This project is to study dispersive estimates for Schroedinger's equation. These estimates are basic to recent developments in the mathematical analysis of Schroedinger's equation and its nonlinear variants. The aim of this project is to obtain minimal regularity and spatial decay conditions on potentials that imply dispersive estimates in each dimension n and to use these results to study related issues including results for nonlinear Schroedinger-type equations.
Schroedinger equations govern the evolution of wave functions in quantum mechanics. Nonlinear analogues are of importance in chemistry and the transmission of information in fiber optic cables. This research will provide mathematical information about the processes involved in quantum mechanics and the applications of quantum physics.
