Asymptotic completeness for N -body short-range quantum systems

G. M. Graf

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

  • page 1-9

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Graf, G. M.. "Asymptotic completeness for $N$-body short-range quantum systems." Séminaire Équations aux dérivées partielles (Polytechnique) (1989-1990): 1-9. <http://eudml.org/doc/111980>.

@article{Graf1989-1990,
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 = {http://eudml.org/doc/111980},
year = {1989-1990},
}

TY - JOUR
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 - http://eudml.org/doc/111980
ER -

References

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  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) 

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