Rigorous Studies in Quantum Mechanics

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9703751 Hagedorn This project concentrates on several mathematical problems in quantum mechanics that are of interest in chemistry and physics. The main goal is to study "surface hopping models" in an effort to develop useful improved approximations for the computation of non-adiabatic phenomena in chemical dynamics. A second goal is to study the effect of oscillating electromagnetic fields on molecules. A third goal is to analyze the utility of high order time-independent Born-Oppenheimer approximations and to improve those approximations to obtain accurate results for molecular states with large vibrational and rotational quantum numbers. A final goal is to study the impact parameter approximation for many body scattering and to examine the high energy behavior of "charge transfer" scattering amplitudes. The principal goal of this interdisciplinary project is to derive new, more accurate approximations that can be used in practical situations by chemists and physicists. The equations that describe the motions of molecules in chemical reactions cannot be solved exactly, so chemists and physicists must rely on approximate solutions. Improved approximations could conceivably lead to applications in areas as diverse as the synthesis of new chemical compounds, the design of new catalysts, or the theoretical underpinnings of rational drug design.