  We review the Landau problem of an electron in a constant uniform magnetic
field. The magnetic translations are the invariant transformations of the free
Hamiltonian. A K\"ahler polarization of the plane has been used for the
geometric quantization. Under the assumption of quasi-periodicity of the
wavefunction the magnetic translations in the Bravais lattice generate a
non-commutative quantum torus. We concentrate on the case when the magnetic
flux density is a rational number. The Bloch wavefunctions form a
finite-dimensional module of the noncommutative torus of magnetic translations
as well as of its commutant which is the non-commutative torus of magnetic
translation in the dual Bravais lattice. The bi-module structure of the Bloch
waves is shown to be the connecting link between two Morita equivalent
non-commutative tori.
