2009/08/27 by Miloslav Znojil
Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #quant-ph
paper · pdf · doi:10.3842/sigma.2009.085
published as SIGMA 5 (2009), 085, 21 pages
openalex publication_date 2009/08/27 · arxiv created 2009/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One-dimensional unitary scattering controlled by non-Hermitian (typically, PT -symmetric) quantum Hamiltonians H = H is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain nonequivalent short-range metric operators = I represented, in Runge-Kutta approximation, by (2R -1)-diagonal matrices.