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'''Quantum mechanics''' (QM) is a set of principles describing the [[physical]] [[reality]] at the deepest level of [[matter]] (molecules and atoms) and the subatomic (electrons, protons, and even smaller particles). These descriptions include the simultaneous [[wave]]-like and [[particle]]-like [[behavior]] of both [[matter]][1] and radiation[2] ("[http://en.wikipedia.org/wiki/Wave–particle_duality wave–particle duality]"). Quantum Mechanics is a [[mathematical]] description of reality, like any scientific [[model]]. Some of its predictions and implications go against our "common sense" of how [[humans]] see a set of bodies (a [[system]]) behave. This isn't necessarily a failure of QM - it's more likely to be a [[reflection]] of how we as humans are used to describing things at the scale of metres and days rather than much smaller. QM says that the most complete description we can make of a [[system]] is its wavefunction, which is just a number varying between [[time]] and [[space|place]]. We can derive things from the wavefunction, such as the position of a particle, or its [[momentum]]. Yet the wavefunction describes [[probabilities]], and it turns out that some physical quantities which we usually assume are both fully defined together simultaneously for a system are not simultaneously given definite [[value]]s in QM. It is not that the [[experimental]] equipment we're using to [[measure]] is not precise enough - the two quantities in question just really aren't defined at the same time by the [[Universe]]. For instance, location and [[velocity]] just do not exist simultaneously for a [[body]] (this is called the [http://en.wikipedia.org/wiki/Uncertainty_principle Heisenberg uncertainty principle]

'''Quantum mechanics''' (QM) is a set of principles describing the [[physical]] [[reality]] at the deepest level of [[matter]] (molecules and atoms) and the subatomic (electrons, protons, and even smaller particles). These descriptions include the simultaneous [[wave]]-like and [[particle]]-like [[behavior]] of both [[matter]][1] and radiation[2] ("[https://en.wikipedia.org/wiki/Wave–particle_duality wave–particle duality]"). Quantum Mechanics is a [[mathematical]] description of reality, like any scientific [[model]]. Some of its predictions and implications go against our "common sense" of how [[humans]] see a set of bodies (a [[system]]) behave. This isn't necessarily a failure of QM - it's more likely to be a [[reflection]] of how we as humans are used to describing things at the scale of metres and days rather than much smaller. QM says that the most complete description we can make of a [[system]] is its wavefunction, which is just a number varying between [[time]] and [[space|place]]. We can derive things from the wavefunction, such as the position of a particle, or its [[momentum]]. Yet the wavefunction describes [[probabilities]], and it turns out that some physical quantities which we usually assume are both fully defined together simultaneously for a system are not simultaneously given definite [[value]]s in QM. It is not that the [[experimental]] equipment we're using to [[measure]] is not precise enough - the two quantities in question just really aren't defined at the same time by the [[Universe]]. For instance, location and [[velocity]] just do not exist simultaneously for a [[body]] (this is called the [https://en.wikipedia.org/wiki/Uncertainty_principle Heisenberg uncertainty principle]

Certain [[system]]s, however, do exhibit quantum mechanical effects on a larger scale; ''superfluidity'' (the frictionless flow of a liquid at temperatures near absolute zero) is one well-known example. Quantum theory also provides accurate descriptions for many previously unexplained [[phenomena]] such as black body radiation and the stability of electron orbitals. It has also given [[insight]] into the workings of many different [[biological]] systems, including smell receptors and protein structures.[3]

Certain [[system]]s, however, do exhibit quantum mechanical effects on a larger scale; ''superfluidity'' (the frictionless flow of a liquid at temperatures near absolute zero) is one well-known example. Quantum theory also provides accurate descriptions for many previously unexplained [[phenomena]] such as black body radiation and the stability of electron orbitals. It has also given [[insight]] into the workings of many different [[biological]] systems, including smell receptors and protein structures.[3]

<center>For lessons on the related [[topic]] of '''''[[Physics]]''''', follow [https://nordan.daynal.org/wiki/index.php?title=Category:Physics/TeaM '''''this link'''''].</center>

<center>For lessons on the related [[topic]] of '''''[[Physics]]''''', follow [https://nordan.daynal.org/wiki/index.php?title=Category:Physics/TeaM '''''this link'''''].</center>

Even so, classical physics often can be a good approximation to results otherwise obtained by quantum physics, typically in circumstances with large numbers of particles or large quantum numbers. (However, some open questions remain in the field of [http://en.wikipedia.org/wiki/Quantum_chaos quantum chaos].)

Even so, classical physics often can be a good approximation to results otherwise obtained by quantum physics, typically in circumstances with large numbers of particles or large quantum numbers. (However, some open questions remain in the field of [https://en.wikipedia.org/wiki/Quantum_chaos quantum chaos].)

==Overview==

==Overview==

The word quantum is [[Latin]] for "how great" or "how much."[4] In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the [[energy]] of an [[atom]] at rest (see Figure 1, at right). The [[discovery]] that [[wave]]s have discrete energy packets (called '''''quanta''''') that behave in a [[manner]] similar to particles led to the branch of physics that deals with atomic and subatomic systems which we today call quantum mechanics. It is the underlying mathematical framework of many fields of [[physics]] and [[chemistry]], including [http://en.wikipedia.org/wiki/Condensed_matter_physics condensed matter physics], [http://en.wikipedia.org/wiki/Solid-state_physics solid-state physics], [http://en.wikipedia.org/wiki/Atomic_physics atomic physics], [http://en.wikipedia.org/wiki/Molecular_physics molecular physics], [http://en.wikipedia.org/wiki/Computational_chemistry computational chemistry], [http://en.wikipedia.org/wiki/Quantum_chemistry quantum chemistry], [http://en.wikipedia.org/wiki/Particle_physics particle physics], and [http://en.wikipedia.org/wiki/Nuclear_physics nuclear physics]. The [[foundations]] of quantum mechanics were established during the first half of the twentieth century by [http://en.wikipedia.org/wiki/Werner_Heisenberg Werner Heisenberg], [http://en.wikipedia.org/wiki/Max_Planck Max Planck], [http://en.wikipedia.org/wiki/Louis_de_Broglie Louis de Broglie], [[Albert Einstein]], [http://en.wikipedia.org/wiki/Niels_Bohr Niels Bohr], [http://en.wikipedia.org/wiki/Erwin_Schrödinger Erwin Schrödinger], [http://en.wikipedia.org/wiki/Max_Born Max Born], [http://en.wikipedia.org/wiki/Von_Neumann John von Neumann], [http://en.wikipedia.org/wiki/Paul_Dirac Paul Dirac], [http://en.wikipedia.org/wiki/Wolfgang_Pauli Wolfgang Pauli], [http://en.wikipedia.org/wiki/David_Hilbert David Hilbert], and [http://en.wikipedia.org/wiki/List_of_physicists#Famous_physicists_of_the_20th_century others].[5] Some fundamental aspects of the theory are still actively studied.[6]

The word quantum is [[Latin]] for "how great" or "how much."[4] In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the [[energy]] of an [[atom]] at rest (see Figure 1, at right). The [[discovery]] that [[wave]]s have discrete energy packets (called '''''quanta''''') that behave in a [[manner]] similar to particles led to the branch of physics that deals with atomic and subatomic systems which we today call quantum mechanics. It is the underlying mathematical framework of many fields of [[physics]] and [[chemistry]], including [https://en.wikipedia.org/wiki/Condensed_matter_physics condensed matter physics], [https://en.wikipedia.org/wiki/Solid-state_physics solid-state physics], [https://en.wikipedia.org/wiki/Atomic_physics atomic physics], [https://en.wikipedia.org/wiki/Molecular_physics molecular physics], [https://en.wikipedia.org/wiki/Computational_chemistry computational chemistry], [https://en.wikipedia.org/wiki/Quantum_chemistry quantum chemistry], [https://en.wikipedia.org/wiki/Particle_physics particle physics], and [https://en.wikipedia.org/wiki/Nuclear_physics nuclear physics]. The [[foundations]] of quantum mechanics were established during the first half of the twentieth century by [https://en.wikipedia.org/wiki/Werner_Heisenberg Werner Heisenberg], [https://en.wikipedia.org/wiki/Max_Planck Max Planck], [https://en.wikipedia.org/wiki/Louis_de_Broglie Louis de Broglie], [[Albert Einstein]], [https://en.wikipedia.org/wiki/Niels_Bohr Niels Bohr], [https://en.wikipedia.org/wiki/Erwin_Schrödinger Erwin Schrödinger], [https://en.wikipedia.org/wiki/Max_Born Max Born], [https://en.wikipedia.org/wiki/Von_Neumann John von Neumann], [https://en.wikipedia.org/wiki/Paul_Dirac Paul Dirac], [https://en.wikipedia.org/wiki/Wolfgang_Pauli Wolfgang Pauli], [https://en.wikipedia.org/wiki/David_Hilbert David Hilbert], and [https://en.wikipedia.org/wiki/List_of_physicists#Famous_physicists_of_the_20th_century others].[5] Some fundamental aspects of the theory are still actively studied.[6]

Quantum mechanics is [[essential]] to understand the [[behavior]] of [[systems]] at atomic length scales and smaller. For example, if classical mechanics governed the workings of an [[atom]], electrons would rapidly travel towards and collide with the nucleus, making stable atoms impossible. However, in the natural world the electrons normally remain in an uncertain, non-deterministic "smeared" (wave-particle wave function) orbital path around or "through" the nucleus, defying classical electromagnetism.[7]

Quantum mechanics is [[essential]] to understand the [[behavior]] of [[systems]] at atomic length scales and smaller. For example, if classical mechanics governed the workings of an [[atom]], electrons would rapidly travel towards and collide with the nucleus, making stable atoms impossible. However, in the natural world the electrons normally remain in an uncertain, non-deterministic "smeared" (wave-particle wave function) orbital path around or "through" the nucleus, defying classical electromagnetism.[7]

In the [[formal]]ism of quantum mechanics, the [[state]] of a [[system]] at a given time is described by a [[complex]] [[wave]] [[function]] (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex [[vector]] space.[9] This abstract mathematical object allows for the calculation of [[probabilities]] of outcomes of concrete [[experiments]]. For example, it allows one to compute the [[probability]] of finding an electron in a particular region around the [[nucleus]] at a particular time. Contrary to classical [[mechanics]], one can never make simultaneous [[predictions]] of conjugate variables, such as position and [[momentum]], with accuracy. For instance, electrons may be considered to be located somewhere within a region of [[space]], but with their exact positions being unknown. Contours of constant [[probability]], often referred to as “clouds,” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate.[10]

In the [[formal]]ism of quantum mechanics, the [[state]] of a [[system]] at a given time is described by a [[complex]] [[wave]] [[function]] (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex [[vector]] space.[9] This abstract mathematical object allows for the calculation of [[probabilities]] of outcomes of concrete [[experiments]]. For example, it allows one to compute the [[probability]] of finding an electron in a particular region around the [[nucleus]] at a particular time. Contrary to classical [[mechanics]], one can never make simultaneous [[predictions]] of conjugate variables, such as position and [[momentum]], with accuracy. For instance, electrons may be considered to be located somewhere within a region of [[space]], but with their exact positions being unknown. Contours of constant [[probability]], often referred to as “clouds,” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate.[10]

The other exemplar that led to quantum mechanics was the study of [http://en.wikipedia.org/wiki/Electromagnetic_wave electromagnetic waves] such as [[light]]. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, [[Albert Einstein]] exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the [[photon]] with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave–particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the world of the very small, it also is needed to explain certain “macroscopic quantum systems” such as superconductors and superfluids.[11]

The other exemplar that led to quantum mechanics was the study of [https://en.wikipedia.org/wiki/Electromagnetic_wave electromagnetic waves] such as [[light]]. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, [[Albert Einstein]] exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the [[photon]] with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave–particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the world of the very small, it also is needed to explain certain “macroscopic quantum systems” such as superconductors and superfluids.[11]

Broadly speaking, quantum mechanics incorporates four classes of [[phenomena]] that classical physics cannot account for: (I) the [http://en.wikipedia.org/wiki/Quantization_(physics) quantization] (discretization) of certain physical quantities, (II) [http://en.wikipedia.org/wiki/Wave-particle_duality wave-particle duality], (III) [http://en.wikipedia.org/wiki/Uncertainty_principle the uncertainty principle], and (IV) [http://en.wikipedia.org/wiki/Quantum_entanglement quantum entanglement]. Each of these phenomena is described in detail in the article found at [http://en.wikipedia.org/wiki/Quantum_mechanics this link].

Broadly speaking, quantum mechanics incorporates four classes of [[phenomena]] that classical physics cannot account for: (I) the [https://en.wikipedia.org/wiki/Quantization_(physics) quantization] (discretization) of certain physical quantities, (II) [https://en.wikipedia.org/wiki/Wave-particle_duality wave-particle duality], (III) [https://en.wikipedia.org/wiki/Uncertainty_principle the uncertainty principle], and (IV) [https://en.wikipedia.org/wiki/Quantum_entanglement quantum entanglement]. Each of these phenomena is described in detail in the article found at [https://en.wikipedia.org/wiki/Quantum_mechanics this link].

==See also==

==See also==

*'''''[[Classical Mechanics]]'''''

*'''''[[Classical Mechanics]]'''''

*Shankar, R. (1994). Principles of Quantum Mechanics. Springer. ISBN 0-306-44790-8.

*Shankar, R. (1994). Principles of Quantum Mechanics. Springer. ISBN 0-306-44790-8.

==External Links==

==External Links==

*[http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html The Modern Revolution in Physics] - an online textbook.

*[https://www.lightandmatter.com/html_books/6mr/ch01/ch01.html The Modern Revolution in Physics] - an online textbook.

* J. O'Connor and E. F. Robertson: [http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html A history of quantum mechanics.]

* J. O'Connor and E. F. Robertson: [https://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html A history of quantum mechanics.]

*[http://www.quantiki.org/wiki/index.php/Introduction_to_Quantum_Theory Introduction to Quantum Theory at Quantiki.]

*[https://www.quantiki.org/wiki/index.php/Introduction_to_Quantum_Theory Introduction to Quantum Theory at Quantiki.]

*[http://bethe.cornell.edu/ Quantum Physics Made Relatively Simple]: three video lectures by [[Hans Bethe]]

*[https://bethe.cornell.edu/ Quantum Physics Made Relatively Simple]: three video lectures by [[Hans Bethe]]

*[http://www.nonlocal.com/hbar/ H is for h-bar.]

*[https://www.nonlocal.com/hbar/ H is for h-bar.]

*[http://www.freebookcentre.net/Physics/Quantum-Mechanics-Books.html Quantum Mechanics Books Collection]: Collection of free books  

*[https://www.freebookcentre.net/Physics/Quantum-Mechanics-Books.html Quantum Mechanics Books Collection]: Collection of free books  

;Course material

;Course material

*MIT OpenCourseWare: [http://ocw.mit.edu/OcwWeb/Chemistry/index.htm Chemistry]. See [http://ocw.mit.edu/OcwWeb/Chemistry/5-61Fall-2004/CourseHome/index.htm 5.61], [http://ocw.mit.edu/OcwWeb/Chemistry/5-73Fall-2005/CourseHome/index.htm 5.73], and [http://ocw.mit.edu/OcwWeb/Chemistry/5-74Spring-2005/CourseHome/index.htm 5.74]

*MIT OpenCourseWare: [https://ocw.mit.edu/OcwWeb/Chemistry/index.htm Chemistry]. See [https://ocw.mit.edu/OcwWeb/Chemistry/5-61Fall-2004/CourseHome/index.htm 5.61], [https://ocw.mit.edu/OcwWeb/Chemistry/5-73Fall-2005/CourseHome/index.htm 5.73], and [https://ocw.mit.edu/OcwWeb/Chemistry/5-74Spring-2005/CourseHome/index.htm 5.74]

*MIT OpenCourseWare: [http://ocw.mit.edu/OcwWeb/Physics/index.htm Physics]. See [http://ocw.mit.edu/OcwWeb/Physics/8-04Spring-2006/CourseHome/index.htm 8.04], [http://ocw.mit.edu/OcwWeb/Physics/8-05Fall-2004/CourseHome/index.htm 8.05], and [http://ocw.mit.edu/OcwWeb/Physics/8-06Spring-2005/CourseHome/index.htm 8.06]

*MIT OpenCourseWare: [https://ocw.mit.edu/OcwWeb/Physics/index.htm Physics]. See [https://ocw.mit.edu/OcwWeb/Physics/8-04Spring-2006/CourseHome/index.htm 8.04], [https://ocw.mit.edu/OcwWeb/Physics/8-05Fall-2004/CourseHome/index.htm 8.05], and [https://ocw.mit.edu/OcwWeb/Physics/8-06Spring-2005/CourseHome/index.htm 8.06]

*[http://www.physics.csbsju.edu/QM/ 5½ Examples in Quantum Mechanics]

*[https://www.physics.csbsju.edu/QM/ 5½ Examples in Quantum Mechanics]

*[http://www.imperial.ac.uk/quantuminformation/qi/tutorials Imperial College Quantum Mechanics Course.]

*[https://www.imperial.ac.uk/quantuminformation/qi/tutorials Imperial College Quantum Mechanics Course.]

*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter19section3.rhtml Spark Notes - Quantum Physics.]

*[https://www.sparknotes.com/testprep/books/sat2/physics/chapter19section3.rhtml Spark Notes - Quantum Physics.]

*[http://arxiv.org/abs/quant-ph/0605180 Doron Cohen: Lecture notes in Quantum Mechanics (comprehensive, with advanced topics).]

*[https://arxiv.org/abs/quant-ph/0605180 Doron Cohen: Lecture notes in Quantum Mechanics (comprehensive, with advanced topics).]

*[http://www.quantum-physics.polytechnique.fr Quantum Physics Online : interactive introduction to quantum mechanics (RS applets).]

*[https://www.quantum-physics.polytechnique.fr Quantum Physics Online : interactive introduction to quantum mechanics (RS applets).]

*[http://www.quantumlab.de Experiments to the foundations of quantum physics with single photons.]

*[https://www.quantumlab.de Experiments to the foundations of quantum physics with single photons.]

*[http://www.motionmountain.net/download.html Motion Mountain, Volume IV] - A modern introduction to quantum theory, with several animations.

*[https://www.motionmountain.net/download.html Motion Mountain, Volume IV] - A modern introduction to quantum theory, with several animations.

;FAQs

;FAQs

*[http://www.hedweb.com/manworld.htm Many-worlds or relative-state interpretation.]

*[https://www.hedweb.com/manworld.htm Many-worlds or relative-state interpretation.]

*[http://www.mtnmath.com/faq/meas-qm.html Measurement in Quantum mechanics.]

*[https://www.mtnmath.com/faq/meas-qm.html Measurement in Quantum mechanics.]

;Media

;Media

*[http://www.newscientist.com/channel/fundamentals/quantum-world Everything you wanted to know about the quantum world] &mdash; archive of articles from ''[[New Scientist]]''.

*[https://www.newscientist.com/channel/fundamentals/quantum-world Everything you wanted to know about the quantum world] &mdash; archive of articles from ''[[New Scientist]]''.

*[http://www.sciencedaily.com/news/matter_energy/quantum_physics/ Quantum Physics Research] from [[Science Daily]]

*[https://www.sciencedaily.com/news/matter_energy/quantum_physics/ Quantum Physics Research] from [[Science Daily]]

* [http://www.nytimes.com/2005/12/27/science/27eins.html?ex=1293339600&en=caf5d835203c3500&ei=5090]

* [https://www.nytimes.com/2005/12/27/science/27eins.html?ex=1293339600&en=caf5d835203c3500&ei=5090]

[[Category: Physics]]

[[Category: Physics]]