Mathematical Sciences: RUI: Spectral Properties of Some Random Schrodinger Operators

小行星9401735 这个建议涉及逆谱理论和随机薛定谔算子理论的问题。在逆谱理论部分提出的问题围绕着从本征值集合中恢复薛定谔算子势的某些类型的奇异性。随机薛定谔算子理论中的问题涉及安德森和泊松模型在d维欧氏空间中的局部化。 现代物理学、量子力学和相对论是二十世纪的产物。它是建立在试图解决物质的微观结构，并掌握在一个距离，电磁和热辐射的概念。这些发展的数学基础，统称为数学物理学，范围从薛定谔算子的详细分析，它控制着粒子的动力学，到统一场论，它试图将四种已知的力统一到一个理论中。 本项目主要是对薛定谔算符组成部分的数学物理进行研究。 ***

9401735 Shubin This proposal concerns problems from inverse spectral theory and random Schrodinger operator theory. The problems proposed in the inverse spectral theory section center around recovering certain types of singularities of the potential of a Schrodinger operator from the set of eigenvalues. The problems from random Schrodinger operator theory concern localization in d-dimensional Euclidean space for Anderson and Poisson type models. Modern physics, quantum mechanics and relativity is a product of the twentieth century. It is founded firmly in the attempt to address the microstructure of matter and to come to grips with the concept of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schrodinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory. This project is focused on the Schrodinger operator component of mathematical physics research. ***