Distinguished Colloquium——The Schrodinger Equation and Beyond
2019-05-31 15:00-16:00 Room 1114, Sciences Building No. 1
Abstract: 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 simulationa and design will be discussed.