  We have recently found that the gravitational field of a static spherical
mass removes the Landau degeneracy of the energy levels of a particle moving
around the mass inside a magnetic field by splitting the energy of the Landau
orbitals. In this paper we present the second part of our investigation of the
effect of gravity on Landau levels. We examine the effect of the gravitational
fields created by an infinitely long massive cylinder and a rotating spherical
mass. In both cases, we show that the degeneracy is again removed thanks to the
splitting of the particle's orbitals. The first case would constitute an
experimental test - which is quantum mechanical in nature - of the
gravitational field of a cylinder. The approach relies on the Newtonian
approximation of the gravitational potential created by a cylinder but, in view
of self-consistency and for future higher-order approximations, the formalism
is based on the full Levi-Civita metric. The second case opens up the
possibility for a novel quantum mechanical test of the well-known rotational
frame-dragging effect of general relativity.
