dorsal/arxiv
View SchemaThe classical limit of quantum theory
| Authors | R. F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9504016 |
| URL | https://arxiv.org/abs/quant-ph/9504016 |
Abstract
For a quantum observable $A_\hbar$ depending on a parameter $\hbar$ we define the notion ``$A_\hbar$ converges in the classical limit''. The limit is a function on phase space. Convergence is in norm in the sense that $A_\hbar\to0$ is equivalent with $\Vert A_\hbar\Vert\to0$. The $\hbar$-wise product of convergent observables converges to the product of the limiting phase space functions. $\hbar^{-1}$ times the commutator of suitable observables converges to the Poisson bracket of the limits. For a large class of convergent Hamiltonians the $\hbar$-wise action of the corresponding dynamics converges to the classical Hamiltonian dynamics. The connections with earlier approaches, based on the WKB method, or on Wigner distribution functions, or on the limits of coherent states are reviewed.
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"abstract": "For a quantum observable $A_\\hbar$ depending on a parameter $\\hbar$ we define\nthe notion ``$A_\\hbar$ converges in the classical limit\u0027\u0027. The limit is a\nfunction on phase space. Convergence is in norm in the sense that $A_\\hbar\\to0$\nis equivalent with $\\Vert A_\\hbar\\Vert\\to0$. The $\\hbar$-wise product of\nconvergent observables converges to the product of the limiting phase space\nfunctions. $\\hbar^{-1}$ times the commutator of suitable observables converges\nto the Poisson bracket of the limits. For a large class of convergent\nHamiltonians the $\\hbar$-wise action of the corresponding dynamics converges to\nthe classical Hamiltonian dynamics. The connections with earlier approaches,\nbased on the WKB method, or on Wigner distribution functions, or on the limits\nof coherent states are reviewed.",
"arxiv_id": "quant-ph/9504016",
"authors": [
"R. F. Werner"
],
"categories": [
"quant-ph",
"cond-mat",
"hep-th"
],
"title": "The classical limit of quantum theory",
"url": "https://arxiv.org/abs/quant-ph/9504016"
},
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