Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems
Ali Mostafazadeh, Seher Ozcelik
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 two-dimensional complex Euclidean space C2. These operators 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.
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