This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{ 1,\infty}(\bar{ \mathbb{ R}^3_{ -}},\R^3)$ and $q \in L^{ \infty}(\bar{ \mathbb{ R}^3_{ -}},\C)$. We prove that $q$ and the curl of $A$ are uniquely determined by the knowledge of the Dirichlet-to-Neumann map on parts of the boundary of the half space. The existence and uniqueness of the corresponding direct problem are also considered.
Categories: math.AP math-ph math.MP