dorsal/arxiv
View SchemaThe Born Rule in Quantum and Classical Mechanics
| Authors | Paul Brumer, Jiangbin Gong |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604178 |
| URL | https://arxiv.org/abs/quant-ph/0604178 |
| DOI | 10.1103/PhysRevA.73.052109 |
| Journal | Phys. Rev. A 73, 052109 (2006) |
Abstract
Considerable effort has been devoted to deriving the Born rule (e.g. that $|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert space formulation of {\it classical} mechanics as well. These results provide new insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.
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"abstract": "Considerable effort has been devoted to deriving the Born rule (e.g. that\n$|\\psi(x)|^2 dx$ is the probability of finding a system, described by $\\psi$,\nbetween $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule\nis not solely quantum mechanical; rather, it arises naturally in the Hilbert\nspace formulation of {\\it classical} mechanics as well. These results provide\nnew insights into the nature of the Born rule, and impact on its understanding\nin the framework of quantum mechanics.",
"arxiv_id": "quant-ph/0604178",
"authors": [
"Paul Brumer",
"Jiangbin Gong"
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"quant-ph"
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"doi": "10.1103/PhysRevA.73.052109",
"journal_ref": "Phys. Rev. A 73, 052109 (2006)",
"title": "The Born Rule in Quantum and Classical Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0604178"
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