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Classical Analogs of Unitarily Equivalent Hamilton Operators

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Abstract

A unitary transformation replaces the given description of a quantum system by an equivalent one. It is observed, however, that not all members of a set of unitarily equivalent Hamilton operators are equally well suited for identifying the corresponding classical systems. A criterion is proposed for recognizing the privileged representatives of the set. A few explicit examples are reported that show the criterion at work.

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REFERENCES

  1. E. Wigner, Phys. Rev. 40, 749 (1932).

    Google Scholar 

  2. J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949).

    Google Scholar 

  3. V. I. Tatarskii, Sov. Phys. Usp. 26, 311 (1983); N. Balasz and B. K. Jennings, Phys. Rep. 104, 347 (1984); M. Hillery et al., Phys. Rep. 106, 121 (1984).

    Google Scholar 

  4. B.-G. Englert, J. Phys. A 22, 625 (1989).

    Google Scholar 

  5. M. V. Berry and K. E. Mount, Rep. Prog. Phys. 35, 315 (1972).

    Google Scholar 

  6. W. H. Miller, Adv. Chem. Phys. 25, 69 (1974).

    Google Scholar 

  7. M. V. Berry, Philos. Trans. R. Soc. London 287, 237 (1977).

    Google Scholar 

  8. M. V. Berry, in Les Houches Lectures XXXVI, G. Iooss, R. H. G. Helleman, and R. Stora, eds. (North-Holland, Amsterdam, 1983), pp. 17-271.

    Google Scholar 

  9. G. B. Folland, Harmonic Analysis in Phase Space (Princeton University Press, Princeton, 1989).

    Google Scholar 

  10. M. A. Shubin, Partial Differential Equations VII (Springer, Berlin, 1994).

    Google Scholar 

  11. R. E. Langer, Phys. Rev. 51, 669 (1937).

    Google Scholar 

  12. B. Rohwedder and B.-G. Englert, Phys. Rev. A 49, 2340 (1994).

    Google Scholar 

  13. B.-G. Englert, Lecture notes on Quantenmechanik im Phasenraum (Universität München, 1995, unpublished).

  14. C. F. von Weizsäcker, Z. Phys. 96, 431 (1935).

    Google Scholar 

  15. E. J. Heller, J. Chem. Phys. 65, 1289 (1976).

    Google Scholar 

  16. A. Einstein, H. Born, and M. Born, Briefwechsel 1916-1955 (Nymphenburger Verlagshandlung, München, 1969).

  17. P. Stifter, C. Leichtle, W. P. Schleich, and J. Marklof, Z. Naturforsch. 52a, 377 (1997).

    Google Scholar 

  18. W. Kinzel, Phys. Bl. 51, 1190 (1995).

    Google Scholar 

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Englert, BG. Classical Analogs of Unitarily Equivalent Hamilton Operators. Foundations of Physics 28, 375–384 (1998). https://doi.org/10.1023/A:1018755726084

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