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Incompleteness of trajectory-based interpretations of quantum mechanics | | Michael J.W. Hall
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9 Jun 2004 | | Journal: | J. Phys. A 37 (2004) 9549 (www.iop.org) | | Subject: | quant-ph | | 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. | | Source: | arXiv, quant-ph/0406054 | | Services: | Forum | Review | PDF | Favorites | |
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