2005/08/16 by Zafar Ahmed, Carl M. Bender, M. V. Berry +1 · 1 citation
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-th #quant-ph
paper · pdf · doi:10.1088/0305-4470/38/39/l01
published as J.Phys.A38:L627-L630,2005 · 4 Pages
arxiv created 2005/08/16 · openalex publication_date 2005/09/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken symmetry. The corresponding quantum theories possess an unconventional scalar product. The eigenvalues are determined by differential equations with boundary conditions imposed in wedges in the complex plane. For a special class of such systems, it is possible to impose the -symmetric boundary conditions on the real axis, which lies on the edges of the wedges. The -symmetric spectrum can then be obtained by imposing the more transparent requirement that the potential be reflectionless.