Mathematical Sciences: The Schrodinger Equation

数学科学：薛定谔方程

• 批准号: 9307147
• 负责人: Ira Herbst
• 金额: $ 7.68万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307147&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Schrodinger; Equation

Herbst will conduct research in the area of partial differential equations in quantum mechanics. The problems to be considered concern scattering theory and the asymptotic behavior of solutions to the Schrodinger equation which describe bound particles. The former work will involve eigenfunction expansions diagonalizing N-particle Hamiltonians and the investigation of the scattering theory of homogeneous potentials of degree zero. 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 Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.

赫布斯特将在局部区域进行研究， 量子力学中的微分方程 存在的问题 考虑关注散射理论和渐进行为 薛定谔方程的解， 粒子 前一项工作将涉及本征函数展开 对角化N粒子哈密顿量和研究 零度均匀势的散射理论。 现代物理学，量子力学和相对论，是一个 二十世纪的产物。 它牢固地建立在 上世纪人们试图研究物质的微观结构 并掌握远距离行动的概念， 电磁和热辐射。 数学 这些发展的基础，统称为 数学物理，范围从详细分析 薛定谔算子，控制着粒子的动力学， 到统一场论，它试图统一四个已知的场论 形成一个单一的理论。