Infinitely many shape invariant potentials and new orthogonal polynomials
Mathematical Physics
2009-09-28 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic P\"oschl-Teller potentials in terms of their degree \ell polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (\ell=1,2,...) in terms of new orthogonal polynomials. Two recently reported shape invariant potentials of Quesne and G\'omez-Ullate et al's are the first members of these infinitely many potentials.
Cite
@article{arxiv.0906.0142,
title = {Infinitely many shape invariant potentials and new orthogonal polynomials},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:0906.0142},
year = {2009}
}
Comments
4 pages; published in Phys.Lett.B, two references and comments added, eqs.(34)(35)(45)(46) simplified