Propagation and local-decay properties for long-range scattering of quantum three-body systems

 Access to full text

 Full (PDF)

1. [1] S. Agmon, Some new results in spectral and scattering theory of differential operators on L2(Rν), Seminaire Goulaouic-Schwartz 1978-1979, Centre de Mathématiques-Polytechnique, Palaiseau. Zbl0406.35052MR557513
2. [2] W.O. Amrein and V. Georgescu, Helv. Phys. Acta, t. 46, 1973, p. 635-658. MR363267
3. [3] K. Asada and D. Fujiwara, Japan. J. Math., t. 4, 1978, p. 299-361. Zbl0402.44008MR528863
4. [4] A.P. Calderon and R. Vaillancourt, J. Math. Soc. Japan, t. 23, 1971, p. 374- 378. Zbl0203.45903MR284872
5. [5] E.B. Davies, Duke Math. J., t. 47, 1980, p. 171-185. Zbl0434.47014MR563374
6. [6] J. Dollard, J. Math. Phys., t. 5, 1964, p. 729-738. MR163620
7. [7] V. Enss, Ann. Phys., t. 119, 1979, p. 117-132. Zbl0408.47009MR535624
8. [8] V. Enss, Completeness of three-body quantum scattering, Conference Proceedings Bielefeld, 1981, to appear in Lecture Notes in Mathematics, Springer, 1983. Zbl0531.47009MR733643
9. [9] V. Enss, in Rigorous Atomic and Molecular Physics, G. Velo and A. S. Wightman eds, Plenum, New York, 1981. 
10. [10] V. Enss, Commun. Math. Phys., t. 89, 1983, p. 245-268. Zbl0543.47008
11. [11] V. Enss, Propagation properties of quantum scattering states, preprint, Institut Mittag-Leffler, 1982. MR707205
12. [12] V. Enss, Three-body quantum scattering theory, in preparation. Zbl0531.47009
13. [13] D. Fujiwara, Proc. Japan Acad., t. 51, 1975, p. 96-99. Zbl0319.44004MR372685
14. [14] J. Ginibre, in Acta Physica Austriaca, Suppl. XVII, W. Thirring and P. Urban eds, Vienne, 1977. 
15. [15] J. Ginibre, La méthode « dépendant du temps » dans le problème de la complétude asymptotique, preprint univ. Paris-Sud, LPTHE 80/10, 1980. 
16. [16] G. Hagedorn and P. Perry, Commun. Pure and Appl. Math., t. 36, 1983, p. 213-232. Zbl0506.35026MR690657
17. [17] L. Hörmander, Math. Z., t. 146, 1976, p. 69-91. Zbl0319.35059MR393884
18. [18] T. Ikebe and H. Isozaki, Integral Equ. and Op. Theory, t. 5, 1982, p. 18-49. Zbl0496.35069MR646878
19. [19] H. Kitada, J. Faculty Sci. Univ. Tokyo, Ser. IA, t. 29, 1982, p. 353-369. Zbl0494.35072MR672067
20. [20] H. Kitada and K. Yajima, Duke Math. J., t. 49, 1982, p. 341-376. Zbl0499.35087MR659945
21. [21] S.P. Merkuriev, Ann. Phys., t. 130, 1980, p. 395-426. Zbl0483.35066MR610668
22. [22] E. Mourre, Commun. Math. Phys., t. 91, 1983, p. 279-300. Zbl0543.47041MR723552
23. [23] E. Mourre, Opérateurs conjugués et propriétés de propagation. Remarques sur la complétude asymptotique des systèmes à 3 corps, preprint CNRS Luminy, 1982. MR723552
24. [24] Pl. Muthuramalingam, Spectral properties of vaguely elliptic pseudo-differential operators with momentum dependent long-range potentials using time-dependent scattering theory, New Delhi, 1982. 
25. [25] Pl. Muthuramalinga- and K.B. Sinha, Asymptotic evolution of certain observables and completeness in Coulomb scattering, to appear in J. Func. Anal. Zbl0531.47008MR734802
26. [26] P. Perry, Commun. Math. Phys., t. 81, 1981, p. 243-259. Zbl0471.47007
27. [27] P. Perry, I. Sigal and B. Simon, Ann. Math., t. 114, 1981, p. 519-567. Zbl0477.35069MR634428
28. [28] M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. II, III and IV, Academic Press, New York, 1975-1979. 
29. [29] D. Ruelle, Nuovo Cimento, t. 61A, 1966, p. 655-662. MR246603
30. [30] I. Sigal, Asymptotic completeness of many-body short-range systems. The Weizmann Inst., preprint 1983. Zbl0559.46036MR750031
31. [31] I. Sigal, Scattering Theory of Many-Body Quantum Mechanical Systems (Rigorous results). Lecture Notes in Mathematics, A. Dold and B. Eckmann eds, Springer-Verlag, Berlin, Heildelberg, 1983. Zbl0522.47006MR715786
32. [32] K.B. Sinha, M. Krishna and Pl. Muthuramalingam, On the completeness of three-body scattering, New Dehli preprint, 1983. Zbl0558.47007
33. [33] M. Combescure, Asymptotic completeness for three-body long-range systems, in preparation.