Mathematical Sciences: Singular Perturbations, Oscillatory Integrals, and Point Interactions

数学科学：奇异扰动、振荡积分和点相互作用

• 批准号: 9002523
• 负责人: Rhonda Hughes
• 金额: $ 4.52万
• 依托单位: Bryn Mawr College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002523&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singular; Perturbations; Oscillatory

Professor Hughes will apply work of Ricci and Stein on oscillatory integrals to singular perturbation problems arising in quantum mechanics. In addition Hughes will consider the solution of the time dependent Schroedinger equation with singular time dependent interactions. A unifying theme will be the use of the interaction representation for solutions of the Schroedinger equation. This work involves the mathematics of quantum mechanics. Professor Hughes will apply new mathematical techniques to understand the behavior of interacting quantum mechanical particles.

Hughes教授将把Ricci和Stein关于振荡积分的工作应用于量子力学中出现的奇异摄动问题。此外，休斯将考虑具有奇异时变相互作用的时变薛定谔方程的解。一个统一的主题将是对薛定谔方程解的相互作用表示的使用。这项工作涉及到量子力学的数学。休斯教授将运用新的数学技术来理解相互作用的量子力学粒子的行为。