On the many body problem in quantum mechanics
Méthodes semi-classiques Volume 1 - École d'Été (Nantes, juin 1991), Astérisque, no. 207 (1992), pp. 109-152 
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     author = {Soffer, Avy},
     title = {On the many body problem in quantum mechanics},
     booktitle = {M\'ethodes semi-classiques Volume 1 - \'Ecole d'\'Et\'e (Nantes, juin 1991)},
     series = {Ast\'erisque},
     pages = {109--152},
     year = {1992},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {207},
     language = {en},
     url = {https://www.numdam.org/item/AST_1992__207__109_0/}
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Soffer, Avy. On the many body problem in quantum mechanics, dans Méthodes semi-classiques Volume 1 - École d'Été (Nantes, juin 1991), Astérisque, no. 207 (1992), pp. 109-152. https://www.numdam.org/item/AST_1992__207__109_0/

[Ag] S. Agmon, Lectures on Exponential Decay of Solutions of Second Order Elliptic Equations, Math. Notes, Princeton. 1982.

[ABG] W. Amrein, A. M. Berthier, V. Georgescu, HPA 61 1-20 (1989).

[BG1] A. Boutet De Monvel-Berthier, V. Georgescu, "Spectral and Scattering Theory by the Conjugate Operator Method," to appear, and cited ref.

[BG2] A. Boutet De Monvel-Berthier, V. Georgescu, Acad. Sci. Paris t. 312 Ser. I, 477-482 (1991).

[Be-K] M. Ben-Artzi, S. Klainerman, "Decay and regularity for the Schrödinger equations", J. d'Analyse Math., to appear.

[Com] J. M. Combes, CMP 12 283 (1969).

[Co-S] P. Constantin, J.-C. Saut, JAMS N2, 413-439 (1988).

[CFKS] H.-L. Cycon et al., Schrödinger Operators, Springer, 1987.

[Comb] M. Combescure, Long range scattering for the two-body Schrödinger equation with "Hörmander-like" potentials, preprint.

[Der1] J. Derezinski, CMP 122 203-231 (1989).

[Der2] J. Derezinski, "The Mourre estimate for dispersive N-body Schrödinger operators," preprint 1988.

[Der3] J. Derezinski, Rev. Math. Phys. 3 162, (1991).

[DS] P. Deift, B. Simon, Comm. PAM 30 573-583 (1977).

[E1] V. Enss, CMP 61 285-291 (1978).

[E2] V. Enss, in Proc. Teubner Texte zur Math. Leipzig (M. Denuth, B.W. Schultze eds.).

[FHP1] R. Froese, P. Hislop, P. Perry, JFA, to appear.

[FHP2] R. Froese, P. Hislop, P. Perry, Inv. Math. 106 295-333 (1991).

[FrL] R. Froese, M. Loss, A time dependent proof of the Mourre's Theorem, preprint.

[FL] C. Fernandez, R. Lavine, Lower bounds for Resonance Widths in Potential and Obstacle Scattering, preprint, 1989.

[FH1] R. Froese, I. Herbst, CMP 87 429-447 (1982).

[FH2] R. Froese, I. Herbst, Duke Math. J. 49 (1982).

[GV1] J. Ginibre, G. Velo, JFA 32 1-71 (1979).

[GV2] J. Ginibre, G. Velo, Smoothing Properties and Retarded Estimates for some dispersive Evolution Equations," preprint.

[Ger1] C. Gerard, IHP, 1991, to appear.

[Ger2] C. Gerard, Sharp Propagation Estimates for N-particle Systems, preprint (1991).

[Ger3] Seminaire Bourbaki, 1989/1990, no. 721.

[Ge-Der] C. Gerard, J. Derezinski, A remark on asymptotic clustering for N-particle quantum systems, preprint, (1991).

[Ger-Sig] C. Gerard, I. M. Sigal, "Space Time Picture of Semiclassical Resonances," preprint, 1991.

[Gr] J. M. Graf, CMP 132 73-101 (1990).

[GJ] J. Glimm, A. Jaffe, Qauntum Physics, Springer (1981).

[Ho] L. Hörmander, The analysis of linear partial differential operators I-IV Springer (1985).

[Her] I. Herbst, Am. J. Math. 113 509-565 (1991).

[H-Sk] I. Herbst, E. Skibsted, to appear.

[Hul] W. Hunziker, CMP 8, 282-299 (1968).

[Hu2] W. Hunziker, private communication.

[If] A. Iftimovicki, "On the asymptotic completeness for Agmon type Hamiltonians," preprint (1992).

[Iw] H. Iwashita, JFA 82, 92-112 (1989) and cited ref.

[J] A. Jensen, CMP, 82 435-456 (1981).

[JSS] J. L. Journë, A. Soffer, C. D. Sogge, Comm. PAM, vol. XLIV, 5 573-604 (1991).

[KPV] C. Kenig, G. Ponce, L. Vega, preprints (1989-1991). see also C. Kenig, Oscillatory integrals and nonlinear dispersive equations, preprint.

[Ka-Ya] T. Kato, K. Yajima, Rev. Math. Phys. 481-496 (1989).

[Kit-Ku] H. Kitada, H. Kumango, Osaka J. Math. 291-360 (1981).

[Kit] H. Kitada, Rev. Math. Phys. (1990).

[L] R. Lavine, JMP 14 376-379. (1973).

[Mo1] E. Mourre, CMP 68 91-94 (1979).

[Mo2] E. Mourre, CMP 91 279 (1983).

[M-R-S] K. Morawetz, J. Ralston, W. Strauss, CPAM 30 447-508 (1977).

[Na] S. Nakamura, CMP 109 397-415 (1987).

[Or] A. Orth, CMP 126 559-573 (1990).

[Pe] P. Perry, Scattering Theory by the Enss Method (Harvard 1983).

[PSS] P. Perry, I. M. Sigal, B. Simon, Ann. Math. 114 519-567 (1981).

[Sig1] I. M. Sigal, Duke Math. J. 60 N2 (1990).

[Sig2] I. M. Sigal, Non Linear Wave and Schrödinger Equations I. Instability of Periodic and Quasiperiodic Solutions, preprint, (1990).

[Sig3] I. M. Sigal, Comm. Math. Phys. 85 309-324 (1982).

[Sig-Sof1] I. M. Sigal, A. Soffer, Ann. Math. 126 35-108. 91987.

[Sig-Sof2] I. M. Sigal, A. Soffer, Local Decay and Velocity Bounds, preprint.

[Sig-Sof3] I. M. Sigal, A. Soffer, Asymptotic Completeness for Three Particle Long Range Potentials, preprint.

[Sig-Sof4] I. M. Sigal, A. Soffer, Inv. Math. 99, 115-143 (1990).

[Sig-Sof5] I. M. Sigal, A. Soffer, Asymptotic Completeness for N≤4 Particle Systems with Coulomb Type Interactions, preprint.

[Sof1] A. Soffer, LMP 8 (1984).

[Sof2] A. Soffer, in preparation.

[Sof-We] A. Soffer, M. Weinstein, CMP (1990) and JDE, to appear.

[Sj] P. Sjölin, Duke Math. J. 55 699-715 (1987).

[Sk] E. Skibsted, Propagation estimates for N-body Schrödinger Operators, preprint (1990).

[Ta] H. Tamura, Comm. PDE 16 1129-1154, (1991).

[V] L. Vega, Proc. AMS 102 874-878 (1988).

[We] R. Weder, Spectral and Scattering theory for Wave Propagation in Perturbed Stratified Media, App. Math. Sci. 87, (1991).