Spectral and scattering theory of Schroedinger equations

本文用泛函分析、微局域分析、真实的分析和概率论方法研究了Schrodinger方程的谱理论、散射理论和解的结构。研究结果包括：1.薛定谔方程解的微局部奇性，2。流形上薛定谔算子的散射理论，3。电磁场中多粒子散射理论，4.薛定谔方程的半经典分析，5.随机薛定谔方程和电荷输运。这些成果已作为39份出版物发表（包括目前已出版的），还有几个项目仍在进行中。

We have investigated the spectral theory, scattering theory and the structure of solutions for Schrodinger equations, using the functional analysis, microlocal analysis, real analysis and probability theory methods. The research results include results on: 1. Microlocal singularities for solutions of Schrodinger equations, 2. Scattering theory for Schrodinger operators on manifolds, 3. Scattering theory for multi-particles in electric/magnetic fields, 4. Semiclassical analysis for Schrodinger equations, 5. Random Schrodinger equations and charge transport. These results are published as 39 publications (including in press, at present), and several projects are still in progress.