Strong Magnetic Field Limits in Linear and Nonlinear Schrodinger Equations

In this thesis we study the dynamics of linear and nonlinear magnetic Schrodinger equations in the strong field limit. First, we derive an approximate equation for a nonlinear Iwatsuka-type model in two dimensions. This relies on high frequency averaging techniques and robust estimates within scaled Sobolev spaces. Second, we compute an approximate solution to the linear Schrodinger equation in three dimensions in the presence of axisymmetric magnetic fields. This is achieved via analytic and singular perturbation theory applied to a family of fibered Hamiltonians. In both cases we demonstrate that the effective dynamics in the strong magnetic field limit result in similar behavior to what is observed in the corresponding classical dynamics.