Kvantna mehanika – razlika između verzija
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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. |
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. |
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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 ([[: |
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). |
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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 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]]. |
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Verzija na datum 3 januar 2011 u 09:02
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
- ~ 1805: Tomas Jungov eksperiment sa dvostrukim prorezom kojim je demonstrirana talasna priroda svetlosti.
- 1896: Anri Bekerelov pronalazak radioaktivnosti.
- 1897: Džozef Džon Tomsonovo otkriće elektrona i njegovog negativnog naeletrisanja u eksperimentima sa katodnom cevi.
- 1850-1900: Ispitivanje zračenja crnog tela koje nije moglo da se objasni bez kvantnog koncepta.
- 1905: Fotoelektrični efekat: Ajnštajnovo objašnjenje efekta (za šta je i dobio Nobelovu nagradu za fiziku) uvođenjem koncepta fotona, čestice svetlosti sa kvantiranom energijom.
- 1909: Robert Milikenov eksperiment sa kapljicama ulja koji je pokazao da je eletrično naeletrisanje javlja u diskretnim (kvantiranim) porcijama.
- 1911: 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: Štern-Gerlahov eksperiment kojim je demonstrirana kvantna priroda spina čestice.
- 1927: Devison (Clinton Davisson) i Džermer (Lester Germer) pokazuju talasnu prirodu elektrona[2] in the Electron diffraction experiment.
- 1955: Kovan (Clyde L. Cowan) i Reines (Frederick Reines) potvrđuju postojanje neutrina u neutrinskom eksperimentu.
- 1961: Jensonov (Claus Jönsson) eksperiment sa rasejanjem elektrona na na dvostrukom prorezu.
- 1980: Klaus fon Klicingovo (Klaus von Klitzing) otkriće kvantnog Halovog efekta. Kvantna verzija Halovog efekta omogućila je definiciju novog standarda za električni otpor i vrlo precizno nezavisno određivanje vrednosti konstante fine strukture.
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
- ↑ 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.
- ↑ The Davisson-Germer experiment, which demonstrates the wave nature of the electron
Spoljašnje veze
Opšte:
- A history of quantum mechanics
- A Lazy Layman's Guide to Quantum Physics
- Introduction to Quantum Theory at Quantiki
- Quantum Physics Made Relatively Simple: three video lectures by Hans Bethe
- Decoherence by Erich Joos
- Getting Started with Quantum an Essay for the Uninitiated
- This Quantum World What is quantum mechanics trying to tell us about the nature of Nature?
Materijal za kurs:
- MIT OpenCourseWare: Chemistry. See 5.61, 5.73, and 5.74
- MIT OpenCourseWare: Physics. See 8.04, 8.05, and 8.06.
- Imperial College Quantum Mechanics Course to Download
- Spark Notes - Quantum Physics
Često postavljana pitanja:
- Many-worlds or relative-state interpretation
- Measurement in Quantum mechanics
- A short FAQ on quantum resonances
Media:
- Everything you wanted to know about the quantum world — archive of articles from New Scientist magazine.
- Quantum Physics Research From ScienceDaily
- „Quantum Trickery: Testing Einstein's Strangest Theory”. The New York Times. December 27, 2005.
- DARPA eyes quantum mechanics for sensor applications Jane's Defence Weekly, 6 October 2006
Filozofija:
- Quantum Mechanics (Stanford Encyclopedia of Philosophy)
- David Mermin on the future directions of physics
- "Quantum Physics Quackery" by Victor Stenger, Skeptical Inquirer (January/February 1997).
- Crank Dot Net's quantum physics page — "cranks, crackpots, kooks & loons on the net"
- Hinduism & Quantum Physics
- Invariantology and Quantum Physics
- "Hidden Variables in Quantum Theory: The Hidden Cultural Variables of their Rejection." Online article.