Mutual compatibility/incompatibility of quasi-Hermitian quantum observables
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908355480518656 |
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| author | Znojil, Miloslav |
| author_facet | Znojil, Miloslav |
| contents | In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_j\neq A_j^\dagger$, $j=1,2, \ldots,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $Θ\neq I$ guaranteeing the quasi-Hermiticity $A_j^\dagger \,Θ=Θ\,A_j$. The task is easy at $K=1$ because there are many eligible metrics $Θ=Θ(A_1)$. In our paper the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric $Θ=Θ(A_1,A_2)$ are presented and discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_00791 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mutual compatibility/incompatibility of quasi-Hermitian quantum observables Znojil, Miloslav Mathematical Physics Functional Analysis Quantum Physics In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_j\neq A_j^\dagger$, $j=1,2, \ldots,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $Θ\neq I$ guaranteeing the quasi-Hermiticity $A_j^\dagger \,Θ=Θ\,A_j$. The task is easy at $K=1$ because there are many eligible metrics $Θ=Θ(A_1)$. In our paper the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric $Θ=Θ(A_1,A_2)$ are presented and discussed. |
| title | Mutual compatibility/incompatibility of quasi-Hermitian quantum observables |
| topic | Mathematical Physics Functional Analysis Quantum Physics |
| url | https://arxiv.org/abs/2505.00791 |