The monopole-hydrogen atom system and its connection with a four-dimensional harmonic oscillator

The Hamiltonian of a hydrogen atom associated with a U(1) monopole is estab lished in parallel to a usual hydrogen atom with conserved angular momentum L and Pauli-Runge-Lenz vector R. Both are associated with monopoles and fo rm an algebra SO(4) for the bound motions. Due to the two corresponding Pau li relations and their bosonic realizations, the system can be connected to a four-dimensional harmonic oscillator with a monopole-dependent constrain t. Furthermore, the monopole harmonics can be obtained by the operator meth od.