Gamow states as continuous linear functional over analytical test functions

Journal of Mathematical Physics

Volumn 37, Issue 9, 1996, Pages 4235-4242

  Bollini, C G ^a   Civitarese, O ^a   De Paoli, A L ^a   Rocca, M C ^a  

^a UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030495129     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531633     Document Type: Article

References (34)

1. G. Gamow, Z. Phys. 51, 204 (1928); 52, 510 (1928).
2. G. Gamow, Z. Phys. 51, 204 (1928); 52, 510 (1928).
3. R. G. Newton, J. Math. Phys. 1, 319 (1960); Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).
4. R. G. Newton, J. Math. Phys. 1, 319 (1960); Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966).
5. A. Bohr and B. Mottelson, Nuclear Structure V.I. (Benjamin, New York, 1969).
6. B. Gyarmati and T. Vertse, Nucl. Phys. A 160, 573 (1971).
7. T. Berggren, Nucl. Phys. A 109, 265 (1968); 389, 261 (1982).
8. T. Berggren, Nucl. Phys. A 109, 265 (1968); 389, 261 (1982).
9. R. J. Liotta, Proceedings of the XVth Workshop on Nuclear Physics, edited by J. Fernandez Niello, C. P. Massolo, and L. Szybisz (World Scientific. Singapore, 1993), p. 99.
10. P. Curuchet, T. Vertse, and R. J. Liotta, Phys. Rev. C 39, 1020 (1989); T. Vertse, P. Curuchet, and R. J. Liotta, Phys. Rev. 42, 2605 (1990); T. Vertse, P. Curuchet, R. J. Liotta, J. Bang, and N. Van Giai, Phys. Lett. B 246, 1 (1991) and references therein.
11. P. Curuchet, T. Vertse, and R. J. Liotta, Phys. Rev. C 39, 1020 (1989); T. Vertse, P. Curuchet, and R. J. Liotta, Phys. Rev. 42, 2605 (1990); T. Vertse, P. Curuchet, R. J. Liotta, J. Bang, and N. Van Giai, Phys. Lett. B 246, 1 (1991) and references therein.
12. P. Curuchet, T. Vertse, and R. J. Liotta, Phys. Rev. C 39, 1020 (1989); T. Vertse, P. Curuchet, and R. J. Liotta, Phys. Rev. 42, 2605 (1990); T. Vertse, P. Curuchet, R. J. Liotta, J. Bang, and N. Van Giai, Phys. Lett. B 246, 1 (1991) and references therein.
13. G. Parravicini, V. Gorini, and E. C. G. Sudarshan, J. Math. Phys. 21, 2208 (1980).
14. A. Bohm, J. Math. Phys. 22, 2813 (1981).
15. A. Bohm, J. Math. Phys. 21, 1040 (1980).
16. M. Gadella, J. Math. Phys. 24, 1462 (1983).
17. M. Gadella, J. Math. Phys. 24, 2142 (1983).
18. M. Gadella, J. Math. Phys. 25, 2481 (1984).
19. A. Bohm, M. Gadella, and G. Bruce Mainland, Am. J. Phys. 57, 1103 (1989); A. Bohm, Quantum Mechanics (Springer, New York, 1979); A. Bohm and M. Gadella, "Dirac Kets, Gamow Vectors and Gelfand Triplets," in Lecture Notes in Physics, edited by H. Araki (Springer-Verlag, New York, 1980).
20. A. Bohm, M. Gadella, and G. Bruce Mainland, Am. J. Phys. 57, 1103 (1989); A. Bohm, Quantum Mechanics (Springer, New York, 1979); A. Bohm and M. Gadella, "Dirac Kets, Gamow Vectors and Gelfand Triplets," in Lecture Notes in Physics, edited by H. Araki (Springer-Verlag, New York, 1980).
21. A. Bohm, M. Gadella, and G. Bruce Mainland, Am. J. Phys. 57, 1103 (1989); A. Bohm, Quantum Mechanics (Springer, New York, 1979); A. Bohm and M. Gadella, "Dirac Kets, Gamow Vectors and Gelfand Triplets," in Lecture Notes in Physics, edited by H. Araki (Springer-Verlag, New York, 1980).
22. Ya. B. Zel'dovich, JETP 12, 542 (1961).
23. T. Berggren, "Expectation value of an operator in a resonant state," Preprint, Department of Mathematical Physics, Lund Institute of Technology, 1995.
24. J. Sebastiao e Silva, Math. Ann. 136, 38 (1958).
25. M. Hasumi, Tôhoku Math. J. 13, 94 (1961).
26. M. Morimoto, Proc. Jpn. Acad. 51, 87 (1975).
27. M. Morimoto, Proc. Jpn. Acad. 51, 213 (1975).
28. C. G. Bollini, L. E. Oxman, and M. C. Rocca, J. Math. Phys. 35, 4429 (1994).
29. I. M. Guelfand and N. Y. Vilenkin, Les distributions (Dunod, Paris, 1967), Tome IV, Chap. 1 §3 sect. 3.6.
30. I. M. Guelfand and N. Y. Vilenkin, Ref. 22, §4.
31. I. M. Guelfand and G. E. Shilov, Les distributions (Dunod, Paris, 1965), Tome III, Chap. 4 §5 sect. 3.6.
32. N. N. Bogolubov, A. A. Logunov, and I. T. Todorov, Axiomatic Quantum Field Theory (Benjamin/Cummings, New York, 1975); S. E. Perez Bergliaffa, H. Vucetich, and G. E. Romero, Int. J. Theor. Phys. 32, 1507 (1993).
33. N. N. Bogolubov, A. A. Logunov, and I. T. Todorov, Axiomatic Quantum Field Theory (Benjamin/Cummings, New York, 1975); S. E. Perez Bergliaffa, H. Vucetich, and G. E. Romero, Int. J. Theor. Phys. 32, 1507 (1993).
34. H. Bremermann, Distributions, Complex Variables and Fourier Transforms (Addison-Wesley, Reading, MA, 1965), p. 174, Table of analytic representations and Fourier Transforms.