Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems

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 C 2. The latter represent the physical observables of a model whose Hamiltonian and Hilbert 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. PACS number: 03.65.-w