Classical and quantum motion on the orbifold limit of the Eguchi-Hanson metric

The authors investigate the behaviour of a particle moving on the orbifold limit of 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 for small values of its arguments. In the quantum case, using Schroedinger's equation, are determine the energy spectra and the radial eigenfunctions for the class of potentials