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

Ali Mostafazadeh; Seher Ozcelik

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

Ali Mostafazadeh·Seher Ozcelik

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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 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.

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Ali Mostafazadeh, Seher Ozcelik. 2006-11-28. Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems. https://arxiv.org/abs/quant-ph/0607120

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