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

9401735舒宾这一建议涉及逆谱理论和随机薛定谔算子理论中的问题。在逆谱理论一节中提出的问题集中在从本征值集合中恢复薛定谔算子势的某些类型的奇点。随机薛定谔算子理论中的问题涉及Anderson和Poisson型模型在d维欧氏空间中的局部化问题。现代物理学、量子力学和相对论是二十世纪的产物。它坚定地建立在试图解决物质的微观结构和掌握远距离作用力、电磁学和热辐射的概念上。这些发展的数学基础统称为数学物理，从控制粒子动力学的薛定谔算符的详细分析，到试图将四种已知力统一为单一理论的统一场论。本项目致力于数学物理研究中的薛定谔算符部分。***

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. ***