Mathematical Sciences: Spectral Properties of a Random Schrodinger Operator

数学科学：随机薛定谔算子的谱性质

• 批准号: 9210806
• 负责人: Carol Christ
• 金额: $ 1.8万
• 依托单位: The University Corporation, Northridge
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9210806&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Spectral; Properties; Random

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.

本研究计划资助资助克里斯特教授对实数随机势的斯塔克-哈密顿量的研究。她将特别研究斯塔克-哈密顿谱及其共振。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对物质微观结构的研究和对超距作用、电磁和热辐射等概念的理解上。这些发展的数学基础，统称为数学物理学，范围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。