  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.
