Asymptotic completeness for N -body short-range quantum systems

G. M. Graf

Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990)

  • page 1-9

How to cite


Graf, G. M.. "Asymptotic completeness for $N$-body short-range quantum systems." Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990): 1-9. <>.

author = {Graf, G. M.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {asymptotic completeness; short-range potentials; remainder estimates},
language = {eng},
pages = {1-9},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Asymptotic completeness for $N$-body short-range quantum systems},
url = {},
year = {1989-1990},

AU - Graf, G. M.
TI - Asymptotic completeness for $N$-body short-range quantum systems
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1989-1990
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 9
LA - eng
KW - asymptotic completeness; short-range potentials; remainder estimates
UR -
ER -


  1. [1] Cycon, H.L., Froese, R.G., Kirsch, W., Simon, B.: Schrödinger Operators, Springer Verlag (1987) Zbl0619.47005MR883643
  2. [2] Deift, P., Simon, B.: A time-dependent approach to the completeness of multiparticle quantum systems. Commun. Pure Appl. Math.30, 573-583 (1977) Zbl0354.47004MR459397
  3. [3] Derezińnski, J.: A new proof of the propagation theorem for N-body quantum systems. Commun. Math. Phys.122, 203-231 (1989) Zbl0677.47006MR994502
  4. [4] Enss, V.: Asymptotic completeness for quantum-mechanical potential scattering, I. Short-range potentials. Commun. Math. Phys.61, 285-291 (1978) Zbl0389.47005MR523013
  5. [5] Enss, V.: Asymptotic completeness for quantum-mechanical potential scattering, II. Singular and long-range potentials. Ann. Phys.119, 117-132 (1979) Zbl0408.47009MR535624
  6. [6] Enss, V.: "Completeness of Three-Body Quantum Scattering", in Dynamics and Processes ed. by P. Blanchard, L. Streit, Lecture Notes in Mathematics, Vol. 1031, pp. 62-88, Springer Verlag (1983) Zbl0531.47009MR733643
  7. [7] Enss, V.: "Introduction to asymptotic observables for multi-particle quantum scattering", in Schrödinger Operators, Aarhus1985, ed. by E. Balslev, Lecture Notes in Mathematics, Vol. 1218, pp. 61-92, Springer Verlag (1986) Zbl0602.35088MR869596
  8. [8] Froese, R.G., Herbst, I.: A new proof of the Mourre estimate. Duke Math. J.49, n°4, 1075-1085 (1982) Zbl0514.35025MR683011
  9. [9] Graf, G.M.: Asymptotic completeness for N-body short-range systems: a new proof. ETH-preprint 89-50. 
  10. [10] Hack, M.N.: Wave operators in multichannel scattering. Nuovo Cimento Ser.X13, 231-236 (1959) Zbl0086.42804
  11. [11] Hunziker, W.: Time dependent scattering theory for singular potentials. Helv. Phys. Acta40, 1052-1062 (1967). Zbl0152.46303
  12. [12] Mourre, E.: Absence of singular continuous spectrum for certain selfadjoint operators. Commun. Math. Phys.78, 391-408 (1981) Zbl0489.47010MR603501
  13. [13] Perry, P., Sigal, I.M., Simon, B.: Spectral analysis of N-body Schrödinger operators. Ann. Math.114, 519-567 (1981) Zbl0477.35069MR634428
  14. [14] Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. I-IV, Academic Press, (1972-79) Zbl0242.46001MR493419
  15. [15] Sigal, I.M., Soffer, A.: The N-particle scattering problem: asymptotic completeness for short-range systems. Ann. Math.126, 35-108 (1987) Zbl0646.47009MR898052
  16. [16] Sigal, I.M., Soffer, A.: Long-range many-body scattering. Asymptotic clustering for Coulomb-type potentials. University of Toronto preprint (1988), to appear in Inventiones Mathematicae Zbl0702.35197MR1029392
  17. [17] Sigal, I.M., Soffer, A.: Local decay and propagation estimates for time-dependent and time-independent Hamiltonians, University of Princeton preprint (1988) 

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.