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, Aj not equal Aj dagger, j=1,2,& mldr;,K. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric Theta not equal I, guaranteeing the quasi-Hermiticity Aj dagger Theta=Theta Aj. The task is easy at K=1 because there are many eligible metrics Theta=Theta(A1). In our paper, the next case with K=2 is analyzed. The criteria of the existence of a shared metric, Theta=Theta(A1,A2), are presented and discussed.