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Resonances and Time Reversal Operator in Rigged Hilbert Spaces

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Abstract

We present a formulation of time reversal forquantum systems with resonances. This interpretationfollows with the idea that these systems areintrinsically irreversible. This formulation is made interms of rigged Hilbert spaces.

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REFERENCES

  1. J. P. Antoine, J. Math. Phys. 10 (1969), 53–69.

    Google Scholar 

  2. I. Antoniou, L. Dimitrieva, Y. Kuperin, and Y. Melnikov, Resonances and the extension of dynamics in rigged Hilbert spaces, Comput. Math. Appl., 34, (1997) 339–425.

    Google Scholar 

  3. I. Antoniou, M. Gadella, and G. P. Pronko, Gamow vectors for degenerate scattering resonances, J. Math. Phys. 39 (1998) 2459–2475.

    Google Scholar 

  4. I Antoniou and S. Tasaki, Int. J. Quant. Chem. 44 (1993), 425.

    Google Scholar 

  5. I. Antoniou and I. Prigogine, Physica A 192 (1993), 443.

    Google Scholar 

  6. A. Bohm, Quantum Mechanics: Foundations and Applications, Springer (1994).

  7. A. Bohm, The rigged Hilbert space in quantum mechanics, Boulder Lectures in Theoretical Physics, No. 9A (1966).

  8. A. Bohm, Lett. Math. Phys. 3 (1979), 455–461.

    Google Scholar 

  9. A. Bohm, J. Math. Phys. 21 (1980), 1040–1043.

    Google Scholar 

  10. A. Bohm, J. Math. Phys. 22 (1981), 2813–2823.

    Google Scholar 

  11. A. Bohm, Phys. Rev. A 51 (1995), 1758–1769.

    Google Scholar 

  12. A. Bohm, I. Antoniou, and P. Kielanowski, J. Math. Phys. 36 (1994), 2593–2604.

    Google Scholar 

  13. A. Bohm, and M. Gadella, Dirac Kets, Gamow Vectors and Gel' fand Triplets, Lecture Notes in Physics 398, Springer, Berlin, 1989.

    Google Scholar 

  14. A. Bohm and S. Wickramasekara, The time reversal operator for semigroup evolutions, Found. Phys., 27 (1997), 969.

    Google Scholar 

  15. P. A. M. Dirac, The Principles of Quantum Mechanics, Clarendon Press, Oxford (1958).

    Google Scholar 

  16. P. Exner, Open Quantum Systems and Feynman Integrals, Reidel (1985).

  17. M. Gadella, Int. J. Theor. Phys. 36 (1997), 2273–2296.

    Google Scholar 

  18. G. Gamow, Z. Phys. 51 (1928), 204.

    Google Scholar 

  19. I. M. Gel' fand and G. P. Shilov, Generalized Functions, Vol. 2, Academic Press, New York (1968).

    Google Scholar 

  20. I. M. Gel' fand and N. A. Vilenkin, Generalized Functions, Vol. 4, Academic Press, New York (1964).

    Google Scholar 

  21. G. Ludwig, Foundations of Quantum Mechanics, Vols. I, II, Springer-Verlag, Berlin (1983, 1985).

    Google Scholar 

  22. G. Ludwig, An Axiomatic Basis of Quantum Mechanics, Vols. I, II, Springer-Verlag, Berlin (1983, 1987).

    Google Scholar 

  23. K. Maurin, General Eigenfunction Expansions and Unitary Representations of Topological Groups, Polish Scientific Publishers, Warsaw (1968).

    Google Scholar 

  24. O. Melsheimer, J. Math. Phys. 15 (1974), 902–916.

    Google Scholar 

  25. R. G. Newton, Scattering Theory of Waves and Particles, Springer-Verlag, New York (1982).

    Google Scholar 

  26. T. Petroski and I. Prigogine, Physica A 175 (1991), 146.

    Google Scholar 

  27. T. Petroski, I. Prigogine, and S. Tasaki, Physica 173A (1991), 175.

    Google Scholar 

  28. I. Prigogine, Phys. Rep. 219 (1992), 93.

    Google Scholar 

  29. I. Prigogine, From Being to Becoming, Freeman, New York (1980).

    Google Scholar 

  30. J. E. Roberts, Commun. Math. Phys. 3 (1966), 98–119.

    Google Scholar 

  31. H. H. Schaeffer, Topological Vector Spaces, Springer-Verlag, New York (1970).

    Google Scholar 

  32. E. P. Wigner, Group Theoretical Concepts and Methods in Elementary Particle Physics, Gordon and Breach, New York (1994), p. 37.

    Google Scholar 

  33. E. P. Wigner, Symmetries and Reflections, Indiana University Press, Bloomington (1967), p. 38.

    Google Scholar 

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Gadella, M., De La Madrid, R. Resonances and Time Reversal Operator in Rigged Hilbert Spaces. International Journal of Theoretical Physics 38, 93–113 (1999). https://doi.org/10.1023/A:1026629106717

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