Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1703.10482

Analytic solutions of the Madelung equation

Imre Ferenc Barna, Mihály András Pocsai, László Mátyás

Published Mar 30, 2017• 2 citations
arXivHTMLPDF

Abstract

We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential.
DOI
10.48550/arxiv.1703.10482

Related papers

Analytic Solutions of the Madelung Equation

Barna IF, Pocsai MA, Matyas L

We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle.There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential.

Journal of Generalized Lie Theory and Applications•Jan 1, 2017•4 citations

Realistic Fluid Models Forhand For de Broglie Waves, and Wave Equations From the Quantum Potential

William M. Honig

Physics Essays•Mar 1, 1998•0 citations

Relating Madelung–Bohm trajectories

Gilberto Silva-Ortigoza, Ramón Silva‐Ortigoza, Israel Julián-Macías +1 more

In this work, we use the quantum potential approach to quantum mechanics to show that the Madelung–Bohm trajectories for a particle in a constant gravitational field can be related to those of a free particle by means of a quantum point transformation defined in the extended configuration space. We find that the point transformation also gives a connection between the corresponding quantum Hamiltonians determined by the solutions of the corresponding Schrödinger equations for these two problems. We show that the Madelung–Bohm trajectories determined by the stationary solutions to the Schrödinger equation for the particle in a constant gravitational field are straight ones, while the corresponding ones for the free particle are parabolic trajectories. The Airy beam is one example of this type of solution. We study the properties of a solution to the Schrödinger equation for a free particle with phase singularities (zeroes), and we find that the corresponding solution to the Schrödinger equation for the particle in a constant gravitational field also has zeroes at the same spacetime points. However, the Madelung–Bohm trajectories determined by the two solutions are totally different. Furthermore, we remark that similar results can be directly obtained for the paraxial wave equation.

Journal of the Optical Society of America B•Dec 10, 2024•1 citation

Lie-Bäcklund transformations for the Madelung quantum fluid

A. J. Purcell

The Madelung quantum fluid is shown to possess an infinite sequence of Lie-B\"acklund transformations; in addition, the effect of the lowest-order transformation on an exact solution of the fluid equations is explicitly calculated.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Nov 15, 1984•3 citations

A Class of Self-Trapped and Self-Focusing Wave Functions in Madelung Fluid Picture of A Single Free Particle Quantum System

Agus Budiyono, Ken Umeno

Using the Madelung fluid picture of Schrödinger equation for a single free particle moving in one spatial dimension, we shall specify a class of wave functions whose quantum probability density is being trapped by the quantum potential it itself generates. The global convexity of the quantum potential generated by the initial self-trapped wave function will then be shown to further localize the quantum probability density through a self-generated focusing equation for a finite interval of time.

arXiv:0903.2300•Mar 13, 2009•0 citations

Toward a Thermo-hydrodynamic Like Description of Schrödinger Equation via the Madelung Formulation and Fisher Information

Eyal Heifetz, Eliahu Cohen

arXiv:1501.00944•Foundations of Physics•Jul 7, 2015•48 citations
In this work, we use the quantum potential approach to quantum mechanics to show that the Madelung–Bohm trajectories for a particle in a constant gravitational field can be related to those of a free particle by means of a quantum point transformation defined in the extended configuration space. We find that the point transformation also gives a connection between the corresponding quantum Hamiltonians determined by the solutions of the corresponding Schrödinger equations for these two problems. We show that the Madelung–Bohm trajectories determined by the stationary solutions to the Schrödinger equation for the particle in a constant gravitational field are straight ones, while the corresponding ones for the free particle are parabolic trajectories. The Airy beam is one example of this type of solution. We study the properties of a solution to the Schrödinger equation for a free particle with phase singularities (zeroes), and we find that the corresponding solution to the Schrödinger equation for the particle in a constant gravitational field also has zeroes at the same spacetime points. However, the Madelung–Bohm trajectories determined by the two solutions are totally different. Furthermore, we remark that similar results can be directly obtained for the paraxial wave equation.