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

Abstract

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 Schrödinger's equation, we determine the energy spectra and the radial eigenfunctions for a class of potentials.