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.

aip.org

pubs.aip.org

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.
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.

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, Bibcode:1997JFAA....3..207F, 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
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.
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.
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.
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.
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
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.
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
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.
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.
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.
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
Robertson, H. P. (1929), "The Uncertainty Principle", Phys. Rev., 34 (1): 163–164, Bibcode:1929PhRv...34..163R, doi:10.1103/PhysRev.34.163
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.
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
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.
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.
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.
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.
Folland, Gerald; Sitaram, Alladi (May 1997), "The Uncertainty Principle: A Mathematical Survey", Journal of Fourier Analysis and Applications, 3 (3): 207–238, Bibcode:1997JFAA....3..207F, doi:10.1007/BF02649110, MR 1448337, S2CID 121355943
Mallat, S. G. (2009). A wavelet tour of signal processing: the sparse way. Amsterdam ; Boston: Elsevier/Academic Press. p. 44. doi:10.1016/B978-0-12-374370-1.X0001-8. ISBN 978-0-12-374370-1.
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.
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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
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.
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
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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.
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Karplus, Martin, and Porter, Richard Needham (1970). Atoms and Molecules. California: Benjamin Cummings. p. 68 ISBN 978-0805352184. OCLC 984466711

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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