Mathematical Sciences: Rigorous Studies in Quantum Mechanics

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This research will apply asymptotic approximation techniques in the study of the dynamics of molecular systems in the so- called Born-Oppenheimer limit. In particular, the principal investigator will consider scattering problems, the effects of electron energy level crossing, avoided crossings and the effects of oscillating electromagnetic fields. This will be accomplished using analytical and numerical methods. Most molecules consist of complicated systems of electrons whose behavior determines the macroscopic (or bulk) properties of materials. It is especially important to have mathematical models of these electron systems, since understanding the behavior of the electrons enables us to understand the conductivity of a material, for example. In this proposal the principal investigator will use analytical and numerical methods to study how electrons behave in crossing from one energy level to another.