Beyond Geometrical Optics and Bohmian Physics: A New Exact and Deterministic Hamiltonian Approach to Wave-Like Features in Classical and Quantum Physics

TL;DR

This paper introduces a new deterministic Hamiltonian framework that explains wave-like phenomena in classical and quantum physics through well-defined trajectories, challenging the indeterministic view of quantum laws.

Contribution

It presents an exact, deterministic Hamiltonian approach to wave phenomena, extending classical Hamiltonian trajectories to quantum wave-like features.

Findings

Provides a Hamiltonian trajectory-based model for wave phenomena

Unifies classical and quantum wave descriptions under a deterministic framework

Offers a new perspective on the interpretation of quantum indeterminism

Abstract

The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories, emerges as the most natural one from the analysis of the time-independent Helmholtz-like equations encountered both in Classical Electromagnetism and in Wave Mechanics. In the case of particle beams a suitable pattern of trajectories is provided (for any set of boundary conditions) by a set of dynamical laws containing the classical ones as a simple limiting case.