dorsal/arxiv
View SchemaTheory of hybrid systems. I. The operator formulation of classical mechanics and semiclassical limit
| Authors | S. Prvanovic, Z. Maric |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103044 |
| URL | https://arxiv.org/abs/quant-ph/0103044 |
Abstract
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$. For the second of these two extreme values, introduced operatorial algebra becomes equivalent to the algebra of observables of quantum mechanical system defined in the standard manner by operators in the Hilbert space. For the vanishing Planck constant, the generalized algebra gives the operator formulation of classical mechanics since it is equivalent to the algebra of variables of classical mechanical system defined, as usually, by functions over the phase space. In this way, the semiclassical limit of kinematical part of quantum mechanics is established through the generalized operatorial framework.
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"abstract": "The algebra of polynomials in operators that represent generalized coordinate\nand momentum and depend on the Planck constant is defined. The Planck constant\nis treated as the parameter taking values between zero and some nonvanishing\n$h_0$. For the second of these two extreme values, introduced operatorial\nalgebra becomes equivalent to the algebra of observables of quantum mechanical\nsystem defined in the standard manner by operators in the Hilbert space. For\nthe vanishing Planck constant, the generalized algebra gives the operator\nformulation of classical mechanics since it is equivalent to the algebra of\nvariables of classical mechanical system defined, as usually, by functions over\nthe phase space. In this way, the semiclassical limit of kinematical part of\nquantum mechanics is established through the generalized operatorial framework.",
"arxiv_id": "quant-ph/0103044",
"authors": [
"S. Prvanovic",
"Z. Maric"
],
"categories": [
"quant-ph"
],
"title": "Theory of hybrid systems. I. The operator formulation of classical mechanics and semiclassical limit",
"url": "https://arxiv.org/abs/quant-ph/0103044"
},
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