Rigorous Studies in Quantum Mechanics

9703751哈格多恩这个项目专注于量子力学中的几个数学问题，这些问题对化学和物理都很感兴趣。其主要目标是研究“表面跳跃模型”，努力发展有用的改进近似来计算化学动力学中的非绝热现象。第二个目标是研究振荡电磁场对分子的影响。第三个目标是分析高阶独立于时间的Born-Oppenheimer近似的实用性，并改进这些近似，以获得具有大的振动和转动量子数的分子态的准确结果。最后一个目标是研究多体散射的碰撞参数近似，并研究“电荷转移”散射幅度的高能行为。这个跨学科项目的主要目标是得出新的、更准确的近似，供化学家和物理学家在实际情况中使用。描述化学反应中分子运动的方程不能精确求解，因此化学家和物理学家必须依靠近似解。可以想象，改进的近似可以导致在新化合物的合成、新催化剂的设计或合理药物设计的理论基础等领域的应用。

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.