2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115839We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η_+, and η_+-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 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.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, 2006Quantum Physicstext