info:eu-repo/semantics/article
On the Eigenvalues of some non-Hermitian oscillators
Fecha
2013-04Registro en:
Fernández, Francisco Marcelo; Garcia, Javier; On the Eigenvalues of some non-Hermitian oscillators; IOP Publishing; Journal of Physics A: Mathematical And Theoretical; 46; 19; 4-2013; 195301-195311
1751-8113
Autor
Fernández, Francisco Marcelo
Garcia, Javier
Resumen
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.