Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

Abstract

The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting 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 space-times. It is thus established the connection among the states and energies of both problems in these topologically non-trivial space-times.