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Canonical quantum phase variable

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Il Nuovo Cimento B (1971-1996)

Summary

The problem of a correct description of phase variable in quantum mechanics has been revisited. The existence of a unique, consistent definition for the quantum phase of the harmonic oscillator is shown starting from the correspondence principle and Born’s statistical rule. Connections with existing approaches are also reported.

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References

  1. Lynch R.,Phys. Rep.,256 (1995) 367.

    Article  MathSciNet  ADS  Google Scholar 

  2. Susskind L. andGlogower J.,Physics (N.Y.),1 (1964) 49.

    Google Scholar 

  3. Carruthers P. andNieto M. M.,Rev. Mod. Phys.,40 (1968) 411.

    Article  ADS  Google Scholar 

  4. Levy-Leblond J.,Ann Phys. (N.Y.),101 (1976) 319.

    Article  MathSciNet  ADS  Google Scholar 

  5. Vogel W. andSchleich W.,Phys. Rev. A,44 (1991) 7642.

    Article  ADS  Google Scholar 

  6. Helstrom C. W.,Quantum Detection and Estimation Theory (Academic Press, New York, N.Y.) 1976.

    Google Scholar 

  7. Hradil Z.,Phys. Rev. A,51 (1995) 1870.

    Article  ADS  Google Scholar 

  8. Paris M. G. A.,Phys. Lett. A,201 (1995) 132.

    Article  ADS  Google Scholar 

  9. Holevo A. S.,Probabilistic and Statistical Aspects of Quantum Theory (North-Holland Publishing, Amsterdam) 1982.

    Google Scholar 

  10. D’Ariano G. M. andParis M. G. A.,Phys. Rev. A,49 (1994) 3022.

    Article  ADS  Google Scholar 

  11. Pegg D. T. andBarnett S. M.,Phys. Rev. A,39 (1989) 1665;Europhys. Lett.,6 (1988) 483.

    Article  ADS  Google Scholar 

  12. Lynch R.,Phys. Rev. A,41 (1990) 2841;Gerry C. C. andUrbanski K. E.,Phys. Rev. A,42 (1990) 662.

    Article  MathSciNet  ADS  Google Scholar 

  13. Nieto M. M.,Phys. Scr.,48 (1993) 5.

    Article  Google Scholar 

  14. Leonhardt U. andPaul H.,Phys. Rev. A,47 (1993) R2460;Barnett S. M. andDalton B. J.,Phys. Scr.,48 (1993) 13.

    Article  ADS  Google Scholar 

  15. Busch P. andLahti P. J.,Riv. Nuovo Cimento,18, No. 4 (1995).

  16. Naimark M. A.,Izv. Akad. Nauk SSSR Ser. Mat,4 (1940) 227;Mlak W.,Hilbert Spaces and Operator Theory (Kluwer Academic, Dordrecht) 1991.

    Google Scholar 

  17. Ozawa M.,Operator algebras and nonstandard analysis inCurrent Topics in Operator Algebras, edited byH. Araki et. al. (World Scientific, Singapore) 1991, p. 52.

    Google Scholar 

  18. Busch P., Grabowski M. andLahti P. J.,Operational Quantum Mechanics, Lect. Notes Phys., Vol.31 (Springer, Berlin) 1995.

    Google Scholar 

  19. Dirac P. A. M.,Proc. R. Soc. London, Ser. A,114 (1927) 243.

    Article  ADS  Google Scholar 

  20. Sz-Nagy B.,Acta Sci. Math. (Szeged),15 (1953) 87;Foias M.,Bull. Soc. Math. France,85 (1957) 263;Mlak W.,Hilbert Spaces and Operator Theory (Kluwer Academic, Dordrecht) 1991, p. 235.

    MathSciNet  Google Scholar 

  21. Shapiro J. H. andShepard S. R.,Phys. Rev. A,43 (1991) 3795.

    Article  MathSciNet  ADS  Google Scholar 

  22. Ban M.,J. Opt. Soc. Am. B,9 (1992) 1189;Phys. Lett. A,176 (1993) 47.

    Article  ADS  Google Scholar 

  23. Shapiro J. H., inThe Workshop on Squeezed States and Uncertainty Relations (NASA Conf. Public. 3135, Washington DC, 1992), p. 107.

    Google Scholar 

  24. D’Ariano G. M. andParis M. G. A.,Phys. Rev. A,48 (1993) R4039.

    Article  ADS  Google Scholar 

  25. London F.,Z. Phys.,40 (1927) 193.

    Article  ADS  Google Scholar 

  26. Leonhardt U., Vaccaro J. A., Böhmer B. andPaul H.,Phys. Rev. A,51 (1995) 84.

    Article  ADS  Google Scholar 

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Author notes

  1. M. G. A. Paris

    Present address: Dipartimento di Fisica «Alessandro Volta», Università di Pavia, via Bassi 6, 27100, Pavia, Italia

Authors and Affiliations

  1. Arbeitsgruppe «Nichtklassiche Strahlung», Max-Planck-Gesellschaft, Humboldt UniversitÄt zu Berlin, Rudower Chaussee 5, 12484, Berlin, Germany

    M. G. A. Paris

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  1. M. G. A. Paris
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Correspondence to M. G. A. Paris.

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Paris, M.G.A. Canonical quantum phase variable. Nuov Cim B 111, 1151–1159 (1996). https://doi.org/10.1007/BF02743225

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  • DOI: https://doi.org/10.1007/BF02743225

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