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Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

J. L. A. Coelho·R. L. P. G. Amaral
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Abstract

The Schrödinger 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.

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J. L. A. Coelho, R. L. P. G. Amaral. 2001-11-30. Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions. https://doi.org/10.1088/0305-4470%2F35%2F25%2F307

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