Radiation conditions and scattering theory for N -particle quantum systems

D. Yafaev

Séminaire Équations aux dérivées partielles (Polytechnique) (1991-1992)

  • page 1-14

How to cite


Yafaev, D.. "Radiation conditions and scattering theory for $N$-particle quantum systems." Séminaire Équations aux dérivées partielles (Polytechnique) (1991-1992): 1-14. <http://eudml.org/doc/112037>.

author = {Yafaev, D.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {asymptotic completeness; smooth perturbations},
language = {eng},
pages = {1-14},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Radiation conditions and scattering theory for $N$-particle quantum systems},
url = {http://eudml.org/doc/112037},
year = {1991-1992},

AU - Yafaev, D.
TI - Radiation conditions and scattering theory for $N$-particle quantum systems
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1991-1992
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 14
LA - eng
KW - asymptotic completeness; smooth perturbations
UR - http://eudml.org/doc/112037
ER -


  1. [1] L.D. Faddeev, Mathematical Aspects of the Three Body Problem in Quantum Scattering Theory, Trudy MIAN69, 1963. (Russian) Zbl0131.43504MR163695
  2. [2] J. Ginibre and M. Moulin, Hilbert space approach to the quantum mechanical three body problem, Ann. Inst. H.Poincaré, A21(1974), 97-145. Zbl0311.47003MR368656
  3. [3] L.E. Thomas, Asymptotic completeness in two- and three-particle quantum mechanical scattering, Ann. Phys.90 (1975), 127-165. MR424082
  4. [4] K. Hepp, On the quantum-mechanical N-body problem, Helv. Phys. Acta42(1969), 425-458. MR247840
  5. [5] I.M. Sigal, Scattering Theory for Many-Body Quantum Mechanical Systems, SpringerLecture Notes in Math. 1011, 1983. Zbl0522.47006MR715786
  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. MR314392
  7. [7] T. Kato, Smooth operators and commutators, Studia Math.31(1968), 535-546. Zbl0215.48802MR234314
  8. [8] R. Lavine, Commutators and scattering theory I: Repulsive interactions, Comm. Math. Phys.20(1971), 301-323. Zbl0207.13706MR293945
  9. [9] R. Lavine, Completeness of the wave operators in the repulsive N-body problem, J. Math. Phys.14 (1973), 376-379. Zbl0269.47005MR317689
  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. Zbl0646.47009MR898052
  11. [11] G.M. Graf, Asymptotic completeness for N-body short-range quantum systems: A new proof, Comm. Math. Phys.132 (1990), 73-101. Zbl0726.35096MR1069201
  12. [12] 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. Zbl0531.47009MR733643
  13. [13] T. Kato, Wave operators and similarity for some non-self-adjoint operators, Math. Ann.162 (1966), 258-279. Zbl0139.31203MR190801
  14. [14] M. Reed and B. Simon, Methods of Modern Mathematical Physics III, Academic Press, 1979. Zbl0405.47007MR529429
  15. [15] S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations, Math. Notes, Princeton Univ. Press, 1982. Zbl0503.35001MR745286
  16. [16] E. Mourre, Absence of singular spectrum for certain self-adjoint operators, Comm. Math. Phys.78 (1981), 391-400. Zbl0489.47010MR603501
  17. [17] P. Perry, I.M. Sigal and B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math.144 (1981), 519-567. Zbl0477.35069MR634428
  18. [18] R. Froese, I. Herbst, A new proof of the Mourre estimate, Duke Math. J.49 (1982), 1075-1085. Zbl0514.35025MR683011
  19. [19] D.R. Yafaev, Remarks on spectral theory for the Schrödinger operator of multiparticle type, Notes of Sci. Seminars of LOMI133 (1984), 277-298. (Russian) Zbl0552.35020MR742163
  20. [20] Y. Saito, Spectral Representation for Schrödinger Operators with Long-Range Potentials, SpringerLecture Notes in Math. 727, 1979. Zbl0414.47012MR540891

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