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This licentiate thesis is concerned with an inverse boundary value problemfor the magnetic Schr\"odinger equation in a half space, for compactlysupported 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 onparts of the boundary of the half space. The existence and uniqueness of thecorresponding direct problem are also considered.

An Inverse Boundary Value Problem for the Magnetic Schr\"odinger Operator on a Half Space