A family of complex potentials with real spectrum

1998/12/14 by F. M. Fernandez, Francisco M. Fernández, R. Guardiola +4 · 8 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum, superfluid, helium dynamics #quant-ph

paper · pdf · doi:10.1088/0305-4470/32/17/303

Six figures and four tables

arxiv created 1998/12/14 · openalex publication_date 1999/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We consider a two-parameter non-Hermitian quantum mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.

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