Propagation of singularities for the Schrodinger equation

薛定谔方程奇点的传播。随时间变化的薛定谔方程支配着量子粒子的演化。在这个项目中，我们的目标是利用数学散射理论的新技术来分析薛定谔方程的解，并获得它们的奇点上的锐界。控制这样的奇点将使我们能够在某些情况下推导出特征值数目的定量界限，并为研究非线性薛定谔方程提供新的技术。

Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Schrodinger equations.