The Dynamics of Wave-Particle Duality
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by
Adriano Orefice, Raffaele Giovanelli, Domenico Ditto
2017
Abstract
Both classical and wave-mechanical monochromatic waves may be treated in
terms of exact ray-trajectories (encoded in the structure itself of
Helmholtz-like equations) whose mutual coupling is the one and only cause of
any diffraction and interference process. In the case of Wave Mechanics, de
Broglie's merging of Maupertuis's and Fermat's principles (see Section 3)
provides, without resorting to the probability-based guidance-laws and
flow-lines of the Bohmian theory, the simple law addressing particles along the
Helmholtz rays of the relevant matter waves. The purpose of the present
research was to derive the exact Hamiltonian ray-trajectory systems concerning,
respectively, classical electromagnetic waves, non-relativistic matter waves
and relativistic matter waves. We faced then, as a typical example, the
numerical solution of non-relativistic wave-mechanical equation systems in a
number of numerical applications, showing that each particle turns out to
"dances a wave-mechanical dance" around its classical trajectory, to which it
reduces when the ray-coupling is neglected. Our approach reaches the double
goal of a clear insight into the mechanism of wave-particle duality and of a
reasonably simple computability. We finally compared our exact dynamical
approach, running as close as possible to Classical Mechanics, with the
hydrodynamic Bohmian theory, based on fluid-like "guidance laws".
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