# Incompleteness of trajectory-based interpretations of quantum mechanics

@article{Hall2004IncompletenessOT, title={Incompleteness of trajectory-based interpretations of quantum mechanics}, author={Michael J. W. Hall}, journal={Journal of Physics A}, year={2004}, volume={37}, pages={9549-9556} }

Trajectory-based approaches to quantum mechanics include the de Broglie?Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition of the Schr?dinger equation into a continuity equation and a modified Hamilton?Jacobi equation, fails for some quantum states. A very simple example is provided by a quantum particle in a box, described by a wavefunction that is initially uniform over the…

## 16 Citations

A Bohmian approach to quantum fractals

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We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical "worlds," and quantum effects arise…

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A solution ψ to Schrödinger’s equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field ~= (5ψ/mψ) . In the…

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Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present…

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The effects induced by the internal fractal structures of trajectories on motion in standard space are described and their main consequence is the transformation of classical dynamics into a generalized, quantum-like self-organized dynamics.

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Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology…

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- 2002

Abstract.
An investigation of two-time correlation functions is reported
within the framework of (i) stochastic quantum mechanics and (ii)
conventional Heisenberg-Schrödinger quantum mechanics. The…

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- Physics
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This note collects, classifies and evaluates common criticism against the de Broglie Bohm theory, including Ockham's razor, asymmetry in the de Broglie Bohm theory, the ``surreal trajectory''…

A SUBTLETY OF THE SCHRÖDINGER PICTURE DYNAMICS

- Mathematics, Physics
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We address a mathematical and physical status of exotic (like e.g. fractal) wave packets and their quantum dynamics. To this end, we extend the formal meaning of the Schrodinger equation beyond the…

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