On the Eigenvalues of some non-Hermitian oscillators

We consider a class of one-dimensional non-Hermitian 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 o...

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Detalles Bibliográficos
Autores principales: Fernández, Francisco Marcelo, García, Javier
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2013
Materias:
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/101472
https://ri.conicet.gov.ar/11336/5051
http://iopscience.iop.org/1751-8121/46/19/195301
http://arxiv.org/abs/1301.1676
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Sumario:We consider a class of one-dimensional non-Hermitian 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. A comparison of the results of the complex rotation and the Riccati–Padé methods reveals that the optimal rotation angle converts the oscillator into either a PT-symmetric or a Hermitian one. In addition to the real positive eigenvalues, the PT-symmetric oscillators exhibit real positive resonances under different boundary conditions. These can be calculated by means of the straightforward diagonalization method. The Riccati–Padé method yields not only the resonances of the non-Hermitian oscillators but also the eigenvalues of the PT-symmetric ones.