On the eigenvalues of some nonhermitian oscillators
Abstract
We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between the strong-coupling expansions for the eigenvalues of those oscillators. Comparison of the results of the complex rotation and the Riccati-Pad\'{e} methods reveals that the optimal rotation angle converts the oscillator into either a PT-symmetric or an Hermitian one. In addition to the real positive eigenvalues the PT-symmetric oscillators exhibit real positive resonances under different boundary conditions. They can be calculated by means of the straightforward diagonalization method. The Riccati-Pad\'e method yields not only the resonances of the nonhermitian oscillators but also the eigenvalues of the PT-symmetric ones.
Keywords
Cite
@article{arxiv.1301.1676,
title = {On the eigenvalues of some nonhermitian oscillators},
author = {Francisco M. Fern/'andez and Javier Garcia},
journal= {arXiv preprint arXiv:1301.1676},
year = {2013}
}