Matter wave

Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.

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Quantum mechanics
${\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }$ Schrödinger equation
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The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie (/dəˈbrɔɪ/) in 1924, and so matter waves are also known as de Broglie waves.

The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h:

Wave-like behavior of matter was first experimentally demonstrated by George Paget Thomson and Alexander Reid's transmission diffraction experiment, and independently in the Davisson–Germer experiment, both using electrons; and it has also been confirmed for other elementary particles, neutral atoms and molecules.