Incompleteness of trajectory-based interpretations of quantum mechanics

Abstract

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 Schroedinger 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 initially uniform over the interior of the box. For this example there is no corresponding continuity or modified Hamilton-Jacobi equation, and the spacetime dependence of the wavefunction has a known fractal structure. Examples with finite average energies are also constructed.

Latex, 13 pages, no figures, refs and clarifications added, to appear in J Phys A

References in corpus (4)

• Schrodinger equation from an exact uncertainty principle
• Time Evolution of Quantum Fractals
• Unravelling quantum carpets: a travelling wave approach
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