Journal of Applied Mathematics

Journal of Applied Mathematics / 2002 / Article

Open Access

Volume 2 |Article ID 725481 | 23 pages | https://doi.org/10.1155/S1110757X02110199

Mechanical analogy for the wave-particle: helix on a vortex filament

Received22 Oct 2001
Revised13 Feb 2002

Abstract

The small amplitude-to-thread ratio helical configuration of a vortex filament in the ideal fluid behaves exactly as de Broglie wave. The complex-valued algebra of quantum mechanics finds a simple mechanical interpretation in terms of differential geometry of the space curve. The wave function takes the meaning of the velocity, with which the helix rotates about the screw axis. The helices differ in type of the screw—right- or left-handed. Two kinds of the helical waves deflect in the inhomogeneous fluid vorticity field in the same way as spin particles in the Stern-Gerlach experiment.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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