dorsal/arxiv
View SchemaClassical mechanics is not h=0 limit of quantum mechanics
| Authors | O. V. Man'ko, V. I. Man'ko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407183 |
| URL | https://arxiv.org/abs/quant-ph/0407183 |
| DOI | 10.1023/B:JORR.0000043735.34372.8f |
| Journal | Journal of Russian Laser Research (2004) 25: 477 |
Abstract
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states which are not admissible in quantum mechanics and vica versa, there exist tomograms of quantum states which are not admissible in classical mechanics. Role of different transformations of reference frames in phase space of classical and quantum systems (scaling and rotation) determining the admissibility of the tomograms as well as the role of quantum uncertainty relations is elucidated. Union of all admissible tomograms of both quantum and classical states is discussed in context of interaction of quantum and classical systems. Negative probabilities in classical mechanics and in quantum mechanics corresponding to the tomograms of classical states and quantum states are compared with properties of nonpositive and nonnegative density operators, respectively.
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"abstract": "Both the set of quantum states and the set of classical states described by\nsymplectic tomographic probability distributions (tomograms) are studied. It is\nshown that the sets have common part but there exist tomograms of classical\nstates which are not admissible in quantum mechanics and vica versa, there\nexist tomograms of quantum states which are not admissible in classical\nmechanics. Role of different transformations of reference frames in phase space\nof classical and quantum systems (scaling and rotation) determining the\nadmissibility of the tomograms as well as the role of quantum uncertainty\nrelations is elucidated. Union of all admissible tomograms of both quantum and\nclassical states is discussed in context of interaction of quantum and\nclassical systems. Negative probabilities in classical mechanics and in quantum\nmechanics corresponding to the tomograms of classical states and quantum states\nare compared with properties of nonpositive and nonnegative density operators,\nrespectively.",
"arxiv_id": "quant-ph/0407183",
"authors": [
"O. V. Man\u0027ko",
"V. I. Man\u0027ko"
],
"categories": [
"quant-ph"
],
"doi": "10.1023/B:JORR.0000043735.34372.8f",
"journal_ref": "Journal of Russian Laser Research (2004) 25: 477",
"title": "Classical mechanics is not h=0 limit of quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0407183"
},
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