matter wave

A matter wave is the wave that quantum mechanics associates with a particle of matter — an electron, an atom, even a large molecule. Its wavelength is set by the particle's momentum through de Broglie's relation, and it is the thing that diffracts and interferes in experiments. When physicists say an electron 'has a wave nature', the matter wave is what they mean.

It is crucial to be honest about what kind of wave this is. A matter wave is not a vibration of any physical stuff, like sound shaking the air; it is the particle's wavefunction, and the square of its size at each point gives the probability of finding the particle there. The wave tells you where the particle is likely to turn up, not that the particle itself is spread thin across the wave like butter.

Matter waves explain why the microscopic world is quantised. Trap a particle in a small region and only certain wavelengths fit neatly inside, like the standing waves on a guitar string; those allowed wavelengths correspond to the discrete energy levels of atoms and other bound systems. The wave nature of matter is therefore not an exotic side note but the very source of the steps and shells that structure all of chemistry.