Mathematical Analysis of Quantum Physics

研究了描述量子粒子动力学的基本方程薛定谔方程的数学问题，得到了以下结果：(1)初值问题的基本解在无穷远处的行为得到了新的结果；(2)找到了研究解奇点传播的新方法；(3)解决了未解决的散射波算符问题；(4)发现了随机薛定谔算子的新的谱性质。

We studied mathematical problems on Schroedinger equations which are fundamental equation for describing the dynamics of quantum particles and obtained following results : (1) New results are obtained on the behavior at infinity of the fundamental solutions of the initial value problems ; (2) new methods for studying the propagation of singularities of solutions are found ; (3) unsolved problems on wave operators of scattering have been solved ; (4) new spectral properties of random Schroedinger operators are found.