I could not quite understand. Are you contemplating a well-defined classical trajectory as, for example, in Bohmian mechanics, or that the particle is defined by a wave packet, perhaps non-spreading?
Okay, I have had alook at your earlier papers now and assume that you are contemplating classical trajectories.
Regards
Dan Shanahan
I'm not exactly contemplating "classical" trajectories. I'm showing that exact dynamical particle trajectories (which have nothing to do with Bohmian hydrodynamical trajectories!) are easily obtained, in stationary external fields, from the time-independent (but energy-dependent!) Schroedinger equation, in full analogy with the classical case of particles launched with an assigned energy into a time-independent external field. The particles are viewed as classical-looking, single-energy point-like masses, and NOT as wave packets. The pilot wave submits the particle trajectories of assigned energy to the coupling action of an energy-dependent "Wave Potential", present in any Helmholtz-like equation. The coupled trajectories are, in general, "classical -looking", but certainly not "classical" (they diffract and interfere, for instance) and reduce to the classical ones when the Wave Potential is negligible, i.e. in the eikonal limit of the matter wave.
In striking difference from the energy-dependent Wave Potential, Bohm's so-called "Quantum Potential" is an average over the full set of energy eigen-values, and may only characterize, therefore, wave-packets (if any).
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