On the eigenvalues of some non hermitian Hamiltonians

FRANCISCO M. FERNÁNDEZ; JAVIER GARCIA

Praga

Jornada; Analytic and Algebraic methods in physics XI; 2013

We consider a class of one-dimensional nonhermitian oscillators and discuss the re-lationship between the real eigenvalues of PT-symmetric oscillators and the reso-nances obtained by different authors. We also show the relationship between thestrong-coupling expansions for the eigenvalues of those oscillators. Comparison ofthe results of the complex rotation and the Riccati-Pad ́e methods reveals that theoptimal rotation angle converts the oscillator into either a PT-symmetric or an Her-mitian one. In addition to the real positive eigenvalues the PT-symmetric oscillatorsexhibit real positive resonances under different boundary conditions. They can becalculated by means of the straightforward diagonalization method. The Riccati-Pad ́e method yields not only the resonances of the nonhermitian oscillators but alsothe eigenvalues of the PT-symmetric ones