New supersymmetry-generated complex potentials with real spectra
Abstract
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation of the Schroedinger type. The superpotentials so constructed are characterized by the Ermakov parameters in such a way that they are always complex-valued and lead to non-Hermitian Hamiltonians with real spectra, whose eigenfunctions form a bi-orthogonal system. As applications we present new complex supersymmetric partners of the free particle that are PT-symmetric and can be either periodic or regular (of the Poeschl-Teller form). A new family of complex oscillators with real frequencies that have the energies of the harmonic oscillator plus an additional real eigenvalue is introduced.
Cite
@article{arxiv.1505.05197,
title = {New supersymmetry-generated complex potentials with real spectra},
author = {Oscar Rosas-Ortiz and Octavio Castanos and Dieter Schuch},
journal= {arXiv preprint arXiv:1505.05197},
year = {2015}
}
Comments
28 pages, 18 figures. New references added, a new section added