matterwaves

Matter waves, also known as de Broglie waves, are the wave-like manifestations of matter predicted by quantum mechanics. According to the de Broglie hypothesis, every particle with momentum p carries an associated wavelength λ = h/p, where h is Planck's constant. For non-relativistic speeds, p ≈ mv. In quantum theory, particles are described by a wave function whose amplitude governs probability distributions for position and momentum. The evolution of the wave function is governed by the Schrödinger equation in non-relativistic settings, and by relativistic equations such as the Dirac or Klein-Gordon equations for high speeds.

The concept of matter waves leads to wave-particle duality: a single particle can produce interference and diffraction, as evidenced by experiments with electrons, neutrons, and atoms. Experimental confirmations include electron diffraction observed by Davisson and Germer (1927) and neutron interferometry. Atom interferometry and Bose-Einstein condensates extend these effects to cold atomic ensembles, enabling precision measurements.

In this framework, the wave’s phase velocity is ω/k, and the group velocity corresponds to the particle’s classical velocity. The probability density of finding a particle near a point is given by the modulus squared of the wave function. Matter waves underpin many technologies and research areas, including electron microscopy, scanning tunneling microscopy, and atom interferometry for metrology and tests of fundamental physics. Decoherence and environmental interactions limit observable coherence of matter waves at larger masses and higher temperatures.