Classical limit of elastic scattering operator of a diatomic molecule in the Born-Oppenheimer approximation
Jecko, Th.
Annales de l'I.H.P. Physique théorique, Tome 69 (1998), p. 83-131 / Harvested from Numdam
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@article{AIHPA_1998__69_1_83_0,
     author = {Jecko, Th.},
     title = {Classical limit of elastic scattering operator of a diatomic molecule in the Born-Oppenheimer approximation},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {69},
     year = {1998},
     pages = {83-131},
     mrnumber = {1635815},
     zbl = {1004.81511},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1998__69_1_83_0}
}

Jecko, Th. Classical limit of elastic scattering operator of a diatomic molecule in the Born-Oppenheimer approximation. Annales de l'I.H.P. Physique théorique, Tome 69 (1998) pp. 83-131. http://gdmltest.u-ga.fr/item/AIHPA_1998__69_1_83_0/

[A] S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations. Princeton University Press, 1982. | MR 745286 | Zbl 0503.35001

[Ba] A. Balazard-Konlein, Calcul fonctionnel pour des opérateurs h-admissibles à symbole opérateur et applications. Thèse de troisième cycle, université de Nantes, 1985.

[Bo] M. Born and R. Oppenheimer, Zur Quantentheorie der Molekeln. Annalen der Physik, Vol. 84, 1927, p. 457. | JFM 53.0845.04

[HR] B. Helffer and D. Robert, Calcul fonctionnel par la transformation de Melin et opérateurs admissibles, J. Funct. Anal., Vol. 53, 1983, pp. 246-268. | MR 724029 | Zbl 0524.35103

[HS] B. Helffer, J. Sjostrand, Opérateurs de Schrödinger avec champs magnétiques faibles et constants. Exposé No. XII, Séminaire EDP, février 1989, École Polytechnique. | Numdam | MR 1032288 | Zbl 0702.35185

[IK] H. Isozaki and H. Kitada, Modified wave operatprs with time-dependent modifiers, J. Fac. Sci. Univ. Tokyo, Vol. 32, 1985, pp. 77-104. | MR 783182 | Zbl 0582.35036

[J] Th. Jecko, Sections efficaces totales d'une molécule diatomique dans l'approximation de Born-Oppenheimer. Thèse de doctorat, Université de Nantes, 1996.

[KMSW] M. Klein, A. Martinez, R. Seiler and X.P. Wang, On the Born-Oppenheimer Expansion for Polyatomic Molecules. Commun. Math. Phys., Vol. 143, 1992, pp. 606-639. | MR 1145603 | Zbl 0754.35099

[KMW1] M. Klein, A. Martinez and X.P. Wang, On the Born-Oppenheimer Approximation of Wave Operators in Molecular Scattering Theory. Commun. Math. Phys., Vol. 152, 1993, pp. 73-95. | MR 1207670 | Zbl 0778.35088

[KMW2] M. Klein, A. Martinez, X.P. Wang, On the Born-Oppenheimer Approximation of Wave Operators II: Singular Potentials, preprint.

[RS3] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Tome III: Scattering Theory. Academic Press 1979. | MR 529429 | Zbl 0405.47007

[RS4] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Tome IV: Analysis of Operators. Academic Press. | Zbl 0401.47001

[Ro] D. Robert, Autour de l'approximation semi-classique, Birkhäuser 1987. | MR 897108 | Zbl 0621.35001

[RT] D. Robert and H. Tamura, Semiclassical estimates for resolvents and asymptotics for total cross-section, Ann. IHP Vol. 46, 1987, pp. 415-442. | Numdam | MR 912158 | Zbl 0648.35066

[SS] 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. | MR 898052 | Zbl 0646.47009

[WI] X.P. Wang, Time-Decay of Scattering Solutions and resolvent Estimates for Semi-classical Schrödinger Operators. J. Diff. Eq., Vol. 71, 1988, pp. 348-396. | Zbl 0651.35022

[W2] X.P. Wang, Time-Decay of Scattering Solutions and Classical Trajectories. Ann. IHP, Vol. 47, 1987, pp. 25-37. | Numdam | MR 912755 | Zbl 0641.35018

[W3] X.P. Wang, Time-Decay Operators in the Semiclassical Limit II, Short Range Potentials. Trans. AMS, Vol. 322, 1990. | MR 987170 | Zbl 0714.35064

[W4] X.P. Wang, Approximation semi-classique de l'équation d'Heisenberg. Commun. in Math. Phys., Vol.104, 1986, pp.77-86. | MR 834482 | Zbl 0611.35085

[Y] K. Yajima, The quasi-classical limit of quantum scattering theory. Comm. in Math. Phys., Vol. 69, 1979, pp. 101-129. | Zbl 0425.35076