Mathematical Sciences: Analysis of Multi-Particle Systems

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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. ***