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

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.