Talasna funkcija

Poređenje pojmova klasičnog i kvantno harmonijskog oscilatora za pojedinačne bezspinske čestice. Ova dva procesa se veoma razlikuju. Klasični proces (A–B) predstavljen je kao kretanje čestice duž putanje. Kvantni proces (C–H) nema takvu putanju. Umesto toga, ona je predstavljena kao talas; ovde, vertikalna osa prikazuje realni deo (plavo) i imaginarni deo (crveno) talasne funkcije. Paneli (C–F) prikazuju četiri različita rešenja stojećeg talasa Šredingerove jednačine. Paneli (G–H) dalje prikazuju dve različite talasne funkcije koje su rešenja Šredingerove jednačine, ali nisu stojeći talasi.

Talasna funkcija u kvantnoj fizici je matematički opis kvantnog stanja izolovanog kvantnog sistema. Talasna funkcija je kompleksna amplituda verovatnoće, i iz nje se mogu izvesti verovatnoće za moguće rezultate merenja u sistemu. Najčešći simboli za talasnu funkciju su grčka slova ψ ili Ψ (malo i veliko psi, respektivno). Talasna funkcija je funkcija čiji stepeni slobode korespondiraju nekom maksimalnom skupu komutacionih opservacija. Kada se jednom odabere takva reprezentacija, talasna funkcija može biti izvedena iz kvantnog stanja.

Za dati sistem, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier transform. Some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom; other discrete variables can also be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g., a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g., z-component of spin) – these values are often displayed in a column matrix (e.g., a 2 × 1 column vector for a non-relativistic electron with spin ​¹⁄₂).

Prema superposition principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions and form a Hilbert space. The inner product between two wave functions is a measure of the overlap between the corresponding physical states, and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality. However, the wave function in quantum mechanics describes a kind of physical phenomenon, still open to different interpretations, which fundamentally differs from that of classic mechanical waves.

U Borovoj statističkoj interpretaciji u nerelativističkoj kvantnoj mehanici, the squared modulus of the wave function, |ψ|², is a real number interpreted as the probability density of measuring a particle's being detected at a given place – or having a given momentum – at a given time, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation. This general requirement that a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured—its value does not, in isolation, tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.

Literatura

• Atkins, P. W. (1974). Quanta: A Handbook of Concepts. ISBN 978-0-19-855494-3. 
• Arons, A. B.; Peppard, M. B. (1965). „Einstein's proposal of the photon concept: A translation of the Annalen der Physik paper of 1905” (PDF). American Journal of Physics. 33 (5): 367. Bibcode:1965AmJPh..33..367A. doi:10.1119/1.1971542. 
• Bohr, N. (1985). J. Kalckar, ур. Niels Bohr - Collected Works: Foundations of Quantum Physics I (1926 - 1932). 6. Amsterdam: North Holland. ISBN 9780444532893. 
• Born, M. (1926a). „Zur Quantenmechanik der Stoßvorgange”. Z. Phys. 37 (12): 863—867. Bibcode:1926ZPhy...37..863B. doi:10.1007/bf01397477. 
• Born, M. (1926b). „Quantenmechanik der Stoßvorgange”. Z. Phys. 38 (11–12): 803—827. Bibcode:1926ZPhy...38..803B. doi:10.1007/bf01397184. 
• Born, M. (1927). „Physical aspects of quantum mechanics”. Nature. 119 (2992): 354—357. Bibcode:1927Natur.119..354B. doi:10.1038/119354a0. 
• Born, M. (1954). „The statistical interpretation of quantum mechanics” (PDF). Nobel Lecture. 11. 12. 1954. CS1 одржавање: Формат датума (веза)
• de Broglie, L. (1923). „Radiations—Ondes et quanta” [Radiation—Waves and quanta]. Comptes Rendus (на језику: French). 177: 507—510, 548, 630. CS1 одржавање: Непрепознат језик (веза) Online copy (French) Online copy (English)
• de Broglie, L. (1960). Non-linear Wave Mechanics: a Causal Interpretation. Amsterdam: Elsevier. 
• Camilleri, K. (2009). Heisenberg and the Interpretation of Quantum Mechanics: the Physicist as Philosopher. Cambridge UK: Cambridge University Press. ISBN 978-0-521-88484-6. 
• Byron, F. W.; Fuller, R. W. (1992) [1969]. Mathematics of Classical and Quantum Physics. Dover Books on Physics (revised изд.). Dover Publications. ISBN 978-0-486-67164-2. 
• Conway, J. B. (1990). A Course in Functional Analysis. Graduate Texts in Mathematics. 96. Springer Verlag. ISBN 978-0-387-97245-9. 
• Dirac, P. A. M. (1982). The principles of quantum mechanics. The international series on monographs on physics (4th изд.). Oxford University Press. ISBN 0 19 852011 5. 
• Dirac, P. A. M. (1939). „A new notation for quantum mechanics”. Mathematical Proceedings of the Cambridge Philosophical Society. 35 (3): 416—418. Bibcode:1939PCPS...35..416D. doi:10.1017/S0305004100021162. 
• Einstein, A. (1905). „Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”. Annalen der Physik (на језику: German). 17 (6): 132—148. Bibcode:1905AnP...322..132E. doi:10.1002/andp.19053220607. CS1 одржавање: Непрепознат језик (веза)
• Einstein, A. (1916). „Zur Quantentheorie der Strahlung”. Mitteilungen der Physikalischen Gesellschaft Zürich. 18: 47—62. 
• Einstein, A. (1917). „Zur Quantentheorie der Strahlung”. Physikalische Zeitschrift (на језику: German). 18: 121—128. Bibcode:1917PhyZ...18..121E. CS1 одржавање: Непрепознат језик (веза)
• Einstein, A. (1998). P. A. Schlipp, ур. Albert Einstein: Philosopher-Scientist. The Library of Living Philosophers. VII (3rd изд.). La Salle Publishing Company, Illinois: Open Court. ISBN 978-0-87548-133-3. 
• Eisberg, R.; Resnick, R. (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (2nd изд.). John Wiley & Sons. ISBN 978-0-471-87373-0. 
• Greiner, W.; Reinhardt, J. (2008). Quantum Electrodynamics (4th изд.). springer. ISBN 9783540875604. 
• Griffiths, D. J. (2004). Introduction to Quantum Mechanics (2nd изд.). Essex England: Pearson Education Ltd. ISBN 978-0131118928. 
• Heisenberg, W. (1958). Physics and Philosophy: the Revolution in Modern Science. New York: Harper & Row. 
• Hanle, P.A. (1977), „Erwin Schrodinger's Reaction to Louis de Broglie's Thesis on the Quantum Theory.”, Isis, 68 (4): 606—609, doi:10.1086/351880 
• Jaynes, E. T. (2003). G. Larry Bretthorst, ур. Probability Theory: The Logic of Science. Cambridge University Press. ISBN 978-0-521 59271-0. 
• Landau, L.D.; Lifshitz, E. M. (1977). Quantum Mechanics: Non-Relativistic Theory. Vol. 3 (3rd изд.). Pergamon Press. ISBN 978-0-08-020940-1.  Online copy
• Lerner, R.G.; Trigg, G.L. (1991). Encyclopaedia of Physics (2nd изд.). VHC Publishers. ISBN 978-0-89573-752-6. 
• Ludwig, G. (1968). Wave Mechanics. Oxford UK: Pergamon Press. ISBN 978-0-08-203204-5. LCCN 66-30631. 
• Murdoch, D. (1987). Niels Bohr's Philosophy of Physics. Cambridge UK: Cambridge University Press. ISBN 978-0-521-33320-7. 
• Newton, R.G. (2002). Quantum Physics: a Text for Graduate Student. New York: Springer. ISBN 978-0-387-95473-8. 
• Pauli, Wolfgang (1927). „Zur Quantenmechanik des magnetischen Elektrons”. Zeitschrift für Physik (на језику: German). 43 (9–10): 601—623. Bibcode:1927ZPhy...43..601P. doi:10.1007/bf01397326. CS1 одржавање: Непрепознат језик (веза)
• Peleg, Y.; Pnini, R.; Zaarur, E.; Hecht, E. (2010). Quantum mechanics. Schaum's outlines (2nd изд.). McGraw Hill. ISBN 978-0-07-162358-2. 
• Rae, A.I.M. (2008). Quantum Mechanics. 2 (5th изд.). Taylor & Francis Group. ISBN 978-1-5848-89700. 
• Schrödinger, E. (1926). „An Undulatory Theory of the Mechanics of Atoms and Molecules” (PDF). Physical Review. 28 (6): 1049—1070. Bibcode:1926PhRv...28.1049S. doi:10.1103/PhysRev.28.1049. Архивирано из оригинала (PDF) 17. 12. 2008. г. CS1 одржавање: Формат датума (веза)
• Shankar, R. (1994). Principles of Quantum Mechanics (2nd изд.). ISBN 978-0306447907. 
• Martin, B.R.; Shaw, G. (2008). Particle Physics. Manchester Physics Series (3rd изд.). John Wiley & Sons. ISBN 978-0-470-03294-7. 
• ter Haar, D. (1967). The Old Quantum Theory. Pergamon Press. стр. 167—183. LCCN 66029628. 
• Tipler, P. A.; Mosca, G.; Freeman (2008). Physics for Scientists and Engineers – with Modern Physics (6th изд.). ISBN 978-0-7167-8964-2. 
• Weinberg, S. (2013), Lectures in Quantum Mechanics, Cambridge University Press, ISBN 978-1-107-02872-2 
• Weinberg, S. (2002), The Quantum Theory of Fields, 1, Cambridge University Press, ISBN 978-0-521-55001-7 
• Young, H. D.; Freedman, R. A. (2008). Pearson, ур. Sears' and Zemansky's University Physics (12th изд.). Addison-Wesley. ISBN 978-0-321-50130-1. 
• Wheeler, J.A.; Zurek, W.H. (1983). Quantum Theory and Measurement. Princeton NJ: Princeton University Press. 
• Zettili, N. (2009). Quantum Mechanics: Concepts and Applications (2nd изд.). ISBN 978-0-470-02679-3. 
• Zwiebach, Barton (2009). A First Course in String Theory. Cambridge University Press. ISBN 978-0-521-88032-9. 
• Yong-Ki Kim (2. 9. 2000). „Practical Atomic Physics” (PDF). National Institute of Standards and Technology: 1 (55 pages). Архивирано из оригинала (PDF) 22. 7. 2011. г. Приступљено 2010-08-17. CS1 одржавање: Формат датума (веза)
• Polkinghorne, John (2002). Quantum Theory, A Very Short Introduction. Oxford University Press. ISBN 978-0-19-280252-1. 

Spoljašnje veze

• Quantum Mechanics for Engineers
• Spin wave functions NYU
• Identical Particles Revisited, Michael Fowler
• The Nature of Many-Electron Wavefunctions
• Quantum Mechanics and Quantum Computation at BerkeleyX
• Einstein, The quantum theory of radiation