Quantum Hydrodynamics: Kirchhoff Equations View Full Text


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Article Info

DATE

2019-03-13

AUTHORS

K. V. S. Shiv Chaitanya

ABSTRACT

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. More... »

PAGES

1-14

References to SciGraph publications

  • 2013-09. Anomalous hydrodynamics of fractional quantum Hall states in JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS
  • 1927-03. Quantentheorie in hydrodynamischer Form in ZEITSCHRIFT FÜR PHYSIK
  • 2014-07. Stieltjes electrostatic model interpretation for bound state problems in PRAMANA
  • Journal

    TITLE

    Foundations of Physics

    ISSUE

    N/A

    VOLUME

    N/A

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10701-019-00252-4

    DOI

    http://dx.doi.org/10.1007/s10701-019-00252-4

    DIMENSIONS

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