Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
Year: 2008
Type: article
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 $\ensuremath{\pi}∕4$. We compare our results with recent conflicting conclusions in the literature. The minimal length may be interpreted as a radius of the cosmic string.
Source: Physical Review A
Authors: Djamil Bouaziz, Michel Bawin
Institutions: University of Jijel, University of Liège
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2000878563