Quantum Hydrodynamics: Kirchhoff Equations

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 demo...

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Veröffentlicht in:Foundations of physics 2019-04, Vol.49 (4), p.351-364
1. Verfasser: Chaitanya, K. V. S. Shiv
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description 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.
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subjects Classical and Quantum Gravitation
Classical Mechanics
Fluid dynamics
Fluid flow
Fluid mechanics
Hermite polynomials
History and Philosophical Foundations of Physics
Hydrodynamics
Mathematical analysis
Philosophy of Science
Physics
Physics and Astronomy
Quantum mechanics
Quantum Physics
Relativity Theory
Schrodinger equation
Statistical Physics and Dynamical Systems
Vortices
title Quantum Hydrodynamics: Kirchhoff Equations
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