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Y(sl(2)) Algebra Application in Extended Hydrogen Atom and Monopole Models

We present the extended hydrogen atom and monopole-hydrogen atom theory through generalizing the usual hydrogen atom model and with a monopole model respectively, in which Y(sl(2)) algebras are realized. We derive the Hamiltonians of the two models based on the Y(sl(2)) and the generalized Pauli equation. The energy spectra of the systems are also given in terms of Yangian algebra and quantum mechanics.