189Chapter 20Wave Mechanics
If quantum mechanics hasn’t profoundly shocked you, you haven't
understood it yet. – Niels Bohr
In the early 1920’s while most atomic physicists were concerning
themselves with different aspects of Bohr’s model of the atom, Louis de
Broglie, working essentially in isolation on his doctoral thesis at the
Universite de Paris, broke new ground. Louis de Broglie was concerned
with the question of the wave-particle duality of light. Light had
classically displayed the behaviour of a wave, which the diffraction and
interference phenomena studied by Fresnel and Young had revealed.
Einstein’s description of the photoelectric effect, and the subsequent
discovery of the Compton effect, however, had also revealed the particle
nature of light. De Broglie tinkered with the notion that the photon might
possess an unobservingly small mass. This perhaps led him to speculate
on the possible wave-particle dual nature of elementary particles such as
electrons. De Broglie dropped the notion of a photon with mass. He
proposed, however, that particles like electrons might possess wave
behaviour. He based his conjecture on the fact that the photon was both a
wave and a particle. Why shouldn’t the same be true for an electron?
To determine the frequency and wavelength of the electron wave,
de Broglie borrowed directly from Planck and Einstein’s concept of the
photon. According to their quantum hypothesis, the energy of a photon
is equal to Planck’s constant, h, times its frequency, f so that E = hf.
De Broglie assumed the identical relation held for the electron and hence,
the frequency, f, of an electron is equal to its energy, E, divided by h.
There still remained the assignment of the electron’s wavelength. The
wavelength of the photon, λ, is related simply to its momentum, p, by
the formula, λ = h/p. This follows from the fact that the momentum of