Mathematical Sciences: Spectral Properties of a Random Schrodinger Operator

这项研究计划拨款支持 Christ 教授的研究，以研究实数上具有随机势的 Stark-Hamiltonian。她将特别研究斯塔克-哈密尔顿的频谱及其共振。 现代物理学、量子力学和相对论，是二十世纪的产物。 它牢固地建立在上个世纪解决物质微观结构并掌握远距离作用、电磁和热辐射概念的尝试中。 这些发展的数学基础统称为数学物理，范围从控制粒子动力学的薛定谔算子的详细分析，到试图将四种已知力统一为一个理论的统一场论。

This research planning grant supports the research of Professor Christ to study the Stark-Hamiltonian with random potentials over the real numbers. In particular she will study the spectrum of the Stark-Hamiltonian and their resonances. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts 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.