Sur l'approximation de Born-Oppenheimer des opérateurs d'onde

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1. [Ag] S. Agmon: Lectures on exponential decay of solutions of second-order elliptic equations, Princeton University Press1982 Zbl0503.35001MR745286
2. [AS] P. Aventini, R. Seiler: On the electronic spectrum of the diatomic molecule, Comm. Math. Phys.22, 269-279 (1971) 
3. [BK] A. Balazard-Konlein: Calcul fonctionel pour des opérateurs h-admissibles à symbole opérateurs et applications, Thèse 3ème cycle, Université de Nantes (1985) 
4. [BoOp] M. Born, R. Oppenheimer: Zur Quantentheorie der Molekeln, Ann. Physik84, 457 (1927) JFM53.0845.04
5. [CDS] J.M. Combes, P. Duclos, R. Seiler: The Born-Oppenheimer approximation, Rigorous Atomic and Molecular Physics, A.S.Wightman and A.Velo eds, New York: Plenum1981 
6. [Ch] M.S. Child: Semiclassical methods in molecular scattering and spectroscopy, Proc. of NATO conf., D.Reidel (1980) 
7. [CS] J.M. Combes, R. Seiler: Regularity and asymptotic properties of the discrete spectrum of electronic Hamiltonians, Int. J. Quant. Chem.XIV, 213-229 (1978) 
8. [Da] JF. Daumer: Equation de Schrödinger avec champ électrique périodique et champ magnétique constant dans l'approximation du tight-binding, Comm. Part. Diff. Eq.18 (5-6), 1021-1041 (1993) Zbl0784.35093MR1218527
9. [De] J.B. Delos: Theory of electronic transitions in slow atomic collisions, Rev. Mod. Phys.53, 287-358 (1981) 
10. [HeRo] B. Helffer, D. Robert: Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles, J. Funct. An.53 (3), 246-268 (1983) Zbl0524.35103MR724029
11. [Ha] G.A. Hagedorn: High order corrections to the time-independent Born-Oppenheimer approximation, Ann. Inst. H. Poincaré47, 1-16 (1987) Zbl0621.41012MR912753
12. [Ka] T. Kato: Perturbation theory for linear operators, Springer1976 Zbl0148.12601MR407617
13. [KMSW] M. Klein, A. Martinez, R. Seiler, X.P. Wang: On the Born-Oppenheimer expansion for polyatomic molecules, Comm. Math. Phys.143, 606-639 (1992) Zbl0754.35099MR1145603
14. [KMW1] M. Klein, A. Martinez, X.P. Wang: On the Born-Oppenheimer approximation of wave operators in molecular scattering theory, Comm. Math. Phys.152, 73-95 (1993) Zbl0778.35088MR1207670
15. [KMW2] M. Klein, A. Martinez, X.P. Wang: On the Born-Oppenheimer approximation of wave operators II : singular potentials, en préparation 
16. [Ma] A. Martinez: Développements asymptotiques et effet tunnel dans l'approximation de Born-Oppenheimer, Ann. Inst. H. Poincaré49, 239-257 (1989) Zbl0689.35063MR1017965
17. [MaGe] A. Martinez, C. Gérard: Principe d'absorption limite pour des opérateurs de Schrödinger à longue portée, C. R. Acad. Sci. Paris906, I, 121-123 (1988) Zbl0672.35013MR929103
18. [Mo] E. Mourre: Absence of singular continuous spectrum for certain self-adjoint operators, Comm. Math. Phys.78, 391-408 (1981) Zbl0489.47010MR603501
19. [Ra] A. Raphaelian: Ion-atom scattering within a Born-Oppenheimer framework, Dissertation T.U.Berlin (1986) 
20. [S] R. Seiler: Does the Born-Oppenheimer approximation work ?, Helv. Phys. Acta46, 230-234 (1973) 
21. [WuOh] T.Y. Wu, T. Ohmura: Quantum theory of scattering, Prentice-Hall1962 Zbl0118.44005MR142315