Mathematical Sciences: Rigorous Studies in Quantum Mechanics

本研究将应用渐近近似技术 在分子系统动力学的研究中， 玻恩-奥本海默极限 特别是，校长 研究人员将考虑散射问题， 电子能级交叉、避免交叉及其影响 振荡电磁场 这将是完成 使用分析和数值方法。 大多数分子由复杂的电子系统组成 其行为决定了宏观（或整体）性质， 材料. 尤其重要的是， 这些电子系统的模型，因为了解 电子的行为使我们能够理解 例如，材料的导电性。 在这项提案中， 主要研究者将使用分析和数值方法 来研究电子从一个能级穿越时的行为 到另

This research will apply asymptotic approximation techniques in the study of the dynamics of molecular systems in the so- called Born-Oppenheimer limit. In particular, the principal investigator will consider scattering problems, the effects of electron energy level crossing, avoided crossings and the effects of oscillating electromagnetic fields. This will be accomplished using analytical and numerical methods. Most molecules consist of complicated systems of electrons whose behavior determines the macroscopic (or bulk) properties of materials. It is especially important to have mathematical models of these electron systems, since understanding the behavior of the electrons enables us to understand the conductivity of a material, for example. In this proposal the principal investigator will use analytical and numerical methods to study how electrons behave in crossing from one energy level to another.