Exact scattering and bound states solutions for novel hyperbolic potentials with inverse square singularity
Quantum Physics
2019-02-01 v1 Mathematical Physics
math.MP
Abstract
We use the Tridiagonal Representation Approach (TRA) to obtain exact scattering and bound states solutions of the Schr\"odinger equation for short-range inverse-square singular hyperbolic potentials. The solutions are series of square integrable functions written in terms of the Jacobi polynomial with the Wilson polynomial as expansion coefficients. The series is finite for the discrete bound states and infinite, but bounded, for the continuum scattering states.
Cite
@article{arxiv.1809.06902,
title = {Exact scattering and bound states solutions for novel hyperbolic potentials with inverse square singularity},
author = {A. D. Alhaidari},
journal= {arXiv preprint arXiv:1809.06902},
year = {2019}
}
Comments
11 pages, 1 table, 1 figure