Radiation conditions and scattering theory for N-particle hamiltonians (main ideas of the approach)
Yafaev, Dimitri R.
Journées équations aux dérivées partielles, (1992), p. 1-11 / Harvested from Numdam
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Publié le : 1992-01-01
@article{JEDP_1992____A2_0,
     author = {Yafaev, Dimitri},
     title = {Radiation conditions and scattering theory for $N$-particle hamiltonians (main ideas of the approach)},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1992},
     pages = {1-11},
     zbl = {0771.35040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_1992____A2_0}
}

Yafaev, Dimitri R. Radiation conditions and scattering theory for $N$-particle hamiltonians (main ideas of the approach). Journées équations aux dérivées partielles,  (1992), pp. 1-11. http://gdmltest.u-ga.fr/item/JEDP_1992____A2_0/

[1] L. D. Faddeev, Mathematical Aspects of the Three Body Problem in Quantum Scattering Theory, Trudy MIAN 69, 1963. (Russian). | MR 29 #995 | Zbl 0131.43504

[2] J. Ginibre and M. Moulin, Hilbert space approach to the quantum mechanical three body problem, Ann. Inst. H. Poincaré, A 21 (1974), 97-145. | Numdam | MR 51 #4897 | Zbl 0311.47003

[3] L. E. Thomas, Asymptotic completeness in two- and three-particle quantum mechanical scattering, Ann. Phys. 90 (1975), 127-165. | MR 54 #12050

[4] K. Hepp, On the quantum-mechanical N-body problem, Helv. Phys. Acta 42 (1969), 425-458. | MR 40 #1101

[5] I. M. Sigal, Scattering Theory for Many-Body Quantum Mechanical Systems, Springer Lecture Notes in Math. 1011, 1983. | MR 87g:81123 | Zbl 0522.47006

[6] R. J. Iorio and M. O'Carrol, Asymptotic completeness for multi-particle Schrödinger Hamiltonians with weak potentials, Comm. Math. Phys. 27 (1972), 137-145. | MR 47 #2944

[7] T. Kato, Smooth operators and commutators, Studia Math. 31 (1968), 535-546. | MR 38 #2631 | Zbl 0215.48802

[8] R. Lavine, Commutators and scattering theory I : Repulsive interactions, Comm. Math. Phys. 20 (1971), 301-323. | MR 45 #3020 | Zbl 0207.13706

[9] R. Lavine, Completeness of the wave operators in the repulsive N-body problem, J. Math. Phys. 14 (1973), 376-379. | MR 47 #6236 | Zbl 0269.47005

[10] I. M. Sigal and A. Soffer, The N-particle scattering problem : Asymptotic completeness for short-range systems, Ann. Math. 126 (1987), 35-108. | MR 88m:81137 | Zbl 0646.47009

[11] J. Derezinski, A new proof of the propagation theorem for N-body quantum systems, Comm. Math. Phys. 122 (1989), 203-231. | MR 91a:81218 | Zbl 0677.47006

[12] H. Tamura, Asymptotic completeness for N-body Schrödinger operators with short-range interactions, Comm. Part. Diff. Eq. 16 (1991), 1129-1154. | MR 92h:35169 | Zbl 0779.35079

[13] G. M. Graf, Asymptotic completeness for N-body short-range quantum systems : A new proof, Comm. Math. Phys. 132 (1990), 73-101. | MR 91i:81100 | Zbl 0726.35096

[14] V. Enss, Completeness of three-body quantum scattering, in : Dynamics and processes, P. Blanchard and L. Streit, eds., Springer Lecture Notes in Math. 103 (1983), 62-88. | MR 85h:81071 | Zbl 0531.47009

[15] T. Kato, Wave operators and similarity for some non-self-adjoint operators, Math. Ann. 162 (1966), 258-279. | MR 32 #8211 | Zbl 0139.31203

[16] D. R. Yafaev, Radiation conditions and scattering theory for three-particle Hamiltonians, Preprint 91-01, Nantes University, 1991.

[17] D. R. Yafaev, Mathematical Scattering Theory, Amer. Math. Soc., 1992. | MR 94f:47012 | Zbl 0761.47001

[18] Y. Saito, Spectral Representation for Schrödinger Operators with Long-Range Potentials, Springer Lecture Notes in Math. 727, 1979. | MR 81a:35083 | Zbl 0414.47012

[19] P. Constantin, Scattering for Schrödinger operators in a class of domains with noncompact boundaries, J. Funct. Anal. 44 (1981), 87-119. | MR 83c:35096

[20] E. M. Il'In, Scattering by unbounded obstacles for elliptic operators of second order, Proc. of the Steklov Inst. of Math. 179 (1989), 85-107. | Zbl 0703.35139

[21] D. R. Yafaev, Remarks on the spectral theory for the multiparticle type Schrödinger operator, J. Soviet Math. 31 (1985), 3445-3459 (translated from Zap. Nauchn. Sem. LOMI 133 (1984), 277-298). | Zbl 0582.35034

[22] S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations, Math. Notes, Princeton Univ. Press, 1982. | Zbl 0503.35001

[23] M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Academic Press, 1979. | MR 80m:81085 | Zbl 0405.47007

[24] E. Mourre, Absence of singular spectrum for certain self-adjoint operators, Comm. Math. Phys. 78 (1981), 391-400. | MR 82c:47030 | Zbl 0489.47010

[25] P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math. 144 (1981), 519-567. | MR 83b:81129 | Zbl 0477.35069

[26] R. Froese, I. Herbst, A new proof of the Mourre estimate, Duke Math. J. 49 (1982), 1075-1085. | MR 85d:35092 | Zbl 0514.35025

[27] P. Deift and B. Simon, A time-dependent approach to the completeness of multiparticle quantum systems, Comm. Pure Appl. Math. 30 (1977), 573-583. | MR 56 #17590 | Zbl 0354.47004