2013/01/07 by Francisco M. Fern 'andez, Francisco M. Fern/'andez, Fern/'andez, Francisco M. +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1301.1676
arxiv created 2013/01/07 · openalex publication_date 2013/01/07 · arxiv updated 2013/01/10 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28
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-Padé 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-Padé method yields not only the resonances of the nonhermitian oscillators but also the eigenvalues of the PT-symmetric ones.