Conditions for complex spectra in a class of PT symmetric potentials

2001/09/28 by G. Levai, G. Lévai, Miloslav Znojil +1 · 3 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.1142/s0217732301005321

published as Mod. Phys. Letters A 16 (2001) 1973 - 1981 · 13 pages

openalex publication_date 2001/09/28 · arxiv created 2001/10/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study a wide class of solvable PT symmetric potentials in order to identify conditions under which these potentials have regular solutions with complex energy. Besides confirming previous findings for two potentials, most of our results are new. We demonstrate that the occurrence of conjugate energy pairs is a natural phenomenon for these potentials. We demonstrate that the present method can readily be extended to further potential classes.

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• Conjecture on the analyticity of \cal PT -symmetric potentials and the reality of their spectra