Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

TL;DR

This paper solves Coulomb and harmonic oscillator quantum problems in conical spaces with arbitrary dimensions, revealing their spectral properties and symmetries in topologically non-trivial space-times.

Contribution

It introduces solutions for Coulomb and harmonic oscillator problems in conical spaces of arbitrary dimensions, generalizing known results and exploring their symmetries.

Findings

Eigenvalues for angular momentum operators are reproduced in conical spaces.

Harmonic oscillator eigenfunctions are constructed algebraically with ladder operators.

Connections between Coulomb and oscillator states are established in non-trivial topologies.

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.