Mathematical Sciences: Analysis of Multi-Particle Systems

9408903 Ruskai将研究多粒子系统数学分析中的几个问题。主要侧重于原子和分子哈密顿量的束缚态，包括磁场中系统的束缚态。还将考虑使用径向小波对库仑奇点进行多尺度分析。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。它是在上个世纪试图解决物质的微观结构并掌握远距离作用力、电磁学和热辐射等概念的过程中建立起来的。这些发展的数学基础统称为数学物理，从控制粒子动力学的薛定谔算符的详细分析，到试图将四种已知力统一为单一理论的统一场论。***

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. ***