Article detail · 2004
Physical aspects of pseudo Hermitian and PT symmetric quantum mechanics
Journal
Journal of Physics A: Mathematical and GeneralISSN 0305-4470
- Year
- 2004
- Type
- article
Data source split
- YÖKSİS YÖKSİS article record
- YÖKSİS venue Journal of Physics A: Mathematical and General
- OpenAlex OpenAlex enrichment (abstract, citations, topics)
Abstract
OpenAlex · English
For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct the observables O α of the quantum mechanics based on H . In particular, we introduce pseudo-Hermitian position and momentum operators and a pseudo-Hermitian quantization scheme that relates the latter to the ordinary classical position and momentum observables. These allow us to address the problem of determining the conserved probability density and the underlying classical system for pseudo-Hermitian and in particular PT -symmetric quantum systems. As a concrete example we construct the Hermitian Hamiltonian h , the physical observables O α , the localized states and the conserved probability density for the non-Hermitian PT -symmetric square well. We achieve this by employing an appropriate perturbation scheme. For this system, we conduct a comprehensive study of both the kinematical and dynamical effects of the non-Hermiticity of the Hamiltonian on various physical quantities. In particular, we show that these effects are quantum mechanical in nature and diminish in the classical limit. Our results provide an objective assessment of the physical aspects of PT -symmetric quantum mechanics and clarify its relationship with both conventional quantum mechanics and classical mechanics.
Topics
Citations
OpenAlex cited_by_count. Not a WoS or Scopus citation count; those sources have no separate column here.
315 citations
OpenAlex cited_by_count (cache / database)
9 publications in the local catalog that cite this work (OpenAlex reference match; not the full global list).
- Delta-Function Potential with Complex Coupling 2006
- Application of pseudo Hermitian quantum mechanics to a complex scattering potential with point interactions 2010
- Bound state solutions of the Schrödinger equation for a symmetric potential with Dirac delta functions 2006
- Bound state solutions of the Schrodinger equation for a PT symmetric potential with Dirac delta functions 2005
- Spectral Singularities and CPA-Laser Action in a Weakly Nonlinear PT-Symmetric Bilayer Slab 2014
- Pseudo-hermiticity, anti-pseudo-hermiticity, and generalized parity-time-reversal symmetry at exceptional points 2025
- Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space 2024
- Bound States of a Non‐Hermitian System With a QES Sine Potential via AIM 2026
- Development of an approximate method for quantum optical models and their pseudo Hermicity 2005