eduzhai > Physical Sciences > Physics Sciences >

The Dynamics of Wave-Particle Duality

  • Save

... pages left unread,continue reading

Document pages: 20 pages

Abstract: Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself ofHelmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and interference process. Inthe case of Wave Mechanics, de Broglie’s merging of Maupertuis’s and Fermat’sprinciples (see Section 3) provides, without resorting to the probability-basedguidance-laws and flow-lines of the Bohmian theory, the simple lawaddressing particles along the Helmholtzrays of the relevant matter waves. The purpose of the present research wasto derive the exact Hamiltonianray-trajectory systems concerning, respectively, classical electromagneticwaves, non-relativistic matter waves and relativistic matter waves. We facedthen, as a typical example, the numerical solution of non-relativisticwave-mechanical equation systems in a number of numerical applications, showingthat each particle turns out to “dances a wave-mechanical dance” around its classical trajectory, to which it reduces when the ray-coupling is neglected. Ourapproach reaches the double goal of a clear insight into the mechanism ofwave-particle duality and of a reasonably simple computability. We finallycompared our exact dynamical approach, running as close as possible to Classical Mechanics, with the hydrodynamic Bohmian theory, based onfluid-like “guidance laws”.

Please select stars to rate!

         

0 comments Sign in to leave a comment.

    Data loading, please wait...
×