A general reduction scheme for the time-dependent Born-Oppenheimer approximation

Comptes Rendus Mathematique

Volumn 334, Issue 3, 2002, Pages 185-188

  Martinez, André ^a   Sordoni, Vania ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038053986     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(02)02212-4     Document Type: Article

References (11)

1. G. Hagedorn, A. Joye, A time-dependent Born-Oppenheimer approximation with exponentially small error estimates, Comm. Math. Phys. 223 (3) (2001) 583-626.
2. M. Klein, A. Martinez, R. Seiler, X.P. Wang, On the Born-Oppenheimer expansion for polyatomic molecules, Comm. Math. Phys. 143 (3) (1992) 607-639.
3. A. Martinez, An Introduction to Semiclassical Analysis, UTX Series, Springer-Verlag, New-York, 2002 (to appear).
4. A. Martinez, V. Sordoni, On the time-dependent Born-Oppenheimer approximation with smooth potentials, Preprint, Bologna, 2001 and Texas mp-arc n. 01-37, 2001.
5. A. Melin, J. Sjöstrand, Fourier integral operators with complex phase functions and parametrix for an interior boundary value problem, Comm. Partial Differential Equations 1 (1976) 313-400.
6. G. Nenciu, V. Sordoni, Semiclassical limit for multistate Klein-Gordon systems: almost invariant subspaces and scattering theory, Preprint, Bologna, 2001 and Texas mp-arc n. 01-36, 2001.
7. D. Robert, Autour de l'approximation semi-classique, Birkhäuser, 1987.
8. D. Robert, Remarks on asymptotic solutions for time dependent Schrödinger equations, Preprint, Nantes, 2000.
9. J. Sjöstrand, Singularités analytiques microlocales, Astérisque 95 (1982).
10. V. Sordoni, Reduction scheme for semiclassical operator-valued Schrödinger type equation and application to scattering, Preprint, Bologna, 2001 and Texas mp-arc n. 01-272, 2001.
11. H. Spohn, S. Teufel, Adiabatic decoupling and time-dependent Born-Oppenheimer theory, Comm. Math. Phys. 224 (1) (2001) 113-132.