Mathematical Sciences: Mathematical Physics

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One of the fundamental problems in mathematical physics is that of understanding the ground-state of atoms. This project will examine this problem in three areas: (1) For a fixed atom of specific nuclear charge, an attempt will be made to understand its ground state energy, (2) There will be a study of the asymptotics of the ground state energy as the nuclear charge approaches infinity, and (3) The project will try to understand qualitative properties of large atoms such as neutrality, together with related observables, such as ionization energies. In addition, this project will include work on random Schrodinger operators, Neumann Laplacians, Scott Correction, and Coulomb scattering. This project supports a research team under the direction of Dr. Barry Simon. This project is in the general area of mathematical physics or theoretical physics and concerns the structure and behavior of atomic particles.