  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.
