Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background

2008/09/15 by Djamil Bouaziz, Michel Bawin, M. Bawin
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Bound state #Classical mechanics #Cosmic string #Dipole #Geometry #Inverse #Mathematical physics #Mathematics #Moment (physics) #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #RADIUS #Square (algebra) #String (physics) #gr-qc #quant-ph

paper · pdf · doi:10.1103/physreva.78.032110

published as Phys.Rev.A78:032110,2008 · 12 pages

openalex publication_date 2008/09/15 · arxiv created 2010/09/05 · arxiv updated 2010/11/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We solve analytically the Schr"odinger equation for the N-dimensional inverse square potential in quantum mechanics with a minimal length in terms of Heun's functions. We apply our results to the problem of a dipole in a cosmic string background. We find that a bound state exists only if the angle between the dipole moment and the string is larger than \ensuremathπ∕4. We compare our results with recent conflicting conclusions in the literature. The minimal length may be interpreted as a radius of the cosmic string.

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