| Scattering problem is one of the most fundamental problems in physics, spanning almost all areas of physics. In this dissertation, we focus on scattering theory in two types of systems: two dimensional electron scattering in the presence of a random potential and light scattering by metallic nanoparticles.;The first scattering problem we study is electron branched flow. In this system, electrons are confined to move in two dimensions while a smoothly changing weak random potential deflects their trajectories, resulting in the so-called branched flow. A semiclassical theory based on ray tracing was developed to explain all the observed features of branched flow. However, this semiclassical theory was challenged by the result of a more recent experiment, which claims to have uncovered "unexpected features of branched flow". We show how these features can actually be explained by the semiclassical theory.;Besides electron scattering, we also investigate light scattering by metallic nanoparticles. In this case, we study the multiple scattering effect in the plasmon dimer system and show that one can use these metallic nanoparticles to put the incoming electromagnetic fields into different shapes by solving an inverse scattering problem. |
