Star Product and Its Application to the MIC-Kepler Problem

Abstract

We show that the MIC-Kepler probrem is simply solved via the phase-space formulation of non-relativistic quantum mechanics. The MIC-Kepler problem is the Hamiltonian system behind the hydrogen atom subjected to the influence of the Dirac’s magnetic monopole field and the square inverse centrifugal potential force besides the Coulomb’s potential force. We get the energy spectrum of the bound states explicitly and construct the Green’s functions for $E ˂ 0$ by means of the Moyal product, which is one of the ‘star’ products denoted by ‘$\ast$’.