The Schrodinger Equation and Beyond
计算数学报告
报告题目(Title)：The Schrodinger Equation and Beyond
报告人(Speaker)：Weizhu Bao（National University of Singapore）
地点(Place)：后主楼1129
时间(Time)：2019年12月5日 10:00-11:00
邀请人(Inviter)：蔡勇勇
报告摘要
In this talk, I will begin with the Schrodinger equation -- the most fundamental equation in quantum mechanics -- for modeling problems with quantum effects, such as wave-particle duality. An eigenvalue problem arising from the Schrodinger operator will be solved under different external potentials and stationary states of the Schrodinger equation will be provided. The fundamental gap conjecture related to the Schrodinger operator will be reviewed. New fundamental gap conjectures of the fractional Schrodinger operator and the nonlinear Schrodinger equation (NLSE) will be formulated. Mathematical theories and numerical methods for the ground states and dynamics of the NLSE will be reviewed. Some typical applications of the NLSE in Bose-Einstein condensation, nonlinear optics, quantum fluids, quantum physics and chemistry, material simulation and design will be discussed.
