Mathematical Sciences: Analysis of Multi-Particle Systems

[408903] Ruskai将研究多粒子系统数学分析中的几个问题。主要的重点是原子和分子哈密顿量的束缚态，包括那些在磁场中的系统。径向小波在库仑奇点多尺度分析中的应用也将被考虑。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。它牢固地建立在上个世纪对物质微观结构的研究和对超距作用、电磁和热辐射等概念的理解上。这些发展的数学基础统称为数学物理学，范围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. ***