High energy asymptotics for N-body scattering matrices with arbitrary channels

X. P. Wang

Annales de l'I.H.P. Physique théorique (1996)

  • Volume: 65, Issue: 1, page 81-108
  • ISSN: 0246-0211

How to cite


Wang, X. P.. "High energy asymptotics for N-body scattering matrices with arbitrary channels." Annales de l'I.H.P. Physique théorique 65.1 (1996): 81-108. <http://eudml.org/doc/76737>.

author = {Wang, X. P.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {generalized -body Schrödinger operators; cluster decomposition},
language = {eng},
number = {1},
pages = {81-108},
publisher = {Gauthier-Villars},
title = {High energy asymptotics for N-body scattering matrices with arbitrary channels},
url = {http://eudml.org/doc/76737},
volume = {65},
year = {1996},

AU - Wang, X. P.
TI - High energy asymptotics for N-body scattering matrices with arbitrary channels
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 65
IS - 1
SP - 81
EP - 108
LA - eng
KW - generalized -body Schrödinger operators; cluster decomposition
UR - http://eudml.org/doc/76737
ER -


  1. [1] S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, J. Analyse Math., Vol. 30, 1976, pp. 1-38. Zbl0335.35013MR466902
  2. [2] W.O. Amrein, D.B. Pearson and K.B. Sinha, Bounds on the total scattering cross section for N-body systems, Nuovo Cimento, Vol. 52A, 1979, pp. 115-131. MR542070
  3. [3] W.O. Amrein and K.B. Sinha, On three-body scattering cross sections, J. Phys. A: Math. Gen., Vol. 15, 1982, pp. 1567-1586. Zbl0491.47005MR656835
  4. [4] A. Bommier, Régularité et prolongement méromorphe de la matrice de diffusion pour les problèmes à N-corps à longue portée, Thèse de Doctorat, École Polytechnique, 1993. MR1240535
  5. [5] H. Cycon, R. Froese, W. Kirsch and B. Simon, Schrödinger Operators, Texts and Monographs in Physics, Springer Verlag, 1987. Zbl0619.47005
  6. [6] V. Enss and B. Simon, Finite total cross-sections in nonrelativistic quantum mechanics, Commun. in Math. Phys., Vol. 76, 1980, pp. 177-209. Zbl0471.35065MR587510
  7. [7] C. Gérard, H. Isozaki and E. Skibsted, Commutator algebra and resolvent estimates, preprint 1993. Zbl0814.35086MR1275395
  8. [8] W. Hunziker, Potential scattering at high energies, Helv. Phys. Acta, Vol. 36, 1963, pp. 838-856. MR180135
  9. [9] H. Isozaki, Structure of S-matrices for three body Schrödinger operators, Comm. Math. Phys., Vol. 146, 1992, pp. 241-258. Zbl0748.35026MR1165182
  10. [10] H.T. Ito, High energy behavior of total scattering cross sections for 3-body quantum systems, preprint 1992. MR1245017
  11. [11] H.T. Ito and H. Tamura, Semi-classical asymptotics for total scattering cross sections of 3-body systems, J. Math. Kyoto Univ., Vol. 32, 1992, pp. 533-555. Zbl0769.35045MR1183366
  12. [12] L.D. Landau and E.M. Lifchitz, Quantum Mechanics, Nonrelativistic Theory, Pergmon Press, Oxford, 1965. Zbl0178.57901
  13. [13] R. Novikov, Le problème de scattering inverse pour les systèmes à trois corps, exposé au Séminaire des E.D.P., Univ. de Nantes, Mai 1994. 
  14. [14] M. Reed and B. Simon, Methods of Modern Mathematical Physics, IV. Analysis of Operators, Academic Press, New York, 1978. Zbl0401.47001MR493421
  15. [15] D. Robert, Asymptotique de la phase de diffusion à haute énergie pour des perturbations du second ordre du Laplacien, Ann. Sci. École Norm. Sup., Vol. 25, 1992, pp. 107-134. Zbl0801.35100MR1169349
  16. [16] D. Robert and H. Tamura, Semiclassical estimates for resolvents and asymptotics for total scattering cross sections, Ann. Inst. H. Poincaré, Vol. 46, 1987, pp. 415-442. Zbl0648.35066MR912158
  17. [17] D. Robert and X.P. Wang, Pointwise semiclassical asymptotics for total cross sections in N-body problems, preprint 1992, Univ. Nantes, in "Spectral and Scattering Theory", M. Ikawa ed., Marcel Dekker. MR1291643
  18. [18] I.M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for short range systems, Ann. of Math., Vol. 126, 1987, pp. 35-108. Zbl0646.47009MR898052
  19. [19] E. Skibsted, Smoothness of N-body scattering amplitudes, Rev. Math. Phys., Vol. 4(4), 1992, pp. 619-658. Zbl0781.35047MR1197552
  20. [20] A.V. Sobolev and D.R. Yafaev, On the quasiclassical limit of total scattering cross–section in non-relativistic quantum mechanics, Ann. Inst. H. Poincaré, Vol. 44, 1986, pp. 195-210. Zbl0607.35070MR839284
  21. [21] X.P. Wang, On the three-body long-range scattering problems, Letters in Math. Phys., Vol. 25, 1992, pp. 267-276.Detailed version: Propagation estimates and asymptotic completeness in three-body long-range scattering, J. of Funct. Analysis, Vol. 125(1), 1994, pp. 1-36. Zbl0776.35045MR1188806
  22. [22] X.P. Wang, Microlocal resolvent estimates of N-body Schrödinger operators, J. of the Fac. Sc., Univ. Tokyo, Sect. IA, Mathematics, Vol. 40(2), 1993, pp. 337-385. Zbl0810.35073MR1255046
  23. [23] X.P. Wang, Sections efficaces dans le problème à N-corps, Exposé No. IX au Séminaire EDP à l'École Polytechnique, Palaiseau, Décembre 1992. Zbl0875.35023
  24. [24] X.P. Wang, Total cross sections in N-body problems: Finiteness and high energy asymptotics, Commun. Math. Phys., Vol. 156, 1993, pp. 333-354. Zbl0839.35113MR1233849
  25. [25] X.P. Wang, On the uniqueness of inverse scattering for N-body systems, Inverse Problems, Vol. 10, 1994, pp. 765-784. Zbl0803.35169MR1278586
  26. [26] D.R. Yafaev, The eikonal approximation for the Schrödinger equation, Proc. of the Steklov Inst. Math., Vol. 179(2), 1989, pp. 251-266. Zbl0693.35125MR964920
  27. [27] D.R. Yafaev, Quasiclassical asymptotics of the scattering cross-section for the Schrödinger equation, Math. USSR Izv., Vol. 32(1), 1989, pp. 141-165. Zbl0672.35054MR936527
  28. [28] D.R. Yafaev, Resolvent estimates and scattering matrix for N-particle hamiltonians, preprint Univ. Rennes 1, September 1993. 
  29. [29] K. Yajima, The quasiclassical limit of scattering amplitude - L2 approach for short range potentials-, Japan J. Math., Vol. 13, 1987, pp. 77-126. Zbl0648.35067MR914315

NotesEmbed ?


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.