Radiation conditions and scattering theory for N -particle hamiltonians (main ideas of the approach)

Dimitri R. Yafaev

Journées équations aux dérivées partielles (1992)

  • page 1-11
  • ISSN: 0752-0360

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Yafaev, Dimitri R.. "Radiation conditions and scattering theory for $N$-particle hamiltonians (main ideas of the approach)." Journées équations aux dérivées partielles (1992): 1-11. <http://eudml.org/doc/93254>.

@article{Yafaev1992,
author = {Yafaev, Dimitri R.},
journal = {Journées équations aux dérivées partielles},
keywords = {asymptotic completeness; theory of smooth perturbations},
language = {eng},
pages = {1-11},
publisher = {Ecole polytechnique},
title = {Radiation conditions and scattering theory for $N$-particle hamiltonians (main ideas of the approach)},
url = {http://eudml.org/doc/93254},
year = {1992},
}

TY - JOUR
AU - Yafaev, Dimitri R.
TI - Radiation conditions and scattering theory for $N$-particle hamiltonians (main ideas of the approach)
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 11
LA - eng
KW - asymptotic completeness; theory of smooth perturbations
UR - http://eudml.org/doc/93254
ER -

References

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  1. [1] L. D. Faddeev, Mathematical Aspects of the Three Body Problem in Quantum Scattering Theory, Trudy MIAN 69, 1963. (Russian). Zbl0131.43504MR29 #995
  2. [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. Zbl0311.47003MR51 #4897
  3. [3] L. E. Thomas, Asymptotic completeness in two- and three-particle quantum mechanical scattering, Ann. Phys. 90 (1975), 127-165. MR54 #12050
  4. [4] K. Hepp, On the quantum-mechanical N-body problem, Helv. Phys. Acta 42 (1969), 425-458. MR40 #1101
  5. [5] I. M. Sigal, Scattering Theory for Many-Body Quantum Mechanical Systems, Springer Lecture Notes in Math. 1011, 1983. Zbl0522.47006MR87g:81123
  6. [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. MR47 #2944
  7. [7] T. Kato, Smooth operators and commutators, Studia Math. 31 (1968), 535-546. Zbl0215.48802MR38 #2631
  8. [8] R. Lavine, Commutators and scattering theory I : Repulsive interactions, Comm. Math. Phys. 20 (1971), 301-323. Zbl0207.13706MR45 #3020
  9. [9] R. Lavine, Completeness of the wave operators in the repulsive N-body problem, J. Math. Phys. 14 (1973), 376-379. Zbl0269.47005MR47 #6236
  10. [10] I. M. Sigal and A. Soffer, The N-particle scattering problem : Asymptotic completeness for short-range systems, Ann. Math. 126 (1987), 35-108. Zbl0646.47009MR88m:81137
  11. [11] J. Derezinski, A new proof of the propagation theorem for N-body quantum systems, Comm. Math. Phys. 122 (1989), 203-231. Zbl0677.47006MR91a:81218
  12. [12] H. Tamura, Asymptotic completeness for N-body Schrödinger operators with short-range interactions, Comm. Part. Diff. Eq. 16 (1991), 1129-1154. Zbl0779.35079MR92h:35169
  13. [13] G. M. Graf, Asymptotic completeness for N-body short-range quantum systems : A new proof, Comm. Math. Phys. 132 (1990), 73-101. Zbl0726.35096MR91i:81100
  14. [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. Zbl0531.47009MR85h:81071
  15. [15] T. Kato, Wave operators and similarity for some non-self-adjoint operators, Math. Ann. 162 (1966), 258-279. Zbl0139.31203MR32 #8211
  16. [16] D. R. Yafaev, Radiation conditions and scattering theory for three-particle Hamiltonians, Preprint 91-01, Nantes University, 1991. Zbl0795.58009
  17. [17] D. R. Yafaev, Mathematical Scattering Theory, Amer. Math. Soc., 1992. Zbl0761.47001MR94f:47012
  18. [18] Y. Saito, Spectral Representation for Schrödinger Operators with Long-Range Potentials, Springer Lecture Notes in Math. 727, 1979. Zbl0414.47012MR81a:35083
  19. [19] P. Constantin, Scattering for Schrödinger operators in a class of domains with noncompact boundaries, J. Funct. Anal. 44 (1981), 87-119. MR83c:35096
  20. [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. Zbl0703.35139
  21. [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). Zbl0582.35034
  22. [22] S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations, Math. Notes, Princeton Univ. Press, 1982. Zbl0503.35001
  23. [23] M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Academic Press, 1979. Zbl0405.47007MR80m:81085
  24. [24] E. Mourre, Absence of singular spectrum for certain self-adjoint operators, Comm. Math. Phys. 78 (1981), 391-400. Zbl0489.47010MR82c:47030
  25. [25] P. Perry, I. M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math. 144 (1981), 519-567. Zbl0477.35069MR83b:81129
  26. [26] R. Froese, I. Herbst, A new proof of the Mourre estimate, Duke Math. J. 49 (1982), 1075-1085. Zbl0514.35025MR85d:35092
  27. [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. Zbl0354.47004MR56 #17590

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