BALIAN-LOW THEOREM FOR LANDAU-LEVELS

The Balian-Low theorem is applied to the motion of an electron in the xy plane with a magnetic field B perpendicular to this plane. The ener gy spectrum for this problem is the Landau levels. It is shown that th e eigenfunctions for the Landau levels cannot be chosen sufficiently l ocalized in order to make both uncertainties Delta x and Delta y finit e. A similar result holds for the coordinates of the orbit center. Wit h this restriction on the localization, complete orthonormal sets are defined on von Neumann lattices.