Publication: Asymptotic formulae for the quantum Rényi entropies of position: application to the infinite well
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1999-05-07
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IOP
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Abstract
General asymptotic formulae are derived by means of the WKB approximation for the continuous and discrete Rényi entropies of position of one-dimensional quantum systems in energy eigenstates, in terms of the corresponding entropies for a microcanonical ensemble of analogous classical systems. These results are checked in the simplest particular case of the infinite potential well, where the asymptotic formula for continuous entropies holds as an exact identity. For the discrete entropies, analytical expressions are obtained from which the asymptotic formulae given for the limiting cases of large and small measurement resolution can both be verified.
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14 pages, 2 figures.-- PACS nrs.: 03.65.Sq.-- MSC2000 codes: 81Q20, 94A17, 81P15, 81Q05.
MR#: MR1687434 (2000a:81051)
Zbl#: Zbl 1031.81520
MR#: MR1687434 (2000a:81051)
Zbl#: Zbl 1031.81520
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[PACS] Semiclassical theories and applications, [MSC] Semiclassical techniques including WKB and Maslov methods, [MSC] Measures of information, entropy, [MSC] Quantum measurement theory, [MSC] Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations, Quantum information and quantum mechanics
Bibliographic citation
Journal of Physics A: Mathematical and Theoretical, 1999, vol. 32, n. 18, p. 3419-3432