Eigenfunction asymptotics on Riemannian manifolds

黎曼流形上的本征函数渐近

• 批准号: 170280-2010
• 负责人: Toth, John
• 金额: $ 2.19万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=545819
• 关键词: Eigenfunction; asymptotics; Riemannian; manifolds

The Bohr correspondence principle in quantum mechanics asserts that quantum mechanical systems "approach" the associated classical dynamical systems in the semiclassical (ie. high-energy) limit. Over the past decade, there has been a great deal of interest amongst mathematicians, physicists and quantum chemists in quantifying this correspondence in a mathematically precise way. My research proposal is largely devoted to studying this important and fundamental issue using the methods of semiclassical microlocal analysis, where the main problem is to understand the precise concentration properties of the eigenfunctions (ie. wave

量子力学中的玻尔对应原理断言量子力学系统在半经典（即量子力学）中“接近”相关的经典动力学系统。高能量）限制。在过去的十年里，数学家、物理学家和量子化学家对以数学精确的方式量化这种对应关系产生了极大的兴趣。我的研究计划主要致力于使用半经典微局部分析方法来研究这个重要而基本的问题，其中主要问题是了解本征函数（即本征函数）的精确浓度特性。波