Classical and semi-classical analysis of magnetic fields in two dimensions

My talk is combined by two parts: Classical mechanics and semi-classical analysis, especially in the presence of magnetic field. In classical mechanics, I used Hamiltonian dynamics to describe the movement of a charged particle in a domain affected by magnetic field. I worked on two classical physical problems: the confinement and the scattering problem. In the semi-classical case, I will talk about the magnetic Laplacian. Under some assumption on the magnetic field, I investigated the eigenvalues and eigenfunctions of the magnetic Laplacian in semiclassical limit through the view of the WKB method.