## Star product and its application to the MIC-Kepler problem.(English)Zbl 1262.81082

Summary: We show that the MIC-Kepler problem 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.

### MSC:

 81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics 81V45 Atomic physics 53D50 Geometric quantization 53D55 Deformation quantization, star products 70F05 Two-body problems