Quantum Foundations

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Wave Mechanics

The behavior of classical and quantum wave beams in time independent media may be shown to be ruled by a wave potential function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the case of Schrödinger's time independent equation, the form of Bohm's quantum potential - which is therefore not so much a quantum as a wave property.
Deterministic motion laws, entangled by this term, may be obtained and treated in terms of well defined Hamiltonian trajectories, and reduce to the laws of usual geometrical optics and/or classical dynamics when this term is neglected.

Present status

Deterministic motion laws and trajectories, holding for monochromatic wave beams traveling through a time independent medium, were shown to be provided, both in classical and quantum cases, by a Hamiltonian set of equations ruled by a wave potential due to the structure itself of Helmholtz-like equations (including Schrödinger's equation) and to the beam amplitude distribution.
Diffraction and/or interference are described by direct numerical integration of these Hamiltonian equations. The dispersive character of the wave potential is the basic reason for the adoption of a monochromatic beam, since only in this case the concept of "trajectory" has a definite meaning.. [ see arXiv:1506.08016].

International Collaborations

A synergy was established in 2009 with the Grup d'Òptica of the Universitat Autònoma de Barcelona (UAB) (Spain) on the subject of Bohm's realistic approach to Quantum Physics which led to write the book Applied Bohmian Mechanics: from Nanoscale Systems to Cosmology (Pan Stanford Publishing, 2012)



Last Update 10.12.2015

A. Orefice, R. Giovanelli and D. Ditto
Chapter 7: Beyond the Eikonal Approximation in Classical Optics and Quantum Physics
in Applied Bohmian Mechanics - From Nanoscale Systems to Cosmology
by Xavier Oriols and Jordi Mompart
Pan Stanford Publishing, 2012. ISBN: 9789814316392