Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems
Abstract
We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators \eta_+, and \eta_+-pseudo-Hermitian operators acting in two-dimensional complex Euclidean space C^2. These operators represent the physical observables of a model whose Hamiltonian and Hilbert space are respectively H and C^2 endowed with the inner product defined by \eta_+. Our calculations allows for a direct demonstration of the fact that the choice of an irreducible family of observables fixes the metric operator up to a multiplicative factor.
Keywords
Cite
@article{arxiv.quant-ph/0607120,
title = {Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems},
author = {Ali Mostafazadeh and Seher Ozcelik},
journal= {arXiv preprint arXiv:quant-ph/0607120},
year = {2007}
}
Comments
published version, 11 pages, contributed to the Proceedings of the 5th Worksop on Quantization, Dualities, and Integrable Systems, held in Pamukkale University, Denizle, Turkey, 23-27 January, 2006