Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

Details Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

2001-11-30

arxiv.org/abs/gr-qc/0111114v2

J.Phys.A35:5255-5266,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages

Scientific paper

10.1088/0305-4470/35/25/307

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.

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