The Schrodinger equations for the Coulomb and the harmonic oscillator potentials are solved in the cosmic string conical spacetime. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunction is performed through the introduction of non-local ladder operators. By exploring the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular momentum operators in three dimensions are reproduced. A generalization for N dimensions is performed for both Coulomb and harmonic oscillator problems in angular deficit spacetimes. The connection among the states and energies of both problems in these topologically non-trivial spacetimes is thus established. [References: 13]
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