Biorthogonal quantum systems

2005/07/31 by Thomas Curtright, Luca Mezincescu · 1 citation
Mathematics · Physics and Astronomy · #Algebra over a field #Biorthogonal system #Computer science #Formalism (music) #Hermitian matrix #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum field theory #Quantum mechanics #Simple (philosophy) #Theoretical physics #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1063/1.2196243

published as J.Math.Phys.48:092106,2007 · 34 pages, 5 eps figures; references added and other changes made to conform to journal version

arxiv created 2006/03/20 · openalex publication_date 2007/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+ν)2+∑k>0μkexp(ikx). In some nontrivial cases, equivalent Hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.

Citations

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