During the last century, an equation that has sparked interest among mathematicians is the nonlinear Schrödinger Equation, due to its applications in nonlinear optics and in quantum field theory. The aim of this work is to present ome basic concepts of the study of a variant of this particular equation (the Nonautonomous Schrödinger Equation) in one dimension as well as introduce some results of scattering theory. To achieve this we divide this work in three stages: in the first section, we analyse the linear equation and the local well-posedness of the nonautonomous variant; in the second section, we provide a proof of the existence of scattering states of the global solution; and, in the third section, we present some stronger results regarding the existence of scattering using the Pseudo-Conformal Transformation

Orientador: Simão Correia