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The Emergence of Classical Properties from Quantum Mechanics: New Problems from Old

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Fundamental Problems in Quantum Physics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 73))

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Abstract

The ongoing debates about the interpretation of quantum mechanics have often taken place in forums such as the measurement problem and Schrödinger’s cat paradox. I urge that we move beyond those old forums, and consider instead the more general problem of how classical properties emerge from quantum mechanics. Quantum chaos appears as a special case of this general problem, being the study of the emergence of classical chaos from QM. Such a study quickly leads to the following conclusion: the classical limit of a quantum state is typically an ensemble of classical orbits, and not a single classical orbit. This fact enables us to understand the relation between several quantum and classical dynamical models. This study also reveals interesting connections between old and new problems.

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References

  1. L. E. Ballentine, Int. J. Theor. Phys. 27, 211–218 (1988).

    Article  Google Scholar 

  2. L. E. Ballentine, Found. Phys. 20, 1329–1343 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  3. L. E. Ballentine, Quantum Mechanics (Prentice-Hall, Englewood Cliffs, New Jersey, 1990 ).

    Google Scholar 

  4. L. E. Ballentine, Yumin Yang, and J. P. Zibin, Phys. Rev. A (to be published).

    Google Scholar 

  5. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics ( Springer, New York, 1991 ).

    Google Scholar 

  6. G. Casati, editor, Chaotic Behavior in Quantum Systems ( Plenum, New York, 1985 ).

    Google Scholar 

  7. H. A. Cerdeira, R. Ramaswamy, M. C. Gutzwiller, and G. Casati, editors, Quantum Chaos ( World Scientific, Singapore, 1991 ).

    Google Scholar 

  8. P. Cvitanovic, I. Percival, and A. Wirtzba, editors, Quantum Chaos - Quantum Measurement ( 1992, Kluwer, Dordrecht ).

    Google Scholar 

  9. L. E. Ballentine, Phys. Rev. A 44, 4126–4132 (1991).

    Article  ADS  Google Scholar 

  10. L. E. Ballentine, Phys. Rev. A 44, 4133–4141 (1991).

    Article  ADS  Google Scholar 

  11. L. E. Ballentine, Phys. Rev. A 47, 2592–2600 (1993).

    Google Scholar 

  12. J. E. G. Farina, Am. J. Phys. 45 1200 (1977). This paper gives a simple example in which the symmetrized correlation between the position and momentum operators arises, and is the natural analog of the corresponding classical correlation.

    Google Scholar 

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© 1995 Springer Science+Business Media Dordrecht

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Ballentine, L.E. (1995). The Emergence of Classical Properties from Quantum Mechanics: New Problems from Old. In: Ferrero, M., van der Merwe, A. (eds) Fundamental Problems in Quantum Physics. Fundamental Theories of Physics, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8529-3_3

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  • DOI: https://doi.org/10.1007/978-94-015-8529-3_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4608-6

  • Online ISBN: 978-94-015-8529-3

  • eBook Packages: Springer Book Archive

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