Laser surface velocimeter: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
Newer edit →
en>Arcandam
m →‎External links: clean up, replaced: ==Weblinks== → == External links == using AWB
 
→‎The differential Doppler process: fixed typo... "practically" missing "p" at the beginning
Line 1: Line 1:
Many homeowners never get started on their home improvement projects. The cost, mess and hassles are enough to make anyone shy away from such projects. However, home improvement does not to be a struggle or inconvenience. If you plan these projects the right way and have the right info beforehand, you will be happy!<br><br>Wires and cords can be a safety hazard and unsightly. When doing home improvements, consider adding your home surround sound and networking wires into your attic. If everything is ready to go and wired for these amenities, you will be able to use this as a selling point for your home later.<br><br>It is important to work from the bottom up in a home improvement project. This is the exact opposite approach than you would take for many other projects, but there is a lot more mess involved in home improvement. Make sure to consider the order that you want your projects completed in.<br><br>Update your bathroom to make your house feel like a home. Every member of the family spends quite a bit of time in this room, but we often overlook giving it an update during a remodel. You can do easy changes by replacing wallpapers, lighting fixtures, and cabinetry, to create a fresh look.<br><br>Buying used chairs with bad upholstery on the seat portion isn't all bad. A lot of times, you can easily remove the seat, take out the staples holding the stretched fabric across the cushion and switch it out. You can mix match any fabric of your choice, and staple it back to the bottom with a heavy duty stapler.<br><br>Before you begin your next home improvement project, take the time to assess the current state of your home. Walking through the residence and figuring out what projects are necessities will help you plan your time and allow you to be more efficient with your work. Any projects that aren't immediately necessary can be saved for a later date.<br><br>You should always check to see if the company you have hired is legitimate. A company operating only over the phone without an actual address is probably small potatoes and potentially unreliable. Stick with firms with great reputations.<br><br>Install a pergola to add character to your home's exterior. This garden fixture will add both romance and tranquility to the [http://www.guardian.Co.uk/search?q=aesthetics aesthetics]. With a kit and a few helpers, you can install the pergola in just a weekend.<br><br>Remember those annoying little [http://Www.Dailymail.Co.uk/home/search.html?sel=site&searchPhrase=paper+jewelry paper jewelry] boxes that you get with every purchase? Don't throw them out. Instead utilize them to clean your desk or bathroom drawer. Remove the lids and clip the boxes together to fit the inside of your drawer. You can now use them to categorize and store your little things such as paper clips, erasers, notepads and other small items.<br><br>If you have repairs that need to be done on your apartment, and your landlord is not doing them, you can withhold your rent. While you do not have to pay rent for those months, you do have to place the money in an escrow account and write a certified letter to your landlord explaining why.<br><br>If you need fencing that is both affordable and versatile, opt for a wooden fence. You can choose from a variety of wood types to find the most appropriate material for your particular climate and moisture levels. Wooden fencing is very diverse and can easily be stained to one of many natural-looking colors.<br><br>If you feel that the front exterior of your house lacks character or style, consider purchasing and installing a pergola. With its rich, natural wooden look, a pergola is perfect for adding shade, visual interest and texture to the exterior of your home. You and a few friends can install a pergola in one weekend.<br><br>Take inventory of your kitchen cabinet order as soon as it arrives in your home. Make sure all of the cabinets you ordered are present, as well as all hardware, knobs and pulls. Check the finish to be sure it is correct and examine the cabinets for scratches and defects. It is far easier to fix these errors now than to discover them halfway through your remodel.<br><br>With the housing market still being so depressed, it can seem like a waste of money to even do any remodeling on your home. But the truth of the matter is that buyers are still expecting a certain level of updates in the homes that they purchase. Following these tips will ensure that you have what buyers want.<br><br>If you adored this article and you would certainly such as to obtain more information relating to [https://www.rebelmouse.com/snobbishcuff2345/need-a-roof-look-no-further-th-775445702.html specs] kindly browse through the web site.
<!-- Please leave this line alone! -->
{{Infobox scientist
| name              = Maurice de Gosson
| image            = Maurice.charlyne.degosson.png
| image_size        =
| caption          = Maurice and Charlyne de Gosson
| birth_date        = {{birth date|1948|03|13|df=y}}
| birth_place      = [[Berlin]], [[Germany]]
| residence        = [[Vienna]], [[Austria]]
| field            = [[Harmonic analysis]], [[Symplectic geometry]],<br>[[Quantum mechanics]]
| alma_mater        = [[University of Nice]]<br>[[University of Paris 6]]
| known_for        = Applications of the principle of the symplectic camel to physics
| spouse            = Charlyne de Gosson
}}
 
'''Maurice A. de Gosson''' (born 13 March 1948), (also known as Maurice Alexis de Gosson de Varennes) is an  [[Austria]]n mathematician and mathematical physicist, born in 1948 in Berlin.<ref>Biography at the NuHAG website – University of Vienna, ([http://homepage.univie.ac.at/maurice.de.gosson/])</ref> He is currently a Senior Researcher at the Numerical Harmonic Analysis Group (NuHAG)<ref>Numerical Harmonic Analysis Group website, University of Vienna ([http://www.univie.ac.at/nuhag-php/home/])</ref> of the [[University of Vienna]].<ref>Homepage at the NuHAG website – University of Vienna, ([http://homepage.univie.ac.at/maurice.de.gosson/])</ref>
 
== Work ==
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.<ref>University website, short biography – 2011 ([http://homepage.univie.ac.at/maurice.de.gosson/])</ref><ref>University website, Research section([http://homepage.univie.ac.at/maurice.de.gosson/research.htm])</ref>
 
== Visiting positions ==
 
Maurice de Gosson has held longer visiting positions at [[Yale University]]
,<ref>AMS.org - Mathematics Calendar([http://www.ams.org/notices/199801/people.pdf])</ref><ref>IOPscience, ip.org ([http://iopscience.iop.org/0305-4470/31/18/013])</ref> [[University of Colorado]] in [[Boulder]] (Ulam Visiting Professor)
,<ref>AMS.org - Mathematics Calendar([http://www.ams.org/notices/199906/mathcal.pdf])</ref> [[University of Potsdam]], [[Albert-Einstein-Institut]] (Golm), [[Max-Planck-Institut für Mathematik]] ([[Bonn]]), [[Université Paul Sabatier]] ([[Toulouse]]), [[Jacobs Universität]] ([[Bremen]])
 
== The symplectic camel ==
 
Maurice de Gosson was the first to prove that [[Mikhail Leonidovich Gromov|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).<ref>Reich, New Scientist – ([http://www.newscientist.com/article/mg20126973.900-how-camels-could-explain-quantum-uncertainty.html]), 2009</ref> This rather unexpected result was discussed in the media.<ref name="www.newscientist.com">{{Cite web  | last = Samuel Reich| first = Eugenie | title = How camels could explain quantum uncertainty | url = http://www.newscientist.com/article/mg20126973.900-how-camels-could-explain-quantum-uncertainty.html | publisher = New Scientist | date = 26 February 2009 | accessdate = 18 December 2013 }}</ref>
 
== Quantum blobs ==
 
In 2004/2005,<ref>M. de Gosson (2004), Phys. Lett. A, vol.&nbsp;330, pp.&nbsp;161 ff., and M. de Gosson (2005), Bull. Sci. Math., vol.&nbsp;129, pp.&nbsp;211, both cited according to M. de Gosson (2005), ''Symplectically covariant Schrödinger equation in phase space'', ''Journal of Physics A, Mathematics and General'', vol.&nbsp;38, pp.&nbsp;9263-9287 (2005)</ref> de Gosson showed that Gromov's non-squeezing theorem allows a coarse graining of phase space by ''symplectic quantum cells'', each described by a mean momentum and a mean position. The cell is invariant under [[canonical transformation]]s. De Gosson called such a quantum cell a ''quantum blob'':
:The quantum blob is the image of a phase space ball with radius <math>\sqrt{ \hbar }</math> by a (linear) [[symplectic transformation]].<ref name="de-gosson-2004-0407129v1">Maurice A. de Gosson: ''On the goodness of "quantum blobs" in phase space quantization'', [http://arxiv.org/abs/quant-ph/0407129v1 arXiv:quant-ph/0407129v1], submitted 16 July 2004 (however, dated February 1, 2008)</ref>
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.”<ref name="de-gosson-2011-quantum-blobs">Maurice A. de Gosson: ''Quantum blobs'', [http://arxiv.org/abs/1106.5468v1 http://arxiv.org/abs/1106.5468v1], submitted 27 June 2011</ref>
 
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.<ref>[http://www.freewebs.com/cvdegosson/thesymplecticcamel.htm The symplectic camel: the tip of an iceberg?], website of Maurice A. de Gosson, downloaded October 5, 2012</ref><ref>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</ref>
 
== Influence ==
 
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;<ref name="de-gosson-2011-quantum-blobs"/><ref>D. Dragoman: ''Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem'', 2005 Physica Scripta, vol.&nbsp;72, no.&nbsp;2, pp.&nbsp;290–295, {{DOI|10.1238/Physica.Regular.072a00290}}, [http://arxiv.org/abs/quant-ph/0402100 arXiv:quant-ph/0402100] submitted 16 February 2004</ref> 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.<ref>D. Dragoman: ''Quantum-like classical mechanics in non-commutative phase space'', Proceedings of the Romanian Academy, Series A, vol.&nbsp;12, no.&nbsp;2/2011, pp.&nbsp;95–99 ([http://www.acad.ro/sectii2002/proceedings/doc2011-2/03-Dragoman.pdf full text])</ref>
 
== Publications ==
 
=== Books ===
 
[[File:Symplectic Geometry and Quantum Mechanics.jpg|thumb|Symplectic Geometry and Quantum Mechanics (2006)]]
* Symplectic Methods in Harmonic Analysis and Applications to Mathematical Physics; Birkhäuser (2011)<ref name="springer.com">Springer, ([http://www.springer.com/?SGWID=0-102-24-0-0&searchType=EASY_CDA&queryText=de+Gosson])</ref> ISBN 3-7643-9991-0
* Symplectic Geometry and Quantum Mechanics. Birkhäuser, Basel, series "Operator Theory: Advances and Applications" (2006)<ref name="springer.com"/> 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 ===
* The symplectic egg. [http://arxiv.org/abs/1208.5969v1 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: [http://arxiv.org/abs/1104.5198v1 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<ref>Journal de Mathématiques Pures et Appliquées Volume 96, Issue 5, ([http://www.sciencedirect.com/science/journal/00217824])</ref>
* (With B. Hiley) Imprints of the Quantum World in Classical Mechanics. Foundations of Physics (26 February 2011), pp.&nbsp;1–22, {{doi|10.1007/s10701-011-9544-5}} ([http://www.springerlink.com/content/qn76575r55543453 abstract], [http://arxiv.org/abs/1001.4632 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<ref>J. Pseudo-Differ. Oper. Appl. 2 (2011), no. 1, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=291105])</ref>
* (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<ref>Phys. Rep. 484 (2009), no. 5, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=278137])</ref>
* The symplectic camel and the uncertainty principle: the tip of an iceberg? Found. Phys. 39 (2009), no. 2, 194–214<ref>Found. Phys. 39 (2009), no. 2, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/journaldoc.html?cn=Found_Phys])</ref>
* 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.<ref>J. Math. Pures Appl. (9) 91(2009), no. 6, ([https://univpn.univie.ac.at/+CSCO+dh756767633A2F2F6A6A6A2E6E7A662E626574++/mathscinet/search/publications.html?pg1=ISSI&s1=274281])</ref>
* 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.&nbsp;38 (2005), no.&nbsp;42, pp.&nbsp;9263, {{DOI|10.1088/0305-4470/38/42/007}}, [http://arxiv.org/abs/math-ph/0505073v3 arXiv:math-ph/0505073v3] submitted 27 May 2005, version of 30 July 2005
 
== References ==
{{Reflist}}
 
== External links ==
* [http://www.freewebs.com/cvdegosson/ Personal homepage]
* Lectures:
** M. de Gosson, [[Basil Hiley|B. Hiley]]: [http://www.freewebs.com/cvdegosson/TalkBileyFest.pdf Zeno paradox for Bohmian trajectories: The unfolding of the metatron], November 2010
** Maurice A. de Gosson: [http://www.freewebs.com/cvdegosson/Oxford2010.pdf Imprints of classical mechanics in the quantum world. Schrödinger equation and the uncertainty principle], October 2010
* http://books.google.at/books/about/Symplectic_Geometry_And_Quantum_Mechanic.html?id=q9SHRvay75IC&redir_esc=y
* http://iopscience.iop.org/0305-4470/34/47/313/
* http://rd.springer.com/article/10.1007/s10701-009-9272-2
* http://www.amazon.com/Metaplectic-Representation-Lagrangian-Quantization-Mathematical/dp/3527400877
* http://adsabs.harvard.edu/abs/2007RvMaP..19.1149D
* http://rd.springer.com/article/10.1007/s11005-007-0150-6
* http://iopscience.iop.org/0305-4470/36/48/L01/
* http://rd.springer.com/article/10.1007/s11005-008-0261-8
* http://rd.springer.com/article/10.1007/s10455-008-9106-z
* http://adsabs.harvard.edu/abs/2011arXiv1106.5468D
* http://adsabs.harvard.edu/abs/2004quant.ph..7129D
* https://www.interllective.com/arxiv/article/1106.5468
* https://www.researchgate.net/publication/51968170_The_Reconstruction_Problem_and_Weak_Quantum_Values
 
{{Persondata
| NAME              = Gosson, Maurice A. De
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Austrian mathematician
| DATE OF BIRTH    = 13 March 1948
| PLACE OF BIRTH    = [[Berlin]], [[Germany]]
| DATE OF DEATH    =
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Gosson, Maurice A. De}}
[[Category:Articles created via the Article Wizard]]
[[Category:Austrian mathematicians]]
[[Category:20th-century mathematicians]]
 
 
 
<!--Please don't change anything and press save -->
[[Category:1948 births]]
[[Category:Living people]]

Revision as of 15:37, 17 October 2013

Template:Infobox scientist

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]

Work

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

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

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

In 2004/2005,[11] de Gosson showed that Gromov's non-squeezing theorem allows a coarse graining of phase space by symplectic quantum cells, each described by a mean momentum and a mean position. The cell is invariant under canonical transformations. De Gosson called such a quantum cell a quantum blob:

The quantum blob is the image of a phase space ball with radius by a (linear) symplectic transformation.[12]

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.”[13]

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.[14][15]

Influence

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;[13][16] 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.[17]

Publications

Books

Symplectic Geometry and Quantum Mechanics (2006)
  • Symplectic Methods in Harmonic Analysis and Applications to Mathematical Physics; Birkhäuser (2011)[18] ISBN 3-7643-9991-0
  • Symplectic Geometry and Quantum Mechanics. Birkhäuser, Basel, series "Operator Theory: Advances and Applications" (2006)[18] 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

  • 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[19]
  • (With B. Hiley) Imprints of the Quantum World in Classical Mechanics. Foundations of Physics (26 February 2011), pp. 1–22, 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park. (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[20]
  • (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[21]
  • The symplectic camel and the uncertainty principle: the tip of an iceberg? Found. Phys. 39 (2009), no. 2, 194–214[22]
  • 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.[23]
  • 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, Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting ., arXiv:math-ph/0505073v3 submitted 27 May 2005, version of 30 July 2005

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

Template:Persondata

  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. ↑ IOPscience, ip.org ([7])
  8. ↑ AMS.org - Mathematics Calendar([8])
  9. ↑ Reich, New Scientist – ([9]), 2009
  10. ↑ Template:Cite web
  11. ↑ 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)
  12. ↑ Maurice A. de Gosson: On the goodness of "quantum blobs" in phase space quantization, arXiv:quant-ph/0407129v1, submitted 16 July 2004 (however, dated February 1, 2008)
  13. ↑ 13.0 13.1 Maurice A. de Gosson: Quantum blobs, http://arxiv.org/abs/1106.5468v1, submitted 27 June 2011
  14. ↑ The symplectic camel: the tip of an iceberg?, website of Maurice A. de Gosson, downloaded October 5, 2012
  15. ↑ 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
  16. ↑ D. Dragoman: Phase Space Formulation of Quantum Mechanics. Insight into the Measurement Problem, 2005 Physica Scripta, vol. 72, no. 2, pp. 290–295, Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting ., arXiv:quant-ph/0402100 submitted 16 February 2004
  17. ↑ 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)
  18. ↑ 18.0 18.1 Springer, ([10])
  19. ↑ Journal de Mathématiques Pures et Appliquées Volume 96, Issue 5, ([11])
  20. ↑ J. Pseudo-Differ. Oper. Appl. 2 (2011), no. 1, ([12])
  21. ↑ Phys. Rep. 484 (2009), no. 5, ([13])
  22. ↑ Found. Phys. 39 (2009), no. 2, ([14])
  23. ↑ J. Math. Pures Appl. (9) 91(2009), no. 6, ([15])
Retrieved from "https://en.formulasearchengine.com/index.php?title=Laser_surface_velocimeter&oldid=27105"