This duality can be shown by shooting electrons one at a time at two slits, and observing the pattern on a screen placed behind the slits. If the electrons were particles, we should see them arriving one by one on the screen. If they were waves, they should go through the two slits at the same time and the two small waves coming from each slit should juxtapose and make a new wave that could be seen on the screen as fringes (we call them “interference fringes”).
In this video recorded in a Hitachi laboratory, you can see both effects at the same time. The electrons do arrive one by one as particles, but at the end, they form fringes! This is impossible to understand if you do not accept the fact that each electron is a wave that can be measured on the screen. The same experiment showed the same results with individual photons (the particles composing light), or with bigger objects such as fullerenes, large molecules made of sixty carbon atoms.
Physicists characterize this wave with a quantity called the wavefunction, with an amplitude and a phase. De Broglie thought that the energy of an object could be proportionnal to its wave frequency (how many times a second it beats), and that its momentum (mass times speed) would be proportionnal to the inverse of the wavelength (the distance between two peaks).
Quantum theory can predict exactly how this wavefunction will behave in space through time, using the Schrödinger equation. It is only when the wavefunction is measured that it becomes “only” a particle.
In this experiment, electrons sent one after the other are detecetd as particles on the screen. However, after a while, all the electrons form a pattern characteristic of a wave.
