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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.
In his paper, "Quantum mechanics, matter waves and moving clocks", Müller has suggested that "The description of matter waves as matter-wave clocks ... has recently been applied to tests of general relativity, matter-wave experiments, the foundations of quantum mechanics, quantum space-time decoherence, the matter wave clock/mass standard, and led to a discussion on the role of the proper ...
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 ...
The wave function of an initially very localized free particle. In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex ...
Wave functions that fulfill this constraint are called normalizable. The Schrödinger equation, describing states of quantum particles, has solutions that describe a system and determine precisely how the state changes with time. Suppose a wave function ψ(x, t) gives a description of the particle (position x at a given time t).
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
The end of the first era of quantum mechanics was triggered by de Broglie's publication of his hypothesis of matter waves, [1]: 268 leading to Schrödinger's discovery of wave mechanics for matter. Accurate predictions of the absorption spectrum of hydrogen ensured wide acceptance of the new quantum theory.
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.