  We study the motion of a particle in a 3-dimensional lattice in the presence
of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories
will always remain in a plane which can be taken as a rectangular lattice. The
Hamiltonian model for this problem is the conservative tight-binding one with
lattice constants a, b and hopping elements A, B in the XY axes, respectively.
We use the semiclassical and quantum formalisms; for the latter we apply the
pseudo-spectral algorithm to integrate the Schroedinger equation. Since the
lattice discrete subspace is not isotropic, the angular momentum is not
conserved, which has interesting consequences as chaotic trajectories and
precession trajectories, similar to the astronomical precession trajectories
due to non-central gravitational forces, notably, the non-relativistic
Mercury's perihelion precession. Although the elements of the mass tensor are
naturally different in a rectangular lattice, these can be chosen to be still
different in the continuum, which permits to study the motion with the usual
Newtonian kinetic energies. We calculate also the contour plots of an initial
Gaussian wavepacket as it moves in the lattice and we propose an "intrinsec
angular momentum" associated to its asymmetrical deformation, such that the
quantum and semiclassical angular momenta could be simply related.
