Rigorous Studies in Quantum Mechanics

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This project has three main goals. The first is to develop new techniques in time-dependent molecular quantum mechanics that are specifically designed to describe proton transfer reactions. These reactions are fundamental to many chemical and biological processes. The second goal is to study Anderson localization phenomena for certain random quantum mechanical models recently developed by physicists. These phenomena are crucial to the understanding of how electrons move in various materials. The third goal is to study the breakup of chemical states that have finite lifetimes. Secondary goals involve the study of electric dipole moments of molecules, bound states of rapidly rotating molecules, and molecules in magnetic fields.The principal investigators, their collaborators, and their graduate students will concentrate on mathematical problems in two areas. One area is chemistry, where the project will develop new techniques for use by computational chemists studying chemical reactions. The second area is the physics of disordered media, where the project will provide further insight for why some materials are conductors while others are insulators.