Abstract
The quantum formalism ofdistinguishable, yetequivalent particles (with symmetric or antisymmetric wave functions) is here worked out. The result is an entirely explicit formulation of the way in which classical mechanics emerges from quantum mechanics for such particles. Distinguishability is achieved at the cost of dynamical precision; the two are, in fact, complementary.
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References
A. Siegel, On the classical approximation in the quantum statistics of equivalent particles,Foundations of Physics 1, No. 2 (1970) (to be published).
J. von Neumann,Mathematische Grundlagen der Quantenmechanik (Julius Springer, Berlin, 1932) [English translation:Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, N. J., 1955)], Chapter 5, Section 4.
D. ter Haar,Elements of Thermostatistics (McGraw-Hill, New York, 1966), p. 78.
H. Margenau, Exclusion principle and measurement theory, inQuantum Theory of Atoms, Molecules and the Solid State, P. O. Löwdin, ed. (Academic Press, New York, 1966).
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Research sponsored in part by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 557–67.
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Siegel, A. Distinguishable equivalent particles with symmetrized wave functions. Found Phys 1, 57–68 (1970). https://doi.org/10.1007/BF00708655
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DOI: https://doi.org/10.1007/BF00708655