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Maurice A. de Gosson

October 28, 2023

Maurice A. de Gosson (born 13 March 1948), (also known as Maurice Alexis de Gosson de Varennes) is an Austrian mathematician and mathematical physicist, born in 1948 in Berlin.[1] He is currently a Senior Researcher at the Numerical Harmonic Analysis Group (NuHAG)[2] of the University of Vienna.[3]

Maurice de Gosson
Maurice and Charlyne de Gosson
Born (1948-03-13) 13 March 1948 (age 75)
Berlin, Germany
Alma materUniversity of Nice
University of Paris 6
Known forApplications of the principle of the symplectic camel to physics
SpouseCharlyne de Gosson
Scientific career
FieldsHarmonic analysis, Symplectic geometry,
Quantum mechanics

Work edit

After completing his PhD in microlocal analysis at the University of Nice in 1978 under the supervision of Jacques Chazarain, de Gosson soon became fascinated by Jean Leray's Lagrangian analysis. Under Leray's tutorship de Gosson completed a Habilitation à Diriger des Recherches en Mathématiques at the University of Paris 6 (1992). During this period he specialized in the study of the Leray–Maslov index and in the theory of the metaplectic group, and their applications to mathematical physics. In 1998 de Gosson met Basil Hiley, who triggered his interest in conceptual question in quantum mechanics. Basil Hiley wrote a foreword to de Gosson's book The Principles of Newtonian and Quantum Mechanics (Imperial College Press, London). After having spent several years in Sweden as Associate Professor and Professor in Sweden, de Gosson was appointed in 2006 at the Numerical Harmonic Analysis Group of the University of Vienna, created by Hans Georg Feichtinger (see www.nuhag.eu). He currently works in symplectic methods in harmonic analysis, and on conceptual questions in quantum mechanics, often in collaboration with Basil Hiley.[4][5]

Visiting positions edit

Maurice de Gosson has held longer visiting positions at Yale University ,[6][7] University of Colorado in Boulder (Ulam Visiting Professor) ,[8] University of Potsdam, Albert-Einstein-Institut (Golm), Max-Planck-Institut für Mathematik (Bonn), Université Paul Sabatier (Toulouse), Jacobs Universität (Bremen)

The symplectic camel edit

Maurice de Gosson was the first to prove that Mikhail Gromov's symplectic non-squeezing theorem (also called „the Principle of the Symplectic Camel“) allowed the derivation of a classical uncertainty principle formally totally similar to the Robertson–Schrödinger uncertainty relations (i.e. the Heisenberg inequalities in a stronger form where the covariances are taken into account).[9] This rather unexpected result was discussed in the media.[10]

Quantum blobs edit

In 2003, Gosson introduced the notion of quantum blobs, which are defined in terms of symplectic capacities and are invariant under canonical transformations.[11] Shortly after,[12] he showed that Gromov's non-squeezing theorem allows a coarse graining of phase space by such quantum blobs (or symplectic quantum cells), each described by a mean momentum and a mean position:

The quantum blob is the image of a phase space ball with radius   by a (linear) symplectic transformation.[13]

and

"Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture."[14]

Their invariance property distinguishes de Gosson's quantum blobs from the "quantum cells" known in thermodynamics, which are units of phase space with a volume of the size of Planck's constant h to the power of 3.[15][16]

Together with G. Dennis and Basil Hiley, de Gosson laid out examples of how the quantum blob can be seen as a "blow-up" of a particle in phase space. To demonstrate this, they picked up on "Fermi's trick"[17] which allows to identify an arbitrary wavefunction as a stationary state for some Hamiltonian operator. They showed that this blow-up requires internal energy that comes from the particle itself, involving the kinetic energy and David Bohm's quantum potential.[18][19]

In the classical limit, the quantum blob becomes a point particle.[20]

Influence edit

De Gosson's notion of quantum blobs has given rise to a proposal for a new formulation of quantum mechanics, which is derived from postulates on quantum-blob-related limits to the extent and localization of quantum particles in phase space;[14][21] this proposal is strengthened by the development of a phase space approach that applies to both quantum and classical physics, where a quantum-like evolution law for observables can be recovered from the classical Hamiltonian in a non-commutative phase space, where x and p are (non-commutative) c-numbers, not operators.[22]

Publications edit

Books edit

 
Symplectic Geometry and Quantum Mechanics (2006)
  • Symplectic Methods in Harmonic Analysis and Applications to Mathematical Physics; Birkhäuser (2011)[23] ISBN 3-7643-9991-0
  • Symplectic Geometry and Quantum Mechanics. Birkhäuser, Basel, series "Operator Theory: Advances and Applications" (2006)[23] ISBN 3-7643-7574-4
  • The Principles of Newtonian and Quantum Mechanics: the Need for Planck's Constant h; with a foreword by B. Hiley. Imperial College Press (2001) ISBN 1-86094-274-1
  • Maslov Classes, Metaplectic Representation and Lagrangian Quantization. Mathematical Research 95, Wiley VCH (1997), ca 190 pages ISBN 3-527-40087-7
  • In preparation: Mathematical and Physical Aspects of Quantum Processes (with Basil Hiley)
  • In preparation: Pseudo-Differential operators and Quantum Mechanics

Selected recent papers edit

  • The symplectic egg. arXiv:1208.5969v1, to appear in American Journal of Physics (2013)
  • Symplectic Covariance Properties for Shubin and Born Jordan Pseudo-Differential Operators. Trans. Amer. Math. Soc. (2012) (abridged version: arXiv:1104.5198v1 submitted 27 April 2011)
  • A pseudo-differential calculus on non-standard symplectic space; Spectral and regularity results in modulation spaces. Journal de Mathématiques Pures et Appliquées Volume 96, Issue 5, November 2011, Pages 423-445[24]
  • (With B. Hiley) Imprints of the Quantum World in Classical Mechanics. Foundations of Physics (26 February 2011), pp. 1–22, doi:10.1007/s10701-011-9544-5 (abstract, arXiv:1001.4632 submitted 26 January 2010, version of 15 December 2010)
  • (with F. Luef) Preferred quantization rules: Born-Jordan versus Weyl. The pseudo-differential point of view. J. Pseudo-Differ. Oper. Appl. 2 (2011), no. 1, 115–139[25]
  • (with N. Dias F. Luef, J. Prata, João) A deformation quantization theory for noncommutative quantum mechanics. J. Math. Phys. 51 (2010), no. 7, 072101, 12 pp.
  • (with F. Luef) Symplectic capacities and the geometry of uncertainty: the irruption of symplectic topology in classical and quantum mechanics.Phys. Rep. 484 (2009), no. 5, 131–179[26]
  • The symplectic camel and the uncertainty principle: the tip of an iceberg? Found. Phys. 39 (2009), no. 2, 194–214[27]
  • On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths. J. Math. Pures Appl. (9) 91(2009), no. 6, 598–613.[28]
  • Spectral properties of a class of generalized Landau operators. Comm. Partial Differential Equations 33 (2008), no. 10-12, 2096–2104
  • Metaplectic representation, Conley–Zehnder index, and Weyl calculus on phase space. Rev. Math. Phys. 19 (2007), no. 10, 1149–1188.
  • Symplectically covariant Schrödinger equation in phase space. Journal of Physics A, vol. 38 (2005), no. 42, pp. 9263, doi:10.1088/0305-4470/38/42/007, arXiv:math-ph/0505073v3 submitted 27 May 2005, version of 30 July 2005

References edit

  1. ^ Biography at the NuHAG website – University of Vienna, ([1])
  2. ^ Numerical Harmonic Analysis Group website, University of Vienna ([2])
  3. ^ Homepage at the NuHAG website – University of Vienna, ([3])
  4. ^ University website, short biography – 2011 ([4])
  5. ^ University website, Research section([5])
  6. ^ AMS.org - Mathematics Calendar([6])
  7. ^ Gosson, Maurice de (1998). "The quantum motion of half-densities and the derivation of Schrödinger's equation". Journal of Physics A: Mathematical and General. 31 (18): 4239–4247. Bibcode:1998JPhA...31.4239D. doi:10.1088/0305-4470/31/18/013.
  8. ^ AMS.org - Mathematics Calendar([7])
  9. ^ Reich, New Scientist – ([8]), 2009
  10. ^ Samuel Reich, Eugenie (26 February 2009). "How camels could explain quantum uncertainty". New Scientist. Retrieved 18 December 2013.
  11. ^ de Gosson, Maurice A (2003). "Phase space quantization and the uncertainty principle". Physics Letters A. 317 (5–6): 365–369. Bibcode:2003PhLA..317..365D. doi:10.1016/j.physleta.2003.09.008. ISSN 0375-9601.
  12. ^ M. de Gosson (2004), Phys. Lett. A, vol. 330, pp. 161 ff., and M. de Gosson (2005), Bull. Sci. Math., vol. 129, pp. 211, both cited according to M. de Gosson (2005), Symplectically covariant Schrödinger equation in phase space, Journal of Physics A, Mathematics and General, vol. 38, pp. 9263-9287 (2005)
  13. ^ Maurice de Gosson (2004). "On the goodness of "quantum blobs" in phase space quantization". arXiv:quant-ph/0407129.
  14. ^ a b De Gosson, Maurice A. (2013). "Quantum Blobs". Foundations of Physics. 43 (4): 440–457. arXiv:1106.5468. Bibcode:2013FoPh...43..440D. doi:10.1007/s10701-012-9636-x. PMC 4267529. PMID 25530623.
  15. ^ The symplectic camel: the tip of an iceberg?, website of Maurice A. de Gosson, downloaded October 5, 2012
  16. ^ M. A. de Gosson: The Principles of Newtonian & Quantum Mechanics: The Need for Planck's Constant, h, Imperial College Press, 2001, ISBN 978-1860942747, p. 120
  17. ^ de Gosson, Maurice A. (2012). "A Geometric Picture of the Wave Function: Fermi's Trick". arXiv:1208.0908 [quant-ph].
  18. ^ Dennis, Glen; de Gosson, Maurice A.; Hiley, Basil J. (2014). "Fermi's ansatz and Bohm's quantum potential". Physics Letters A. 378 (32–33): 2363–2366. Bibcode:2014PhLA..378.2363D. doi:10.1016/j.physleta.2014.05.020. ISSN 0375-9601.
  19. ^ Dennis, Glen; De Gosson, Maurice A.; Hiley, Basil J. (2015). "Bohm's quantum potential as an internal energy". Physics Letters A. 379 (18–19): 1224–1227. arXiv:1412.5133. Bibcode:2015PhLA..379.1224D. doi:10.1016/j.physleta.2015.02.038. S2CID 118575562.
  20. ^ See for example: B. J. Hiley: Foundations of Quantum Theory in the Light of Bohmian Non-commutative Dynamics, The Finnish Society for Natural Philosophy 25 Years K.V. Laurikainen Honorary Symposium 2013 / 2 April 2014
  21. ^ Dragoman, D. (2005). "Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem". Physica Scripta. 72 (4): 290–296. arXiv:quant-ph/0402021. Bibcode:2005PhyS...72..290D. doi:10.1238/Physica.Regular.072a00290. S2CID 404487.
  22. ^ D. Dragoman: Quantum-like classical mechanics in non-commutative phase space, Proceedings of the Romanian Academy, Series A, vol. 12, no. 2/2011, pp. 95–99 (full text)
  23. ^ a b Springer, ([9])
  24. ^ Journal de Mathématiques Pures et Appliquées Volume 96, Issue 5, ([10])
  25. ^ J. Pseudo-Differ. Oper. Appl. 2 (2011), no. 1, ([11])
  26. ^ Phys. Rep. 484 (2009), no. 5, ([12])
  27. ^ Found. Phys. 39 (2009), no. 2, ([13])
  28. ^ J. Math. Pures Appl. (9) 91(2009), no. 6, ([14])

External links edit

  • Personal homepage
  • Lectures:
    • M. de Gosson, B. Hiley: Zeno paradox for Bohmian trajectories: The unfolding of the metatron, November 2010
    • Maurice A. de Gosson: Imprints of classical mechanics in the quantum world. Schrödinger equation and the uncertainty principle, October 2010
  • De Gosson, Maurice A. (6 August 2006). Symplectic Geometry and Quantum Mechanics. ISBN 9783764375751.
  • Gosson, Maurice de (2001). "The symplectic camel and phase space quantization". Journal of Physics A: Mathematical and General. 34 (47): 10085–10096. Bibcode:2001JPhA...3410085D. doi:10.1088/0305-4470/34/47/313.
  • De Gosson, Maurice A. (2009). "The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?". Foundations of Physics. 39 (2): 194–214. Bibcode:2009FoPh...39..194D. doi:10.1007/s10701-009-9272-2. S2CID 35394694.
  • https://www.amazon.com/Metaplectic-Representation-Lagrangian-Quantization-Mathematical/dp/3527400877
  • De Gosson, Maurice (2007). "Metaplectic Representation, Conley-Zehnder Index, and Weyl Calculus on Phase Space". Reviews in Mathematical Physics. 19 (10): 1149. Bibcode:2007RvMaP..19.1149D. doi:10.1142/S0129055X07003152.
  • De Gosson, Maurice; Luef, Franz (2007). "Quantum States and Hardy's Formulation of the Uncertainty Principle: A Symplectic Approach". Letters in Mathematical Physics. 80 (1): 69–82. arXiv:quant-ph/0703063. Bibcode:2007LMaPh..80...69D. doi:10.1007/s11005-007-0150-6. S2CID 16029948.
  • Gosson, Maurice de; Gosson, Serge de (2003). "The Maslov indices of Hamiltonian periodic orbits". Journal of Physics A: Mathematical and General. 36 (48): L615–L622. arXiv:math-ph/0310022. doi:10.1088/0305-4470/36/48/L01. S2CID 119175694.
  • Gosson, Maurice De; Luef, Franz (2008). "A New Approach to the ∗ -Genvalue Equation". Letters in Mathematical Physics. 85 (2–3): 173–183. doi:10.1007/s11005-008-0261-8. S2CID 122222083.
  • De Gosson, Maurice; De Gosson, Serge; Piccione, Paolo (2008). "On a product formula for the Conley–Zehnder index of symplectic paths and its applications". Annals of Global Analysis and Geometry. 34 (2): 167–183. doi:10.1007/s10455-008-9106-z. S2CID 17093414.
  • De Gosson, Maurice A. (2013). "Quantum Blobs". Foundations of Physics. 43 (4): 440–457. arXiv:1106.5468. Bibcode:2013FoPh...43..440D. doi:10.1007/s10701-012-9636-x. PMC 4267529. PMID 25530623.
  • De Gosson, Maurice (2004). "On the goodness of "quantum blobs" in phase space quantization". arXiv:quant-ph/0407129. Bibcode:2004quant.ph..7129D. {{cite journal}}: Cite journal requires |journal= (help)
  • De Gosson, Maurice A. (2013). "Quantum Blobs". Foundations of Physics. 43 (4): 440–457. arXiv:1106.5468. Bibcode:2013FoPh...43..440D. doi:10.1007/s10701-012-9636-x. PMC 4267529. PMID 25530623.
  • De Gosson, Maurice A.; De Gosson, Serge M. (2012). "The reconstruction problem and weak quantum values". Journal of Physics A: Mathematical and Theoretical. 45 (11): 115305. arXiv:1112.5773. Bibcode:2012JPhA...45k5305D. doi:10.1088/1751-8113/45/11/115305. S2CID 119296643.

October 28, 2023
maurice, gosson, born, march, 1948, also, known, maurice, alexis, gosson, varennes, austrian, mathematician, mathematical, physicist, born, 1948, berlin, currently, senior, researcher, numerical, harmonic, analysis, group, nuhag, university, vienna, maurice, g. Maurice A de Gosson born 13 March 1948 also known as Maurice Alexis de Gosson de Varennes is an Austrian mathematician and mathematical physicist born in 1948 in Berlin 1 He is currently a Senior Researcher at the Numerical Harmonic Analysis Group NuHAG 2 of the University of Vienna 3 Maurice de GossonMaurice and Charlyne de GossonBorn 1948 03 13 13 March 1948 age 75 Berlin GermanyAlma materUniversity of NiceUniversity of Paris 6Known forApplications of the principle of the symplectic camel to physicsSpouseCharlyne de GossonScientific careerFieldsHarmonic analysis Symplectic geometry Quantum mechanics Contents 1 Work 2 Visiting positions 3 The symplectic camel 4 Quantum blobs 5 Influence 6 Publications 6 1 Books 6 2 Selected recent papers 7 References 8 External linksWork editAfter completing his PhD in microlocal analysis at the University of Nice in 1978 under the supervision of Jacques Chazarain de Gosson soon became fascinated by Jean Leray s Lagrangian analysis Under Leray s tutorship de Gosson completed a Habilitation a Diriger des Recherches en Mathematiques at the University of Paris 6 1992 During this period he specialized in the study of the Leray Maslov index and in the theory of the metaplectic group and their applications to mathematical physics In 1998 de Gosson met Basil Hiley who triggered his interest in conceptual question in quantum mechanics Basil Hiley wrote a foreword to de Gosson s book The Principles of Newtonian and Quantum Mechanics Imperial College Press London After having spent several years in Sweden as Associate Professor and Professor in Sweden de Gosson was appointed in 2006 at the Numerical Harmonic Analysis Group of the University of Vienna created by Hans Georg Feichtinger see www nuhag eu He currently works in symplectic methods in harmonic analysis and on conceptual questions in quantum mechanics often in collaboration with Basil Hiley 4 5 Visiting positions editMaurice de Gosson has held longer visiting positions at Yale University 6 7 University of Colorado in Boulder Ulam Visiting Professor 8 University of Potsdam Albert Einstein Institut Golm Max Planck Institut fur Mathematik Bonn Universite Paul Sabatier Toulouse Jacobs Universitat Bremen The symplectic camel editMaurice de Gosson was the first to prove that Mikhail Gromov s symplectic non squeezing theorem also called the Principle of the Symplectic Camel allowed the derivation of a classical uncertainty principle formally totally similar to the Robertson Schrodinger uncertainty relations i e the Heisenberg inequalities in a stronger form where the covariances are taken into account 9 This rather unexpected result was discussed in the media 10 Quantum blobs editIn 2003 Gosson introduced the notion of quantum blobs which are defined in terms of symplectic capacities and are invariant under canonical transformations 11 Shortly after 12 he showed that Gromov s non squeezing theorem allows a coarse graining of phase space by such quantum blobs or symplectic quantum cells each described by a mean momentum and a mean position The quantum blob is the image of a phase space ball with radius ℏ displaystyle sqrt hbar nbsp by a linear symplectic transformation 13 and Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics of which they are a phase space picture 14 Their invariance property distinguishes de Gosson s quantum blobs from the quantum cells known in thermodynamics which are units of phase space with a volume of the size of Planck s constant h to the power of 3 15 16 Together with G Dennis and Basil Hiley de Gosson laid out examples of how the quantum blob can be seen as a blow up of a particle in phase space To demonstrate this they picked up on Fermi s trick 17 which allows to identify an arbitrary wavefunction as a stationary state for some Hamiltonian operator They showed that this blow up requires internal energy that comes from the particle itself involving the kinetic energy and David Bohm s quantum potential 18 19 In the classical limit the quantum blob becomes a point particle 20 Influence editDe Gosson s notion of quantum blobs has given rise to a proposal for a new formulation of quantum mechanics which is derived from postulates on quantum blob related limits to the extent and localization of quantum particles in phase space 14 21 this proposal is strengthened by the development of a phase space approach that applies to both quantum and classical physics where a quantum like evolution law for observables can be recovered from the classical Hamiltonian in a non commutative phase space where x and p are non commutative c numbers not operators 22 Publications editBooks edit nbsp Symplectic Geometry and Quantum Mechanics 2006 Symplectic Methods in Harmonic Analysis and Applications to Mathematical Physics Birkhauser 2011 23 ISBN 3 7643 9991 0 Symplectic Geometry and Quantum Mechanics Birkhauser Basel series Operator Theory Advances and Applications 2006 23 ISBN 3 7643 7574 4 The Principles of Newtonian and Quantum Mechanics the Need for Planck s Constant h with a foreword by B Hiley Imperial College Press 2001 ISBN 1 86094 274 1 Maslov Classes Metaplectic Representation and Lagrangian Quantization Mathematical Research 95 Wiley VCH 1997 ca 190 pages ISBN 3 527 40087 7 In preparation Mathematical and Physical Aspects of Quantum Processes with Basil Hiley In preparation Pseudo Differential operators and Quantum MechanicsSelected recent papers edit The symplectic egg arXiv 1208 5969v1 to appear in American Journal of Physics 2013 Symplectic Covariance Properties for Shubin and Born Jordan Pseudo Differential Operators Trans Amer Math Soc 2012 abridged version arXiv 1104 5198v1 submitted 27 April 2011 A pseudo differential calculus on non standard symplectic space Spectral and regularity results in modulation spaces Journal de Mathematiques Pures et Appliquees Volume 96 Issue 5 November 2011 Pages 423 445 24 With B Hiley Imprints of the Quantum World in Classical Mechanics Foundations of Physics 26 February 2011 pp 1 22 doi 10 1007 s10701 011 9544 5 abstract arXiv 1001 4632 submitted 26 January 2010 version of 15 December 2010 with F Luef Preferred quantization rules Born Jordan versus Weyl The pseudo differential point of view J Pseudo Differ Oper Appl 2 2011 no 1 115 139 25 with N Dias F Luef J Prata Joao A deformation quantization theory for noncommutative quantum mechanics J Math Phys 51 2010 no 7 072101 12 pp with F Luef Symplectic capacities and the geometry of uncertainty the irruption of symplectic topology in classical and quantum mechanics Phys Rep 484 2009 no 5 131 179 26 The symplectic camel and the uncertainty principle the tip of an iceberg Found Phys 39 2009 no 2 194 214 27 On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths J Math Pures Appl 9 91 2009 no 6 598 613 28 Spectral properties of a class of generalized Landau operators Comm Partial Differential Equations 33 2008 no 10 12 2096 2104 Metaplectic representation Conley Zehnder index and Weyl calculus on phase space Rev Math Phys 19 2007 no 10 1149 1188 Symplectically covariant Schrodinger equation in phase space Journal of Physics A vol 38 2005 no 42 pp 9263 doi 10 1088 0305 4470 38 42 007 arXiv math ph 0505073v3 submitted 27 May 2005 version of 30 July 2005References edit Biography at the NuHAG website University of Vienna 1 Numerical Harmonic Analysis Group website University of Vienna 2 Homepage at the NuHAG website University of Vienna 3 University website short biography 2011 4 University website Research section 5 AMS org Mathematics Calendar 6 Gosson Maurice de 1998 The quantum motion of half densities and the derivation of Schrodinger s equation Journal of Physics A Mathematical and General 31 18 4239 4247 Bibcode 1998JPhA 31 4239D doi 10 1088 0305 4470 31 18 013 AMS org Mathematics Calendar 7 Reich New Scientist 8 2009 Samuel Reich Eugenie 26 February 2009 How camels could explain quantum uncertainty New Scientist Retrieved 18 December 2013 de Gosson Maurice A 2003 Phase space quantization and the uncertainty principle Physics Letters A 317 5 6 365 369 Bibcode 2003PhLA 317 365D doi 10 1016 j physleta 2003 09 008 ISSN 0375 9601 M de Gosson 2004 Phys Lett A vol 330 pp 161 ff and M de Gosson 2005 Bull Sci Math vol 129 pp 211 both cited according to M de Gosson 2005 Symplectically covariant Schrodinger equation in phase space Journal of Physics A Mathematics and General vol 38 pp 9263 9287 2005 Maurice de Gosson 2004 On the goodness of quantum blobs in phase space quantization arXiv quant ph 0407129 a b De Gosson Maurice A 2013 Quantum Blobs Foundations of Physics 43 4 440 457 arXiv 1106 5468 Bibcode 2013FoPh 43 440D doi 10 1007 s10701 012 9636 x PMC 4267529 PMID 25530623 The symplectic camel the tip of an iceberg website of Maurice A de Gosson downloaded October 5 2012 M A de Gosson The Principles of Newtonian amp Quantum Mechanics The Need for Planck s Constant h Imperial College Press 2001 ISBN 978 1860942747 p 120 de Gosson Maurice A 2012 A Geometric Picture of the Wave Function Fermi s Trick arXiv 1208 0908 quant ph Dennis Glen de Gosson Maurice A Hiley Basil J 2014 Fermi s ansatz and Bohm s quantum potential Physics Letters A 378 32 33 2363 2366 Bibcode 2014PhLA 378 2363D doi 10 1016 j physleta 2014 05 020 ISSN 0375 9601 Dennis Glen De Gosson Maurice A Hiley Basil J 2015 Bohm s quantum potential as an internal energy Physics Letters A 379 18 19 1224 1227 arXiv 1412 5133 Bibcode 2015PhLA 379 1224D doi 10 1016 j physleta 2015 02 038 S2CID 118575562 See for example B J Hiley Foundations of Quantum Theory in the Light of Bohmian Non commutative Dynamics The Finnish Society for Natural Philosophy 25 Years K V Laurikainen Honorary Symposium 2013 2 April 2014 Dragoman D 2005 Phase Space Formulation of Quantum Mechanics Insight into the Measurement Problem Physica Scripta 72 4 290 296 arXiv quant ph 0402021 Bibcode 2005PhyS 72 290D doi 10 1238 Physica Regular 072a00290 S2CID 404487 D Dragoman Quantum like classical mechanics in non commutative phase space Proceedings of the Romanian Academy Series A vol 12 no 2 2011 pp 95 99 full text a b Springer 9 Journal de Mathematiques Pures et Appliquees Volume 96 Issue 5 10 J Pseudo Differ Oper Appl 2 2011 no 1 11 Phys Rep 484 2009 no 5 12 Found Phys 39 2009 no 2 13 J Math Pures Appl 9 91 2009 no 6 14 External links editPersonal homepage Lectures M de Gosson B Hiley Zeno paradox for Bohmian trajectories The unfolding of the metatron November 2010 Maurice A de Gosson Imprints of classical mechanics in the quantum world Schrodinger equation and the uncertainty principle October 2010 De Gosson Maurice A 6 August 2006 Symplectic Geometry and Quantum Mechanics ISBN 9783764375751 Gosson Maurice de 2001 The symplectic camel and phase space quantization Journal of Physics A Mathematical and General 34 47 10085 10096 Bibcode 2001JPhA 3410085D doi 10 1088 0305 4470 34 47 313 De Gosson Maurice A 2009 The Symplectic Camel and the Uncertainty Principle The Tip of an Iceberg Foundations of Physics 39 2 194 214 Bibcode 2009FoPh 39 194D doi 10 1007 s10701 009 9272 2 S2CID 35394694 https www amazon com Metaplectic Representation Lagrangian Quantization Mathematical dp 3527400877 De Gosson Maurice 2007 Metaplectic Representation Conley Zehnder Index and Weyl Calculus on Phase Space Reviews in Mathematical Physics 19 10 1149 Bibcode 2007RvMaP 19 1149D doi 10 1142 S0129055X07003152 De Gosson Maurice Luef Franz 2007 Quantum States and Hardy s Formulation of the Uncertainty Principle A Symplectic Approach Letters in Mathematical Physics 80 1 69 82 arXiv quant ph 0703063 Bibcode 2007LMaPh 80 69D doi 10 1007 s11005 007 0150 6 S2CID 16029948 Gosson Maurice de Gosson Serge de 2003 The Maslov indices of Hamiltonian periodic orbits Journal of Physics A Mathematical and General 36 48 L615 L622 arXiv math ph 0310022 doi 10 1088 0305 4470 36 48 L01 S2CID 119175694 Gosson Maurice De Luef Franz 2008 A New Approach to the Genvalue Equation Letters in Mathematical Physics 85 2 3 173 183 doi 10 1007 s11005 008 0261 8 S2CID 122222083 De Gosson Maurice De Gosson Serge Piccione Paolo 2008 On a product formula for the Conley Zehnder index of symplectic paths and its applications Annals of Global Analysis and Geometry 34 2 167 183 doi 10 1007 s10455 008 9106 z S2CID 17093414 De Gosson Maurice A 2013 Quantum Blobs Foundations of Physics 43 4 440 457 arXiv 1106 5468 Bibcode 2013FoPh 43 440D doi 10 1007 s10701 012 9636 x PMC 4267529 PMID 25530623 De Gosson Maurice 2004 On the goodness of quantum blobs in phase space quantization arXiv quant ph 0407129 Bibcode 2004quant ph 7129D a href Template Cite journal html title Template Cite journal cite journal a Cite journal requires journal help De Gosson Maurice A 2013 Quantum Blobs Foundations of Physics 43 4 440 457 arXiv 1106 5468 Bibcode 2013FoPh 43 440D doi 10 1007 s10701 012 9636 x PMC 4267529 PMID 25530623 De Gosson Maurice A De Gosson Serge M 2012 The reconstruction problem and weak quantum values Journal of Physics A Mathematical and Theoretical 45 11 115305 arXiv 1112 5773 Bibcode 2012JPhA 45k5305D doi 10 1088 1751 8113 45 11 115305 S2CID 119296643 Retrieved from https en wikipedia org w index php title Maurice A de Gosson amp oldid 1179829522, wikipedia, wiki, book, books, library,

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