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arXiv · 2505.00791

Mutual compatibility/incompatibility of quasi-Hermitian quantum observables

Miloslav Znojil
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Abstract

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 $\Theta\neq I$ guaranteeing the quasi-Hermiticity $A_j^\dagger \,\Theta=\Theta\,A_j$. The task is easy at $K=1$ because there are many eligible metrics $\Theta=\Theta(A_1)$. In our paper the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric $\Theta=\Theta(A_1,A_2)$ are presented and discussed.

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Miloslav Znojil. 2025-05-01. Mutual compatibility/incompatibility of quasi-Hermitian quantum observables. https://doi.org/10.3390/sym17050708

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