We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Complete Hamiltonian Description of Wave-Like Features in Classical and Quantum Physics.
- Authors
Orefice, A.; Giovanelli, R.; Ditto, D.
- Abstract
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.
- Subjects
HAMILTONIAN systems; RAYS (Graph theory); OPTICS; HELMHOLTZ equation; MATHEMATICS
- Publication
Foundations of Physics, 2009, Vol 39, Issue 3, p256
- ISSN
0015-9018
- Publication type
Article
- DOI
10.1007/s10701-009-9280-2