Abstract

The Hamiltonian of a hydrogen atom associated with a U(1) monopole is established in parallel to a usual hydrogen atom with conserved angular momentum and Pauli-Runge-Lenz vector . Both are associated with monopoles and form an algebra SO(4) for the bound motions. Due to the two corresponding Pauli relations and their bosonic realizations, the system can be connected to a four-dimensional harmonic oscillator with a monopole-dependent constraint. Furthermore, the monopole harmonics can be obtained by the operator method.

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