报告人：Peter Gibson Professor York University Dept. of Mathematics & Statistics
报告时间：2024年10月26日 15：00-16：00
报告地点：红瓦楼726室
报告内容简介：The classical one-dimensional Schrôdinger equation comprises one of the most basic and most intensively studied quantum mechanical models. Its variants, obtained by simple transformations, also model acoustic wave propagation in layered media, and provide the building blocks for quantum graphs. Inverse scattering for the Schrôdinger equation relates to quantum mechanical experiments, acoustic imaging, and to the nonlinear KdV equation. Since the middle of the last century, many different approaches to analysis of the Schrôdinger operator have been developed, most of which do not translate easily into computational methods applicable to experimental data. In this talk we present a new approach motivated by applications to acoustic imaging. We use approximation by orthogonal polynomials on the unit circle (OPUC) to derive a new differential equation that is a continuum analogue of the classical three-term recurrence for OPUC. Solutions to this equation provide the basis for an explicit general solution to the 1D Schrôdinger equation in impedance form, and provide a new set of tools with which to analyze inverse scattering, leading to new theoretical results as well as computational methods.
报告邀请人：江渝