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

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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.