Details
| Original language | English |
|---|---|
| Pages (from-to) | 155-159 |
| Number of pages | 5 |
| Journal | Phys. Lett. A |
| Volume | 202 |
| Issue number | 2-3 |
| Publication status | Published - 1995 |
Abstract
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In: Phys. Lett. A, Vol. 202, No. 2-3, 1995, p. 155-159.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Classical mechanics as quantum mechanics with infinitesimal hbar
AU - Werner, R. F.
AU - Wolff, M. P. H.
PY - 1995
Y1 - 1995
N2 - We define the classical limit of quantum theory in the mathematical framework of nonstandard analysis, choosing h as an infinitesimal number. Up to corrections of infinitesimally small norm, bounded observables which change continuously on the standard (non-infinitesimal) phase space scale, are identified with functions on phase space. We discuss the convergence of commutators to Poisson brackets, and the quantum time evolution to the classical one. These results are also shown for the classical limit of spin systems, by choosing the spin as an infinite half-integer.
AB - We define the classical limit of quantum theory in the mathematical framework of nonstandard analysis, choosing h as an infinitesimal number. Up to corrections of infinitesimally small norm, bounded observables which change continuously on the standard (non-infinitesimal) phase space scale, are identified with functions on phase space. We discuss the convergence of commutators to Poisson brackets, and the quantum time evolution to the classical one. These results are also shown for the classical limit of spin systems, by choosing the spin as an infinite half-integer.
U2 - 10.1016/0375-9601(95)00344-3
DO - 10.1016/0375-9601(95)00344-3
M3 - Article
VL - 202
SP - 155
EP - 159
JO - Phys. Lett. A
JF - Phys. Lett. A
SN - 1873-2410
SN - 1873-2429
IS - 2-3
ER -