Rational solutions for the Riccati-Schr\"odinger equations associated to translationally shape invariant potentials
Mathematical Physics
2014-11-20 v3 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as terminating continued fractions in an appropriate variable. We give explicit formulas for all the eigenstates, their specific form depending on the Barclay-Maxwell class to which the considered potential belongs.
Keywords
Cite
@article{arxiv.0910.4810,
title = {Rational solutions for the Riccati-Schr\"odinger equations associated to translationally shape invariant potentials},
author = {Yves Grandati and Alain Bérard},
journal= {arXiv preprint arXiv:0910.4810},
year = {2014}
}