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 η-, and η+-pseudo-Hermitian operators acting in ℂ2. The latter represent the physical observables of a model whose Hamiltonian and Hubert space are respectively H and ℂ2 endowed with the inner product defined by η+. 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.