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.
Cite
@article{arxiv.gr-qc/0111114,
title = {Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions},
author = {J. L. A. Coelho and R. L. P. G. Amaral},
journal= {arXiv preprint arXiv:gr-qc/0111114},
year = {2016}
}
Comments
15 pages