Mathematical Studies in Quantum Mechanics

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This award will support several projects that involve the mathematics of quantum mechanics. One main goal is the development of computer algorithms for studying the quantum mechanical motion of nuclei in molecules. Another main goal is to study adiabatic theory for weakly coupled quantum mechanical systems beyond the lifetime of a resonance. Other goals involve the break-up of certain unstable molecules and the study of molecular resonance states. Graduate students involved in the project will be trained in adiabatic quantum computing, quantum mechanics in random potentials, and many body scattering phenomena.The principal investigators, their collaborators, and their graduate students will use support from this award to study mathematical problems in quantum mechanics. One project will involve how to use computers efficiently when computing the quantum mechanical motion of the nuclei in reacting molecules. Other projects will study various theoretical aspects of quantum computing. In addition, unstable molecules and other systems with finite lifetimes will be studied. Graduate students will receive training involving these and other aspects of quantum theory.