The doublet representation of non-Hilbert eigenstates of the Hamiltonian

Journal of Mathematical Physics

Volumn 37, Issue 5, 1996, Pages 2107-2120

  Castagnino, M ^a,b   Domenech, G ^b   Levinas, M ^b   Umerez N ^b  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^b INSTITUTO DE ASTRONOMÍA Y FÍSICA DEL ESPACIO   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030525898     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531500     Document Type: Article

References (33)

1. G. Gamow, Z. Physik 51, 204 (1928).
2. A. Bohm and M. Gadella, Dirac kets, Gamow vectors and the Gel'fand triplets, Lecture Notes in Physics, Vol. 348 (Springer, Berlin, 1989).
3. A. Bohm, The Rigged Hilbert Space and Quantum Mechanics, Lecture Notes in Physics, Vol. 78 (Springer, Berlin, 1986).
4. A. Bohm, M. Gadella, and B. Mainland, Am. J. Phys. 57, 1103 (1989).
5. M. Pour-el and J. Ian Richards, Computability in Analysis and Physics (Springer, Berlin, 1990).
6. I. M. Gel'fand, M. I. Graev, G. E. Shilov, and N. Ya. Vilenkin, Generalized Functions (Academic, New York, 1964).
7. K. Maurin, General Eigenfunction Expansions and Unitary Representations of Topological Groups (PWN, Warsaw, 1968).
8. O. Meisheimer, J. Math. Phys. 15, 902 and 917 (1974).
9. G. Parravicini, V. Gorini, and E. C. G. Sudarsham, J. Math. Phys. 21, 2208 (1980).
10. A. Bohm, Quantum Mechanics Foundations and Applications (Springer-Verlag, Berlin, 1986), 2nd ed.
11. M. Gadella, J. Math. Phys. 22, 1462 (1981).
12. M. Gadella, J. Math. Phys. 24, 2142 (1983).
13. M. Gadella, J. Math. Phys. 25, 2461 (1984).
14. M. Castagnino, F. Gaioli, and E. Gunzig "Cosmological features on time asymmetry," submitted to Found. Cosm. Phys. (1995).
15. I. Antoniou and I. Prigogine, Phys. A 192, 443 (1993).
16. I. Prigogine, Non-equilibrium Statistical Mechanics (Wiley, New York, 1961).
17. E. C. G. Sudarsham, C. Chiu, and V. Gorini, Phys. Rev. D 18, 2914 (1978).
18. A. Ordóñez, "Prigogine's A and rigged Hilbert Spaces," preprint IFIR (1995).
19. I. Gel'fand and G. Shilov, Generalized Functions (Academic, New York, 1968), Vol. 2.
20. N. Nakanishi, Prog. Th. Phys. 19, 607 (1958).
21. We thank Prof. R. Laura for having advised us of this fact.
22. L. E. Ballantine, Quantum Mechanics (Prentice Hall, Englewood Cliffs, New Jersey, 1990).
23. R. Feynman, "Negative Probability," in Hiley and Peats, 1987.
24. R. Feynman, Int. J. Theor. Phys. 21, 467 (1982).
25. E. C. G. Sudarsham and C. Chiu, Phys. Rev. D. 47, 2602 (1993).
26. E. C. G. Sudarsham, Phys. Rev. A 46, 37 (1992).
27. A. Böhm, M. Gadella, and S. Mexon, "Extending the Stationary Quantum Mechanics of Being to a Non-Stationary quantum Theory of Becoming and Decaying," Univ. Austin preprint (1994).
28. M. Castagnino, E. Gunzig, and F. Lombardo, Gen. Rel. Grav. 27, 257 (1995).
29. M. Castagnino, E. Gunzig, P. Nardone, I. Prigogine, and S. Tasaki, "Quantum Gravity and Large Poincaré Systems," in Fundamental Papers on Theoretical Physics, edited by M. Namiki (AIS, New York, 1993).
30. B. Misra and E. C. G. Sudarsham, J. Math. Phys. 18, 756 (1977).
31. K. Kraus, Found. Phys. 11, 547 (1981).
32. L. A. Khalfin, Sov. Phys. JETP 6, 1053 (1958).
33. L. A. Khalfin, JETP Lett. 8, 65 (1968).