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[[image:HAtomOrbitals.png|thumb|275px|Slika. 1: [[Talasna funkcija|Talasne funkcije]] [[elektron]]a u vodonikovom atomu. [[Energija]] raste nadole: ''n''=1,2,3,... i [[moment impulsa]] (ugaoni moment) raste s leva na desno: ''s'', ''p'', ''d'',... Svetlija područja odgovaraju većoj verovatnoći gde bi mogao eksperimentalno nađe elektron.<!--
[[Datoteka:HAtomOrbitals.png|thumb|275px|Slika. 1: [[Talasna funkcija|Talasne funkcije]] [[elektron]]a u vodonikovom atomu. [[Energija]] raste nadole: ''n''=1,2,3,... i [[moment impulsa]] (ugaoni moment) raste s leva na desno: ''s'', ''p'', ''d'',... Svetlija područja odgovaraju većoj verovatnoći gde bi mogao eksperimentalno nađe elektron.<!--


Brighter areas correspond to higher [[probability amplitude|probability density]] for a position measurement. Wavefunctions like these are directly comparable to [[Chladni's figures]] of [[acoustics|acoustic]] modes of vibration in [[classical physics]] and are indeed modes of oscillation as well: they possess a sharp energy and thus a sharp frequency. The angular momentum and energy are [[quantization (physics)|quantized]], and only take on discrete values like those shown (as is the case for [[Resonant frequency|resonant frequencies]] in acoustics).-->]]
Brighter areas correspond to higher [[probability amplitude|probability density]] for a position measurement. Wavefunctions like these are directly comparable to [[Chladni's figures]] of [[acoustics|acoustic]] modes of vibration in [[classical physics]] and are indeed modes of oscillation as well: they possess a sharp energy and thus a sharp frequency. The angular momentum and energy are [[quantization (physics)|quantized]], and only take on discrete values like those shown (as is the case for [[Resonant frequency|resonant frequencies]] in acoustics).-->]]
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== Uvod ==
== Uvod ==


Izraz kvant (od latinskog quantum (množina quanta) = količina, mnoštvo, svota, iznos, deo) odnosi se na diskretne jedinice koje teorija pripisuje izvesnim fizičkim veličinama kao što su [[energija]] i [[moment impulsa]] (ugaoni moment) [[atom]]a kao što je pokazano na slici. Otkriće da talasi mogu da se prostiru kao čestice, u malim energijskim paketima koji se nazivaju kvanti dovelo je do pojave nove grane fizike koja se bavi atomskim i subatomskim sistemima a koju danas nazivamo Kvantna mehanika. Temelje kvantnoj mehanici položili su u prvoj polovini dvadesetog veka [[Verner Hajzenberg]], [[Maks Plank]], [[Luj de Brolj|Luj de Broj]], [[Nils Bor]], [[Ervin Šredinger]], [[Maks Born]], [[Džon fon Nojman]], [[Pol Dirak]], [[Albert Ajnštajn]], [[Volfgang Pauli]] i brojni drugi poznati fizičari 20. veka. Neki bazični aspekti kvantne mehanike još uvek se aktivno izučavaju.
Izraz kvant (od latinskog quantum (množina quanta) = količina, mnoštvo, svota, iznos, deo) odnosi se na diskretne jedinice koje teorija pripisuje izvesnim fizičkim veličinama kao što su [[energija]] i [[moment impulsa]] (ugaoni moment) [[atom]]a kao što je pokazano na slici. Otkriće da talasi mogu da se prostiru kao čestice, u malim energijskim paketima koji se nazivaju kvanti dovelo je do pojave nove grane fizike koja se bavi atomskim i subatomskim sistemima a koju danas nazivamo Kvantna mehanika. Temelje kvantnoj mehanici položili su u prvoj polovini dvadesetog veka [[Verner Hajzenberg]], [[Maks Plank]], [[Luj de Brolj|Luj de Broj]], [[Nils Bor]], [[Ervin Šredinger]], [[Maks Born]], [[Džon fon Nojman]], [[Pol Dirak]], [[Albert Ajnštajn]], [[Volfgang Pauli]] i brojni drugi poznati fizičari 20. veka. Neki bazični aspekti kvantne mehanike još uvek se aktivno izučavaju.


<!--{{main|Introduction to quantum mechanics}}
<!--{{main|Introduction to quantum mechanics}}
Quantum mechanics is a more fundamental theory than [[Classical mechanics|Newtonian mechanics]] and classical [[electromagnetism]], in the sense that it provides [[accuracy and precision|accurate and precise]] descriptions for many [[physical phenomenon|phenomena]] that these "classical" theories simply cannot explain on the atomic and subatomic level. It is necessary to use quantum mechanics to understand the behavior of systems at [[atom]]ic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electron normally remains in a stable orbit around a nucleus &mdash; seemingly defying classical electromagnetism.
Quantum mechanics is a more fundamental theory than [[Classical mechanics|Newtonian mechanics]] and classical [[electromagnetism]], in the sense that it provides [[accuracy and precision|accurate and precise]] descriptions for many [[physical phenomenon|phenomena]] that these "classical" theories simply cannot explain on the atomic and subatomic level. It is necessary to use quantum mechanics to understand the behavior of systems at [[atom]]ic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electron normally remains in a stable orbit around a nucleus — seemingly defying classical electromagnetism.


Quantum mechanics was initially developed to explain the atom, especially the [[spectrum|spectra]] of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron's staying in its [[atomic orbital|orbital]], which could not be explained by Newton's laws of motion and by classical electromagnetism.
Quantum mechanics was initially developed to explain the atom, especially the [[spectrum|spectra]] of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron's staying in its [[atomic orbital|orbital]], which could not be explained by Newton's laws of motion and by classical electromagnetism.
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Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the [[quantization (physics)|quantization]] (discretization) of [[Canonical conjugate variables|certain physical quantities]], (ii) [[wave-particle duality]], (iii) the [[uncertainty principle]], and (iv) [[quantum entanglement]]. Each of these phenomena will be described in greater detail in subsequent sections.
Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the [[quantization (physics)|quantization]] (discretization) of [[Canonical conjugate variables|certain physical quantities]], (ii) [[wave-particle duality]], (iii) the [[uncertainty principle]], and (iv) [[quantum entanglement]]. Each of these phenomena will be described in greater detail in subsequent sections.


Since the early days of quantum theory, physicists have made many attempts to combine it with the other highly successful theory of the twentieth century, [[Albert Einstein]]'s [[General Theory of Relativity]]. While quantum mechanics is entirely consistent with [[special relativity]], serious problems emerge when one tries to join the quantum laws with ''general'' relativity, a more elaborate description of spacetime which incorporates [[gravitation]]. Resolving these inconsistencies has been a major goal of twentieth- and twenty-first-century physics. Despite the proposal of many novel ideas, the unification of quantum mechanics&mdash;which reigns in the domain of the very small&mdash;and general relativity&mdash;a superb description of the very large&mdash;remains a tantalizing future possibility. (''See [[quantum gravity]], [[string theory]].'')
Since the early days of quantum theory, physicists have made many attempts to combine it with the other highly successful theory of the twentieth century, [[Albert Einstein]]'s [[General Theory of Relativity]]. While quantum mechanics is entirely consistent with [[special relativity]], serious problems emerge when one tries to join the quantum laws with ''general'' relativity, a more elaborate description of spacetime which incorporates [[gravitation]]. Resolving these inconsistencies has been a major goal of twentieth- and twenty-first-century physics. Despite the proposal of many novel ideas, the unification of quantum mechanics—which reigns in the domain of the very small—and general relativity—a superb description of the very large—remains a tantalizing future possibility. (''See [[quantum gravity]], [[string theory]].'')


Because everything is composed of quantum-mechanical particles, the laws of classical physics must approximate the laws of quantum mechanics in the appropriate limit. This is often expressed by saying that in case of large [[quantum number]]s quantum mechanics "reduces" to classical mechanics and classical electromagnetism. This requirement is called the [[correspondence principle|correspondence, or classical limit]].-->
Because everything is composed of quantum-mechanical particles, the laws of classical physics must approximate the laws of quantum mechanics in the appropriate limit. This is often expressed by saying that in case of large [[quantum number]]s quantum mechanics "reduces" to classical mechanics and classical electromagnetism. This requirement is called the [[correspondence principle|correspondence, or classical limit]].-->
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== Teorija ==
== Teorija ==


Postoje brojne matematički ekvivalentne formulacije kvantne mehanike. Jedna od najstarijih i najčešće korišćenih je transformaciona teorija koju je predložio [[Pol Dirak]] a koja ujedinjuje i uopštava dve ranije formulacije, [[matrična mehanika|matričnu mehaniku]] (koju je uveo [[Verner Hajzenberg]]) <ref> Nakon što je 1932. godine Hajzenberg dobio Nobelovu nagradu za stvaranje kvantne mehanike uloga [[Maks Born|Maksa Borna]] u tome bila je umanjena. Biografija Maksa Borna iz 2005. detaljno opisuje njegovu ulogu u stvaranju matrične mehanike. To je i sam Hajzenberg priznao 1950. godine u radu posvećenom [[Maks Plank|Maksu Planku]]. Videti: Nancy Thorndike Greenspan, “The End of the Certain World: The Life and Science of Max Born (Basic Books, 2005), pp. 124 - 128, and 285 - 286. </ref> i [[talasna mehanika|talasnu mehaniku]] (koju je formulisao [[Ervin Šredinger]]).
Postoje brojne matematički ekvivalentne formulacije kvantne mehanike. Jedna od najstarijih i najčešće korišćenih je transformaciona teorija koju je predložio [[Pol Dirak]] a koja ujedinjuje i uopštava dve ranije formulacije, [[matrična mehanika|matričnu mehaniku]] (koju je uveo [[Verner Hajzenberg]]) <ref> Nakon što je 1932. godine Hajzenberg dobio Nobelovu nagradu za stvaranje kvantne mehanike uloga [[Maks Born|Maksa Borna]] u tome bila je umanjena. Biografija Maksa Borna iz 2005. detaljno opisuje njegovu ulogu u stvaranju matrične mehanike. To je i sam Hajzenberg priznao 1950. godine u radu posvećenom [[Maks Plank|Maksu Planku]]. Videti: Nancy Thorndike Greenspan, “The End of the Certain World: The Life and Science of Max Born (Basic Books, 2005), pp. 124 - 128, and 285 - 286. </ref> i [[talasna mehanika|talasnu mehaniku]] (koju je formulisao [[Ervin Šredinger]]).


<!--In this formulation, the [[quantum state|instantaneous state of a quantum system]] encodes the probabilities of its measurable properties, or "[[observable]]s". Examples of observables include [[energy]], [[position]], [[momentum]], and [[angular momentum]]. Observables can be either [[Continuous function|continuous]] (e.g., the position of a particle) or [[Discrete mathematics|discrete]] (e.g., the energy of an electron bound to a hydrogen atom).
<!--In this formulation, the [[quantum state|instantaneous state of a quantum system]] encodes the probabilities of its measurable properties, or "[[observable]]s". Examples of observables include [[energy]], [[position]], [[momentum]], and [[angular momentum]]. Observables can be either [[Continuous function|continuous]] (e.g., the position of a particle) or [[Discrete mathematics|discrete]] (e.g., the energy of an electron bound to a hydrogen atom).
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===Matematička formulacija===
=== Matematička formulacija ===
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{{Main|Mathematical formulation of quantum mechanics}}
{{Main|Mathematical formulation of quantum mechanics}}
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===Veza sa drugim naučnim teorijama===
=== Veza sa drugim naučnim teorijama ===


<!--The fundamental rules of quantum mechanics are very broad. They state that the state space of a system is a [[Hilbert space]] and the observables are [[Hermitian operators]] acting on that space, but do not tell us which Hilbert space or which operators. These must be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the [[correspondence principle]], which states that the predictions of quantum mechanics reduce to those of classical physics when a system moves to higher energies or equivalently, larger quantum numbers. This "high energy" limit is known as the ''classical'' or ''correspondence limit''. One can therefore start from an established classical model of a particular system, and attempt to guess the underlying quantum model that gives rise to the classical model in the correspondence limit.
<!--The fundamental rules of quantum mechanics are very broad. They state that the state space of a system is a [[Hilbert space]] and the observables are [[Hermitian operators]] acting on that space, but do not tell us which Hilbert space or which operators. These must be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the [[correspondence principle]], which states that the predictions of quantum mechanics reduce to those of classical physics when a system moves to higher energies or equivalently, larger quantum numbers. This "high energy" limit is known as the ''classical'' or ''correspondence limit''. One can therefore start from an established classical model of a particular system, and attempt to guess the underlying quantum model that gives rise to the classical model in the correspondence limit.
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===Hronologija utemeljivačkih eksperimenata===
=== Hronologija utemeljivačkih eksperimenata ===
*'''~ 1805:''' [[Tomas Jung]]ov eksperiment sa dvostrukim prorezom kojim je demonstrirana talasna priroda svetlosti.
* '''~ 1805:''' [[Tomas Jung]]ov eksperiment sa dvostrukim prorezom kojim je demonstrirana talasna priroda svetlosti.
*'''1896:''' [[Anri Bekerel]]ov pronalazak [[radioaktivnost]]i.
* '''1896:''' [[Anri Bekerel]]ov pronalazak [[radioaktivnost]]i.
*'''1897:''' [[Džozef Džon Tomson]]ovo otkriće eletrona i njegovog negativnog naeletrisanja u eksperimentima sa katodnom cevi.
* '''1897:''' [[Džozef Džon Tomson]]ovo otkriće eletrona i njegovog negativnog naeletrisanja u eksperimentima sa katodnom cevi.
*'''1850-1900:''' Ispitivanje [[zračenje crnog tela|zračenja crnog tela]] koje nije moglo da se objasni bez kvantnog koncepta.
* '''1850-1900:''' Ispitivanje [[zračenje crnog tela|zračenja crnog tela]] koje nije moglo da se objasni bez kvantnog koncepta.
*'''1905:''' [[Fotoelektrični efekat]]: [[Albert Ajnštajn|Ajnštajn]]ovo objašnjenje efekta (za šta je i dobio Nobelovu nagradu za fiziku) uvođenjem koncepta [[foton]]a, čestice svetlosti sa kvantiranom energijom.
* '''1905:''' [[Fotoelektrični efekat]]: [[Albert Ajnštajn|Ajnštajnovo]] objašnjenje efekta (za šta je i dobio Nobelovu nagradu za fiziku) uvođenjem koncepta [[foton]]a, čestice svetlosti sa kvantiranom energijom.
*'''1909:''' [[Robert Miliken]]ov eksperiment sa kapljicama ulja koji je pokazao da je eletrično naeletrisanje javlja u diskretnim (kvantiranim) porcijama.
* '''1909:''' [[Robert Miliken]]ov eksperiment sa kapljicama ulja koji je pokazao da je eletrično naeletrisanje javlja u diskretnim (kvantiranim) porcijama.
*'''1911:''' [[Ernest Raderford|Raderfordov]] ogled sa rasejanjem alfa čestica na zlatnoj foliji kojim je napušten atomski model "pudinga od šljiva" u kojem je sugerisano da su masa i naeletrisanje atoma uniformno raspoređeni po zapremini atoma.
* '''1911:''' [[Ernest Raderford|Raderfordov]] ogled sa rasejanjem alfa čestica na zlatnoj foliji kojim je napušten atomski model "pudinga od šljiva" u kojem je sugerisano da su masa i naeletrisanje atoma uniformno raspoređeni po zapremini atoma.
*'''1920:''' [[Oto Štern|Štern]]-[[Valter Gerlah|Gerlah]]ov [[Štern-Gerlahov eksperiment|eksperiment]] kojim je demonstrirana kvantna priroda [[spin]]a čestice.
* '''1920:''' [[Oto Štern|Štern]]-[[Valter Gerlah|Gerlahov]] [[Štern-Gerlahov eksperiment|eksperiment]] kojim je demonstrirana kvantna priroda [[spin]]a čestice.
*'''1927:''' [[Klinton Devison|Devison]] (Clinton Davisson) i [[Lester Džermer|Džermer]] (Lester Germer) pokazuju talasnu prirodu [[elektron]]a<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html The Davisson-Germer experiment, which demonstrates the wave nature of the electron]</ref> in the [[Electron diffraction]] experiment.
* '''1927:''' [[Klinton Devison|Devison]] (Clinton Davisson) i [[Lester Džermer|Džermer]] (Lester Germer) pokazuju talasnu prirodu [[elektron]]a<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html The Davisson-Germer experiment, which demonstrates the wave nature of the electron]</ref> in the [[Electron diffraction]] experiment.
*'''1955:''' [[Klajd Kovan|Kovan]] (Clyde L. Cowan) i [[Frederik Reines|Reines]] (Frederick Reines) potvrđuju postojanje neutrina u neutrinskom eksperimentu.
* '''1955:''' [[Klajd Kovan|Kovan]] (Clyde L. Cowan) i [[Frederik Reines|Reines]] (Frederick Reines) potvrđuju postojanje neutrina u neutrinskom eksperimentu.
*'''1961:''' [[Klaus Jenson|Jenson]]ov (Claus Jönsson) eksperiment sa rasejanjem elektrona na na dvostrukom prorezu.
* '''1961:''' [[Klaus Jenson|Jensonov]] (Claus Jönsson) eksperiment sa rasejanjem elektrona na na dvostrukom prorezu.
*'''1980:''' [[Klaus fon Klicing]]ovo (Klaus von Klitzing) otkriće [[kvantni Halov efekat|kvantnog Halovog efekta]]. Kvantna verzija [[Halov efekat|Halovog efekta]] omogućila je definiciju novog standarda za [[električni otpor]] i vrlo precizno nezavisno određivanje vrednosti [[konstanta fine strukture|konstante fine strukture]].
* '''1980:''' [[Klaus fon Klicing]]ovo (Klaus von Klitzing) otkriće [[kvantni Halov efekat|kvantnog Halovog efekta]]. Kvantna verzija [[Halov efekat|Halovog efekta]] omogućila je definiciju novog standarda za [[električni otpor]] i vrlo precizno nezavisno određivanje vrednosti [[konstanta fine strukture|konstante fine strukture]].




==Vidi još==
== Vidi još ==
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==Literatura==
== Literatura ==
*[[Pol Dirak|P. A. M. Dirac]], ''The Principles of Quantum Mechanics'' (1930) -- the beginning chapters provide a very clear and comprehensible introduction
* [[Pol Dirak|P. A. M. Dirac]], ''The Principles of Quantum Mechanics'' (1930) -- the beginning chapters provide a very clear and comprehensible introduction
*[[David J. Griffiths]], ''Introduction to Quantum Mechanics'', Prentice Hall, 1995. ISBN 0-13-111892-7 -- {{Please check ISBN|0-13-111892-7 -- }} A standard undergraduate level text written in an accessible style.
* [[David J. Griffiths]], ''Introduction to Quantum Mechanics'', Prentice Hall, 1995. ISBN 0-13-111892-7 -- {{Please check ISBN|0-13-111892-7 -- }} A standard undergraduate level text written in an accessible style.
*[[Ričard Fejnman|Richard P. Feynman]], [[Robert B. Leighton]] and Matthew Sands (1965). ''[[The Feynman Lectures on Physics]]'', Addison-Wesley. Richard Feynman's original lectures (given at [[Caltech]] in early 1962) can also be downloaded as an MP3 file from www.audible.com[http://www.audible.com]
* [[Ričard Fejnman|Richard P. Feynman]], [[Robert B. Leighton]] and Matthew Sands (1965). ''[[The Feynman Lectures on Physics]]'', Addison-Wesley. Richard Feynman's original lectures (given at [[Caltech]] in early 1962) can also be downloaded as an MP3 file from www.audible.com[http://www.audible.com]
*[[Hugh Everett]], Relative State Formulation of Quantum Mechanics, ''Reviews of Modern Physics'' vol 29, (1957) pp 454-462.
* [[Hugh Everett]], Relative State Formulation of Quantum Mechanics, ''Reviews of Modern Physics'' vol 29, (1957) pp 454-462.
*[[Bryce DeWitt]], [[R. Neill Graham]], eds, ''The Many-Worlds Interpretation of Quantum Mechanics'', Princeton Series in Physics, [[Princeton University Press]] (1973), ISBN 0-691-08131-X
* [[Bryce DeWitt]], [[R. Neill Graham]], eds, ''The Many-Worlds Interpretation of Quantum Mechanics'', Princeton Series in Physics, [[Princeton University Press]] (1973), ISBN 0-691-08131-X
*Albert Messiah, ''Quantum Mechanics'', English translation by G. M. Temmer of ''Mécanique Quantique'', 1966, John Wiley and Sons, vol. I, chapter IV, section III.
* Albert Messiah, ''Quantum Mechanics'', English translation by G. M. Temmer of ''Mécanique Quantique'', 1966, John Wiley and Sons, vol. I, chapter IV, section III.
*[[Ričard Fejnman|Richard P. Feynman]], ''[[QED (book)|QED: The Strange Theory of Light and Matter]]'' -- a popular science book about quantum mechanics and [[quantum field theory]] that contains many enlightening insights that are interesting for the expert as well
* [[Ričard Fejnman|Richard P. Feynman]], ''[[QED (book)|QED: The Strange Theory of Light and Matter]]'' -- a popular science book about quantum mechanics and [[quantum field theory]] that contains many enlightening insights that are interesting for the expert as well
*Marvin Chester, ''Primer of Quantum Mechanics'', 1987, John Wiley, N.Y. ISBN 0-486-42878-8
* Marvin Chester, ''Primer of Quantum Mechanics'', 1987, John Wiley, N.Y. ISBN 0-486-42878-8
*[[Hagen Kleinert]], ''Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets'', 3th edition, [http://www.worldscibooks.com/physics/5057.html World Scientific (Singapore, 2004)](also available online [http://www.physik.fu-berlin.de/~kleinert/b5 here])
* [[Hagen Kleinert]], ''Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets'', 3th edition, [http://www.worldscibooks.com/physics/5057.html World Scientific (Singapore, 2004)](also available online [http://www.physik.fu-berlin.de/~kleinert/b5 here])
*[[George Mackey]] (2004). ''The mathematical foundations of quantum mechanics''. Dover Publications. ISBN 0-486-43517-2.
* [[George Mackey]] (2004). ''The mathematical foundations of quantum mechanics''. Dover Publications. ISBN 0-486-43517-2.
*{{cite book | author=Griffiths, David J.| title=Introduction to Quantum Mechanics (2nd ed.) | publisher=Prentice Hall |year=2004 |id=ISBN 0-13-805326-X}}
* {{cite book | author=Griffiths, David J.| title=Introduction to Quantum Mechanics (2nd ed.) | publisher=Prentice Hall |year=2004 |id=ISBN 0-13-805326-X}}
*{{cite book | author=Omnes, Roland | title=Understanding Quantum Mechanics | publisher=Princeton University Press |year=1999 |id=ISBN 0-691-00435-8}}
* {{cite book | author=Omnes, Roland | title=Understanding Quantum Mechanics | publisher=Princeton University Press |year=1999 |id=ISBN 0-691-00435-8}}
*J. [[Džon fon Nojman|von Neumann]], ''Mathematical Foundations of Quantum Mechanics'', Princeton University Press, 1955.
* J. [[Džon fon Nojman|von Neumann]], ''Mathematical Foundations of Quantum Mechanics'', Princeton University Press, 1955.
*H. [[Weyl]], ''The Theory of Groups and Quantum Mechanics'', Dover Publications 1950.
* H. [[Weyl]], ''The Theory of Groups and Quantum Mechanics'', Dover Publications 1950.
*[[Max Jammer]], "The Conceptual Development of Quantum Mechanics" (McGraw Hill Book Co., 1966)
* [[Max Jammer]], "The Conceptual Development of Quantum Mechanics" (McGraw Hill Book Co., 1966)
*Gunther Ludwig, "Wave Mechanics" (Pergamon Press, 1968) ISBN 0-08-203204-1
* Gunther Ludwig, "Wave Mechanics" (Pergamon Press, 1968) ISBN 0-08-203204-1
*Albert Messiah, ''Quantum Mechanics'' (Vol. I), English translation from French by G. M. Temmer, fourth printing 1966, North Holland, John Wiley & Sons.
* Albert Messiah, ''Quantum Mechanics'' (Vol. I), English translation from French by G. M. Temmer, fourth printing 1966, North Holland, John Wiley & Sons.
*Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics. ISBN 0-19-530573-6
* Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics. ISBN 0-19-530573-6
*Slobodan Macura, Jelena Radić-Perić, ATOMISTIKA, Fakultet za fizičku hemiju Univerziteta u Beogradu/Službeni list, Beograd, 2004. (stara kvantna teorija i većina utemeljivaćkih eksperimentata)
* Slobodan Macura, Jelena Radić-Perić, ATOMISTIKA, Fakultet za fizičku hemiju Univerziteta u Beogradu/Službeni list, Beograd, 2004. (stara kvantna teorija i većina utemeljivaćkih eksperimentata)




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==Spoljašnje veze==
== Spoljašnje veze ==
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'''Opšte:'''
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*[http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html A history of quantum mechanics]
* [http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html A history of quantum mechanics]
*[http://higgo.com/quantum/laymans.htm A Lazy Layman's Guide to Quantum Physics]
* [http://higgo.com/quantum/laymans.htm A Lazy Layman's Guide to Quantum Physics]
*[http://cam.qubit.org/wiki/index.php/Introduction_to_Quantum_Theory Introduction to Quantum Theory at Quantiki]
* [http://cam.qubit.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]]
* [http://bethe.cornell.edu/ Quantum Physics Made Relatively Simple]: three video lectures by [[Hans Bethe]]
*[http://www.decoherence.de/ Decoherence] by Erich Joos
* [http://www.decoherence.de/ Decoherence] by Erich Joos
*[http://www.canadaconnects.ca/quantumphysics/10050/1074/ Getting Started with Quantum] an Essay for the Uninitiated
* [http://www.canadaconnects.ca/quantumphysics/10050/1074/ Getting Started with Quantum] an Essay for the Uninitiated
*[http://thisquantumworld.com/ht/index.php This Quantum World] What is quantum mechanics trying to tell us about the nature of Nature?
* [http://thisquantumworld.com/ht/index.php This Quantum World] What is quantum mechanics trying to tell us about the nature of Nature?


'''Materijal za kurs:'''
'''Materijal za kurs:'''


*[[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]]: [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: [http://ocw.mit.edu/OcwWeb/Physics/index.htm Physics]. See [http://ocw.mit.edu/OcwWeb/Physics/8-04Quantum-Physics-ISpring2003/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: [http://ocw.mit.edu/OcwWeb/Physics/index.htm Physics]. See [http://ocw.mit.edu/OcwWeb/Physics/8-04Quantum-Physics-ISpring2003/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].
*[http://www.imperial.ac.uk/quantuminformation/qi/tutorials Imperial College Quantum Mechanics Course to Download]
* [http://www.imperial.ac.uk/quantuminformation/qi/tutorials Imperial College Quantum Mechanics Course to Download]
*[http://www.sparknotes.com/testprep/books/sat2/physics/chapter19section3.rhtml Spark Notes - Quantum Physics]
* [http://www.sparknotes.com/testprep/books/sat2/physics/chapter19section3.rhtml Spark Notes - Quantum Physics]


'''Često postavljana pitanja:'''
'''Često postavljana pitanja:'''


*[http://www.hedweb.com/manworld.htm Many-worlds or relative-state interpretation]
* [http://www.hedweb.com/manworld.htm Many-worlds or relative-state interpretation]
*[http://www.mtnmath.com/faq/meas-qm.html Measurement in Quantum mechanics]
* [http://www.mtnmath.com/faq/meas-qm.html Measurement in Quantum mechanics]
*[http://www.thch.uni-bonn.de/tc/people/brems.vincent/vincent/faq.html A short FAQ on quantum resonances]
* [http://www.thch.uni-bonn.de/tc/people/brems.vincent/vincent/faq.html A short FAQ on quantum resonances]


'''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]]'' magazine.
* [http://www.newscientist.com/channel/fundamentals/quantum-world Everything you wanted to know about the quantum world] — archive of articles from ''[[New Scientist]]'' magazine.
*[http://www.sciencedaily.com/news/matter_energy/quantum_physics/ Quantum Physics Research] From ScienceDaily
* [http://www.sciencedaily.com/news/matter_energy/quantum_physics/ Quantum Physics Research] From ScienceDaily
*{{cite news|url=http://www.nytimes.com/2005/12/27/science/27eins.html?ex=1293339600&en=caf5d835203c3500&ei=5090|title=Quantum Trickery: Testing Einstein's Strangest Theory|date=[[December 27]], [[2005]]|publisher=The New York Times}}
* {{cite news|url=http://www.nytimes.com/2005/12/27/science/27eins.html?ex=1293339600&en=caf5d835203c3500&ei=5090|title=Quantum Trickery: Testing Einstein's Strangest Theory|date=[[December 27]], [[2005]]|publisher=The New York Times}}
*[http://www.janes.com/defence/news/jdw/jdw061006_2_n.shtml DARPA eyes quantum mechanics for sensor applications] Jane's Defence Weekly, 6 October 2006
* [http://www.janes.com/defence/news/jdw/jdw061006_2_n.shtml DARPA eyes quantum mechanics for sensor applications] Jane's Defence Weekly, 6 October 2006


'''Filozofija:'''
'''Filozofija:'''


*[http://plato.stanford.edu/entries/qm/ Quantum Mechanics (''Stanford Encyclopedia of Philosophy'')]
* [http://plato.stanford.edu/entries/qm/ Quantum Mechanics (''Stanford Encyclopedia of Philosophy'')]
*[http://www.physicstoday.org/pt/vol-54/iss-2/p11.html David Mermin on the future directions of physics]
* [http://www.physicstoday.org/pt/vol-54/iss-2/p11.html David Mermin on the future directions of physics]
*[http://www.csicop.org/si/9701/quantum-quackery.html "Quantum Physics Quackery"] by Victor Stenger, ''Skeptical Inquirer'' (January/February 1997).
* [http://www.csicop.org/si/9701/quantum-quackery.html "Quantum Physics Quackery"] by Victor Stenger, ''Skeptical Inquirer'' (January/February 1997).
*[http://www.crank.net/quantum.html Crank Dot Net's quantum physics page] &mdash; "cranks, crackpots, kooks & loons on the net"
* [http://www.crank.net/quantum.html Crank Dot Net's quantum physics page] — "cranks, crackpots, kooks & loons on the net"
* [http://www.hinduism.co.za/hinduism.htm Hinduism & Quantum Physics]
* [http://www.hinduism.co.za/hinduism.htm Hinduism & Quantum Physics]
* [http://wwf.edula.com Invariantology and Quantum Physics]
* [http://wwf.edula.com Invariantology and Quantum Physics]
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[[Kategorija:Kvantna mehanika| ]]
[[Kategorija:Kvantna mehanika| ]]


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[[als:Quantenmechanik]]
[[als:Quantenmechanik]]
[[an:Mecanica cuantica]]
[[an:Mecanica cuantica]]
[[ar:ميكانيكا الكم]]
[[ar:ميكانيكا الكم]]
[[az:Kvant mexanikası]]
[[bat-smg:Kvantėnė mekanėka]]
[[bat-smg:Kvantėnė mekanėka]]
[[be:Квантавая механіка]]
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Verzija na datum 20 decembar 2009 u 00:13

Slika. 1: Talasne funkcije elektrona u vodonikovom atomu. Energija raste nadole: n=1,2,3,... i moment impulsa (ugaoni moment) raste s leva na desno: s, p, d,... Svetlija područja odgovaraju većoj verovatnoći gde bi mogao eksperimentalno nađe elektron.

Kvantna mehanika je fundamentalna grana teorijske fizike kojom su zamenjene klasična mehanika i klasična elektrodinamika pri opisivanju atomskih i subatomskih pojava. Ona predstavlja teorijsku podlogu mnogih disciplina fizike i hemije kao što su fizika kondenzovane materije, atomska fizika, molekulska fizika, fizička hemija, kvantna hemija, fizika čestica i nuklearna fizika. Zajedno sa Opštom teorijom relativnosti Kvantna mehanika predstavlja jedan od stubova savremene fizike.


Uvod

Izraz kvant (od latinskog quantum (množina quanta) = količina, mnoštvo, svota, iznos, deo) odnosi se na diskretne jedinice koje teorija pripisuje izvesnim fizičkim veličinama kao što su energija i moment impulsa (ugaoni moment) atoma kao što je pokazano na slici. Otkriće da talasi mogu da se prostiru kao čestice, u malim energijskim paketima koji se nazivaju kvanti dovelo je do pojave nove grane fizike koja se bavi atomskim i subatomskim sistemima a koju danas nazivamo Kvantna mehanika. Temelje kvantnoj mehanici položili su u prvoj polovini dvadesetog veka Verner Hajzenberg, Maks Plank, Luj de Broj, Nils Bor, Ervin Šredinger, Maks Born, Džon fon Nojman, Pol Dirak, Albert Ajnštajn, Volfgang Pauli i brojni drugi poznati fizičari 20. veka. Neki bazični aspekti kvantne mehanike još uvek se aktivno izučavaju.


Teorija

Postoje brojne matematički ekvivalentne formulacije kvantne mehanike. Jedna od najstarijih i najčešće korišćenih je transformaciona teorija koju je predložio Pol Dirak a koja ujedinjuje i uopštava dve ranije formulacije, matričnu mehaniku (koju je uveo Verner Hajzenberg) [1] i talasnu mehaniku (koju je formulisao Ervin Šredinger).


Matematička formulacija

Veza sa drugim naučnim teorijama

Primene

Kvantna mehanika uspeva izvanredno uspešno da objasni brojen fizičke pojave u prirodi. Na primer osobine subatomskih čestica od kojih su sačinjeni svi oblici materije mogu biti potpuno objašnjene preko kvantne mehanike. Isto, kombinovanje atoma u stvaranju molekula i viših oblika organizacije materije može se dosledno objasniti primenom kvantne mehanike iz čega je izrasla kvantna hemija, jedna od disciplina fizičke hemije. Relativistička kvantna mehanika, u principu, može da objasni skoro celokupnu hemiju. Drugim rečima, nema pojave u hemiji koja ne može da bude objašnjena kvantnomehaničkom teorijom.


Filozofske posledice

Zbog brojnih rezultata koji protivureče intuiciji kvantna mehanika je od samog zasnivanja inicirala brojne filozofske debate i tumačenja. Protekle su decenije pre nego što su bili prihvaćeni i neki od temelja kvantne mehanike poput Bornovog tumačenja amplitude verovatnoće.


Istorija

Da bi objasnio spektar zračenja koje emituje crno telo Maks Plank je 1900. godine uveo ideju o diskretnoj, dakle, kvantnoj prirodi energije. Da bi objasnio fotoelektrični efekat Ajnštajn je postulirao da se svetlosna energija prenosi u kvantima koji se danas nazivaju fotonima. Ideja da se energija zračenja prenosi u porcijama (kvantima) predstavlja izvanerdno dostignuće jer je time Plankova formula zračenja crnog tela dobila konačno i svoje fizičko objašnjenje. Godine 1913. Bor je objasnio spektar vodonikovog atoma, opet koristeći kvantizaciju ovog puta i ugaonog momenta. Na sličan način je Luj de Broj 1924. godine izložio teoriju o talasima materije tvrdeći da čestice imaju talasnu prirodu, upotpunjujući Ajnštajnovu sliku o čestičnoj prirodi talasa.



Hronologija utemeljivačkih eksperimenata


Vidi još


Literatura

  • P. A. M. Dirac, The Principles of Quantum Mechanics (1930) -- the beginning chapters provide a very clear and comprehensible introduction
  • David J. Griffiths, Introduction to Quantum Mechanics, Prentice Hall, 1995. ISBN 0-13-111892-7 -- Šablon:Please check ISBN A standard undergraduate level text written in an accessible style.
  • Richard P. Feynman, Robert B. Leighton and Matthew Sands (1965). The Feynman Lectures on Physics, Addison-Wesley. Richard Feynman's original lectures (given at Caltech in early 1962) can also be downloaded as an MP3 file from www.audible.com[1]
  • Hugh Everett, Relative State Formulation of Quantum Mechanics, Reviews of Modern Physics vol 29, (1957) pp 454-462.
  • Bryce DeWitt, R. Neill Graham, eds, The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, Princeton University Press (1973), ISBN 0-691-08131-X
  • Albert Messiah, Quantum Mechanics, English translation by G. M. Temmer of Mécanique Quantique, 1966, John Wiley and Sons, vol. I, chapter IV, section III.
  • Richard P. Feynman, QED: The Strange Theory of Light and Matter -- a popular science book about quantum mechanics and quantum field theory that contains many enlightening insights that are interesting for the expert as well
  • Marvin Chester, Primer of Quantum Mechanics, 1987, John Wiley, N.Y. ISBN 0-486-42878-8
  • Hagen Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3th edition, World Scientific (Singapore, 2004)(also available online here)
  • George Mackey (2004). The mathematical foundations of quantum mechanics. Dover Publications. ISBN 0-486-43517-2.
  • Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X. 
  • Omnes, Roland (1999). Understanding Quantum Mechanics. Princeton University Press. ISBN 0-691-00435-8. 
  • J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.
  • H. Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications 1950.
  • Max Jammer, "The Conceptual Development of Quantum Mechanics" (McGraw Hill Book Co., 1966)
  • Gunther Ludwig, "Wave Mechanics" (Pergamon Press, 1968) ISBN 0-08-203204-1
  • Albert Messiah, Quantum Mechanics (Vol. I), English translation from French by G. M. Temmer, fourth printing 1966, North Holland, John Wiley & Sons.
  • Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics. ISBN 0-19-530573-6
  • Slobodan Macura, Jelena Radić-Perić, ATOMISTIKA, Fakultet za fizičku hemiju Univerziteta u Beogradu/Službeni list, Beograd, 2004. (stara kvantna teorija i većina utemeljivaćkih eksperimentata)


Beleške

  1. ↑ Nakon što je 1932. godine Hajzenberg dobio Nobelovu nagradu za stvaranje kvantne mehanike uloga Maksa Borna u tome bila je umanjena. Biografija Maksa Borna iz 2005. detaljno opisuje njegovu ulogu u stvaranju matrične mehanike. To je i sam Hajzenberg priznao 1950. godine u radu posvećenom Maksu Planku. Videti: Nancy Thorndike Greenspan, “The End of the Certain World: The Life and Science of Max Born (Basic Books, 2005), pp. 124 - 128, and 285 - 286.
  2. ↑ The Davisson-Germer experiment, which demonstrates the wave nature of the electron

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