Are quantum trajectories suitable for semiclassical approximations?

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Authors: Alfredo M. Ozorio de Almeida
Cited by: 0
References: 31

Abstract

The quantum trajectories in the de Broglie-Bohm formulation of quantum mechanics depend on an additional quantum potential derived from the full wave solution of Schrödinger's equation. The task of supplying collectively all the correct quantum results strongly alters the characteristics of the corresponding classical trajectories, which underlie semiclassical approximations to the evolving wave function. Both classical and quantum trajectories are here considered to be conservative with no influence of an external environment, even though this is the source of eventual classicality in quantum systems, that is, decoherence. The concept of integrability, closely correspondent in classical and quantum mechanics, is not preserved by the quantum trajectories. General systems, in which classical chaotic motion participates, are much harder to treat semiclassically, but quantum trajectories can be chaotic even for integrable systems. This discrepancy between the character of classical and quantum trajectories in the de Broglie-Bohm interpretation does not clarify the singular classical-quantum transition.

Fields of Study & Subjects

Quantum Mechanics and Applications Quantum chaos and dynamical systems Numerical methods for differential equations

Publication details

Journal / source
The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics
Pages
1–10
Publication date
15 February 2026
Language
EN