  We investigate the behaviour of a particle moving on the quotient manifold
$M=C^2/Z_$ which is derived from the EH metric as the two centers approach each
other. In the classical region of the configuration space we specify the
physically acceptable solutions and observe a tendency of the radial wave
function to concentrate around the conical singularity. Fot the quantum case,
using Schr\"{o}dinger's equation, we determine the energy spectra and the
radial eigenfunctions for a class of potentials.
