Hydrodynamic Model of Quantum Mechanics

Wilhelm, H. E.

doi:10.1103/physrevd.1.2278

Cited by 91 publications

(53 citation statements)

References 16 publications

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“…However, it is interesting to examine the hydrodynamic model of quantum mechanics, 26,[40][41][42][43][44][45] where the concept of trajectory is reintroduced. It will emerge that, in line with arguments developed in Sec.…”

Section: Trajectories In Quantum Mechanicsmentioning

confidence: 99%

“…In this approach, the evolution of the system is interpreted in terms of a flowing fluid that is approximated by a finite collection of representative particles. The wave function is put in its polar form [40][41][42][43] ψ (x,t) = A(x,t) e i S(x, t)/ , (8.1) in which S has the dimension of an action, whereas A is the square root of a density function that has the dimension L …”

Section: Trajectories In Quantum Mechanicsmentioning

confidence: 99%

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Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

Lorquet

2015

The Journal of Chemical Physics

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The purpose of the present work is to determine initial conditions that generate reacting, recrossingfree trajectories that cross the conventional dividing surface of transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) without ever returning to it. Local analytical equations of motion valid in the neighborhood of this planar surface have been derived as an expansion in Poisson brackets. We show that the mere presence of a saddle point implies that reactivity criteria can be quite simply formulated in terms of elements of this series, irrespective of the shape of the potential energy function. Some of these elements are demonstrated to be equal to a sum of squares and thus to be necessarily positive, which has a profound impact on the dynamics. The method is then applied to a three-dimensional model describing an atom-diatom interaction. A particular relation between initial conditions is shown to generate a bundle of reactive trajectories that form reactive cylinders (or conduits) in phase space. This relation considerably reduces the phase space volume of initial conditions that generate recrossing-free trajectories. Loci in phase space of reactive initial conditions are presented. Reactivity is influenced by symmetry, as shown by a comparative study of collinear and bent transition states. Finally, it is argued that the rules that have been derived to generate reactive trajectories in classical mechanics are also useful to build up a reactive wave packet. C 2015 AIP Publishing LLC. [http://dx

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Section: Trajectories In Quantum Mechanicsmentioning

confidence: 99%

Section: Trajectories In Quantum Mechanicsmentioning

confidence: 99%

Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

Lorquet

2015

The Journal of Chemical Physics

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“…Ä ÐÈÏ n a ÒÓÑÔÕÑ ÊÂÏÇÐâÇÕÔâ ÄÇÎËÚËÐÑÌ n (ÕÂÍËÏ ÑÃÓÂÊÑÏ, ÊÂAEÂÈÕÔâ "ÖÓÂÄÐÇÐËÇ ÔÑÔÕÑâÐËâ" (7) AEÎâ ÍÄÂÐÕÑ-ÄÑÅÑ AEÂÄÎÇÐËâ, ÔÄâÊÞÄÂáÜÇÇ P q Ë n). ÇÕÓÖAEÐÑ ÖÃÇAEËÕßÔâ Ô ÒÑÏÑÜßá ÒÓÑÔÕÑÌ ÒÑAEÔÕÂ-ÐÑÄÍË n a 3 jc a j 2 Ô c a xY t a a xY t exp iS a xY ta" h Ä ÎÇ-ÄÖá ÚÂÔÕß (15), ÚÕÑ ÒÓÇAEÒÑÎÑÉÇÐËÇ (15) £ ÔÎÖÚÂÇ ÒÓÑAEÑÎßÐÞØ àÎÇÍÕÓÑÐÐÞØ ÑÔÙËÎÎâÙËÌ (ÔÏ. ÓÂÊAEÇÎ 5) ÖÔÎÑÄËÇ kl F 5 1 ÔÑÑÕÄÇÕÔÕÄÖÇÕ ÎÇÐÅÏáÓÑÄÔÍÑÌ ÚÂÔÕË ÔÒÇÍÕÓÂ [9,18],…”

Section: £äçAeçðëç°ôunclassified

On description of a collisionless quantum plasma

Владимиров¹,

Tyshetsky²

2011

Usp. Fiz. Nauk

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“…Using the solution for the test particle in the spherically symmetric Coulomb or Newton fields together with the method from [25], one verifies that:…”

Section: Non-differentiable Entropy Uncertainty Relationsmentioning

confidence: 99%

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

Agop

Gavriluţ

Crumpei³

et al. 2014

Entropy

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Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are introduced.First of all, the dynamics equations of the complex system entities (Schrödinger-type or fractal hydrodynamic-type) are obtained. The last one gives a specific fractal potential, which generates uncertainty relations through non-differentiable entropy. Next, the correlation between informational non-differentiable entropy and informational non-differentiable energy implies specific uncertainty relations through a maximization principle of the informational non-differentiable entropy and for a constant value of the informational non-differentiable energy. Finally, for a harmonic oscillator, the constant value of the informational non-differentiable energy is equivalent to a quantification condition. Keywords:non-differentiable entropy; informational non-differentiable entropy; informational non-differentiable energy; uncertainty relations Entropy 2014, 16 6043

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Hydrodynamic Model of Quantum Mechanics

Cited by 91 publications

References 16 publications

Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

Crossing the dividing surface of transition state theory. III. Once and only once. Selecting reactive trajectories

On description of a collisionless quantum plasma

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

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