Objective Reality of de Broglie's Waves

Abstract: 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.