Deriving Effective PDEs from Many-Body Schrödinger Equations

In this talk, we derive nonlinear Schrödinger equations and the Hartree equation as effective descriptions of the linear many-body Schrödinger equation. Starting with an introduction to the motivation and the mathematical framework, we will explore the Fock space formalism and the coherent state method as tools for deriving these effective equations. The aim is to provide insight into how these techniques capture the dynamics of quantum systems and to discuss the role of dispersive estimates in the derivations.