Mathematical Sciences: Analysis of Multi-Particle Systems

数学科学：多粒子系统分析

• 批准号: 9408903
• 负责人: Mary Beth Ruskai
• 金额: $ 4万
• 依托单位: University of Massachusetts Lowell
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9408903&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analysis; Multi; Particle

9408903 Ruskai Several problems in the mathematical analysis of multi-particle systems will be studied. The main emphasis is on bound states of atomic and molecular Hamiltonians, including those for systems in magnetic fields. The use of radial wavelets for multi-scale analysis of the Coulumb singularity will also be considered. Finally, some related problems in operatorinequalities are proposed. Modern physics, quantum mechanics and relativity, is aproduct of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from the detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory. ***

小行星9408903 研究了多质点系数学分析中的几个问题。主要重点是原子和分子的束缚态的哈密顿量，包括那些系统在磁场中。使用径向小波的库仑奇异性的多尺度分析也将被考虑。最后，提出了算子不等式中的一些相关问题。 现代物理学，量子力学和相对论，是二十世纪的产物。它是建立在上个世纪试图解决物质的微观结构，并开始掌握在一个距离，电磁和热辐射的概念。这些发展的数学基础，统称为数学物理学，范围从薛定谔算子的详细分析，它支配着粒子的动力学，到统一场论，它试图将四种已知的力统一到一个理论中。 ***