arXiv subjects

Adriano Orefice

Publications and source records attributed to Adriano Orefice.

9 recordsLinked to original sources

arXiv2019

de Broglie's Exact Trajectories

De Broglie's quest for a wave-like approach capable of representing the position of a moving particle, is satisfied, in the case of time-independent external fields, by assuming that each particle runs along the virtual trajectories associated, under assigned starting conditions, with a time-independent Schr\"odinger (or Klein-Gordon) equation. Just like in classical Dynamics, indeed, the starting conditions determine, from the beginning, a set of virtual particle trajectories independent from the very presence of the particles.

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arXiv2017

The Dynamics of Wave-Particle Duality

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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arXiv2016

Beyond quasi-optics: an exact approach to self-diffraction, reflection and finite-waist focusing of matter wave trajectories

The "main road" open by de Broglie's and Schroedinger's discovery of matter waves and of their eigen-functions branched off, as is well known, into different "sub-routes". The most widely accepted one is Standard Quantum Mechanics (SQM), interpreting the time-dependent Schroedinger equation as the basic evolution law of a wave-packet which represents the simultaneous probabilistic permanence of a particle in its full set of eigenstates. Another "sub-route" is offered by Bohm's Mechanics, able to reproduce the same results of SQM, while interpreting the stream-lines of the probability current density as the "quantum trajectories" of the moving particles. Reminding that the so-called quasi-optical approximation represents a standard mathematical technique allowing a ray-based treatment of wave-like features, we present here an exact wave-mechanical "sub-route", based on the observation that the time-independent Schroedinger equation may be treated, bypassing any quasi-optical approximation, in terms of a Hamiltonian set of rays mutually coupled by an energy-dependent function (which we call "Wave Potential") encoded in the very structure of any Helmholtz-like equation. These rays lend themselves to be interpreted as the exact wave-dynamical trajectories and motion laws of classical-looking point-particles associated with the de Broglie-Schroedinger matter waves. The role of the Wave Potential, acting perpendicularly to the momentum of the moving particles, is to "pilot" them without any energy exchange: a property which isn't shared by the well-known "Quantum Potential" of the Bohmian theory, involving the entire spectrum of possible eigen-energies of a wave-packet. This property turns out to allow the numerical computation of the particle trajectories, which we perform and discuss here for particles piloted by the Wave Potential in many different and significant force-fields.

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arXiv2015

Is Wave Mechanics consistent with Classical Logic?

Contrary to a wide-spread commonplace, an exact, ray-based treatment holding for any kind of monochromatic wave-like features (such as diffraction and interference) is provided by the structure itself of the Helmholtz equation. This observation allows to dispel - in apparent violation of the Uncertainty Principle - another commonplace, forbidding an exact, trajectory-based approach to Wave Mechanics.

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arXiv2015

From Classical to Wave-Mechanical Dynamics

The time-independent Schroedinger and Klein-Gordon equations - as well as any other Helmholtz-like equation - were recently shown to be associated with exact sets of ray-trajectories (coupled by a "Wave Potential" function encoded in their structure itself) describing any kind of wave-like features, such as diffraction and interference. This property suggests to view Wave Mechanics as a direct, causal and realistic, extension of Classical Mechanics, based on exact trajectories and motion laws of point-like particles "piloted" by de Broglie's matter waves and avoiding the probabilistic content and the wave-packets both of the standard Copenhagen interpretation and of Bohm's theory.

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arXiv2014

Objective Reality of de Broglie's Waves

An exact, ray-based general treatment is shown to hold for any kind of monochromatic wave feature - including diffraction and interference - described by Helmholtz-like equations, under the coupling action of a dispersive function (which we call "Wave Potential") encoded in the structure itself of the Helmholtz equation. Since the time-independent Schroedinger and Klein-Gordon equations (associating particles of assigned total energy with stationary de Broglie waves) are themselves Helmholtz-like equations, the same general approach is extended to the ray-based dynamics of point-like particles, whose exact trajectories and dynamical laws may be obtained without resorting to statistical concepts of any kind, thus suggesting a non-probabilistic nature of de Broglie's waves and of physical reality.

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arXiv2013

Wave Mechanics without Probability

The behavior of monochromatic electromagnetic waves in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief that the very concept of "ray trajectory" is reserved to the eikonal approximation, a general and exact ray-based Hamiltonian treatment, reducing to the eikonal approximation in the absence of Wave Potential, shows that its presence induces a mutual, perpendicular ray-coupling, which is the one and only cause of any typically wave-like phenomenon, such as diffraction and interference. Recalling, then, that the time-independent Schroedinger and Klein-Gordon equations (associating stationary "matter waves" to mono-energetic particles) are themselves Helmholtz-like equations, the exact, ray-based treatment developed for classical electromagnetic waves is extended - without resorting to statistical concepts - to the exact, trajectory-based Hamiltonian dynamics of mono-energetic point-like particles, both in the non-relativistic and in the relativistic case. The trajectories turn out to be perpendicularly coupled, once more, by an exact, stationary, energy-dependent Wave Potential, coinciding in the form, but not in the physical meaning, with the statistical, time-varying, energy-independent "Quantum Potential" of Bohm's theory, which views particles, just like the standard Copenhagen interpretation, as traveling wave-packets. These results, together with the connection which is shown to exist between Wave Potential and Uncertainty Principle, suggest a novel, non-probabilistic interpretation of Wave Mechanics.

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arXiv2013

The Helmholtz Wave Potential: a non-probabilistic insight into Wave Mechanics

The behavior of classical monochromatic waves in stationary media is shown to be ruled by a novel, frequency-dependent function which we call Wave Potential, and which we show to be encoded in the structure of the Helmholtz equation. An exact, Hamiltonian, ray-based kinematical treatment, reducing to the usual eikonal approximation in the absence of Wave Potential, shows that its presence induces a mutual, perpendicular ray-coupling, which is the one and only cause of wave-like phenomena such as diffraction and interference. The Wave Potential, whose discovery does already constitute a striking novelty in the case of classical waves, turns out to play an even more important role in the quantum case. Recalling, indeed, that the time-independent Schroedinger equation (associating the motion of mono-energetic particles with stationary monochromatic matter waves) is itself a Helmholtz-like equation, the exact, ray-based treatment developed in the classical case is extended - without resorting to statistical concepts - to the exact, trajectory-based Hamiltonian dynamics of mono-energetic point-like particles. Exact, classical-looking particle trajectories may be defined, contrary to common belief, and turn out to be perpendicularly coupled by an exact, energy-dependent Wave Potential, similar in the form, but not in the physical meaning, to the statistical, energy-independent "Quantum Potential" of Bohm's theory, which is affected, as is well known, by the practical necessity of representing particles by means of statistical wave packets, moving along probability flux lines. This result, together with the connection shown to exist between Wave Potential and Uncertainty Principle, allows a novel, non-probabilistic interpretation of Wave Mechanics.

quant-ph↗

arXiv2012

Quantum trajectories and Cushing's historical contingency

With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by a dispersive "Wave Potential" function, encoded in the structure of the Helmholtz equation. An exact, ray-based Hamiltonian description, revealing a strong ray coupling due to the Wave Potential, and reducing to the geometrical optics approximation when this function is neglected, is shown to hold even for typically wave-like phenomena such as diffraction and interference. Recalling, then, that the time-independent Schroedinger equation (associating the quantum motion of mono-energetic particles with stationary monochromatic matter waves) is itself a Helmholtz-like equation, the mathematical treatment holding in the classical case is extended, without resorting to statistical concepts, to the exact, trajectory-based, Hamiltonian quantum dynamics of point-like particles. The particle trajectories and motion laws turn out to be coupled, in this case, by a function strictly analogous to the Wave Potential and formally assuming the familiar form of Bohm's "Quantum Potential", which is therefore not so much a "quantum" as a "wave" property - in whose absence the quantum particle dynamics reduces to the classical one. The time-independent Schroedinger equation is argued to be not a trivial particular case of the time-dependent one, but the exact quantum dynamical ground on which Schroedinger's time-dependent statistical description (representing particles as travelling wave-packets) is based. It provides indeed the (exact) link between classical particle dynamics and Bohm's hydrodynamics.

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