Thought Experiments on Diffraction

Diffraction of photons, electrons, and neutrons has been observed (see the pictures) and used to study crystal structure.

To understand the experimental input in a simplified way, we consider some thought experiments on the diffraction of photons, electrons, and bullets through two slits. For example, photons, which make up all electromagnetic waves, show a diffraction pattern exactly as predicted by the theory of EM waves, but we always detect an integer number of photons with the Plank's relation, $E=h\nu$, between wave frequency and particle energy satisfied.

Electrons, neutrons, and everything else behave in exactly the same way, exhibiting wave-like diffraction yet detection of an integer number of particles and satisfying $\lambda={h\over p}$. This deBroglie wavelength formula relates the wave property $\lambda$ to the particle property $p$.