Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length
Quantum Physics
2010-12-01 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically the s-wave bound states equation in terms of Heun's functions. We discuss in detail the bound states spectrum for a specific form of the generalized uncertainty relation. The minimal length may be interpreted as characterizing the dimension of the system.
Cite
@article{arxiv.0711.0599,
title = {Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length},
author = {Djamil Bouaziz and Michel Bawin},
journal= {arXiv preprint arXiv:0711.0599},
year = {2010}
}
Comments
30 pages, 3 figures