en>BD2412: /* Discussion */minor fixes, mostly disambig links using AWB

2015-01-06T17:11:39Z

Discussion: minor fixes, mostly disambig links using AWB

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	~~{{Quantum mechanics\|cTopic=[[Interpretation of quantum mechanics\|Interpretations]]}}~~		Même 20 ans après sa mort, des fans du monde entier continuent à glorifier le petit génie de la musique, fascinés par sa manière de jouer, de penser et simplement de vivreRetour sur Claude Nougaro Salut l'ArtisteClaude Nougaro s'est éteint le jeudi 4 [http://search.huffingtonpost.com/search?q=mars+dernier&s_it=header_form_v1 mars dernier] à l'âge de 74 ans, laissant derrière lui quelques uns des plus beaux textes de la chanson française. Parce que ce rimeur hors pair était aussi un mélomane averti, AudioFanzine revient sur la carrière de celui qu'on nommait "le petit taureau".Alhambra, Bataclan, Transbordeur, Bikini, Espace Julien, Rocher de Palmer, Ferrailleur, Liberté, joue live dans 15 villes en France dans les plus belles salles du panorama. Description : De la cour des Miracles aux territoires [http://www.squidoo.com/search/results?q=contemporains contemporains] de la misère ou de la pègre, l'existence des bas fonds revient régulièrement hanter nos imaginaires. Gueux, mendiants, misérables, prostituées, criminels, grands délinquants, détenus, peuplent de leurs figures hideuses, à la fois réelles et fantasmées, l'envers pour ne pas dire le Milieu de nos sociétés. <br>[http://www.littlecornerkitchen.com/nikepascher/?fr=chaussure-nike-jordan.html chaussure nike jordan] [http://www.gatheringoftitans.com/nikepascher/?fr=chaussure-nike-homme-pas-cher.html chaussure nike homme pas cher] [http://vpv.vn/wp-includes/nikepascher/?fr=nike-running-pas-cher.html nike running pas cher]<br><br>Also visit my homepage :: [http://www.orangemast.com/nikepascher/?fr=chaussure-nike-pas-cher.html chaussure nike pas cher]
	~~The '''Madelung equations'~~'' ~~are~~ [~~[Erwin Madelung]]'s alternative formulation of the [[Schrödinger equation]]~~.

	~~==Equations~~==
	~~The Madelung equations are quantum [[Euler equations (fluid dynamics)\|Euler equations]~~]:

	:~~<math>\partial_t \rho+\nabla\cdot(\rho\bold u)=0,<~~/~~math>~~

	~~:<math>\partial_t\bold u+\bold u\cdot\nabla\bold u=-\frac{1}{m}\nabla\left(\frac{1}{\sqrt{\rho}}\hat H\sqrt{\rho}\right)=-\frac{1}{\rho}\nabla\cdot\bold p_Q-\frac{1}{m}\nabla U,<~~/~~math>~~

	~~where <math>\bold u</math> is the [[fluid dynamics\|hydrodynamic]]-like velocity in the quantum probability space with mass density <math>\bold \rho=m\|\psi\|^2~~.</~~math> The term in the brackets represents a quantum chemical potential. The kinetic energy operator from the [[Hamiltonian system\|Hamiltonian]] <math>\hat H<~~/~~math>~~ results ~~in a non-local quantum pressure tensor~~

	~~:<math>\bold p_Q~~=~~-(\hbar/2m)^2 \rho \nabla\otimes\nabla \ln \rho</math>~~

	~~or alternatively to the [[Bohm quantum potential]~~]. ~~While the latter is the icon of the [[~~de ~~Broglie–Bohm theory]]~~, ~~the quantum symbol of the Madelung hydrodynamics is <math>\bold p_Q~~.<~~/math~~> ~~The integral energy stored in the quantum pressure tensor is proportional to the~~ [~~[Fisher information]], which accounts for the quality of measurements~~.

	~~== See also ==~~
	* [[Quantum potential]]

	~~== References ==~~
	* {{cite journal \| doi = 10.~~1007~~/~~BF01504657 \| first~~ = E. ~~\| last = Madelung \| title = Eine anschauliche Deutung der Gleichung von Schrödinger \| journal = Naturwissenschaften \| year = 1926 \| volume= 14 \| pages = 1004–1004\|bibcode = 1926NW~~..~~...14.1004M \| issue~~ = ~~45 }}~~
	* {{cite journal \| doi = 10.~~1007~~/~~BF01400372 \| first = E~~. ~~\| last~~ = ~~Madelung \| title = Quantentheorie in hydrodynamischer Form \| journal = Z~~. ~~Phys. \| year = 1927 \| volume= 40 \| pages = 322–326\|bibcode = 1927ZPhy~~..~~.40..322M \| issue = 3–4 }}~~
	* {{cite journal \| doi = 10.1007/~~BF02820368 \| first~~ = M. \| last = Schönberg \| authorlink = Mário Schenberg \| title = On the hydrodynamical model of the quantum mechanics \| journal = Il Nuovo Cimento \| year = 1954 \| volume= 12 \| pages = 103–133 \|bibcode = \| issue = 1 }}
	* {{cite paper \| first = R. ~~\| last = Tsekov \| title = Bohmian Mechanics versus Madelung Quantum Hydrodynamics\| work = ArXiv Preprint \| year = 2009 \| arxiv= 0904.0723 \|bibcode = 2009arXiv0904.0723T }}~~

	~~{{DEFAULTSORT:Madelung Equations}}~~
	~~[[Category:Partial differential equations]]~~
	~~[[Category:Quantum mechanics]~~]

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en>BD2412: /* Discussion */minor fixes, mostly disambig links using AWB

en>Duoduoduo: copy editing

en>Squids and Chips: WPCleaner (v1.09) Repaired link to disambiguation page - (You can help) - Cross section