Eigenvalue problem for radial potentials in space with SU(2) fuzziness

Abstract

The eigenvalue problem for radial potentials is considered in a space whose spatial coordinates satisfy the SU(2) Lie algebra. As the consequence, the space has a lattice nature and the maximum value of momentum is bounded from above. The model shows interesting features due to the bound, namely, a repulsive potential can develop bound-states, or an attractive region may be forbidden for particles to propagate with higher energies. The exact radial eigen-functions in momentum space are given by means of the associated Chebyshev functions. For the radial stepwise potentials the exact energy condition and the eigen-functions are presented. For a general radial potential it is shown that the discrete energy spectrum can be obtained in desired accuracy by means of given forms of continued fractions.