ua nt - p h / 04 06 05 4 v 2 2 9 A ug 2 00 4 Incompleteness of trajectory - based interpretations of quantum mechanics ∗
نویسنده
چکیده
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 Schrödinger 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.
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