Are quantum trajectories suitable for semiclassical approximations?

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.

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Publication Details

Journal
The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics
Published
2026-02-15
DOI
https://doi.org/10.1080/14786435.2026.2627728
Primary Topic
Spectral Theory in Mathematical Physics
Type
article
Field-Weighted Citation Impact
0.00

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article

Are quantum trajectories suitable for semiclassical approximations?

Alfredo M. Ozorio de Almeida
The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics
Spectral Theory in Mathematical Physics
article

Are quantum trajectories suitable for semiclassical approximations?

Alfredo M. Ozorio de Almeida
article en

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.

The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics
Centro Brasileiro de Pesquisas Físicas (BR)
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Reduced inequalities
Openalex Percentile: Top 49%
Spectral Theory in Mathematical Physics
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Are quantum trajectories suitable for semiclassical approximations? — Alfredo M. Ozorio de Almeida · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics (2026) | TGRS Research Map | TGRS