Uncertainty principle (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Uncertainty principle" in English language version.

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Aharonov, Y.; Bohm, D. (June 1, 1961). "Time in the Quantum Theory and the Uncertainty Relation for Time and Energy" (PDF). Physical Review. 122 (5): 1649–1658. Bibcode:1961PhRv..122.1649A. doi:10.1103/PhysRev.122.1649. Archived from the original (PDF) on 2014-01-09. Retrieved 2012-01-21.

agilescientific.com

Matt Hall, "What is the Gabor uncertainty principle?" Archived 2018-02-09 at the Wayback Machine

aip.org

pubs.aip.org

Hilgevoord, Jan (1996-12-01). "The uncertainty principle for energy and time". American Journal of Physics. 64 (12): 1451–1456. Bibcode:1996AmJPh..64.1451H. doi:10.1119/1.18410. ISSN 0002-9505. Archived from the original on 2024-02-23. Retrieved 2023-11-12.
Davidson, Ernest R. (1965-02-15). "On Derivations of the Uncertainty Principle". The Journal of Chemical Physics. 42 (4): 1461–1462. Bibcode:1965JChPh..42.1461D. doi:10.1063/1.1696139. ISSN 0021-9606. Archived from the original on 2024-02-23. Retrieved 2024-01-20.
Cassidy, David; Saperstein, Alvin M. (2009), "Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb", Physics Today, 63 (1), New York: Bellevue Literary Press: 185, Bibcode:2010PhT....63a..49C, doi:10.1063/1.3293416, archived from the original on Jan 4, 2024

ams.org

mathscinet.ams.org

Folland, Gerald; Sitaram, Alladi (May 1997), "The Uncertainty Principle: A Mathematical Survey", Journal of Fourier Analysis and Applications, 3 (3): 207–238, doi:10.1007/BF02649110, MR 1448337, S2CID 121355943

aps.org

link.aps.org

Lynch, F. J.; Holland, R. E.; Hamermesh, M. (1960-10-15). "Time Dependence of Resonantly Filtered Gamma Rays from Fe 57". Physical Review. 120 (2): 513–520. doi:10.1103/PhysRev.120.513. ISSN 0031-899X.
Bohm, Arno R.; Sato, Yoshihiro (2005-04-28). "Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution". Physical Review D. 71 (8): 085018. arXiv:hep-ph/0412106. Bibcode:2005PhRvD..71h5018B. doi:10.1103/PhysRevD.71.085018. ISSN 1550-7998. S2CID 119417992.
Peres, Asher; Terno, Daniel R. (2004-01-06). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123 [111]. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Archived from the original on 2024-02-23. Retrieved 2024-01-25.

aps.org

"This Month in Physics History". www.aps.org. Archived from the original on 2011-01-30. Retrieved 2023-11-04.

archive.org

Landau, Lev Davidovich; Lifshitz, Evgeny Mikhailovich (1977). Quantum Mechanics: Non-Relativistic Theory. Vol. 3 (3rd ed.). Pergamon Press. ISBN 978-0-08-020940-1.
Frauenfelder, H. (1962). The Mössbauer Effect. W. A. Benjamin. p. 66. LCCN 61018181.
Tipler, Paul A.; Llewellyn, Ralph A. (1999), Modern Physics, vol. 3, W.H. Freeman & Co., p. 3, ISBN 978-1572591646, LCCN 98046099
Mehra, Jagdish; Rechenberg, Helmut (2001), The Historical Development of Quantum Theory, Springer, ISBN 978-0-387-95086-0

arxiv.org

See Appendix B in Bialynicki-Birula, Iwo; Bialynicka-Birula, Zofia (2009), "Why photons cannot be sharply localized", Physical Review A, 79 (3): 7–8, arXiv:0903.3712, Bibcode:2009PhRvA..79c2112B, doi:10.1103/PhysRevA.79.032112, S2CID 55632217
Bohm, Arno R.; Sato, Yoshihiro (2005-04-28). "Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution". Physical Review D. 71 (8): 085018. arXiv:hep-ph/0412106. Bibcode:2005PhRvD..71h5018B. doi:10.1103/PhysRevD.71.085018. ISSN 1550-7998. S2CID 119417992.
Ozawa, Masanao (2003), "Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement", Physical Review A, 67 (4): 42105, arXiv:quant-ph/0207121, Bibcode:2003PhRvA..67d2105O, doi:10.1103/PhysRevA.67.042105, S2CID 42012188
Rozema, L. A.; Darabi, A.; Mahler, D. H.; Hayat, A.; Soudagar, Y.; Steinberg, A. M. (2012). "Violation of Heisenberg's Measurement–Disturbance Relationship by Weak Measurements". Physical Review Letters. 109 (10): 100404. arXiv:1208.0034v2. Bibcode:2012PhRvL.109j0404R. doi:10.1103/PhysRevLett.109.100404. PMID 23005268. S2CID 37576344.
Maccone, Lorenzo; Pati, Arun K. (31 December 2014). "Stronger Uncertainty Relations for All Incompatible Observables". Physical Review Letters. 113 (26): 260401. arXiv:1407.0338. Bibcode:2014PhRvL.113z0401M. doi:10.1103/PhysRevLett.113.260401. PMID 25615288. S2CID 21334130.
Huang, Yichen (10 August 2012). "Variance-based uncertainty relations". Physical Review A. 86 (2): 024101. arXiv:1012.3105. Bibcode:2012PhRvA..86b4101H. doi:10.1103/PhysRevA.86.024101. S2CID 118507388.
Tóth, Géza; Fröwis, Florian (31 January 2022). "Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices". Physical Review Research. 4 (1): 013075. arXiv:2109.06893. Bibcode:2022PhRvR...4a3075T. doi:10.1103/PhysRevResearch.4.013075. S2CID 237513549.
Tóth, Géza; Petz, Dénes (20 March 2013). "Extremal properties of the variance and the quantum Fisher information". Physical Review A. 87 (3): 032324. arXiv:1109.2831. Bibcode:2013PhRvA..87c2324T. doi:10.1103/PhysRevA.87.032324. S2CID 55088553.
Yu, Sixia (2013). "Quantum Fisher Information as the Convex Roof of Variance". arXiv:1302.5311 [quant-ph].
Fröwis, Florian; Schmied, Roman; Gisin, Nicolas (2 July 2015). "Tighter quantum uncertainty relations following from a general probabilistic bound". Physical Review A. 92 (1): 012102. arXiv:1409.4440. Bibcode:2015PhRvA..92a2102F. doi:10.1103/PhysRevA.92.012102. S2CID 58912643.
Curtright, T.; Zachos, C. (2001). "Negative Probability and Uncertainty Relations". Modern Physics Letters A. 16 (37): 2381–2385. arXiv:hep-th/0105226. Bibcode:2001MPLA...16.2381C. doi:10.1142/S021773230100576X. S2CID 119669313.
Giovannetti, V.; Lloyd, S.; Maccone, L. (2011). "Advances in quantum metrology". Nature Photonics. 5 (4): 222. arXiv:1102.2318. Bibcode:2011NaPho...5..222G. doi:10.1038/nphoton.2011.35. S2CID 12591819.; arXiv Archived 2020-08-06 at the Wayback Machine
Luis, Alfredo (2017-03-13). "Breaking the weak Heisenberg limit". Physical Review A. 95 (3): 032113. arXiv:1607.07668. Bibcode:2017PhRvA..95c2113L. doi:10.1103/PhysRevA.95.032113. ISSN 2469-9926. S2CID 55838380.
Busch, P.; Lahti, P.; Werner, R. F. (2013). "Proof of Heisenberg's Error-Disturbance Relation". Physical Review Letters. 111 (16): 160405. arXiv:1306.1565. Bibcode:2013PhRvL.111p0405B. doi:10.1103/PhysRevLett.111.160405. PMID 24182239. S2CID 24507489.
Busch, P.; Lahti, P.; Werner, R. F. (2014). "Heisenberg uncertainty for qubit measurements". Physical Review A. 89 (1): 012129. arXiv:1311.0837. Bibcode:2014PhRvA..89a2129B. doi:10.1103/PhysRevA.89.012129. S2CID 118383022.
Erhart, J.; Sponar, S.; Sulyok, G.; Badurek, G.; Ozawa, M.; Hasegawa, Y. (2012). "Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin measurements". Nature Physics. 8 (3): 185–189. arXiv:1201.1833. Bibcode:2012NatPh...8..185E. doi:10.1038/nphys2194. S2CID 117270618.
Ringbauer, M.; Biggerstaff, D.N.; Broome, M.A.; Fedrizzi, A.; Branciard, C.; White, A.G. (2014). "Experimental Joint Quantum Measurements with Minimum Uncertainty". Physical Review Letters. 112 (2): 020401. arXiv:1308.5688. Bibcode:2014PhRvL.112b0401R. doi:10.1103/PhysRevLett.112.020401. PMID 24483993. S2CID 18730255.
Björk, G.; Söderholm, J.; Trifonov, A.; Tsegaye, T.; Karlsson, A. (1999). "Complementarity and the uncertainty relations". Physical Review. A60 (3): 1878. arXiv:quant-ph/9904069. Bibcode:1999PhRvA..60.1874B. doi:10.1103/PhysRevA.60.1874. S2CID 27371899.
Fujikawa, Kazuo (2012). "Universally valid Heisenberg uncertainty relation". Physical Review A. 85 (6): 062117. arXiv:1205.1360. Bibcode:2012PhRvA..85f2117F. doi:10.1103/PhysRevA.85.062117. S2CID 119640759.
Huang, Yichen (24 May 2011). "Entropic uncertainty relations in multidimensional position and momentum spaces". Physical Review A. 83 (5): 052124. arXiv:1101.2944. Bibcode:2011PhRvA..83e2124H. doi:10.1103/PhysRevA.83.052124. S2CID 119243096.
Chafaï, D. (2003), "Gaussian maximum of entropy and reversed log-Sobolev inequality", Séminaire de Probabilités XXXVI, Lecture Notes in Mathematics, vol. 1801, pp. 194–200, arXiv:math/0102227, doi:10.1007/978-3-540-36107-7_5, ISBN 978-3-540-00072-3, S2CID 17795603
Chiew, Shao-Hen; Gessner, Manuel (31 January 2022). "Improving sum uncertainty relations with the quantum Fisher information". Physical Review Research. 4 (1): 013076. arXiv:2109.06900. Bibcode:2022PhRvR...4a3076C. doi:10.1103/PhysRevResearch.4.013076. S2CID 237513883.
Terence Tao (2005), "An uncertainty principle for cyclic groups of prime order", Mathematical Research Letters, 12 (1): 121–127, arXiv:math/0308286, doi:10.4310/MRL.2005.v12.n1.a11, S2CID 8548232
Jaming, Ph. (2007), "Nazarov's uncertainty principles in higher dimension", J. Approx. Theory, 149 (1): 30–41, arXiv:math/0612367, doi:10.1016/j.jat.2007.04.005, S2CID 9794547
Bonami, A.; Demange, B.; Jaming, Ph. (2003), "Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms", Rev. Mat. Iberoamericana, 19: 23–55, arXiv:math/0102111, Bibcode:2001math......2111B, doi:10.4171/RMI/337, S2CID 1211391
Hedenmalm, Haakan (2012), "Heisenberg's uncertainty principle in the sense of Beurling", Journal d'Analyse Mathématique, 118 (2): 691–702, arXiv:1203.5222, Bibcode:2012arXiv1203.5222H, doi:10.1007/s11854-012-0048-9, S2CID 54533890
Hänggi, Esther; Wehner, Stephanie (2013). "A violation of the uncertainty principle implies a violation of the second law of thermodynamics". Nature Communications. 4: 1670. arXiv:1205.6894. Bibcode:2013NatCo...4.1670H. doi:10.1038/ncomms2665. PMID 23575674. S2CID 205316392.
Peres, Asher; Terno, Daniel R. (2004-01-06). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123 [111]. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Archived from the original on 2024-02-23. Retrieved 2024-01-25.

books.google.com

Naber, Gregory L. (2021). Quantum Mechanics: An Introduction to the Physical Background and Mathematical Structure. Walter de Gruyter GmbH & Co KG. p. 230. ISBN 978-3-11-075194-9. Archived from the original on 2024-02-23. Retrieved 2024-01-20.
Enz, Charles Paul; von Meyenn, Karl (1994). Writings on Physics and Philosophy by Wolfgang Pauli. Translated by Robert Schlapp. Springer-Verlag. p. 43. ISBN 3-540-56859-X. Archived from the original on 2020-08-19. Retrieved 2018-02-10.

cambridge.org

Griffiths, David J.; Schroeter, Darrell F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press. Bibcode:2018iqm..book.....G. doi:10.1017/9781316995433. ISBN 978-1-316-99543-3. Archived from the original on 2024-02-23. Retrieved 2024-01-27.

currentscience.ac.in

Sen, D. (2014). "The Uncertainty relations in quantum mechanics" (PDF). Current Science. 107 (2): 203–218. Archived (PDF) from the original on 2019-09-24. Retrieved 2016-02-14.

doi.org

Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Dolling, Lisa M.; Gianelli, Arthur F.; Statile, Glenn N., eds. (2003). The Tests of Time. doi:10.1515/9781400889167. ISBN 978-1400889167.
Kennard, E. H. (1927), "Zur Quantenmechanik einfacher Bewegungstypen", Zeitschrift für Physik (in German), 44 (4–5): 326–352, Bibcode:1927ZPhy...44..326K, doi:10.1007/BF01391200, S2CID 121626384.
Jaeger, Gregg (September 2014). "What in the (quantum) world is macroscopic?". American Journal of Physics. 82 (9): 896–905. Bibcode:2014AmJPh..82..896J. doi:10.1119/1.4878358.
See Appendix B in Bialynicki-Birula, Iwo; Bialynicka-Birula, Zofia (2009), "Why photons cannot be sharply localized", Physical Review A, 79 (3): 7–8, arXiv:0903.3712, Bibcode:2009PhRvA..79c2112B, doi:10.1103/PhysRevA.79.032112, S2CID 55632217
Busch, Paul (2002). "The Time-Energy Uncertainty Relation". In Muga, J. G.; Mayato, R. Sala; Egusquiza, I. L. (eds.). Time in Quantum Mechanics. Lecture Notes in Physics. Vol. 72. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 69–98. doi:10.1007/3-540-45846-8_3. ISBN 978-3-540-43294-4.
Wigner, E. P. (1997). "On the Time–Energy Uncertainty Relation". In Wightman, Arthur S. (ed.). Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 538–548. doi:10.1007/978-3-662-09203-3_58. ISBN 978-3-642-08179-8.
Hilgevoord, Jan (1996-12-01). "The uncertainty principle for energy and time". American Journal of Physics. 64 (12): 1451–1456. Bibcode:1996AmJPh..64.1451H. doi:10.1119/1.18410. ISSN 0002-9505. Archived from the original on 2024-02-23. Retrieved 2023-11-12.
Lynch, F. J.; Holland, R. E.; Hamermesh, M. (1960-10-15). "Time Dependence of Resonantly Filtered Gamma Rays from Fe 57". Physical Review. 120 (2): 513–520. doi:10.1103/PhysRev.120.513. ISSN 0031-899X.
Bohm, Arno R.; Sato, Yoshihiro (2005-04-28). "Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution". Physical Review D. 71 (8): 085018. arXiv:hep-ph/0412106. Bibcode:2005PhRvD..71h5018B. doi:10.1103/PhysRevD.71.085018. ISSN 1550-7998. S2CID 119417992.
The broad linewidth of fast-decaying states makes it difficult to accurately measure the energy of the state, and researchers have even used detuned microwave cavities to slow down the decay rate, to get sharper peaks. Gabrielse, Gerald; H. Dehmelt (1985). "Observation of Inhibited Spontaneous Emission". Physical Review Letters. 55 (1): 67–70. Bibcode:1985PhRvL..55...67G. doi:10.1103/PhysRevLett.55.67. PMID 10031682.
Hilgevoord, Jan (March 2005). "Time in quantum mechanics: a story of confusion". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 36 (1): 29–60. Bibcode:2005SHPMP..36...29H. doi:10.1016/j.shpsb.2004.10.002. Archived from the original on 2022-10-23. Retrieved 2024-01-28.
Bohm, Arno (January 2011). "Resonances/decaying states and the mathematics of quantum physics". Reports on Mathematical Physics. 67 (3): 279–303. Bibcode:2011RpMP...67..279B. doi:10.1016/S0034-4877(11)60018-9. Archived from the original on 2023-12-04. Retrieved 2024-01-24.
Aharonov, Y.; Bohm, D. (June 1, 1961). "Time in the Quantum Theory and the Uncertainty Relation for Time and Energy" (PDF). Physical Review. 122 (5): 1649–1658. Bibcode:1961PhRv..122.1649A. doi:10.1103/PhysRev.122.1649. Archived from the original (PDF) on 2014-01-09. Retrieved 2012-01-21.
Griffiths, David J.; Schroeter, Darrell F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press. Bibcode:2018iqm..book.....G. doi:10.1017/9781316995433. ISBN 978-1-316-99543-3. Archived from the original on 2024-02-23. Retrieved 2024-01-27.
Ozawa, Masanao (2003), "Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement", Physical Review A, 67 (4): 42105, arXiv:quant-ph/0207121, Bibcode:2003PhRvA..67d2105O, doi:10.1103/PhysRevA.67.042105, S2CID 42012188
Wheeler, John Archibald (1978-01-01), Marlow, A. R. (ed.), "The 'Past' and the 'Delayed-Choice' Double-Slit Experiment", Mathematical Foundations of Quantum Theory, Academic Press, pp. 9–48, doi:10.1016/b978-0-12-473250-6.50006-6, ISBN 978-0-12-473250-6, archived from the original on 2022-12-10, retrieved 2023-07-19
Wheeler, John Archibald (1977), Lopes, José Leite; Paty, Michel (eds.), "Include the Observer in the Wave Function?", Quantum Mechanics, A Half Century Later: Papers of a Colloquium on Fifty Years of Quantum Mechanics, Held at the University Louis Pasteur, Strasbourg, May 2–4, 1974, Episteme, Dordrecht: Springer Netherlands, pp. 1–18, doi:10.1007/978-94-010-1196-9_1, ISBN 978-94-010-1196-9, archived from the original on 2024-02-23, retrieved 2023-07-19
Rozema, L. A.; Darabi, A.; Mahler, D. H.; Hayat, A.; Soudagar, Y.; Steinberg, A. M. (2012). "Violation of Heisenberg's Measurement–Disturbance Relationship by Weak Measurements". Physical Review Letters. 109 (10): 100404. arXiv:1208.0034v2. Bibcode:2012PhRvL.109j0404R. doi:10.1103/PhysRevLett.109.100404. PMID 23005268. S2CID 37576344.
De Broglie, Louis (October 1923). "Waves and Quanta". Nature. 112 (2815): 540. Bibcode:1923Natur.112..540D. doi:10.1038/112540a0. ISSN 1476-4687. S2CID 186242764.
Robertson, H. P. (1929), "The Uncertainty Principle", Phys. Rev., 34 (1): 163–164, Bibcode:1929PhRv...34..163R, doi:10.1103/PhysRev.34.163
Davidson, E. R. (1965), "On Derivations of the Uncertainty Principle", J. Chem. Phys., 42 (4): 1461–1462, Bibcode:1965JChPh..42.1461D, doi:10.1063/1.1696139
Jackiw, Roman (1968), "Minimum Uncertainty Product, Number-Phase Uncertainty Product, and Coherent States", J. Math. Phys., 9 (3): 339–346, Bibcode:1968JMP.....9..339J, doi:10.1063/1.1664585
Carruthers, P.; Nieto, M. M. (1968), "Phase and Angle Variables in Quantum Mechanics", Rev. Mod. Phys., 40 (2): 411–440, Bibcode:1968RvMP...40..411C, doi:10.1103/RevModPhys.40.411
Maccone, Lorenzo; Pati, Arun K. (31 December 2014). "Stronger Uncertainty Relations for All Incompatible Observables". Physical Review Letters. 113 (26): 260401. arXiv:1407.0338. Bibcode:2014PhRvL.113z0401M. doi:10.1103/PhysRevLett.113.260401. PMID 25615288. S2CID 21334130.
Huang, Yichen (10 August 2012). "Variance-based uncertainty relations". Physical Review A. 86 (2): 024101. arXiv:1012.3105. Bibcode:2012PhRvA..86b4101H. doi:10.1103/PhysRevA.86.024101. S2CID 118507388.
Tóth, Géza; Fröwis, Florian (31 January 2022). "Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices". Physical Review Research. 4 (1): 013075. arXiv:2109.06893. Bibcode:2022PhRvR...4a3075T. doi:10.1103/PhysRevResearch.4.013075. S2CID 237513549.
Tóth, Géza; Petz, Dénes (20 March 2013). "Extremal properties of the variance and the quantum Fisher information". Physical Review A. 87 (3): 032324. arXiv:1109.2831. Bibcode:2013PhRvA..87c2324T. doi:10.1103/PhysRevA.87.032324. S2CID 55088553.
Fröwis, Florian; Schmied, Roman; Gisin, Nicolas (2 July 2015). "Tighter quantum uncertainty relations following from a general probabilistic bound". Physical Review A. 92 (1): 012102. arXiv:1409.4440. Bibcode:2015PhRvA..92a2102F. doi:10.1103/PhysRevA.92.012102. S2CID 58912643.
Curtright, T.; Zachos, C. (2001). "Negative Probability and Uncertainty Relations". Modern Physics Letters A. 16 (37): 2381–2385. arXiv:hep-th/0105226. Bibcode:2001MPLA...16.2381C. doi:10.1142/S021773230100576X. S2CID 119669313.
Likharev, K. K.; A. B. Zorin (1985), "Theory of Bloch-Wave Oscillations in Small Josephson Junctions", J. Low Temp. Phys., 59 (3/4): 347–382, Bibcode:1985JLTP...59..347L, doi:10.1007/BF00683782, S2CID 120813342
Davidson, Ernest R. (1965-02-15). "On Derivations of the Uncertainty Principle". The Journal of Chemical Physics. 42 (4): 1461–1462. Bibcode:1965JChPh..42.1461D. doi:10.1063/1.1696139. ISSN 0021-9606. Archived from the original on 2024-02-23. Retrieved 2024-01-20.
Giovannetti, V.; Lloyd, S.; Maccone, L. (2011). "Advances in quantum metrology". Nature Photonics. 5 (4): 222. arXiv:1102.2318. Bibcode:2011NaPho...5..222G. doi:10.1038/nphoton.2011.35. S2CID 12591819.; arXiv Archived 2020-08-06 at the Wayback Machine
Luis, Alfredo (2017-03-13). "Breaking the weak Heisenberg limit". Physical Review A. 95 (3): 032113. arXiv:1607.07668. Bibcode:2017PhRvA..95c2113L. doi:10.1103/PhysRevA.95.032113. ISSN 2469-9926. S2CID 55838380.
Busch, P.; Lahti, P.; Werner, R. F. (2013). "Proof of Heisenberg's Error-Disturbance Relation". Physical Review Letters. 111 (16): 160405. arXiv:1306.1565. Bibcode:2013PhRvL.111p0405B. doi:10.1103/PhysRevLett.111.160405. PMID 24182239. S2CID 24507489.
Busch, P.; Lahti, P.; Werner, R. F. (2014). "Heisenberg uncertainty for qubit measurements". Physical Review A. 89 (1): 012129. arXiv:1311.0837. Bibcode:2014PhRvA..89a2129B. doi:10.1103/PhysRevA.89.012129. S2CID 118383022.
Erhart, J.; Sponar, S.; Sulyok, G.; Badurek, G.; Ozawa, M.; Hasegawa, Y. (2012). "Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin measurements". Nature Physics. 8 (3): 185–189. arXiv:1201.1833. Bibcode:2012NatPh...8..185E. doi:10.1038/nphys2194. S2CID 117270618.
Baek, S.-Y.; Kaneda, F.; Ozawa, M.; Edamatsu, K. (2013). "Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation". Scientific Reports. 3: 2221. Bibcode:2013NatSR...3E2221B. doi:10.1038/srep02221. PMC 3713528. PMID 23860715.
Ringbauer, M.; Biggerstaff, D.N.; Broome, M.A.; Fedrizzi, A.; Branciard, C.; White, A.G. (2014). "Experimental Joint Quantum Measurements with Minimum Uncertainty". Physical Review Letters. 112 (2): 020401. arXiv:1308.5688. Bibcode:2014PhRvL.112b0401R. doi:10.1103/PhysRevLett.112.020401. PMID 24483993. S2CID 18730255.
Björk, G.; Söderholm, J.; Trifonov, A.; Tsegaye, T.; Karlsson, A. (1999). "Complementarity and the uncertainty relations". Physical Review. A60 (3): 1878. arXiv:quant-ph/9904069. Bibcode:1999PhRvA..60.1874B. doi:10.1103/PhysRevA.60.1874. S2CID 27371899.
Fujikawa, Kazuo (2012). "Universally valid Heisenberg uncertainty relation". Physical Review A. 85 (6): 062117. arXiv:1205.1360. Bibcode:2012PhRvA..85f2117F. doi:10.1103/PhysRevA.85.062117. S2CID 119640759.
Judge, D. (1964), "On the uncertainty relation for angle variables", Il Nuovo Cimento, 31 (2): 332–340, Bibcode:1964NCim...31..332J, doi:10.1007/BF02733639, S2CID 120553526
Bouten, M.; Maene, N.; Van Leuven, P. (1965), "On an uncertainty relation for angle variables", Il Nuovo Cimento, 37 (3): 1119–1125, Bibcode:1965NCim...37.1119B, doi:10.1007/BF02773197, S2CID 122838645
Louisell, W. H. (1963), "Amplitude and phase uncertainty relations", Physics Letters, 7 (1): 60–61, Bibcode:1963PhL.....7...60L, doi:10.1016/0031-9163(63)90442-6
Hirschman, I. I. Jr. (1957), "A note on entropy", American Journal of Mathematics, 79 (1): 152–156, doi:10.2307/2372390, JSTOR 2372390.
Beckner, W. (1975), "Inequalities in Fourier analysis", Annals of Mathematics, 102 (6): 159–182, doi:10.2307/1970980, JSTOR 1970980, PMC 432369, PMID 16592223.
Bialynicki-Birula, I.; Mycielski, J. (1975), "Uncertainty Relations for Information Entropy in Wave Mechanics", Communications in Mathematical Physics, 44 (2): 129–132, Bibcode:1975CMaPh..44..129B, doi:10.1007/BF01608825, S2CID 122277352, archived from the original on 2021-02-08, retrieved 2021-08-17
Huang, Yichen (24 May 2011). "Entropic uncertainty relations in multidimensional position and momentum spaces". Physical Review A. 83 (5): 052124. arXiv:1101.2944. Bibcode:2011PhRvA..83e2124H. doi:10.1103/PhysRevA.83.052124. S2CID 119243096.
Chafaï, D. (2003), "Gaussian maximum of entropy and reversed log-Sobolev inequality", Séminaire de Probabilités XXXVI, Lecture Notes in Mathematics, vol. 1801, pp. 194–200, arXiv:math/0102227, doi:10.1007/978-3-540-36107-7_5, ISBN 978-3-540-00072-3, S2CID 17795603
Chiew, Shao-Hen; Gessner, Manuel (31 January 2022). "Improving sum uncertainty relations with the quantum Fisher information". Physical Review Research. 4 (1): 013076. arXiv:2109.06900. Bibcode:2022PhRvR...4a3076C. doi:10.1103/PhysRevResearch.4.013076. S2CID 237513883.
Folland, Gerald; Sitaram, Alladi (May 1997), "The Uncertainty Principle: A Mathematical Survey", Journal of Fourier Analysis and Applications, 3 (3): 207–238, doi:10.1007/BF02649110, MR 1448337, S2CID 121355943
Donoho, D.L.; Stark, P.B (1989). "Uncertainty principles and signal recovery". SIAM Journal on Applied Mathematics. 49 (3): 906–931. doi:10.1137/0149053.
Terence Tao (2005), "An uncertainty principle for cyclic groups of prime order", Mathematical Research Letters, 12 (1): 121–127, arXiv:math/0308286, doi:10.4310/MRL.2005.v12.n1.a11, S2CID 8548232
Amrein, W.O.; Berthier, A.M. (1977), "On support properties of L^p-functions and their Fourier transforms", Journal of Functional Analysis, 24 (3): 258–267, doi:10.1016/0022-1236(77)90056-8.
Benedicks, M. (1985), "On Fourier transforms of functions supported on sets of finite Lebesgue measure", J. Math. Anal. Appl., 106 (1): 180–183, doi:10.1016/0022-247X(85)90140-4
Jaming, Ph. (2007), "Nazarov's uncertainty principles in higher dimension", J. Approx. Theory, 149 (1): 30–41, arXiv:math/0612367, doi:10.1016/j.jat.2007.04.005, S2CID 9794547
Hardy, G.H. (1933), "A theorem concerning Fourier transforms", Journal of the London Mathematical Society, 8 (3): 227–231, doi:10.1112/jlms/s1-8.3.227
Hörmander, L. (1991), "A uniqueness theorem of Beurling for Fourier transform pairs", Ark. Mat., 29 (1–2): 231–240, Bibcode:1991ArM....29..237H, doi:10.1007/BF02384339, S2CID 121375111
Bonami, A.; Demange, B.; Jaming, Ph. (2003), "Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms", Rev. Mat. Iberoamericana, 19: 23–55, arXiv:math/0102111, Bibcode:2001math......2111B, doi:10.4171/RMI/337, S2CID 1211391
Hedenmalm, Haakan (2012), "Heisenberg's uncertainty principle in the sense of Beurling", Journal d'Analyse Mathématique, 118 (2): 691–702, arXiv:1203.5222, Bibcode:2012arXiv1203.5222H, doi:10.1007/s11854-012-0048-9, S2CID 54533890
Cassidy, David; Saperstein, Alvin M. (2009), "Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb", Physics Today, 63 (1), New York: Bellevue Literary Press: 185, Bibcode:2010PhT....63a..49C, doi:10.1063/1.3293416, archived from the original on Jan 4, 2024
Einstein, A.; Podolsky, B.; Rosen, N. (1935-05-15). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?". Physical Review. 47 (10): 777–780. Bibcode:1935PhRv...47..777E. doi:10.1103/PhysRev.47.777.
Popper, Karl; Carl Friedrich von Weizsäcker (1934), "Zur Kritik der Ungenauigkeitsrelationen (Critique of the Uncertainty Relations)", Naturwissenschaften, 22 (48): 807–808, Bibcode:1934NW.....22..807P, doi:10.1007/BF01496543, S2CID 40843068.
Compton, A. H. (1931). "The Uncertainty Principle and Free Will". Science. 74 (1911): 172. Bibcode:1931Sci....74..172C. doi:10.1126/science.74.1911.172. PMID 17808216. S2CID 29126625.
Heisenberg, M. (2009). "Is free will an illusion?". Nature. 459 (7244): 164–165. Bibcode:2009Natur.459..164H. doi:10.1038/459164a. PMID 19444190. S2CID 4420023.
Davies, P.C.W. (2004). "Does quantum mechanics play a non-trivial role in life?". Biosystems. 78 (1–3): 69–79. Bibcode:2004BiSys..78...69D. doi:10.1016/j.biosystems.2004.07.001. PMID 15555759.
Hänggi, Esther; Wehner, Stephanie (2013). "A violation of the uncertainty principle implies a violation of the second law of thermodynamics". Nature Communications. 4: 1670. arXiv:1205.6894. Bibcode:2013NatCo...4.1670H. doi:10.1038/ncomms2665. PMID 23575674. S2CID 205316392.
Peres, Asher; Terno, Daniel R. (2004-01-06). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123 [111]. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Archived from the original on 2024-02-23. Retrieved 2024-01-25.
Elion, W. J.; Matters, M.; Geigenmüller, U.; Mooij, J. E. (1994), "Direct demonstration of Heisenberg's uncertainty principle in a superconductor", Nature, 371 (6498): 594–595, Bibcode:1994Natur.371..594E, doi:10.1038/371594a0, S2CID 4240085
Smithey, D. T.; M. Beck, J. Cooper, M. G. Raymer; Cooper, J.; Raymer, M. G. (1993), "Measurement of number–phase uncertainty relations of optical fields", Phys. Rev. A, 48 (4): 3159–3167, Bibcode:1993PhRvA..48.3159S, doi:10.1103/PhysRevA.48.3159, PMID 9909968{{citation}}: CS1 maint: multiple names: authors list (link)
Caves, Carlton (1981), "Quantum-mechanical noise in an interferometer", Phys. Rev. D, 23 (8): 1693–1708, Bibcode:1981PhRvD..23.1693C, doi:10.1103/PhysRevD.23.1693

elsevier.com

linkinghub.elsevier.com

Hilgevoord, Jan (March 2005). "Time in quantum mechanics: a story of confusion". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 36 (1): 29–60. Bibcode:2005SHPMP..36...29H. doi:10.1016/j.shpsb.2004.10.002. Archived from the original on 2022-10-23. Retrieved 2024-01-28.
Bohm, Arno (January 2011). "Resonances/decaying states and the mathematics of quantum physics". Reports on Mathematical Physics. 67 (3): 279–303. Bibcode:2011RpMP...67..279B. doi:10.1016/S0034-4877(11)60018-9. Archived from the original on 2023-12-04. Retrieved 2024-01-24.

encyclopediaofmath.org

Sitaram, A (2001) [1994], "Uncertainty principle, mathematical", Encyclopedia of Mathematics, EMS Press

harvard.edu

ui.adsabs.harvard.edu

Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Kennard, E. H. (1927), "Zur Quantenmechanik einfacher Bewegungstypen", Zeitschrift für Physik (in German), 44 (4–5): 326–352, Bibcode:1927ZPhy...44..326K, doi:10.1007/BF01391200, S2CID 121626384.
Jaeger, Gregg (September 2014). "What in the (quantum) world is macroscopic?". American Journal of Physics. 82 (9): 896–905. Bibcode:2014AmJPh..82..896J. doi:10.1119/1.4878358.
See Appendix B in Bialynicki-Birula, Iwo; Bialynicka-Birula, Zofia (2009), "Why photons cannot be sharply localized", Physical Review A, 79 (3): 7–8, arXiv:0903.3712, Bibcode:2009PhRvA..79c2112B, doi:10.1103/PhysRevA.79.032112, S2CID 55632217
Hilgevoord, Jan (1996-12-01). "The uncertainty principle for energy and time". American Journal of Physics. 64 (12): 1451–1456. Bibcode:1996AmJPh..64.1451H. doi:10.1119/1.18410. ISSN 0002-9505. Archived from the original on 2024-02-23. Retrieved 2023-11-12.
Bohm, Arno R.; Sato, Yoshihiro (2005-04-28). "Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution". Physical Review D. 71 (8): 085018. arXiv:hep-ph/0412106. Bibcode:2005PhRvD..71h5018B. doi:10.1103/PhysRevD.71.085018. ISSN 1550-7998. S2CID 119417992.
The broad linewidth of fast-decaying states makes it difficult to accurately measure the energy of the state, and researchers have even used detuned microwave cavities to slow down the decay rate, to get sharper peaks. Gabrielse, Gerald; H. Dehmelt (1985). "Observation of Inhibited Spontaneous Emission". Physical Review Letters. 55 (1): 67–70. Bibcode:1985PhRvL..55...67G. doi:10.1103/PhysRevLett.55.67. PMID 10031682.
Hilgevoord, Jan (March 2005). "Time in quantum mechanics: a story of confusion". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 36 (1): 29–60. Bibcode:2005SHPMP..36...29H. doi:10.1016/j.shpsb.2004.10.002. Archived from the original on 2022-10-23. Retrieved 2024-01-28.
Bohm, Arno (January 2011). "Resonances/decaying states and the mathematics of quantum physics". Reports on Mathematical Physics. 67 (3): 279–303. Bibcode:2011RpMP...67..279B. doi:10.1016/S0034-4877(11)60018-9. Archived from the original on 2023-12-04. Retrieved 2024-01-24.
Aharonov, Y.; Bohm, D. (June 1, 1961). "Time in the Quantum Theory and the Uncertainty Relation for Time and Energy" (PDF). Physical Review. 122 (5): 1649–1658. Bibcode:1961PhRv..122.1649A. doi:10.1103/PhysRev.122.1649. Archived from the original (PDF) on 2014-01-09. Retrieved 2012-01-21.
Griffiths, David J.; Schroeter, Darrell F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press. Bibcode:2018iqm..book.....G. doi:10.1017/9781316995433. ISBN 978-1-316-99543-3. Archived from the original on 2024-02-23. Retrieved 2024-01-27.
Ozawa, Masanao (2003), "Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement", Physical Review A, 67 (4): 42105, arXiv:quant-ph/0207121, Bibcode:2003PhRvA..67d2105O, doi:10.1103/PhysRevA.67.042105, S2CID 42012188
Rozema, L. A.; Darabi, A.; Mahler, D. H.; Hayat, A.; Soudagar, Y.; Steinberg, A. M. (2012). "Violation of Heisenberg's Measurement–Disturbance Relationship by Weak Measurements". Physical Review Letters. 109 (10): 100404. arXiv:1208.0034v2. Bibcode:2012PhRvL.109j0404R. doi:10.1103/PhysRevLett.109.100404. PMID 23005268. S2CID 37576344.
De Broglie, Louis (October 1923). "Waves and Quanta". Nature. 112 (2815): 540. Bibcode:1923Natur.112..540D. doi:10.1038/112540a0. ISSN 1476-4687. S2CID 186242764.
Robertson, H. P. (1929), "The Uncertainty Principle", Phys. Rev., 34 (1): 163–164, Bibcode:1929PhRv...34..163R, doi:10.1103/PhysRev.34.163
Davidson, E. R. (1965), "On Derivations of the Uncertainty Principle", J. Chem. Phys., 42 (4): 1461–1462, Bibcode:1965JChPh..42.1461D, doi:10.1063/1.1696139
Hall, B. C. (2013), Quantum Theory for Mathematicians, Springer, p. 245, Bibcode:2013qtm..book.....H
Jackiw, Roman (1968), "Minimum Uncertainty Product, Number-Phase Uncertainty Product, and Coherent States", J. Math. Phys., 9 (3): 339–346, Bibcode:1968JMP.....9..339J, doi:10.1063/1.1664585
Carruthers, P.; Nieto, M. M. (1968), "Phase and Angle Variables in Quantum Mechanics", Rev. Mod. Phys., 40 (2): 411–440, Bibcode:1968RvMP...40..411C, doi:10.1103/RevModPhys.40.411
Hall, B. C. (2013), Quantum Theory for Mathematicians, Springer, Bibcode:2013qtm..book.....H
Maccone, Lorenzo; Pati, Arun K. (31 December 2014). "Stronger Uncertainty Relations for All Incompatible Observables". Physical Review Letters. 113 (26): 260401. arXiv:1407.0338. Bibcode:2014PhRvL.113z0401M. doi:10.1103/PhysRevLett.113.260401. PMID 25615288. S2CID 21334130.
Huang, Yichen (10 August 2012). "Variance-based uncertainty relations". Physical Review A. 86 (2): 024101. arXiv:1012.3105. Bibcode:2012PhRvA..86b4101H. doi:10.1103/PhysRevA.86.024101. S2CID 118507388.
Tóth, Géza; Fröwis, Florian (31 January 2022). "Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices". Physical Review Research. 4 (1): 013075. arXiv:2109.06893. Bibcode:2022PhRvR...4a3075T. doi:10.1103/PhysRevResearch.4.013075. S2CID 237513549.
Tóth, Géza; Petz, Dénes (20 March 2013). "Extremal properties of the variance and the quantum Fisher information". Physical Review A. 87 (3): 032324. arXiv:1109.2831. Bibcode:2013PhRvA..87c2324T. doi:10.1103/PhysRevA.87.032324. S2CID 55088553.
Fröwis, Florian; Schmied, Roman; Gisin, Nicolas (2 July 2015). "Tighter quantum uncertainty relations following from a general probabilistic bound". Physical Review A. 92 (1): 012102. arXiv:1409.4440. Bibcode:2015PhRvA..92a2102F. doi:10.1103/PhysRevA.92.012102. S2CID 58912643.
Curtright, T.; Zachos, C. (2001). "Negative Probability and Uncertainty Relations". Modern Physics Letters A. 16 (37): 2381–2385. arXiv:hep-th/0105226. Bibcode:2001MPLA...16.2381C. doi:10.1142/S021773230100576X. S2CID 119669313.
Likharev, K. K.; A. B. Zorin (1985), "Theory of Bloch-Wave Oscillations in Small Josephson Junctions", J. Low Temp. Phys., 59 (3/4): 347–382, Bibcode:1985JLTP...59..347L, doi:10.1007/BF00683782, S2CID 120813342
Davidson, Ernest R. (1965-02-15). "On Derivations of the Uncertainty Principle". The Journal of Chemical Physics. 42 (4): 1461–1462. Bibcode:1965JChPh..42.1461D. doi:10.1063/1.1696139. ISSN 0021-9606. Archived from the original on 2024-02-23. Retrieved 2024-01-20.
Hall, B. C. (2013), Quantum Theory for Mathematicians, Springer, p. 245, Bibcode:2013qtm..book.....H
Hall, B. C. (2013), Quantum Theory for Mathematicians, Springer, p. 246, Bibcode:2013qtm..book.....H
Giovannetti, V.; Lloyd, S.; Maccone, L. (2011). "Advances in quantum metrology". Nature Photonics. 5 (4): 222. arXiv:1102.2318. Bibcode:2011NaPho...5..222G. doi:10.1038/nphoton.2011.35. S2CID 12591819.; arXiv Archived 2020-08-06 at the Wayback Machine
Luis, Alfredo (2017-03-13). "Breaking the weak Heisenberg limit". Physical Review A. 95 (3): 032113. arXiv:1607.07668. Bibcode:2017PhRvA..95c2113L. doi:10.1103/PhysRevA.95.032113. ISSN 2469-9926. S2CID 55838380.
Busch, P.; Lahti, P.; Werner, R. F. (2013). "Proof of Heisenberg's Error-Disturbance Relation". Physical Review Letters. 111 (16): 160405. arXiv:1306.1565. Bibcode:2013PhRvL.111p0405B. doi:10.1103/PhysRevLett.111.160405. PMID 24182239. S2CID 24507489.
Busch, P.; Lahti, P.; Werner, R. F. (2014). "Heisenberg uncertainty for qubit measurements". Physical Review A. 89 (1): 012129. arXiv:1311.0837. Bibcode:2014PhRvA..89a2129B. doi:10.1103/PhysRevA.89.012129. S2CID 118383022.
Erhart, J.; Sponar, S.; Sulyok, G.; Badurek, G.; Ozawa, M.; Hasegawa, Y. (2012). "Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin measurements". Nature Physics. 8 (3): 185–189. arXiv:1201.1833. Bibcode:2012NatPh...8..185E. doi:10.1038/nphys2194. S2CID 117270618.
Baek, S.-Y.; Kaneda, F.; Ozawa, M.; Edamatsu, K. (2013). "Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation". Scientific Reports. 3: 2221. Bibcode:2013NatSR...3E2221B. doi:10.1038/srep02221. PMC 3713528. PMID 23860715.
Ringbauer, M.; Biggerstaff, D.N.; Broome, M.A.; Fedrizzi, A.; Branciard, C.; White, A.G. (2014). "Experimental Joint Quantum Measurements with Minimum Uncertainty". Physical Review Letters. 112 (2): 020401. arXiv:1308.5688. Bibcode:2014PhRvL.112b0401R. doi:10.1103/PhysRevLett.112.020401. PMID 24483993. S2CID 18730255.
Björk, G.; Söderholm, J.; Trifonov, A.; Tsegaye, T.; Karlsson, A. (1999). "Complementarity and the uncertainty relations". Physical Review. A60 (3): 1878. arXiv:quant-ph/9904069. Bibcode:1999PhRvA..60.1874B. doi:10.1103/PhysRevA.60.1874. S2CID 27371899.
Fujikawa, Kazuo (2012). "Universally valid Heisenberg uncertainty relation". Physical Review A. 85 (6): 062117. arXiv:1205.1360. Bibcode:2012PhRvA..85f2117F. doi:10.1103/PhysRevA.85.062117. S2CID 119640759.
Judge, D. (1964), "On the uncertainty relation for angle variables", Il Nuovo Cimento, 31 (2): 332–340, Bibcode:1964NCim...31..332J, doi:10.1007/BF02733639, S2CID 120553526
Bouten, M.; Maene, N.; Van Leuven, P. (1965), "On an uncertainty relation for angle variables", Il Nuovo Cimento, 37 (3): 1119–1125, Bibcode:1965NCim...37.1119B, doi:10.1007/BF02773197, S2CID 122838645
Louisell, W. H. (1963), "Amplitude and phase uncertainty relations", Physics Letters, 7 (1): 60–61, Bibcode:1963PhL.....7...60L, doi:10.1016/0031-9163(63)90442-6
Bialynicki-Birula, I.; Mycielski, J. (1975), "Uncertainty Relations for Information Entropy in Wave Mechanics", Communications in Mathematical Physics, 44 (2): 129–132, Bibcode:1975CMaPh..44..129B, doi:10.1007/BF01608825, S2CID 122277352, archived from the original on 2021-02-08, retrieved 2021-08-17
Huang, Yichen (24 May 2011). "Entropic uncertainty relations in multidimensional position and momentum spaces". Physical Review A. 83 (5): 052124. arXiv:1101.2944. Bibcode:2011PhRvA..83e2124H. doi:10.1103/PhysRevA.83.052124. S2CID 119243096.
Chiew, Shao-Hen; Gessner, Manuel (31 January 2022). "Improving sum uncertainty relations with the quantum Fisher information". Physical Review Research. 4 (1): 013076. arXiv:2109.06900. Bibcode:2022PhRvR...4a3076C. doi:10.1103/PhysRevResearch.4.013076. S2CID 237513883.
Hörmander, L. (1991), "A uniqueness theorem of Beurling for Fourier transform pairs", Ark. Mat., 29 (1–2): 231–240, Bibcode:1991ArM....29..237H, doi:10.1007/BF02384339, S2CID 121375111
Bonami, A.; Demange, B.; Jaming, Ph. (2003), "Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms", Rev. Mat. Iberoamericana, 19: 23–55, arXiv:math/0102111, Bibcode:2001math......2111B, doi:10.4171/RMI/337, S2CID 1211391
Hedenmalm, Haakan (2012), "Heisenberg's uncertainty principle in the sense of Beurling", Journal d'Analyse Mathématique, 118 (2): 691–702, arXiv:1203.5222, Bibcode:2012arXiv1203.5222H, doi:10.1007/s11854-012-0048-9, S2CID 54533890
Cassidy, David; Saperstein, Alvin M. (2009), "Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb", Physics Today, 63 (1), New York: Bellevue Literary Press: 185, Bibcode:2010PhT....63a..49C, doi:10.1063/1.3293416, archived from the original on Jan 4, 2024
Einstein, A.; Podolsky, B.; Rosen, N. (1935-05-15). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?". Physical Review. 47 (10): 777–780. Bibcode:1935PhRv...47..777E. doi:10.1103/PhysRev.47.777.
Popper, Karl; Carl Friedrich von Weizsäcker (1934), "Zur Kritik der Ungenauigkeitsrelationen (Critique of the Uncertainty Relations)", Naturwissenschaften, 22 (48): 807–808, Bibcode:1934NW.....22..807P, doi:10.1007/BF01496543, S2CID 40843068.
Compton, A. H. (1931). "The Uncertainty Principle and Free Will". Science. 74 (1911): 172. Bibcode:1931Sci....74..172C. doi:10.1126/science.74.1911.172. PMID 17808216. S2CID 29126625.
Heisenberg, M. (2009). "Is free will an illusion?". Nature. 459 (7244): 164–165. Bibcode:2009Natur.459..164H. doi:10.1038/459164a. PMID 19444190. S2CID 4420023.
Davies, P.C.W. (2004). "Does quantum mechanics play a non-trivial role in life?". Biosystems. 78 (1–3): 69–79. Bibcode:2004BiSys..78...69D. doi:10.1016/j.biosystems.2004.07.001. PMID 15555759.
Hänggi, Esther; Wehner, Stephanie (2013). "A violation of the uncertainty principle implies a violation of the second law of thermodynamics". Nature Communications. 4: 1670. arXiv:1205.6894. Bibcode:2013NatCo...4.1670H. doi:10.1038/ncomms2665. PMID 23575674. S2CID 205316392.
Peres, Asher; Terno, Daniel R. (2004-01-06). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123 [111]. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Archived from the original on 2024-02-23. Retrieved 2024-01-25.
Elion, W. J.; Matters, M.; Geigenmüller, U.; Mooij, J. E. (1994), "Direct demonstration of Heisenberg's uncertainty principle in a superconductor", Nature, 371 (6498): 594–595, Bibcode:1994Natur.371..594E, doi:10.1038/371594a0, S2CID 4240085
Smithey, D. T.; M. Beck, J. Cooper, M. G. Raymer; Cooper, J.; Raymer, M. G. (1993), "Measurement of number–phase uncertainty relations of optical fields", Phys. Rev. A, 48 (4): 3159–3167, Bibcode:1993PhRvA..48.3159S, doi:10.1103/PhysRevA.48.3159, PMID 9909968{{citation}}: CS1 maint: multiple names: authors list (link)
Caves, Carlton (1981), "Quantum-mechanical noise in an interferometer", Phys. Rev. D, 23 (8): 1693–1708, Bibcode:1981PhRvD..23.1693C, doi:10.1103/PhysRevD.23.1693

jstor.org

Hirschman, I. I. Jr. (1957), "A note on entropy", American Journal of Mathematics, 79 (1): 152–156, doi:10.2307/2372390, JSTOR 2372390.
Beckner, W. (1975), "Inequalities in Fourier analysis", Annals of Mathematics, 102 (6): 159–182, doi:10.2307/1970980, JSTOR 1970980, PMC 432369, PMID 16592223.

loc.gov

lccn.loc.gov

Frauenfelder, H. (1962). The Mössbauer Effect. W. A. Benjamin. p. 66. LCCN 61018181.
Tipler, Paul A.; Llewellyn, Ralph A. (1999), Modern Physics, vol. 3, W.H. Freeman & Co., p. 3, ISBN 978-1572591646, LCCN 98046099

narod.ru

daarb.narod.ru

L. I. Mandelstam, I. E. Tamm, The uncertainty relation between energy and time in nonrelativistic quantum mechanics Archived 2019-06-07 at the Wayback Machine, 1945.

nasa.gov

ntrs.nasa.gov

Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik

nih.gov

pubmed.ncbi.nlm.nih.gov

The broad linewidth of fast-decaying states makes it difficult to accurately measure the energy of the state, and researchers have even used detuned microwave cavities to slow down the decay rate, to get sharper peaks. Gabrielse, Gerald; H. Dehmelt (1985). "Observation of Inhibited Spontaneous Emission". Physical Review Letters. 55 (1): 67–70. Bibcode:1985PhRvL..55...67G. doi:10.1103/PhysRevLett.55.67. PMID 10031682.
Rozema, L. A.; Darabi, A.; Mahler, D. H.; Hayat, A.; Soudagar, Y.; Steinberg, A. M. (2012). "Violation of Heisenberg's Measurement–Disturbance Relationship by Weak Measurements". Physical Review Letters. 109 (10): 100404. arXiv:1208.0034v2. Bibcode:2012PhRvL.109j0404R. doi:10.1103/PhysRevLett.109.100404. PMID 23005268. S2CID 37576344.
Maccone, Lorenzo; Pati, Arun K. (31 December 2014). "Stronger Uncertainty Relations for All Incompatible Observables". Physical Review Letters. 113 (26): 260401. arXiv:1407.0338. Bibcode:2014PhRvL.113z0401M. doi:10.1103/PhysRevLett.113.260401. PMID 25615288. S2CID 21334130.
Busch, P.; Lahti, P.; Werner, R. F. (2013). "Proof of Heisenberg's Error-Disturbance Relation". Physical Review Letters. 111 (16): 160405. arXiv:1306.1565. Bibcode:2013PhRvL.111p0405B. doi:10.1103/PhysRevLett.111.160405. PMID 24182239. S2CID 24507489.
Baek, S.-Y.; Kaneda, F.; Ozawa, M.; Edamatsu, K. (2013). "Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation". Scientific Reports. 3: 2221. Bibcode:2013NatSR...3E2221B. doi:10.1038/srep02221. PMC 3713528. PMID 23860715.
Ringbauer, M.; Biggerstaff, D.N.; Broome, M.A.; Fedrizzi, A.; Branciard, C.; White, A.G. (2014). "Experimental Joint Quantum Measurements with Minimum Uncertainty". Physical Review Letters. 112 (2): 020401. arXiv:1308.5688. Bibcode:2014PhRvL.112b0401R. doi:10.1103/PhysRevLett.112.020401. PMID 24483993. S2CID 18730255.
Beckner, W. (1975), "Inequalities in Fourier analysis", Annals of Mathematics, 102 (6): 159–182, doi:10.2307/1970980, JSTOR 1970980, PMC 432369, PMID 16592223.
Compton, A. H. (1931). "The Uncertainty Principle and Free Will". Science. 74 (1911): 172. Bibcode:1931Sci....74..172C. doi:10.1126/science.74.1911.172. PMID 17808216. S2CID 29126625.
Heisenberg, M. (2009). "Is free will an illusion?". Nature. 459 (7244): 164–165. Bibcode:2009Natur.459..164H. doi:10.1038/459164a. PMID 19444190. S2CID 4420023.
Davies, P.C.W. (2004). "Does quantum mechanics play a non-trivial role in life?". Biosystems. 78 (1–3): 69–79. Bibcode:2004BiSys..78...69D. doi:10.1016/j.biosystems.2004.07.001. PMID 15555759.
Hänggi, Esther; Wehner, Stephanie (2013). "A violation of the uncertainty principle implies a violation of the second law of thermodynamics". Nature Communications. 4: 1670. arXiv:1205.6894. Bibcode:2013NatCo...4.1670H. doi:10.1038/ncomms2665. PMID 23575674. S2CID 205316392.
Smithey, D. T.; M. Beck, J. Cooper, M. G. Raymer; Cooper, J.; Raymer, M. G. (1993), "Measurement of number–phase uncertainty relations of optical fields", Phys. Rev. A, 48 (4): 3159–3167, Bibcode:1993PhRvA..48.3159S, doi:10.1103/PhysRevA.48.3159, PMID 9909968{{citation}}: CS1 maint: multiple names: authors list (link)

ncbi.nlm.nih.gov

Baek, S.-Y.; Kaneda, F.; Ozawa, M.; Edamatsu, K. (2013). "Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation". Scientific Reports. 3: 2221. Bibcode:2013NatSR...3E2221B. doi:10.1038/srep02221. PMC 3713528. PMID 23860715.
Beckner, W. (1975), "Inequalities in Fourier analysis", Annals of Mathematics, 102 (6): 159–182, doi:10.2307/1970980, JSTOR 1970980, PMC 432369, PMID 16592223.

projecteuclid.org

Bialynicki-Birula, I.; Mycielski, J. (1975), "Uncertainty Relations for Information Entropy in Wave Mechanics", Communications in Mathematical Physics, 44 (2): 129–132, Bibcode:1975CMaPh..44..129B, doi:10.1007/BF01608825, S2CID 122277352, archived from the original on 2021-02-08, retrieved 2021-08-17

sciencedirect.com

Wheeler, John Archibald (1978-01-01), Marlow, A. R. (ed.), "The 'Past' and the 'Delayed-Choice' Double-Slit Experiment", Mathematical Foundations of Quantum Theory, Academic Press, pp. 9–48, doi:10.1016/b978-0-12-473250-6.50006-6, ISBN 978-0-12-473250-6, archived from the original on 2022-12-10, retrieved 2023-07-19

scientificamerican.com

Furuta, Aya (2012), "One Thing Is Certain: Heisenberg's Uncertainty Principle Is Not Dead", Scientific American, archived from the original on 2022-04-01, retrieved 2018-10-20

semanticscholar.org

api.semanticscholar.org

Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Kennard, E. H. (1927), "Zur Quantenmechanik einfacher Bewegungstypen", Zeitschrift für Physik (in German), 44 (4–5): 326–352, Bibcode:1927ZPhy...44..326K, doi:10.1007/BF01391200, S2CID 121626384.
See Appendix B in Bialynicki-Birula, Iwo; Bialynicka-Birula, Zofia (2009), "Why photons cannot be sharply localized", Physical Review A, 79 (3): 7–8, arXiv:0903.3712, Bibcode:2009PhRvA..79c2112B, doi:10.1103/PhysRevA.79.032112, S2CID 55632217
Bohm, Arno R.; Sato, Yoshihiro (2005-04-28). "Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution". Physical Review D. 71 (8): 085018. arXiv:hep-ph/0412106. Bibcode:2005PhRvD..71h5018B. doi:10.1103/PhysRevD.71.085018. ISSN 1550-7998. S2CID 119417992.
Ozawa, Masanao (2003), "Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement", Physical Review A, 67 (4): 42105, arXiv:quant-ph/0207121, Bibcode:2003PhRvA..67d2105O, doi:10.1103/PhysRevA.67.042105, S2CID 42012188
Rozema, L. A.; Darabi, A.; Mahler, D. H.; Hayat, A.; Soudagar, Y.; Steinberg, A. M. (2012). "Violation of Heisenberg's Measurement–Disturbance Relationship by Weak Measurements". Physical Review Letters. 109 (10): 100404. arXiv:1208.0034v2. Bibcode:2012PhRvL.109j0404R. doi:10.1103/PhysRevLett.109.100404. PMID 23005268. S2CID 37576344.
De Broglie, Louis (October 1923). "Waves and Quanta". Nature. 112 (2815): 540. Bibcode:1923Natur.112..540D. doi:10.1038/112540a0. ISSN 1476-4687. S2CID 186242764.
Maccone, Lorenzo; Pati, Arun K. (31 December 2014). "Stronger Uncertainty Relations for All Incompatible Observables". Physical Review Letters. 113 (26): 260401. arXiv:1407.0338. Bibcode:2014PhRvL.113z0401M. doi:10.1103/PhysRevLett.113.260401. PMID 25615288. S2CID 21334130.
Huang, Yichen (10 August 2012). "Variance-based uncertainty relations". Physical Review A. 86 (2): 024101. arXiv:1012.3105. Bibcode:2012PhRvA..86b4101H. doi:10.1103/PhysRevA.86.024101. S2CID 118507388.
Tóth, Géza; Fröwis, Florian (31 January 2022). "Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices". Physical Review Research. 4 (1): 013075. arXiv:2109.06893. Bibcode:2022PhRvR...4a3075T. doi:10.1103/PhysRevResearch.4.013075. S2CID 237513549.
Tóth, Géza; Petz, Dénes (20 March 2013). "Extremal properties of the variance and the quantum Fisher information". Physical Review A. 87 (3): 032324. arXiv:1109.2831. Bibcode:2013PhRvA..87c2324T. doi:10.1103/PhysRevA.87.032324. S2CID 55088553.
Fröwis, Florian; Schmied, Roman; Gisin, Nicolas (2 July 2015). "Tighter quantum uncertainty relations following from a general probabilistic bound". Physical Review A. 92 (1): 012102. arXiv:1409.4440. Bibcode:2015PhRvA..92a2102F. doi:10.1103/PhysRevA.92.012102. S2CID 58912643.
Curtright, T.; Zachos, C. (2001). "Negative Probability and Uncertainty Relations". Modern Physics Letters A. 16 (37): 2381–2385. arXiv:hep-th/0105226. Bibcode:2001MPLA...16.2381C. doi:10.1142/S021773230100576X. S2CID 119669313.
Likharev, K. K.; A. B. Zorin (1985), "Theory of Bloch-Wave Oscillations in Small Josephson Junctions", J. Low Temp. Phys., 59 (3/4): 347–382, Bibcode:1985JLTP...59..347L, doi:10.1007/BF00683782, S2CID 120813342
Giovannetti, V.; Lloyd, S.; Maccone, L. (2011). "Advances in quantum metrology". Nature Photonics. 5 (4): 222. arXiv:1102.2318. Bibcode:2011NaPho...5..222G. doi:10.1038/nphoton.2011.35. S2CID 12591819.; arXiv Archived 2020-08-06 at the Wayback Machine
Luis, Alfredo (2017-03-13). "Breaking the weak Heisenberg limit". Physical Review A. 95 (3): 032113. arXiv:1607.07668. Bibcode:2017PhRvA..95c2113L. doi:10.1103/PhysRevA.95.032113. ISSN 2469-9926. S2CID 55838380.
Busch, P.; Lahti, P.; Werner, R. F. (2013). "Proof of Heisenberg's Error-Disturbance Relation". Physical Review Letters. 111 (16): 160405. arXiv:1306.1565. Bibcode:2013PhRvL.111p0405B. doi:10.1103/PhysRevLett.111.160405. PMID 24182239. S2CID 24507489.
Busch, P.; Lahti, P.; Werner, R. F. (2014). "Heisenberg uncertainty for qubit measurements". Physical Review A. 89 (1): 012129. arXiv:1311.0837. Bibcode:2014PhRvA..89a2129B. doi:10.1103/PhysRevA.89.012129. S2CID 118383022.
Erhart, J.; Sponar, S.; Sulyok, G.; Badurek, G.; Ozawa, M.; Hasegawa, Y. (2012). "Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin measurements". Nature Physics. 8 (3): 185–189. arXiv:1201.1833. Bibcode:2012NatPh...8..185E. doi:10.1038/nphys2194. S2CID 117270618.
Ringbauer, M.; Biggerstaff, D.N.; Broome, M.A.; Fedrizzi, A.; Branciard, C.; White, A.G. (2014). "Experimental Joint Quantum Measurements with Minimum Uncertainty". Physical Review Letters. 112 (2): 020401. arXiv:1308.5688. Bibcode:2014PhRvL.112b0401R. doi:10.1103/PhysRevLett.112.020401. PMID 24483993. S2CID 18730255.
Björk, G.; Söderholm, J.; Trifonov, A.; Tsegaye, T.; Karlsson, A. (1999). "Complementarity and the uncertainty relations". Physical Review. A60 (3): 1878. arXiv:quant-ph/9904069. Bibcode:1999PhRvA..60.1874B. doi:10.1103/PhysRevA.60.1874. S2CID 27371899.
Fujikawa, Kazuo (2012). "Universally valid Heisenberg uncertainty relation". Physical Review A. 85 (6): 062117. arXiv:1205.1360. Bibcode:2012PhRvA..85f2117F. doi:10.1103/PhysRevA.85.062117. S2CID 119640759.
Judge, D. (1964), "On the uncertainty relation for angle variables", Il Nuovo Cimento, 31 (2): 332–340, Bibcode:1964NCim...31..332J, doi:10.1007/BF02733639, S2CID 120553526
Bouten, M.; Maene, N.; Van Leuven, P. (1965), "On an uncertainty relation for angle variables", Il Nuovo Cimento, 37 (3): 1119–1125, Bibcode:1965NCim...37.1119B, doi:10.1007/BF02773197, S2CID 122838645
Bialynicki-Birula, I.; Mycielski, J. (1975), "Uncertainty Relations for Information Entropy in Wave Mechanics", Communications in Mathematical Physics, 44 (2): 129–132, Bibcode:1975CMaPh..44..129B, doi:10.1007/BF01608825, S2CID 122277352, archived from the original on 2021-02-08, retrieved 2021-08-17
Huang, Yichen (24 May 2011). "Entropic uncertainty relations in multidimensional position and momentum spaces". Physical Review A. 83 (5): 052124. arXiv:1101.2944. Bibcode:2011PhRvA..83e2124H. doi:10.1103/PhysRevA.83.052124. S2CID 119243096.
Chafaï, D. (2003), "Gaussian maximum of entropy and reversed log-Sobolev inequality", Séminaire de Probabilités XXXVI, Lecture Notes in Mathematics, vol. 1801, pp. 194–200, arXiv:math/0102227, doi:10.1007/978-3-540-36107-7_5, ISBN 978-3-540-00072-3, S2CID 17795603
Chiew, Shao-Hen; Gessner, Manuel (31 January 2022). "Improving sum uncertainty relations with the quantum Fisher information". Physical Review Research. 4 (1): 013076. arXiv:2109.06900. Bibcode:2022PhRvR...4a3076C. doi:10.1103/PhysRevResearch.4.013076. S2CID 237513883.
Folland, Gerald; Sitaram, Alladi (May 1997), "The Uncertainty Principle: A Mathematical Survey", Journal of Fourier Analysis and Applications, 3 (3): 207–238, doi:10.1007/BF02649110, MR 1448337, S2CID 121355943
Terence Tao (2005), "An uncertainty principle for cyclic groups of prime order", Mathematical Research Letters, 12 (1): 121–127, arXiv:math/0308286, doi:10.4310/MRL.2005.v12.n1.a11, S2CID 8548232
Jaming, Ph. (2007), "Nazarov's uncertainty principles in higher dimension", J. Approx. Theory, 149 (1): 30–41, arXiv:math/0612367, doi:10.1016/j.jat.2007.04.005, S2CID 9794547
Hörmander, L. (1991), "A uniqueness theorem of Beurling for Fourier transform pairs", Ark. Mat., 29 (1–2): 231–240, Bibcode:1991ArM....29..237H, doi:10.1007/BF02384339, S2CID 121375111
Bonami, A.; Demange, B.; Jaming, Ph. (2003), "Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms", Rev. Mat. Iberoamericana, 19: 23–55, arXiv:math/0102111, Bibcode:2001math......2111B, doi:10.4171/RMI/337, S2CID 1211391
Hedenmalm, Haakan (2012), "Heisenberg's uncertainty principle in the sense of Beurling", Journal d'Analyse Mathématique, 118 (2): 691–702, arXiv:1203.5222, Bibcode:2012arXiv1203.5222H, doi:10.1007/s11854-012-0048-9, S2CID 54533890
Popper, Karl; Carl Friedrich von Weizsäcker (1934), "Zur Kritik der Ungenauigkeitsrelationen (Critique of the Uncertainty Relations)", Naturwissenschaften, 22 (48): 807–808, Bibcode:1934NW.....22..807P, doi:10.1007/BF01496543, S2CID 40843068.
Compton, A. H. (1931). "The Uncertainty Principle and Free Will". Science. 74 (1911): 172. Bibcode:1931Sci....74..172C. doi:10.1126/science.74.1911.172. PMID 17808216. S2CID 29126625.
Heisenberg, M. (2009). "Is free will an illusion?". Nature. 459 (7244): 164–165. Bibcode:2009Natur.459..164H. doi:10.1038/459164a. PMID 19444190. S2CID 4420023.
Hänggi, Esther; Wehner, Stephanie (2013). "A violation of the uncertainty principle implies a violation of the second law of thermodynamics". Nature Communications. 4: 1670. arXiv:1205.6894. Bibcode:2013NatCo...4.1670H. doi:10.1038/ncomms2665. PMID 23575674. S2CID 205316392.
Peres, Asher; Terno, Daniel R. (2004-01-06). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123 [111]. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Archived from the original on 2024-02-23. Retrieved 2024-01-25.
Elion, W. J.; Matters, M.; Geigenmüller, U.; Mooij, J. E. (1994), "Direct demonstration of Heisenberg's uncertainty principle in a superconductor", Nature, 371 (6498): 594–595, Bibcode:1994Natur.371..594E, doi:10.1038/371594a0, S2CID 4240085

springer.com

link.springer.com

Busch, Paul (2002). "The Time-Energy Uncertainty Relation". In Muga, J. G.; Mayato, R. Sala; Egusquiza, I. L. (eds.). Time in Quantum Mechanics. Lecture Notes in Physics. Vol. 72. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 69–98. doi:10.1007/3-540-45846-8_3. ISBN 978-3-540-43294-4.
Wigner, E. P. (1997). "On the Time–Energy Uncertainty Relation". In Wightman, Arthur S. (ed.). Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 538–548. doi:10.1007/978-3-662-09203-3_58. ISBN 978-3-642-08179-8.

web.archive.org

Sen, D. (2014). "The Uncertainty relations in quantum mechanics" (PDF). Current Science. 107 (2): 203–218. Archived (PDF) from the original on 2019-09-24. Retrieved 2016-02-14.
Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Hilgevoord, Jan (1996-12-01). "The uncertainty principle for energy and time". American Journal of Physics. 64 (12): 1451–1456. Bibcode:1996AmJPh..64.1451H. doi:10.1119/1.18410. ISSN 0002-9505. Archived from the original on 2024-02-23. Retrieved 2023-11-12.
Hilgevoord, Jan (March 2005). "Time in quantum mechanics: a story of confusion". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 36 (1): 29–60. Bibcode:2005SHPMP..36...29H. doi:10.1016/j.shpsb.2004.10.002. Archived from the original on 2022-10-23. Retrieved 2024-01-28.
Bohm, Arno (January 2011). "Resonances/decaying states and the mathematics of quantum physics". Reports on Mathematical Physics. 67 (3): 279–303. Bibcode:2011RpMP...67..279B. doi:10.1016/S0034-4877(11)60018-9. Archived from the original on 2023-12-04. Retrieved 2024-01-24.
Aharonov, Y.; Bohm, D. (June 1, 1961). "Time in the Quantum Theory and the Uncertainty Relation for Time and Energy" (PDF). Physical Review. 122 (5): 1649–1658. Bibcode:1961PhRv..122.1649A. doi:10.1103/PhysRev.122.1649. Archived from the original (PDF) on 2014-01-09. Retrieved 2012-01-21.
L. I. Mandelstam, I. E. Tamm, The uncertainty relation between energy and time in nonrelativistic quantum mechanics Archived 2019-06-07 at the Wayback Machine, 1945.
Naber, Gregory L. (2021). Quantum Mechanics: An Introduction to the Physical Background and Mathematical Structure. Walter de Gruyter GmbH & Co KG. p. 230. ISBN 978-3-11-075194-9. Archived from the original on 2024-02-23. Retrieved 2024-01-20.
Griffiths, David J.; Schroeter, Darrell F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press. Bibcode:2018iqm..book.....G. doi:10.1017/9781316995433. ISBN 978-1-316-99543-3. Archived from the original on 2024-02-23. Retrieved 2024-01-27.
Furuta, Aya (2012), "One Thing Is Certain: Heisenberg's Uncertainty Principle Is Not Dead", Scientific American, archived from the original on 2022-04-01, retrieved 2018-10-20
Wheeler, John Archibald (1978-01-01), Marlow, A. R. (ed.), "The 'Past' and the 'Delayed-Choice' Double-Slit Experiment", Mathematical Foundations of Quantum Theory, Academic Press, pp. 9–48, doi:10.1016/b978-0-12-473250-6.50006-6, ISBN 978-0-12-473250-6, archived from the original on 2022-12-10, retrieved 2023-07-19
Wheeler, John Archibald (1977), Lopes, José Leite; Paty, Michel (eds.), "Include the Observer in the Wave Function?", Quantum Mechanics, A Half Century Later: Papers of a Colloquium on Fifty Years of Quantum Mechanics, Held at the University Louis Pasteur, Strasbourg, May 2–4, 1974, Episteme, Dordrecht: Springer Netherlands, pp. 1–18, doi:10.1007/978-94-010-1196-9_1, ISBN 978-94-010-1196-9, archived from the original on 2024-02-23, retrieved 2023-07-19
Davidson, Ernest R. (1965-02-15). "On Derivations of the Uncertainty Principle". The Journal of Chemical Physics. 42 (4): 1461–1462. Bibcode:1965JChPh..42.1461D. doi:10.1063/1.1696139. ISSN 0021-9606. Archived from the original on 2024-02-23. Retrieved 2024-01-20.
Giovannetti, V.; Lloyd, S.; Maccone, L. (2011). "Advances in quantum metrology". Nature Photonics. 5 (4): 222. arXiv:1102.2318. Bibcode:2011NaPho...5..222G. doi:10.1038/nphoton.2011.35. S2CID 12591819.; arXiv Archived 2020-08-06 at the Wayback Machine
Bialynicki-Birula, I.; Mycielski, J. (1975), "Uncertainty Relations for Information Entropy in Wave Mechanics", Communications in Mathematical Physics, 44 (2): 129–132, Bibcode:1975CMaPh..44..129B, doi:10.1007/BF01608825, S2CID 122277352, archived from the original on 2021-02-08, retrieved 2021-08-17
Matt Hall, "What is the Gabor uncertainty principle?" Archived 2018-02-09 at the Wayback Machine
"This Month in Physics History". www.aps.org. Archived from the original on 2011-01-30. Retrieved 2023-11-04.
Cassidy, David; Saperstein, Alvin M. (2009), "Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb", Physics Today, 63 (1), New York: Bellevue Literary Press: 185, Bibcode:2010PhT....63a..49C, doi:10.1063/1.3293416, archived from the original on Jan 4, 2024
Enz, Charles Paul; von Meyenn, Karl (1994). Writings on Physics and Philosophy by Wolfgang Pauli. Translated by Robert Schlapp. Springer-Verlag. p. 43. ISBN 3-540-56859-X. Archived from the original on 2020-08-19. Retrieved 2018-02-10.
Peres, Asher; Terno, Daniel R. (2004-01-06). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123 [111]. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Archived from the original on 2024-02-23. Retrieved 2024-01-25.

worldcat.org

Heisenberg, W. (1927) [1927-03-01]. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German). 43 (3): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. ISSN 0044-3328. S2CID 122763326.Heisenberg, W (1983) [1927]. "The actual content of quantum theoretical kinematics and mechanics". No. NAS 1.15: 77379. 1983. 43 (3–4): 172. Bibcode:1983ZhPhy..43..172H. Archived from the original on 2023-09-02. Retrieved 2023-08-28. English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Hilgevoord, Jan (1996-12-01). "The uncertainty principle for energy and time". American Journal of Physics. 64 (12): 1451–1456. Bibcode:1996AmJPh..64.1451H. doi:10.1119/1.18410. ISSN 0002-9505. Archived from the original on 2024-02-23. Retrieved 2023-11-12.
Lynch, F. J.; Holland, R. E.; Hamermesh, M. (1960-10-15). "Time Dependence of Resonantly Filtered Gamma Rays from Fe 57". Physical Review. 120 (2): 513–520. doi:10.1103/PhysRev.120.513. ISSN 0031-899X.
Bohm, Arno R.; Sato, Yoshihiro (2005-04-28). "Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution". Physical Review D. 71 (8): 085018. arXiv:hep-ph/0412106. Bibcode:2005PhRvD..71h5018B. doi:10.1103/PhysRevD.71.085018. ISSN 1550-7998. S2CID 119417992.
Karplus, Martin, and Porter, Richard Needham (1970). Atoms and Molecules. California: Benjamin Cummings. p. 68 ISBN 978-0805352184. OCLC 984466711
De Broglie, Louis (October 1923). "Waves and Quanta". Nature. 112 (2815): 540. Bibcode:1923Natur.112..540D. doi:10.1038/112540a0. ISSN 1476-4687. S2CID 186242764.
Davidson, Ernest R. (1965-02-15). "On Derivations of the Uncertainty Principle". The Journal of Chemical Physics. 42 (4): 1461–1462. Bibcode:1965JChPh..42.1461D. doi:10.1063/1.1696139. ISSN 0021-9606. Archived from the original on 2024-02-23. Retrieved 2024-01-20.
Luis, Alfredo (2017-03-13). "Breaking the weak Heisenberg limit". Physical Review A. 95 (3): 032113. arXiv:1607.07668. Bibcode:2017PhRvA..95c2113L. doi:10.1103/PhysRevA.95.032113. ISSN 2469-9926. S2CID 55838380.
Peres, Asher; Terno, Daniel R. (2004-01-06). "Quantum information and relativity theory". Reviews of Modern Physics. 76 (1): 93–123 [111]. arXiv:quant-ph/0212023. Bibcode:2004RvMP...76...93P. doi:10.1103/RevModPhys.76.93. ISSN 0034-6861. S2CID 7481797. Archived from the original on 2024-02-23. Retrieved 2024-01-25.

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Indian Institute of Technology Madras, Professor V. Balakrishnan, Lecture 1 – Introduction to Quantum Physics; Heisenberg's uncertainty principle, National Programme of Technology Enhanced Learning on YouTube