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

多粒子哈密顿量分析（现代分析）：VPW

• 批准号: 9103315
• 负责人: Mary Beth Ruskai
• 金额: $ 13.67万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1993-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103315&HistoricalAwards=false
• 关键词: Analysis; Multi; Particle; Hamiltonians; Modern

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.

研究人员将继续她对多粒子哈密顿量的研究，重点是原子和分子系统的研究。 她将考虑与能量差的单调性以及束缚态数量随核电荷等参数的变化相关的问题。 此外，她将尝试利用小波理论的思想来构造一组正交函数，其动能以上由单粒子密度的半经典函数为界。 该项目的工作具有相当大的实际意义，因为它为理论原子和分子物理提供了数学基础，并且有些与原子和分子系统的实际计算相关。 该项目进一步推进了 VPW 计划的目标，即为女性提供通过研究促进其在科学或工程领域职业发展的机会，并通过提高研究人员作为所在校园榜样的知名度来鼓励其他女性在这些领域追求职业生涯。 在该项目中，拟议的有助于实现第二个目标的活动包括：教授高级课程、参加数学物理研讨会以及参与旨在鼓励密歇根女学生从事数学科学职业的其他活动。