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Compt. rend.

A PHYSICAL MODEL OF THE QUANTUM WAVE

J. C. Aron

Published Aug 22, 1960• 0 citations
OpenAlex

Abstract

It has been established that the energy density derived from the Pauli equation shows an interaction between the spins of neighboring elements, tending to re-establish the parallelism. The spin fluctuations are propagated slowly by this action. In the present work, it is shown that from the hydrodynamic representation of the Dirac equation and the Feynnnan and Gell-Mann equation solutions can be derived which correspond to a vibration. (tr-auth)

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THE HYDRODYNAMIC REPRESENTATION OF THE FEYNMAN AND GELL-MANN EQUATION

J. C. Aron

ABS>A hydrodynamic representation was established for the Dirac equation, eliminating the wave functions and including only physical magnitudes. It is shown, in the present article, that a hydrodyramic representation can also be obtained for the Feynman and Gell-Mann equation. This representation, with some corrective terms, agrees with that of the Pauli and Dirac equations. (tr- auth)

Compt. rend.•Aug 17, 1960•0 citations

The Hydrodynamic Representation of the Quantum Relativistic Dynamics of the Electron

Loris D’Alessi

In this work, the action of the relativistic electron is derived from the hydrodynamic formulation of the Dirac equation. In particular, in the hydrodynamic scenario, the four-velocity of the electron is regarded as an Eulerian field and the electron spin interacts with the corresponding vorticity field. In the second part of the work, it is shown how the second order Dirac equation can be derived from a principle of Minimum Fisher Information.

arXiv:2309.04495•Sep 7, 2023•0 citations

The Quantum Hydrodynamic Formulation of Dirac Equation and Its Generalized Stochastic and Non-linear Analogs

Piero Chiarelli

The quantum hydrodynamic like equations as a function of two real sets of variables, the 4x4 action matrix and the 4 dimensional wave function modulus vector of the Dirac equation, are derived in the present work. The paper shows that in the low velocity limit the equations lead to the hydrodynamic representation of the Pauli equation for charged particle with spin given by Janossy and by Bialynicki.The Lorentz invariance of the relativistic quantum potential that generates the non-local behavior of the quantum mechanics is discussed.

arXiv:1406.0595•Physical Science International Journal•Nov 17, 2014•2 citations

A NONRELATIVISTIC WAVE EQUATION FOR PARTICLES OF SPIN 1

J. Penne

The hypothesis of a permanent structure with spherical symmetry of the particles and the consideration of Euler variables necessary to its description permits, for particles of spin 1, an equation to be written analogous to that found by Pauli for the electron. (tr-auth)

Compt. rend.•Jun 26, 1961•0 citations

The Schrödinger equation and its generalized analogs derived by the quantum hydrodynamic representation

Piero Chiarelli

The derivation of the Schrödinger-like equations from the system of equations of the quantum hydrodynamic analogy (QHA) is analyzed in presence of fluctuations. If in absence of fluctuation each QHA solution can be tracked back to the equivalent one of the Schrödinger problem, in presence of fluctuations the work shows that the ensemble of solution of the QHA equations is wider than the Schrödinger one and the tracking-back procedure from the QHA problem to the original Schrödinger equation is not generally possible. The break-down of the mathematical correspondence is inspected and correlated to the characteristics of the states. Finally, the paper shows that if the form of Schrödinger equation is generalized, the QHA stochastic case as well as its classical limit can be translated into a Schrödinger-like representation.

arXiv:1210.1138•Oct 3, 2012•1 citation

A Notable Quasi-Relativistic Wave Equation and Its Relation to the Schrödinger, Klein-Gordon, and Dirac Equations

Luis Grave de Peralta, Hira Farooq

An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schrödinger and the Klein-Gordon equations, is discussed. This equation allows for a quantum description of a constant number of spin-0 particles moving at quasi-relativistic energies. It is shown how to obtain a Pauli-like version of this equation from the Dirac equation. This Pauli-like quasi-relativistic wave equation allows for a quantum description of a constant number of spin-1/2 particles moving at quasi-relativistic energies and interacting with an external electromagnetic field. In addition, it was found an excellent agreement between the energies of the electron in heavy Hydrogen-like atoms obtained using the Dirac equation, and the energies calculated using a perturbation approach based on the quasi-relativistic wave equation. Finally, it is argued that the notable quasi-relativistic wave equation discussed in this work provides interesting pedagogical opportunities for a fresh approach to the introduction to relativistic effects in introductory quantum mechanics courses.

Journal of Modern Physics•Jan 1, 2021•7 citations
It has been established that the energy density derived from the Pauli equation shows an interaction between the spins of neighboring elements, tending to re-establish the parallelism. The spin fluctuations are propagated slowly by this action. In the present work, it is shown that from the hydrodynamic representation of the Dirac equation and the Feynnnan and Gell-Mann equation solutions can be derived which correspond to a vibration. (tr-auth)
The quantum hydrodynamic like equations as a function of two real sets of variables, the 4x4 action matrix and the 4 dimensional wave function modulus vector of the Dirac equation, are derived in the present work. The paper shows that in the low velocity limit the equations lead to the hydrodynamic representation of the Pauli equation for charged particle with spin given by Janossy and by Bialynicki.The Lorentz invariance of the relativistic quantum potential that generates the non-local behavior of the quantum mechanics is discussed.
The derivation of the Schrödinger-like equations from the system of equations of the quantum hydrodynamic analogy (QHA) is analyzed in presence of fluctuations. If in absence of fluctuation each QHA solution can be tracked back to the equivalent one of the Schrödinger problem, in presence of fluctuations the work shows that the ensemble of solution of the QHA equations is wider than the Schrödinger one and the tracking-back procedure from the QHA problem to the original Schrödinger equation is not generally possible. The break-down of the mathematical correspondence is inspected and correlated to the characteristics of the states. Finally, the paper shows that if the form of Schrödinger equation is generalized, the QHA stochastic case as well as its classical limit can be translated into a Schrödinger-like representation.
An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schrödinger and the Klein-Gordon equations, is discussed. This equation allows for a quantum description of a constant number of spin-0 particles moving at quasi-relativistic energies. It is shown how to obtain a Pauli-like version of this equation from the Dirac equation. This Pauli-like quasi-relativistic wave equation allows for a quantum description of a constant number of spin-1/2 particles moving at quasi-relativistic energies and interacting with an external electromagnetic field. In addition, it was found an excellent agreement between the energies of the electron in heavy Hydrogen-like atoms obtained using the Dirac equation, and the energies calculated using a perturbation approach based on the quasi-relativistic wave equation. Finally, it is argued that the notable quasi-relativistic wave equation discussed in this work provides interesting pedagogical opportunities for a fresh approach to the introduction to relativistic effects in introductory quantum mechanics courses.