Abstract
The Wigner formulation of quantum mechanics in phase space is reviewed. Using this formulation, the classical limit of the quantum mechanical description of a system characterized by a given sharp value A of an observable Â, or by a given expectation value <Â> of the same observable, is discussed. It is shown that, in the limit ħ ® 0, the quantum description of the system reduces to that given by the corresponding classical microcanonical or canonical distributions. In particular, the condition for the classical entropy to coincide with the limiting value of the quantum entropy, is spelled out. The first quantum corrections to the classical description are calculated. It is shown that, for a system of non-interacting identical particles, the first correction due to the Pauli principle is proportional to ħ3. A simple relation between the normal-antinormal correspondence of operators and the Wigner (inverse Weyl) correspondence is established.
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© 1988 Kluwer Academic Publishers
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Tikochinsky, Y., Shalitin, D. (1988). Quantum Statistical Mechanics in Phase Space and the Classical Limit. In: Erickson, G.J., Smith, C.R. (eds) Maximum-Entropy and Bayesian Methods in Science and Engineering. Fundamental Theories of Physics, vol 31-32. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9054-4_4
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DOI: https://doi.org/10.1007/978-94-010-9054-4_4
Publisher Name: Springer, Dordrecht
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