TITLE:
Primary Assumptions and Guidance Laws in Wave Mechanics
AUTHORS:
Adriano Orefice, Raffaele Giovanelli, Domenico Ditto
KEYWORDS:
Helmholtz Equation, Wave Potential, Hamilton-Jacobi Equations, Wave Mechanics, de Broglie’s Duality, Matter Waves, Guidance Laws, Schrödinger Equations, Klein-Gordon Equations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.12,
December
27,
2018
ABSTRACT: In an article written by Louis de
Broglie in 1959 (30 years after the Nobel prize rewarding his foundation of
Wave Mechanics), the most challenging problem raised by the Bohr, Heisenberg
and Born Standard Quantum Mechanics (SQM) was pointed out in the renunciation
to describe “a permanent localization in space, and therefore a well-defined trajectory”
for any moving particle. This challenge is taken up in the present paper,
showing that de Broglie’s Primary Assumption p=hk, predicting the wave-particle duality, does also
allow to obtain from the energy-dependent form of the Schrödinger and/or Klein-Gordon equations the Guidance Laws piloting
particles along well-defined trajectories. The energy-independent equations, on the other hand, may only give rise—both in SQM and in the Bohmian approach—to probabilistic descriptions, overshadowing the role of de Broglie’s matter waves in physical space.