New solvable quantum mechanical potentials by iteration of the free V=0 potential
Quantum Physics
2009-11-10 v1
Abstract
A huge family of solvable potentials can be generated by systematically exploiting the factorization (Darboux) method. Starting from the free case, a large class of the known solvable families is thus reproduced, together with new ones. We explicitly find and solve several new singular potentials obtained by iteration from the V=0 case; some of them have an E=0 bound state and constant phase shift without being explicitly scale invariant. The new potentials are rational functions, and can be related to rational solutions of the KdV family.
Keywords
Cite
@article{arxiv.quant-ph/0311139,
title = {New solvable quantum mechanical potentials by iteration of the free V=0 potential},
author = {Pedro Blecua and Luis J. Boya and Antonio Segui},
journal= {arXiv preprint arXiv:quant-ph/0311139},
year = {2009}
}
Comments
Latex,17 pages,2 figures;to be published in Nuovo Cimento B