Editing Matter wave (section)

{{Short description|Quantum mechanical waves describing matter}}
{{About|wave-like phenomena exhibited by particles of matter|elastic waves propagating through material media|Mechanical wave}}
{{Use dmy dates|date=June 2023}}
{{quantum mechanics}}'''Matter waves''' are a central part of the theory of [[quantum mechanics]], being half of [[wave–particle duality]]. At all scales where measurements have been practical, [[matter]] exhibits [[wave]]-like behavior. For example, a beam of [[electron]]s can be [[diffraction|diffracted]] just like a beam of light or a water wave.

The concept that matter behaves like a wave was proposed by French physicist [[Louis de Broglie]] ({{IPAc-en|d|ə|ˈ|b|r|ɔɪ}}) in 1924, and so matter waves are also known as '''de Broglie waves'''.

The ''de Broglie wavelength'' is the [[wavelength]], {{math|''λ''}}, associated with a particle with [[momentum]] {{math|''p''}} through the [[Planck constant]], {{math|''h''}}:
<math display="block"> \lambda = \frac{h}{p}.</math>

Wave-like behavior of matter has been experimentally demonstrated, first for electrons in 1927 and for other [[elementary particle]]s, neutral [[atom]]s and [[molecule]]s in the years since.

Matter waves have more complex velocity relations than solid objects and they also differ from electromagnetic waves (light). Collective matter waves are used to model phenomena in solid state physics; standing matter waves are used in molecular chemistry. 

Matter wave concepts are widely used in the study of materials where different wavelength and interaction characteristics of electrons, neutrons, and atoms are leveraged for advanced microscopy and diffraction technologies.