Time-dependent version of crypto-Hermitian quantum theory

2008/09/17 by Miloslav Znojil · 2 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Topological Materials and Phenomena #quant-ph

paper · pdf · doi:10.1103/physrevd.78.085003

published as Phys. Rev. D 78, 085003 (2008) · 14 pp

arxiv created 2008/09/17 · openalex publication_date 2008/10/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For many quantum models an apparent non-Hermiticity of observables just corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent may require the use of a manifestly time-dependent representation of the physical Hilbert space of states.

Citations

• Which operator generates time evolution in Quantum Mechanics?
• Making Sense of Non-Hermitian Hamiltonians
• On some meaningful inner product for real Klein—Gordon fields with positive semi-definite norm
• MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Propagation of electromagnetic waves in linear media and pseudo-hermiticity
• Quantum mechanics of Klein–Gordon fields I: Hilbert Space, localized states, and chiral symmetry

Cited by

• Three-Hilbert-Space Formulation of Quantum Mechanics
• Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators