Matter Waves: de Broglie's Hypothesis

Turning the argument around. Sections 11.7-11.8 established that radiation, ordinarily understood as a wave, shows a genuine particle aspect (the photon) in the photoelectric effect, with the particle's momentum related to the wave's own wavelength by $p=h/\lambda$. In 1924, Louis de Broglie proposed a bold symmetry: if a wave can show particle-like behaviour, then a particle of matter -- an electron, for instance -- should, by the same reasoning run in reverse, show wave-like behaviour, with an associated wavelength obtained simply by INVERTING the photon momentum relation. For a particle of mass $m$ moving with speed $v$ (so that its momentum is $p=mv$), de Broglie proposed the wavelength

now called the de Broglie wavelength, and the associated wave a matter wave. De Broglie's hypothesis was, at the time it was proposed, a purely theoretical conjecture, with no direct experimental support -- its confirmation came three years later (Section 11.10).

Why this applies, in principle, to everything. The formula $\lambda=h/mv$ makes no reference at all to WHAT kind of particle is moving -- it applies, in principle, to an electron, a proton, an atom, a cricket ball, or a moving car, with exactly the same logic. What differs enormously between these cases is the resulting NUMERICAL VALUE of $\lambda$, because Planck's constant $h$ is so extraordinarily small ($6.63\times10^{-34}\ \text{J s}$) compared with the momentum $mv$ of anything of everyday, macroscopic mass moving at an everyday speed. …