Dispersive Estimates for the Schrodinger Equation

本课题研究薛定谔方程的色散估计。这些估计是薛定谔方程及其非线性变种数学分析的最新发展的基础。这个项目的目的是得到势的最小正则性和空间衰减性条件，并且利用这些结果来研究相关问题，包括非线性薛定谔方程的结果。薛定谔方程支配着量子力学中波函数的演化。非线性类似物在化学和光缆中的信息传输中具有重要意义。这项研究将提供有关量子力学过程和量子物理应用的数学信息。

This project is to study dispersive estimates for Schroedinger's equation. These estimates are basic to recent developments in the mathematical analysis of Schroedinger's equation and its nonlinear variants. The aim of this project is to obtain minimal regularity and spatial decay conditions on potentials that imply dispersive estimates in each dimension n and to use these results to study related issues including results for nonlinear Schroedinger-type equations. Schroedinger equations govern the evolution of wave functions in quantum mechanics. Nonlinear analogues are of importance in chemistry and the transmission of information in fiber optic cables. This research will provide mathematical information about the processes involved in quantum mechanics and the applications of quantum physics.