The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system describing in terms of ray trajectories, for a stationary refractive medium, a very wide family of wave-like phenomena (including diffraction and interference) going much beyond the limits of the geometrical optics (“eikonal”) approximation, which is contained as a simple limiting case. Due to the fact, moreover, that the time independent Schrödinger equation is itself a Helmholtz-like equation, the same mathematics holding for a classical optical beam turns out to apply to a quantum particle beam moving in a stationary force field, and leads to a system of Hamiltonian equations providing exact and deterministic particle trajectories and dynamical laws, and containing the laws of Classical Mechanics in the eikonal limit.
|Titolo:||Complete Hamiltonian Description of Wave-Like Features in Classical and Quantum Physics|
DITTO, DOMENICO (Ultimo)
|Parole Chiave:||Geometrical optics ; Hamilton equations ; Quantum foundation ; Indeterminism|
|Data di pubblicazione:||gen-2009|
|Digital Object Identifier (DOI):||10.1007/s10701-009-9280-2|
|Appare nelle tipologie:||01 - Articolo su periodico|