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{{Mergeto|#REDIRECT [[Introduction to quantum mechanics|discuss=Talk:Basic]] concepts of quantum mechanics#Merger proposal{{redirect 2|date=Novemberfrom 2009merge}}

:''This article is intended as an accessible, non-technical introduction to the subject. For the main encyclopedia article, see [[Quantum mechanics]]. For a somewhat more technical introduction to the subject that requires some algebra, see [[Introduction to quantum mechanics]].''

{{Quantum mechanics}}

Quantum mechanics explains the behaviour of [[matter]] and [[energy]] on the scale of [[atoms]] and [[subatomic particles]].

[[Classical physics]] explains matter and energy at the macroscopic level of the scale familiar to human experience, including the behavior of astronomical bodies. It remains the key to [[Measure (physics)|measurement]] for much of [[Science|modern science]] and technology; but at the end of the 19th Century observers discovered phenomena in both the large (macro) and the small (micro) worlds which classical physics could not explain.<ref>[http://www.pbs.org/trasnsistor/science/info/quantum.html ''Quantum Mechanics'' from [[National Public Radio]]]</ref>

This article describes the limitations of classical physics, and explains the main concepts of the quantum theory which supplanted it in the early decades of the 20th Century. These concepts are described in roughly [[history of quantum mechanics|the order they were first discovered]].

==Origins in black body radiation==

[[Image:Hot metalwork.jpg|300px|thumb|right|Hot metalwork from a blacksmith. The yellow-orange glow is the visible part of the thermal radiation emitted due to the high temperature. Everything else in the picture is glowing with thermal radiation as well, but less brightly and at longer wavelengths that the human eye cannot see. A far-infrared camera records this radiation.]]

[[Thermal radiation]] is [[electromagnetic radiation]] emitted from the surface of an object due to the object's [[temperature]]. If the object is heated sufficiently, it starts to emit light at the red end of the [[spectrum]]: it is ''red hot''. Heating it further causes the colour to change, as light of shorter wavelengths (higher frequencies) becomes stronger. A good emitter is also a good absorber. When it is cold, such an object looks black, as it emits practically no visible light, absorbing all light that falls on it. Consequently, an ideal emitter is known as a [[black body]], and the radiation it emits is called black body radiation.

In the late 19th Century, thermal radiation had been fairly well characterised experimentally. <!-- The following text copied from [[Black body]] -->The wavelength at which the radiation is strongest is given by [[Wien's displacement law]], and the overall power emitted per unit area is given by the [[Stefan–Boltzmann law]]. As temperature increases, the glow colour changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body continues to appear blue. It never becomes invisible—indeed, the radiation of visible light increases [[monotonic function|monotonically]] with temperature.<ref name="Landau">{{cite book |last=Landau |first=L. D.|coauthors=E. M. Lifshitz |title=Statistical Physics |edition=3rd Edition Part 1 |year=1996 |publisher=Butterworth-Heinemann |___location=Oxford}}</ref>

<!-- The amount of radiation emitted at all frequencies increases, but the increase is relatively larger at shorter wavelengths, and so the peak in the intensity distribution shifts to shorter wavelengths. -->

Physicists were searching for a theoretical explanation of these experimental results.

The answer from classical physics is called the [[Rayleigh–Jeans law]]. This law agrees with experimental results at long wavelengths. At short wavelengths, however, it predicts that energy is emitted by a hot body at an infinite rate. This result, which is clearly wrong, is known as the [[ultraviolet catastrophe]].

[[File:Max Planck Briefmarke 2008.jpg|thumb|125px|right|Max Planck on a German postage stamp]]

The first model which was able to explain the full spectrum of thermal radiation was put forward by [[Max Planck]] in 1900.<ref>This was published (in German) as {{Cite journal | first = Max | last = Planck | author-link = Max Planck | title = Ueber das Gesetz der Energieverteilung im Normalspectrum | url = http://www.physik.uni-augsburg.de/annalen/history/historic-papers/1901_309_553-563.pdf | journal = [[Annalen der Physik|Ann. Phys.]] | year = 1901 | volume = 309 | issue = 3 | pages = 553–63 | doi = 10.1002/andp.19013090310|bibcode = 1901AnP...309..553P }}. English translation: "[http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html On the Law of Distribution of Energy in the Normal Spectrum]".</ref> He modelled the thermal radiation as being in equilibrium by analogy with a set of harmonic oscillators. But to reproduce the experimental results, each oscillator had to have an exact number of energy units, rather than being able to have any arbitrary amount of energy. In other words, the energy of each oscillator was ''quantised''.<ref group="note"> The word "[[quantum]]" comes from the [[Latin language|Latin word]] for "how much" (as does "quantity"). Something that is "quantised", like the energy of Planck's harmonic oscillators, can only have specific values. For example, in most countries money is effectively quantised: the "quantum of money" being the lowest-value coin in circulation. "Mechanics" is the branch of science that deals with the action of forces on objects, and so "quantum mechanics" is the form of mechanics that deals with objects for which particular properties are quantised.</ref> He determined that the energy of each oscillator was proportional to the frequency, i.e. that it was always an exact multiple of a constant now known as the [[Planck constant]]. <!-- Need to be a little cautious with wording here - Planck didn't put forward his theory as a way of dealing with the ultraviolet catastrophe (and it wasn't realised until later that the ultraviolet catastrophe was an inevitable consequence of classical physics), but the ultraviolet catastrophe is why classical physics was ultimately rejected in favour of QM -->

[[Planck's law]] was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".<ref>{{cite web | url=http://nobelprize.org/nobel_prizes/physics/laureates/1918/ | title=The Nobel Prize in Physics 1918 | publisher=[[The Nobel Foundation]] | accessdate=2009-08-01}}</ref> At the time, however, Planck's own view was that quantisation was purely a mathematical trick to explain the unexpected experimental results, rather than (as we now know) a fundamental change in our understanding of the world.<ref name="Kragh">{{Cite web | first = Helge | last = Kragh | url = http://physicsworld.com/cws/article/print/373 | title = Max Planck: the reluctant revolutionary | publisher = PhysicsWorld.com | date = 1 December 2000}}</ref>

==Photons: the quantisation of light==

[[File:Einstein.Painting.jpg|thumb|125px|left|vertical|Einstein's portrait by Harm Kamerlingh Onnes at the University of Leiden in 1920]]

In 1905, [[Albert Einstein]] took an extra step. He suggested that quantisation wasn't just a mathematical trick, but that the energy in a beam of light occurs in individual packets now called [[photon]]s.<ref>{{cite journal | last = Einstein | first = Albert | authorlink = Albert Einstein | title = Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt | journal = Annalen der Physik | volume = 17 | pages = 132–148 | date = 1905 | url = http://www.zbp.univie.ac.at/dokumente/einstein1.pdf }}, translated into English as [http://lorentz.phl.jhu.edu/AnnusMirabilis/AeReserveArticles/eins_lq.pdf On a Heuristic Viewpoint Concerning the Production and Transformation of Light]. The term "photon" was introduced in 1926.</ref> The energy of a single photon is Planck's constant multiplied by the photon's frequency.

Einstein's proposal was able to explain several puzzling properties of the [[photoelectric effect]], which is the way certain metals give off electrons when light falls on them.<ref name="Hawking">Stephen Hawking, ''The Universe in a Nutshell,'' Bantam, 2001.</ref>{{rp|24}} <!-- Could explain here which particular properties, and why a particulate theory was able to explain them --> For centuries, scientists had debated between two possible theories of [[light]]: was it a [[wave]] or did it instead consist of a [[Corpuscular theory of light|stream of tiny particles]]? By the 19th Century, the debate was generally considered to have been settled in favour of the wave theory, because it was able to explain observed effects such as [[refraction]], [[diffraction]] and [[Polarization (waves)|polarisation]]. Because of this, Einstein's proposal was met by great scepticism. Eventually, however, his particle analogy became accepted, as it helped explain how light delivers energy in multiples of certain set values, called quanta of energy. Nevertheless, the wave analogy remained indispensable for helping to explain other phenomena of light, such as [[diffraction]].

Thus, for the first time, was an object demonstrating both wave-like and particle-like characteristics modelled as being based upon discrete energy levels.

==Bohr model of the atom==

{{Main|Bohr model}}

[[File:Niels.Bohr.Sketch.jpg|thumb|125px|right|Sketch by Christian Gori from a photograph of Niels Bohr]]

By the early 20th century, it was known that [[atom]]s consisted of a diffuse cloud of negatively-charged [[electron]]s surrounding a small, dense, positively-charged [[Atomic nucleus|nucleus]]. This suggested a model in which the electrons circled around the nucleus like planets orbiting the sun.<ref group="note">The classical model of the atom is called the planetary model or the [[Rutherford model]], after [[Ernest Rutherford]] who proposed it in 1911, based on the [[Geiger-Marsden experiment|Geiger-Marsden gold foil experiment]] which first demonstrated the existence of the nucleus.</ref> However, it was also known that the atom in this model would be unstable: the orbiting electrons should give off electromagnetic radiation, causing them to lose energy and spiral towards the nucleus, colliding with it in a fraction of a second.

A second, related, puzzle was the [[emission spectrum]] of atoms. When a gas is heated, it gives off light at certain discrete frequencies; for example, the visible light given off by [[hydrogen]] consists of four different colours, as shown in the picture below. In contrast, white light contains light at the whole range of visible frequencies.

[[Image:Emission spectrum-H.png|frame|none|[[Emission spectrum]] of [[hydrogen]]. When excited, hydrogen gas gives off light in four distinct colours (spectral lines) in the visible spectrum, as well as a number of lines in the infra-red and ultra-violet.]]

In 1913 [[Niels Bohr]] proposed a new model of the atom that included quantised electron orbits. This solution became known as the Bohr model of the atom. In Bohr's model, electrons could inhabit only particular orbits around the atomic nucleus. When an atom emits or absorbs energy, the electron does not move in a continuous trajectory from one orbit around the nucleus to another, as might be expected in classical theory. Instead, the electron jumps instantaneously from one orbit to another, giving off the difference in energy as light in the form of a photon.<ref name="WorldBook"/>{{rp|6}} The possible energies of the photons given off by each element in the [[periodic table]] are determined by the difference in energy between the orbits, so the emission spectrum for each element will contain a number of lines.<ref>Dicke and Wittke, ''Introduction to Quantum Mechanics'', p. 10f.</ref> The Bohr model was able to explain the emission spectrum of hydrogen, but wasn't able to make accurate predictions for multi-electron atoms, or to explain why some spectral lines are brighter than others.

==Particle-wave duality==

{{Main|Wave–particle duality}}

[[Image:Chicago Union Station 1943.jpg|thumb|right|Light streaming through windows at Chicago's Union Station in 1943. Quantum mechanics shows that light acts both as waves and as particles.]]

Quantum mechanics is based upon the concept that [[subatomic particles]] can have both wave-like and particle-like properties. This phenomenon is known as wave–particle duality. The explanation stems from a theory proposed by French physicist [[Louis de Broglie]] in 1924, that subatomic particles such as [[electrons]] are associated with waves. Experiments later showed that he was correct: electrons can bend around objects and can display wave shapes.<ref name="WorldBook">''World Book Encyclopedia,'' 2007.</ref>{{rp|6}}

Consequently, neither ''wave'' nor ''particle'' is an entirely satisfactory model to use in understanding light. Indeed, astrophysicist [[Arthur Stanley Eddington|A.S. Eddington]] proposed in 1927 that "We can scarcely describe such an entity as a wave or as a particle; perhaps as a compromise we had better call it a 'wavicle' ".<ref name="Eddington">[http://books.google.com/books?id=PGOTKcxSqMUC&pg=PA201&lpg=PA201&dq=We+can+scarcely+describe+such+an+entity+as+a+wave+or+as+a+particle%3B+perhaps+as+a+compromise+we+had+better+call+it+a+%60wavicle&source=bl&ots=K0IfGzaXli&sig=zgrQiBJbHRLuUzVBT-yy8jZhC1Y&hl=en&ei=i8g1SpOHC4PgtgOu_4jVDg&sa=X&oi=book_result&ct=result&resnum=1 A.S. Eddington, ''The Nature of the Physical World,'' the course of Gifford Lectures that Eddington delivered in the University of Edinburgh in January to March 1927, Kessinger Publishing, 2005, p. 201.]</ref> This term was later popularised by mathematician [[Banesh Hoffmann]].<ref name="Hoffman">Banesh Hoffman, ''The Strange Story of the Quantum,'' Dover, 1959</ref>{{rp|172}}

The concept of waves and particles, and the analogies which use them, are mechanisms of [[classical physics]]. Quantum mechanics, which seeks to explain nature at a level underlying that of the atoms which comprise matter, cannot be understood in such terms. The classical concepts presuppose an artificial division of matter (as particles) and energy (as waves) that has no objective validity on the sub-atomic level. If the distinction no longer holds true, it is not surprising if classes of object can exhibit the characteristics of either.

==Uncertainty principle==

{{Main|Uncertainty principle}}

[[File:Heisenberg 10.jpg|thumb|left|125px|Werner Heisenberg at the age of 26. Heisenberg won the [[Nobel Prize in Physics]] in 1932 for the work that he did at around this time.<ref>[http://nobelprize.org/nobel_prizes/physics/laureates/1932/ Heisenberg's Nobel Prize citation]</ref>]]Suppose that we want to measure the position and speed of an object -- for example a car going through a radar speed trap. Naively, we assume that (at a particular moment in time) the car has a definite position and speed, and how accurately we can measure these values depends on the quality of our measuring equipment -- if we improve the precision of our measuring equipment, we will get a result that is closer to the true value. In particular, we would assume that how precisely we measure the speed of the car does not affect its position, and vice versa.

In 1927 German physicist [[Werner Heisenberg]] proved that in the sub-atomic world such assumptions are 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.|last=Heisenberg|title=Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik|journal=Z. Phys.|volume=43|year=1927|issue=3-4|pages=172–198|doi=10.1007/BF01397280|bibcode = 1927ZPhy...43..172H }}</ref> Quantum mechanics shows that certain pairs of physical properties, such as position and speed, cannot both be known to arbitrary precision. He showed that the more precisely one of them is known, the less precisely the other can be known. This statement is known as the [[uncertainty principle]] (or Heisenberg's uncertainty principle). It is not a statement about the accuracy of our measuring equipment, but about the nature of the system itself -- our naive assumption that an object has a definite position and speed is incorrect. On a scale of cars and people, these uncertainties are still present but are too small to be noticed; yet they are large enough that when dealing with individual atoms and electrons they become critical.<ref>[http://nobelprize.org/nobel_prizes/physics/laureates/1932/press.html Nobel Prize in Physics presentation speech, 1932]</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, but the greater is the disturbance of the electron, which absorbs a random amount of energy, rendering the measurement obtained of its [[momentum]] increasingly uncertain (momentum is velocity multiplied by mass), for one is necessarily measuring its post-impact disturbed momentum, from the collision products, not its original momentum. With a photon of lower frequency the disturbance - hence uncertainty - in the momentum is less, but so is the accuracy of the measurement of the position of the impact.

The uncertainty principle shows mathematically that the product of the uncertainty in the position and momentum of a particle can never be less than a certain value, and that this value is related to Planck's constant. It is, in point of fact, up to a small numerical factor equal to Planck's constant.

==Schrödinger's wave equation==

{{Main|Schrödinger equation}}

[[File:Erwin Schroedinger.jpg|thumb|125px|right|Erwin Schrödinger, about 1933, age 46]]

Although Heisenberg had no problem with the existence of discontinuous quantum jumps, Austrian physicist [[Erwin Schrödinger]] hoped that a theory based on continuous wave-like properties<ref group="note"> Schrödinger's formulation of quantum mechanics based on waves is sometimes referred to as "wave mechanics", to distinguish it from the [[matrix mechanics]] formulation of Heisenberg, [[Max Born]] and [[Pascual Jordan]].</ref> could avoid what he called (in the reported words of [[Wilhelm Wien]]<ref>[http://www.amazon.com/dp/0521437679 W. Moore, ''Schrödinger: Life and Thought'', Cambridge University Press (1989), p. 222]</ref>) "this nonsense about quantum jumps."

Building on [[De Broglie]]'s theoretical model of particles as waves, Schrödinger accordingly brought forth in 1926 what has been called "the fundamental equation" of quantum mechanics.<ref name="EB-SchrEquation">[http://www.britannica.com/EBchecked/topic/528298/Schrodinger-equation "Schrodinger Equation (Physics)," ''Encyclopedia Britannica '']</ref>

In point of fact, Schrödinger's wave equation is as central to quantum mechanics as Einstein's equation <math>E = MC^2</math> is to [[Special relativity|Relativity]].

The equation describes the probability waves which govern the motion of sub-atomic particles, "and it specifies how these waves are altered by external influences. Schrödinger established the correctness of the equation by applying it to the [[hydrogen atom]], predicting many of its properties with remarkable accuracy. The equation is used extensively in atomic, nuclear, and [[solid-state physics]]."<ref name="EB-SchrEquation"/>

==Atomic orbital model==

{{Main|Atomic orbital model}}

Bohr's model of the atom was essentially two-dimensional — an electron orbiting in a plane around its nuclear "sun." In modern theory, ''orbital'' has replaced the earlier word ''orbit'' concerning the position of an electron in relation to the [[Atomic nucleus|nucleus of an atom]]. It is often depicted as a three-dimensional region within which there is a 95 percent probability of finding the electron.<ref name="EB-orbital">[http://www.britannica.com/EBchecked/topic/431159/orbital "Orbital (chemistry and physics)," ''Encyclopedia Britannica '']</ref>

The uncertainty principle states that an electron cannot be viewed as having an exact ___location at any given time. The concepts of exact position and exact [[velocity]] (distance traveled per unit of time) taken together really have no meaning in nature.<ref name="EB-uncertainty">[http://www.britannica.com/EBchecked/topic/614029/uncertainty-principle "Uncertainty principle," ''Encyclopedia Britannica'']</ref> An orbital, then, is a "cloud" of possible locations in which an electron might be found, a distribution of probabilities rather than a precise ___location.<ref>[http://www.physicsforums.com/archive/index.php/t-58605.html "What paths do electronics actually take in an orbital..." ''Physics Forums,'' January 4, 2005]</ref>

==Quantum field theory==

[[File:Paul.Dirac.monument.jpg|125px|thumb|vertical|This sculpture in Bristol, England — a series of clustering cones — presents the idea of small worlds which Paul Dirac studied to reach his discovery of anti-matter.]]

{{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)|quantise]] the [[electromagnetic field]] — a procedure for constructing a quantum theory starting from a classical theory.

A ''field'' in physics is "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">[http://www.britannica.com/EBchecked/topic/206162/field "Field," ''Encyclopedia Britannica '']</ref> In 2008, physicist [[Richard Hammond (physicist)|Richard Hammond]] wrote that

<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 . . . goes a step further and allows for the creation and annihilation of particles . . . .</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 978-1-60163-003-2</ref>{{rp|108}}

In 1931, Dirac proposed the existence of particles that later became known as [[anti-matter]].<ref>[http://www.physicalworld.org/restless_universe/html/ru_dira.html The Physical World website]</ref> Dirac shared the [[Nobel Prize in physics]] for 1933 with [[Erwin Schrödinger|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=[[The Nobel Foundation]] | accessdate=2007-11-24}}</ref>

==Practical use==

{{Main|Quantum_mechanics#Applications|l1=Quantum mechanics: applications}}

The main value of the quantum mechanics [[Theory#Pedagogical_definition|theory]] is its practical applications. Examples include the [[laser]], the [[transistor]], the [[electron microscope]], and [[Magnetic Resonance Imaging|magnetic resonance imaging]]. The study of semiconductors led to the invention of the [[diode]] and the [[transistor]], which are indispensable for modern [[electronics]].

In even the simple [[light switch]], [[quantum tunneling|quantum tunnelling]] is 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 drive]]s also use quantum tunnelling, to erase their memory cells.<ref>

{{Cite book

| last = Durrani

| first = Z. A. K.

| last2 = Ahmed

| first2 = H.

| editor = Vijay Kumar

| authorlink =

| coauthors =

| title = Nanosilicon

| publisher = Elsevier

| date = 2008

| ___location =

| page = 345

| url =

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| isbn = 9780080445281}}

</ref>

==Notes==

{{Reflist|group=note}}

==References==

{{reflist|2}}

==Further reading==

* [[Richard Feynman]], 1985. ''[[QED: The Strange Theory of Light and Matter]]'', Princeton University Press. ISBN 0-691-08388-6

==Related information==<!-- see [[wp:NAVHEAD]] -->

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