Mutual compatibility/incompatibility of quasi-Hermitian quantum observables

Abstract

In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_j\ne A_j^{†}$, $j=1,2,\dots ,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $\Theta \ne I$ guaranteeing the quasi-Hermiticity $A_j^{†}\Theta =\Theta A_j$. 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.

20 pp

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