Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials
Mathematical Physics
2017-04-05 v1 math.MP
Quantum Physics
Abstract
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.
Keywords
Cite
@article{arxiv.1701.08236,
title = {Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials},
author = {Axel Schulze-Halberg and Pinaki Roy},
journal= {arXiv preprint arXiv:1701.08236},
year = {2017}
}
Comments
21 pages,9 figures