Editing Quantum mechanics (section)

{{Short description|Description of physical properties at the atomic and subatomic scale}}
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[[File:Hydrogen Density Plots.png|thumb|upright=1.35|[[Wave function]]s of the [[electron]] in a hydrogen atom at different energy levels. Quantum mechanics cannot predict the exact location of a particle in space, only the probability of finding it at different locations.<ref name=Born1926>{{cite journal |author-link1=Max Born |last=Born |first=M. |title=Zur Quantenmechanik der Stoßvorgänge |trans-title=On the Quantum Mechanics of Collision Processes |journal=Zeitschrift für Physik |volume=37 |pages=863–867 |year=1926 |doi=10.1007/BF01397477 |bibcode=1926ZPhy...37..863B |issue=12 |s2cid=119896026 |issn=1434-6001 |language=de}}</ref> The brighter areas represent a higher probability of finding the electron.]]
{{Quantum mechanics}}
'''Quantum mechanics''' is the fundamental physical [[Scientific theory|theory]] that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of [[atom]]s.<ref name="Feynman">{{cite book |last1=Feynman |first1=Richard |last2=Leighton |first2=Robert |last3=Sands |first3=Matthew |title=The Feynman Lectures on Physics |volume=3 |publisher=California Institute of Technology |date=1964 |url=https://feynmanlectures.caltech.edu/III_01.html  |access-date=19 December 2020}} Reprinted, Addison-Wesley, 1989, {{isbn|978-0-201-50064-6}}</ref>{{rp|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. Classical physics can describe many aspects of nature at an ordinary ([[macroscopic]] and [[Microscopic scale|(optical) microscopic]]) scale, but is not sufficient for describing them at very small [[submicroscopic]] (atomic and [[subatomic]]) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales.<ref>{{cite journal |last1=Jaeger |first1=Gregg |title=What in the (quantum) world is macroscopic? |journal=American Journal of Physics |date=September 2014 |volume=82 |issue=9 |pages=896–905 |doi=10.1119/1.4878358 |bibcode=2014AmJPh..82..896J}}</ref>

Quantum systems have [[Bound state|bound]] states that are [[Quantization (physics)|quantized]] to [[Discrete mathematics|discrete values]] of [[energy]], [[momentum]], [[angular momentum]], and other quantities, in contrast to classical systems where these quantities can be measured continuously. Measurements of quantum systems show characteristics of both [[particle]]s and [[wave]]s ([[wave–particle duality]]), and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the [[uncertainty principle]]).

Quantum mechanics [[History of quantum mechanics|arose gradually]] from theories to explain observations that could not be reconciled with classical physics, such as [[Max Planck]]'s solution in 1900 to the [[black-body radiation]] problem, and the correspondence between energy and frequency in [[Albert Einstein]]'s [[Annus Mirabilis papers#Photoelectric effect|1905 paper]], which explained the [[photoelectric effect]]. These early attempts to understand microscopic phenomena, now known as the "[[old quantum theory]]", led to the full development of quantum mechanics in the mid-1920s by [[Niels Bohr]], [[Erwin Schrödinger]], [[Werner Heisenberg]], [[Max Born]], [[Paul Dirac]] and others. The modern theory is formulated in various [[mathematical formulations of quantum mechanics|specially developed mathematical formalisms]]. In one of them, a mathematical entity called the [[wave function]] provides information, in the form of [[probability amplitude]]s, about what measurements of a particle's energy, momentum, and other physical properties may yield.