Mathematical Sciences: Mathematical Studies in Quantum Mechanics

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The primary goal of this research will be to study molecular systems. Earlier work which used the Born-Oppenheimer approximation to study electron energy level crossings, (infinite time) scattering problems, and problems that involve oscillating external electric fields will be extended. Numerical calculations will be used to test the usefulness of high order Born-Oppenheimer expansions on realistic systems. Also studied will be a particular family of one-dimensional Schrodinger operators. This research should have impact on the study of quasicrystals.