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{{Kvantna mehanika}}
[[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.]]
 
[[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).-->]]
 
'''Kvantna mehanika''' je fundamentalna grana [[teorijska fizika|teorijske fizike]] kojom su zamenjene [[klasična mehanika]] i [[Elektromagnetizam|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 [[Opšta teorija relativnosti|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) [[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}}
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.
 
In the formalism of quantum mechanics, the state of a system at a given time is described by a [[complex number|complex]] [[wave function]] (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex [[vector space]]. 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 cannot ever make simultaneous predictions of [[conjugate variables]], such as position and momentum, with arbitrary 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 conceptualise where the electron might be located with the most probability. It should be stressed that the electron itself is not spread out over such cloud regions. It is either in a particular region of space, or it is not. Heisenberg's [[uncertainty principle]] quantifies the inability to precisely locate the particle.
 
The other [[exemplar]] that led to quantum mechanics was the study of [[electromagnetic wave]]s 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 [[Photon polarization|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 [[superconductivity|superconductors]] and [[superfluid]]s.
 
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—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]].-->
 
== 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]]).
 
<!--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).
 
Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about [[probability distribution]]s; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. These are known as "eigenstates" of the observable ("eigen" meaning "own" in [[German language|German]]). In the everyday world, it is natural and intuitive to think of everything being in an eigenstate of every observable. Everything appears to have a definite position, a definite momentum, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values for the position or momentum of a certain particle in a given space in a finite time, but, rather, it only provides a range of probabilities of where that particle might be. Therefore, it became necessary to use different words for a) the state of something having an uncertainty relation and b) a state that has a definite value. The latter is called the "eigenstate" of the property being measured.
 
A concrete example will be useful here. Let us consider a [[free particle]]. In quantum mechanics, there is [[wave-particle duality]] so the properties of the particle can be described as a wave. Therefore, its [[quantum state]] can be represented as a [[wave]], of arbitrary shape and extending over all of space, called a [[wave function|wavefunction]]. The position and momentum of the particle are observables. The [[Uncertainty Principle]] of quantum mechanics states that both the position and the momentum cannot simultaneously be known with infinite precision at the same time. However, we can measure just the position alone of a moving free particle creating an eigenstate of position with a wavefunction that is [[Dirac delta function|very large]] at a particular position ''x'', and zero everywhere else. If we perform a position measurement on such a wavefunction, we will obtain the result ''x'' with 100% probability. In other words, we will know the position of the free particle. This is called an eigenstate of position. If the particle is in an eigenstate of position then its momentum is completely unknown. An eigenstate of momentum, on the other hand, has the form of a [[plane wave]]. It can be shown that the [[wavelength]] is equal to ''h/p'', where ''h'' is [[Planck's constant]] and ''p'' is the momentum of the [[eigenstate]]. If the particle is in an eigenstate of momentum then its position is completely blurred out.
 
Usually, a system will not be in an eigenstate of whatever observable we are interested in. However, if we measure the observable, the wavefunction will instantaneously be an eigenstate of that observable. This process is known as [[wavefunction collapse]]. It involves expanding the system under study to include the measurement device, so that a detailed quantum calculation would no longer be feasible and a classical description must be used. If we know the wavefunction at the instant before the measurement, we will be able to compute the probability of collapsing into each of the possible eigenstates. For example, the free particle in our previous example will usually have a wavefunction that is a [[wave packet]] centered around some mean position ''x<sub>0</sub>'', neither an eigenstate of position nor of momentum. When we measure the position of the particle, it is impossible for us to predict with certainty the result that we will obtain. It is probable, but not certain, that it will be near ''x<sub>0</sub>'', where the amplitude of the wavefunction is large. After we perform the measurement, obtaining some result ''x'', the wavefunction collapses into a position eigenstate centered at ''x''.
 
Wave functions can change as time progresses. An equation known as the [[Schrödinger equation]] describes how wave functions change in time, a role similar to [[Newton's second law]] in classical mechanics. The Schrödinger equation, applied to our free particle, predicts that the center of a wave packet will move through space at a constant velocity, like a classical particle with no forces acting on it. However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain. This also has the effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave packets that are no longer position eigenstates.
 
Some wave functions produce probability distributions that are constant in time. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single [[electron]] in an unexcited [[atom]] is pictured classically as a particle moving in a circular trajectory around the [[atomic nucleus]], whereas in quantum mechanics it is described by a static, [[spherical coordinate system|spherically symmetric]] wavefunction surrounding the nucleus ([[:Datoteka:HAtomOrbitals.png|Fig. 1]]). (Note that only the lowest angular momentum states, labeled ''s'', are spherically symmetric).
 
The time evolution of wave functions is [[determinism|deterministic]] in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a [[quantum measurement|measurement]], the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., [[random]].
 
The [[probability|probabilistic]] nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous [[Bohr-Einstein debates]], in which the two scientists attempted to clarify these fundamental principles by way of thought experiments. In the decades after the formulation of quantum mechanics, the question of what constitutes a "measurement" has been extensively studied. [[Interpretation of quantum mechanics|Interpretations]] of quantum mechanics have been formulated to do away with the concept of "wavefunction collapse"; see, for example, the [[relative state interpretation]]. The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become [[entangled]], so that the original quantum system ceases to exist as an independent entity. For details, see the article on [[measurement in quantum mechanics]].-->
 
=== Matematička formulacija ===
<!--
{{Main|Mathematical formulation of quantum mechanics}}
{{See also|Quantum logic}}
 
In the mathematically rigorous formulation of quantum mechanics, developed by [[Paul Dirac]] and [[John von Neumann]], the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors") residing in a [[complex number|complex]] [[Separable space|separable]] [[Hilbert space]] (variously called the "state space" or the "associated Hilbert space" of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the [[projective space|projectivization]] of a Hilbert space. The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of [[square-integrable]] functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a densely defined [[Hermitian]] (or [[self-adjoint operator|self-adjoint]]) linear [[operator]] acting on the state space. Each eigenstate of an observable corresponds to an [[eigenvector]] of the operator, and the associated [[eigenvalue]] corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can only attain those discrete eigenvalues.
 
The time evolution of a quantum state is described by the [[Schrödinger equation]], in which the [[Hamiltonian (quantum mechanics)|Hamiltonian]], the [[Operator (physics)|operator]] corresponding to the total energy of the system, generates time evolution.
 
The [[inner product]] between two state vectors is a complex number known as a [[probability amplitude]]. During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the [[absolute value]] of the probability amplitudes between the initial and final states. The possible results of a measurement are the eigenvalues of the operator - which explains the choice of ''Hermitian'' operators, for which all the eigenvalues are real. We can find the probability distribution of an observable in a given state by computing the [[spectral theorem|spectral decomposition]] of the corresponding operator. Heisenberg's [[uncertainty principle]] is represented by the statement that the operators corresponding to certain observables do not [[Commutator|commute]].
 
The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its [[phase (waves)|phase]] encodes information about the [[interference]] between quantum states. This gives rise to the wave-like behavior of quantum states.
 
It turns out that analytic solutions of Schrödinger's equation are only available for a small number of model Hamiltonians, of which the [[quantum harmonic oscillator]], the particle in a box, the hydrogen-molecular '''ion''' and the [[hydrogen atom]] are the most important representatives. Even the [[helium]] atom, which contains just one more electron than hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions. For instance, in the method known as [[perturbation theory (quantum mechanics)|perturbation theory]] one uses the analytic results for a simple quantum mechanical model to generate results for a more complicated model related to the simple model by, for example, the addition of a weak [[potential energy]]. Another method is the "semi-classical equation of motion" approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of [[quantum chaos]].
 
An alternative formulation of quantum mechanics is [[Feynman]]'s [[path integral formulation]], in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of [[action principle]]s in classical mechanics.-->
 
=== 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.
 
{{unsolved|physics|In the [[correspondence limit]] of '''quantum mechanics''': Is there a preferred interpretation of quantum mechanics? How does the quantum description of [[reality]], which includes elements such as the [[superposition]] of states and [[wavefunction collapse]], give rise to the reality we [[perception|perceive]]?}}
When quantum mechanics was originally formulated, it was applied to models whose
correspondence limit was [[theory of relativity|non-relativistic]] [[classical mechanics]]. For instance, the well-known model of the [[quantum harmonic oscillator]] uses an explicitly non-relativistic expression for the [[kinetic energy]] of the oscillator, and is thus a quantum version of the [[harmonic oscillator|classical harmonic oscillator]].
 
Early attempts to merge quantum mechanics with [[special relativity]] involved the replacement of the Schrödinger equation with a covariant equation such as the [[Klein-Gordon equation]] or the [[Dirac equation]]. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of [[quantum field theory]], which applies quantization to a field rather than a fixed set of particles. The first complete quantum field theory, [[quantum electrodynamics]], provides a fully quantum description of the [[electromagnetism|electromagnetic interaction]].
 
The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one employed since the inception of quantum mechanics, is to treat [[electric charge|charged]] particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the [[hydrogen atom]] describes the electric field of the hydrogen atom using a classical <math>-\frac{e^2}{4 \pi\ \epsilon_0\ } \frac{1}{r}</math> Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of [[photon]]s by charged particles.
 
Quantum field theories for the [[strong nuclear force]] and the [[weak nuclear force]] have been developed. The quantum field theory of the strong nuclear force is called [[quantum chromodynamics]], and describes the interactions of the subnuclear particles: [[quark]]s and [[gluon]]s. The [[weak nuclear force]] and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory known as [[electroweak force|electroweak theory]].
 
It has proven difficult to construct quantum models of [[gravity]], the remaining [[fundamental force]]. Semi-classical approximations are workable, and have led to predictions such as [[Hawking radiation]]. However, the formulation of a complete theory of [[quantum gravity]] is hindered by apparent incompatibilities between [[general relativity]], the most accurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as [[string theory]] are among the possible candidates for a future theory of quantum gravity.-->
 
== Primene ==
Kvantna mehanika uspeva izvanredno uspešno da objasni brojen fizičke pojave u prirodi. Na primer osobine [[Subatomske čestice|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 [[fizička hemija|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.
 
<!--Much of modern [[technology]] operates at a scale where quantum effects are significant. 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]].
 
Researchers are currently seeking robust methods of directly manipulating quantum states. Efforts are being made to develop [[quantum cryptography]], which will allow guaranteed secure transmission of [[information]]. A more distant goal is the development of [[quantum computer]]s, which are expected to perform certain computational tasks exponentially faster than classical [[computer]]s. Another active research topic is [[quantum teleportation]], which deals with techniques to transmit quantum states over arbitrary distances.-->
 
== 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 [[Maks Born|Bornovog]] tumačenja [[amplituda verovatnoće|amplitude verovatnoće]].
<!--Main article: ''[[Interpretation of quantum mechanics]]''-->
 
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 [[Maks Born|Bornovog]] tumačenja [[amplituda verovatnoće|amplitude verovatnoće]].
 
<!--The [[Copenhagen interpretation]], due largely to the Danish theoretical physicist [[Niels Bohr]], is the interpretation of quantum mechanics most widely accepted amongst physicists. According to it, the probabilistic nature of quantum mechanics predictions cannot be explained in terms of some other deterministic theory, and does not simply reflect our limited knowledge. Quantum mechanics provides [[probabilistic]] results because the physical universe is itself probabilistic rather than [[Determinism|deterministic]].
 
[[Albert Einstein]], himself one of the founders of quantum theory, disliked this loss of determinism in measurement (Hence his famous quote "God does not play dice with the universe."). He held that there should be a [[local hidden variable theory]] underlying quantum mechanics and consequently the present theory was incomplete. He produced a series of objections to the theory, the most famous of which has become known as the [[EPR paradox]]. [[John Stewart Bell|John Bell]] showed that the EPR paradox led to experimentally testable differences between quantum mechanics and local hidden variable theories. Experiments have been taken as confirming that quantum mechanics is correct and the real world cannot be described in terms of such hidden variables. "[[Bell test loopholes|Potential loopholes]]" in the experiments, however, mean that the question is still not quite settled.
 
The writer [[C.S. Lewis]] viewed QM as incomplete, because notions of indeterminism did not agree with his religious beliefs.<ref>[http://www.hawking.org.uk/lectures/dice.html]</ref> Lewis, a professor of English, was of the opinion that the [[Heisenberg uncertainty principle]] was more of an [[Epistemology|epistemic]] limitation than an indication of [[Ontology|ontological]] indeterminacy, and in this respect believed similarly to many advocates of hidden variables theories. The ''[[Bohr-Einstein debates]]'' provide a vibrant critique of the Copenhagen Interpretation from an epistemological point of view.
 
The [[Everett many-worlds interpretation]], formulated in 1956, holds that all the possibilities described by quantum theory simultaneously occur in a "[[Multiverse (science)|multiverse]]" composed of mostly independent parallel universes. This is not accomplished by introducing some new axiom to quantum mechanics, but on the contrary by ''removing'' the axiom of the collapse of the wave packet: All the possible consistent states of the measured system and the measuring apparatus (including the observer) are present in a ''real'' physical (not just formally mathematical, as in other interpretations) [[quantum superposition]]. (Such a superposition of consistent state combinations of different systems is called an [[entangled state]].) While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we can observe only the universe, i.e. the consistent state contribution to the mentioned superposition, we inhabit. Everett's interpretation is perfectly consistent with [[John Stewart Bell|John Bell]]'s experiments and makes them intuitively understandable. However, according to the theory of [[quantum decoherence]], the parallel universes will never be accessible for us, making them physically meaningless. This inaccessiblity can be understood as follows: once a measurement is done, the measured system becomes [[entanglement|entangled]] with both the physicist who measured it and a huge number of other particles, some of which are [[photon]]s flying away towards the other end of the universe; in order to prove that the wave function did not collapse one would have to bring all these particles back and measure them again, together with the system that was measured originally. This is completely impractical, but even if one can theoretically do this, it would destroy any evidence that the original measurement took place (including the physicist's memory).-->
 
== 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]] [[Albert Ajnštajn|Ajnštajn]] je postulirao da se svetlosna energija prenosi u kvantima koji se danas nazivaju [[foton]]ima. 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. [[Nils Bor|Bor]] je objasnio [[spektar]] vodonikovog atoma, opet koristeći kvantizaciju ovog puta i ugaonog momenta. Na sličan način je [[Luj de Brolj|Luj de Broj]] 1924. godine izložio teoriju o talasima materije tvrdeći da čestice imaju talasnu prirodu, upotpunjujući Ajnštajnovu sliku o čestičnoj prirodi talasa.
 
<!--
These theories, though successful, were strictly [[phenomenology (science)|phenomenological]]: there was no rigorous justification for quantization (aside, perhaps, for [[Henri Poincaré]]'s discussion of Planck's theory in his 1912 paper ''Sur la théorie des quanta''). They are collectively known as the ''old quantum theory''.
The phrase "quantum physics" was first used in Johnston's ''Planck's Universe in Light of Modern Physics''.-->
 
<!--Modern quantum mechanics was born in 1925, when the German physicist [[Werner Heisenberg|Heisenberg]] developed [[matrix mechanics]] and the Austrian physicist [[Erwin Schrödinger|Schrödinger]] invented [[wave mechanics]] and the non-relativistic Schrödinger equation. Schrödinger subsequently showed that the two approaches were equivalent.-->
<!--Heisenberg formulated his [[uncertainty principle]] in 1927, and the Copenhagen interpretation took shape at about the same time. Starting around 1927, [[Paul Dirac]] began the process of unifying quantum mechanics with [[special relativity]] by proposing the [[Dirac equation]] for the [[electron]]. He also pioneered the use of operator theory, including the influential [[bra-ket notation]], as described in his famous 1930 textbook. During the same period, Hungarian polymath [[John von Neumann]] formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces, as described in his likewise famous 1932 textbook. These, like many other works from the founding period still stand, and remain widely used.-->
<!--The field of [[quantum chemistry]] was pioneered by physicists [[Walter Heitler]] and [[Fritz London]], who published a study of the [[covalent bond]] of the [[hydrogen molecule]] in 1927. Quantum chemistry was subsequently developed by a large number of workers, including the American theoretical chemist [[Linus Pauling]] at Cal Tech, and John Slater into various theories such as Molecular Orbital Theory or Valence Theory.-->
<!--Beginning in 1927, attempts were made to apply quantum mechanics to fields rather than single particles, resulting in what are known as [[Quantum field theory|quantum field theories]]. Early workers in this area included [[Paul Dirac|Dirac]], [[Wolfgang Pauli|Pauli]], [[Victor Weisskopf|Weisskopf]], and [[Pascual Jordan|Jordan]]. This area of research culminated in the formulation of [[quantum electrodynamics]] by [[Richard Feynman|Feynman]], [[Freeman Dyson|Dyson]], [[Julian Schwinger|Schwinger]], and [[Sin-Itiro Tomonaga|Tomonaga]] during the 1940s. Quantum electrodynamics is a quantum theory of [[electron]]s, [[positron]]s, and the [[electromagnetic field]], and served as a role model for subsequent quantum field theories.-->
<!--The theory of [[quantum chromodynamics]] was formulated beginning in the early 1960s. The theory as we know it today was formulated by [[H. David Politzer|Politzer]], [[David J. Gross|Gross]] and [[Frank Wilczek|Wilzcek]] in 1975. Building on pioneering work by [[Julian Schwinger|Schwinger]], [[Peter Higgs|Higgs]], [[Jeffrey Goldstone|Goldstone]], [[Sheldon Lee Glashow|Glashow]], [[Steven Weinberg|Weinberg]] and [[Abdus Salam|Salam]] independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single [[electroweak force]].-->
 
=== Hronologija utemeljivačkih eksperimenata ===
 
== Vidi još ==
* [[Polarizacija fotona]]
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* [[Kvantna hemija]]
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<!--*[[Interpretation of quantum mechanics]]
*[[Measurement in quantum mechanics]]
*[[Photon dynamics in the double-slit experiment]]
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<!--*[[Quantum electrochemistry]]
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* [[Kvantni računar]]i
* [[Kvantna elektronika]]
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* [[Kvantna teorija polja]]
* [[Teorijska hemija]]
<!--*[[Quantum information]]
 
*[[Quantum mind]]
== Beleške ==
*[[Quantum thermodynamics]]
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*[[Theoretical and experimental justification for the Schrödinger equation]]
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<!--*[[The Pondicherry interpretation of quantum mechanics]]
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== Literatura ==
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* [[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.
* 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).
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== Beleške ==
<references/>
 
== Eksterni linkovi ==
{{Commonscat|Quantum mechanics}}
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{{Commons2|Quantum mechanics}}
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'''Opšte:'''
* [http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_Quantum_age_begins.html A history of quantum mechanics]
 
{{Opće grane u fizici}}
 
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