Extensions of solvable potentials with finitely many discrete eigenstates
Mathematical Physics
2015-06-12 v2 High Energy Physics - Theory
math.MP
Quantum Physics
Abstract
We address the problem of rational extensions of six examples of shape-invariant potentials having finitely many discrete eigenstates. The overshoot eigenfunctions are proposed as candidates unique in this group for the virtual state wavefunctions, which are an essential ingredient for multi-indexed and iso-spectral extensions of these potentials. They have exactly the same form as the eigenfunctions but their degrees are much higher than n_{max} so that their energies are lower than the groundstate energy.
Keywords
Cite
@article{arxiv.1301.3980,
title = {Extensions of solvable potentials with finitely many discrete eigenstates},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:1301.3980},
year = {2015}
}
Comments
22 pages, 3 figures. Typo corrected, comments and references added. To appear in J.Phys.A. arXiv admin note: text overlap with arXiv:1212.6595