Page 26 - Photonics Essentials an introduction with experiments

Electrons and Photons

20 Introductory Concepts

2.5 Some History
The proposition of de Broglie (pronounced duh Broy-yuh) was ab-
solutely revolutionary, but not at all obvious at the time. The princi-
pal result of his idea was to open the way for the development of
Schrödinger’s wave equation and the first quantitative description of
the behavior of electrons and atoms. de Broglie had the advantage
that he was a student. He knew a little bit, but not too much. This fea-
ture was key, in my opinion, because it allowed him to see the forest
in spite of the trees. Later in life, when he knew more, he was much
less productive, and because of his celebrity, his views took on an im-
portance unsupported by their content alone.
de Broglie defended his thesis in late November of 1924. The cover
page is shown in Fig. 2.5. The thesis is short, about 100 pages in all.
Almost all of the chapters are concerned with the effect of special rela-
tivity on the properties of various fundamental particles such as the
energy and phase of a propagating light beam.
In Chapter 3 of the thesis, there is an abrupt change of subject, and
de Broglie addresses hypothesis proposed by Bohr to explain the exis-
tence of discrete atomic energy levels. Seven years earlier, Neils Bohr
proposed that the electrons in atoms traveled in stable orbits, thus al-
lowing atoms to have long lifetimes, an experimental truth we all rec-
ognize. The condition originally proposed by Bohr was
h
m 0 R = n (2.28)
2
2
where m is the mass of the electron, the angular frequency of rota-
tion around the atom, and R the radius of its orbit. For a circular or-
bit, = v/R, and Bohr’s condition becomes
h
m 0 vR = n (2.29)
2
This has the simple interpretation that the angular momentum of the
electron (= mvR) is quantized in units of
h
=
2
However, in 1924 there was no idea about why this quantization oc-
curred, or what properties of the electron assured this behavior.
On page 44 of his thesis (Fig. 2.6), de Broglie offered an interpreta-
tion that was consistent with his everyday experience: the Bohr condi-
tion was similar to the behavior of waves of water in a closed circular
tank. Stable states occur when there are standing waves. The condi-

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