dorsal/arxiv
View SchemaIncompleteness of trajectory-based interpretations of quantum mechanics
| Authors | Michael J. W. Hall |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406054 |
| URL | https://arxiv.org/abs/quant-ph/0406054 |
| DOI | 10.1088/0305-4470/37/40/015 |
| Journal | J. Phys. A 37 (2004) 9549 (www.iop.org) |
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.
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"abstract": "Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm\ninterpretation and Nelson\u0027s stochastic interpretation. It is shown that the\nusual route to establishing the validity of such interpretations, via a\ndecomposition of the Schroedinger equation into a continuity equation and a\nmodified Hamilton-Jacobi equation, fails for some quantum states. A very simple\nexample is provided by a quantum particle in a box, described by a wavefunction\ninitially uniform over the interior of the box. For this example there is no\ncorresponding continuity or modified Hamilton-Jacobi equation, and the\nspacetime dependence of the wavefunction has a known fractal structure.\nExamples with finite average energies are also constructed.",
"arxiv_id": "quant-ph/0406054",
"authors": [
"Michael J. W. Hall"
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"quant-ph"
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"doi": "10.1088/0305-4470/37/40/015",
"journal_ref": "J. Phys. A 37 (2004) 9549 (www.iop.org)",
"title": "Incompleteness of trajectory-based interpretations of quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0406054"
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