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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 electrons can be diffracted just like a beam of light or a water wave.
The phase velocity varies with frequency. The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
Wave-particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave properties according to the experimental circumstances. [1]: 59 It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects ...
Time crystals: A state of matter where an object can have movement even at its lowest energy state. Hidden states of matter: Phases that are unattainable or do not exist in thermal equilibrium, but can be induced e.g. by photoexcitation. Microphase separation: Constituent units forming diverse phases while also keeping united.
The difference between these states and classical states of matter is that classically, materials exhibit different phases which ultimately depends on the change in temperature and/or density or some other macroscopic property of the material whereas quantum phases can change in response to a change in a different type of order parameter (which ...
Such a wave, which later received the name matter wave, or de Broglie wave, in the process of body movement remains in phase with the internal periodic process. Having then examined the motion of an electron in a closed orbit, the scientist showed that the requirement for phase matching directly leads to the quantum Bohr-Sommerfeld condition ...
The Davisson–Germer experiment confirmed the de Broglie hypothesis that matter has wave-like behavior. This, in combination with the Compton effect discovered by Arthur Compton (who won the Nobel Prize for Physics in 1927), [ 9 ] established the wave–particle duality hypothesis which was a fundamental step in quantum theory.
Phase velocity is the rate at which the phase of the wave propagates in space: any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and period T as v p = λ T . {\displaystyle v_{\mathrm {p} }={\frac {\lambda }{T}}.}