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Day January 10, 2013

On the eigenvalues of some nonhermitian oscillators

Francisco M. Fernandez, Javier Garcia

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.

http://arxiv.org/abs/1301.1676
Mathematical Physics (math-ph); Quantum Physics (quant-ph)