On the SU(2) Kepler problem

Using the idea that the symmetry generators commuting with a Landau-like Ha miltonian containing non-Abelian gauge fields will be matrix-valued differe ntial operators, we reconsider the eigenvalue problem of the five-dimension al (5-D) Kepler problem on a SU(2) instanton background. We quickly reprodu ce the result of Pletyukhov and Tolkachev [J. Math. Phys. 40, 93-100 (1999) ], obtained for the energy spectrum. The eigenstates can be expressed in te rms of the SU(2) monopole harmonics. The relevance of the theory of induced representations for solving similar problems is emphasized. (C) 2000 Ameri can Institute of Physics. [S0022-2488(00)01105-1].