We investigate Euler-type local momentum conservation laws valid for various stochastic phase - space processes. The involved pressure contribution notoriously appears in a characteristic functional form $\\pm \\overrightarrow{\\nabla} [ 2d^2(t) \\frac{\\triangle \\rho ^{1/2}}{\\rho ^{1/2}}]$ which stays in close affinity with the quantum mechanical notion of the de Broglie - Bohm potential and its role in the hydrodynamical formulation of quantum dynamics.We investigate Euler-type local momentum conservation laws valid for various stochastic phase - space processes. The involved pressure contribution notoriously appears in a characteristic functional form $\\pm \\overrightarrow{\\nabla} [ 2d^2(t) \\frac{\\triangle \\rho ^{1/2}}{\\rho ^{1/2}}]$ which stays in close affinity with the quantum mechanical notion of the de Broglie - Bohm potential and its role in the hydrodynamical formulation of quantum dynamics.

Mar 5, 20026 citations

Phase-space dynamics and quantum mechanics

Jens Peder Dahl

Theoretical Chemistry AccountsJan 1, 19927 citations

Quantum Potential and Symmetries in Extended Phase Space

S. Nasiri

The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique.This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space.It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation.The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one.The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation.The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique.This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space.It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation.The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one.The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation.

arXiv:quant-ph/0511125Symmetry Integrability and Geometry Methods and ApplicationsJun 27, 20063 citations

Marginal behavior of the quantum potential in Extended Phase Space

Samira Bahrami, S. Nasiri

Here, the concept of quantum potential that has been illustrated in Extended Phase Space (EPS) in previous works is explored for its marginal behavior. Unlike in configuration space, different representations of the quantum mechanics can be found in EPS when exploiting appropriate canonical transformations. These canonical transformations revealed that there exist several representations in which the quantum potential could be removed not only for a particle in constant, linear and quadratic potentials, but also for a free particle. In these representations one still has the form-invariance of the ordinary Hamilton-Jacobi equation. The present work is an attempt to show that the Squeezed Wigner representation is a possible representation in which, for large values of squeezing parameter, the quantum potential disappears from the dynamical equation for a particle in the general potentialHere, the concept of quantum potential that has been illustrated in Extended Phase Space (EPS) in previous works is explored for its marginal behavior. Unlike in configuration space, different representations of the quantum mechanics can be found in EPS when exploiting appropriate canonical transformations. These canonical transformations revealed that there exist several representations in which the quantum potential could be removed not only for a particle in constant, linear and quadratic potentials, but also for a free particle. In these representations one still has the form-invariance of the ordinary Hamilton-Jacobi equation. The present work is an attempt to show that the Squeezed Wigner representation is a possible representation in which, for large values of squeezing parameter, the quantum potential disappears from the dynamical equation for a particle in the general potential

Iranian Journal of ScienceJul 6, 20110 citations

Phase-space dynamics and quantum mechanics

Walter J. Deal

Theoretical Chemistry AccountsJan 1, 19905 citations

\\pm \\overrightarrow{\\nabla} [ 2d^2(t) \\frac{\\triangle \\rho ^{1/2}}{\\rho ^{1/2}}]

which stays in close affinity with the quantum mechanical notion of the de Broglie - Bohm potential and its role in the hydrodynamical formulation of quantum dynamics.