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:1609.06159

Steiljes electrostatic model with imaginary charges resolves wave-particle duality

K. V. S. Shiv Chaitanya, Srinivasan

Published Sep 20, 2016• 0 citations
arXivHTMLPDF

Abstract

In this paper, we show that the quantum bound state problems are mapped to $N$ point vortices with the identical circulation or strength using the Steiljes electrostatic model with imaginary charges. We also show that these $N$ point charges or vortices, become imaginary, in a constant background field will admit a wave solution under paraxial wave approximation. Therefore, in quantum mechanics as long as paraxial approximation is valid it behaves like a wave.

DOI
10.48550/arxiv.1609.06159

Related papers

Quantum Mechanics is consistent with Classical Mechanics: Schr\"odinger meets Kirchhoff

K. V. S. Shiv Chaitanya

In this paper, we show that in two dimensions quantum mechanics can be mapped onto classical mechanics, by transforming the Schr\odinger equation into system of $n$ linear equations known as Kirchhoff equations. These Kirchhoff equations equations satisfy the a poison bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that quantum mechanics is consistent with classical mechanics atleast in two dimensions. This allows us to address the wave particle duality in terms of relative phase. As an illustration we show that the equation for optical vortices can be derived as Kirchhoff equation admit a paraxial wave equation in presence of real constant background.

•Sep 13, 2018•0 citations

Quantum Hydrodynamics: Kirchhoff Equations

K. V. S. Shiv Chaitanya

In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of $n$ point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions.

arXiv:1809.09964•Sep 13, 2018•0 citations

Duality between Poisson and Schrödinger equations in three dimensions

Gabriel González

A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schrödinger equation by using electrostatic results is generalized to three dimensions. Here, it is demonstrated that the same transformation technique is also applicable to the s-wave Schrödinger equation in three dimensions for central potentials. This approach leads to a general relationship between the electrostatic potential and the s-wave function and the electric energy density to the quantum mechanical energy.

arXiv:2107.04669•Jun 25, 2021•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

Wave-particle duality in classical mechanics

Alexander Y Davydov

Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in a strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propel via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, an observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may emerge as approximation from a more profound theory on a deeper level.

arXiv:1201.4509•Journal of Physics Conference Series•May 10, 2012•1 citation

Wave-particle duality in classical mechanics

Alexander Y. Davydov

Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propell via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only {\it probabilistically} and they manifest {\it weird} features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may \emph{emerge} as approximation from a more profound theory on a deeper level.

•Aug 17, 2016•4 citations
In this paper, we show that the quantum bound state problems are mapped to NNN point vortices with the identical circulation or strength using the Steiljes electrostatic model with imaginary charges. We also show that these NNN point charges or vortices, become imaginary, in a constant background field will admit a wave solution under paraxial wave approximation. Therefore, in quantum mechanics as long as paraxial approximation is valid it behaves like a wave.
In this paper, we show that in two dimensions quantum mechanics can be mapped onto classical mechanics, by transforming the Schr\odinger equation into system of nnn linear equations known as Kirchhoff equations. These Kirchhoff equations equations satisfy the a poison bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that quantum mechanics is consistent with classical mechanics atleast in two dimensions. This allows us to address the wave particle duality in terms of relative phase. As an illustration we show that the equation for optical vortices can be derived as Kirchhoff equation admit a paraxial wave equation in presence of real constant background.
In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of nnn point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions.
A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schrödinger equation by using electrostatic results is generalized to three dimensions. Here, it is demonstrated that the same transformation technique is also applicable to the s-wave Schrödinger equation in three dimensions for central potentials. This approach leads to a general relationship between the electrostatic potential and the s-wave function and the electric energy density to the quantum mechanical energy.
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.
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in a strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propel via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, an observer can describe such objects only probabilistically and they manifest weird features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may emerge as approximation from a more profound theory on a deeper level.
Until recently, wave-particle duality has been thought of as quantum principle without a counterpart in classical physics. This belief was challenged after (i) finding that average dynamics of a classical particle in strong inhomogeneous oscillating field resembles that of a quantum object and (ii) experimental discovery of "walkers" - macroscopic droplets that bounce on a vertically vibrating bath of the same fluid and can self-propell via interaction with the surface waves they generate. This paper exposes a new family of objects that can display both particle and wave features all together while strictly obeying laws of the Newtonian mechanics. In contrast to the previously known duality examples in classical physics, oscillating field or constant inflow of energy are not required for their existence. These objects behave deterministically provided that all their degrees of freedom are known to an observer. If, however, some degrees of freedom are unknown, observer can describe such objects only {\it probabilistically} and they manifest {\it weird} features similar to that of quantum particles. We show new classical counterparts of such quantum phenomena as particle interference, tunneling, above-barrier reflection, trapping on top of a barrier, and spontaneous emission of radiation. In the light of these findings, we hypothesize that quantum mechanics may \emph{emerge} as approximation from a more profound theory on a deeper level.