  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.
