An SO(4) Invariant Hamiltonian and the Two-Body Bound State. I: Coulomb Interaction between Two Spinless Particles

摘要

We consider the nonrelativistic treatment of a hydrogenic atom in a four-dimensional Euclidean space. The focus of this work is on the angular part of the problem, as this is potentially more generally applicable. Using a suitable coordinate system, the su(2) x su(2) structure of the so(4) Lie algebra is exploited. The hyperspherical harmonic solutions of the angular part of the problem are obtained in two ways: as solutions of a partial differential equation and by means of a ladder operator approach. The solutions of the radial equation and energy spectrum are determined and possible implications of the model are briefly discussed. (C) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2885-2896, 2009