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On the Born-Oppenheimer approximation of wave operators in molecular scattering theory |
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| Authors: | M Klein A Martinez X P Wang |
| Institution: | (1) Department of Physics, Technion, 3200 Haifa, Israel;(2) Departement de Mathématiques et d'Informatique, Université de Paris-Nord, Avenue Jean-Baptiste Clément, F-93430 Villetaneuse, France;(3) Departement de Mathématiques, Université de Nantes, F-44072 Nantes Cedex 03, France;(4) Present address: Fachbereich Mathematik MA 7-2, Technische Universität Berlin, 1000 Berlin 12, FRG;(5) Present address: Departement of Mathematics, Peking University, 100871 Beijing, China |
| Abstract: | In this paper we study the diatomic molecular scattering by reducing the number of particles through Born-Oppenheimer approximation. Under a non-trapping assumption on the effective potential of the molecular Hamiltonian we use semiclassical resolvent estimates to show that non-adiabatic corrections to the adiabatic (or Born-Oppenheimer) wave operators are small. Furthermore we study the classical limit of the adiabatic wave operators by computing its action on quantum observables microlocalized by use of coherent states. |
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