Trajectories in the Context of the Quantum Newton's Law

Details Trajectories in the Context of the Quantum Newton's Law Trajectories in the Context of the Quantum Newton's Law

2001-08-06

arxiv.org/abs/quant-ph/0108022v3

Phys.Scripta 66 (2002) 97-104

Physics

Quantum Physics

17 pages, LateX, 6 eps figures, minor modifications, Title changed, to appear in Physica Scripta

Scientific paper

10.1238/Physica.Regular.066a0009

In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic oscillator. In the classically allowed regions, we show that to each classical trajectory there is a family of quantum trajectories which all pass through some points constituting nodes and belonging to the classical trajectory. We also discuss the generalization to any potential and give a new definition for de Broglie's wavelength in such a way as to link it with the length separating adjacent nodes. In particular, we show how quantum trajectories have as a limit when $\hbar \to 0$ the classical ones. In the classically forbidden regions, the nodal structure of the trajectories is lost and the particle velocity rapidly diverges.

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