Factorization method and new potentials from the inverted oscillator
Quantum Physics
2016-12-12 v3 Mathematical Physics
math.MP
Abstract
In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.
Keywords
Cite
@article{arxiv.1206.4519,
title = {Factorization method and new potentials from the inverted oscillator},
author = {David Bermudez and David J. Fernandez C},
journal= {arXiv preprint arXiv:1206.4519},
year = {2016}
}
Comments
19 pages, 8 figures, 2 tables. The new version has a new section for the algebras of the harmonic and inverted oscillators, a new appendix, and color figures