Matter waves and de Broglie

Light shows its wave side in interference, diffraction and polarisation, and its particle side in the photoelectric and Compton effects, which involve transfers of energy and momentum. Which description fits depends on the experiment.

Seeing uses both. The eye-lens gathers and focuses light as a wave, but the rods and cones of the retina absorb it as photons.

In 1924 Louis Victor de Broglie proposed that if radiation has two sides, so should matter: moving particles should show wave-like properties in suitable conditions. His argument was that nature is symmetrical between its two basic entities, matter and energy.

De Broglie relation: a particle of momentum p has wavelength λ = h/p = h/mv (Eq. 11.5), where m is its mass and v its speed. This λ is the de Broglie wavelength, and the wave is a matter wave.

The relation joins the two sides in one line: λ on the left belongs to a wave, p on the right to a particle, and Planck's constant links them.

For a material particle the relation is a hypothesis that only experiment can test. It does hold for a photon: with p = hν/c (Eq. 11.6), h/p = c/ν = λ (Eq. 11.7), the ordinary wavelength of the radiation.

The de Broglie wavelength does not depend on the particle's charge or on what it is made of; only its momentum matters.