Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
Mathematical Physics
2015-06-12 v2 High Energy Physics - Theory
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
For eleven examples of one-dimensional quantum mechanics with shape-invariant potentials, the Darboux-Crum transformations in terms of multiple pseudo virtual state wavefunctions are shown to be equivalent to Krein-Adler transformations deleting multiple eigenstates with shifted parameters. These are based upon infinitely many polynomial Wronskian identities of classical orthogonal polynomials, i.e. the Hermite, Laguerre and Jacobi polynomials, which constitute the main part of the eigenfunctions of various quantum mechanical systems with shape-invariant potentials.
Keywords
Cite
@article{arxiv.1212.6595,
title = {Krein-Adler transformations for shape-invariant potentials and pseudo virtual states},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1212.6595},
year = {2015}
}
Comments
33 pages, 1 figure. Typo corrected, comments and references added. To appear in J.Phys.A