Abstract
Making use of an adiabatic operator that takes several electronic states into account, we derive a Born–Oppenheimer approximation of the resolvent for a diatomic molecule. This is an improvement of a result in [KMW1]. Such a resolvent approximation is useful to obtain an adiabatic approximation of total cross-sections (see [Jec2]). The strategy we use, based on Mourre's commutator method and on a new kind of global escape function, may be carried over to control the resolvent of some matricial Schrodinger operators. In the same way, we obtain a semiclassical estimate for the resolvent of the semiclassical Dirac operator with scalar electric potential, extending a result of [Ce].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
