De Broglie equation

The relation λ = h/p assigns wavelength λ to a particle with momentum p, where h is Planck’s constant. It expresses the wave nature of matter.

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Planck constant: A fundamental constant that sets the scale of quantum effects. Its value converts a particle’s momentum into its associated wavelength.
Louis de Broglie: A French physicist who proposed that particles have associated wavelengths. He introduced the relation in his 1924 doctoral thesis.
Davisson–Germer experiment: A 1927 experiment that observed electron diffraction from a nickel crystal. Its measured diffraction supported the wavelength predicted for electrons.
Photon momentum: The momentum carried by a photon, equal to its energy divided by the speed of light. For light, the same relation links photon momentum and wavelength.
Momentum: A measure of an object's motion, equal to mass times velocity in classical mechanics. The equation predicts shorter wavelengths for particles with greater momentum.
Thesis of Louis de Broglie: A 1924 doctoral thesis proposing wave properties for material particles. It presented the hypothesis that became the de Broglie equation.
Electron diffraction: The scattering of electrons by matter in a pattern governed by their wave behavior. Diffraction angles reveal the electron wavelength associated with its momentum.
Compton wavelength: A characteristic wavelength associated with a particle’s mass, equal to h divided by its mass times the speed of light. Unlike the de Broglie wavelength, it depends on rest mass rather than motion momentum.
Matter wave: A wave associated with a material particle, described by its quantum state. The equation quantifies the wavelength assigned to moving matter.
Photoelectric effect: The emission of electrons from a material when it absorbs light of sufficient frequency. Einstein’s light-quantum explanation provided a precedent for matter’s wave-particle symmetry.