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Trajectories
"It is clear that [diffraction and interference] can in no way be reconciled with the idea that electrons move in paths. In Quantum Mechanics there is no such concept as the path of a particle."
L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 1965).
In our approach [arXiv:1406.4968v3], on the contrary, a Hamiltonian dynamical system may be directly obtained from Schroedinger's time-independent equation, providing exact (non-statistical) point-particle trajectories.
The physical objectivity of monochromatic de Broglie's waves is testified by Davisson-Germer's experiments: they are therefore real pilot-waves, while Born's wave-function is a merely statistical abstraction.
Diffraction of a wave beam launched along the z-axis with an amplitude of the Gaussian form: R = Exp[-(x/Wo)^2]

Left: particle trajectories; right: red line = launching wave intensity; blue line = final wave intensity. The two (green) heavy lines are the analytical paraxial approximation of the trajectories starting (at z = 0) from the waist positions: x/Wo = +-1.
Diffraction of a single non-Gaussian wave beam

Left: particle trajectories; right: red line = launching wave intensity; blue line = final wave intensity.
Interference of two wave beams

Left: particle trajectories; right: red line = launching wave intensity; blue line = final wave intensity.

Photograph by woodahl.physics.iupui.edu

See, for comparison:

Particle-wave duality demonstrated with largest molecules yet

One of the bizarre features of quantum mechanics is that individual particles (...)
Copyright (C) 2012, Nature Nanotechnology, DOI: 10.1038/nnano.2012.34
Copyright (C) 2015. www.wave-mechanics.eu - Last Update: 09.03.2015