Analysis of Multi-Particle Hamiltonians (Modern Analysis): VPW

研究人员将继续研究多粒子 哈密顿量，重点是那些原子和分子 系统. 她将考虑与 能量差的单调性和 结合态的数量与参数，如核 消费标准. 此外，她将尝试使用小波的想法， 理论来构造一组正交函数， 能量是有界的半经典泛函的 单粒子密度 本项目的工作具有一定的实用性 重要性，因为它提供了数学基础， 理论原子和分子物理学，有些是相关的 原子和分子系统的实际计算。 的 项目进一步VPW计划的目标，以提供 妇女在科学领域发展事业的机会， 通过研究工程，并鼓励其他妇女， 通过调查人员在这些领域的职业生涯， 提高了作为东道校园榜样的知名度。 在 这一项目，拟议的活动，有助于 第二个目标包括：教授一门高级课程， 参加数学物理研讨会， 在其他旨在鼓励女学生参加的活动中， 密歇根州追求职业生涯中的数学科学。

The investigator will continue her study of multi-particle Hamiltonian, with emphasis on those for atomic and molecular systems. She will consider problems related to the monotonicity of energy differences and the variation in the number of bound states with parameters such as the nuclear charge. In addition, she will try to use ideas from wavelet theory to construct a set of orthogonal functions whose kinetic energy is bounded above by a semi-classical functional of the one-particle density. The work in this project is of considerable practical importance since it provides the mathematical foundation for theoretical atomic and molecular physics, and some is relevant to practical computations on atomic and molecular systems. The project furthers VPW program objectives to provide opportunities for women to advance their careers in science or engineering through research, and to encourage other women to pursue careers in these areas through the investigators' enhanced visibility as role models on the host campuses. In this project, the proposed activities which contribute to the second objective include: teaching an upper division course, participating in the mathematical physics seminar, and engaging in other activities intended to encourage women students at Michigan to pursue careers in the mathematical sciences.