Abstract. We review the Landau levels of an electron moving in a constant magnetic field transversal to a plane. In the spirit of the work of Gerald Dunne the Landau levels are lifted on a sphere via a stereographic projection and one recovers the Haldane spherical geometry of radial magnetic field originating at a Dirac monopole with a magnetic charge g. The Hilbert space of states living on the Haldane sphere are expressed with the monopole harmonics and in the limit of large magnetic charge one recovers the planar Landau levels. We push the analogy between the 2D harmonic oscillator and the planar Landau problem further and propose the 4D harmonic oscillator as a lift of the Haldane spherical geometry. We employ the Newton-Hooke duality between Coulomb problem and harmonic oscillator to introduce the MICZ-Kepler problem, i.e., the quantum Coulomb-Kepler problem for a motion of an electron in the background field of a dyon (a particle having both electric and magnetic charge). We conclude that MICZ-Kepler model is a natural generalization of the Haldane spherical geometry for the Landau levels.

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