Problems in Mathematical Physics

数学物理问题

• 批准号: 0140592
• 负责人: Barry Simon
• 金额: $ 45万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0140592&HistoricalAwards=false
• 关键词: Problems; Mathematical; Physics

PI: Barry Simon, California Institute of TechnologyDMS-0140592AbstractProfessor Simon will continue his research focusing on direct and inversespectral problems for Schrodinger operators and their discrete analogs. Heplans to explore the impact of sum rules for spectral theory both for Jacobimatrices (where he and Killip recently solved several long open conjecturesfrom the Orthogonal Polynomial community using sum rules) and Schrodingeroperators. Other problems he expects to look at include the structure ofthe isospectral manifold for problems with discrete spectrum, resonancecounting in higher dimensions, and the study of mixed singular continuousand point spectrum.A fundamental problem in wide swaths of science is determining the relationbetween some object that can only be observed indirectly and the informationyou can observe indirectly. There are two sides of issue: determine whatis indirectly observed for a given state of the system, called the directproblem, and trying to induce properties of the system from the indirectobservations, called the inverse problem. Professor Simon will studyvarious aspects of direct and inverse problems in quantum mechanics. Whilethe focus will be on the equations of quantum theory, there are potentialspinoffs to tomography and radar/sonar direct and inverse problems.

PI：加利福尼亚州理工学院DMS-0140592AbtractProfessor Simon的Barry Simon将继续他的研究，重点关注Schrodinger操作员及其离散类似物的直接和偏置问题。 Heplans探讨了jacobimatrices的光谱理论的总和规则的影响（他和Killip最近使用总和规则从正交多项式群落解决了几个长期的猜想）和Schrodingeroperator。 他期望研究的其他问题包括离散频谱问题，更高维度的重置问题以及对混合奇异连续和点频谱的研究的结构。广泛的科学中的一个基本问题是确定只能独立观察和信息可以观察到的一些对象之间的关系。 问题有两个方面：确定对系统状态（称为直接问题）的间接观察到的内容，并试图从indirectobservations中诱导系统的属性，称为逆问题。 西蒙教授将研究量子力学中直接和反向问题的方面。 尽管重点将放在量子理论的方程式上，但对层析成像以及雷达/声纳直接和反面问题有潜在的启动。