Toʻlqin funksiyasi

Yakka spinsiz zarra uchun klassik va kvant garmonik osilator tushunchalarini solishtirish. Ikki jarayon juda katta farq qiladi. Klassik jarayon (A-B) zarrachaning traektoriya bo'ylab harakati sifatida namoyon bo'ladi. Kvant jarayoni (C–H) bunday traektoriyaga ega emas. Aksincha, u to'lqin sifatida ifodalanadi; bu erda vertikal o'q to'lqin funktsiyasining haqiqiy qismini (ko'k) va xayoliy qismini (qizil) ko'rsatadi. Panellar (C–F) Shredinger tenglamasining toʻrt xil toʻlqinli yechimini koʻrsatadi. Panellar (G-H) qo'shimcha ravishda Shredinger tenglamasining yechimlari bo'lgan, ammo turg'un to'lqinlar bo'lmagan ikki xil to'lqin funktsiyasini ko'rsatadi.

• Arons, A. B.; Peppard, M. B. (1965). "Einstein's proposal of the photon concept: A translation of the Annalen der Physik paper of 1905". American Journal of Physics 33 (5): 367. doi:10.1119/1.1971542. http://astro1.panet.utoledo.edu/~ljc/PE_eng.pdf. 
• Atkins, P. W.. Quanta: A Handbook of Concepts, 1974. ISBN 978-0-19-855494-3. 
• Bohr, N.. Niels Bohr - Collected Works: Foundations of Quantum Physics I (1926 - 1932) Kalckar: . Amsterdam: North Holland, 1985. ISBN 978-044453289-3. 
• Born, M. (1926a). "Zur Quantenmechanik der Stoßvorgange". Z. Phys. 37 (12): 863–867. doi:10.1007/bf01397477. 
• Born, M. (1926b). "Quantenmechanik der Stoßvorgange". Z. Phys. 38 (11–12): 803–827. doi:10.1007/bf01397184. 
• Born, M. (1927). "Physical aspects of quantum mechanics". Nature 119 (2992): 354–357. doi:10.1038/119354a0. 
• Born, M. (11 December 1954). "The statistical interpretation of quantum mechanics". Nobel Lecture (Nobel Foundation) 122 (3172): 675–9. doi:10.1126/science.122.3172.675. PMID 17798674. https://www.nobelprize.org/prizes/physics/1954/born/lecture/. 
• de Broglie, L. (1923). "Radiations—Ondes et quanta [Radiation—Waves and quanta]" (fr). Comptes Rendus 177: 507–510, 548, 630.  Online copy (French) Online copy (English)
• de Broglie, L.. Non-linear Wave Mechanics: a Causal Interpretation. Amsterdam: Elsevier, 1960. 
• Byron, F. W.. Mathematics of Classical and Quantum Physics, revised, Dover Books on Physics, Dover Publications [First published 1969], 1992. ISBN 978-0-486-67164-2. 
• Camilleri, K.. Heisenberg and the Interpretation of Quantum Mechanics: the Physicist as Philosopher. Cambridge UK: Cambridge University Press, 2009. ISBN 978-0-521-88484-6. 
• Conway, J. B.. A Course in Functional Analysis, Graduate Texts in Mathematics. Springer Verlag, 1990. ISBN 978-0-387-97245-9. 
• Dirac, P. A. M. (1939). "A new notation for quantum mechanics". Mathematical Proceedings of the Cambridge Philosophical Society 35 (3): 416–418. doi:10.1017/S0305004100021162. 
• Dirac, P. A. M.. The principles of quantum mechanics, 4th, The international series on monographs on physics, Oxford University Press, 1982. ISBN 0-19-852011-5. 
• Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" (de). Annalen der Physik 17 (6): 132–148. doi:10.1002/andp.19053220607. 
• Einstein, A. (1916). "Zur Quantentheorie der Strahlung". Mitteilungen der Physikalischen Gesellschaft Zürich 18: 47–62. 
• Einstein, A. (1917). "Zur Quantentheorie der Strahlung" (de). Physikalische Zeitschrift 18: 121–128. 
• Einstein, A.. Albert Einstein: Philosopher-Scientist, 3rd, The Library of Living Philosophers Schilpp: , La Salle Publishing Company, Illinois: Open Court, 1998. ISBN 978-0-87548-133-3. 
• Eisberg, R.. Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, 2nd, John Wiley & Sons, 1985. ISBN 978-0-471-87373-0. 
• Greiner, W.. Quantum Electrodynamics, 4th, springer, 2008. ISBN 978-354087560-4. 
• Griffiths, D. J.. Introduction to Quantum Mechanics, 2nd, Essex England: Pearson Education, 2004. ISBN 978-013111892-8. 
• Griffiths, David. Introduction to elementary particles. Wiley-VCH, 2008 — 162ff bet. ISBN 978-3-527-40601-2. 
• ter Haar, D.. The Old Quantum Theory. Pergamon Press, 1967 — 167–183 bet. 
• 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
• Heisenberg, W.. Physics and Philosophy: the Revolution in Modern Science. New York: Harper & Row, 1958. 
• Jaynes, E. T.. Probability Theory: The Logic of Science Larry: . Cambridge University Press, 2003. ISBN 978-0-521 59271-0. 
• Landau, L.D.. Quantum Mechanics: Non-Relativistic Theory, 3rd, Pergamon Press, 1977. ISBN 978-0-08-020940-1.  Online copy
• Lerner, R.G.. Encyclopaedia of Physics, 2nd, VHC Publishers, 1991. ISBN 978-0-89573-752-6. 
• Ludwig, G.. Wave Mechanics. Oxford UK: Pergamon Press, 1968. ISBN 978-0-08-203204-5. 
• Martin, B.R.. Particle Physics, 3rd, Manchester Physics Series, John Wiley & Sons, 2008. ISBN 978-0-470-03294-7. 
• Murdoch, D.. Niels Bohr's Philosophy of Physics. Cambridge UK: Cambridge University Press, 1987. ISBN 978-0-521-33320-7. 
• Newton, R.G.. Quantum Physics: a Text for Graduate Student. New York: Springer, 2002. ISBN 978-0-387-95473-8. 
• Pauli, Wolfgang (1927). "Zur Quantenmechanik des magnetischen Elektrons" (de). Zeitschrift für Physik 43 (9–10): 601–623. doi:10.1007/bf01397326. 
• Peleg, Y.. Quantum mechanics, 2nd, Schaum's outlines, McGraw Hill, 2010. ISBN 978-0-07-162358-2. 
• Rae, A.I.M.. Quantum Mechanics, 5th, Taylor & Francis Group, 2008. ISBN 978-1-5848-89700. 
• Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and Molecules". Physical Review 28 (6): 1049–1070. doi:10.1103/PhysRev.28.1049. Archived from the original on 17 December 2008. https://web.archive.org/web/20081217040121/http://home.tiscali.nl/physis/HistoricPaper/Schroedinger/Schroedinger1926c.pdf. 
• Shankar, R.. Principles of Quantum Mechanics, 2nd, 1994. ISBN 978-030644790-7. 
• Tipler, P. A.. Physics for Scientists and Engineers – with Modern Physics, 6th, 2008. ISBN 978-0-7167-8964-2. 
• Weinberg, S. (2002), The Quantum Theory of Fields, 1-jild, Cambridge University Press, ISBN 978-0-521-55001-7
• Weinberg, S. (2013), Lectures in Quantum Mechanics, Cambridge University Press, ISBN 978-1-107-02872-2
• Wheeler, J.A.. Quantum Theory and Measurement. Princeton NJ: Princeton University Press, 1983. 
• Young, H. D.. Sears' and Zemansky's University Physics, 12th Pearson: , Addison-Wesley, 2008. ISBN 978-0-321-50130-1. 
• Zettili, N.. Quantum Mechanics: Concepts and Applications, 2nd, 2009. ISBN 978-0-470-02679-3. 
• Zwiebach, Barton. A First Course in String Theory. Cambridge University Press, 2009. ISBN 978-0-521-88032-9.