Is wave mechanics consistent with classical logic?

Orefice, A.; Giovanelli, Raffaele; Ditto, Domenico

doi:10.4006/0836-1398-28.4.515

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…The general demonstration of the equivalence between classical and wave-mechanical Helmholtz-like equations and exact, trajectory-based Hamiltonian systems was given in Refs. [23] [24] [25] [26] [27], and led to extensive application both in relativistic electrodynamics and in the analysis of experimental arrangements and devices employed for light transmission and guiding [28] [29] [30]. Let us finally remind that the equivalence between the time-dependent Schrödinger equation and Hamiltonian Me-Journal of Applied Mathematics and Physics chanics was demonstrated in Ref.…”

Section: An Experimentally Tested Hamiltonian Description Of Wave-likmentioning

confidence: 99%

The Dynamics of Wave-Particle Duality

Orefice¹,

Giovanelli²,

Ditto³

2018

JAMP

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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". Journal of Applied Mathematics and Physics redly leading to Bohm's Mechanics [2]-[7], with its probability-based guidance-laws and hydrodynamic flow-lines.

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Section: An Experimentally Tested Hamiltonian Description Of Wave-likmentioning

confidence: 99%

The Dynamics of Wave-Particle Duality

Orefice¹,

Giovanelli²,

Ditto³

2018

JAMP

Self Cite

View full text Add to dashboard Cite

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De Broglie's Exact Trajectories

Orefice

Giovanelli²,

Ditto³

2021

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Primary Assumptions and Guidance Laws in Wave Mechanics

Orefice¹,

Giovanelli²,

Ditto³

2018

JAMP

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In an article written by Louis de Broglie in 1959 (30 years after the Nobel prize rewarding his foundation of Wave Mechanics), the most challenging problem raised by the Bohr, Heisenberg and Born Standard Quantum Mechanics (SQM) was pointed out in the renunciation to describe "a permanent localization in space, and therefore a well-defined trajectory" for any moving particle. This challenge is taken up in the present paper, showing that de Broglie's Primary Assumption = p k  , predicting the wave-particle duality, does also allow to obtain from the energy-dependent form of the Schrödinger and/or Klein-Gordon equations the Guidance Laws piloting particles along well-defined trajectories. The energy-independent equations, on the other hand, may only give rise-both in SQM and in the Bohmian approach-to probabilistic descriptions, overshadowing the role of de Broglie's matter waves in physical space.

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Is wave mechanics consistent with classical logic?

Cited by 3 publications

References 26 publications

The Dynamics of Wave-Particle Duality

The Dynamics of Wave-Particle Duality

De Broglie's Exact Trajectories

Primary Assumptions and Guidance Laws in Wave Mechanics

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