ABSTRACT
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system describing in terms of ray trajectories a very wide family of wave-like phenomena containing the eikonal approximation as a simple limiting case. A suitable set of Hamiltonian equations is shown to provide both the exact and deterministic trajectories of the particles and their dynamical laws, reducing to the laws of classical mechanics in the eikonal limit. Wave-like features in Hamiltonian form are presented in some typical numerical cases. Beyond the physical and even philosophical insight given by the observations into the nature of quantum potential, a practical consequence is the possibility of exchanging all numerical techniques between the quantum and classical cases. The trajectory pattern, in its turn, is a stationary structure determined at the very outset along which rays and particles move in a way strongly reminding the spirit of classical variational principles, such as the ones of Fermat and Maupertuis, in time-independent media.
