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22 September 2002 Mechanical analogy for the wave-particle: helix on a vortex filament
Valery P. Dmitriyev
J. Appl. Math. 2(5): 241-263 (22 September 2002). DOI: 10.1155/S1110757X02110199


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.


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Valery P. Dmitriyev. "Mechanical analogy for the wave-particle: helix on a vortex filament." J. Appl. Math. 2 (5) 241 - 263, 22 September 2002.


Published: 22 September 2002
First available in Project Euclid: 30 March 2003

zbMATH: 1007.81004
MathSciNet: MR1933635
Digital Object Identifier: 10.1155/S1110757X02110199

Primary: 76B47 , 81P99
Secondary: 35Q55 , 37K40 , 76B25

Rights: Copyright © 2002 Hindawi

Vol.2 • No. 5 • 22 September 2002
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