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{{Short description|Non-mathematical introduction}}
{{for|the book by David J. Griffiths|Introduction to Quantum Mechanics (book){{!}}''Introduction to Quantum Mechanics'' (book)}}
{{Introductory article|Quantum mechanics}}
{{Use dmy dates|date=July 2020}}
{{Quantum mechanics}}

'''Quantum mechanics''' is the study of [[matter]] and its interactions with [[energy]] on the [[orders of magnitude (length)|scale]] of [[atom]]ic and [[elementary particle|subatomic particles]]. By contrast, [[classical physics]] explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the 19th century, scientists discovered phenomena in both the large ([[Macroscopic scale|macro]]) and the small ([[Microscopic scale|micro]]) worlds that classical physics could not explain.<ref>{{cite web|title=Quantum Mechanics|url=https://www.pbs.org/transistor/science/info/quantum.html|publisher=[[National Public Radio]]|access-date=22 June 2016}}</ref> The desire to resolve inconsistencies between observed phenomena and classical theory led to a revolution in physics, a shift in the original [[scientific paradigm]]:<ref>Kuhn, Thomas S. ''The Structure of Scientific Revolutions''. Fourth ed. Chicago; London: The University of Chicago Press, 2012. Print.</ref> the development of [[quantum mechanics]].

Many aspects of quantum mechanics are counterintuitive<ref>{{cite web |url=https://www.socratease.in/chapters/intro/intro-to-quantum-mechanics-1 |title=Introduction to Quantum Mechanics |archive-date=2017-09-15|website = Socratease |archive-url = https://web.archive.org/web/20170915203853/https://www.socratease.in/chapters/intro/intro-to-quantum-mechanics-1 }}</ref> and can seem [[paradox]]ical because they describe behavior quite different from that seen at larger scales. In the words of quantum physicist [[Richard Feynman]], quantum mechanics deals with "nature as She is—absurd".<ref>{{cite book|last=Feynman|first=Richard P.|title=QED: the strange theory of light and matter |year=1988|publisher=Princeton University Press|location=Princeton, NJ|isbn=978-0691024172|pages=[https://archive.org/details/qedstrangetheory00feyn/page/10 10]|edition=1st Princeton pbk., seventh printing with corrections.|url= https://archive.org/details/qedstrangetheory00feyn/page/10}}</ref> Features of quantum mechanics often defy simple explanations in everyday language. One example of this is the [[uncertainty principle]]: precise measurements of position cannot be combined with precise measurements of velocity. Another example is [[Quantum entanglement|entanglement]]: a measurement made on one particle (such as an [[electron]] that is measured to have [[Spin (physics)|spin]] 'up') will correlate with a measurement on a second particle (an electron will be found to have spin 'down') if the two particles have a shared history. This will apply even if it is impossible for the result of the first measurement to have been transmitted to the second particle before the second measurement takes place.

Quantum mechanics helps people understand [[chemistry]], because it explains how atoms interact with each other and form [[molecule]]s. Many remarkable phenomena can be explained using quantum mechanics, like [[superfluidity]]. For example, if liquid [[helium]] cooled to a temperature near [[absolute zero]] is placed in a container, it spontaneously flows up and over the rim of its container; this is an effect which cannot be explained by classical physics.

== History ==
{{main | History of quantum mechanics}}

[[James Clerk Maxwell|James C. Maxwell]]'s [[History of Maxwell's equations|unification of the equations]] governing electricity, magnetism, and light in the late 19th century led to experiments on the interaction of light and matter. Some of these experiments had aspects which could not be explained until quantum mechanics emerged in the early part of the 20th century.<ref name="Whittaker">{{Cite book |last=Whittaker |first=Edmund T. |title=A history of the theories of aether & electricity. 2: The modern theories, 1900 – 1926 |date=1989 |publisher=Dover Publ |isbn=978-0-486-26126-3 |edition=Repr |location=New York}}</ref>

=== Evidence of quanta from the photoelectric effect ===
{{main | Photoelectric effect}}
The seeds of the quantum revolution appear in the discovery by [[J.J. Thomson]] in 1897 that [[cathode rays]] were not continuous but "corpuscles" ([[electrons]]). Electrons had been named just six years earlier as part of the emerging theory of [[atoms]]. In 1900, [[Max Planck]], unconvinced by the [[atomic theory]], discovered that he needed discrete entities like atoms or electrons to explain [[black-body radiation]].<ref name=Baggott>{{Cite book |last=Baggott |first=J. E. |title=The quantum story: a history in 40 moments |date=2013 |publisher=Oxford Univ. Press |isbn=978-0-19-965597-7 |edition=Impression: 3 |location=Oxford}}</ref>

[[File:Black body.svg|thumb|upright=1.4|[[Black-body radiation]] intensity vs color and temperature. The rainbow bar represents visible light; 5000 [[Kelvin|K]] objects are "white hot" by mixing differing colors of visible light. To the right is the invisible infrared. Classical theory (black curve for 5000 K) fails to predict the colors; the other curves are correctly predicted by quantum theories.]]
Very hot – red hot or white hot – objects look similar when heated to the same temperature. This look results from a common curve of light intensity at different frequencies (colors), which is called black-body radiation. White hot objects have intensity across many colors in the visible range. The lowest frequencies above visible colors are [[infrared light]], which also give off heat. Continuous wave theories of light and matter cannot explain the black-body radiation curve. Planck spread the heat energy among individual "oscillators" of an undefined character but with discrete energy capacity; this model explained black-body radiation.

At the time, electrons, atoms, and discrete oscillators were all exotic ideas to explain exotic phenomena. But in 1905 [[Albert Einstein]] proposed that light was also corpuscular, consisting of "energy quanta", in contradiction to the established science of light as a continuous wave, stretching back a hundred years to [[Thomas Young (scientist)|Thomas Young]]'s work on [[diffraction]].

Einstein's revolutionary proposal started by reanalyzing Planck's black-body theory, arriving at the same conclusions by using the new "energy quanta". Einstein then showed how energy quanta connected to Thomson's electron. In 1902, [[Philipp Lenard]] directed light from an arc lamp onto freshly cleaned metal plates housed in an evacuated glass tube. He measured the electric current coming off the metal plate, at higher and lower intensities of light and for different metals. Lenard showed that amount of current – the number of electrons – depended on the intensity of the light, but that the velocity of these electrons did not depend on intensity. This is the [[photoelectric effect]]. The continuous wave theories of the time predicted that more light intensity would accelerate the same amount of current to higher velocity, contrary to this experiment. Einstein's energy quanta explained the volume increase: one electron is ejected for each quantum: more quanta mean more electrons.<ref name=Baggott/>{{rp|23}}

Einstein then predicted that the electron velocity would increase in direct proportion to the light frequency above a fixed value that depended upon the metal. Here the idea is that energy in energy-quanta depends upon the light frequency; the energy transferred to the electron comes in proportion to the light frequency. The type of metal gives a [[work function|barrier]], the fixed value, that the electrons must climb over to exit their atoms, to be emitted from the metal surface and be measured.

Ten years elapsed before Millikan's definitive experiment<ref>{{Cite journal |last=Millikan |first=R. A. |date=1916-03-01 |title=A Direct Photoelectric Determination of Planck's " h " |url=https://link.aps.org/doi/10.1103/PhysRev.7.355 |journal=Physical Review |language=en |volume=7 |issue=3 |pages=355–388 |doi=10.1103/PhysRev.7.355 |bibcode=1916PhRv....7..355M |issn=0031-899X|url-access=subscription }}</ref> verified Einstein's prediction. During that time many scientists rejected the revolutionary idea of quanta.<ref name=pais>{{Cite journal |last=Pais |first=A. |date=1979-10-01 |title=Einstein and the quantum theory |url=https://link.aps.org/doi/10.1103/RevModPhys.51.863 |journal=Reviews of Modern Physics |language=en |volume=51 |issue=4 |pages=863–914 |doi=10.1103/RevModPhys.51.863 |bibcode=1979RvMP...51..863P |issn=0034-6861|url-access=subscription }}</ref> But Planck's and Einstein's concept was in the air and soon began to affect other physics and quantum theories.

=== Quantization of bound electrons in atoms ===
{{main | Atomic theory | Bohr atom | Bohr-Sommerfeld model}}{{Further|Spectral lines}}
Experiments with light and matter in the late 1800s uncovered a reproducible but puzzling regularity. When light was shown through purified gases, certain frequencies (colors) did not pass. These dark absorption 'lines' followed a distinctive pattern: the gaps between the lines decreased steadily. By 1889, the [[Rydberg formula]] predicted the lines for hydrogen gas using only a constant number and the integers to index the lines.<ref name=Whittaker/>{{rp|v1:376}} The origin of this regularity was unknown. Solving this mystery would eventually become the first major step toward quantum mechanics.

Throughout the 19th century evidence grew for the [[atomic theory|atomic]] nature of matter. With Thomson's discovery of the electron in 1897, scientist began the search for a model of the interior of the atom. Thomson proposed [[Plum pudding model|negative electrons swimming in a pool of positive charge]]. Between 1908 and 1911, [[Rutherford model|Rutherford]] showed that the positive part was only 1/3000th of the diameter of the atom.<ref name=Baggott/>{{rp|26}}

Models of "planetary" electrons orbiting a nuclear "Sun" were proposed, but cannot explain why the electron does not simply fall into the positive charge. In 1913 [[Niels Bohr]] and [[Ernest Rutherford]] connected the new atom models to the mystery of the Rydberg formula: the orbital radius of the electrons were constrained and the resulting energy differences matched the energy differences in the absorption lines. This meant that absorption and emission of light from atoms was energy quantized: only specific energies that matched the difference in orbital energy would be emitted or absorbed.<ref name=Baggott/>{{rp|31}}

Trading one mystery – the regular pattern of the Rydberg formula – for another mystery – constraints on electron orbits – might not seem like a big advance, but the new atom model summarized many other experimental findings.  The quantization of the photoelectric effect and now the quantization of the electron orbits set the stage for the final revolution.

Throughout the first and the modern era of quantum mechanics the concept that classical mechanics must be valid macroscopically constrained possible quantum models. This concept was formalized by Bohr in 1923 as the [[correspondence principle]]. It requires quantum theory to converge to classical limits.<ref name=messiah>{{Cite book|last=Messiah|first=Albert|title=Quantum Mechanics|date=1966|publisher=North Holland, John Wiley & Sons|isbn=0486409244|language=en}}</ref>{{rp | 29}}
A related concept is [[Ehrenfest's theorem]], which shows that the average values obtained from quantum mechanics (e.g. position and momentum) obey classical laws.<ref>{{cite web|title=Remarks concerning the status & some ramifications of EHRENFEST'S THEOREM|url=https://www.reed.edu/physics/faculty/wheeler/documents/Quantum%20Mechanics/Miscellaneous%20Essays/Ehrenfest's%20Theorem.pdf |archive-url=https://web.archive.org/web/20210710112443/https://www.reed.edu/physics/faculty/wheeler/documents/Quantum%20Mechanics/Miscellaneous%20Essays/Ehrenfest's%20Theorem.pdf |archive-date=2021-07-10 }}</ref>

=== Quantization of spin ===
{{Main|Stern–Gerlach experiment}}[[File:Stern-Gerlach experiment.svg|thumb|upright=1.35|'''Stern–Gerlach experiment''': Silver atoms travelling through an inhomogeneous magnetic field, and being deflected up or down depending on their spin; (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic field, (4) classically expected result, (5) observed result]]
In 1922 [[Otto Stern]] and [[Walther Gerlach]] [[Stern–Gerlach experiment|demonstrated]] that the magnetic properties of silver atoms defy classical explanation, the work contributing to Stern’s 1943 [[Nobel Prize in Physics]]. They fired a beam of silver atoms through a magnetic field. According to classical physics, the atoms should have emerged in a spray, with a continuous range of directions. Instead, the beam separated into two, and only two, diverging streams of atoms.<ref name="cigar">{{Cite journal |last1=Friedrich |first1=Bretislav |last2=Herschbach |first2=Dudley |date=December 2003 |title=Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics |journal=Physics Today |language=en |volume=56 |issue=12 |pages=53–59 |bibcode=2003PhT....56l..53F |doi=10.1063/1.1650229 |issn=0031-9228 |doi-access=free}}</ref> Unlike the other quantum effects known at the time, this striking result involves the state of a single atom.<ref name="Whittaker" />{{rp|v2:130}} In 1927, T.E. Phipps and J.B. Taylor obtained a similar, but less pronounced effect using [[hydrogen]] atoms in their [[ground state]], thereby eliminating any doubts that may have been caused by the use of [[silver]] atoms.<ref>{{cite journal |last1=Phipps |first1=T.E. |last2=Taylor |first2=J.B. |year=1927 |title=The Magnetic Moment of the Hydrogen Atom |journal=[[Physical Review]] |volume=29 |issue=2 |pages=309–320 |bibcode=1927PhRv...29..309P |doi=10.1103/PhysRev.29.309}}</ref>

In 1924, Wolfgang Pauli called it "two-valuedness not describable classically" and associated it with electrons in the outermost shell.<ref>{{cite web |author=Wolfgang Pauli |date=13 December 1946 |title=Exclusion Principle and Quantum Mechanics |url=https://www.nobelprize.org/prizes/physics/1945/pauli/lecture/ |work=Nobel Lecture |publisher=[[Nobel Prize]]}}</ref> The experiments lead to formulation of its theory described to arise from spin of the electron in 1925, by [[Samuel Goudsmit]] and [[George Uhlenbeck]], under the advice of [[Paul Ehrenfest]].<ref>{{Cite journal |last=Ehrenfest |first=P. |date=November 1925 |title=Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons |journal=Die Naturwissenschaften |language=de |volume=13 |issue=47 |pages=953–954 |doi=10.1007/bf01558878 |issn=0028-1042 |s2cid=32211960}}</ref>

=== Quantization of matter ===
{{main | Matter wave | Schrödinger equation }}In 1924 [[Louis de Broglie]] proposed<ref name=Broglie>{{cite web |last1=de Broglie |first1=Louis Victor |title=On the Theory of Quanta |url=https://fondationlouisdebroglie.org/LDB-oeuvres/De_Broglie_Kracklauer.pdf |access-date=25 February 2023 |website=Foundation of Louis de Broglie |edition=English translation by A.F. Kracklauer, 2004.}}</ref> that electrons in an atom are constrained not in "orbits" but as standing waves. In detail his solution did not work, but his hypothesis – that the electron "corpuscle" moves in the atom as a wave – spurred [[Erwin Schrödinger]] to develop a [[Schrödinger equation|wave equation]] for electrons; when applied to hydrogen the Rydberg formula was accurately reproduced.<ref name=Baggott/>{{rp|65}}
[[File:A565 G P Thomson Electron Diffraction.jpg|thumb|Example original electron diffraction photograph from the laboratory of G. P. Thomson, recorded 1925–1927]]
[[Max Born]]'s 1924 paper ''"Zur Quantenmechanik"'' was the first use of the words "quantum mechanics" in print.<ref>Max Born, ''My Life: Recollections of a Nobel Laureate'', Taylor & Francis, London, 1978. ("We became more and more convinced that a radical change of the foundations of physics was necessary, i.e., a new kind of  mechanics for which we used the term quantum mechanics.  This word appears for the first time in physical literature in a paper of mine...")</ref><ref>{{Cite journal |last1=Fedak |first1=William A. |last2=Prentis |first2=Jeffrey J. |date=2009-02-01 |title=The 1925 Born and Jordan paper "On quantum mechanics" |url=https://people.isy.liu.se/icg/jalar/kurser/QF/references/onBornJordan1925.pdf |journal=American Journal of Physics |language=en |volume=77 |issue=2 |pages=128–139 |doi=10.1119/1.3009634 |bibcode=2009AmJPh..77..128F |issn=0002-9505}}</ref> His later work included developing quantum collision models; in a footnote to a 1926 paper he proposed the [[Born rule]] connecting theoretical models to experiment.<ref name=Zeitschrift>
{{cite journal
 |last=Born
 |first=Max
 |author-link=Max Born
 |title=Zur Quantenmechanik der Stoßvorgänge
 |journal=Zeitschrift für Physik
 |volume=37
 |issue=12
 |trans-title=On the quantum mechanics of collisions
 |date=1926
 |bibcode = 1926ZPhy...37..863B
 |doi=10.1007/BF01397477
 |pages=863–867
}}
Reprinted as {{cite book 
 |last=Born
 |first=Max
 |author-link=Max Born
 |title=Quantum Theory and Measurement
 |editor1-last=Wheeler 
 |editor1-first=J. A.
 |editor1-link=John Archibald Wheeler
 |editor2-last=Zurek
 |editor2-first=W. H.
 |editor2-link=Wojciech H. Zurek
 |publisher=Princeton University Press
 |publication-date=1983
 |isbn=978-0-691-08316-2
 |chapter=On the quantum mechanics of collisions
 |pages=52–55
}}
</ref>

In 1927 at Bell Labs, [[Clinton Davisson]] and [[Lester Germer]] [[Davisson–Germer experiment|fired]] slow-moving [[electron]]s at a [[crystal]]line [[nickel]] target which showed a diffraction pattern<ref name="DG12">{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=Diffraction of Electrons by a Crystal of Nickel |journal=Physical Review |volume=30 |issue=6 |pages=705–740 |bibcode=1927PhRv...30..705D |doi=10.1103/physrev.30.705 |issn=0031-899X |doi-access=free}}</ref><ref name="DG22">{{Cite journal |last1=Davisson |first1=C. J. |last2=Germer |first2=L. H. |date=1928 |title=Reflection of Electrons by a Crystal of Nickel |journal=Proceedings of the National Academy of Sciences |language=en |volume=14 |issue=4 |pages=317–322 |bibcode=1928PNAS...14..317D |doi=10.1073/pnas.14.4.317 |issn=0027-8424 |pmc=1085484 |pmid=16587341 |doi-access=free}}</ref><ref name="DG02">{{Cite journal |last1=Davisson |first1=C. |last2=Germer |first2=L. H. |date=1927 |title=The Scattering of Electrons by a Single Crystal of Nickel |url=http://dx.doi.org/10.1038/119558a0 |journal=Nature |volume=119 |issue=2998 |pages=558–560 |doi=10.1038/119558a0 |bibcode=1927Natur.119..558D |issn=0028-0836|url-access=subscription }}</ref><ref name=":02">{{Cite journal |last1=Davisson |first1=C. J. |last2=Germer |first2=L. H. |date=1928 |title=Reflection and Refraction of Electrons by a Crystal of Nickel |journal=Proceedings of the National Academy of Sciences |language=en |volume=14 |issue=8 |pages=619–627 |bibcode=1928PNAS...14..619D |doi=10.1073/pnas.14.8.619 |issn=0027-8424 |pmc=1085652 |pmid=16587378 |doi-access=free}}</ref> indicating wave nature of electron whose theory was fully explained by [[Hans Bethe]].<ref name="Bethe">{{Cite journal |last=Bethe |first=H. |date=1928 |title=Theorie der Beugung von Elektronen an Kristallen |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19283921704 |journal=Annalen der Physik |language=de |volume=392 |issue=17 |pages=55–129 |bibcode=1928AnP...392...55B |doi=10.1002/andp.19283921704|url-access=subscription }}</ref> A similar experiment by [[George Paget Thomson]] and Alexander Reid, firing electrons at thin celluloid foils and later metal films, observing rings, independently discovered [[matter wave]] nature of electrons.<ref>{{Cite journal |last1=Thomson |first1=G. P. |last2=Reid |first2=A. |date=1927 |title=Diffraction of Cathode Rays by a Thin Film |journal=Nature |language=en |volume=119 |issue=3007 |pages=890 |bibcode=1927Natur.119Q.890T |doi=10.1038/119890a0 |issn=0028-0836 |s2cid=4122313 |doi-access=free}}</ref>

=== Further developments ===
In 1928 [[Paul Dirac]] published his [[Dirac equation|relativistic wave equation]] simultaneously incorporating [[Theory of relativity|relativity]], predicting [[anti-matter]], and providing a complete theory for the Stern–Gerlach result.<ref name=Baggott/>{{rp|131}} These successes launched a new fundamental understanding of our world at small scale: '''''[[quantum mechanics]].'''''

Planck and Einstein started the revolution with quanta that broke down the continuous models of matter and light. Twenty years later "corpuscles" like electrons came to be modeled as continuous waves. This result came to be called wave-particle duality, one iconic idea along with the uncertainty principle that sets quantum mechanics apart from older models of physics.

=== Quantum radiation, quantum fields ===
{{main | History of quantum field theory}}
In 1923 [[Compton scattering|Compton]] demonstrated that the Planck-Einstein energy quanta from light also had momentum; three years later the "energy quanta" got a new name "[[photon]]"<ref name="photon-named">.{{Cite web|url=https://www.aps.org/publications/apsnews/201212/physicshistory.cfm|title=December 18, 1926: Gilbert Lewis coins "photon" in letter to Nature| website=www.aps.org|language=en|access-date=2019-03-09}}</ref> Despite its role in almost all stages of the quantum revolution, no explicit model for light quanta existed until 1927 when [[Paul Dirac]] began work on a quantum theory of radiation<ref>{{Cite journal |date=1927-03-01 |title=The quantum theory of the emission and absorption of radiation |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |language=en |volume=114 |issue=767 |pages=243–265 |doi=10.1098/rspa.1927.0039 |bibcode=1927RSPSA.114..243D |issn=0950-1207 |last1=Dirac |first1=P. A. M. |doi-access=free }}</ref> that became [[quantum electrodynamics]]. Over the following decades this work evolved into [[quantum field theory]], the basis for modern [[quantum optics]] and [[particle physics]].

== Wave–particle duality ==
{{Main|Wave–particle duality | Double-slit experiment}}
The concept of wave–particle duality says that neither the classical concept of "particle" nor of "wave" can fully describe the behavior of quantum-scale objects, either photons or matter.  Wave–particle duality is an example of the [[complementarity (physics)|principle of complementarity]] in quantum physics.<ref name="Zettili">
{{cite book
 | last1  = Zettili
 | first1 = Nouredine
 | title  = Quantum Mechanics: Concepts and Applications
 | publisher = John Wiley and Sons
 | date   = 2009
 | pages  = 26–27
 | url    = https://books.google.com/books?id=6jXlpJCSz98C&q=%22complementarity+principle%22+%22wave-particle+duality%22&pg=PA26
 | isbn   = 978-0470026786
}}</ref><ref name="Selleri">
{{cite book
 | last1  = Selleri
 | first1 = Franco
 | title  = Wave-Particle Duality
 | publisher = Springer Science and Business Media
 | date   = 2012
 | pages  = 41
 | url    = https://books.google.com/books?id=r8bkBwAAQBAJ&q=%22complementarity+principle%22+%22wave-particle+duality%22&pg=PA41
 | isbn   = 978-1461533320
}}</ref><ref name="Podgorsak">
{{cite book
 | last1  = Podgorsak
 | first1 = Ervin B.
 | title  = Compendium to Radiation Physics for Medical Physicists
 | publisher = Springer Science and Business Media
 | date   = 2013
 | pages  = 88
 | url    = https://books.google.com/books?id=7zfBBAAAQBAJ&q=%22complementarity+principle%22+%22wave-particle+duality%22&pg=PA88
 | isbn   = 978-3642201868
}}</ref><ref name="Halliday&Resnick">{{cite book
 |last1     = Halliday
 |first1    = David
 |last2     = Resnick
 |first2    = Robert
 |title     = Fundamentals of Physics, 10th Ed.
 |publisher = John Wiley and Sons
 |date      = 2013
 |pages     = 1272
 |url       = https://books.google.com/books?id=nQZyAgAAQBAJ&q=%22complementarity+principle%22+%22wave-particle+duality%22&pg=SL9-PA21
 |isbn      = 978-1118230619
}}{{Dead link|date=November 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref name="Myers">
{{cite book
 | last1  = Myers
 | first1 = Rusty L.
 | title  = The Basics of Physics
 | publisher = Greenwood Publishing Group
 | date   = 2006
 | pages  = [https://archive.org/details/basicsofphysics0000myer/page/172 172]
 | url    = https://archive.org/details/basicsofphysics0000myer
 | url-access = registration
 | quote  = complementarity principle wave-particle duality.
 | isbn   = 0313328579
}}</ref> An elegant example of wave-particle duality is the double-slit experiment. 
[[File:Single slit and double slit2.jpg|left|upright=1.5|thumb|The diffraction pattern produced when light is shone through one slit (top) and the interference pattern produced by two slits (bottom). Both patterns show oscillations due to the wave nature of light. The double slit pattern is more dramatic.]]
[[File:Wave-particle duality.ogv|thumb|right|The double-slit experiment for a classical particle, a wave, and a quantum particle demonstrating wave-particle duality]]
In the double-slit experiment, as originally performed by [[Thomas Young (scientist)|Thomas Young]] in 1803,<ref name="ShamosGreatExperiments">{{cite book |last1=Shamos |first1=Morris H |title=Great Experiments in Physics: Firsthand Accounts from Galileo to Einstein |date=1 January 1987 |publisher=Courier Corporation |page=108 }}</ref> and then [[Augustin Fresnel]] a decade later,<ref name="ShamosGreatExperiments"/> a beam of light is directed through two narrow, closely spaced slits, producing an [[interference (wave propagation)|interference pattern]] of light and dark bands on a screen. The same behavior can be demonstrated in water waves: the double-slit experiment was seen as a demonstration of the wave nature of light.

Variations of the double-slit experiment have been performed using electrons, atoms, and even large molecules,<ref>{{cite journal|last1=Merali|first1=Zeeya|title=Quantum physics: What is really real?|journal=Nature|date=21 May 2015|volume=521 |issue=7552 |pages=278–80|doi=10.1038/521278a|pmid=25993941 |bibcode=2015Natur.521..278M|s2cid=4452144 |doi-access=free}}</ref><ref>{{cite journal|last1=Eibenberger|first1=Sandra|title=Matter–wave interference of particles selected from a molecular library with masses exceeding 10 000 amu|journal=Physical Chemistry Chemical Physics|date=2013|volume=15|issue=35|pages=14696–700|doi=10.1039/C3CP51500A|pmid=23900710|quote=[I]n a three-grating interferometer... We observe high-contrast quantum fringe patterns of molecules... having 810 atoms in a single particle.|arxiv=1310.8343|bibcode=2013PCCP...1514696E|s2cid=3944699}}</ref> and the same type of interference pattern is seen. Thus it has been demonstrated that all [[matter]] possesses wave characteristics.

If the source intensity is turned down, the same interference pattern will slowly build up, one "count" or particle (e.g. photon or electron) at a time. The quantum system acts as a wave when passing through the double slits, but as a particle when it is detected. This is a typical feature of quantum complementarity: a quantum system acts as a wave in an experiment to measure its wave-like properties, and like a particle in an experiment to measure its particle-like properties. The point on the detector screen where any individual particle shows up is the result of a random process. However, the distribution pattern of many individual particles mimics the diffraction pattern produced by waves.

== Uncertainty principle ==
{{Main|Uncertainty principle}}
[[File:Heisenberg 10.jpg|upright|thumb|right|[[Werner Heisenberg]] at the age of 26. Heisenberg won the [[Nobel Prize in Physics]] in 1932 for the work he did in the late 1920s.<ref>{{cite web|url=https://www.nobelprize.org/prizes/physics/1932/summary/|title=The Nobel Prize in Physics 1932|website=NobelPrize.org}}</ref>]]
Suppose it is desired to measure the position and speed of an object—for example, a car going through a radar speed trap. It can be assumed that the car has a definite position and speed at a particular moment in time. How accurately these values can be measured depends on the quality of the measuring equipment. If the precision of the measuring equipment is improved, it provides a result closer to the true value. It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired.

In 1927, Heisenberg proved that this last assumption is not correct.<ref>Heisenberg first published his work on the uncertainty principle in the leading German physics journal ''Zeitschrift für Physik'': {{Cite journal|first1=W.|last1=Heisenberg|title=Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik|journal=Z. Phys.|volume=43|year=1927|pages=172–98|doi=10.1007/BF01397280|issue=3–4|bibcode = 1927ZPhy...43..172H |s2cid=122763326}}</ref> Quantum mechanics shows that certain pairs of physical properties, for example, position and speed, cannot be simultaneously measured, nor defined in operational terms, to arbitrary precision: the more precisely one property is measured, or defined in operational terms, the less precisely can the other be thus treated. This statement is known as the [[uncertainty principle]]. The uncertainty principle is not only a statement about the accuracy of our measuring equipment but, more deeply, is about the conceptual nature of the measured quantities—the assumption that the car had simultaneously defined position and speed does not work in quantum mechanics. On a scale of cars and people, these uncertainties are negligible, but when dealing with atoms and electrons they become critical.<ref>{{cite web|url=https://www.nobelprize.org/prizes/physics/1932/ceremony-speech/|title=The Nobel Prize in Physics 1932|website=NobelPrize.org}}</ref>

Heisenberg gave, as an illustration, the measurement of the position and [[momentum]] of an electron using a photon of light. In measuring the electron's position, the higher the frequency of the photon, the more accurate is the measurement of the position of the impact of the photon with the electron, but the greater is the disturbance of the electron. This is because from the impact with the photon, the electron absorbs a random amount of energy, rendering the measurement obtained of its momentum increasingly uncertain, for one is necessarily measuring its post-impact disturbed momentum from the collision products and not its original momentum (momentum which should be simultaneously measured with position). With a photon of lower frequency, the disturbance (and hence uncertainty) in the momentum is less, but so is the accuracy of the measurement of the position of the impact.<ref name="EB-uncertainty">[https://www.britannica.com/EBchecked/topic/614029/uncertainty-principle "Uncertainty principle", ''Encyclopædia Britannica'']</ref>

At the heart of the uncertainty principle is a fact that for any mathematical analysis in the position and velocity domains, achieving a sharper (more precise) curve in the position domain can only be done at the expense of a more gradual (less precise) curve in the speed domain, and vice versa. More sharpness in the position domain requires contributions from more frequencies in the speed domain to create the narrower curve, and vice versa. It is a fundamental tradeoff inherent in any such related or [[Complementarity (physics)|complementary]] measurements, but is only really noticeable at the smallest (Planck) scale, near the size of [[elementary particles]].

The uncertainty principle shows mathematically that the product of the uncertainty in the position and [[momentum]] of a particle (momentum is velocity multiplied by mass) could never be less than a certain value, and that this value is related to the [[Planck constant]].

== Wave function collapse ==
{{Main|Wave function collapse}}

''Wave function collapse'' means that a measurement has forced or converted a quantum (probabilistic or potential) state into a definite measured value. This phenomenon is only seen in quantum mechanics rather than classical mechanics.

For example, before a photon actually "shows up" on a detection screen it can be described only with a set of probabilities for where it might show up. When it does appear, for instance in the [[Charge-coupled device|CCD]] of an electronic camera, the time and space where it interacted with the device are known within very tight limits. However, the photon has disappeared in the process of being captured (measured), and its quantum [[wave function]] has disappeared with it. In its place, some macroscopic physical change in the detection screen has appeared, e.g., an exposed spot in a sheet of photographic film, or a change in electric potential in some cell of a CCD.

== Eigenstates and eigenvalues ==
{{Further|Introduction to eigenstates}}

Because of the uncertainty principle, statements about both the position and momentum of particles can assign only a [[probability]] that the position or momentum has some numerical value. Therefore, it is necessary to formulate clearly the difference between the state of something indeterminate, such as an electron in a probability cloud, and the state of something having a definite value. When an object can definitely be "pinned-down" in some respect, it is said to possess an [[eigenstate]].

In the Stern–Gerlach experiment discussed [[#Spin|above]], the quantum model predicts two possible values of spin for the atom compared to the magnetic axis. These two eigenstates are named arbitrarily 'up' and 'down'. The quantum model predicts these states will be measured with equal probability, but no intermediate values will be seen. This is what the Stern–Gerlach experiment shows.

The eigenstates of spin about the vertical axis are not simultaneously eigenstates of spin about the horizontal axis, so this atom has an equal probability of being found to have either value of spin about the horizontal axis. As described in the section [[#Spin|above]], measuring the spin about the horizontal axis can allow an atom that was spun up to spin down: measuring its spin about the horizontal axis collapses its wave function into one of the eigenstates of this measurement, which means it is no longer in an eigenstate of spin about the vertical axis, so can take either value.
<!-- unknown -> Sz measurement -> Sz+, 1/sqrt(2) (Sx+ + Sx-) -> Sx measurement -> Sx+, 1/sqrt(2) (Sz+ + Sz-) -> Sz measurement -> Sz-. Therefore, Sx and Sz are non commuting operators. -->

== The Pauli exclusion principle ==
[[File:Wolfgang Pauli young.jpg|right|thumb|upright|[[Wolfgang Pauli]]]]
{{main|Pauli exclusion principle}}
In 1924, [[Wolfgang Pauli]] proposed a new quantum degree of freedom (or [[quantum number]]), with two possible values, to resolve inconsistencies between observed molecular spectra and the predictions of quantum mechanics. In particular, the [[hydrogen spectrum|spectrum of atomic hydrogen]] had a [[Doublet (physics)|doublet]], or pair of lines differing by a small amount, where only one line was expected. Pauli formulated his ''exclusion principle'', stating, "There cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers."<ref name="Pauling">{{cite book|last1=Pauling|first1=Linus|title=The Nature of the Chemical Bond|date=1960|publisher=Cornell University Press|location=Itahca, NY|isbn=0801403332|page=[https://archive.org/details/natureofchemical0000paul_3ed/page/47 47]|edition=3rd|url=https://archive.org/details/natureofchemical0000paul_3ed|url-access=registration|access-date=1 March 2016}}</ref>

A year later, [[George Eugene Uhlenbeck|Uhlenbeck]] and [[Samuel Goudsmit|Goudsmit]] identified Pauli's new degree of freedom with the property called [[Spin (physics)|spin]] whose effects were observed in the [[Stern–Gerlach experiment]].

== Dirac wave equation ==
{{Main|Dirac equation}}
[[File:Paul Dirac, 1933, head and shoulders portrait, bw.jpg|upright|thumb|right|Paul Dirac (1902–1984)]]
In 1928, Paul Dirac extended the [[Pauli equation]], which described spinning electrons, to account for [[special relativity]]. The result was a theory that dealt properly with events, such as the speed at which an electron orbits the nucleus, occurring at a substantial fraction of the [[speed of light]]. By using the simplest [[electromagnetic interaction]], Dirac was able to predict the value of the magnetic moment associated with the electron's spin and found the experimentally observed value, which was too large to be that of a spinning charged sphere governed by [[classical physics]]. He was able to solve for the [[hydrogen spectrum|spectral lines of the hydrogen atom]] and to reproduce from physical first principles [[Arnold Sommerfeld|Sommerfeld]]'s successful formula for the [[fine structure]] of the hydrogen spectrum.

Dirac's equations sometimes yielded a negative value for energy, for which he proposed a novel solution: he posited the existence of an [[antielectron]] and a dynamical vacuum. This led to the many-particle [[quantum field theory]].

== Quantum entanglement ==
{{Main|Quantum entanglement}}
In quantum physics, a group of [[particle]]s can interact or be created together in such a way that the [[quantum state]] of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. This is known as [[quantum entanglement]].

An early landmark in the study of entanglement was the [[EPR paradox|Einstein–Podolsky–Rosen (EPR) paradox]], a [[thought experiment]] proposed by Albert Einstein, [[Boris Podolsky]] and [[Nathan Rosen]] which argues that the description of physical reality provided by [[quantum mechanics]] is incomplete.<ref name="EPR">{{cite journal | title = Can Quantum-Mechanical Description of Physical Reality be Considered Complete? | date = 1935-05-15 | first = A | last = Einstein |author2=B Podolsky |author3=N Rosen  | journal = [[Physical Review]] | volume = 47 | issue = 10 | pages = 777–780 | url=https://cds.cern.ch/record/405662/files/PhysRev.47.777.pdf|bibcode = 1935PhRv...47..777E |doi = 10.1103/PhysRev.47.777 | doi-access = free }}</ref> In a 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", they argued for the existence of "elements of reality" that were not part of quantum theory, and speculated that it should be possible to construct a theory containing these [[Hidden-variable theory|hidden variables]].

The thought experiment involves a pair of particles prepared in what would later become known as an entangled state. Einstein, Podolsky, and Rosen pointed out that, in this state, if the position of the first particle were measured, the result of measuring the position of the second particle could be predicted. If instead the momentum of the first particle were measured, then the result of measuring the momentum of the second particle could be predicted. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is forbidden by the [[theory of relativity]]. They invoked a principle, later known as the "EPR criterion of reality", positing that: "If, without in any way disturbing a system, we can predict with certainty (i.e., with [[probability]] equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity." From this, they inferred that the second particle must have a definite value of both position and of momentum prior to either quantity being measured. But quantum mechanics considers these two observables [[Observable#Incompatibility of observables in quantum mechanics|incompatible]] and thus does not associate simultaneous values for both to any system. Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality.<ref>{{cite book |last=Peres |first=Asher |author-link=Asher Peres |title=Quantum Theory: Concepts and Methods |title-link=Quantum Theory: Concepts and Methods |page=149 |publisher=Kluwer |year=2002}}</ref> In the same year, [[Erwin Schrödinger]] used the word "entanglement" and declared: "I would not call that ''one'' but rather ''the'' characteristic trait of quantum mechanics."<ref>{{cite journal|first=E. |last=Schrödinger |title=Discussion of probability relations between separated systems |journal=Proceedings of the Cambridge Philosophical Society |volume=31 |year=1935 |issue=4 |page=555 |doi=10.1017/S0305004100013554  |bibcode=1935PCPS...31..555S |quote=When two systems, of which we know the states by their respective representation, enter into a temporary physical interaction due to known forces between them and when after a time of mutual influence the systems separate again, then they can no longer be described as before, viz., by endowing each of them with a representative of its own. I would not call that ''one'' but rather ''the'' characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.}}</ref>

The Irish physicist [[John Stewart Bell]] carried the analysis of quantum entanglement much further. He deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. This constraint would later be named the [[Bell inequality]]. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles are able to interact instantaneously no matter how widely they ever become separated.<ref name="C.B. Parker 1994 542">{{cite book | first = Sybil B. | last = Parker | title = McGraw-Hill Encyclopaedia of Physics | edition = 2nd | page = [https://archive.org/details/mcgrawhillencycl1993park/page/542 542] | date = 1994 | publisher = McGraw-Hill | isbn = 978-0-07-051400-3 | url = https://archive.org/details/mcgrawhillencycl1993park| url-access = registration }}</ref><ref name = "ND Mermin 1993-07">{{cite journal | last = Mermin |first = N. David |author-link=N. David Mermin |title = Hidden Variables and the Two Theorems of John Bell | journal = [[Reviews of Modern Physics]] | volume = 65 |pages = 803–15 | number = 3| date = July 1993  | url = http://cqi.inf.usi.ch/qic/Mermin1993.pdf |arxiv=1802.10119|doi = 10.1103/RevModPhys.65.803 |bibcode = 1993RvMP...65..803M |s2cid = 119546199 }}</ref> Performing experiments like those that Bell suggested, physicists have found that nature obeys quantum mechanics and violates Bell inequalities. In other words, the results of these experiments are incompatible with any local hidden variable theory.<ref name="NAT-20180509">{{cite journal |author=The BIG Bell Test Collaboration |title=Challenging local realism with human choices |date=9 May 2018 |journal=[[Nature (journal)|Nature]] |volume=557 |issue=7704 |pages=212–216 |doi=10.1038/s41586-018-0085-3 |pmid=29743691 |bibcode=2018Natur.557..212B |arxiv=1805.04431 |s2cid=13665914 }}</ref><ref>{{Cite web|url=https://www.quantamagazine.org/20170207-bell-test-quantum-loophole/|title=Experiment Reaffirms Quantum Weirdness|last=Wolchover|first=Natalie|author-link=Natalie Wolchover|date=2017-02-07|work=[[Quanta Magazine]]|language=en-US|access-date=2020-02-08}}</ref>

== Quantum field theory ==
{{Main|Quantum field theory}}

The idea of quantum field theory began in the late 1920s with British physicist Paul Dirac, when he attempted to [[quantization (physics)|quantize]] the energy of the [[electromagnetic field]]; just as in quantum mechanics the energy of an electron in the hydrogen atom was quantized. Quantization is a procedure for constructing a quantum theory starting from a classical theory.

''[[Merriam-Webster]]'' defines a ''field'' in physics as "a region or space in which a given effect (such as [[magnetism]]) exists".<ref>[http://www.merriam-webster.com/dictionary/field "Mechanics", ''Merriam-Webster Online Dictionary'']</ref> Other effects that manifest themselves as fields are [[gravitation]] and [[static electricity]].<ref name="EB-field">[https://www.britannica.com/EBchecked/topic/206162/field "Field"], ''Encyclopædia Britannica''</ref> In 2008, physicist Richard Hammond wrote:

<blockquote>Sometimes we distinguish between quantum mechanics (QM) and quantum field theory (QFT). QM refers to a system in which the number of particles is fixed, and the fields (such as the electromechanical field) are continuous classical entities.  QFT&nbsp;... goes a step further and allows for the creation and annihilation of particles&nbsp;...</blockquote>

He added, however, that ''quantum mechanics'' is often used to refer to "the entire notion of quantum view".<ref name="Hammond">Richard Hammond, ''The Unknown Universe'', New Page Books, 2008. {{ISBN|978-1601630032}}</ref>{{rp|108}}

In 1931, Dirac proposed the existence of particles that later became known as [[antimatter]].<ref>{{cite web|url=http://www.physicalworld.org/restless_universe/html/ru_dira.html|title=Featured Physicists – Paul Dirac 1902–1984|website=www.physicalworld.org|access-date=1 December 2011|archive-date=4 March 2016|archive-url=https://web.archive.org/web/20160304001555/http://www.physicalworld.org/restless_universe/html/ru_dira.html|url-status=dead}}</ref> Dirac shared the [[Nobel Prize in Physics]] for 1933 with Schrödinger "for the discovery of new productive forms of atomic theory".<ref name=nobel>{{cite web | url=http://nobelprize.org/nobel_prizes/physics/laureates/1933/ | title=The Nobel Prize in Physics 1933 | publisher=[[Nobel Foundation]] | access-date=2007-11-24}}</ref>

=== Quantum electrodynamics ===
{{Main|Quantum electrodynamics}}
Quantum electrodynamics (QED) is the name of the quantum theory of the [[electromagnetic force]]. Understanding QED begins with understanding [[electromagnetism]]. Electromagnetism can be called "electrodynamics" because it is a dynamic interaction between electrical and [[magnetic force]]s. Electromagnetism begins with the [[electric charge]].

Electric charges are the sources of and create, [[electric field]]s. An electric field is a field that exerts a force on any particles that carry electric charges, at any point in space. This includes the electron, proton, and even [[quark]]s, among others. As a force is exerted, electric charges move, a current flows, and a magnetic field is produced. The changing magnetic field, in turn, causes [[electric current]] (often moving electrons). The physical description of interacting [[charged particle]]s, electrical currents, electrical fields, and magnetic fields is called electromagnetism.

In 1928 Paul Dirac produced a relativistic quantum theory of electromagnetism. This was the progenitor to modern quantum electrodynamics, in that it had essential ingredients of the modern theory. However, the problem of unsolvable infinities developed in this [[relativistic quantum theory]]. Years later, [[renormalization]] largely solved this problem. Initially viewed as a provisional, suspect procedure by some of its originators, renormalization eventually was embraced as an important and self-consistent tool in QED and other fields of physics.  Also, in the late 1940s [[Feynman diagram]]s provided a way to make predictions with QED by finding a probability amplitude for each possible way that an interaction could occur. The diagrams showed in particular that the electromagnetic force is the exchange of photons between interacting particles.<ref>{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/expar.html|title=Exchange Particles|website=hyperphysics.phy-astr.gsu.edu|access-date=16 October 2018}}</ref>

The [[Lamb shift]] is an example of a quantum electrodynamics prediction that has been experimentally verified. It is an effect whereby the quantum nature of the electromagnetic field makes the energy levels in an atom or ion deviate slightly from what they would otherwise be. As a result, spectral lines may shift or split.

Similarly, within a freely propagating electromagnetic wave, the current can also be just an abstract [[displacement current]], instead of involving charge carriers. In QED, its full description makes essential use of short-lived [[virtual particles]]. There, QED again validates an earlier, rather mysterious concept.

=== Standard Model ===
{{Main|Standard Model}}

The [[Standard Model]] of particle physics is the quantum field theory that describes three of the four known [[fundamental force]]s ([[electromagnetism|electromagnetic]], [[weak interaction|weak]] and [[strong interaction]]s – excluding [[gravity]]) in the [[universe]] and classifies all known [[elementary particle]]s. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon [[experimental confirmation]] of the existence of [[quark]]s. Since then, proof of the [[top quark]] (1995), the [[tau neutrino]] (2000), and the [[Higgs boson]] (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of [[weak neutral current]]s and the [[W and Z bosons]] with great accuracy.

Although the Standard Model is believed to be theoretically self-consistent and has demonstrated success in providing [[experimental prediction]]s, it leaves some [[physics beyond the standard model|physical phenomena unexplained]] and so falls short of being a [[theory of everything|complete theory of fundamental interactions]]. For example, it does not fully explain [[baryon asymmetry]], incorporate the full [[theory of gravitation]] as described by [[general relativity]], or account for the [[accelerating expansion of the universe|universe's accelerating expansion]] as possibly described by [[dark energy]]. The model does not contain any viable [[dark matter]] particle that possesses all of the required properties deduced from observational [[physical cosmology|cosmology]]. It also does not incorporate [[neutrino oscillation]]s and their non-zero masses. Accordingly, it is used as a basis for building more exotic models that incorporate [[hypothetical particle]]s, [[extra dimensions]], and elaborate symmetries (such as [[supersymmetry]]) to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations.

== Interpretations ==
{{Main|Interpretations of quantum mechanics}}

The physical measurements, equations, and predictions pertinent to quantum mechanics are all consistent and hold a very high level of confirmation. However, the question of what these abstract models say about the underlying nature of the real world has received competing answers. These interpretations are widely varying and sometimes somewhat abstract. For instance, the [[Copenhagen interpretation]] states that before a measurement, statements about a particle's properties are completely meaningless, while the [[many-worlds interpretation]] describes the existence of a [[multiverse]] made up of every possible universe.<ref>{{cite web|url=http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec15.html|title=Copenhagen Interpretation|website=abyss.uoregon.edu|access-date=16 October 2018|archive-date=27 February 2020|archive-url=https://web.archive.org/web/20200227150532/http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec15.html|url-status=dead}}</ref>

Light behaves in some aspects like particles and in other aspects like waves. Matter—the "stuff" of the universe consisting of particles such as [[electron]]s and [[atom]]s—exhibits [[wave–particle duality|wavelike behavior]] too. Some light sources, such as [[neon lighting|neon lights]], give off only certain specific frequencies of light, a small set of distinct pure colors determined by neon's atomic structure. Quantum mechanics shows that light, along with all other forms of [[electromagnetic radiation]], comes in discrete units, called [[photon]]s, and predicts its [[spectrum|spectral]] energies (corresponding to pure colors), and the [[intensity (physics)|intensities]] of its light beams. A single photon is a ''[[quantum]]'', or smallest observable particle, of the electromagnetic field. A partial photon is never experimentally observed. More broadly, quantum mechanics shows that many properties of objects, such as position, speed, and [[angular momentum]], that appeared continuous in the zoomed-out view of classical mechanics, turn out to be (in the very tiny, zoomed-in scale of quantum mechanics) ''[[Quantization (physics)|quantized]]''. Such properties of [[elementary particles]] are required to take on one of a set of small, discrete allowable values, and since the gap between these values is also small, the discontinuities are only apparent at very tiny (atomic) scales.

== Applications ==
{{Main|Applications of quantum mechanics|l1 = Applications of quantum mechanics}}

=== Everyday applications ===
The relationship between the frequency of electromagnetic radiation and the energy of each photon is why [[ultraviolet]] light can cause [[sunburn]], but visible or [[infrared]] light cannot. A photon of ultraviolet light delivers a high amount of [[energy]]—enough to contribute to cellular damage such as occurs in a sunburn. A photon of infrared light delivers less energy—only enough to warm one's skin. So, an infrared lamp can warm a large surface, perhaps large enough to keep people comfortable in a cold room, but it cannot give anyone a sunburn.<ref>[https://www.livescience.com/50326-what-is-ultraviolet-light.html Jim Lucas: 'What Is Ultraviolet Light?', 15 September 2017, at livescience.com] Accessed 27 December 2017</ref>

=== Technological applications ===

Applications of quantum mechanics include the [[laser]], the [[transistor]], the [[electron microscope]], and [[Magnetic Resonance Imaging|magnetic resonance imaging]]. A special class of quantum mechanical applications is related to [[macroscopic quantum phenomena]] such as superfluid helium and superconductors. The study of semiconductors led to the invention of the [[diode]] and the [[transistor]], which are indispensable for modern [[electronics]].

In even a simple [[light switch]], [[quantum tunneling]] is absolutely vital, as otherwise the electrons in the [[electric current]] could not penetrate the potential barrier made up of a layer of oxide. [[Flash memory]] chips found in [[USB flash drive|USB drives]] also use quantum tunneling, to erase their memory cells.<ref>
{{cite book
 | last1 = Durrani
 | first1 = Z. A. K.
 | last2 = Ahmed
 | first2 = H.
 | editor = Vijay Kumar
 | title = Nanosilicon
 | publisher = Elsevier
 | year = 2008
 | page = 345
 | isbn = 978-0080445281
}}</ref>

== See also ==
{{Portal|Physics}}
* [[Einstein's thought experiments]]
* [[Macroscopic quantum phenomena]]
* [[Philosophy of physics]]
* [[Quantum computing]]
* [[Virtual particle]]
* [[Teaching quantum mechanics]]
* [[List of textbooks on classical mechanics and quantum mechanics|List of textbooks on classical and quantum mechanics]]

== References ==
{{reflist}}
<!-- Dead note "SearsO11": See Sears, ''Optics'', pp. 282–93. -->
<!-- Dead note "Planck1": Planck is quoted by Louis de Broglie, ''The Revolution in Physics,'' p. 106. The material in this paragraph summarizes de Broglie's account given on pages 105 to 108. (Noonday Press, New York, 1953) -->
<!-- Dead note "geottingen": The German and English forms of this quotation appear in slightly different versions from place to place, probably because Einstein repeated his original remark several time. The earliest German version can be found at http://www.goettingen.de/kultur/gott_wuerfelt_nicht.htm.  In it, Einstein first speaks of God and then says, "And ''this one'' does not (dice =) play dice." -->

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* {{cite book |last=Peat |first=F. David |year=2002 |title=From Certainty to Uncertainty: The Story of Science and Ideas in the Twenty-First Century |publisher=[[Joseph Henry Press]] }}
* {{cite book |last=Reichenbach |first=Hans |author-link=Hans Reichenbach |year=1944 |title=Philosophic Foundations of Quantum Mechanics |url=https://archive.org/details/in.ernet.dli.2015.212027 |publisher=University of California Press |lccn=a44004471 |isbn=0486404595}}
* {{cite book |last=Schilpp |first=Paul Arthur |author-link=Paul Arthur Schilpp |year=1949 |title=Albert Einstein: Philosopher-Scientist |publisher=Tudor Publishing Company |lccn=50005340}}
* ''Scientific American Reader'', 1953.
* {{cite book |last=Sears |first=Francis Weston |author-link=F. W. Sears |year=1949 |title=Optics |edition=3rd |publisher=Addison-Wesley |lccn=51001018 |isbn=0195046013 |url-access=registration |url=https://archive.org/details/neutronopticsint0000sear }}
* {{cite conference |last=Shimony |first=A. |author-link=Abner Shimony |title=(title not given in citation) |book-title=Foundations of Quantum Mechanics in the Light of New Technology (S. Kamefuchi et al., eds.) |pages=225 |publisher=Japan Physical Society |year=1983 |location=Tokyo}}; cited in: {{cite arXiv|last=Popescu|first=Sandu|author2=Daniel Rohrlich|title=Action and Passion at a Distance: An Essay in Honor of Professor Abner Shimony |eprint=quant-ph/9605004 |year=1996}}
* {{cite book |last1=Tavel |first1=Morton |last2=Tavel |first2=Judith (illustrations) | title=Contemporary physics and the limits of knowledge | publisher=Rutgers University Press |year=2002 | isbn = 978-0813530772   | url = https://books.google.com/books?id=SELS0HbIhjYC&q=Wave+function+collapse&pg=PA200}}
* Van Vleck, J. H.,1928, "The Correspondence Principle in the Statistical Interpretation of Quantum Mechanics", ''Proc. Natl. Acad. Sci.'' 14: 179.
* {{cite arXiv |eprint=quant-ph/9801014 |author1=Westmoreland |author2=Benjamin Schumacher |title=Quantum Entanglement and the Nonexistence of Superluminal Signals |year=1998}}
* {{cite journal | last1=Wheeler | first1=John Archibald | author-link=John Archibald Wheeler |last2=Feynman |first2=Richard P. |author2-link=Richard Feynman |title=Classical Electrodynamics in Terms of Direct Interparticle Action |journal=[[Reviews of Modern Physics]] |volume=21 |issue=3 |pages=425–33 |year=1949 |doi=10.1103/RevModPhys.21.425|bibcode = 1949RvMP...21..425W |url=https://cds.cern.ch/record/1062647/files/RevModPhys.21.425.pdf |doi-access=free }}
* {{cite journal |last1=Wieman |first1=Carl |last2=Perkins |first2=Katherine |author2-link=Katherine K. Perkins|year=2005 |title=Transforming Physics Education |journal=[[Physics Today]] |doi=10.1063/1.2155756 |volume=58 |issue=11 |pages=36|bibcode = 2005PhT....58k..36W }}

== Further reading ==
{{Update section|date=September 2021}}

The following titles, all by working physicists, attempt to communicate quantum theory to laypeople, using a minimum of technical apparatus.
* [[Jim Al-Khalili]] (2003). ''Quantum: A Guide for the Perplexed''. Weidenfeld & Nicolson. {{ISBN|978-1780225340}}.
* Chester, Marvin (1987). ''Primer of Quantum Mechanics''. John Wiley. {{ISBN|0486428788}}.
* [[Brian Cox (physicist)|Brian Cox]] and [[Jeff Forshaw]] (2011) ''[[The Quantum Universe]]''. Allen Lane. {{ISBN|978-1846144325}}.
* [[Richard Feynman]] (1985). ''[[QED: The Strange Theory of Light and Matter]]''. Princeton University Press.  {{ISBN|0691083886}}.
* Ford, Kenneth (2005). ''The Quantum World''. Harvard Univ. Press. Includes elementary particle physics.
* [[Giancarlo Ghirardi|Ghirardi, GianCarlo]] (2004). ''Sneaking a Look at God's Cards'', Gerald Malsbary, trans. Princeton Univ. Press. The most technical of the works cited here. Passages using [[algebra]], [[trigonometry]], and [[bra–ket notation]] can be passed over on a first reading.
* [[Tony Hey]] and Walters, Patrick (2003). ''The New Quantum Universe''. Cambridge Univ. Press. Includes much about the technologies quantum theory has made possible. {{ISBN|978-0521564571}}.
* Vladimir G. Ivancevic, Tijana T. Ivancevic (2008). ''Quantum leap: from Dirac and Feynman, Across the universe, to human body and mind''. World Scientific Publishing Company. Provides an intuitive introduction in non-mathematical terms and an introduction in comparatively basic mathematical terms. {{ISBN|978-9812819277}}.
* J. P. McEvoy and Oscar Zarate (2004). ''Introducing Quantum Theory''. Totem Books. {{ISBN|1840465778}}'
* [[N. David Mermin]] (1990). "Spooky actions at a distance: mysteries of the QT" in his ''Boojums all the way through''. Cambridge Univ. Press: 110–76. The author is a rare physicist who tries to communicate to philosophers and humanists. {{ISBN|978-0521388801}}.
* [[Roland Omnès]] (1999). ''Understanding Quantum Mechanics''. Princeton Univ. Press. {{ISBN|978-0691004358}}.
* [[Victor Stenger]] (2000). ''Timeless Reality: Symmetry, Simplicity, and Multiple Universes''. Buffalo NY: Prometheus Books. Chpts. 5–8. {{ISBN|978-1573928595}}.
* [[Martinus Veltman]] (2003). ''Facts and Mysteries in Elementary Particle Physics''. World Scientific Publishing Company. {{ISBN|978-9812381491}}.

== External links ==
{{Wikibooks
 |1=Quantum Mechanics
 |2=Introduction to QM
 |3=Introduction to Quantum Mechanics}}
* "[http://ne.phys.kyushu-u.ac.jp/seminar/MicroWorld1_E/MicroWorld_1_E.html Microscopic World&nbsp;– Introduction to Quantum Mechanics".] by Takada, Kenjiro, emeritus professor at [[Kyushu University]]
* [https://www.compadre.org/quantum/? The Quantum Exchange] (tutorials and open-source learning software).
* [https://www.chem1.com/acad/webtext/atoms/ Atoms and the Periodic Table]
* [https://web.archive.org/web/20111125050834/http://intro.phys.psu.edu/class/251Labs/10_Interference_%26_Diffraction/Single_and_Double-Slit_Interference.pdf Single and double slit interference]
* [https://demonstrations.wolfram.com/TimeEvolutionOfAWavepacketInASquareWell/ Time-Evolution of a Wavepacket in a Square Well] An animated demonstration of a wave packet dispersion over time.
* {{cite web|title=Quantum Mechanics (an embarrassment)|url=http://www.sixtysymbols.com/videos/quantum_mechanics.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the University of Nottingham|author=Carroll, Sean M.|author-link=Sean M. Carroll}}

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