Mathematical Sciences: Mathematical Physics

数学物理中的一个基本问题是理解原子的基态。这个项目将从三个方面研究这个问题：(1)对于一个特定核电荷的固定原子，将试图了解其基态能量，(2)将研究当核电荷接近无穷大时基态能量的渐近性，以及(3)该项目将试图了解大原子的定性属性，如中性，以及相关的观测值，如电离能。此外，这个项目还将包括关于随机薛定谔算符、诺依曼·拉普拉斯算符、斯科特修正和库仑散射的工作。该项目支持一个由巴里·西蒙博士领导的研究团队。这个项目属于数学物理或理论物理的一般领域，涉及原子粒子的结构和行为。

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.