Rigorous Studies in Quantum Mechanics

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。这个项目有三个主要目标。首先是开发时间相关分子量子力学的新技术，专门用于描述质子转移反应。这些反应是许多化学和生物过程的基础。第二个目标是研究物理学家最近发展的某些随机量子力学模型的安德森局域化现象。这些现象对于理解电子如何在各种材料中运动至关重要。第三个目标是研究寿命有限的化学状态的分解。次要目标包括研究分子的电偶极矩、快速旋转分子的束缚态和磁场中的分子。主要研究人员、他们的合作者和他们的研究生将集中研究两个领域的数学问题。其中一个领域是化学，该项目将开发用于计算化学家研究化学反应的新技术。第二个领域是无序介质的物理学，该项目将进一步深入了解为什么有些材料是导体，而另一些材料是绝缘体。

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.