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Optical propagator of quantum systems in the probability representation

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Abstract

The evolution equation for the propagator of the quantum system in the optical probability representation (optical propagator) is obtained. The relations between the optical and quantum propagators for the Schrödinger equation and the optical propagator of an arbitrary quadratic system are found explicitly.

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References

  1. L. De Broglie, Compt. Rend., 183, 447 (1926).

    MATH  Google Scholar 

  2. L. De Broglie, Compt. Rend., 184, 273 (1927).

    MATH  Google Scholar 

  3. L. De Broglie, Compt. Rend., 185, 380 (1927).

    MATH  Google Scholar 

  4. D. Bohm, Phys. Rev., 85, 166 (1952).

    Article  MathSciNet  ADS  Google Scholar 

  5. D. Bohm, Phys. Rev., 85, 180 (1952).

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  7. K. Husimi, Proc. Phys. Math. Soc. Jpn, 23, 264 (1940).

    Google Scholar 

  8. R. J. Glauber, Phys. Rev. Lett., 10, 84 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  9. E. C. G. Sudarshan, Phys. Rev. Lett., 10, 277 (1963).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. K. E. Cahill and R. J. Glauber, Phys. Rev., 177 1882 (1969).

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  ADS  Google Scholar 

  12. S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett., A 213, 1 (1996).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. S. Mancini, V. I. Man’ko, and P. Tombesi, Found. Phys. 27, 801 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  14. S. Mancini, V. I. Man’ko, and P. Tombesi, Quantum Semiclass. Opt., 7, 615 (1995).

    Article  ADS  Google Scholar 

  15. G. M. D’Ariano, S. Mancini, V. I. Man’ko, and P. Tombesi, Quantum Semiclass. Opt., 8, 1017 (1996).

    Article  ADS  Google Scholar 

  16. S. Mancini, V. I. Man’ko, and P. Tombesi, Europhys. Lett., 37, 79 (1997).

    Article  ADS  Google Scholar 

  17. A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).

    Article  ADS  Google Scholar 

  18. J. Bertrand and P. Bertrand, Found. Phys., 17, 397 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  19. K. Vogel and H. Risken, Phys. Rev. A, 40, 2847 (1989).

    Article  ADS  Google Scholar 

  20. D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett., 70, 1244 (1993).

    Article  ADS  Google Scholar 

  21. Ya. A. Korennoy and V. I. Man’ko, ArXiv quant-ph:1101.2537v1 (2011).

  22. V. I. Man’ko, “Optical symplectic tomography and classical probability instead of the wave function in quantum mechanics,” in: H.-D. Doebner, W. Scherer, and C. Schultz (eds), GROUP21. Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, World Scientific, Singapore (1997), Vol. 2, p. 764.

  23. V. I. Man’ko, J. Russ. Laser Res., 17, 579 (1996).

    Article  Google Scholar 

  24. V. I. Man’ko, “Quantum mechanics and classical probability theory,” in: B. Gruber and M. Ramek (eds.), Symmetries in Science IX, Plenum Press, New York (1997), p. 215.

    Google Scholar 

  25. O. V. Manko, Teor. Mat. Fiz., 121, 285 (1999) [Theor. Math. Phys., 121, 1496 (1999)].

    Google Scholar 

  26. V. I. Man’ko, L. Rosa, and P. Vitale, ArXiv quant-ph:9802030v1 (1998).

  27. V. V. Dodonov and V. I. Man’ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the Lebedev Physical Institute, Nova Science, Nev York (1989), Vol. 183.

  28. I. A. Malkin and V. I. Man’ko, Dynamic Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).

    Google Scholar 

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Correspondence to Yakov A. Korennoy.

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Korennoy, Y.A., Man’ko, V.I. Optical propagator of quantum systems in the probability representation. J Russ Laser Res 32, 153–162 (2011). https://doi.org/10.1007/s10946-011-9201-7

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  • DOI: https://doi.org/10.1007/s10946-011-9201-7

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