know where Schrödinger’s equation
came from? It came from nowhere; or more correctly it came straight from
Schrödinger’s head, not unlike Pallas Athene who is reputed to have sprung out